Stefan Pauly
email: stefan.pauly@sciencespo.fr

Fernando Stipanicic
email: fernando.stipanicic@berkeley.edu

Guillermo Alves

Tiziana Assenza

Antonin Bergeaud

Matteo Bobba

Christian Bontemps

Felipe Carozzi

Thomas Chaney

Fabrice Collard

Patrick Fève

Ruben Gaetani

Victor Gay

Ulrich Hege

Patrick Llerena

João Pereira

Dos Santos

Mohamed Saleh

Mark Schankerman

Andrea Smurra

Nicolas Werquin

Alex Whalley

Miguel Zerecero

During

The Creation and Diffusion of Knowledge: Evidence from the Jet Age *

Keywords: JEL Classification: O31, O33, R41, N72, F60

This paper provides new causal evidence of the impact of air travel time on the creation and diffusion of knowledge. We exploit the beginning of the Jet Age as a quasi-natural experiment. We digitize airlines' historical flight schedules and construct a novel data set of the flight network in the United States. Between 1951 and 1966, travel time between locations more than 2,000 km apart decreased on average by 41%. The reduction in travel time explains 33% of the increase in knowledge diffusion as measured by patent citations. The increase in knowledge diffusion further caused an increase in the creation of new knowledge. The results provide evidence that jet airplanes led to innovation convergence across locations and contributed to the shift in innovation activity towards the South and the West of the United States.

Introduction

"If I have seen further it is by standing on the shoulders of Giants."

-Isaac Newton (1675) 1 "(...) if one man starts a new idea, it is taken up by others and combined with suggestions of their own; and thus becomes the source of further new ideas."

-Alfred Marshall (1890) 2 In their famous quotations Isaac Newton and Alfred Marshall illustrate that access to knowledge is key for the creation of new knowledge. Understanding the process of creation of new knowledge is crucial as it has been characterized as one of the main causes of economic growth (Lucas (1993), Aghion and Howitt (1997) and Jones (2002)).

Access to knowledge spurs the creation of new knowledge (Furman and Stern (2011), Acemoglu et al. (2016)). Physical proximity, by facilitating face to face interactions, is a key driver of the diffusion of knowledge and hence of access to knowledge (Storper and Venables (2004), Glaeser (2011)).

Providing evidence of the effect of access to knowledge on the creation of new knowledge is an empirical challenge. Agents who are highly productive in terms of creation of knowledge may endogenously sort towards locations with high access to knowledge, leading to reverse causality. Additionally, access to knowledge is correlated with other drivers of innovation as access to markets, resulting in a potential omitted variable bias due to confounding factors.

This paper provides new causal evidence on this question by exploiting as a quasinatural experiment the beginning of the Jet Age in the United States. During the 1950s the introduction of jet engines into civil aviation led to a large reduction in travel time.

1 Quoted from a letter of Isaac Newton to Robert Hooke, 1675. A digital copy of the letter can be found at: https://digitallibrary.hsp.org/index.php/Detail/objects/9792 2 Quoted from Duranton and Puga (2004), page 2066.

1

We exploit changes in travel time to identify changes in knowledge diffusion, which are further translated into changes in access to knowledge. Then, we exploit changes in access to knowledge to study the impact on the creation of new knowledge. The results provide evidence that jet airplanes led to innovation convergence across locations and contributed to the shift in innovation activity towards the South and the West of the United States.

We start by constructing a new dataset of the flight network in the United States during the 1950s and 1960s. We digitize historical flight schedules of the major interstate airlines operating in the period and obtain the fastest route between every two airports in the network. 3 We document that between 1951 and 1966 travel time decreased on average by 29%, and the decrease is on average of 41% for airports located more than 2,000km apart. 4 This nationwide shock was arguably exogenous as it happened in a strictly regulated environment. We decompose the change in travel time and find that 90% of the change is due to the improvement in aircrafts' speed, while 10% is due to a change in the flight routes. This is consistent with the fact that during this period the Civil Aeronautics Board (CAB) was imposing strong regulation in the interstate airline market. With the objective to promote a stable airline industry, the CAB determined ticket prices and restricted entry of airlines into new or existing routes.

Additionally, during the 1950s and 1960s airplanes were predominantly used to transport people and not goods. Hence, the change in travel time represented a shock to the mobility of people while not significantly affecting the shipment of goods.

To study knowledge creation and diffusion we use patent data. We follow Jaffe et al. (1993) and use patent citations as our observable measure of knowledge flow. We assemble one dataset with all corporate patents granted by the United States Patent and Trademark Office (USPTO) with filing year between 1949 and 1968, which includes for each patent: filing year, technology classification, location (Metropolitan Statistical Area, MSA) of the inventors when they applied for the patent, owner of the patent and citations to other patents which were granted by the USPTO.

We document three facts of patenting activity during our sample period. First, patent growth was stronger both in initially less innovative MSAs and in MSAs in the South and the West of the US. Second, over time multi-establishment firms expanded geographically and accounted for a larger share of patents. Third, the mass of citations shifted towards longer distances. Our results show that the decrease in travel time contributed to all three facts.

We do our analysis in three steps. In the first step, we estimate a gravity equation to obtain the elasticity of citations to travel time. We identify the elasticity exploiting only within establishment-pair across-time variation in citations and travel time. The estimated elasticity implies that citations increased on average 2.4% due to the decrease in travel time between 1951 and 1966. We find that the absolute value of the elasticity is increasing with the distance between the citing and cited establishments. At a distance of more than 2,000km, the change in travel time implies an increase in citations of 6.9%. This accounts for 32.7% of the observed increase in citations in this distance range.

In order to rule out the possibility that the opening of new routes or the timing of adoption of jets at the route level was driven by variables that also affected knowledge flows, we perform an instrumental variables estimation. We instrument the observed travel time with a fictitious travel time computed by fixing routes to the initial time period and assuming in each year all routes are operated with the year's average airplane. Hence, changes in fictitious travel time are only due to the nationwide roll out of jets and is thus independent of decisions at the route level. The results do not change significantly, reflecting the reduced scope for endogeneity of travel time. In addition, the results are robust to controlling for potential confounding factors such as changes in highway travel time, telephone connectivity and flight ticket prices. Finally, the results also remain after restricting the sample to contain only establishments that existed in the initial time period.

In the second step, using the estimated elasticity of diffusion of knowledge, we compute a measure of knowledge access that is specific to each location-technology. The measure captures changes in knowledge access that are only consequence of the change in travel time. We use knowledge access as an externality that affects the production of new patents and estimate the elasticity of new patents to knowledge access. We identify the elasticity at the establishment level comparing only across time variation in patents and knowledge access across establishments within a location, conditional on aggregate technological trends. Thus, the identification is independent of location specific changes in local population or R&D subsidies. The estimated elasticity implies that the amount of new patents filed increased at a yearly growth rate of 3.5% due to the increase in knowledge access, which accounts for 79.5% of the observed yearly growth rate.

Given the reduction in travel time was larger for longer distances, the increase in knowledge access was stronger in locations geographically far from the initial innovation centers located in the Midwest and the Northeast. Hence, by increasing access to knowledge, the reduction in travel time led to a shift in the distribution of innovative activity towards the South and the West of the US. The South and the West had an average yearly growth rate of patenting 2.1 percentage points higher than the Northeast and the Midwest during our sample period. The change in travel time explains 35% of the observed differential growth.

We find that the value of the elasticity of patents to knowledge access is bigger in magnitude for establishments located in initially less innovative locations. Within each technology class, we rank locations according to the amount of patents in the initial time period and split them into four quartiles. We find that the increase in knowledge access predicts a 4.5% yearly growth rate of patenting in locations in the lowest quartile of initial innovativeness, while it predicts a 3.4% yearly growth rate in the highest quartile.

The difference in growth rates indicates that the increase in knowledge access acted as a convergence force between locations, and it can explain 21% of the convergence observed in the data. Results go in the same direction if we rank locations in terms of patents per capita.

Our results are robust to controlling for changes in market access by highway, changes in market access by airplanes and time changing telephone connectivity. Results do not change if we compute knowledge access using only knowledge located at long distances. Additionally, we present suggestive evidence that the results are not driven by a decrease in financial frictions.

In the third step, we uncover the sources of the increase in patenting. We find that most of the effect of knowledge access on new patents happens through two entry margins: entry of establishments of new firms and entry of subsidiaries of firms that expanded from other locations. The two entry margins are stronger in initially less innovative locations, meaning that convergence comes both from new firms and the geographic expansion of multi-establishment firms.

To more directly test the firm expansion channel, we study if a firm's subsidiary's location decision depends on travel time to headquarters. We estimate a probability model to analyze if the locations in which firms have inventors applying for patents depends on travel time to the firm's headquarters. We identify the change in the probability only from changes in travel time and locations in which the firm starts patenting or stops patenting. We find that the probability that a firm has inventors applying for patents in a certain location goes up when then travel time from that location to the firm's headquarters reduces. In addition, the change in the probability is stronger for potential recipient locations that were initially less innovative, again highlighting the importance of this channel for convergence. This paper contributes to multiple branches of literature. First, it contributes to the literature on agglomeration and knowledge spillovers. Agglomeration forces are usually understood as happening in a geographically localized manner (Glaeser (2011), Arzaghi and Henderson (2008)). The literature on tech clusters also documents this fact (Duranton et al. (2009), Kerr and Robert-Nicoud (2020), Moretti (2021)). The seminal paper Jaffe et al. (1993) finds that patent citations decay rapidly with distance. Our results show that jet airplanes allowed long distance knowledge spillovers, facilitating the development of tech clusters in other regions. The literature that provides evidence of knowledge spillovers usually focuses on changes in the supply of knowledge (Bloom et al. (2013), Acemoglu et al. (2016)). In our case we fix the supply of knowledge and focus on changes in the degree of accessibility.

We contribute to the literature on transportation by studying a new quasi-natural experiment that isolates a shock to the mobility of people. To do so we construct a new dataset that could be used to answer many other questions. 5 Other papers have studied the impact of transportation improvements on innovation. Agrawal et al. (2017) study the impact on innovation of a region's stock of highways, while Perlman (2016) uses 19th century data on locations' density of railroads. Andersson et al. (2017) and Tsiachtsiras (2021) do so using the historical railroad expansion in Sweden and France.

Relative to them, we contribute by exploiting a quasi-natural experiment that allows us to isolate a channel of face to face interaction, with little scope for a trade channel. In contemporaneous work Bai et al. (2021) estimate the elasticity of patent citations to air travel time using the introduction of new airline routes in a more recent period, post deregulation of the airline market. Relative to them, we contribute by exploiting a set up in which the risk for endogeneity of travel time is limited. Our work is related to other literature which found that business travel affects innovation (Hovhannisyan and Keller (2015)), trade (S öderlund (2020)) and industrial activity (Coscia et al. (2020)). Also, air travel shapes collaboration between researchers (Catalini et al. (2020)).

The impact of transportation improvements in economic outcomes has long been a subject of study (Fogel (1963), Baum-Snow (2007), Michaels (2008), Donaldson and Hornbeck (2016), Jaworski and Kitchens (2019) and Herzog (2021)). Our convergence result contrasts with previous studies on improvements in other means of transport. Pascali (2017) finds that the introduction of steam engine vessels in the second half of the 19th century led to an increase in international trade which contributed to economic divergence between countries. Faber (2014) finds that the expansion of the highway system in China led to a reduction of GDP growth of peripheral counties, with evidence suggesting a trade channel. While both papers emphasize a trade channel, in our set up the trade channel would not be of first order. Hence, we uncover a new effect of improved connectivity.

Finally, we contribute to the literature on firm's location decision. Our result about firms deciding their establishments' locations based on travel time to headquarters is comparable to the one found by Giroud (2013), who finds that a reduction in air travel time to headquarters increases plant level investment and total factor productivity. Similarly, Campante and Yanagizawa-Drott (2017) finds that firms' cross country investment decision depends on connectivity to headquarters.

The paper is structured as follows. First, we present a simple theoretical framework which lays the foundations of how to think about the creation and diffusion of knowledge. The framework shows the two key parameters to estimate. Second, we describe the historical context in which jet airplanes were introduced. Third, we present the two datasets that we use: travel times and patents. Fourth, we perform the analysis to estimate the impact of travel time on the diffusion of knowledge, the creation of knowledge, and firm's location decision. Fifth, we conclude.

Conceptual framework

This section lays out a simple theoretical framework to think about the creation of knowledge. The framework clearly shows the two key parameters to estimate empirically: the elasticity of knowledge diffusion to travel time and the elasticity of knowledge creation to knowledge access.

Following Carlino and Kerr (2015) we consider a production function of knowledge which includes external returns in the form of knowledge spillovers. Knowledge output of a firm depends not only on firm's specific characteristics as its idiosyncratic productivity and input decisions, but also on an externality due to knowledge spillovers.

We consider a production function of knowledge of the following form:

New Knowledge Fi = f (z Fi , inputs Fi ) × Knowledge Access ρ i (1)
where New Knowledge Fi is the knowledge created by firm F located in i. The output of Fi depends on an internal component and on an external component. The internal component is the firm's idiosyncratic productivity z Fi and choice of inputs inputs Fi .

The external component represents the externality to which all firms F in location i are exposed to: Knowledge Access i . This externality, Knowledge Access, represents the total amount of knowledge spillovers that the firm is exposed to. The degree to which the externality affects the production of knowledge is governed by the parameter ρ. If ρ is zero then knowledge spillovers have no effect on the creation of new knowledge. On the other hand, a positive ρ implies that, keeping productivity and inputs constant, an increase in the level of knowledge spillovers leads to an increase in firm F's creation of new knowledge.

A long standing literature studies the importance of knowledge spillovers for the creation of new knowledge. 6 The concept of knowledge spillovers goes back at least to Marshall (1890) who explains it as one of the agglomeration forces. Krugman (1991) refers to knowledge spillovers as one of the justifications for external increasing returns, and that the degree of spillovers are dependent on physical distance. The geographic decay of spillovers is grounded in the fact that not all knowledge is easy to codify, usually referred to as tacit knowledge, and geographic proximity increases the degree of knowledge spillovers by facilitating face to face interactions (Storper and Venables (2004), Glaeser (2011)). Hence, we consider the total amount of knowledge spillovers to which the firm F in location i is exposed to has the following functional form:

Knowledge Access i = ∑ j Knowledge stock j × distance β ij (2)
where Knowledge stock j is the total amount of knowledge in location j (which is nonnegative) that could potentially spill over to location i and distance ij is a measure of distance from j to i. The amount of knowledge that spills over from j to i depends on distance and the degree with which distance impedes spillovers, governed by the parameter β. If β is zero, then distance does not affect knowledge spillovers from j to i and all locations perfectly share the same level of Knowledge Access. On the contrary, a negative β implies a decay in knowledge spillovers when distance increases. In other words, a negative β implies that if we reduce the distance from j to i while keeping every other distance constant, the amount of spillovers from j to i will weakly increase.

This theoretical framework bears resemblance to the concept of Market Access presented in Donaldson and Hornbeck (2016) and Redding and Venables (2004). If we interpret Knowledge Access as one of the inputs in the production function of knowledge, then Knowledge Access i could be interpreted as a measure of Input Market Access. This measure captures how cheaply firms in location i can access pre-existing knowledge, where the cost of accessing knowledge depends on distance between i and j. Also, Knowledge Access is similar to a measure of network centrality. The centrality of each location i (node) is the weighted sum of distance (edges) to every location, where the their geographic decay and how they affect the creation of knowledge.

weight of each location is given by its knowledge stock.

The theoretical framework highlights the two parameters to estimate: ρ and β. Empirically, we use travel time as a measure of distance to first estimate β and then conditional on β we estimate ρ. Changes in travel time due to improvements in commercial aviation allow us to estimate both parameters. First, we use citations between patents as a proxy for the diffusion of knowledge. We estimate β by relating changes in travel time between research establishments to changes in citations between them. Second, we use the stock of patents filed by inventors in each location as proxy for each location's stock of knowledge. We construct a measure of knowledge access using the patent stock, travel times and the value of β. New patents in each location proxy for new knowledge.

Changes in travel time lead to changes in knowledge access which allow us to estimate ρ.

Historical context

Air transport: moving people, not goods

During the 1950s and 1960s, air transportation served to transport people but not goods. We observe that, while transport of people by rail decreased and by motor remained relatively constant, transport of people by air multiplied by 6 in a 16-year period, which translates to around 12% compound annual growth. In 1966, air transport accounted for more passenger-miles than both rail and motor transportation together, reflecting the growing importance of this mean of transport.

8 AA and TWA had transcontinental non-stop propeller flights scheduled since at least 1954. These flights were scheduled to take 7 hours 55 minutes, just under the maximum flight time allowed by regulation in domestic flights: regulation impeded pilots from being on duty more than 8 hours within a 24 hours window. Nonetheless, the propeller aircrafts used in these flights, the Douglas DC-7 and the Lockheed Super Constellation, overheated their engines due to excessive demand to cover the route in less than 8 hours. AA fought intensely until the CAB approved a waiver that allowed non-stop transcontinental flights to take up to 10 hours to accomplish the non-stop transcontinental flight. See page 16 of the edition of the 21st of June 1954 of the Aviation Week magazine https://archive.org/details/Aviation_Week_1954-06-21/page/n7/mode/2up

Regulation

As explained in Borenstein and Rose (2014), in the 1930s the airline industry was seen as suffering from coordination issues, destructive competition and entry. Additionally, the industry was developing in a context of financial instability and increasing military concerns post Great Depression. A strong domestic airline industry was perceived as an interest of national defense. As consequence, the Civil Aeronautics Board (CAB)

was created in 1938 with the objective to promote, encourage and develop civil aeronautics. 11 It was empowered to control entry, fares, subsidies and mergers. 12 In other words, the CAB regulated the market by deciding which airlines could fly, in which routes they could operate, the price that they charged in each route, the structure of subsidies and merger decisions. The CAB regulated the airline industry in a barely unchanged manner until it ceased to exist in 1985.

When the CAB was created, it conceived special rights to the existing airlines over the connections they were operating. The CAB did not permit entry of new airlines on interstate routes and gradually allowed current airlines to expand their routes. The CAB controlled both the system and each airline's network. The network was designed to maintain industry stability and minimize subsidies, leading to a system where each route was mainly operated by one or two airlines. 13 Importantly, Borenstein and Rose (2014) in pages 68-69 explain that "the regulatory route award process largely prevented airlines from reoptimizing their networks to reduce operation costs or improve service as technology and travel patterns changed." As a consequence, any technological improvement such as increases in aircraft speed, capacity or range would not affect each airline's flight network in the short term.

By regulating fares, the CAB explicitly encouraged airlines to adopt new aircraft.

Airlines, when operating an older aircraft, would apply for a fare reduction arguing that it is needed in order to preserve demand for low quality service. The CAB would refuse this application, hence airlines would have to adopt new aircraft or risk losing consumers who would choose another airline which flies newer aircrafts.

