Gianluca Pallante
email: gianluca.pallante@santannapisa.it-

Emanuele Russo

Andrea Roventini

Does mission-oriented funding stimulate private R&D? Evidence from military R&D for US states

Keywords: R&D, Innovation policy, Defense, Mission-oriented innovation JEL classification: O30, O31, 032, O38, H56

US military Research and Development (R&D) expenditures arguably represent the best example of mission-oriented policy. They are sizeable, with a clear-cut public purpose (national defense

Introduction

Firms' innovation activities play a crucial role in fostering productivity and economic growth [START_REF] Nelson | An evolutionary theory of economic change[END_REF][START_REF] Dosi | Sources, procedures, and microeconomic effects of innovation[END_REF][START_REF] Romer | Endogenous technological change[END_REF][START_REF] Aghion | A model of growth through creative destruction[END_REF][START_REF] Dosi | Schumpeter meeting keynes: A policyfriendly model of endogenous growth and business cycles[END_REF]). Yet, R&D underinvestment is a well documented feature of contemporary economies, and governments are seeking new ways to boost research in the private sector [START_REF] Bloom | A toolkit of policies to promote innovation[END_REF]. The large presence of knowledge spillovers makes social returns to R&D considerably higher than private ones, thus, resulting in lower R&D efforts than the socially desired level [START_REF] Nelson | The simple economics of basic scientific research[END_REF][START_REF] Arrow | Economic welfare and the allocation of resources for invention[END_REF][START_REF] Lucking | Have R&D spillovers declined in the 21st century?[END_REF]. This is exacerbated by financial constraints on innovative firms and by the inherent uncertainty associated to research investments [START_REF] Hall | The financing of R&D and innovation[END_REF][START_REF] Garicano | Survive another day: Using changes in the composition of investments to measure the cost of credit constraints[END_REF].

Against this background, the effectiveness of public support in stimulating private R&D expenditures is subject to large empirical and theoretical debates and shall not be taken for granted (see e.g. [START_REF] David | Is public R&D a complement or substitute for private R&D? A review of the econometric evidence[END_REF][START_REF] Becker | Public R&D policies and private R&D investment: A survey of the empirical evidence[END_REF], for surveys on the topic). In this work, we contribute to these debates providing empirical evidence about the impact of defense-related R&D funded by the US government, and empirically assess whether it stimulates or substitutes privately-financed and conducted R&D.

Especially in the US, among different types of non-conventional innovation policies, the experience of public support to military R&D appears to be the most relevant and clearly mission-oriented [START_REF] Mowery | Military R&D and innovation[END_REF][START_REF] Mowery | Defense-related R&D as a model for grand challenges technology policies[END_REF][START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF]. Missionoriented policies are gaining increasing popularity among innovation scholars and policy makers (see e.g. [START_REF] Mazzucato | Which industrial policy does europe need?[END_REF].1 For instance, [START_REF] Bloom | A toolkit of policies to promote innovation[END_REF] explicitly include them in their review of the main innovation policy levers available to governments. However, much of the empirical evidence on mission-oriented policies is anecdotal and based on historical case studies [START_REF] Nelson | Government and Technical Progress[END_REF][START_REF] Mazzucato | The entrepreneurial state: Debunking public vs. private sector myths[END_REF][START_REF] Foray | Public R&D and social challenges: What lessons from mission R&D programs?[END_REF][START_REF] Foray | Smart specialization strategies as a case of mission-oriented policy-a case study on the emergence of new policy practices[END_REF]Azoulay et al., 2019), while quantitative econometric assessments are relatively few and rarely focused on the estimation of causal effects.2 As a first notable exception, [START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF] focuses on defense-related 1An example is the Horizon Europe framework programme financed by the European Commission.

2Early studies investigating the effectiveness of public R&D in promoting private R&D and innovation lacked a causal perspective [START_REF] Mansfield | Effects of federal support on company-financed R&D: The case of energy[END_REF][START_REF] Lichtenberg | The relationship between federal contract R&D and company R&D[END_REF][START_REF] Lichtenberg | The effect of government funding on private industrial research and development: A re-assessment[END_REF]. More recently, empirical papers have identified causal effects of R&D support for selected public agencies. Some examples include: [START_REF] Howell | Financing innovation: Evidence from R&D grants[END_REF], Azoulay et al. (2019) and [START_REF] Gross | Inventing the endless frontier: The effects of the world war II research effort on post-war innovation[END_REF] for the US; [START_REF] Santoleri | The causal effects of R&D grants: Evidence from a regression discontinuity[END_REF] for Europe; [START_REF] Bronzini | Are incentives for R&D effective? Evidence from a regression discontinuity approach[END_REF] for Italy and Moretti R&D and find a positive impact on private R&D in a panel of industries from OECD countries and at the firm-level for France.3 Moreover, [START_REF] Gross | Inventing the endless frontier: The effects of the world war II research effort on post-war innovation[END_REF] analyze the long run impact of the Office of Scientific Research and Development (OSRD), a large mission-driven organization supporting R&D during World War II in the US. They find long-lasting impacts in the post-war period on the direction of patenting and on the rise of geographical technology clusters.

We add to this stream of research by adopting a macro-regional perspective and focusing on US states as our unit of analysis.4 More specifically, we combine different data sources to assemble a longitudinal dataset that associates, at the US state-level, defense and non-defense federal R&D obligations to non-federally funded private R&D expenditures for the period 1968-2017, as well as to hightech employment for the period 1998-2018. We then exploit the geographical and temporal variations in our data to estimate the elasticity of non-federally funded private R&D investment to defense R&D expenditures employing panel fixed effect regressions.

Endogeneity problems may arise in this setting primarily because military funds for R&D are not randomly assigned geographically. Their allocation may well be driven by characteristics that likely determine the amount of private R&D conducted in a given state. To address endogeneity concerns and infer causal effects we use a recently developed identification strategy that builds on differential state exposures to national spending shocks [START_REF] Nakamura | Fiscal stimulus in a monetary union: Evidence from US regions[END_REF][START_REF] Guren | Housing Wealth Effects: The Long View[END_REF]. More specifically, we leverage two inherent characteristic of defense R&D funding: (i) as for general military procurement, national changes in military R&D obligations are arguably exogenous to the business cycle and to producitivity levels, being driven by geopolitical events [START_REF] Ramey | Identifying government spending shocks: It's all in the timing[END_REF][START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF]; (ii) the total R&D funds assigned to each state are differently sensitive (with respect to other states) to changes in national R&D budget. Drawing upon these two facts, we instrument changes in state-level defense R&D obligations using variations in et al. (2019) for a panel of OECD countries and industries. At the theoretical level, [START_REF] Dosi | The entrepreneurial state at work: An agent-based exploration. LEM working paper series[END_REF] test mission-oriented policies in a macroeconomic agent-based model and find positive effects on innovation, productivity and GDP growth.

3Similarly to [START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF], [START_REF] Draca | Reagans innovation dividend? Technological impacts of the 1980s us defense build-up[END_REF] finds positive effects of defense procurement on R&D and patenting at the firm level for the US.

4The focus on region-wide effects is a unique feature of our analysis which allow us to capture potential within-state R&D spillovers among performers and to link our results also to the macroeconomic literature on regional and local effects of public spending [START_REF] Fishback | The multiplier for federal spending in the states during the great depression[END_REF][START_REF] Auerbach | Local fiscal multipliers and fiscal spillovers in the USA[END_REF][START_REF] Bernardini | Heterogeneous government spending multipliers in the era surrounding the great recession[END_REF]. national defense R&D obligations interacted with state dummies.

