David Guerrero

Hidekazu Itoh

Kenmei Tsubota

Freight rates up and down the urban hierarchy

Keywords: Urban hierarchy, freight flows, freight rates, truck transport, commodity flow survey, regression model, Japan

This paper investigates how freight rates paid by shippers are affected by the characteristics of urban areas of origin and destination. It is based on a commodity flow survey between 45 Japanese prefectures from 2000 to 2010. Through an analysis of freight rates, authors seek to identify the advantages and disadvantages faced by shippers depending on the spatial arrangement of their freight flows. The results show that shipping cargo from small to large urban areas is less costly than in the reverse direction, other things being equal. This difference may be due to the higher probability for truck companies to find back-haul cargo when the destination is a large urban area, usually involving a larger truck transport market. Another important finding of this study is that intra-urban freight rates are positively correlated with population size. The latter may result from higher levels of congestion, labour costs, weight and size restrictions on vehicles, as well as higher proportions of light goods such parcels and courier flows.

Introduction

This paper analyses freight between urban areas (UAs). It aims to take account of the UA in context as part of the region and also as the origin and destination point for freight movements. It analyses the spatial distribution of freight rates between UAs. It discusses whether the positions of UAs of origin and destination of flows are likely to affect freight rates 1 . It considers evidence from a Commodity Flow Survey between Japanese prefectures and discusses the potential relationship between the population size of urban areas of origin and destination, the flow of freight flows and freight rates.

Freight volumes and rates are analysed between different levels of the urban hierarchy. The aim is to identify regularities in Japan, which can eventually be compared with other regions in the world where commodity flow surveys are available.

By providing an insight into the spatial patterns of inter-urban freight, this paper also aims to support with empirical evidence how transport remains a critical and a scarce resource, whose proprieties greatly vary from one place to another [START_REF] Hall | Reexploring the interface between economic and transport geography[END_REF] The paper contributes to the extant literature in several ways. First, for the first time, it measures the relationship between freight rates and the position of origin and destination firms within the urban hierarchy. Former studies have analysed the geographical organisation of freight rates [START_REF] Alexander | Freight rates: selected aspects of uniform and nodal regions[END_REF][START_REF] Sagers | The freight rate structure on Soviet railroads[END_REF] but without considering the relationships of urban areas within the urban hierarchy. Other works have analysed the geographical/hierarchical distribution of freight flows but without taking in account the relationships with freight rates [START_REF] Guerrero | Freight flows and urban hierarchy[END_REF][START_REF] Ullman | American commodity flow[END_REF][START_REF] Pred | Toward a typology of manufacturing flows[END_REF][START_REF] Murayama | Japanese urban system[END_REF][START_REF] Murayama | Japanese urban system[END_REF]. Hence, "freight rates 1 Freight rates are the price of transport services provided by transport firms and paid by shippers.

are of greatest value in outlining regions and in affecting their organisation" (Alexander et al., 1958, p. 1). Second, while the existing works on the determinants of freight rates have indirectly tackled the interrelation with urban hierarchy through the population density of urban areas [START_REF] Tanaka | Directional imbalance in freight rates: evidence from Japanese inter-prefectural data[END_REF], the relative positions of origins and destination UAs within the urban hierarchy have not been considered. Here, we demonstrate that freight rates also depend on the trade patterns of shippers with regard to an urban hierarchy. Third, this paper contributes to the further understanding of freight advantages affect the ability of regions to position themselves more effectively in national space economies (Lim and Thill, 2008[START_REF] Chisholm | Accessibility and regional development in Britain: some questions arising from data on freight flows[END_REF][START_REF] Chisholm | Britain, the European Community, and the centralisation of production: theory and evidence, freight movements[END_REF]. By revealing the structure of freight rates between urban areas of different size, the paper also aims to contribute to existing research on urban freight. This is particularly relevant to studies aiming to simulate the generation of freight flows within urban areas but often neglecting the relationships with other urban areas [START_REF] Gonzalez-Feliu | A simulation framework for evaluating the impacts of urban goods transport in terms of road occupancy[END_REF][START_REF] Lawson | Estimated generation of freight trips based on land use[END_REF]. Finally, the paper uses the case of Japan to contribute to existing theories related to urban hierarchy and freight transportation within transport geography more broadly [START_REF] Nojiri | Physical distribution studies in Japanese geography[END_REF].