Air travel data

We We digitize flight schedules for the years 1951, 1956, 1961 and 1966 of six domestic airlines: American Airlines (AA), Eastern Airlines (EA), United Airlines (UA), Trans World Airlines (TWA), Braniff International Airways (BN), Northwest Airlines (NW), 14

14 These are six of the fifteen trunk (interstate) airlines operating in 1951. Many of the remaining trunk airlines would merge with another trunk airline over the years, and there would be zero entry of new airlines. We are currently digitizing the remaining trunk airlines and we plan to add them to the travel time dataset in the future. We have already digitized: Allegheny Airlines, Capital Airlines, Colonial Airlines, Continental Airlines and Delta Air Lines. We have also digitized the year 1970 for and one international airline: Pan American Airways (PA). This group of airlines includes the Big 4: AA, EA, UA and TWA, which accounted for between 69% and 74% of interstate air revenue passenger miles in the US in the years collected. BN and NW were digitized in order to have a wide geographical coverage, while PA provides international flights. Based on C. A.B. (1966), in the years collected, the six domestic airlines together accounted for between 77% and 81% of interstate air revenue passenger miles.

In total we have digitized 6,143 US flights (unique combinations of flight numberyear, 7,007 worldwide). However, flights often have multiple stops. If we count each non-stop part (leg) of these flights separately, our sample contains 17,737 legs in the US the six airlines used in this paper and Pan American. Due to a time constraint we have not included them in the current analysis. We plan to digitize BOAC to obtain more international flights, and to cover the time period 1930 to 2000 for all airlines that is possible. Once the fastest route between every two airports is computed, we match every airport to 1950 Metropolitan Statistical Areas (MSA) using the shape file from Manson et al. (2020). We consider only MSAs in contiguous United States. We use MSAs as the geographical unit of analysis because they are constructed taking into account commuting flows. We assume that people in an MSA would use, for each desired route, the most appropriate airport lying inside or nearby the MSA. We match each airport to all MSAs for which it lies inside the MSA or is at most 15km away from its boundary. 16 176 out of 275 US airports are matched to at least one MSA. Meanwhile, 142 out of 168 MSAs are matched to one or more airports in at least one year, and 108 MSAs are matched to one or more airports in the four years. We use the sample of 108 MSAs that had an airport in the four years as our baseline travel time data.17 Between 1951 and 1956, there is an average reduction in travel time of 9.2% which is roughly constant for all distances over 500km. Between 1951 and 1961, there is a reduction in travel time that is increasing with distance. The average decrease in travel time is of 16.8%, while the reduction is of 29.4% for a distance of more than 2,000km and 39.2% for a distance of 4, 250-4,500km. Between 1951 and 1966, there is an even stronger decrease in travel time at all distances. The average reduction in travel time is 28.7% across all distances, 40.8% for a distance of more than 2,000km and 48.4% for a distance of 4,250-4,500km. The increased adoption of jets for short distance flights implied that both non-stop flights at short distance and connecting flights at farther distance had a decrease in travel time. Interestingly, for MSA-pairs more than 2,000km apart travel time reduced on average 42% for those pairs that were connected indirectly in both periods, and 51% for those that switched from indirect to direct. This fact shows the relevance of improvements in flight technology even for MSAs that were not directly connected.

It could be the case that a reduction in the amount of legs or an increase in frequency of flights reduces layover time, which then translates into a reduction of travel time.

In Appendix Figure 28 we compare the change in travel time from 1951 to 1966 with a counterfactual change in travel time in which we eliminate layover time in both time periods. We observe that the average change in travel time is stronger at every distance in the counterfactual scenario without layover time. This implies that the relative importance of layover time to total travel time within a route increased between 1951 and 1966, so total travel time did not decrease proportionally to the change of in-flight travel time. In short, layover time attenuated the reduction in travel time.

Constructing an instrument

In this section we construct an instrumental travel time that is based on the pre-existing flight routes and the time-varying nationwide roll out of jets. In this way, the instrument abstracts from the endogenous decisions of two agents: First, regulator's decision on the opening/closure of routes. Second, airlines' decision about to which routes allocate 21 Appendix Figure 27 repeats the exercise discarding layover time in all time periods. By comparing Figure 26 and Figure 27 we can disentangle the effect of layover time and the change in in-flight time.

For MSA pairs less than 250km that changed from direct to indirect connection, 80% of the increase in travel time is due to the increase in layover time (which was previously zero as it was a non-stop flight), and 20% is due to the increase of in-flight time.

jet vs propeller airplanes and scheduling (frequency of flights and layover time). We first explain the idea and identifying assumptions of the instrument, and then we detail how it is constructed.

In Borenstein and Rose (2014) it is argued that, due to strict regulation, it was difficult for airlines to adapt their flight network when technology to fly changed. However, we may be concerned that the decision of the regulator to grant new routes could be targeted to specific pairs or correlated with unobservable variables that also affect the creation and diffusion of knowledge. 22 Hence, as the first step in the construction of our instrument, we fix routes to the ones we observe in 1951. In this way the instrumental travel time is computed only using non-stop flights present in 1951, and does not consider appearance or disappearance of non-stop flights in the data. The identifying assumption is that the network of flight routes in 1951 did not yet include the changes that would be optimal to operate with jet airplanes. In other words, we require that the regulator did not change routes already by 1951 in anticipation of the arrival of jet airplanes. 23,24 Airlines could decide on two factors that affect travel time: the type of airplane (jet vs. propeller) operated in each route and scheduling, which consists on the frequency of flights and layover time in case of connecting flights. 25 We may be concerned that, as with the regulator, airlines' decisions could be correlated with unobservables that also affect the creation and diffusion of knowledge. 26 The second step in the construction of our instrument is to discard layover time (hence discarding all scheduling decisions) in all time periods, and assume that in each year all routes are operated with a fictitious average airplane of the year. Hence, the change in instrumental travel time in a route is independent of the type of airplane used in the route and it only depends on the nationwide roll out of jets. The identifying assumption is that no single route had the power to shift the average speed of the year.

To construct the instrumental travel time we first estimate, separately for each year, a linear regression of travel time on flight distance using only the fastest non-stop flight in each origin-destination airport pairs.27 These yearly regressions provide us with the fictitious average airplane of each year: the intercept gives the take-off and landing time of the airplane while the slope provides the (inverse) speed. Second, we fit these regressions to obtain predicted travel time in each non-stop flight and year. Third, for each year, we compute the fastest travel time using the Dijkstra algorithm. The Dijkstra algorithm looks for the fastest path using only 1951 non-stop flights, while the travel time in each non-stop flight in each year is given by the predicted travel time from the previous step. Layover time is set to zero in all years.

Patent data

We use patent data as our source of innovation information. We construct a dataset of all patents granted by the United States Patent and Trademark Office (USPTO) with filing year29 between 1949 and 1968, which includes for each patent: filing year, technology classification, location of the inventors when they applied for the patent, owner of the patent and citations to other patents also granted in the United States. This dataset provides the distribution of patents and citations over the geographic space, allowing to take into account ownership structure.

To construct the patent dataset we downloaded from Google Patents all patents granted by the USPTO with filing year between 1949 and 1968. This dataset contains patent number, filing year and citations. 30,31 Based on the patent number we merge it with multiple datasets. First, we obtained technology class from the USPTO Master Classification File32 and we aggregated them to the six technology categories of Hall et al. (2001). Second, we obtained geographic location of inventors from three datasets:

HistPat (Petralia et al. (2016)) and HistPat International (Petralia (2019)) for patents published until 1975, Fung Institute (Balsmeier et al. (2018)) for patents published after 1975. 33 We match all inventors' locations to 1950 Metropolitan Statistical Areas (MSAs)

in contiguous United States. To do the match we obtain geographical coordinates from the GeoNames US Gazetteer file and Open Street Maps, and use the MSAs shape file from Manson et al. (2020). Third, we obtain ownership of patents from two sources: Kogan et al. (2017) for patents owned by firms listed in the US stock market and Patstat (Magerman et al. (2006)) for the remaining unmatched patents. 34 For the descriptives presented below and the posterior analysis we truncate and aggregate the data in the following way. We drop patents that are owned by universities or government organizations. To count patents that are classified into multiple technology categories, we do a fractional count by assigning proportionally a part of the patent to each category. Citations are counted as the multiplication of the technology weight of the citing and cited patents. We drop patents (and their citations) that have inventors in multiple MSAs 35 and citations in which the citing owner is the same as the cited owner. 36 We aggregate the patent data to 4 time periods of 5 years each, with the center of each period being the year of travel time data collected. The periods are: 1951 (which contains the years 1949-1953), 1956 (1954-1958), 1961 (1959-1963) and 1966 (1964-1968).

We consider only patents in MSAs that are matched to an airport in the four periods. 37 The final dataset contains 108 MSAs with patents and travel time.

Descriptive statistics: Patents

This section presents three facts about US patents over our sample period: First, initially less innovative locations had a higher patenting growth rate. The average yearly 34 Patent ownership in both datasets comes from the patent text, which is self declared by the patent applicant. Particularly, Kogan et al. (2017) does not explicitly state if it takes into account firmownership structure to determine the ultimate owner of a patent, neither does Patstat. 35 Working with multi-MSA patents requires an assumption on how to compute distance and travel time between the citing and cited patents, as it is not a single origin-destination location pair. We hence prefer to abstract from multi-MSA patents. In the other hand, collaboration of inventors located in different MSAs is a interesting subject and it is part of our research agenda. 36 Incentives to self-cite may be different than to cite patents of other owners. 37 We drop around 9% of patents that are in MSAs which are not matched to an airport in the four time periods. Descriptive statistics including those patents are similar to the ones presented here.

growth rate of locations in the lowest quartile of initial innovativeness was 7.2% while it was 1.9% for those in the highest quartile. High growth locations were also primarily in the South and the West of the US. The South and the West grew three times as fast as the Midwest and the Northeast. Second, over time firms grew larger as measured by the amount of MSAs in which they had research establishments. At the same time, the share of patents filed by large multi-establishment firms increased. The amount of firms with research establishments in more than 10 MSAs almost tripled over the time period and their share of patents doubled. Third, the mass of citations shifted towards longer distances. While the first quartile of citation distance remained relative stable over the time period, the third quartile increased its distance by 39%. At the same time, the share of citations at more than 2,000km increased by 30%.

We compute descriptives by technology. In here we present descriptives of averages across technologies. Technology specific descriptives are included in Appendix B.

Fact 1.a.: Initially less innovative locations had a higher patenting growth rate

In the period 1951 to 1966 we observe that the highest growth of patenting takes place in locations that were initially less innovative. The differential growth rate implies a convergence rate of 5.3% per year.

Figure 8 shows the geographic distribution of patenting in 1951. Darker colors refer to a higher level of initial innovativeness, which is defined as the amount of patents filed by inventors in the MSA in 1951. 38 We observe that MSAs in the top quartile of patenting are concentrated in the Northeast (which includes New York) and the 38 To compute the level of initial innovativeness we only use patents filed in 1951 (years 1949-1953).

We aggregate patents to the MSA-technology level and then compute the quantile-position of each MSA in the technology. Lower values of quantile-position refers to lower amount of patents in the technology (relative to other MSAs). Each MSA has a different value of quantile-position in each of the 6 technology categories. To obtain the MSA level quantile we take the average quantile across technologies within the MSA. Finally we classify MSAs into quartiles depending on whether the average quantile is higher or lower than the thresholds 0.25, 0.50, 0.75.

Midwest (which includes Chicago), with few additional MSAs in the West. 39,40 Figure 9 shows the geographic distribution of patenting growth in 1951-1966. 41 We observe a striking pattern relative to Figure 8: high growth MSAs were those that were initially less innovative. High growth happens in initially less innovative locations in the South and the West but also in the Northeast. We confirm this pattern in Fig-

ure 10, which shows the MSA's ranking of innovativeness in 1951 and its subsequent patenting growth rate in 1951-1966. Figure 10 shows that MSAs that were initially more innovative (lower values in the ranking) are those that saw lower values of subsequent patenting growth. 42,43 We estimate a linear regression with an intercept and a slope, and find that the slope is positive and statistically different from zero. At the mean, lowering initial innovativeness by 10 positions in the ranking was associated with a subsequent 0.42 percentage points higher yearly growth rate of patenting.

Figure 10 presents average growth rates across technologies within a MSA. We obtain a result that goes in the same direction if we compute the average growth rates across MSAs within a technology and quartile of initial innovativeness, and then take the average across technologies. The average yearly growth rate of MSA-technologies in the lowest quartile of initial innovativeness is 7.2% while it is 1.9% in the highest quartile. 44 The percentage point difference between the two growth rates implies that locations in the lowest quartile converged towards locations in the highest quartile at a speed of 5.3% per year. 45 The convergence in patenting across MSAs is consistent with The Postwar Decline in Concentration, 1945-1990 described in Andrews and Whalley (2021). take averages across MSAs within a quartile-technology, and after take averages across technologies within a quartile. Finally, we convert the 19-year growth rate into an average yearly growth rate. 45 We note that the aggregate growth of patents is much smaller than the across MSAs unweighted average, and this is exactly because initially less innovative MSAs grew faster. If we compute the growth rate in nationwide amount of patents in each of the technologies and then average across technologies we obtain a yearly growth rate of 1.5%. Figure 12 shows that in the period 1951-1966 the South and the West increased their amount of patenting by 80%, while the Midwest and the Northeast had a 22% growth. 47

46 In Appendix C we present a map with the four Census Regions. 47 Growth rates are computed by region-technology and then averaged across technologies within region.

29

Translated into yearly growth rates, the South and the West grew three times as fast as the Midwest and the Northeast (3.14% vs. 1.05% per year). 48 Using all the patents of the same owner we identify all locations in which a patent owner had inventors applying for patents. We label a patent owner a firm and assume that a firm has a research establishment in the MSAs in which it has inventors applying for patents. Combining all patents belonging to the same firm we know if a firm has research establishments in multiple MSAs, if a firm expands over time and where it locates its establishments.

In Table 1 we count the number of firms and compute their share of patents according to whether the firm had 1, 2 to 5, 6 to 10, 11 to 20, or more than 20 establishments in each respective year. As we can see, the vast majority of firms had one establishment (95.8% in 1951), while very few had 11 or more establishments (0.1% in 1951). In 1951, single-establishment firms accounted for 57% of all patents. At the same time, firms

48 3.14% = 1.80 (1/19) × 100, 1.05% = 1.22 (1/19) × 100
with 11 or more establishments (42 firms, 0.1% of all firms) accounted for 15% of all patents.

From 1951 to 1966, the amount of single establishment firms declined by 1% while the amount of firms with 11 or more establishments increased by 283%. In other words, the amount of firms with presence in 11 MSAs or more grew from 42 to 119 firms. At the same time, the share of patents accounted by firms with 11 or more establishments increased from 15% to 31%. Simultaneously, the share of patents of single-establishment firms decreased from 57% to 46%. Hence, Table 1 illustrates that both the amount of multi-establishment firms and their share of patents grew over time. 49 In Appendix B

we show that multi-establishment firms increased their share of patents in all quartiles of MSAs' initial innovativeness, with a stronger increase in initially less innovative MSAs. While we observe an increase in the number of multi-establishment firms, we also observe an increase in the distance between establishments of the same firm. Figure 13 shows that, for firms that have multiple establishments in the respective year, the average distance across establishments within the firm increased over time. 50 existing knowledge upon which Y builds." (page 580). 51 We compute the distance between the citing inventor and the cited inventor. Figure 14 shows the evolution over time of the first, second and third quartile of citation distance. 52 We observe that 25% of citations happened between inventors located less than 300km apart throughout our sample period. For the middle 50% of citations we observe that over time inventors cited other inventors located farther away. The third quartile of citation distance in- 50 The increase in distance across establishments within firms could well be the result of firms that are growing and randomly producing new patents in different locations. However, in Section 8 we show that the process firms' geographic expansion was not random: firm's expansion was directed towards locations that got larger reductions in travel time to the firm's headquarters. 51 Jaffe et al. (1993) discusses the reasons why to cite and why not to cite. Using a survey of inventors, Jaffe et al. (2000) find that there is communication among inventors and citations are a "noisy signal of the presence of spillovers." 52 We compute distance between MSA centroids. creased from 1,642km in 1951 to 2,284km in 1961, a 39% increase in the distance. 53 In other words, the mass of citations shifted towards longer distances.

Number of firms

In Figure 15 we present the share of citations by distance range between the citing and cited inventors. 54 The distance cutoffs where chosen in order to have a balanced share of citations in the initial time period, and considering the changes in travel time presented in Section 4.1. The share of citations that happen between inventors located more than 2,000km apart grew from 21.5% in 1951 to 27.9% in 1966. The 6.4 percentage points increase represents an increase of 30% of the share of citations at more than 2,000km.

Diffusion of knowledge

In this section we show that the reduction in travel time led to an increase in knowledge diffusion, especially over long distances. In doing so we estimate the parameter β highlighted in equation ( 2): the elasticity of knowledge diffusion to travel time.

To perform the analysis we merge the Air Travel and Patent datasets to obtain a final dataset that contains for each patent owner-location, the amount of patents filed in a certain 5-year period and technology class, the amount of citations to other patents with their respective owner identifier, location and technology class, and the travel time to every location. We aggregate citations to the citing-cited establishment-technology within each period. We assume that passengers take a return flight, hence we make travel times symmetric. 55 We estimate a gravity equation which relates citations between two establishmentstechnologies with their pairwise travel time. 56 We estimate the following regression:

citations FiGjhkt = exp [β log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt (3)
where citations FiGjhkt is the amount of citations from patents filed by the establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. We call Fi the research establishment of firm F in location i. travel time ijt is the air travel time (in minutes) between location i and j at time period t. The parameter of interest in the regression is β, which represents the elasticity of citations to travel time. 57 If citations are affected negatively by travel time we would expect a negative value of β. stands for the travel time between MSA i and j at time period t. 56 For explanation and micro foundations of the gravity equation see Head and Mayer (2014) and references thereof. 57 A 1 percent increase in travel time has an effect of β percent increase (or decrease in the case of a negative β) in citations.

Given the panel structure of our data, we can include the fixed effect FE FiGjhk that absorbs any time invariant citation behavior within the citing establishment-technology and cited establishment-technology. This fixed effect flexibly controls for persistent relationships within an establishment pair that would lead to relatively more (or less) citations. That includes characteristics like physical distance, but also pre-existing commercial relationships between establishments. The fixed effects FE Fiht and FE Gjkt control for the time changing general level of citations specific to each establishment and technology. For example FE Fiht controls for the fact that if Fih files more patents in a given period, it would mechanically make more citations to every establishment.

On the other hand, FE Gjkt controls for Gjk filing more patents or higher quality patents that would receive more citations from every establishment. 58 The inclusion of FE FiGjhk implies that only variation across time within an establishmentpair is used for identification. By additionally including the fixed effect FE Fiht , the across-time variation is compared only between citing-cited establishment-technology pairs FiGjhk within a citing establishment-technology Fih in period t. As we also include FE Gjkt , the comparison is done while controlling for the size of the cited establishment-technology Gjk in period t. Put differently and simplifying slightly, the identification of β relies on changes in citations and travel time within an establishmentpair, relative to another establishment-pair with the same citing establishment, conditional on the two cited establishments' sizes.