The empirical results show that federally-financed military R&D crowds-in privately-funded R&D. In particular, IV estimates are systematically above the OLS coefficients with elasticities in the range 0.11% -0.14% over a 4-5 year horizon. This suggests that final impact of public defense R&D on total R&D significantly exceeds its dollar value. Such stimulus also translates to employment in R&Dintensive industries and in particular for engineering occupations with elasticities between 0.05% -0.1%. Our results are robust to a series of tests and alternative specifications including the presence of weak instruments; the inclusion of other innovation policy variables; measurement errors; corrections for outliers and missing values.

The rest of the paper is organized as follows: Section 2 motivates our focus on military R&D pointing at its mission-oriented nature; Section 3 presents the econometric specification and the identification strategy; Section 4 describes our dataset while Section 5 presents and discusses the results; finally, Section 6 concludes.

Public military R&D as a mission-oriented innovation policy

Mission-oriented policies refer to a set of public interventions aimed not only at promoting innovation but also at directing technical change towards the achievement of well-defined technological or social goals [START_REF] Mazzucato | The entrepreneurial state: Debunking public vs. private sector myths[END_REF]. Identifying mission-oriented policies in empirical studies is a complex task. Major conceptual issues are involved and often a clear-cut distinction with respect to other forms of intervention is not available. Yet, public defense R&D in the US stands out as a natural example of mission-oriented innovation policy [START_REF] Mowery | Military R&D and innovation[END_REF][START_REF] Mowery | Defense-related R&D as a model for grand challenges technology policies[END_REF]. Military R&D programmes financed by the government are typically focused on welldefined objectives defined by the funding agency. Their rationale has little to do with the standard market failure argument in support of public R&D investments [START_REF] Arrow | Economic welfare and the allocation of resources for invention[END_REF]. On the contrary, they are commonly linked to the development of innovative solutions to complex technical challenges which reflect the pursue of a general public interest (i.e. national defense). Defense R&D projects are often multidisciplinary and involve different sectors and performers with a large role played by private companies (accounting for about 65% of total spending in 2015, National Science Board, 2018) and a less relevant, but still significant, contribution by government labs and universities.

The mission-oriented nature of defense R&D is also supported by the fact that the government is the sole and ultimate user of the research outcome [START_REF] Campbell | Federal support for research and development[END_REF]. Albeit military technologies may have large civilian spillovers, the results of defense R&D, in fact, have rarely a direct non-military application. For this reason R&D projects in this area are largely financed through contracts that are subject to strict governmental accountability. Accordingly, defense agencies use various tools to manage uncertainty and keep track of the advancements made by performers including prototyping, "technology demonstration" and the use of non-R&D procurement. Also in line with the mission-oriented interpretation, military R&D is strongly biased towards development expenditures (accounting for about 90% of total funding in 2015, National Science Board, 2018), which largely prevail over funds for basic and applied research.

Consistently with our view, historical studies have pointed out that public defense R&D in the US played a key role in shaping both the rate and the direction of technical change in various industries, ranging from aircraft and transportation to computer and electronics [START_REF] Nelson | Government and Technical Progress[END_REF]. Interestingly, it has been also argued that US military research fostered the emergence and diffusion of radical innovations and general purpose technologies [START_REF] Ruttan | Is war necessary for economic growth?: military procurement and technology development[END_REF][START_REF] Mazzucato | The entrepreneurial state: Debunking public vs. private sector myths[END_REF].5 Nevertheless, it shall be noticed that, when acknowledging the mission-oriented features of defense-related R&D, one has to be cautious in generalizing the applicability of the same "model" to contemporary societal challenges, in particular climate change.

As pointed out by [START_REF] Mowery | Defense-related R&D as a model for grand challenges technology policies[END_REF] -albeit key insights may be drawn in terms of competition among performers, public accountability and procurement policiesthe scope for adopting the lessons from military R&D in other areas is limited as there are substantial differences regarding the characteristics of new technological challenges.

In our analysis, focusing on defense R&D has also a dual practical relevance.

On the one hand, it is the largest component of the total federal R&D budget (with a share ranging from 40% to 60%, cf. Figure 1) and exhibits sizable temporal and spatial variation (across US states). On the other, changes in military expenditures 5As an illustrative example, consider the ARPANET project led by the DARPA agency of the Department of Defense. ARPANET is widely seen as the ancestor of the Internet [START_REF] Mowery | Military R&D and innovation[END_REF]. For a recent discussion of the DARPA model see Azoulay et al. (2019).

are mainly driven by non-economic and geopolitical factors [START_REF] Ramey | Identifying government spending shocks: It's all in the timing[END_REF][START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF]. Together with some specific characteristics of their geographical distribution, this allows us to implement a clear identification strategy (cf. 3.2) which would not be available for other categories of public R&D. 3 Econometric specification and identification strategy

Econometric specification

To measure the effects of military R&D spending on private R&D we build a longitudinal dataset relating defense R&D obligations (i.e. our public R&D spending proxy) to private R&D expenditure (cf. Section 4). We use the geographical and temporal variation of our data to estimate the following model:

Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣 𝑖,𝑡 = 𝛽Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 𝑖,𝑡 + 𝛾 ′ Δ ℎ W i,t + 𝛼 𝑖 + 𝜆 𝑡 + 𝜀 𝑖,𝑡 , (1)
where Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣 stands for log changes of company-financed R&D between year 𝑡 and 𝑡 -ℎ in state 𝑖, Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 denotes ℎ-year log changes of total R&D obligations from the Department of Defense (DoD) between year 𝑡 and 𝑡 -ℎ in state 𝑖, and Δ ℎ 𝑊 is a vector of state by year observables used as control variables. All re-gressions include state fixed effects (𝛼 𝑖 ) to control for state-invariant characteristics and year dummies (𝜆 𝑡 ) to absorb US-wide shocks over time.

Notice that this model is equivalent to a log-level specification allowing for statespecific linear trends. One needs to account for state-specific trends as U.S. states experienced rather heterogeneous trajectories in terms of R&D investments and innovation performances [START_REF] Akcigit | The rise of american ingenuity: Innovation and inventors of the golden age[END_REF], as shown by Figure A.2. In turn, our specification may be rationalized as a first-order approximation of the steady-state demand for R&D from a CES production function [START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF].6

We take variables in per capita terms to normalize for the different population size [START_REF] Nakamura | Fiscal stimulus in a monetary union: Evidence from US regions[END_REF][START_REF] Guren | Housing Wealth Effects: The Long View[END_REF].7 Also, to account for the potential geographical correlation in the error structure we cluster standard errors by state.

The identification strategy

Our focus is on the identification of the 𝛽 parameter associated to public defense R&D. Our baseline regressions already take into account a large set of potentially confounding factors including invariant country trends (e.g. geography, size), US-wide shocks, other innovation policy tools (i.e. non-military R&D, tax credits, non-R&D procurement), state GDP and population. Nevertheless, even after controlling for these factors, different sources of endogeneity may bias our estimates. A major concern is represented by the political nature of government R&D [START_REF] Mintz | The political economy of military spending in the United States[END_REF]. Indeed, as other forms of public spending, R&D obligations are not randomly distributed across states as the criteria adopted for their allocation are often likely correlated with unobserved state-specific characteristics that may well be determinants of R&D investing decisions by firms. For instance, politicians may pick winners (or losers), thus, financing states that are doing particularly well (or are struggling). Similarly, variations in public R&D may be accompanied by state-specific regulatory norms that influence private spending decisions. Finally, a second endogeneity concern comes from the potential measurement error affecting our spending variable. Obligations may measure imperfectly effective R&D 6For the sake of comparison we also estimated a log-level specification without state-specific trends and symmetrical to the baseline model in [START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF]. Results are very similar and reported in Table B.1 and show less conservative estimates when compared to ours.