The paper is structured as follows:

The next section reviews the relevant contributions in the literature and the third section develops the theoretical framework. Section four presents data and geographical context, while section five presents the results of a regression analysis. The sixth section concludes by highlighting the main implications of this paper.

Related literature

The interrelationships between freight rates and the urban hierarchy have not been studied as such in the literature, but they have rather been approached transversally. In this section, the related literature is reviewed in terms of how the urban hierarchy interrelates with freight flows, and how the flows affect freight rates. [START_REF] Zipf | Human Behaviour and the Principle of Least Effort. Addison-Wesley, Cambody Mus[END_REF] empirically analysed the concept of urban hierarchy and observed the distribution of urban areas followed a simple rule: the population size of the largest urban area is twice the size of the second largest one, thrice the third and so on. This regularity in the spatial arrangement of urban regions is considered to be the result of a tension between the advantages for geographic concentration of industry within a metropolitan area on one side, and diseconomies associated with large urban areas in the other [START_REF] Henderson | The types and size of cities[END_REF]. Although the distribution of population between urban areas within a country is relatively simple and easy to predict, the factors that create it are complex (Krugman, 1996, Fujita and[START_REF] Fujita | Structural stability and evolution of urban systems[END_REF] and beyond the scope of this paper.

Urban hierarchy and freight distribution

What matters for our purpose is that large urban areas tend to be more attractive for firms than smaller ones, even if 'population alone' is not an accurate measure of their central importance [START_REF] Ullman | A theory of location for cities[END_REF]. The attractiveness of large urban areas is particularly strong for certain types of activities, either serving final or nonfinal consuming markets [START_REF] Pred | Toward a typology of manufacturing flows[END_REF], such as wholesale trade, transportation, warehousing, and certain types of manufacturing activities related to the former. This attractiveness has been approached in the transportation literature through the prism of accessibility.

Holguin-Veras et al (2005) showed that accessibility was an important decision criteria for most of the firms recently established in New Jersey. However these firms are not necessarily sensitive to the same scope of accessibility. While the firms selling goods and services to distant areas place a premium on inter-urban accessibility, other services are more attached to local / intra-urban accessibility.

These differences have been empirically analysed through commodity flow surveys (for example, [START_REF] Ullman | American commodity flow[END_REF][START_REF] Berry | Essays on Commodity Flows and the Spatial Structure of the Indian Economy[END_REF][START_REF] Murayama | Japanese urban system[END_REF]. A recent study, based on the results of the French shippers' survey, studied these differences through the prism of the urban hierarchy [START_REF] Guerrero | Freight flows and urban hierarchy[END_REF]. Manufacturing flows are not dominated by an upward (ex. from small urban area (UA) to a large ones) or downward pattern (ex. from large UA to small UA). These result from the fact that manufacturing activities are spread in urban areas of different size. On the other hand, wholesaling flows are strongly organised from Paris and large urban areas to smaller ones. Although most wholesalers are located in large urban areas, highly differentiated patterns are observed depending on the activity type: some are concentrated mainly in large urban areas, while others are ubiquitous. Medium-sized urban areas act as intermediate centres between large and small urban areas. Therefore, the wholesale trade organisation looks like a water stream falling step-by-step from the top to the bottom of the urban hierarchy. This hierarchical pattern is strongly suggestive of the concept of step migration used to explain movements of people from rural areas to small UAs, and then to large UAs [START_REF] Ravenstein | The laws of migration[END_REF][START_REF] Plane | Migration up and down the urban hierarchy and across the life course[END_REF], although in the opposite direction.

Another significant characteristic of wholesale trade is that inbound flows tend to travel over longer distances than outbound ones [START_REF] Guerrero | Freight flows and urban hierarchy[END_REF][START_REF] Hayashi | Spatial patterns of the distribution system in Japan and their recent changes[END_REF]. This is because wholesale trade activities tend to locate close to the markets (retailers and manufacturers), especially in large urban areas, to deliver manufactured goods produced everywhere, both within countries and abroad.

Freight rates and directionality

The hierarchical organisation of inter-urban freight flows reflected by rates, which vary not only depending on the distance and size of urban areas but also the direction of flows [START_REF] Alexander | Freight rates: selected aspects of uniform and nodal regions[END_REF]. The impact of directionality on rates was investigated for different transport modes (i.e., [START_REF] Felton | The impact of rate regulation upon ICC-regulated truck backhauls[END_REF][START_REF] Cariou | An analysis of bunker adjustment factors and freight rates in the Europe/Far East market (2000-2004)[END_REF].