Following Silva and Tenreyro (2006), we estimate the gravity equation by Poisson

Pseudo Maximum Likelihood (PPML). 59 This estimation methodology has two advantages over a multiplicative model that is then log-linearized to obtain a log-log specification. First, it only requires the conditional mean of the dependent variable to be correctly specified, while the OLS estimation of the log-linearized model would lead to biased estimates in the presence of heteroskedascity. Second, it allows to include zeros in the dependent variable, which is especially relevant when using disaggregated data.

One downside of estimating PPML with the fixed effects that we include is that both coefficients and standard errors have to be corrected due to the incidental parameter problem (Weidner and Zylkin (2021)). We follow Weidner and Zylkin (2021) to use split-panel jackknife bias-correction on the coefficients and Dhaene and Jochmans (2015) to bootstrap standard errors which we also bias-correct with split-panel jackknife. 60 Whenever FiGjhk has positive citations in at least one period and missing value in another, we impute zero citations in the missing period. 61 Travel time is set to one minute whenever i = j. 62

Column (1) in Table 2 presents the results of estimating equation ( 3). The value of the elasticity of citations to travel time is estimated to be -0.083, statistically significant at the 1% level. Given the average reduction in travel time of 31.4% in the full estimating sample, the elasticity implies that citations increased on average 2.6% as consequence of the reduction in travel time. If we consider the average decrease in travel time across all MSAs in the baseline travel time data, the implied increase is 2.4%. 63 The importance of air transport relative to other means of transport potentially depends on the distance to travel. Also, we observed in section 4.1 that the improvements in air travel time depended on the distance to travel, with a difference in jet adoption 60 Details on the bias correction and bootstrap procedures are provided in Appendix D. 61 We do not impute zeros in FiGjhk that are always zero, as those observations would be dropped due to not being able to identify FE FiGjhk . 62 We measure air travel time in minutes. In our sample 13% of citations happen within the same MSA.

The inclusion of those citations in the estimation increases the amount of observations available to identify of FE Fiht and FE Gjkt , and hence keeping them increases the amount of FiGjhkt that remain in the effective sample to identify β. In order to include them we then need to impute a within-location travel time. We assume that within-location (air) travel time is not changing across time periods. Nonetheless, the identification of β is not affected by the value chosen for the within-location (time invariant) travel time, as β is identified by across time variation. In the appendix we show results using other values of (time invariant) within MSA travel time and the coefficients remain equal. 63 These values come from the multiplication of the elasticity of citations to travel time 0.083 and the average decrease in travel time between 1951 and 1966: 31.4%

) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt ,
for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Column (2) includes the interaction of travel time ijt with a dummy for distance bin between the citing establishment Fi and the cited establishment Gj. Column (3) and ( 4) show the result of two step instrumental variables estimation, where log(travel time ijt ) is instrumented with log(travel time fix routes ijt ), the travel time that would have taken place if routes were fixed to the ones observed in 1951 and in each year routes were operated with the average airplane of the year. Bootstrap standard errors are presented in parentheses. The coefficients and standard errors in columns ( 1) and ( 2) are jackknife bias-corrected. R2 is computed as the squared correlation between observed and fitted values.

for travel distances under and over 2,000km. Taking these two characteristics into account, we estimate a variation of equation ( 3) in which we allow the elasticity of citations to travel time to vary by distance interval between the locations of citing and cited establishments.64 Column (2) in Table 2 shows the result of this estimation. 65 The estimated value of the elasticity in absolute terms increases with distance, reaching -0.169 for distances of more than 2,000km. Between 1951 and 1966 the average change in travel time in the full estimating sample is 47.7% for a distance of more than 2,000km.

The estimated elasticity implies that citations between establishments at more than 2,000km apart increased by 8.1% due to the decrease in travel time. In total citations at more than 2,000km increased by 21%, implying that the change in travel time can account for 38.2% of the observed increase. If instead we consider the 40.8% average reduction in travel time across MSAs in the raw data, the elasticity implies an increase in citations of 6.9%, accounting for 32.7% of the total citation increase.

In Appendix B we investigate different heterogeneous effects. We study how travel time affects the extensive margin of citations (whether an establishment cites another establishment or not) and the intensive margin (conditional on citing, how much it cites). We find the effect comes from both margins. We estimate an heterogeneous elasticity depending on the level of spatial concentration of the citing technology and the cited technology, we do not find a statistical difference. We also look at whether it is older patents or younger patents that get diffused, finding some slight evidence that it is technologies that take longer time to diffuse that increase more their diffusion with the reduction in travel time. We study citations to and from government patents, and self citations, on the whole we do not find a different pattern from the baseline.

We also do not find a particular pattern of the elasticity depending on the citing firm's size as measured by the amount of patents filed in 1949-1953. Finally, we estimate the elasticity by citing and cited technology and most of the effect seems to come when the citing and cited technologies are the same.

There are two types of threats to identification in estimating equation ( 3): (i) the potentially targeted changes in travel time, which could be due to the opening of new routes, the allocation of jets across routes, or changes in scheduling, and (ii) time changes in other variables at the MSA-pair level which also drive the diffusion of knowledge and are correlated with the changes in travel time. In the remaining of this section we address the first type of threat by estimating the model by instrumental variables. In the following subsection we address the second type of threat by adding multiple controls. In both cases we show that results do not change.

As mentioned in Section 4.2, we may be concerned that the timing and allocation of jets to routes and that the opening/closure of routes were not random. In case there is an omitted variable that drives both the change in travel time at the MSA pair level and the change in citations across establishments within the same MSA, we would estimate biased coefficients. In order to tackle the endogeneity concern due to omitted variable we do an instrumental variables estimation using the instrument proposed in Section 4.2. To implement the instrumental variables estimation we follow a control function approach described in Wooldridge (2014). We proceed in two steps estimating the following two equations:

log(travel time) FiGjhkt = λ 2 log(travel time fix routes FiGjhkt ) + FE FiGjhk + FE Fiht + FE Gjkt + u FiGjhkt (4) citations FiGjhkt = exp [β log(travel time ijt ) + λ ûFiGjhkt + FE FiGjhk + FE Fiht + FE Gjkt ] × v FiGjhkt (5)
In a first step we estimate equation ( 4) and obtain estimated residuals ûFiGjhkt . In a second step we use the estimated residuals as a regressor in equation (5) which controls for the endogenous component of travel time. To perform inference we bootstrap standard errors. 66 According to Wooldridge (2014), there would be evidence of endogeneity 66 Appendix D includes details on the bootstrap procedure.

if the parameter λ in equation ( 5) is estimated to be statistically different from zero.

Columns (3) and (4) of Table 2 show the results of the instrumental variables estimation. If airlines were allocating jet airplanes to routes that would have witnessed a higher degree of exchange of knowledge even in the absence of jets, then we would expect the instrumental variables estimate to be smaller in absolute terms relative to the baseline coefficient. On the other hand, if the regulator targeted the opening of new routes between places that were in a lower trend of exchange of knowledge, we would expect the instrumented coefficient to be larger in absolute terms. Column (3) estimates the elasticity to be -0.152, bigger in absolute value compared to the non-instrumented estimate. The instrumental variables corrects for a downward bias in absolute terms, which represents evidence in favor of the regulator targeting the opening of new routes between places that had a lower degree of exchange of knowledge. 67,68 In column (4) of Table 2 we see the coefficients of the instrumental variable estimation by distance between the citing and cited establishments. We observe the presence of a bias in the same direction as in column (3), however the magnitude of the bias is smaller except for the distance bin 0-300km, which is not precisely estimated. In particular, at more than 2,000km, the coefficient is relatively similar to the baseline estimation.

In Appendix E we show the regression including coefficients on the residual controls. If the coefficients on controls are statistically significant, that is evidence of endogeneity. While the control is statistically significant when using only one coefficient for all distances, none of them is statistically significant when opening the coefficient 67 The incidental parameter problem is potential present also in the instrumental variables estimation (IV PPML). However, there is currently no bias-correction procedure available for IV-PPML that we are aware off. Hence, columns (3) and ( 4) in Table 2 are not bias-corrected. In column (2) of Table 3 we present the PPML estimation not bias-corrected. 68 The literature on weak instruments for non-linear instrumental variables is scarce. The rule of thumb of Staiger and Stock (1997) based on the F statistic is constructed using the bias that a weak instrument generates in a linear second stage (see Staiger and Stock (1997), Stock and Yogo (2005) and Sanderson and Windmeijer (2016) for testing for weak instruments in linear IV regression). For informative purposes, in the first stage of the model estimated in column (3) in Table 2 we obtain λ2 = 0.95 with a standard error 0.039 (clustered at the non-directional location pair level, ij is the same location pair as ji), and a within R2 of 0.38 (the share of residual variation explained by the instrument, after projecting out fixed effects).

by distance range. In other words, we do not find evidence of endogeneity at long distances, especially at +2,000km.

The instrument used in the instrumental variables estimation is constructed using the 1951 flight network. We may be concerned that the 1951 flight network is correlated with future changes of citations. 69 In order to address this concern in Appendix E we estimate equation ( 3) by restricting the sample to establishments in MSA-pairs that are always indirectly connected. Results go in the same direction.

Diffusion of knowledge: Robustness

We may be concerned that there are other variables that could drive the diffusion of knowledge and at the same time be correlated with the change in travel time. In order to bias the coefficients, such omitted variables should be time-changing at the origindestination MSA pair and be systematically correlated with the change in MSA-pair air travel time. 70 We consider three potential variables that could bias our estimates:

improvements in highways, improvements in telephone communication and changes in flight ticket prices. In Table 3 we show the results controlling for this variables separately, while in Appendix E we include them simultaneously. Estimates are robust to including these controls.

Columns (1) and ( 2) in Table 3 present the elasticity of citations to travel time by distance bin. In column (1) the elasticity is bias-corrected while in column (2) it is not. 71 We observe that not doing the bias correction does not qualitatively affect the results.

Columns (3) to ( 6) include the additional controls and should be compared to column

(2). 69 We include a establishment pair fixed effect in the regressions, so a potential correlation between the 1951 flight network and the level of citations between research establishments does not affect our estimation. 70 Variables that are not time changing or that are time changing at the MSA or establishment level do not represent a threat to identification, as they are flexibly controlled for with the fixed effects. 71 The jackknife bias-correction due to the incidental parameter problem is computationally intensive.

Due to the computational burden, we have still not bias-corrected all estimations. Columns (2) to (6) of Table 3 do not include bias-correction. We aggregate the variable to the MSA level. For each MSA-pair, we take the log of the mean share of households with telephone lines. 72 To include the variable as control we interact it with a time dummy to make the measure time variant. The assumption behind the interaction is that, if telephone lines expanded or changed their price over the time period, this time-change specific to each year was proportional to the 1960 log mean share of the MSA-pair.

Third, during the period of analysis ticket prices were set by the Civil Aeronautics Board, so airlines could not set prices of their own tickets. Some airlines included a sample of prices in the last page of their booklet of flight schedules, which we digitized. In Appendix E we document multiple facts about prices. The relevant fact for this section is that during 1962-1963 we observe a drop in prices of around 20% for routes of more than 1,000km distance. We may be concerned that the change in flow of knowledge is actually consequence of the change in prices, which happens to be correlated with the change in travel time. Given that we do not have ticket prices for each route and year, we use an estimated route price which is time varying. We obtain estimated prices by using the sample of prices that we digitized and fitting, for each year, price on a third degree polynomial of distance between origin and destination. We use log of estimated prices as control. 73 Column (3) to (5) of Table 3 include the described controls. Assuming the covariance across coefficients is zero, none of the coefficients is statistically different from the baseline coefficients either in column (1) or (2). 74 Fourth, we control for a time varying effect of distance on citations. We may believe that other variables may have an effect on the diffusion of knowledge, and those variables are related to the distance between the citing and cited establishments. In column (6) we include as control log(distance) interacted with a time dummy. We observe that the coefficients reduce in magnitude, potentially due to the fact that the change in travel time is also correlated with distance, hence controlling for a time-varying effect of distance absorbs part of the effect. In spite of that, the coefficient for distance of more than 2,000km remains statistically significant at the 5%. This result shows that travel time and distance are not equivalent measures. Hence, it highlights the importance of the origin-destination time varying travel time data when studying the impact of face to face interactions. At the same time, this result differentiates our analysis from the one of Feyrer ( 2019) who uses two types of time-invariant distance (sea distance and geographical distance) interacted with time dummies. 73 In order to perform inference we should adjust standard errors by the fact that we have a predicted regressor as control variable. 74 To perform a test of statistical difference across coefficients of different regressions we need to estimate the covariance between them. We are currently doing a joint-bootstrap to obtain the covariance and perform the test.

= exp [∑ d β d 1{distance ij ∈ d} log(travel time ijt ) + ∑ d α d 1{distance ij ∈ d} 1{X FiGjhkt } log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt ,
for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. d are distance intervals:

[0 -300km], (300km -1000km], (1000km -2000km], (2000km -max].
Column (1) presents jackknife bias-corrected coefficients and bias-corrected bootstrap standard errors. Column (2) repeats column (1) without bias-correction. Relative to (2), columns (3) through ( 6) contain additional controls. Column (3) controls for log highway time between i and j at period t. Column (4) controls for the log of the mean share of households with telephone line in 1960 in ij pair interacted with a time dummy. Column (5) controls for log flight ticket price between i and j at period t. Column (6) controls for log distance ij interacted with a time dummy. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Columns (2) through (6) present standard errors clustered at the non-directional location in parentheses (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values.

Finally, as we will see in section 8.2, the entry and exit of research establishments was not uniform across locations during the sample period. We may then be concerned that the change in diffusion of knowledge is only consequence of the change in the geographic location of innovation. In Appendix E we re-estimate equation (3) with different samples: first, using only citing establishments that were present in 1949-1953, and second using only citing and cited establishments that were present in 1949-1953. We find the coefficient at more than 2,000km remains comparable to the one in the baseline regression, statistically significant at the 1%.

Creation of knowledge

In this section we show that the reduction in travel time to innovative locations led to an increase in knowledge creation. We show that the effect on knowledge creation was stronger in initially less innovative locations, leading to convergence across locations in terms of innovation. Additionally, the reduction in travel time contributed to a change in the geographic distribution of knowledge creation, increasing the relative importance of locations in the South and the West of the United States.

We construct a measure of Knowledge Access by adapting equation (2) to an empirical set up with multiple technology categories and time periods. The measure of Knowledge Access (KA iht ) shows how easy it is in time period t for research establishments in location i and technology h to access knowledge created in other locations. We compute Knowledge Access as follows:

KA iht = ∑ k ω hk ∑ j, j =i Patent stock jk,t=1953 × travel time β ijt (6)
where, from right to left, travel time β ijt is the travel time between locations i and j at time period t, to the power of the elasticity of diffusion of knowledge to travel time.

Patent stock jk,t=1953 is the discounted sum of patents produced in location j and tech-nology k between 1941 and 1953. 75 ω hk is the share of citations of technology h that go to technology k at the aggregate level in 1949-1953, similar to an input-output weight. 76 Then, KA iht is a weighted sum of the patent stock in each other location and technology, where the weights are how easy it is to access that patent stock (travel time β ijt ) multiplied by how relevant that knowledge is (ω hk ).

In order to reduce concerns of potential endogeneity of accessing knowledge and creating knowledge, we exclude the patent stock in the location itself from the sum (we only use j = i). 77 The measure of Knowledge Access contains across-time variation within a locationtechnology ih, and cross-sectional variation across technologies h within a location i.

The across-time variation is only due to the change in travel time between locations, every other component of the measure is fixed to its 1949-1953 level. The cross-sectional variation comes from a distribution of Patent stock jk,t=1953 within k that is not uniform across j, and from the input-output weights ω hk . The joint across-time and crosssectional variation means that if travel time for ij reduces, there will be a differential change in Knowledge Access across h within i which depends on the initial patent stock and input-output weights.

The degree with which changes in travel time are reflected in access to knowledge 75 Patent stock jk,t=1953 = ∑ y∈ [1941,1953] Patents jky × (1depreciation rate) 1953-y . We use a depreciation rate of 5%, which is in the range of average depreciation rates of R&D found by De Rassenfosse and Jaffe (2017). We decided to fix the patent stock and not to allow it to change over time, as changes in travel time will potentially lead to changes in patent stock creating a dynamic reinforcing effect between knowledge access and new knowledge. In this sense, we abstract from dynamic externalities that could be at play. 76 ω hk = citations hk,t= [1949,1953] /citations h,t= [1949,1953] is included to weight each source technology category k by how important it is for the destination technology category h. 77 The theory makes no distinction on whether the knowledge stock is in i or j, so in principle we would like to include the patent stock of i in the knowledge access of i. However, this could lead to econometric problems. First, we do not have exogenous variation of travel time within i. Second, if knowledge creation in i is a persistent process, by including the patent stock of i we would introduce a mechanical relationship between knowledge access and knowledge creation. Hence, our baseline measure of knowledge access of i does not consider the patent stock of i. In Appendix E we show that the inclusion of i's patent stock does not affect the results.

depend on how important travel time is to get knowledge to diffuse, which is the elasticity of knowledge diffusion to travel time that we estimated in Section 6. As the baseline we use β = 0.185, which is the elasticity of citations to travel time at more than 2,000 km not bias corrected. In robustness we use distance-specific β and in Appendix E we do sensitivity analysis of the results to changing the value of β.

The With the measure of Knowledge Access we then adapt equation (1) to estimate:

Patents Fiht = exp [ ρ log(KA iht ) + FE Fih + FE it + FE ht ] × ξ Fiht (7)
where Patents Fiht are patents applied by establishment of firm F in location i and technology h at time period t. The measure of knowledge access KA iht is at the iht location-technology-time level, meaning that all establishments within an iht share the same level of knowledge access. The parameter of interest ρ is the elasticity of (the creation of new) patents to knowledge access. In the presence of knowledge spillovers as suggested in section 2, we would expect ρ to be positive and statistically significant. Column (1) in Table 4 shows the result of estimating equation ( 7). The elasticity of patents to knowledge access is estimated to be 10.14, significant at the one percent level. The average change in knowledge access at the location-technology level 78 is 9%, implying that on average the change in travel time predicts a 3.5% average yearly growth rate of patents. 79 The observed average yearly growth rate of new patents at the location-technology is 4.4%. 80 Comparing the predicted and observed growth rates, the improvement in air travel time has the power to account for 79.5% of the observed average yearly patent growth rate. 81 We aggregate predicted changes in patent growth at the Census Region level. The change in travel time predicts a yearly growth rate 0.74 percentage points higher in the South and the West relative to the Midwest and Northeast. In the data we observe 2.1 percentage points difference in the growth rate, implying that the change in travel time can account for 35% of the observed differential growth rate. 82 Section 5.1 showed that in the data, initially less innovative MSAs had a larger growth rate of patenting. In column (2) in Table 4 we investigate if the increase in knowledge access had an heterogeneous effect on the amount of new patents created depending on the initial innovativeness of the location i in technology h. We compute the quartile of innovativeness of location i in technology h in the time period 1949-1953 and interact it with log(KA iht ). 83 We use as reference category the highest quartile of initial innovativeness, hence the coefficient on log(KA iht ) without interaction is the elasticity for the highest quartile. Coefficients on other quartiles should be interpreted relative to the highest quartile.