7To check for potential biases arising from normalizing by population, we run regressions without dividing variables by population. Results are reported in Table B.3 and do not differ significantly from those obtained with per capita variables.

spending as outlays occurs with some lags or because revisions and de-obligations may correct the initially obligated amount.

To deal with endogeneity we draw upon a well-established macro identification strategy (Nakamura andSteinsson, 2014, 2018;[START_REF] Guren | Housing Wealth Effects: The Long View[END_REF][START_REF] Cloyne | Decomposing the fiscal multiplier[END_REF].

We leverage two fundamental characteristics of public defense R&D. The left panel in Figure 2 shows that, similarly to general defense procurement, R&D obligations by the DoD at the national level are driven by exogenous (mainly geopolitical) events underlying military buildups. For instance, for the time period covered by our dataset, we can easily find the increase in military spending and R&D during the Reagan administration and following the 9/11 terrorist attacks. Second, data suggest that US states display systematically different sensitivities to changes in national R&D spending (cf. the right panel in Figure 2). For instance, when national defense R&D rises, obligations allocated to California increase much more than in Michigan. These patterns are remarkably stable over time and suggest that state-specific variations in public military R&D display a systematic component which is arguably exogenous to current private R&D shocks. Following [START_REF] Nakamura | Fiscal stimulus in a monetary union: Evidence from US regions[END_REF], we isolate this component by instrumenting Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 𝑖,𝑡 using national growth rates interacted with state dummies:

𝐼𝑉 𝑖 = 𝜃 𝑖 𝐼 𝑖 Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 𝑈𝑆,𝑡 , (2)
where 𝐼 𝑖 is a dummy variable for state 𝑖, Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 𝑈𝑆,𝑡 denotes log changes of US defense obligations between 𝑡 and 𝑡 -ℎ, while 𝜃 𝑖 represents the idiosyncratic coefficient accounting for different state-specific sensitivities to national shocks.

A way to interpret this identification strategy is as an exposure research design [START_REF] Goldsmith-Pinkham | Bartik instruments: What, when, why, and how[END_REF]. States are differentially exposed to common national spending shocks. We identify state exposures (i.e. the idiosyncratic parameters 𝜃 𝑖 from the first-stage regression, cf. Eq. 2) by focusing just on the systematic response to national policies, thus, arguably ruling out the influence of possible, time-varying omitted determinants of private R&D.

In this setting, US variation in DoD R&D obligations over a given time horizon represents a treatment that is assigned to states with different intensities (according to 𝜃 𝑖 ). Our IV regressions estimate a weighted average of treatment responses across states and years.

The exclusion restriction form this type of identification comes from the exo- geneity of state exposures [START_REF] Goldsmith-Pinkham | Bartik instruments: What, when, why, and how[END_REF]. To put it differently, factors determining exposure of different states to national policies -after conditioning on a set of state-specific observables and state-invariant characteristicsshould affect the outcome variable only via changes in 𝑅𝐷𝑑𝑒 𝑓 . This assumption entails that 𝜃 𝑖 is as good as randomly determined, conditionally on our control variables and fixed effects.

To investigate the validity of our research design, Figure 2 contrasts the estimated exposure parameters from the first stage regression with the average log changes in 𝑅𝐷𝑝𝑟𝑖𝑣. Notice, first, that the estimated sensitivity coefficients (𝜃 𝑖 )

show substantial heterogeneity, spanning considerable variation across states. Second, they are not correlated with averages of the outcome variable (Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣), that is, states responding more to shocks in federal defense-related R&D do not exhibit larger increases in private R&D spending. We take this evidence as bearing support to our identification strategy.

Finally, notice that the our exclusion restriction is less likely to be satisfied when (log) levels are used instead of (log) changes as the outcome variable. This possibly stems from the fact that exposure to shocks and the outcome variable are more likely to be co-determined when considered in levels [START_REF] Goldsmith-Pinkham | Bartik instruments: What, when, why, and how[END_REF]. That is why estimating the model in log differences would likely provide more reliable results.

Data

Our longitudinal dataset comprises data for 50 US states and the District of Columbia for the period 1968-2017.8 The main variables are described below. In Appendix A, we report figures and summary statistics concerning our dataset.

Public R&D expenditures. We employ data from Survey of Federal Funds for Research and Development led by the National Science Foundation (NSF) to measure defense and non-defense R&D spending. The survey provides annual data on federal R&D obligations disaggregated by funding agency and state of performance from 1968 onwards.9 Federal R&D obligations represent the amounts committed 8Data are available from the authors upon request. 9Only 10 large agencies report data on the geographic distribution of obligations including: the Departments of Agriculture, Commerce, Energy, Defense, Health and Human Services, the Interior, and Transportation; the Environmental Protection Agency; NASA; and NSF. These agencies account in a given fiscal year regardless of when the actual payment takes place.10 As such, they should be intended as a broad measure of public support including both R&D procurement (i.e. contracts for R&D services) and grants such as those awarded by the Small Business Innovation Research program.11 We select only obligations by the Department of Defense to build our defense-related R&D variable. As a control variable, we also aggregate obligations from other agencies to get a proxy of non-defense R&D. The series are deflated using the price indexes (with base year 2012) respectively for federal defense R&D investment and for federal non-defense R&D investment provided by the Bureau of Economic Analysis (BEA).12 Private R&D expenditures. Data on private R&D expenditures come from the Business R&D and Innovation Survey (BRDIS).13 BRDIS provides data on total private R&D expenditures by state, disaggregated by funding source. To avoid double counting and to get a reliable proxy of additional R&D investments, we only consider the non-federally financed component of private R&D. The series present a non-negligible number of missing values for two main reasons. First, for the period 1981-1997 the survey was biannual. Second, confidentiality issues prevent publication of data for those states with a small number of surveyed firms. We linearly interpolate missing values between observations only when the gap is not greater than one year in order to minimize potential biases due to measurement errors.14 On the contrary, no forward or backward extrapolation is performed.

for roughly the 97% of total R&D obligations [START_REF] Pece | Federal R&D obligations increase 8.8% in FY 2018[END_REF]. Survey respondents are asked to indicate the state where the research was performed by the primary contractor or grantee. In absence of this information, federal agencies should assign obligations to a specific state based on the headquarters of the performer.

10This implies that the actual outlays associated to a given obligations may be distributed through one or more payment tranches in subsequent periods. Unfortunately, data on federal R&D outlays are not collected at the state-level and, therefore, cannot be used for our purposes. We discuss the issue in Section 5 and provide results using national outlays to construct our instrumental variables.

11For detailed definition of federal obligations see the Circular A-11 by the US Office of Management and Budget which provides guidance for federal agencies on budget preparation.

12The price index for federal defense R&D is contained in Table 3.11.4 from the BEA website "Price Indexes for National Defense Consumption Expenditures and Gross Investment by Type". The price index for federal non-defense R&D is contained in Table 3.9.4 from the BEA website "Price Indexes for Government Consumption Expenditures and Gross Investment".

13This is a stratified survey jointly run by the NSF and the Census Bureau that is representative for the population of for-profit non-farm companies with five or more employees. The BRDIS initial year is 2008. The predecessor of BRDIS is the Survey of Industrial Research and Development (SIRD) which covers the period 1953-2007. According to the NSF [START_REF] Wolfe | NSF announces new U.S. business R&D and innovation survey[END_REF], there is no evidence suggesting that the redesign of the survey from SIRD to BRDIS introduced structural breaks in the data. Nevertheless, in our analysis, potential changes affecting all states in 2008 are absorbed by the specific time dummy.