In the case of truck transport, when a truck firm is working from A to B, the transport costs of AB cannot be separated from those of BA. This results, for example, by the need of bringing the driver and vehicle back to the origin. Economists refer to this as joint costs, being the result of producing two or more outputs in fixed proportions: "for each outbound truck movement, there is a corresponding inbound truck movement; the ratio is fixed and unchanging." (Felton, 1981, p. 255). Despite some additional costs incurred on returning a vehicle loaded rather than empty, the total production cost (per mile) is lower when trucks are fully loaded in both directions.

For truck firms, the probability of finding backhaul cargo is usually higher while transporting between large urban areas than between smaller ones, as presented by [START_REF] Ferguson | Joint products and road transport rates in transport models[END_REF] within the context of Australia. Freight rates are then estimated on different types of routes based on their backhaul potential. [START_REF] Tanaka | Directional imbalance in freight rates: evidence from Japanese inter-prefectural data[END_REF] in Japan have recently confirmed the impact of the characteristics of urban areas of origin and destination on freight rates. Their work showed that freight rate imbalances basically resulted from differences in population density of the urban regions of origin and destination. Namely, the widest is the gap in population density between the origin and destination UAs, the highest the gap between front and backhaul rates. This paper aims to expand the former works on freight rates by considering the relative positions of urban areas within an urban hierarchy.

Theoretical framework

The following hypotheses are tested to analyse the hierarchical structure of freight flows and rates between urban areas:

Distance and inter-urban freight rates

Road transport cost consists of several components. Some of them vary with distance, for example, driver's salary, fuel, maintenance and use costs, or the tolls paid for using the motorways. Other components are distant-invariants such as loading and unloading operations, moving the truck from the parking to the pick-up point in shippers' establishment, complying with administrative formalities, and so on. Given the above, the following hypothesis is expected to hold:

(1) H1: The longer the distance of the freight movement, the lower is the interurban freight rates (by tonne-km).

The relationship between distance and freight rates is already verified within other regional contexts. In France, using a survey with 53,000 truck movements, [START_REF] Jeger | Les déterminants des prix du transport routier de marchandises[END_REF] confirmed that transport freight rates by tonne-km were lower for distant trips.

Population size of the urban area and intra-urban freight rates

A truck performing the collection and distribution of load units usually move in densely urbanised and/or industrialised zones. They may experience congestion and the consequent private delays, and may also impose delays on other vehicles whose costs are counted as an externality [START_REF] Janic | Modelling the full costs of an intermodal and road freight transport network[END_REF].

(2) H2: The larger the UA, the higher the intra-urban freight rate.

Several factors cause this situation. On the one hand, prices such as labour and land costs in large urban areas tend to be higher. Conversely, the average distance of trips is slightly shorter in large urban areas [START_REF] Allen | Investigating relationships between road freight transport, facility location, logistics management and urban form[END_REF], which means that the share of fixed costs per t-km is generally higher. On the other hand, larger urban areas are more congested and transport is generally less efficient, with a higher proportion of empty running and lower lading factors [START_REF] Allen | Investigating relationships between road freight transport, facility location, logistics management and urban form[END_REF] The former effects are somewhat limited due to more intense competition between truck companies in large urban areas.

City size (or urban hierarchy) and inter-urban freight rates

(3) H3: Shipping downwards is more expensive than upwards.

This situation results from the difficulty for truck companies to find backhaul cargo when going to less-populated areas with less local demand for truck transportation. The lower probability of finding a backhaul cargo locally, make truck firms to charge higher rates on fronthaul trips, as shown by [START_REF] Ferguson | Joint products and road transport rates in transport models[END_REF].

Conversely, opportunities for finding backhaul cargo when going to large urban areas are more because of higher local demand, which will contribute to lower the front haul freight rates.

City size, trade (or freight) flow, and inter-urban freight rates

(4) H4: The larger is the total flow between an OD (Origin-Destination) pair, the lower are the freight rates. This is related to scale economies in truck transportation, namely the opportunities to optimise the capacity of trucks. Moreover, a larger market allows more room for competition between truck companies.

(5) H5: The characteristics of the origin UA have a stronger impact on freight rates than the characteristics of destination UA.

The most common incoterm in Japan is 'Cost Insurance Freight' (CIF), meaning the transport cost to the destination is usually included in the total (or final) price of the good. Therefore, the characteristics of the shippers' UA would determine more the freight rates than the characteristics of consignees' UA.