We find that the coefficients on lower quartiles of initial innovativeness are positive and statistically different from the coefficient in the highest quartile. Thus, knowledge access had a greater effect on patenting for establishments that were located in initially less innovative locations. 84 Given the difference in the coefficients, the increase in knowledge access predicts an average yearly growth of new patents of 4.5% for the initially lowest quartile of innovativeness, while it predicts 3.4% for the highest quartile. 85 The change in knowledge access predicts differential growth rate of 1.1 percentage points. In the data we observe that the average yearly growth rate of patents in the lowest quartile is 5.3 percentage points higher than in the highest quartile. Comparing the predicted and observed differential growth rates, the improvement in knowledge access as consequence of the reduction in travel time explains 21% of the difference in growth rates of new patents between locations in the lowest and highest quartile of innovativeness. 86 As in Section 6, we may be concerned that decisions of the regulator or airlines which affect travel time are endogenous to the diffusion of knowledge and consequently to knowledge access. Therefore, we construct an instrument for knowledge access in which instead of using observed travel time, we use the fictitious travel time presented in section 4.2 in which routes are fixed to the ones in 1951 and each route is operated with the average airplane of the year:

KA iht = ∑ k ω hk ∑ j, j =i Patent stock jk,t=1953 × (travel time fix routes ijt ) β (8)
We then implement the instrumental variables estimation by control function as in 84 A given percentage change in knowledge access led to a stronger increase in patenting in initially less innovative locations. 85 The change in knowledge access for the lowest quartile is on average 9.1%, which multiplied by the coefficient 14.36 (obtained by doing 9.36+5.00=14.36) gives a predicted growth of 131% over 19 years. Translated into average yearly growth it is 4.5% = [(1 + 1.31) (1/19) -1] × 100. For the highest quartile, knowledge access changed on average 9.5%, which multiplied by the coefficient 9.36 predicts 89% growth rate, which is 3.4% yearly growth rate. 86 21% ≈ 1.2/5.1 × 100 Section 6. The results are presented in columns (3) and ( 4) in Table 4. The coefficients do not show an important change and the convergence prediction obtained using non-instrumented PPML remains valid. 87,88 Figure 17 shows in the left panel the patent growth observed in the data (it replicates The result in column (2) implies that a given change in Knowledge Access had a stronger effect on patenting growth in less innovative locations. In other words, knowledge spillovers as an externality had a more predominant role in the production of 87 The first stage of the model estimated in column (3) of Table 4 gives a λ2 = 1.01 with standard error 0.03 (clustered at the location-technology level ih), and a within R2 of 0.53. 88 Using IV estimates, the predicted yearly patent growth rate in the lowest quartile is 4.9% while it is 3.7% in the highest quartile. The predicted differential growth rate is then 1.2 percentage points, meaning that the change in knowledge access can explain (1.2/5.3) × 100 ≈ 23% of the observed differential growth rate.

knowledge in locations that initially produced relatively fewer patents. Theoretically, this result implies that the parameter ρ in equation ( 1) varies depending on the level of previous production of knowledge of location i. Empirically the implication is that a given increase in knowledge spillovers leads to innovation convergence across locations. As seen in section 5.1, during 1949-1968 we observe innovation-convergence across locations and that is exactly what the estimated coefficients predict following a reduction in travel time.

In order to understand the convergence result and compare it with other findings in the literature it is important to remember that commercial airplanes during 1950s and 1960s were a means of transportation mainly for people. On the other hand, other transportation improvements as those in water transport, railroads or highways also contain another ingredient: they were used to carry goods. Hence, other means of transportation have a simultaneous impact on face to face interactions and trade.

Pascali (2017) finds that the introduction of the steam engine vessels in the second half of the 19th century had an impact on international trade that led to economic divergence between countries. Faber (2014) finds that the expansion of the highway system in China led to a reduction of GDP growth in peripheral counties, with evidence suggesting a trade channel due to reduction in trade costs. In our setup, the introduction of jet airplanes represented a big shock to the mobility of people while not affecting significantly the transport of merchandise. Therefore, studying the introduction of jet airplanes allows us to focus on improved face to face interactions, while the trade channel would be a second order effect.

Creation of knowledge: Robustness

In this section we show that the effect of Knowledge Access on the creation of new patents and the convergence effect remains after including different controls. Table 5 shows the results.

by airplane and θ is set to -1,22, the elasticity of trade to travel time from S öderlund (2020). The results are shown in columns ( 5) and ( 6) of Table 5. While the coefficients in all quartiles are reduced, the estimated value of ρ is positive and significant and the result on convergence remains.

Potential contemporaneous improvements in other means of communication, like telephones, could have spurred the creation of new patents. In columns ( 7) and ( 8)

we include the log of the MSA's share of households with telephones in 1960 and double-interact it with a technology dummy and a time dummy. The results remain invariant with respect to the baseline.

Another potential explanation for the increase of patenting could be that better connectivity decreased technology-specific financial frictions. The potential reduction in financial frictions, rather than a confounder, would be a mechanism through which airplanes increased innovation. However, according to Jayaratne and Strahan (1996) during 1950s and 1960s interstate lending and bank branching were limited. Prior to the 1970s, banks and holdings were restricted in their geographic expansion within and across state borders. Additionally, the Douglas Amendment to the Bank Holding Company Act prevented holding companies from acquiring banks in other states. Therefore, it is unlikely that interstate bank financing would be a driving force. Nonetheless, if other sector-specific modes of financing like venture capital were active, it could be confounding the results. In Appendix E we construct multiple measures of access to capital by using market capitalization of patenting firms listed in the stock market. The results present suggestive evidence that access to capital is not driving the results.

Finally, in Appendix E we include additional robustness checks. We compute different versions of Knowledge Access: we use distance-specific β from section 6, we consider the patent stock only of locations j far from i, we do sensitivity analysis using different values of β. Also, we re estimate the effects by quartile of initial innovativeness using patents per capita. Last, we re-do the baseline regression using OLS 4) control for technology specific effect of log(highway market access), columns ( 5) and ( 6) control for technology specific effect of log(airplane market access), columns ( 7) and (8) control for technology and time specific effect of log(telephone share). Standard errors clustered at the location-technology ih are presented in parentheses. R2 is computed as the squared correlation between observed and fitted values.

sults go in the same direction: an increase in knowledge access leads to an increase in patenting and the effect is stronger in initially less innovative locations.

Firms' geographic expansion

In section 5.1 we showed that there was innovation-convergence across regions and this happened simultaneously with an increase in the amount of multi-establishment firms. In section 7 we showed that the reduction in travel time predicts innovationconvergence across locations. In this section we uncover one of the mechanisms that led to innovation-convergence: the geographic expansion of multi-establishment firms.

We proceed in two steps. First, we show that the increase in patenting is driven by two types of entry: entry of establishments of new firms, and entry of establishments of pre-existing firms. The second type of entry is due to the geographic expansion of firms.

Second, we show that the decrease in travel time led firms to expand geographically and this expansion was stronger towards initially less innovative locations.

Entry of new establishments

We use all patents of the same firm to identify all locations in which the firm had research establishments in each time period. 89 Using patents applied during the first time period (1949-1953), we classify all the research establishments that applied for patents in every subsequent period. We classify research establishments into three mutually exclusive categories: the establishment (and hence the firm) applied for patents in

Geographic expansion of multi-establishment firms

In this subsection we show that the decrease in travel time gave rise to the geographic expansion of multi-establishment firms. We focus on all firms that patented in the initial time period and follow their subsequent opening and closure of establishments. We find that firms directed the opening (closure) of new establishments towards locations that got larger (smaller) reductions in travel time to the firm's headquarters.

We define the headquarters location q of firm F as the location in which the firm filed the largest amount of patents in the period 1945-1953. If firm F did not file any patent in 1945-1953, or there is no unique location with the maximum amount of patents (e.g. two locations have the maximum amount of patents), then no headquarters is assigned. 91 Firms with no headquarters assigned are dropped from the estimations that required headquarters location.

We compute the travel time of every firm F's headquarters's location q to each other location j. We then estimate a linear probability model to study if the location decision of establishments of a firm depend on travel time to a firm's headquarters. We estimate the following regression:

1{establishment Fqjt } = γ log(travel time qjt ) + FE Fqj + FE Fqt + FE jt + ζ Fqjt (11)
where 1{establishment Fqjt } is a dummy variable that takes value 1 if firm F with headquarters in location q has a research establishment in location j at time period t. 92

The coefficient γ is a semi-elasticity: γ/100 is the change in percentage points of the probability that firm F has an establishment in location j when travel time increases by one percent. If travel time has a negative impact on the probability then we would expect γ to be negative.

The inclusion of the fixed effect FE Fqj implies that γ is identified only from changes in travel time and opening and closure of research establishments across time. 93 Fixed effects FE Fqt and FE jt control flexibly for changes in firm F expanding and the opening establishments everywhere else, and j becoming more attractive for every firm.

Table 8 presents the results jointly with predicted and observed growth rate of the probability. Column (1) presents the results of estimating equation ( 11). We find that the probability of firm F having a subsidiary research establishment in location j increases when the travel time between the firm's headquarters's location q and j decreases.

The coefficient is -0.0364, which if we multiply it by the average change in travel time between headquarters' location and every other potential location (-34.7%), the decrease in travel time predicts an increase in the share of existing subsidiaries of 0.0126 percentage points. The result goes in the same direction as Giroud (2013) who finds 92 1{establishment Fqjt } takes value 0 if firm F does not file patents in location j at time period t. The headquarters location q remains fixed for all time periods. 93 Opening refers from 1{establishment Fqjt } switching from 0 to 1, while closure refers to the inverse. that a reduction in travel time between a firm's subsidiary and its headquarters leads to an increase in investment in the subsidiary. headquarters in location q has an establishment open in location j at time period t. We define an establishment of firm F in location j at time period t as open if F has inventors located in j that apply for patents at time period t. travel time qjt is the travel time in minutes between F's headquarters location q and location j at time period t. Column (2) includes an interaction of log(travel time qjt ) with the across-technology average quartile of initial level of innovativeness of j. j's quantile of initial innovativeness in technology h is computed using the level of patents of j in 1949-1953 in technology h. Standard errors at the non-directional location pair are presented in parentheses (qj is the same non-directional location pair as jq). Predicted growth rates are obtained using the estimated coefficient and the change in travel time, relative to the initial probability. Yearly growth rates g are obtained by computing g = [(1 + nineteen year growth rate) (1/19) -1] × 100, where 19 is the amount of years between 1949 and 1968.

Column (2) of Table 8 estimates the semi-elasticity of the probability of having an establishment to travel time by the quartile of innovativeness of location j in 1949-1953. We compute the quartile of innovativeness at the location level by taking the average quantile across technologies within a location, only for those technologies in which the location has positive patents in 1949-1953. To be able to compare the relative impact of travel time on the growth rate of the probability, we need to relate the semi-elasticity to the baseline probability. The semi-elasticity in the lowest quartile of initial innovativeness is around 1/10th the one in the highest quartile. However, the initial probability in the lowest quartile is around 1/30th of the one in the highest quartile. Therefore, a given percentage change in travel time has an impact on the growth rate of the probability in the lowest quartile that is around 3 times the one in the highest quartile. 94 In other words, given the very low initial probability of locations in the lowest quartile of innovativeness to receive a subsidiary from a firm headquartered in another location, the small increase in percentage points represents a big relative increase in the probability.

The yearly growth rate of subsidiaries implied by the change in travel time is 21.4%

for the lowest quartile while it is 15.4% for the highest quartile, implying a predicted difference of 6 percentage points in the yearly growth rate. 95 In the data we observe an average yearly growth rate which is 4.8 percentage points higher for the lowest quartile relative to the highest quartile. 96 Hence, the reduction in travel time not only predicts a geographic expansion of firms, but it also predicts that the geographic expansion is tilted towards initially less innovative locations. This pattern of geographic expansion is in line with the one observed in the data. 94 These are approximate numbers. The precise computations: the ratio of coefficients is 0.106 = (-0.0079)/(-0.0749), the ratio of initial probability is 0.036 = 0.000068/0.001895, the ratio of the growth rate is 2.94 = (-0.0079/0.000068)/(-0.0749/0.001895). The initial probabilities are computed as the amount of observed subsidiaries in 1949-1953 divided by the amount of (time invariant) potential subsidiaries. The amount of potential subsidiaries is the amount of firms for which we identify headquarters multiplied by the amount of locations other than headquarters location (we have 108 locations in the data, meaning that each firm has 107 potential locations for subsidiaries). 95 For the lowest quartile, the model predicts a 3,869% increase in the probability over 19 years (19 = 1968 -1949) 96 The average yearly growth rate of the probability for the lowest quartile is 5.75% while it is 0.98% for the highest quartile.

Conclusion

A. Appendix: Travel Time Data

A.1. Data Construction

We construct a dataset of travel times by plane between US MSAs for the years 1951, 1956, 1961, 1966. We get information of direct flights from airline flight schedules and feed this information into an algorithm to allow for indirect flights. For each MSA pair with airports served by at least one of the airlines in our dataset we compute the fastest travel time in each of the four years.

Using images of flight schedules, we digitized the flight network for six major airlines: American Airlines (AA), Eastern Air Lines (EA), Trans World Airlines (TWA), United Airlines (UA), Braniff International Airways (BN) and Northwest Airlines (NW).

Note that the first four in this list were often referred to as the Big Four, highlighting their dominant position in the market. They alone accounted for 74% of domestic trunk revenue passenger-miles from February 1955 to January 1956. Together the six airlines accounted for 82% of revenue passenger-miles in that same period, 77%

from February 1960 to January 1961 and 78% from February 1965 to January 1966 (C.A.B., 1966). Our sample of airlines thus covers a vast share of the domestic market for air transport. In addition, the airlines were chosen to maximize geographic coverage.

In total we obtain a sample of 5,910 flights. These flights often have multiple stops. If we count each origin-destination pair of these flights separately, our sample contains 17,469 legs.

Table 9 lists the exact dates of when flight schedules we digitized became effective.

Due to limited data availability not all flight schedules are drawn from the same part of the year. As seasonality of the network seems limited and given the large market share of the airlines we consider, our data is a good approximation of the network in a given year. To obtain exact geographical information on where airports are located, we match city names to their IATA airport codes. We use the addresses of ticket offices that are indicated on the last pages of the flight schedules. Most of the ticket offices were located directly at the airport, allowing to infer the airport the airline was serving in a given year. For some flight schedules we are missing these last pages and used information from adjacent years in order to identify airports. We also manually verified the airport match using various online sources. We then obtain geographical coordinates from a dataset provided by https://ourairports.com/ (downloaded July 2020).

From the flight schedule we also collect information on the aircraft model, indicated next to the flight number. Using various online sources, we manually identified aircraft models that are powered by a jet engine. We thus know on which connections airlines were using jet aircraft.

Flight Schedules also contain information on connecting flights. For example, the second column in figure 18 indicates a departure from Boston leaving at 12.00 local time.

A footnote is added to the departure time indicating that this departure is a connection via New York. It is thus not operated by flight 287 otherwise described in column 2, but it is just supplementary information for the passenger. As we are interested in the speed of aircraft and the actual travel time on a given link, this information on connecting flights would pollute our data and we thus delete this supplementary information.

As outlined above, the digitization requires human input. It is thus prone error-prone.

The travel time calculation relies on each link in the network, and if one important connection has a miscoded flight, it might potentially distort the travel time between many MSA pairs. We thus implement an elaborate method to detect mistakes in the digitization process. In particular, after the initial transcription, we regress the observed duration of the flight on a set of explanatory variables: the full interaction of distance, a set of airline indicators, a set of year indicators and a dummy variable indicating whether the aircraft is powered by a jet engine or not. This linear model yields an R 2 above 95%. We then compute the predicted duration of each flight and obtain the relative deviation from the observed duration. If the deviation is above 50%, we manually check whether the transcribed information is correct. If we find a mistake, we correct the raw data, rerun the regression and recompute relative deviations, until all the observations with more than 50% deviation have been manually verified.

For 15 connections, the information was correctly transcribed from the flight schedule, but the flight time differed a lot from other flights with similar distances that used the same aircraft. The implied aircraft speed for these cases is either unrealistically high or low, in one case the implied flight time is even negative. These cases seem to be typos introduced when the flight schedule was created (e.g. a "2" becomes a "3").

Instead of inferring what the true flight schedule was which is not always obvious, we drop these cases. The flight schedule format requires us to make one assumption. In particular, the flight schedule for a multi-stop flight may either indicate the arrival time or the departure time for a particular stop. If the flight schedule only lists the departure time, we need to infer the arrival time and vice versa. We allow for five minutes between arrival and departure. This is relatively low, but still in the range of observed difference between departure and arrival for cases where we observe both. As correspondences may have been ensured by airlines in reality, i.e. one aircraft waiting with departure until other aircraft arrive, we opted for the lower end of the observed range of stopping times.

Finally, since the shortest travel time measure may not capture the benefits of a highly frequented hub, we also calculate the daily average of the shortest travel time.

In particular, we compute the shortest travel time at every full hour of the day and take the average. This measure thus captures the benefits of being located near an airport where flights depart many times per day.

To conclude, we end up with a set of four origin-destination matrices indicating the fastest travel time (and another set with the average daily travel time) between US MSAs in 1951, 1956, 1961 and 1966.

A.2. Descriptive Statistics

Table 12 shows the number of non-stop connections between MSAs by year and airline.

It underlines the dominant position of the Big Four (AA, EA, TW, UA) which were much bigger than their competitors (BN and NW). The growth of the airline industry is also apparent. All airlines had the lowest number of connections in 1951 and subsequently relatively stable over time with more than three quarters of connections remaining intact within a five-year window. Interestingly, during the beginning of the jet age (i.e. 1956 to 1961), the network appears to have been especially stable, with only 11% of connections either disappearing or newly being added. Thus, the rise of jet aircraft did not lead to a vast reshaping of the network. Given the very different technology, this may be surprising, but may partly be due to heavy regulation.

The table also shows that newly introduced routes were over long distances whereas those discontinued were operating on shorter distances. When changes in the network took place, they thus seemed to improve the network for places further apart. Figure 20 shows all non-stop connections in our data weighted by the (log) frequency.

Initially, the network was concentrated in the Eastern states and transcontinental routes

were not yet established, due to technological limitations. In contrast, in the 1960s, after the jet is introduced, intercontinental routes quickly emerge and are operated at a high frequency. Similarly, direct connections from the Northeast to Florida intensify. The figure echos the findings from table 14 which illustrates that the overall number of MSA pairs with a direct connection increases over time. Airlines differed in their speed of adoption of the newly arrived jet aircraft. Table 12 shows that, in 1961, 65% of UA's connections between MSAs were flown using a jet aircraft (weighted by distance), whereas this was only true for 13% of EA's connections.

While adoption was heterogeneous across airlines, adoption was fast. By 1966, all airlines were operating 75% of their connections with jet aircraft (weighted by distance).