14To evaluate possible distortions arising form the interpolation we report in Section 5 results for Private R&D data are transformed in real terms using the R&D price index (base year 2012) from the BEA.15

Employment in R&D-intensive industries. We rely on the BEA Regional Accounts, which provide employment figures by state and 3-digit industries. Scientists and related workers 19-3000.17

Additional variables. We complement our dataset with data on state-level GDP and population from the BEA Regional Accounts.18 Also, as additional control variables, we include some state-specific measures of innovation policies. First, we obtain data on defense non-R&D procurement from the Federal Procurement Data SystemNext Generation (FPDS-NG), provided by the General Services Administrathe period 1999-2017 which displays almost no missing values. Results appear to be robust to the presence of missing observations. 15This is available in Table 1.2.4 "Price Indexes for Gross Domestic Product by Major Type of Product" from the BEA website.

16For selected sectors we observe only 2-digit, whilst for other the aggregation becomes more granular at 4-digit level 17The 2010 SOC revision introduced some minor classification changes. In aggregating, we considered only those occupations that allows us to keep consistency at the 3-digit level before and after the revision. Notice that, in the 2010 classification, the group 15-1100 "Computer occupations" coincides with the 3-digit category 15-1000. Due to the high number of missing values, we could not retrieve reliable data for the 15-2000 category "Mathematical Science Occupations".

18GDP series are transformed in constant dollars (base year 2012) using the US GDP deflator. Concerning population data, we also used data from the Census Bureau and find no significant differences with respect to the BEA data. tion (GSA). FPDS reports all primary contracts from agencies subject to mandatory reporting and for purchases above the threshold value of $2, 500 from 1980 onwards. Each entry is classified by funding agency and has a 4-digit Product Service Code (PSC) which allow us to rule out contracts associated to the performance of R&D (PSC codes starting with A). Second, we use data from Lucking (2019) on state tax credits, corporate income taxes and user cost of R&D capital to capture possible variations in the regional tax system.

Results

We estimate our model in Eq. 1 over different time spans (ℎ) via both OLS and IV, employing the instrumental variables specified in Eq. 2. The estimation results are reported in Table 1. We do find positive and statistically significant effects of defense R&D obligations on private R&D over time horizons of 4 and 5 years. We progressively include controls (i.e. state GDP and non-defense R&D obligations) and show that our estimates remain remarkably stable.

A comparison between OLS and IV coefficients shows that OLS estimates are always downward biased. This may suggest that the allocation process of defense R&D expenditures tend to favor states that are under-investing in private R&D. At the same time, "attenuation bias" due to measurement errors may also drive the downward bias. Overall, IV results suggest that a 1% increase in military R&D funding over 4-5 years crowds-in private R&D expenditures with an elasticity between 0.11% and 0.14%. Our findings, thus, indicate that the impact of defense R&D on total R&D is significantly above its dollar value, as federally financed military R&D is able to stimulate additional private R&D expenditures.

Over shorter time intervals, we do not find significant effects of defense-related R&D on private one. Quite plausibly, private R&D expenditures appear to be sticky and respond only to spending shocks occurring over sufficiently large time horizons. This may also be related to the duration of R&D projects, as well as the appointment of project managers, which is typically in the 3-5 years range (Azoulay et al., 2019). On the contrary, standard macroeconomic variables such as GDP are typically sensitive also to 2-year spending variations as found, for instance, in [START_REF] Nakamura | Fiscal stimulus in a monetary union: Evidence from US regions[END_REF] and [START_REF] Auerbach | Local fiscal multipliers and fiscal spillovers in the USA[END_REF].

From a theoretical perspective, different mechanisms may drive these results.19

First, defense R&D programs may lead to the formation of new bodies and agglomeration economies fostering the emergence of R&D networks among private and public entities [START_REF] Gruber | Jump-starting America: How breakthrough science can revive economic growth and the American dream[END_REF]. This is likely to result in additional private investments, mostly driven by localized spillovers. For instance, [START_REF] Gross | Inventing the endless frontier: The effects of the world war II research effort on post-war innovation[END_REF] and universities. Second, firms may have incentives to engage in spinoff projects with civilian applications. In this respect, direct funding by the DoD may also help relaxing credit constraints and overcoming fixed costs associated with these projects [START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF].

Robustness analysis

The foregoing results may be affected by different issues which could introduce substantial biases in the estimates. In this section, we control for different potential problems resulting from weak instruments, the omission of relevant variables, measurement errors, missing values, model specification (level vs. growth rates), outliers, the influence of key states, and population normalization. We find that the main result of our empirical analysis is confirmed: defense-related public R&D does crowd-in private R&D expenditures. In the following, we provide more details about the robustness checks we performed.

The first issue is linked to our identification strategy. TSLS estimates and the associated standard errors may not be reliable if instruments are weakly correlated with the endogenous regressor. Under weak instruments TSLS coefficients are biased towards OLS ones and standard inference procedures may not be reliable. In this work, a weak first-stage regression could also result from the many-instrument problem as we have 51 instruments (i.e. 51 state dummies interacted with national variations in defense R&D). To investigate the relevance of these concerns, Figure 3 compares the TSLS with the Limited Information Maximum Likelihood (LIML) estimator which tends to reduce biases from many and weak instruments. Estima-19For a detailed conceptual framework on the effects of military R&D on innovation see [START_REF] Mowery | Military R&D and innovation[END_REF]. tions using LIML show higher and significant coefficients over 4-5 year variations, largely confirming our baseline results. Furthermore, we report in Table 2 the values of the effective 𝐹-statistic by [START_REF] Olea | A robust test for weak instruments[END_REF].20 At any time horizon ℎ, we are able to reject at the 5% confidence level the null of a non-negligible bias for both TSLS and LIML. Thus, also first stage pre-screening clearly hints at the general reliability of our results.

We then consider some alternative specifications and robustness checks. Results are reported in Table 3. First, differences in tax policies across states may influence R&D investments and employment [START_REF] Wilson | Beggar thy neighbor? The in-state, out-of-state, and aggregate effects of R&D tax credits[END_REF][START_REF] Chang | Tax policy endogeneity: Evidence from R&D tax credits[END_REF][START_REF] Lucking | Do R&D tax credits create jobs[END_REF],

thus, acting as a potential confounding factor in our analysis. To control for different taxation regimes, we include in our regressions state-specific R&D tax credits, corporate income tax rates and the user cost of R&D capital (which combines both).21 Results show that the estimated elasticity between military R&D and private R&D slightly increases and remains statistically significant, as compared to our baseline specifications.

Another possible concern comes from the omission of non-R&D procurement.

The magnitude and composition of government demand may indeed act as a de 20The use of the effective 𝐹-statistic is highly recommended in settings with heteroscedasticity and clustering [START_REF] Andrews | Weak instruments in instrumental variables regression: Theory and practice[END_REF], as in our case. This is a test for the null hypothesis of weak instruments. Rejection entails that the bias of the TSLS or LIML is not large, relative to a "worst-case" benchmark.