Data and geographic context

Japan provides an interesting area for studying the patterns of inter-urban freight rates for several reasons. First, its insular context and the extensive use of road transport imply less interference of transit flows and other modes. Second, the large size of the top three metropolitan areas, each covering several neighbouring prefectures, allows the analysis of freight flow movements at intra-metropolitan level. Last, but not least, this work has been made possible by the availability of two reliable data sources providing detailed information on the movements of cargo between prefectures in Japan.

Data: RCMS and CFS surveys

We use two complementary surveys to measure the freight flows and rates between the different levels of urban hierarchy Both were conducted by the Japanese Ministry of Land, Infrastructure, Transport and Tourism (MLIT)..: The, and The. The Regional Cargo Movement Survey (RCMS) is an exhaustive annual vehicle survey, providing information on cargo movements (tonnes) by mode and type of goods, at the level of prefectures. The Commodity Flow Survey (CFS) is a shippers' survey conducted every 5 years recording cargo movements and freight rates paid by shippers.

The CFS survey provides data on the activity of shippers during 3 days. In our analysis we used RCMS data for freight flows and CFS data for freight rates, for three time points: 2000, 2005 and 2010. .

Delimitation of urban areas and definition of hierarchical levels

Figure 1 displays a map representing the largest freight flows between prefectures based on the RCMS survey. It highlights the largest prefectures and the relationships over short distances, mainly along the Fukuoka-Tokyo manufacturing belt, which includes four major industrial areas (Tokyo, Nagoya, Osaka, and Fukuoka). It also confirms the metropolitan structures revealed by commuting, migrations, or firms' headquarters [START_REF] Fujita | Regional growth in post-war Japan[END_REF]. Most of freight flows involve the prefectures around Tokyo area, which seem to constitute an urban system itself. Suburban prefectures are strongly interconnected with the core and between each other.

The map in Figure 2 represents the dominant freight flows. It provides an alternative view to the main flows (Figure 1) by highlighting the hierarchy between prefectures, even outside the top urban areas. According to this method [START_REF] Nystuen | A graph theory interpretation of nodal regions[END_REF], a prefecture i is dominated by a prefecture j, (a) if the most important flow from i is emitted towards j, and; (b) if the sum of the flows received by j is greater than the sum of the flows received by i. While on the East freight movements are generally organised around large cities, on the West, the freight flows are less polarised.

Again, the prefectures around Tokyo exhibit a complex hierarchical pattern with several levels, converging to the core. Paradoxically, the core of the Tokyo freight system is not dominated by Tokyo Prefecture, but by Yokohama (Kanagawa prefecture). This result,

Empirical analysis and discussion

Specifications

a) For the sake of simplicity, in the regression analysis we try to explain freight rates as a function of the spatial organization of freight flows.. However, it is obvious that freight flows and freight rates are simultaneously determined.

Our starting point is the explanation of the spatial structure of the trade flows.

As the distributions of manufacturing activities and population are typically stable across time, the demand for freight may be well-shaped in advance, suggesting that freight rates may be determined by a specific structure of trade flows. As discussed in Section 3, six hypotheses are to be examined by mainly concerning freight rates.

However, it is necessary to understand the trends of freight flows, and hence, freight flows are estimated before freight rates. A preliminary analysis raised differences in the spatial organization of freight flows depending on their hierarchical structure.

Therefore, two samples were used: one for vertical flows (either upward or downward), and another for horizontal flows,when the UAs of origin and destination belong to the same hierarchical level.

The following equation estimates the vertical and horizontal freight flows:

ln 𝑄 𝑟𝑠𝑐𝑡 = 𝛼 + � 𝛽 𝑟 𝐶𝑙𝑎𝑠𝑠 𝑢 𝑢=𝑁 + γ𝑋 𝑟𝑡 + θ t + δ c + ϵ.
𝑄 𝑟𝑠𝑐𝑡 is the freight flow from the region (prefecture) r to s of commodity c at year t, Class is a categorical dummy variable of urban hierarchy discussed in Section 4 where the total number of categories is N, and X rt is a vector of regional variables capturing the regional characteristics. Fixed effects in time (three-time points),θ t , and commodity (**types of commodities), δ c are also included.