Figure 21 show the average speed of jet and propeller aircraft by distance. Generally, jet aircraft were substantially faster, but especially so on long-distance flights, where they could be up to twice as fast as propeller-driven aircraft. This particularly stark difference in speed for long-haul flights is also reflected by adoption. Figure 22 shows that jet aircraft were first introduced on long-haul flights. Only 50% of MSA pairs at around 1,500 km distance had at least one jet aircraft operating, whereas 100% of pairs above 3,000 km. Then, in the late 1960s, they were also gradually introduced on shorter distances. In fact, for all pairs above 2,000 km there was at least one jet engine-powered flight. We obtain that around 90% of the change in travel time is due to the change in speed of aircrafts, while around 10% of the change is due to the change in the flight routes. In the figure 30 in the appendix we show that the proportion is relatively constant for all distances. This confirms that most of the observed changes in the network are due to improvements in the flight technology. 99 Fixes the origin-destination airports that are connected with a non-stop flight

B. Appendix: Patent data

In this appendix we describe facts that we observe in the US patent data, for patents For the analysis presented in this appendix we will use the resulting dataset from the matching procedure, where unless evident or noticed, we will use only patents that have inventors within MSAs. We discard patents that have inventors in multiple

MSAs and patents that belong to government organizations or universities. We assign patents to technology categories using fractional count: if a patent is listed in two technology categories, then we assign half a patent to each category. We discard self citations (citations in which the citing patent owner is the same as the cited patent owner) because self-citations may be due to different incentives.

B.1. Matching patents to locations

In figure 32 we observe that the matching rate decreases from around 95% before 1970, to around 80% in 1971 and 1972, and then it stabilizes around 99% after 1975.

capacity of the patent office to revise applications) and changes over time. Hence filing year is the date in our data that approximates the best to the date of invention.

B.2. Input-Output of patents

In the same spirit as how Input-Output tables of industries are constructed, we can use citations as a reflection of sourced (input) knowledge. In this case, we interpret the cited patent as being a source of knowledge, and the citing patent as being a destination. In Figure 35

B.3. General Electric research establishments

Using the patent owner identifier we can display the geographical distribution of research establishments for a selected firm. Figure 36 shows the research establishments of General Electric in the period 1945-1953. We say that a firm F had a research establishment in location i in time period t if firm F filed at least one patent in time period t with inventors located in location i. The headquarters location q of firm F is defined as the location in which the firm filed the largest amount of patents in the Weidner and Zylkin (2021) show that PPML estimation of gravity equations with threeway fixed effects (origin-time, destination-time, origin-destination) is consistent but asymptotically biased. In their words: "the asymptotic distribution of the estimates is not centered at the truth as N → ∞" (page 2). The asymptotic bias concerns both point estimates and standard errors. In order to correct the bias we apply their suggested split-panel jackknife bias correction of section 3.4.1 to both point estimates and bootstrap standard errors. The idea of the jackknife bias correction is to estimate the model in many subsamples and then subtract the average coefficients of the subsamples from (twice) the original coefficient.

As suggested in Weidner and Zylkin (2021) when using real world data (as opposite to simulated data), we estimate the bias correction repeatedly. We modify equation ( 14)

in Weidner and Zylkin (2021) to define the bias corrected coefficient as:

βJ N := 2 × β - 1 Z ∑ z ∑ p β(p,z) 4 ( 12
)
where p is a random subsample of size 1/4th of the original sample, and Z is the amount of times to subsample.

The procedure to estimate bias corrected point estimate βJ N is as follows:

1. Estimate β: the not-bias-corrected estimate of equation ( 3 6. Repeat Z times steps 2 to 5.

Compute equation 12

To compute bias-corrected bootstrap standard errors we need to bias-correct the point estimate βJ m of each bootstrap iteration m. The procedure to estimate bias corrected standard errors is as follows:

1. Sample establishment-technology-pairs FiGjhk with replacement such that we obtain a re-sampled data of the same size as the original data (hence, some FiGjhk will be repeated in the re-sampled data). Sampled FiGjhk are kept for all time periods in order to keep the source of identification of β: across time variation within a establishment pair. Label this new dataset data m . The bias correction of point estimates and bias correction of bootstrap standard errors implies estimating Z × 4 + Z M × M × 4 models. This is a computationally demanding task. To estimate columns (1) and (2) of Table 2 we set Z = 100, Z M = 5 and M = 200, adding up to 1, 100 models to estimate for each column.

As recommended in Hansen (2021), in the ] × ε FiGjhkt , for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Column (2) includes the interaction of travel time ijt with a dummy for distance bin between the citing establishment Fi and the cited establishment Gj. Column (3) and (4) show the result of two step instrumental variables estimation, where log(travel time ijt ) is instrumented with log(travel time fix routes ijt ), the travel time that would have taken place if routes were fixed to the ones observed in 1951 and in each year routes were operated with the average airplane of the year. 0.025 and 0.975 quantile bootstrap estimates are presented in parentheses. The coefficients and bootstrap estimates in columns (1) and ( 2) are jackknife bias-corrected. R2 is computed as the squared correlation between observed and fitted values.

D.2. Instrumental variables PPML

To implement the instrumental variables of Poisson estimation we follow the control function approach described in Wooldridge (2014). We explain the procedure using the estimation of the elasticity of citations to travel time. The procedure is similar for the elasticity of (new) patents to knowledge access. We proceed in two steps estimating the following two equations: log(travel time) FiGjhkt = λ 2 log(travel time fix routes FiGjhkt )

+ FE FiGjhk + FE Fiht + FE Gjkt + u FiGjhkt (13) citations FiGjhkt = exp [β log(travel time ijt ) + λ ûFiGjhkt + FE FiGjhk + FE Fiht + FE Gjkt ] × v FiGjhkt (14)
In a first step we estimate equation ( 13) and obtain estimated residuals ûFiGjhkt . In a second step we use the estimated residuals as a regressor in equation ( 14) which controls for the endogenous component of travel time.

To perform inference we bootstrap standard errors in the following way:

1. Sample establishment-technology-pairs FiGjhk with replacement such that we obtain a re-sampled data of the same size as the original data (hence, some FiGjhk will be repeated in the re-sampled data). Sampled FiGjhk are kept for all time periods in order to keep the source of identification of β: across time variation within a establishment pair. Label this new dataset data m 2. Using data m , estimate equations ( 13) and ( 14) to obtain the bootstrap estimate βm .

Store βm .

3. Repeat M times steps 1 and 2. First, we perform an intensive margin/extensive margin decomposition of the effect of travel time on citations. We find that the effect is coming from both margins. In the instrumental variables approach, the intensive margin is only statistically different from zero for distance greater than 2,000km, while for the extensive margin it is for distance greater than 300km. Results for the baseline analysis are shown in Table 17 and for the IV estimation in Table 18.

Second, we investigate if the elasticity varies by the degree of concentration of patents across establishments in the citing technology or cited technology, we find no statistically significant heterogeneous effect. Results are shown in columns ( 1) and ( 2) of Table 20.

Third, we check if the elasticity varies by the median forward and backward citation lags of the cited and citing technologies. We find that the elasticity of citations to travel time is more negative both for technologies that accumulate citations during a longer time period and for technologies that cite older patents. To be able to precisely show if it is newer or older technologies that diffuse better as consequence of the jet requires an analysis with the citation level forward and backward lag, and not using the median lag in the technology. Nonetheless, the results seem to suggest that jets improved the diffusion of older technologies. Results are shown in columns ( 3) and ( 4) of Table 20.

Fourth, we extend the sample of patents to include patents with a patent owner identified as a government organization or university. Column (5) of Table 20 opens the elasticity of citations to travel time by whether the citing patent belongs to a government organization of university. Column (6) includes a dummy for whether the cited patent belongs to a government organization or university. We do not observe a particular change in the pattern of the elasticity of citations to travel time.

Sixth, we extend the sample to include self citations (citations in which the citing and cited patents belong to the same patent owner F). Column (7) of Table 20 shows that the elasticity is not statistically different for self citations.

Seventh, we check if the elasticity varies with the level of innovativeness of the citing firm. It may be the case that those firms that actually have the -time and monetarybudget to take a plane are only the most innovative ones. We rank firms F in technology h according to the amount of patents filed by F in technology h at the initial time period 1949-1953. We define quantile 0.00 as all those firms that did not file patents in 1949-1953, while quantile 0.01 is assigned to those that filed patents but not as many as to be in the quantile 0.25 or higher. Results are shown in Table 19. We do not find a particular pattern related to the initial innovativeness.

Eighth, we check if the elasticity varies with the citing technology, cited technology and citing-cited technology pair. Results are shown in Table 21 andTable 24. We find that the elasticity is negative and significant mainly when the citing and cited technology are the same. In Appendix B we show that most citations happen within a technology, so most identification power would be when citing and cited technologies are the same. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. The variable ûFiGjhkt is constructed as ûFiGjhkt = travel time FiGjhkt -λ2 travel time fix network

PPML

FiGjhkt

. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Column (3) shows the result of an IV-2SLS estimation of log(citations FiGjhkt ) = α log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt + ε FiGjhkt , with a sample of establishment-technology pairs (FiGjhk) that have positive citations in all periods. Column (5) shows the result of an IV-2SLS estimation of 1{citations FiGjhkt > 0} = γ log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt + ε FiGjhkt , with the same sample as (1). Columns (3) and (5) use travel time fix network ijt as an instrument for travel time ijt . Column (2), ( 4) and (6) open, respectively, the coefficients β, α, γ by distance between the citing establishment Fi and the cited establishment Gj. Standard errors are presented in parenthesis. In Columns (1) and (2) standard errors are bootstrapped. In Columns (3) to (6) standard errors clustered at the non-directional location pair (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values.

= exp [∑ d β d 1{distance ij ∈ d} log(travel time ijt ) + ∑ d α d 1{distance ij ∈ d} 1{X FiGjhkt } log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt ,
for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. d are distance intervals: [0 -300km], (300km -1000km], (1000km -2000km], (2000kmmax]. The variable X takes different value depending on the column: in column (1) it is the across-MSA Herfindahl index of the citing technology, in column (2) it is the across-MSA Herfindahl index of the cited technology, in column (3) it is median forward citation lag of the cited technology, in column (4) it is median backward citation lag of the citing technology. In column ( 5) and ( 6) the sample includes government and university patents, in column (5) X is a dummy that takes value one if the citing patent belongs to a university or government organisation, in column (6) it is a dummy that takes value one if the cited patent belongs to a university or government organisation. In column (7) the sample includes self citations, the variable X is a dummy that takes value one if the citing firm F cited firm G are the same. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Standard errors clustered at the non-directional location pair are presented in parenthesis (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values. In column (1) we include the baseline results. 103 In column (2) we use only citing establishments Fi that filed patents during the initial time period 1949-1953. In column (3) we further restrict the sample to both citing establishments Fi and cited establishments Gj that filed patents in 1949-1953. 104 We find that the coefficient at more than 2,000km remains comparable to the one in the baseline regression, statistically significant at the 1%.

Ticket prices

During the period of analysis ticket prices were set by the Civil Aeronautics Board, so airlines could not set prices of their own tickets. Some airlines included a sample of prices in the last page of their booklet of flight schedules a sample of prices, which we digitized. We have digitized American Airlines 1951Airlines , 1961Airlines , 1966;;TWA 1951and United Airlines 1956and 1961. 105 . The sample includes prices for 11,590 directional airport pair years. We document multiple facts about prices.

First, prices were set in the form of an intercept plus a variable increment depending on distance between origin and destination (until 1962-1963). A linear regression with an intercept and a slope estimated separately for each year (including 1966), service class (first class or coach service), and aircraft type (propeller or jet) gives a R2 of 0.98 or higher in each regression, with an average R2 of 0.993.

Second, all airlines operating within the same route charged exactly the same price.

In 1951, in our digitized price data we have 432 airport pairs in which both American Airlines and TWA were operating and reported the price for first class service. 94% of those airport pairs had exactly the same price in both airlines.

Third, ticket prices of flights operated by jet airplanes had a surcharge of around 6%

on top of the one operated by propeller airplanes.

Fourth, the change in prices over time had a similar pattern until 1961: a stronger increase in short distances (probably due to an increase in fixed costs of take-off and landing, although not reflected in the intercept of the linear regressions), and a relatively constant increase for flights between airports more than 1,000 km apart. In the period 1961 to 1966 we observe a drop in prices of around 20% for routes of more than 1,000km distance, breaking the linearity of prices in distance previously observed. We had visually inspected price tables and detected that the drop in prices happened in 1962-1963. 3)). In this case the estimated regression has a slope of 0.73 statistically significant at the 1% level and a R2 of 0.09.107

In Tables 5 and26 we present the results of adding highway travel time as control.

The low correlation between the change in travel time by highway and airplane implies that the estimated elasticity of citations to air travel time remains almost unchanged, relative to the baseline estimation.108

Frequency adjusted travel time

The frequency of flights may have changed simultaneously with the introduction of jet airplanes. The change in travel time could then be consequence of higher frequency rather than changes in airplanes' speed. Given that some MSA pairs are connected indirectly (with connecting flights), accounting for frequency is not straight forward:

the frequency of each leg of the flight route matters (actually, it is not only frequency of each leg but also the synchronization among all potential legs). In order to take into account potential changes in the frequency of flights we computed the daily average travel time. This travel time is the average across all fastest travel times if the passenger was to depart at each full hour (1am, 2am, ..., 1pm, 2pm, etc.). The computation of this travel time includes the waiting time that is affected by frequency: the time until first departure and layover time of each connecting flight. Hence, the daily average travel time is a frequency-adjusted travel time: changes in the daily average travel time that are larger than in the fastest travel time denote that frequency of flights increased and therefore there is less waiting time. If we observe the reverse that means that frequency did not improve as much as the speed of airplanes. In table 27 we estimated the elasticity of citations to travel time using first the fastest travel time (baseline, columns 1 and 2) and the daily average travel time (columns 3 and 4). The estimated elasticity is similar using both measures, which gives confidence that our results are not driven by changes in the frequency of flights. ] × ε FiGjhkt , for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Column (2) includes the interaction of travel time ijt with a dummy for distance bin between the citing establishment Fi and the cited establishment Gj. Column (3) and (4) use the daily average travel time, which is computed as the average of the fastest travel time departing at every full hour (the average across all 24 potential departing times). Standard errors clustered at the non-directional location are presented between parentheses (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values.

Access to capital

We construct four measures of access to capital using 1949-1953 market capitalization of firms listed in the stock market. The four measures are similar in their essence but differ in the computation of a firm's technology and the firm's location. The measure is computed as follows:

capital access iht = ∑ k ψ hk ∑ j, j =i Capital stock jk,t=1951 × travel time ξ ijt ( 15
)
where Capital stock jk,t=1951 is a proxy for the capital which is specific to technology k located in j at the initial time period 1951. ψ hk is an input-output weight of capital flows and ξ is the elasticity of capital flows between to travel time. As a proxy for capital we use market capitalization of firms.

We construct four measures of capital access iht which differ on: (i) the way we define the allocation of the firm's capital to each location (either using all inventors' locations or only the assigned headquarters), and (ii) the way we allocate a firm's capital across technologies (using the share of a technology within the firm, or relative to the national share of that technology). We use COMPUSTAT as our source of data for market capitalization.

We proceed as follows:

1. Use share's market price at closure calendar year multiplied by the number shares outstanding. We use the variables prcc c and csho to maximize coverage of firms given that other variables have missing value for many firms.

2. Take the yearly average market capitalization to maximize coverage (many firms have missing in a certain year). This step potentially introduces measurement error due to changes in total stock market capitalization but allows us to increase the amount of firms included in the sample.

3. Determine a firm's MSA using patent inventor location. Two ways to determine the location, 1. only HQ location, 2. all locations where the firm had inventors applying for patents in 1949-1953 4. Determine the share of each technology firm's technology using patent technology.

Two ways to determine the share oftechnology: 1. the share of each tech within firm + share within firm relative to national share 5. In the absence of data on a capital input-output weight, assume it is the same as the technology input-output weight, i.e. ψ hk = ω hk 6. In the absence of data on the elasticity of capital flows to travel time assume ξ = -1

The four measures of access to capital are as follows:

1. Attribute all capital to headquarters and use the absolute share of each technology in the firm 2) are the baseline regressions (all MSA-pairs), columns (3) and (4) drop MSA-pairs that are ever connected with one leg (a non-stop flight), and columns ( 5) and ( 6) drop MSA-pairs that are ever connected with one flight number. The difference between non-stop and one flight number is that one flight number could serve multiple MSAs by making intermediate stops. 110 The estimated coefficients are in the ballpark of the initial estimates, especially for +2,000km, providing evidence that it is reasonable to use the pre-existing network as the baseline to construct the instrument.

3. 1 .

 1 Air transport: jet arrival The jet aircraft was first invented in 1939 for military use, with the German Heinkel He 178 being the first jet aircraft to fly. The first commercial flight by a jet aircraft was in 1952 by the British Overseas Airways Corporation (BOAC) from London, UK to Johannesburg, South Africa with a Havilland Comet 1. Nonetheless, given the amount of accidents of the Havilland Comet 1 due to metal fatigue, jet commercial aviation did not truly take off until the Boeing 707 entered commercial service in late 1958. The 24th of January of 1959 represented a major milestone in the jet era: American Airlines Flight 2 flew with a Boeing 707 jet aircraft from Los Angeles to New York, the first non-stop transcontinental commercial jet flight. 7 In 1951 New York City and Los Angeles were connected with a one-stop flight in 10 hours and 20 minutes. The flight had a forced stop in Chicago and was operated with the propeller aircraft Douglas DC-6, which had a cruise of 500 kmh. By 1956, New York City and Los Angeles were connected with a non-stop flight in 8 hours and 30 minutes. This was accomplished due to the introduction of the propeller aircraft Douglas DC-7 which had a cruise speed of 550kmh, and a change in regulation which increased maximum flight time of a crew from 8 to 10 hours within a 24-hour window. 8 In 1961, the route was covered with the jet aircraft Boeing 707 in a non-stop flight in 5 hours 15 minutes, reaching 5 hours 10 minutes in 1966. The Boeing 707 had a cruise speed of 1000kmh, cutting travel time from New York City to Los Angeles in half between 1951 and 1966.

Figures 1

 1 Figures 1 and 2 are images (edited for better readability) from annual reports of the Interstate Commerce Commission of 1967 and 1965 respectively. Figure 1 displays the amount of passenger-miles 9 for Air, Motor and Rail transportation from 1949 to 1966.

Figure 2 Figure

 2 Figure2shows shipments in ton-miles for the period 1939 to 1964 by mean of transport: Airways, Pipelines, Inland Waterways, Motor, Railroads. Interestingly, we observe that air transport of goods, even if it increased, it accounted for less than 0.1% of transport of goods in 1964.10

  construct a new data set of the flight network in the United States during the 1950s and 1960s. We collected and digitized information of all the flights operated by the main airlines and obtained the fastest route and travel time between every two airports in the network.To construct the flight network we use historical flight schedules of the main airlines operating in 1950s and 1960s. Figure3is a fragment from an example page of the 1961 flight schedule of American Airlines. In the flight schedule we observe in the center column the name of departure and arrival cities (which we match to airports using airlines' historical ticket office geographical location), while the small columns on the sides depict flights. In the top of the small columns we observe the type of service provided (first class, coach or both), aircraft operated, days operated (daily if information is missing) and flight number. The content of the small columns displays the departure and arrival time (local time, bold numbers represent PM) at each city, including all intermediate stops.