21Notice that, in order to be consistent with our specification, we included the variation between 𝑡 and 𝑡 + ℎ of these variables. We also run regressions using levels at time 𝑡 a find no substantial differences. Results are available upon request from the authors. facto innovation policy [START_REF] Edler | Public procurement and innovation-resurrecting the demand side[END_REF][START_REF] Guerzoni | Demand-side vs. supply-side technology policies: Hidden treatment and new empirical evidence on the policy mix[END_REF][START_REF] Slavtchev | Does the technological content of government demand matter for private R&D? Evidence from US states[END_REF][START_REF] Raiteri | A time to nourish? Evaluating the impact of public procurement on technological generality through patent data[END_REF]. This is especially relevant for defense procurement as DoD R&D contracts have been often substantially complemented by purchases of the developed product/technology [START_REF] Mowery | Military R&D and innovation[END_REF].22

Thus, we expect military R&D obligations to be correlated with non-R&D procurement. To guard against this concern, we aggregated total non-R&D procurement by state and included it as a control in our regression. Results largely confirm our baseline estimations, albeit with a small loss in precision.

Our empirical analysis could be also biased by measurement errors due to the fact that we do not observe the effective outlays at the state level, as we can only use obligation measures. Luckily enough, data on defense R&D outlays are available at the national level. Leveraging this information we constructed our IV interacting state dummies with national variations in military R&D outlays.

Under the assumption that the timing of the mismatch between national obligations and outlays is correlated with the one unobserved at the state level, this new IV estimation will correct for the aforementioned measurement error. Even with this correction, estimates appear not to change significantly, thus, suggesting that this specific form of measurement error may not play a crucial role for our analysis.

Data on private R&D display a non-negligible number of missing values in the first period of our sample. For this reason, we also estimated our model for the period 1998-2017 in which we observe almost no missing values (as the SIRD survey becomes annual). We show that even in this restricted sample our main results hold with elasticities close to those estimated employing the whole time period.

Finally, in the Appendix B we report some additional robustness checks. First, we estimate a model in levels using the same specification in [START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF].

More specifically, we regress levels of private R&D against lagged values of defense R&D obligations. Differently from our difference specification, in this setting state fixed effects do not absorb state-specific trends but only allow for heterogeneous intercepts. The model yields less conservative estimates (cf Table B.1) with higher elasticities of defense R&D that are in line with those reported in [START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF]. Moreover, we assess whether our results are driven by the dynamics of 22The independent R&D program represents an even more extreme example in this respect (Lichtenberg, 1995). Overhead funds included in non-R&D procurement contracts were used by the Department of Defense to finance indirectly R&D performers. We show that estimates remain remarkably stable with North Dakota having the largest (slightly negative) influence. We also investigate the potential impact of outliers using winsorized variables and find no substantial effect (cf. Table B.2). To conclude, we ran regressions without normalizing variables by population. Results

in Table B.3 also corroborate our general findings.

Employment effects in R&D intensive sectors and occupations

So far we robustly documented crowding-in effects of public military R&D funding on private R&D expenditures. Yet, higher expenditures may translate either in higher R&D employment or in increasing costs (e.g. wages and intermediate goods). Whether one of these two effects prevails may depend on the supply elasticity of R&D workers and inputs, as well as on other characteristics of the innovation system (e.g. firms organizational routines, private and public R&D networks). To shed a light on these issues, we empirically study the impact of public military R&D expenditures on employment. However, data on private R&D employment are not available at the state level. Therefore, we focus on employment in R&D-intensive industries and occupations (cf. Section 4) and we estimate the following model:23

Δ ℎ 𝑅𝐷𝑒𝑚𝑝 𝑖,𝑘,𝑡 = 𝛽Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 𝑖,𝑡 + 𝛾 ′ Δ ℎ W i,t + 𝛼 𝑖 + 𝜆 𝑡 + 𝜀 𝑖,𝑡 , (3)
where Δ ℎ 𝑅𝐷𝑒𝑚𝑝 𝑖,𝑘,𝑡 stands for log changes of employment between year 𝑡 and 𝑡 -ℎ in state 𝑖 and industry/occupation 𝑘 (this is the only difference with respect to the previous model, cf. Eq. 1).

Table 4 displays the results for selected R&D-intensive industries. We find positive and significant employment effects in Computer and electronic product manufacturing (NAICS 334) and Transportation Equipment (NAICS 336). Not surprisingly, effects appear to be concentrated in sectors that receive a disproportional amount of defense R&D funds [START_REF] Mowery | Military R&D and innovation[END_REF], highlights that about 75% of de-23We focus on the top 5 R&D-intensive industries. We also run regressions for other R&Dintensive industries and find no statistically significant results except for Miscellaneous manufacturing (NAICS 339) which shows elasticities in the 0.035 -0.05 range. Results are available upon request from the authors. Regarding occupations, we aggregated at the 3 digit level occupations classified as "Research, Development, Design, and Practitioners". More details are reported in Section 4. fense R&D is concentrated in the aircraft and electrical equipment industries). The estimated employment elasticities are in the range of 0.08-0.1% and are lower than those of private R&D expenditures. The timing of the response is instead similar as also employment appears to respond mainly to spending shocks occurring in 4-5 year time horizons.

Results for different R&D-related occupational categories are provided in Table 5. We find sizeable effects only for the employment of engineers with elasticities between 0.05 and 0.07%. Notice that in this occupational group, a large space is occupied by jobs that are very much related to defense R&D, such as aerospace and electrical engineers. In contrast to effects at the industry level, the employment of engineers turns out to be stimulated also by 2-3 year spending shocks.

Also for employment regressions, we run a series of robustness checks controlling for confounding factors (i.e. tax policies and non-R&D procurement), measurement errors stemming from the use of obligation data, and normalization by population. Results are presented in Table B.4. They largely confirm our base-

Conclusion

In this paper we study whether government-financed defense R&D is effective in fostering privately-funded R&D investment and employment. Our interest in military R&D is motivated by its widely acknowledged "mission-oriented" nature, that is, its ability to direct technological change towards solving tall complex technological problems [START_REF] Mowery | Military R&D and innovation[END_REF][START_REF] Mowery | Defense-related R&D as a model for grand challenges technology policies[END_REF][START_REF] Mazzucato | The entrepreneurial state: Debunking public vs. private sector myths[END_REF]. In this respect, our research may inform the policy debate on mission-oriented innovation with evidence-based results regarding the possible crowding-in effects of these policies.

We assembled a longitudinal dataset for U.S. states including R&D obligations from the DoD, private R&D expenditures, employment in R&D-intensive industries and occupations. Leveraging some characteristics of defense R&D funding, we employed a state-of-the-art IV identification strategy (Nakamura andSteinsson, 2014, 2018;[START_REF] Guren | Housing Wealth Effects: The Long View[END_REF][START_REF] Cloyne | Decomposing the fiscal multiplier[END_REF] based on differential state exposures to national shocks in order to isolate exogenous variations in defense R&D and provide a causal interpretation to our estimates.

Our results shows that an increase in defense R&D over 4-5 years crowds-in privately-funded R&D investments with an elasticity between 0.11% and 0.14%.

This implies that the final impact of federally-financed military R&D on total R&D significantly exceeds its dollar value, as it spurs additional private R&D expenditures. We also find positive effects of defense-related R&D on employment in high-tech sectors and in engineering occupations, albeit with lower elasticities (i.e. 0.05-0.1 %). Such results are robust to a wide ensemble of robustness checks including additional controls (e.g. tax policies, non-R&D procurement), outliers sensitivity and alternative specifications.

The main conclusion from this work is that large mission-oriented programs can stimulate additional innovation efforts in the private sector. Nevertheless, further research is needed in order to deliver more comprehensive policy prescriptions.