Figure 3 :

 3 Figure 3: Fragment of flight schedule American Airlines 1961 The center column displays the name of departure and arrival cities. The small columns on the sides display flights with departure and arrival time (local time, bold numbers represent PM). The top of the small columns shows the type of service provided (first class, coach or both), aircraft operated, days operated (daily if information is missing) and flight number.

  and 21,210 worldwide. Our data connects 275 US airports (434 worldwide) creating 2,563 unique origin-destination (directional) airport links (3,466 worldwide). Figure 4 displays the flight network in continental United States pooling all years together. In Appendix A.2 we show the US flight network by year, around 80% of the non-stop flights remain year-on-year.

Figure 4 :

 4 Figure 4: United States flight network 1951-1966

4. 1 .

 1 Descriptive statistics: Air travelTo understand the changes in travel time we will first study travel time of non-stop flights and then of all routes including connecting flights. Figure5displays the nonstop fastest flight within each MSA pair that was operating in each year. In 1951 the longest non-stop flight across MSAs was between Chicago and San Francisco using the Douglas DC-6, covering a distance of 2,960 km in 7 hours 40 minutes. This travel time was just under 8 hours, the maximum flight time allowed for a crew in a 24-hour period. 18 In 1956, new regulation allowed up to 10 hour flights for transcontinental flights, the longest non-stop flight between MSAs was New York to San Francisco with the Douglas DC-7, covering a distance of 4,151 km in 9 hours. Between 1951 and 1956, while we observe an increase in average flight speed that went up to 17%, the main change observed is that longer non-stop routes were possible.In 1961, the first year in which we have jet aircrafts in the travel time data, there is a reduction in travel time between MSA-pairs, especially for those far apart from each other. In 1966, there is a further decrease in travel time due to a widespread adoption of jet aircrafts in shorter distances. In Appendix Figure22we show the jet adoption rate by distance for MSAs connected with a non-stop flight. All MSA-pairs more than 3,000km apart connected with a non-stop flight operated at least one jet flight in 1961, and this expanded to all those more than 2,000km apart in 1966. The speed gain of jets relative to propeller aircrafts is increasing with the amount of time that the jet can fly at its cruise speed, arguing in favor of an adoption that is increasing with the distance between origin and destination.19

Figure 5 :

 5 Figure 5: Non-stop fastest flights United States MSAs

Figure 6 :

 6 Figure 6: Change in MSAs travel time

Figure 7

 7 Figure 7 shows the percentage change in observed and instrumental travel time relative to 1951. We compute the percentage change within each MSA-pair for each year and then take averages within 250km bins. We observe that the instrumental travel time follows pretty closely the observed change in travel time in each year. Especially, it replicates the pattern of a stronger decrease in travel time for MSAs located farther apart. It is only for MSAs less than 250-500km apart that the change in the instrumental travel time departs from the observed change. 28 This finding shows that most of the change in travel time that we observe is due to the change in speed of airplanes, and

Figure 7 :

 7 Figure 7: Instrumental Travel Time between US MSAs.

Figure 8 :

 8 Figure 8: Geography of Patenting 1951 Figure 9: Patent growth 1951-1966

Figure 10 :

 10 Figure 10: Patent growth rate by initial innovativeness ranking of MSA

Figure 11 :

 11 Figure 11: Share of patents by region Figure 12: Patent growth by region

Figure 13 :

 13 Figure 13: Average distance across establishments within the firm

Figure 14 :

 14 Figure 14: Quantiles of citation distance Figure 15: Share of citations by distance

First

  , in 1947 the Congress published the official plan for the Interstate Highway System, a nationwide infrastructure plan to improve existing highways and build new ones (seeBaum-Snow (2007),Michaels (2008),Jaworski and Kitchens (2019) and Herzog (2021)). In case the change in travel time by air is correlated with the change in travel time by highway, we would have an omitted variable bias if we include only one of them in the estimation. Taylor Jaworski and Carl Kitchens have graciously shared with us data on county-to-county highway travel time and travel costs for 1950, 1960 and 1970, which we converted to MSA-to-MSA and linearly interpolated to convert to the same years of our air travel data. Hence we have a MSA-to-MSA time-varying measure of travel time. In Appendix E we show the correlation of MSA-to-MSA change in air travel time and highway travel time. Second, other means of communication like telephone lines may have expanded or changed their price during the period of analysis. Haines et al. (2010) contains information on the share of households within each city with telephone lines in 1960.

  measure of Knowledge Access allows us to translate changes in travel time between pairs of MSAs into a single location-technology specific characteristic, and to represent it on the same scale as patent growth in Figure 9. Figure 16 depicts the time change in log Knowledge Access from 1951 to 1966, averaged across technologies within each MSA. Darker colors represent higher growth in Knowledge Access. As with patent growth, we observe that MSAs that had the strongest growth are generally located in the South and the West of the United States, far from the knowledge centers of New York and Chicago. The reduction in travel time was larger between locations far apart, implying that locations which happened to be far from knowledge centers increased relatively more their Knowledge Access.

Figure 16 :

 16 Figure 16: Change in log Knowledge Access 1951 -1966

Figure 9 )

 9 Figure 9), while in the right panel it is the predicted patent growth. We compute the prediction using the observed change in travel time and quartile specific elasticities of column (2) in Table 4. Similarly to what is observed in the data, the change in travel time predicts a larger patenting growth rate in the South and the West. At the same time, the change in travel time predicts smaller growth rates in New York, Chicago and their surroundings.

Figure 17 :

 17 Figure 17: Observed vs. predicted patent growth 1951 -1966

  This paper constructed a new dataset of the flight network in the United States during the beginning of the Jet Age and studied the impact of improvements of air travel on the creation and diffusion of knowledge. We found that the reduction in travel time led to an increase in knowledge diffusion, especially between research establishments located far apart. The reduction in travel time also led to an increase in the general access to knowledge, which had positive spillovers for the creation of new knowledge. The effect in the increase of creation of knowledge was stronger in locations initially less innovative, generating a convergence force which goes in the same direction as what is observed in the data. One of the drivers of the increase in the creation of knowledge and convergence was the geographical expansion of firms.We provide causal evidence of standing on the shoulders of giants: new knowledge builds upon pre-existing knowledge. We do so by first estimating one new key parameter: the elasticity of diffusion of knowledge to travel time. Second, extending a production function of knowledge proposed inCarlino and Kerr (2015), we estimate the impact of knowledge spillovers on the creation of new knowledge. Conditional on the pre-existing distribution of knowledge, changes in travel time translate into changes in knowledge spillovers. The results show that knowledge spillovers are important for the creation of new knowledge and more so in locations which are initially less innovative.Our novel dataset document a historical country wide event that dramatically changed the way we see time and space. Our results provide new evidence of how the introduction of jet airplanes changed the geography of innovation. Better connectivity to innovation centers in the Midwest and the Northeast led to an increase in innovation in the South and the West of the United States. In this way, jet airplanes were one of the contributing factors in the shift of innovative activity towards the South and the West of the United States.

Figure 18

 18 Figure 18 shows two pages of the flight schedule published by American Airlines in 1961. Each column corresponds to one flight. As can be seen, one flight often has multiple stops. Departure and arrival times in most flight schedules are indicated using the 12-hour system. PM times can be distinguished from AM times by their bold print. In the process of digitization we converted the flight schedules to the 24-hour system. Times in most tables are in local time. We thus recorded the time zones that are indicated next to the city name and converted them to Eastern Standard Time.

Figure 18 :

 18 Figure 18: Flight Schedule American Airlines 1961.

Figure 20 :

 20 Figure 20: Flight Network by Year. Weighted by log weekly frequency.

Figure 21 :

 21 Figure 21: Speed by Aircraft Type. Pooling all Years.

Figure

  Figure 22: Jet Adoption

Figure 23 :

 23 Figure 23: Jet Adoption by Year

Figure 24 :

 24 Figure 24: Travel Times between US MSAs.

Figure 25

 25 Figure 25 that the change in travel time is accompanied by a reduction of the amount of legs needed to connect two MSAs at every distance. This reduction is speciallymarked between 1951 and 1956, and 1961 and 1966. In Figure 26we open up the change in travel time by the way an MSA pair was connected in 1951 and 1966: either directly (non-stop flight) or indirectly (connecting flight). We observe that much of the increase in travel time for MSA pairs less than 250km apart comes from routes that were operated non-stop and then it needed a connecting flight. Interestingly, for MSA-pairs more than 2,000km apart travel time reduced on average 42% for those pairs that were connected indirectly in both periods, and 51% for those that switched from indirect to direct. This fact shows the relevance of improvements in flight technology even for MSAs not directly connected. It could be the case that a reduction in the amount of legs or an increase in frequency of flights reduces layover time. In Figure28we compare the

Figure 25 :Figure 27 :Figure 28 :

 252728 Figure 25: Average amount of legs per route

Figure 29 :

 29 Figure 29: Counterfactual change in travel time

Figure 31 :

 31 Figure 31: Flight Network in 1956 by Airline (weighted by log frequency).

  filed 100 between 1945 and 1975. US patents data containing citations and filing year have been downloaded from Google Patents. Then, it was merged with multiple datasets (see Appendix Patent Data Construction for more details): • Technology classification: NBER patent database. • Geographic location of inventors: Histpat and Histpat International for patents published until 1975, Fung Institute for patents published after 1975. Both matched to 1950s Metropolitan Statistical Areas (MSAs).• Ownership:Kogan et al. (2017) for patents owned by firms listed in the US stock market, Patstat for the remaining patents not matched toKogan et al. (2017).We highlight two details from the matching process: 1. During filing years1971-1972 the rate of non-geocoded patents increases, possibly due to Histpat and Fung data not being a perfect continuation one of the other. 2.Kogan et al. (2017) seems to use a matching method based on the patent owner declared in the patent text, as Patstat does. Specially,Kogan et al. (2017) does not explicitly say if it takes into account firmownership structure to determine patent ownership, neither does Patstat.

Figure 33 :

 33 Figure 33: Share patents in Metropolitan Statistical Areas

  we aggregate citations by citing-cited technology category in the years 1949-1953. Rows represent the source technology and columns the destination technology. Columns should sum to 1 (round errors may exist). We highlight in bold those IO coefficients that are higher than 0.1. We observe that the diagonal has coefficients greater than 0.5, implying that technologies rely on themselves to create new knowledge. At the same time, we observe the importance of Electrical to create Communication technologies, and the small relevance of Drugs for every other technology.

Figure 35 :

 35 Figure 35: Input-Output of technologies 1949-1953

  Figure 36: Research establishments of General Electric 1949-1953

Figure 40 :Figure

 40 Figure 40: Patent growth by initial innovativeness ranking of MSA

Figure 46 :

 46 Figure 46: Quantiles of citation distance

) 2 .

 2 Randomly allocate all citing establishment-technology Fih into two equally sized groups (groups are time-invariant). Call them citing groups a and b.3. Randomly allocate all cited establishment-technologyGjk into two equally sized groups (groups are time-invariant). Call them cited groups a and b. 4. Create four p subsamples of the original data: (a,a), (a,b), (b,a), (b,b). Subsamples keep the same granularity as the original data FiGjhkt.5. Estimate equation (3) (gravity equation of the main text) in each of the subsamples from the previous step to obtain β(p,z) . 102 Store the four estimated coefficients.

2.. 5 .

 5 Using data m , estimate equation (3) to obtain βm (this is a point estimate of the specific data m ) 3. Using data m , repeat Z M times steps 2 to 5 of the procedure to estimate bias corrected point estimate. This step provides Z M × 4 point estimates β(p,m,z M ) 4. Compute the bias corrected point estimate of bootstrap m βJ m = 2 × βm -1 Z M ∑ z M ∑ p β(p,m,z M ) 4 Store the bias corrected point estimate of bootstrap m 6. Repeat steps 1 to 5 M times to obtain M bias corrected bootstrap point estimates βJ m 7. Compute the variance-covariance matrix of bias corrected bootstrap coefficients βJ m and use it to compute standard errors of βJ N

4.

  Compute the variance-covariance matrix of βm and use it to compute standard errors of β For columns (3) and (4) of

Figure 49

 49 Figure 49 shows prices for first class service by year and aircraft type, deflated by the consumer price index to 1951 values. Figure 50 presents the percentage change in deflated prices of first class service. Both figures show the previous facts: prices are generally linear in distance until 1966 in which we observe a break after 1,000 km.

Figure 49 :

 49 Figure 49: Flight ticket prices, deflated by CPI

Figure 51 :

 51 Figure 51: Change travel time by airplane and highway 1951-1966 Figure 52: Change travel time by airplane and highway 1951-1966, weighted

Figure 53

 53 Figure 53 shows the within MSA-pair decrease in the fastest travel time and the daily average travel time. 109 Both measures of travel time follow a similar pattern: slight decrease in 1956, a stronger decrease in 1961 especially for long distance routes, and a further decline in 1966. However, we observe that the decrease of the fastest travel time is on average larger than the one of the daily average travel time: the frequency of flights, if any, attenuated the potential decrease in travel time from the improvements in airplanes' speed. This observation is also in line with a comparison of the fastest travel time with and without layover time (Figure 28 in the Appendix of the paper): layover time attenuated the change in travel time.

133 2 .

 2 Attribute all capital to headquarters and use the share of each technology in the firm relative to the national share 3. Attribute capital to establishments using their pat share and use the absolute share of each technology in the firm 4. Attribute capital to establishments using their pat share and use the share of each technology in the firm relative to the national share

Table 1 :

 1 Number of firms and share of patents by firm's geographic coverage

	Share of patents

Geographic coverage is computed as the amount of Metropolitan Statistical Areas (MSAs) in which the firm has inventors applying for patents (research establishments) in a certain year. Bins of geographic coverage are 1 MSA, 2 to 5 MSAs, 6 to 10 MSAs, 11 to 20 MSAs, more than 20 MSAs. The maximum possible is 108 MSAs.

  in the full estimating sample and 28.7% in the raw data of travel time across MSAs.

		PPML		IV PPML
	Dep. variable: citations		citatitions FiGjhkt
		(1)	(2)	(3)	(4)
	log(travel time)	-0.083 * * * (0.019)		-0.152 * * * (0.029)
	log(travel time) × 0-300km		0.019 (0.036)		-0.076 (0.221)
	log(travel time) × 300-1,000km	-0.089 * * * (0.023)		-0.134 * * * (0.044)
	log(travel time) × 1,000-2,000km	-0.094 * * * (0.033)		-0.112 * * (0.047)
	log(travel time) × +2,000km	-0.169 * * * (0.039)		-0.203 * * * (0.043)
	N obs. effective	4, 703, 010 4, 703, 010 4, 703, 010 4, 703, 010
	R2	0.88	0.88	0.88	0.88

* * * p < 0.01; * * p < 0.05; * p < 0.10 Table 2: Elasticity of citations to travel time Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt = exp [β log(travel time ijt

Table 3 :

 3 Robustness: Elasticity of citations to travel time Part 1 Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt

Table 4 :

 4 The inclusion of FE Fih implies that only across-time variation within an establishmenttechnology is used to identify ρ. The inclusion of FE it implies that only variation acrosstechnologies within a location-time is exploited, so across-time variation is compared across establishments within a location, and not across locations. The inclusion of FE ht implies that the identifying across-time variation is conditional on aggregate trends of the technology. In short, identification of ρ relies on across-time changes in the amount of patents and knowledge access of an establishment, relative to other establishments in the same location, conditional on aggregate technological trends. Effect of knowledge access on patents, by MSA innovativeness quartile

	PPML	PPML q innovation	IV PPML	IV PPML q innovation

The fixed effect FE Fih absorbs time invariant characteristics at the firm-locationtechnology level, as for example the productivity of the establishment-technology. This fixed effect is more fine grained than just a location-technology, which would absorb the comparative advantage of a location in a certain technology. The fixed effect FE it absorbs characteristics that are time variant at the location level. For example, changes in R&D subsidies that are location specific and common across all technologies would be absorbed by this fixed effect. Also, better flight connectivity could spur economic activity as shown in

Campante and Yanagizawa-Drott (2017)

, leading to an increase in patenting activity in the location. If that increase is general across technologies within the location, then FE it would absorb it. Finally, the fixed effect FE ht absorbs characteristics that are time variant at the technology level. If technologies had different time-trends at the national level, then the fixed effect would control for these trends in a flexible way. * * * p < 0.01; * * p < 0.05; * p < 0.10

Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of Patents

Fiht = exp [ ρ log(KA iht ) + FE Fih + FE it + FE ht ] × ξ Fiht ,

for patents filed by establishment of firm F in location i, technology h and time period t. KA iht is knowledge access of establishments in location i technology h and time period t. Column (2) opens the coefficient ρ by the quartile of innovativeness of location i within technology h, computed using patents filed in 1949-1953. Higher quartile indicates higher initial level of innovativeness. The fourth quartile is used as reference category. Column (3) and (4) show the result of two step instrumental variables estimation, where KA iht is instrumented with KA iht , knowledge access computed using the counterfactual travel time that would have taken place if routes were fixed to the ones in 1951 and each year routes were operated at the average aggregate flying speed of the year. Standard errors are presented in parentheses. Column (1) and (

2

) present clustered at the location-technology ih. Column (3) and (4) present bootstrap standard errors. R2 is computed as the squared correlation between observed and fitted values.

Table 6 :

 6 1949-1953 (existing firm and est), the establishment did not apply for patents but the firm had establishments in other locations applying for patents in1949-1953 (existing firm new est), neither the establishment nor the firm applied for patents in 1949-1953 (new firm new est). 90 The dummies new firm new est and existing firm new est capture two types of entry margin. new firm new est captures a new establishment of a new firm, while existing firm new est captures entry due to the geographic expansion of firms. The dummy existing firm and est captures jointly an intensive and exit margin. log(KA iht ) × 1{Fi ∈ e} + FE Fih + FE it + FE ht ] × ν Fiht (10) where Patents Fiht are patents applied by establishment of firm F in location i and technology h at time period t. KA iht is the knowledge access at the location-technology-time level. 1{Fi ∈ e} is an indicator variable that takes value 1 of Fi is of the type e = {new * * p < 0.01; * * p < 0.05; * p < 0.10 Patents and knowledge access: Entry, exit and continuing firms Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of Patents Fiht = exp [ ρ log(KA iht ) + FE Fih + FE it + FE ht ] × ξ Fiht , for patents filed by establishment of firm F in location i, tech- nology h and time period t. KA iht is knowledge access of establishments in location i technology h and time period t. Column (2) adds an interaction of log(KA iht ) with e the type of establishment Fi in a classification on whether the establishment and/or the firm existed in 1949-1953. Standard errors clustered at the location-technology ih are presented in parentheses. R2 is computed as the squared correlation between observed and fitted values. * * * p < 0.01; * * p < 0.05; * p < 0.10

	We estimate a variation of equation (7) that includes interactions with dummies
	which indicate the status of the establishment in 1949-1953:
	Patents Fiht = exp [ ∑

e ρ e firm new est, existing firm new est, existing firm and est}. The results are displayed in column (2) of Table

6

. The results show that the effect of innovation access on the increase of patenting happened through the two entry margins: entry of new establishments of new firms and entry of new establishments of firms that previously existed in other locations.