First, as mission-oriented programs are not all alike, we plan to investigate in a comparative fashion whether programs focused on different societal goals are equally effective in influencing private R&D spending.24 Second, we ought to asses mission-oriented policies vis-á-vis more conventional tools such as tax credits and horizontal subsidies, as well as possible policy mixes. Finally, an investigation from a more granular geographic perspective may shed further light on some of the mechanisms underlying our results (e.g. spillovers within state).

Appendix A Main variables and descriptives

Appendix B Additional results and robustness checks

Figure 1 :

 1 Figure 1: Levels of federal R&D obligations -defense vs non-defense.

Figure 2 :

 2 Figure 2: Characteristics of defense R&D: national patterns and geographical allocation

  posit that the R&D programs led by the US Office of Scientific Research and Development (OSRD) during the World War II nurtured local innovation ecosystems and promoted the growth of technology clusters in the post-war period, with a major role played by Federally Funded Research Centers (FFRCs)

  16

Figure 3 :

 3 Figure 3: Comparison across estimators: OLS, TSLS, LIML

Figure

  Figure A.1: Defense R&D obligations per capita by state

Figure B. 1 :Figure B. 2 :

 12 Figure B.1: State sensitivities to changes in national defense R&D vs. average log changes in private R&D

Table 1 :

 1 Main estimates: elasticity of non-federally funded private R&D to defense R&D obligationsNotes: the table reports OLS and TSLS estimations. The sample period is 1968-2017. For each ℎ, the dependent variable is the ℎ-year log-change in private R&D (privately financed, in real per capita terms). The main regressor is the ℎ-year log-change in defense R&D obligations (in real per capita terms). Control variables include the ℎ-year log-changes of non-military R&D obligations and state GDP (both in real per capita terms). All regressions include state and time fixed effects. Standard errors in parenthesis are clustered by state.

				Dependent variable:
			Privately-funded R&D (Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣)
	Military R&D		OLS			IV
	(Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 )	(1)	(2)	(3)	(4)	(5)	(6)
	(ℎ = 2)	0.018	0.017	0.017	0.093	0.098	0.095
		(0.02) (0.02)	(0.02) (0.08) (0.079) (0.076)
	(ℎ = 3)	0.023	0.022	0.021	0.07	0.067	0.066
		(0.021) (0.021) (0.021) (0.058) (0.059) (0.055)
	(ℎ = 4)	0.044 *	0.041	0.04	0.134 * 0.137 * 0.138 *
		(0.026) (0.026) (0.025) (0.08) (0.079) (0.07)
	(ℎ = 5)	0.043	0.04	0.04	0.11 * 0.112 * * 0.109 * *
		(0.027) (0.027) (0.027) (0.056) (0.055) (0.053)
	Non Military R&D
	State GDP

* p<0.1; * * p<0.05; * * * p<0.01

Table 2 :

 2 First-stage effective 𝐹-statisticsNotes: the table reports for each ℎ the effective 𝐹-statistics by[START_REF] Olea | A robust test for weak instruments[END_REF] and the associated 5% critical values for the TSLS and LIML estimators. The null hypothesis is that of weak instruments. Rejections imply that the bias is not large, relative to a "worst-case" benchmark. The 𝐹-statistics refer to the first stage of the baseline model including non-military R&D obligations and state GDP as controls.

	Effective F-statistics
	ℎ = 2 ℎ = 3 ℎ = 4 ℎ = 5

Table 3 :

 3 Alternative specifications and robustness checks R&D obligations and state GDP (both in real per capita terms) as control variables as well as state and time fixed effects. The sample period is 1968-2017 except for the "Non-R&D procurement" case which uses 1980-2017 and the "Restricted sample" regression which uses 1998-2017. The top three specifications include respectively ℎ-year variations in corporate tax rates, R&D tax credits and user costs of R&D capital as controls. The "Non-R&D procurement" regression includes ℎ-year log-changes in total non-R&D procurement. The "Outlays" specification uses national variations in outlays (instead of obligations) interacted with state dummies as instrumental variables. Standard errors in parenthesis are clustered by state. * p<0.05; * * * p<0.01 single states by dropping observations of one state at the time (cf. Figure B.2).

	Dependent variable:
	Privately-funded R&D (Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣)

Notes: the table reports TSLS estimations for different specifications and time horizons ℎ. Across all specifications, the dependent variable is the ℎ-year log-change in private R&D (privately financed, in real per capita terms) while the main regressor is the ℎ-year log-change in defense R&D obligations (in real per capita terms). All regressions include the ℎ-year log-changes of non-military * p<0.1; *

Table 4 :

 4 Employment elasticities of defense R&D obligations in high-tech industries

	Dependent variable:
	Employment (Δ ℎ 𝑅𝐷𝑒𝑚𝑝)

Notes: the table reports industry-by-industry TSLS estimations. The sample period is 1998-2018. For each ℎ, the dependent variable is the ℎ-year log-change in industry employment (normalized by state population). The main regressor is the ℎ-year log-change in defense R&D obligations (in real per capita terms). All regression include state and time fixed effects as well as baseline control variables, i.e. the ℎ-year log-changes of non-military R&D obligations and state GDP (both in real per capita terms). Standard errors in parenthesis are clustered by state. * p<0.1; * * p<0.05; * * * p<0.01

Table 5 :

 5 Employment elasticities of defense R&D obligations in R&D-related occupations All regression include state and time fixed effects as well as baseline control variables, i.e. the ℎ-year log-changes of non-military R&D obligations and state GDP (both in real per capita terms). Standard errors in parenthesis are clustered by state. * p<0.05; * * * p<0.01 line estimations, albeit with reduced statistical significance for employment in the Computer and Electronic Products industry.

	Dependent variable:
	Employment (Δ ℎ 𝑅𝐷𝑒𝑚𝑝)

Notes: the table reports occupation-by-occupation TSLS estimations. The sample period is 1999-2018. For each ℎ, the dependent variable is the ℎ-year log-change in occupation employment (normalized by state population). The main regressor is the ℎ-year log-change in defense R&D obligations (in real per capita terms). * p<0.1; *

Table A .

 A 1: Summary statistics by state (5-years log variations of defense and private R&D)