In Table

7

we open up the effect by including a double interaction of Fi establishment type and location-technology ih quartile of initial innovativeness. We use the highest quartile as the reference category. The two margins of entry are active in all quartiles of initial innovativeness, with a stronger effect in lower quartiles. In the case of the *

The results of Table

6 and Table 7

indicate that one part of the increase in patenting is consequence of multi-establishment firms that expand across locations, and more so in initially less innovative locations. Hence, multi-establishment firms contributed to innovation-convergence across locations by expanding geographically.

Table 7 :

 7 Patents and knowledge access: entry, exit and continuing firms The table shows the results of one Poisson Pseudo Maximum Likelihood (PPML) estimation of Patents Fiht= exp [ ∑ e ρ e log(KA iht ) × 1{Fi ∈ e} + ∑ q∈{1,2,3},e ρ q,e log(KA iht ) × 1{ih ∈ q} × 1{Fi ∈ e} + FE Fih + FE it + FE ht ] ×ν Fiht , for patents filed by establishment of firm F in location i, technology h and time period t. KA ikt is knowledge access of establishments in location i technology h and time period t. q is the quartile of initial innovativeness of location i within technology h, computed using patents filed in 1949-1953. Higher quartile indicates higher initial level of innovativeness. The fourth quartile is used as reference category. e is the type of establishment Fi in a classification on whether the establishment and/or the firm existed in1949-1953. Standard errors clustered at the location-technology ih are presented in parentheses. R2 is computed as the squared correlation between observed and fitted values. All columns and rows belong to the same regression. The number of observations is 991,480.

  , which translates into an average yearly growth rate of 21.4%. For the highest quartile the predicted increase is 1,422%, an average yearly growth rate of 15.4%. Consistent with the computation of the relative growth rate presented in the main text: 1, 422/3, 869 = 0.36 ≈ 0.34 × (33.8/36.0), where 0.34 has to be adjusted by the fact that the average change in travel time is not the same across quartiles. The 19-year growth rates are obtained by multiplying the change

	in travel time (-33.8% vs -36.0%) by the coefficient (-0.0079 vs -0.0749) divided by 100, and finally
	dividing by the initial probability (0.000069 vs 0.001895) and multiplying by 100. For the lowest
	quartile: 3, 869 = [(-33.8) × (-0.0079/100)/0.000069] × 100, and for the highest quartile:[1, 422 =
	(-36.0) × (-0.0749/100)/0.001895] × 100. The average yearly growth rates are computed as 21.4 ≈
	[(1 + 38.69) 1/19 -1] × 100 and 15.4 ≈ [(1 + 14.22) 1/19 -1] × 100.

Table 9 :

 9 Date of Digitized Flight Schedules

	Airline	1951	1956	1961	1966
	AA	September 30	April 29	April 30 April 24
	EA	August 1	October 28	April 1	April 24
	TWA	August 1	September 1 April 30	May 23
	UA	April 29	July 1	June 1	April 24
	BN	August	August 15	April 30 April 24
	NW	April 29	April 29	May 28	March 1
	PA	June 1	July 1	August 1 August 1

  Table 10 lists all 15 cases.As our analysis is at the MSA level, we match airports to 1950 MSA boundaries. Each airport is matched to all MSAs for which it lies inside the MSA boundary or at most account for the required time at the location of the layover. We repeat this procedure for every possible departure time t at origin city o and then take the minimum that gives us the fastest travel time from o to d, τ od .

			Table 10: Dropped Connections
	Airline Year Origin Destination Departure Time Arrival Time
	0 UA	66	TYS	DCA	1940	2036
	1 UA	66	LAX	BWI	2150	1715
	2 UA	66	CHA	TYS	1635	1909
	3 PA	66	SFO	LAX	2105	1850
	4 PA	66	SEA	PDX	705	935
	5 PA	56	PAP	SDQ	830	835
	6 PA	51	HAV	MIA	800	903
	7 PA	51	SJU	SDQ	825	830
	8 NW	66	HND OKA	655	1135
	9 EA	66	ORD	MSP	2340	2340
	10 EA	56	SDF	MDW	1352	1418
	11 EA	56	GSO	RIC	2207	2204
	12 AA	56	PHX	TUS	1630	1655
	13 PA	51	STR	FRA	1320	1540
	14 EA	66	TPA	JFK	1330	1548

Table 13 :

 13 Network Changes (weighted by frequency)

	Period	Remain connected Newly connected Disconnected
	Share of Non-stop Connections (%)
	1951 to 1956	78.47	16.79	4.74
	1956 to 1961	88.96	6.43	4.6
	1961 to 1966	80.64	12.37	6.99
	Mean distance (km)
	1951 to 1956	411	1075	337
	1956 to 1961	524	914	972
	1961 to 1966	568	769	450

Table 14 :

 14 Network ChangesChanges in the number of connected MSAs and connections among them. A MSA is connected if in our data it appears as having at least one incoming and one outgoing flight. A non-stop connection refers to a pair of origin MSA-destination MSA between which a non-stop flight operates.

	Period	Remain connected Newly connected Disconnected
	Connected MSAs
	1951 to 1956	119	7	8
	1956 to 1961	122	0	4
	1961 to 1966	114	7	8
	Non-stop Connections
	1951 to 1956	721	357	124
	1956 to 1961	908	231	170
	1961 to 1966	912	331	227

Table 15 :

 15 Number of firms and share of patents by firm's geographic coverageGeographic coverage is computed as the amount of Metropolitan Statistical Areas (MSAs) in which the firm has inventors applying for patents (research establishments) in a certain year. Research establishments are defined irrespective of the technology in which technology it patents. Hence a firm applying for patents in technology h in one establishment and technology k in another establishment is defined as having two establishments, and counts as a two-establishment firm both in technology h and technology k. Bins of geographic coverage are 1 MSA, 2 to 5 MSAs, 6 to 10 MSAs, 11 to 20 MSAs, more than 20 MSAs. The maximum possible is 108 MSAs.

		1951	6,773	892	72	34	8	0.39 0.25	0.13	0.18	0.06
	Chemical	1956 1961	7,196 6,728 1067 953	108 125	60 80	12 0.38 0.22 18 0.32 0.21	0.11 0.15	0.19 0.15	0.10 0.17
		1966	7,092 1120	125	89	30 0.29 0.17	0.13	0.19	0.22
		1951	1,956	270	43	24	8	0.42 0.18	0.18	0.04	0.18
	Communication	1956 1961	2,292 2,413	337 441	56 62	43 63	11 0.36 0.19 15 0.34 0.16	0.15 0.09	0.18 0.20	0.12 0.20
		1966	2,320	414	75	66	29 0.32 0.14	0.08	0.17	0.29
		1,951	1675	163	20	21	5	0.76 0.19	0.02	0.04	0.00
	Drugs	1956 1961	1,706 1,705	198 247	40 57	35 45	9 16 0.62 0.19 0.66 0.18	0.07 0.09	0.06 0.07	0.02 0.04
		1966	2,115	251	49	53	24 0.62 0.13	0.08	0.11	0.06
		1,951	7394	789	73	33	8	0.47 0.20	0.08	0.08	0.18
	Electrical	1956 1961	8,182 8,077 1,092 962	97 123	59 80	12 0.44 0.19 18 0.40 0.19	0.10 0.07	0.12 0.17	0.15 0.17
		1966	7,885 1,006	126	87	30 0.37 0.16	0.09	0.16	0.23
		1951	18,509 1,348	75	34	8	0.64 0.20	0.06	0.05	0.04
	Mechanical	1956 1961	18,735 1,498 16,873 1,703	109 130	60 80	12 0.59 0.20 18 0.54 0.21	0.06 0.07	0.08 0.10	0.06 0.08
		1966	17,856 1,669	132	89	30 0.52 0.17	0.09	0.11	0.11
		1951	24,994 1,343	75	34	8	0.76 0.15	0.04	0.03	0.02
	Others	1956 1961	24,650 1,527 20,914 1,683	110 131	60 80	12 0.71 0.16 18 0.65 0.16	0.05 0.06	0.05 0.08	0.03 0.05
		1966	22,982 1,625	132	89	30 0.63 0.15	0.05	0.08	0.08

Table 16

 16

	we repeat Table 2 but reporting

Table 16 :

 16 Elasticity of citations to travel time Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt = exp [β log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt

  Table 2, and columns (3) and (4) of Table 4 we set M = 200.

	E. Appendix: Additional results
	E.1. Diffusion of knowledge
	E.1.1. Heterogeneous effects

Table 17 :

 17 * * p < 0.01; * * p < 0.05; * p < 0.10 Elasticity of citations to travel time: intensive and extensive margin Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt = exp [β log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt , for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Column (3) shows the result of an OLS estimation of log(citations FiGjhkt ) = α log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt + ε FiGjhkt , with a sample of establishment-technology pairs (FiGjhk) that have positive citations in all periods. Column (5) shows the result of an OLS estimation of 1{citations FiGjhkt > 0} = γ log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt + ε FiGjhkt , with the same sample as (1). * * p < 0.01; * * p < 0.05; * p < 0.10

	log-log	linear probability

* *

Table 18 :

 18 Elasticity of citations to travel time: IV estimation intensive and extensive marginColumn (1) shows the result of Instrumental Variables Poisson estimation of citations FiGjhkt = exp [β log(travel time ijt ) + λ ûFiGjhkt + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt , for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k.

Table 20 :

 20 Elasticity of citations to travel time: Heterogeneity (part 1) Result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt

	Concentration	Concentration	Cited lag	Citing lag	Citing	Cited	Self
	citing	cited	forward	backward	govnt & uni	govnt & univ	citation

Table 19 :

 19 * * p < 0.01; * * p < 0.05; * p < 0.10 Elasticity of citations to travel time: Heterogeneity (part 2)Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt = exp [∑ q β q log(travel time ijt ) 1{quantile Fh ∈ q} + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt , for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. quantile Fh is the quantile of firm F in the distribution of firms within technology h, using patents applied by F in h in the time period 1949-1953. Column (2) repeats the analysis using the quantile of the cited firm G in technology k. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Standard errors clustered at the non-directional location in parentheses (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values. * * p < 0.01; * * p < 0.05; * p < 0.10

	Citing quantile Cited quantile

* *

Table 21 :

 21 Elasticity of citations to travel time by citing and cited technology Part 1 Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt= exp [∑ tech β h 1{tech = h} × log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt ,for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G located in j, in technology k. 1{tech = h} is a dummy variable that takes value 1 when the citing technology h is equal to technology tech. In column (2) the dummy is modified to 1{tech = k} such that it takes value 1 when the cited technology k is equal to technology tech. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Standard errors clustered at the non-directional location pair are presented in parenthesis (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values.During the time period there was entry and exit of research establishments that was not uniform across locations. We may then think that the change in diffusion of knowledge is only consequence of the change in the geographical location of innovation. To test this possibility, in Table25we estimate the baseline regression 3 with different samples. * * p < 0.01; * * p < 0.05; * p < 0.10

	E.1.2. IV PPML: first and second stage estimation
	E.1.3. Robustness
	Sample of establishments

*

Table 22 :

 22 Elasticity of citations to travel time: first and second stage IV PPML

		OLS First stage	OLS First stage	OLS First stage	OLS First stage	Second stage
		0-300km	300-1,000km	1,000-2,000km	+2,000km	PPML
	Dep. variable:		log(travel time)		cit FiGjhkt
		(1)	(2)	(3)	(4)	(5)
	log(travel time fix routes) × 0-300km	0.278 * * (0.122)	0.073 (0.057)	0.024 (0.026)	0.040 * (0.022)
	log(travel time fix routes) × 300-1,000km	-0.103 * * * (0.032)	1.113 * * * (0.041)	-0.013 (0.011)	0.010 (0.011)
	log(travel time fix routes) × 1,000-2,000km	-0.064 * * * (0.024)	-0.052 * * * (0.020)	1.059 * * * (0.044)	0.017 * (0.009)
	log(travel time fix routes) × +2,000km	-0.058 * * * (0.022)	-0.046 * * * (0.017)	-0.020 * * (0.010)	1.097 * * * (0.018)
	log(travel time) × 0-300km					-0.076 (0.221)
	log(travel time) × 300-1,000km					-0.134 * * * (0.044)
	log(travel time) × 1,000-2,000km					-0.112 * * (0.047)
	log(travel time) × +2,000km					-0.203 * * * (0.043)
	residual × 0-300km					0.100 (0.196)
	residual × 300-1,000km					0.045 (0.053)
	residual × 1,000-2,000km					0.026 (0.069)
	residual × +2,000km					0.043 (0.078)
	N obs. effective	10, 106, 940	10, 106, 940	10, 106, 940	10, 106, 940	4, 703, 010
	R2	0.99	0.99	0.99	0.99	0.88
	Within R2	0.04	0.46	0.80	0.88
	* * * p < 0.01; * * p < 0.05;

* p < 0.10

Table 23 :

 23 Elasticity of citations to travel time: first and second stage IV PPML

	119

Table 24 :

 24 Elasticity of citations to travel time by citing and cited technology Part 2Column (1) shows the result of one single Poisson Pseudo Maximum Likelihood (PPML) estimation ofcitations FiGjhkt = exp [∑ tech pair β hk 1{tech pair = hk} × log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt ,for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G located in j, in technology k. 1{tech pair = hk} is a dummy variable that takes value 1 when the citing technology h is equal to technology tech. In column (2) the dummy is modified to 1{tech = k} such that it takes value 1 when the cited technology k is equal to technology tech. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Standard errors clustered at the non-directional location pair are presented in parenthesis (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values. The amount of observation in the effective sample is 4,703,010.

Table 25 :

 25 * * p < 0.01; * * p < 0.05; * p < 0.10 Elasticity of citations to travel time: Fix sample of establishments Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt= exp [∑ d β d × 1{distance ij ∈ d} × log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt , for citations of patentsfiled by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. d are distance intervals:[0 -300km], (300km -1000km], (1000km -2000km], (2000kmmax].Column (2) truncates the sample keeping only citing establishments Fi that where present in the initial time period 1949 -1953. Column (3) truncates the sample keeping only citing establishments Fi and cited establishments Gj that where present in the initial time period. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Standard errors clustered at the non-directional location pair are presented in parenthesis (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values.

	Citing & Cited
	establishment

*

Table 26 :

 26 Elasticity of citations to travel time: additional controls Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt= exp [∑ d β d 1{distance ij ∈ d} log(travel time ijt ) + ∑ d α d 1{distance ij ∈ d} 1{X FiGjhkt } log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt ] × ε FiGjhkt ,for citations of patents filed by establishment of firm F in location i, technology h and time period t, to patents filed by establishment of firm G in location j and technology k. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. d are distance intervals: [0 -300km], (300km -1000km], (1000km -2000km], (2000kmmax]. Relative to (1), columns (2) to (8) contain additional controls. Log highway time between i and j changes in every time period t. The log mean share of households with telephone line in ij pair interacted in 1960 is interacted with a time dummy. Log distance ij is interacted with a time dummy. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Standard errors clustered at the non-directional location in parentheses (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values.

	PPML

log(travel time) × 300-1,000km -0.0990 * * * -0.1040 * * * -0.0935 * * * -0.0745 * * -0.1014 * * * -0.0857 * * * -0.0748 * * -0.0861 * * * * * * p < 0.01; * * p < 0.05; * p < 0.10

Table 27 :

 27 Elasticity of citations to travel time: daily average travel time Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of citations FiGjhkt = exp [β log(travel time ijt ) + FE FiGjhk + FE Fiht + FE Gjkt

	travel

Figure 53: Change in MSAs travel time: fastest travel time and daily average * * * p < 0.01; * * p < 0.05; * p < 0.10

Table 28 :

 28 * * p < 0.01; * * p < 0.05; * p < 0.10 Elasticity of patents to knowledge access: first and second stage IV PPML * * p < 0.01; * * p < 0.05; * p < 0.10

	128

* *

Table 29 :

 29 Elasticity of patents to knowledge access: first and second stage IV PPML * * p < 0.01; * * p < 0.05; * p < 0.10

	129

*

Table 30 :

 30 Elasticity of new patents to knowledge access: absolute and per capita MSA innovativenessColumn (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of Patents Fiht = exp [ ρ log(KA iht ) + FE Fih + FE it + FE ht ] × ξ Fiht , for patents filed by establishment of firm F in location i, tech- nology h and time period t. KA iht is knowledge access of establishments in location i technology h and time period t. Column (2) opens the coefficient ρ by the quartile of innovativeness of location i within technology h, computed within technology using the absolute level of patents in theMSA-technology in 1949-1953. Column (3) computes the quartile of innovativeness using patents per capita in theMSA-technology in 1949-1953 using 1950 population. Higher quartile indicates higher initial level of innovativeness. The fourth quartile is used as reference category. Standard errors clustered at the location-technology ih are presented in parentheses. R2 is computed as the squared correlation between observed and fitted values. * * 9.36 * * 18.17 * * * 16.50 * * 10.09 * * 8.70 * 18.82 * * * 19.08 * * *

	130

* * * * p < 0.01; * * p < 0.05; * p < 0.10

Table 31 :

 31 Elasticity of new patents to knowledge access, varying beta or distance.Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of Patents Fiht = exp [ ρ log(KA iht ) + FE Fih + FE it + FE ht ] × ξ Fiht , for patents filed by establishment of firm F in location i, technology h and time period t. KA iht is knowledge access of establishments in location i technology h and time period t. Column (2) opens the coefficient ρ by the quartile of innovativeness of location i within technology h, computed using patents in 1949-1953. Higher quartile indicates higher initial level of innovativeness. The fourth quartile is used as reference category. Relative to columns (1) and (2), columns (3) and (4) compute Knowledge Access using four distance-specific β parameter according to distance bins between i and j. The bins are [0km, 300km], (300km, 1000km], (1000km, 2000km], +2,000km. Columns (5) to (10) use the same β as column (1) and (2), but computing Knowledge Access with a truncated sample of j that are further than a certain distance threshold from i. Standard errors clustered at the location-technology ih are presented in parentheses. R2 is computed as the squared correlation between observed and fitted values. * * p < 0.01; * * p < 0.05; * p < 0.10

	131

*

Table 32 :

 32 Elasticity of new patents to knowledge access: PPML and OLS Column (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of Patents Fiht = exp [ ρ log(KA iht ) + FE Fih + FE it + FE ht ] × ξ Fiht , for patents filed by establishment of firm F in location i, tech- nology h and time period t. KA iht is knowledge access of establishments in location i technology h and time period t. Column (3) estimates log(Patents) Fiht = ρ log(KA iht ) + FE Fih + FE it + FE ht + ξ Fiht . Columns (2) and (4) open the coefficient ρ by the quartile of innovativeness of location i within technology h, computed within technology using the absolute level of patents in the MSA-technology in 1949-1953. Higher quartile indicates higher initial level of innovativeness. The fourth quartile is used as reference category. Difference in amount of observations is due to dropping zeros in columns (3) and (4). Standard errors clustered at the location-technology ih are presented in parentheses. R2 is computed as the squared correlation between observed and fitted values.