			Private R&D (Δ 5 𝑅𝐷𝑝𝑟𝑖𝑣)			Defense R&D (Δ 5 𝑅𝐷𝑑𝑒 𝑓 )
		mean	sd	min	max	mean	sd	min	max
	State
	AK	0.08	1.10	-1.16	3.28	-0.24	1.53	-1.53	3.06
	AL	0.31	0.69	-0.83	2.62	0.22	0.38	-0.55	0.98
	AR	-0.00	0.33	-0.56	0.69	0.53	1.19	-1.43	2.15
	AZ	0.11	0.30	-0.44	0.77	0.02	0.52	-1.19	1.08
	CA	0.30	0.17	-0.02	0.69	-0.13	0.49	-1.22	0.95
	CO	0.09	0.28	-0.49	0.52	-0.17	0.86	-1.96	1.56
	CT	0.11	0.36	-0.56	0.97	0.11	0.68	-0.91	2.03
	DC	0.05	1.24	-1.69	3.23	0.06	0.71	-1.95	2.34
	DE	-0.03	0.34	-0.79	0.56	-0.09	0.58	-1.32	0.75
	FL	0.08	0.35	-1.20	1.05	-0.20	0.33	-1.01	0.56
	GA	0.20	0.14	-0.06	0.48	-0.56	0.85	-1.46	2.69
	HI	0.17	0.45	-0.57	0.80	0.01	0.77	-0.99	1.34
	IA	0.10	0.32	-0.71	0.43	0.56	0.89	-0.71	1.81
	ID	0.04	0.32	-0.56	0.46	0.06	0.63	-1.08	1.23
	IL	0.12	0.13	-0.09	0.40	0.07	0.57	-0.71	1.14
	IN	0.12	0.32	-0.33	1.19	-0.18	0.57	-0.97	0.85
	KS	0.12	0.27	-0.40	0.32	-1.78	1.19	-3.28	-0.39
	KY	0.09	0.31	-0.43	0.58	0.28	0.99	-1.16	2.75
	LA	-0.04	0.40	-0.59	1.04	-0.45	1.55	-3.75	2.05
	MA	0.17	0.24	-0.34	0.89	-0.04	0.42	-0.86	0.78
	MD	0.04	0.45	-1.11	0.92	-0.01	0.21	-0.49	0.36
	ME	0.04	0.30	-0.54	0.59	-0.60	0.75	-1.64	0.75
	MI	0.13	0.49	-0.42	2.66	0.05	0.64	-1.18	1.24
	MN	0.19	0.22	-0.20	0.72	-0.09	0.76	-1.43	1.06
	MO	0.18	0.15	0.03	0.46	-0.30	1.20	-2.23	1.98
	MS	-0.02	0.29	-0.48	0.74	-0.08	0.54	-1.11	0.44
	MT	0.14	0.37	-0.63	0.67	-0.18	0.88	-1.48	2.01
	NC	0.14	0.23	-0.31	0.58	-0.17	0.37	-1.04	0.57
	ND	0.27	0.82	-0.65	1.78	-0.51	1.94	-3.17	2.25
	NE	0.09	0.22	-0.29	0.50	0.07	1.40	-2.44	2.50
	NH	0.30	0.62	-0.36	1.31	-0.24	0.58	-0.82	0.49
	NJ	0.12	0.24	-0.41	0.83	-0.11	0.48	-1.02	0.83
	NM	0.09	0.48	-0.72	0.95	-0.11	0.29	-0.75	0.45
	NV	-0.06	0.35	-0.79	0.40	-0.08	1.02	-1.89	1.68
	NY	0.09	0.18	-0.32	0.45	-0.11	0.58	-1.08	1.14
	OH	0.11	0.25	-0.22	1.41	-0.02	0.52	-1.14	1.28
	OK	0.02	0.32	-0.44	0.71	0.13	1.12	-1.96	2.20
	OR	0.44	0.28	0.11	0.99	-0.02	0.81	-1.48	1.33
	PA	0.12	0.18	-0.23	0.52	-0.03	0.43	-1.06	1.05
	RI	0.19	0.19	-0.03	0.45	-0.23	0.22	-0.52	0.08
	SC	-0.06	0.21	-0.38	0.26	0.11	0.64	-0.93	1.17
	SD	0.50	0.79	-0.57	2.59	0.29	1.51	-3.51	2.62
	TN	-0.10	0.13	-0.27	0.17	0.04	0.58	-0.92	1.58
	TX	0.10	0.22	-0.49	0.58	-0.06	0.60	-1.03	1.19
	US	0.16	0.10	-0.03	0.35	-0.03	0.29	-0.61	0.45
	UT	0.22	0.25	-0.23	0.69	0.01	0.79	-1.17
				-0.58	0.89			-0.60	1.00
		-0.06	0.46	-0.71	1.38	-0.39	1.87	-3.10	3.37
	WA	0.13	0.16	-0.21	0.45	0.01	1.07	-2.24	1.30
	WI	0.15	0.09	0.02	0.35	0.07	0.66	-0.80	1.35
	WV	-0.14	0.27	-0.46	0.26	-0.95	1.03	-3.24	0.45
	WY	0.17	1.08	-2.17	2.77	0.06	1.30	-3.03	1.95

Table A

 A

		.2: Cross-correlations among main variables
		Private R&D Military R&D Non Military R&D State GDP
	ℎ = 5
	Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣	1
	Δ ℎ 𝑅𝐷𝑑𝑒 𝑓	0.12	1
	Δ ℎ 𝑅𝐷𝑛𝑜𝑛 -𝑑𝑒 𝑓 0.17	0.1	1
	Δ ℎ 𝐺𝐷𝑃	0.12	0.14	0.05	1
	ℎ = 4
	Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣	1
	Δ ℎ 𝑅𝐷𝑑𝑒 𝑓	0.08	1
	Δ ℎ 𝑅𝐷𝑛𝑜𝑛 -𝑑𝑒 𝑓 0.18	0.08	1
	Δ ℎ 𝐺𝐷𝑃	0.06	0.1	0.01	1
	ℎ = 3
	Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣	1
	Δ ℎ 𝑅𝐷𝑑𝑒 𝑓	0.04	1
	Δ ℎ 𝑅𝐷𝑛𝑜𝑛 -𝑑𝑒 𝑓 0.15	0.05	1
	Δ ℎ 𝐺𝐷𝑃	0.02	0.08	-0.02	1

Notes: 𝑅𝐷𝑝𝑟𝑖𝑣 stands for private, non-federally funded R&D. 𝑅𝐷𝑑𝑒 𝑓 represents total defense R&D obligations. 𝑅𝐷𝑛𝑜𝑛 -𝑑𝑒 𝑓 stands for total non-defense R&D obligations. 𝐺𝐷𝑃 is total state GDP. All variables are taken in real per capita terms. Correlations are computed for log changes over different time horizons (ℎ).

Table B .

 B 1: Estimates from the log level specificationNotes: OLS and TSLS estimations with state and year fixed effects. The level specification is: ln 𝑅𝐷𝑝𝑟𝑖𝑣 𝑖,𝑡 = 𝛽 ln 𝑅𝐷𝑑𝑒 𝑓 𝑖,𝑡-1 + 𝛿 ′ 𝑊 𝑖,𝑡 + 𝛼 𝑖 + 𝜆 𝑡 + 𝜀 𝑖,𝑡 ,. The dependent variable is the log of nonfederally funded R&D expenditures. The main regressor is the lagged log of defense R&D obligations. The vector of controls include the contemporaneous and lagged logs of non-defense R&D obligations and state GDP. All variables are taken in real per capita terms. In TSLS estimations we use a simple No correction 0.134 * 0.137 * 0.138 * 0.132 * 0.134 * 0.134 * No correction 0.11 * 0.112 * * 0.109 * * 0.108 * * 0.109 * * 0.106 * * (0.056) (0.055) (0.053) (0.05) (0.049) (0.049) Winsorized 0.113 * 0.114 * * 0.111 * * 0.111 * * 0.111 * * 0.107 * * TSLS estimations with state and year fixed effects. The sample period is 1968-2017. For each ℎ, the dependent variable is the ℎ-year log-change in private R&D (privately financed, in real per capita terms). The main regressor is the ℎ-year log-change in defense R&D obligations (in real per capita terms). Winsorization occurs at the 1st and 99th percentiles. Control variables include the ℎ-year log-changes of non-military R&D obligations and state GDP (both in real per capita terms). Standard errors in parenthesis are clustered by state. * p<0.05; * * * p<0.01 Table B.3: Regressions without normalizing by population OLS and TSLS estimations with state and year fixed effects. The sample period is 1968-2017. For each ℎ, the dependent variable is the ℎ-year log-change in firms R&D (privately financed, in real terms). The main regressor is the ℎ-year log-change in defense R&D obligations (in real terms). Baseline controls include ℎ-year log-changes of state population, GDP and non-defense R&D obligations (in real terms). Standard errors in parenthesis are clustered by state. * p<0.05; * * * p<0.01 Table B.4: Employment regressions: robustness checks Dependent variable: Employment (Δ ℎ 𝑅𝐷𝑒𝑚𝑝) (ℎ = 3) (ℎ = 4) (ℎ = 5) (ℎ = 2) (ℎ = 3) (ℎ = 4) (ℎ = 5) Engineers 0.048 * * 0.062 * * 0.062 * * 0.069 * * 0.042 * * 0.056 * * 0.059 * * 0.064 * * * 0.059 * * 0.065 * * 0.07 * * 0.055 * * * 0.068 * * * 0.069 * * * 0.069 * * * Transportation equipment -0.147 0.104 * * * 0.09 * * * 0.071 * * 0.01 0.123 * * * 0.102 * * * 0.074 * 0.06 * * * 0.076 * * * 0.08 * * * 0.082 * * * Notes: the table reports TSLS estimations by industry/occupation for different specifications and time horizons ℎ. Across all specifications, the dependent variable is the ℎ-year log-change of employment in the industry/occupation (in per capita terms) while the main regressor is the ℎ-year log-change in defense R&D obligations (in real per capita terms). All regressions include the ℎ-year log-changes of non-military R&D obligations and state GDP (both in real per capita terms) as control variables as well as state and time fixed effects. The sample period is 1968-2017 except for the "Non-R&D procurement" regression which uses 1980-2017. The first three specifications include respectively ℎ-year variations in corporate tax rates, R&D tax credits and user costs of R&D capital as controls. The "Non-R&D procurement" regression includes ℎ-year log-changes in total non-R&D procurement. The "Outlays" specification uses national variations in outlays (instead of obligations) interacted with state dummies as instrumental variables. "No population normalization" refers to a regression in which both the main regressor and the controls are not divided by population. Standard errors in parenthesis are clustered by state. p<0.1; * * p<0.05; * * * p<0.01