Table 33

 33 shows the results of estimating the elasticity of new patents to knowledge access while at the same time controlling for capital access. * 11.29 * * * 10.67 * * 12.90 * * *

	Dependent Variable: Patents					Patents Fiht
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
	log(knowledge access)	10.14 * * * 9.96 (3.66) (4.50)	(4.32)	(4.70)	(4.43)
	log(finance access hq)		0.54 * * (0.26)				0.02 (0.30)
	log(finance access hq rel)			0.40 (0.25)				-0.14 (0.28)
	log(finance access est)				0.56 * (0.31)				-0.07 (0.39)
	log(finance access est rel)					0.31 (0.30)				-0.39 (0.38)
	N obs. effective	991,480 991,480 991,480 991,480 991,480 991,480 991,480 991,480 991,480
	R2	0.85	0.85	0.85	0.85	0.85	0.85	0.85	0.85	0.85

* * * * p < 0.01; * * p < 0.05; * p < 0.10

Table 33 :

 33 Elasticity of new patents to knowledge access and finance accessColumn (1) shows the result of Poisson Pseudo Maximum Likelihood (PPML) estimation of Patents Fiht = exp [ ρ log(KA iht ) + FE Fih + FE it + FE ht ] × ξ Fiht , for patents filed by establishment of firm F in location i, technology h and time period t. KA iht is knowledge access of establishments in location i technology h and time period t. Column (2) to (5) use as regressor the finance access of establishments in location i technology h and time period t, where the measure of finance access changes across columns. Columns (6) to (9) estimate the regression using both knowledge access and finance access. Standard errors clustered at the location-technology ih are presented in parentheses. R2 is computed as the squared correlation between observed and fitted values.Indirectly connected MSAsIf the 1951 flight network was constructed in order to connect city pairs that would see future growth in citations, we can alleviate this endogeneity concern by focusing only

	Sensitivity to β

Table 34 :

 34 Effect of knowledge access on new patents: varying the value of elasticity of knowledge diffusion on indirectly connected pairs.

Table 35

 35

presents PPML regressions not bias-corrected. Columns (1) and (

The 6 domestic airlines in our data accounted for 75% of total air passenger transport.

New York and Boston are about 300km apart, while New York and San Francisco are located about 4,130 km apart. Between 1951 and 1966 we observe a reduction of travel time of 23% (13 minutes reduction) between New York and Boston, while the reduction is of

50% (5 hours 30 minutes reduction) between New York and San Francisco.

Our dataset also includes international flights. We are currently digitizing more airlines to increase coverage both inside the US and internationally.

The chapters of[START_REF] Audretsch | Knowledge spillovers and the geography of innovation[END_REF] and[START_REF] Carlino | Agglomeration and innovation[END_REF] in the Handbook of Regional and Urban Economics provide an excellent review on the literature on knowledge spillovers,

The reader passionate of aviation history would enjoy reading the following New York Times article which tells the experience of the first transcontinental jet flight: https://www.nytimes.com/2009/ 01/26/nyregion/26american.html

Passenger-miles is a standard unit of measurement in transport, where one passenger-mile accounts for one person traveling one mile. The reasoning is the same for ton-miles, with one ton of goods traveling one mile.

We have not found data about shipments by mean of transport measured in monetary values.

The CAB was a federal agency hence, in principle, would not have control over intrastate routes. Nonetheless, according to[START_REF] Borenstein | How Airline Markets Work[END_REF] the CAB managed to have some intrastate markets under its control using legal arguments.

Safety regulation was under the control of the Federal Aviation Administration.

[START_REF] Borenstein | How Airline Markets Work[END_REF] in page 68, based on[START_REF] Caves | Air transport and its regulators: an industry study[END_REF], expose "In 1958, for example, twentythree of the hundred largest city-pair markets were effectively monopolies; another fifty-seven were effectively duopolies; and in only two did the three largest carriers have less than a 90 percent share."

We are currently working on setting a minimum waiting time for switching airplanes, such that the change is not permitted unless waiting time is more than the minimum. For the time being we have set the minimum waiting time to zero, meaning that in our calculation one passenger would be able to switch from one airplane to another if departure of the following flight is one minute later than arrival of the previous flight. This a rather implausible assumption and we are estimating the minimum waiting time in each airport depending on the airport's congestion.

The 15km distance was chosen after inspecting airports near the border that should arguably be matched, as for example, Atlanta ATL airport.

In Appendix A.2 we include a table with the 168 MSAs, those connected at least once and those connected in the four years. Among the MSAs not connected is San Jose, California, which in our patent sample accounted for around 2% of patents. San Jose had an airport (SJC) during our time period but it was not served by any of our airlines, so it is not included in our analysis. In the future we plan to include the currently non-connected MSAs by matching them to airports that may have served them and accounting for the commuting travel time.

Honolulu was not concerned by the regulation. Honolulu was connected with non-stop flights to San Francisco (9 hours 40 minutes), Los Angeles (11 hours) and Portland (12 hours 55 minutes).

We are currently exploring the differential timing of jet adoption across airlines. Differences in (preexisting) route distance and past contractual relationships with aircraft suppliers potentially led to different adoption rates at each time period. For example, Eastern Airlines' routes were particularly shorter than for other airlines. Also, those committed to buy Douglas airplanes (the leader US commercial aircraft supplier pre-jet era) would have adopted jets later, as Douglas launched jet airplanes later than Boeing.

 20 The plot includes only MSA-pairs with travel time in all time periods. The standard deviation for MSA-pairs less than 250km apart is big relative to the ones at other distances. Hence we decided not

For example, the regulator could have targeted the opening of new routes between places in order to boost their economic activity.

For example, in the instrument there are no non-stop transcontinental routes.

In our estimations we exploit time variation for identification. Hence, if pre-existing routes affect the levels at the origin-destination level, this does not drive our identification. However, we may be concerned that pre-existing routes could affect future growth and not only levels. To address this concern, in robustness analysis we estimate the elasticity of citations to travel time using only MSA-pairs that are always indirectly connected. Results go in the same direction.

In 1961, all non-stop flights of more than 3,000km had at least one jet operating within them, while in 1966 it was the case in all non-stop flights of more than 2,000km. Therefore the endogeneity of jet adoption is a smaller concern for long distance flights.

For example, airlines may have decided to prioritize the allocation of jets to routes which had a higher share of business travel, which may be correlated with the diffusion of knowledge.

The use of a linear regression is motivated by the linearity between travel time and distance displayed in Figure5. To estimate these regressions we use all routes appearing in each year.

We observe an increase in travel time for short distances in 1961 relative to 1951. Given that non-stop routes are fixed and that for longer distances there is a decrease in travel time, the increase in travel time in short distances comes from an increase in the value of the intercept relative to the slope in 1961, relative to 1951.

Filing year, also called application year, is the closest date to the date of invention that is present in the data and it represents the date of the first administrative event in order to obtain a patent. In the other hand, the publishing (also called granting year) is a later year in which the patent is granted. The difference between filing and publishing year depends on diverse non-innovation related factors (as capacity of the patent office to revise applications) and changes over time. Hence filing year is the date in our data that approximates the best to the date of invention.

Very few patents had missing information on filing year. We complemented both missing filing year and citations with the OCR USPTO dataset.

We note that the patent citation record starts in 1947, year in which the USPTO made it compulsory to have front page citations of prior art.[START_REF] Gross | The consequences of invention secrecy: Evidence from the uspto patent secrecy program in world war ii[END_REF]

https://www.google.com/googlebooks/uspto-patents-class.html

Due to the gap between the filing year and publishing year we also do the matching to patents published after 1968. Our underlying patent data actually covers a longer time period of filing years, which we need for example to construct forward and backward citation lags. However, there are limitations to use the geographic data in filing years1971-1972. In Appendix B we show that during filing years 1971-1972 the rate of unmatched patents to inventors' location increases. This is probably due to Histpat and Fung data not being a perfect continuation one of the other.

In Appendix B we show that the 1951 geographic distribution of patents looks similar across technology categories.

The top 5 patenting MSAs in 1951 were: New York City (25% of all patents), Chicago (11%), Los Angeles (8%), Philadelphia (6%) and Boston (4%).

We compute the growth rate of patenting in each technology within a MSA and then take the average across technologies within the MSA.

Each dot in Figure10is an MSA. To compute the MSA ranking we need to double-rank MSAs. First we rank all MSAs in each technology. Second we take the across-technology average ranking of each MSA. Third we rank all MSA's averages. To compute the MSA's yearly growth rate we first take the 1951-1966 growth rate for each technology in the MSA. We then take the average across technology. Finally we obtain the MSA's yearly growth rate by computing: yearly growth rate = (1 + 19 year growth rate) (1/19) -1 (the 1951 to 1966 period is a 20 year window, we take growth rates as being from the first year 1949 to the last one 1968, which is 19 year growth).

In Appendix B we show replicate the plot differentiating geographic regions. MSAs that were initially less innovative and had high subsequent growth were located in all four regions, although they were primarily located in the South and the West.

We first compute the 1951-1966 growth rate (19-year growth rate) for each MSA-technology. We then

Within each year and bin of firm size, we compute the share of patents by technology and then take the average across technologies. We have computed the across-firms Herfindahl index within technology (so it shows the level of across-firm concentration within a technology) and we do not observe a clear pattern of either concentration or deconcentration.

As a reference, the distance from New York City NY to other places is: Boston MA 300km, Chicago IL 1,140km, Dallas TX 2,200km, San Francisco CA 4,130km. The quantile 0.10 of was at 0km in every period, implying that 10% of citations took place within MSA. The quantile 0.90 was around 3,611km to 3,789km over the sample period.

While Figure14shows how the distance of each quantile changes over time, Figure15shows the mass of citations (and hence the quantile to which belongs) in a certain distance cutoff. For example, in 1951 the share of citations in the 0-300km range was 31.6%, which is equal to saying that the quantile 0.316 in 1951 was 300km.

In the International Trade literature, the parallel of the fixed effects (simplified for exposition) would be: FE ij country-pair fixed effect, FE jt origin-time fixed effect and FE it destination-time fixed effect.

We use the package fixest[START_REF] Bergé | Efficient estimation of maximum likelihood models with multiple fixed-effects: the R package FENmlm[END_REF]) in R to estimate high dimensional fixed effects generalized linear models feglm with Poisson link function.

We compute distance between the geographical center of each MSA.

The share of observations (citations) in each distance interval is: 0-300km 26.1% (28.5%), 300-1,000km 30.7% (28.5%), 1,000-2,000km 19.7% (23.4%), +2,000km 23.4% (19.6%).

Data from the 1962 City Data Book which comes from the US Bureau of the Census. log(mean telephone share ij = log((telephone share i +telephone share j )/2). We take the log of the mean share because the share is a linear combination of origin MSA and destination MSA characteristics, hence perfectly explained by origin and destination fixed effects. Taking the log prevents this.

Due to entry, we cannot compute the growth rate at the establishment-technology level for 70% of establishment-technology, given that they had 0 patents in the initial time period. In the case of location-technology, 5% did not have patents in the initial period. We the prefer to interpret coefficients using location-technology growth rates, which we compute using the remaining 95% of location-technologies that had positive patents in the initial time period.

The elasticity of 10.14 predicts an increase of 91.3% over the time period of 19 years (10.14 × 0.09 = 0.913), which translates into a 3.5% average yearly growth rate ((1+0.913) 1/19 -1≈0.035).

From the first time period(1949)(1950)(1951)(1952)(1953) to the last time period(1964)(1965)(1966)(1967)(1968) we observe an average growth rate of new patents of 127%. We obtain 0.044 ≈ ((1 + 1.27) 1/19 -1

79.5 = 3.5/4.4 × 100

Using the coefficient of column (1) in Table4, we compute the MSA-technology predicted level of patents for 1966 and aggregate it at the Census region -technology level. Then, we compute yearly growth rates within each region-technology and take averages across technologies. Next, we take the average between S and W, and MW and NE, and finally compute the differential predicted growth. If we use the quartile-specific coefficients of column (2) in Table4we obtain a predicted differential growth rate of 0.86 percentage points, which implies that the change in travel time can account for 41% of the observed differential growth rate.

We use the quartiles of innovativeness defined in section 5.1, computed using the amount of patents of location i in technology h filed in the time period[1949][1950][1951][1952][1953]. Each location i has (potentially) a different value quartile in each technology h. The 1st quartile refers to the 25% initially least innovative MSAs in technology h.

All our firm and research establishment information comes from the patent data. Hence, we only observe an establishment in a certain time period if it applies for patents in that time period.

We define if an establishment exists or not if it applied for patents in any technology h in 1949-1953. We define the establishment at the Fi level (as opposed to Fih) as our object of interest a firm-location.

An interesting avenue of research is to study within-establishment changes in the technological composition of patenting.

Using patents applied in the period 1949-1953 does not significantly affect the results. We use 1945-1953 instead as it allows us to identify headquarters location for 7% more firms.

Filing year, also called application year, is the closest date to the date of invention that is present in the data and it represent the date of the first administrative event in order to obtain a patent. In the other hand, publishing or also called granting year, is the later year in which the patent is granted. The difference between filing and granting year depends on diverse non-innovation related factors (as

Given that we require to identify the fixed effects, the effective subsample in all four p estimations does not have the same amount of observations. However, in our estimations the effective subsample size across p subsamples does not differ by more than 5%.

Coefficients are not bias corrected.

We require Fi and Gj to have positive amount of patents applied during 1949-1953. However, those establishments need not to have cited each other.

The sample of prices digitized was limited due to data availability.

8.7% of MSA-pairs had an increase in travel time either by highway or by airplane. The regression with all MSA-pairs has a slope of 0.60 significant at the 1% level. However, the R2 of the regression remains very low: 0.0046.

With all MSA-pairs the slope is 1.01 statistically significant at the 1% level and the R2 is 0.04.

In order to perform a test of statistical difference of coefficients we would need to compute the covariance between the two regressions. Assuming the covariance is zero, in columns (1) and (2) 26 the coefficients of air travel time at +2,000km are not significantly different.

The within MSA-pair correlation of the(1951)(1952)(1953)(1954)(1955)(1956)(1957)(1958)(1959)(1960)(1961)(1962)(1963)(1964)(1965)(1966) change in fastest travel time and the change daily average travel time is 0.60.

For example, in 1951 NYC-LA was connected with one flight number that included one stop in Chicago, that is two legs but only one flight number: passengers did not have to change airplanes).

show that improvements in the Interstate Highway System led to local increases in income through an increased market access. In our set up, if the effect of market access affects innovation in the same way across technologies, then it would be absorbed by the MSA-time fixed effect FE it in equation ( 7). However, if the effect of market access on innovation varies across technologies, then it would be a confounder. To control for this potential confounder, we compute market access by highway and interact it with a technology dummy. We compute market access as:

where Population j,t=1950 is population in MSA j in 1950, τ ijt are the shipping costs provided in the data of Taylor Jaworski and Carl Kitchens computed using each year's highway driving distance, highway travel time, petrol cost and truck driver's wage. θ is the elasticity of trade to trade costs which we set to -8.28, the preferred value of Eaton and Kortum (2002) and in the range of many other estimates in the literature (Head and Mayer (2014), Caliendo and Parro (2015), Donaldson and Hornbeck (2016)). Columns

(3) and (4) of Table 5 show the results, we do not observe an important difference with the baseline estimates. Campante and Yanagizawa-Drott (2017) shows that better connectivity by airplane leads to an increase in economic activity as measured by satellite-measured night light. S öderlund (2020) shows that an increase in business travel in the late 1980s and early 1990s led to an increase in trade between countries. In a similar way to market access, we could think that better connectivity by airplane could have led to an increase in market access due to a reduction in information frictions, with goods being shipped by land. Similarly to highway market access, if the effect of market access by airplane is common to all technology categories the effect would be absorbed by the MSA-time fixed effect FE it . In order to account for a technology-specific effect, we construct a measure of airplane market access and interact it with a technology dummy. The measure of airplane market access is similar to equation (9) where τ is the travel time We would like to point to the limitations of the current analysis. The results found in this paper are identified by exploiting differential time changes across establishments.

As consequence, we are able to identify differential impacts and not aggregate ones. The results obtained could be consequence of general increase in the amount of diffusion and creation of knowledge, a relocation of previous diffusion and creation, or a mix of both. At the same time, the potential relocation of resources as consequence of the reduction in travel time may have increased the allocative efficiency and therefore increasing the amount of knowledge creation.

In order to separately identify the aggregate effects of travel time from relocation we plan to estimate a structural model. We consider two types of models that could potentially account for the increase in the diffusion of knowledge and the increase of innovation in the South and the West. The first option is to extend Donaldson and Hornbeck (2016) including an intermediate sector which produces knowledge, where knowledge access would enter the production function of knowledge. The second option is to modify Davis and Dingel (2019), who find that a system of cities is an equilibrium outcome in the presence of localized knowledge spillovers. We would extend the model to allow for knowledge spillovers across cities, where the degree of across-city spillovers depends on the across-city travel time. To include multi-establishment firms we would build upon Oberfield et al. (2020) who present a model of spatial equilibrium with multi-establishment firms. This model includes the location interdependency of establishments within a firm: the ideal location of an establishment of a firm depends on the location of every other establishment of the firm. Next, we compute the shortest travel time for every airport pair, and then take the minimum to obtain shortest travel time at the MSA pair level. In particular, we apply Dijkstra's algorithm to compute shortest paths (Dijkstra et al., 1959). We adjust this algorithm to take into account the exact timing of the flight schedules. We consider New York. Figure 37 shows the location of patents cited by patents filed by General Electric with inventors in Fort Wayne, Indiana, in the period 1949-1953. Figure 38 shows the research establishments of General Electric during periods 1949-1953 and 1964-1968.

General Electric had research establishments in 51 MSAs in 1949-1953 and in 76 MSAs in 1964-1968. 42 out of them appear in both time periods. travel time ijt is the travel time in minutes between location i and j at time period t, and it is set to 1 when i = j. When FiGjhk has positive citations in at least one period and no citations in another, we attribute zero citations in the missing period. Column (2) includes the interaction of travel time ijt with a dummy for distance bin between the citing establishment Fi and the cited establishment Gj. Column (3) and ( 4) discards all ij that are ever connected with one leg (non-stop flight), while columns ( 5) and ( 6) discard all ij that are ever connected with one flight number. The difference between non-stop and one flight number is that one flight number could serve multiple MSAs by making intermediate stops. Standard errors clustered at the non-directional location are presented between parentheses (ij is the same non-directional location pair as ji). R2 is computed as the squared correlation between observed and fitted values.

E.3. Firms' geographic expansion

To be completed.