		Dependent variable: Dependent variable:
	Privately-funded R&D (ln 𝑅𝐷𝑝𝑟𝑖𝑣) R&D tax credit OLS Corporate tax Privately-funded R&D (Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣) IV (𝑘 = 5) (𝑘 = 10) (𝑘 = 15) 0.106 * * * 0.107 * * * 0.247 * * * 0.249 * * * 0.314 * * 0.315 * * 0.427 * * 0.423 * * Table B.2: Outliers robustness: regressions using winsorized data (at 1st and 99th ln𝑅𝐷𝑑𝑒 𝑓 𝑡-1 Military R&D OLS IV (Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 ) (1) (2) (3) (4) (5) (6) Industry/Occupation (ℎ = 2) (SOC 17-2000) (0.018) (0.024) (0.025) (0.03) (0.018) (0.023) (0.024) (0.029) percentiles) (0.035) (0.036) (0.089) (0.089) (0.138) (0.137) (0.195) (0.189) Non Military R&D Military R&D (Δ ℎ 𝑅𝐷𝑑𝑒 𝑓 ) ℎ = 2 0.017 0.017 0.016 0.088 0.086 0.088 Computer and electronic 0.011 0.011 0.065 0.068 * 0.013 0.015 0.06 0.062 Dependent variable: Private R&D (Δ ℎ 𝑅𝐷𝑝𝑟𝑖𝑣) No correction Winsorized (0.02) (0.02) products (NAICS 334) (0.039) (0.048) (0.042) (0.04) (0.038) (0.046) (0.04) (0.039) (0.02) (0.078) (0.072) (0.069) Transportation equipment -0.121 0.101 * * * 0.081 * * * 0.058 -0.142 0.1 * * * 0.085 * * * 0.068 * * Non Military R&D (lagged) State GDP ℎ = 2 No correction 0.093 0.098 0.095 0.102 0.107 0.105 ℎ = 3 0.021 0.02 0.019 0.063 0.05 0.046 (NAICS 336) (0.188) (0.027) (0.026) (0.036) (0.212) (0.026) (0.021) (0.033)
	State GDP(lagged)	(0.08) (0.079) (0.076) (0.074) (0.074) (0.071) (0.02) (0.02) (0.02) (0.056) (0.049) (0.048) User cost of R&D capital Non-R&D procurement
	Winsorized ℎ = 3 No correction ℎ = 4 Engineers 0.044 (SOC 17-2000) 0.082 (0.081) (0.08) (0.078) (0.076) (0.076) (0.073) 0.086 0.083 0.091 0.094 0.092 0.07 0.067 0.066 0.075 0.074 0.041 0.041 * 0.038 0.126 0.107 0.111 * (0.025) (0.024) (0.024) (0.076) (0.066) (0.062) (0.018) (0.023) (0.025) (0.029) (0.019) (0.023) (0.023) (0.023) 0.073 (0.058) (0.059) (0.055) (0.055) (0.055) (0.052) Winsorized 0.072 0.07 0.069 0.077 0.076 (0.058) (0.058) (0.054) (0.055) (0.055) (0.052) (0.027) (0.027) (0.026) (0.054) (0.054) (0.053) 0.075 ℎ = 5 0.041 0.041 0.038 Computer and electronic 0.012 0.014 0.061 0.064 0.021 0.033 0.079 * 0.084 * 0.102 * 0.099 * 0.099 * products (NAICS 334) (0.039) (0.047) (0.042) (0.04) (0.038) (0.047) (0.043) (0.043)
	No controls (NAICS 336) ℎ = 4 (0.08) (0.079) (0.07) (0.073) (0.073) (0.067) (0.214) (0.028) (0.022) (0.034) (0.077) (0.023) (0.024) (0.037) Winsorized Only Population Outlays No population normalization 0.139 (0.083) (0.081) (0.073) (0.076) (0.075) (0.069) Baseline (includ. pop) Engineers 0.019 0.02 0.039 0.049 (SOC 17-2000) (0.027) (0.031) (0.031) (0.028) (0.02) (0.025) (0.024) (0.024) Computer and electronic 0.045 0.045 0.073 0.072 0.014 0.016 0.059 0.065 products (NAICS 334) (0.041) (0.045) (0.045) (0.045) (0.036) (0.046) (0.047) (0.049) ℎ = 5 (0.057) (0.057) (0.055) (0.051) (0.051) (0.051) Transportation equipment 0.055 0.067 * 0.08 * * 0.066 -0.019 0.115 * * * 0.091 * * * 0.074 *
	Non Military R&D (NAICS 336)	(0.033) (0.034) (0.033) (0.043) (0.103) (0.023) (0.025) (0.037)
	State GDP

Bartik-type of instrument, also similar to

[START_REF] Moretti | The intellectual spoils of war? Defense R&D, productivity and international spillovers[END_REF]

: 𝐼𝑉 = 𝑠 ℎ𝑎𝑟𝑒 𝑖,𝑡-1 𝑅𝐷𝑑𝑒 𝑓 𝑈𝑆,𝑡-1 . Where 𝑠 ℎ𝑎𝑟𝑒 stands for a 𝑘-years moving average of the state share in public R&D and 𝑅𝐷𝑑𝑒 𝑓 𝑈𝑆 is national defense R&D. We report results for three different values for 𝑘 (i.e. 5, 10 and 15). Standard errors in parenthesis are clustered by state. * p<0.1; * * p<0.05; * * * p<0.01 * 0.142 * 0.141 * 0.137 * 0.138 * 0.137 * Notes: * p<0.1; * Notes: * p<0.1; * * * *

Acknowledgements: We thank, among others, Francesco Lamperti, Andrea Mina, Giuseppe Ragusa, Pietro Santoleri, Willi Semmler, and Federico Tamagni for helpful comments and suggestions. The authors acknowledge the support by the European Unions Horizon 2020 research and innovation program under grant agreement No. 822781 -GROWINPRO.