On the determinants of freight rates, the equation to be estimated is written as follows:

ln 𝑃 𝑟𝑠𝑐𝑡 = 𝛼 + � 𝛽 𝑟 𝐶𝑙𝑎𝑠𝑠 𝑢 𝑢=𝑁 + 𝜎ln𝑄 𝑟𝑠𝑐𝑡 + γ𝑋 𝑟𝑡 + θ t + δ c + ϵ,
Where 𝑃 𝑟𝑠𝑐𝑡 is the freight rate from region r to s of commodity c at year t. Note that there are restrictions of samples for vertical freight flows as r≠s and N=20, and for horizontal freight flows as r=s and N=5, and total N=25 (=5 levels *5 levels). Table 1 summarises the statistics on freight flows and freight rates.

Regression results

Table 2 reviews a short version of the results on vertical freight flows and rates..

Appendix 1 presents the complete estimation results. To control for regional characteristics, we introduce the distance, and to characterize origins and destinations, we used the log of population and the log of per capita income..

The population sizes of origin and destination UAs largely determine freight flows. Log of per capita GDP of origin is positive and statistically significant, while the one of destination is negative and statistically significant. These are the most critical variables explaining the variations in freight flows.

After controlling for these factors, some other time-invariant factors can capture regional differences. We considered the OD pairs of the different levels of the urban hierarchy as dummies (results in Table 2). All these coefficients are different from the benchmark, which are the freight flows bounding from class 1 to class 3. From or to class 1, comparison of downward and upward reveals that upward flows are always larger. For class 2 and class 4, downward flows are larger, whereas upward flows are larger for class 3. Among these, the statistical significance remains at 1-2, 1-5, 2-3, and 4-5, depicted in the right column of Table 2. As we have a smaller coefficient size for flows from-and to-higher classes 1 and 2, these suggest that flows from-and to-class 3, 4, and 5 are large after controlling for the population size.

Freight rates are negatively correlated with freight flows, meaning that a 10% increase in freight flows is associated with a 2.1% decrease in freight rates (see Appendix 1). This demonstrates the presence of economies-of-scale in truck transportation. This negative relation is substantial given the wide variations in freight flows among regions.

A further analysis of the results on the class dummies reveals that upward flows often have smaller coefficients. This means that after controlling for the population size and GDP of origins and destinations, t and the freight flows between o/d pairs, freight rates remain lower for upward flows. The differences between upward and downward are found for flows between 1-4, 1-5, 2-4, 2-5, and 3-5.

Table 3 presents the results for freight flows between UA belonging to a same level of the urban hierarchy. The freight flow is positively correlated with the population size from column (1). Namely, a 1% increase in the population size is associated with a 1.35% increase of freight flows. Column (2) shows negative relations between freight rates and flows. Instead of an all-in-one specification, an interaction term of the urban level with freight flow has been introduced. This result suggests that the extent of economies of scale is particularly important for class 1, and secondarily for class 2 [column (3)].

So far, the determinants of freight rates were explored, which revealed that freight flows explain the bulk of freight rate variations. An additional specification is searched to check the robustness of these arguments. All variables were converted to ratios (Table 4) to analyse the gaps in freight rates between back and front haul. They re-confirm the economies of density from the negative sign in the coefficient of the ratio of the log of freight flows. This means that a smaller gap in freight rates induces a larger gap in freight flows. Such a tendency may widen if the per capita GDP of the origin (of numerator) is comparatively larger. Interestingly, road distance is not statistically significant, suggesting that the degree of distance economy may be symmetric for a pair of UA.

Results and discussion

H1: The longer the distance, the lower the freight rates

This relationship is statistically significant and explained by the fixed/variable cost composition of road transport. The share of fixed cost per tk is lower for flows conveyed over longer distances. The road distance is negatively correlated with freight rates, as per Appendix 1.

H2:

The larger the UA, the higher the intra-urban freight rate

The nature of the cargo and its value explains this, which is different depending on the size of the city. Road congestion, which is highly dependent on the population density of the urban area, is usually higher in large metropolitan areas. Finally, yet importantly, labour costs and price index are also higher in large urban areas, which means that road transport companies should support higher costs, which are at least partly reflected in freight rates.

The regression analysis in Table 3 of column 3 does not verify this relationship.

The intra-urban freight rates are surprisingly cheaper at the highest level of the urban hierarchy when controlling population and GDP per capita effects. This could result from a higher efficiency of truck transport markets in large urban areas.

The UAs at the top levels of the urban hierarchy have a larger population and higher per capita GDP. As there are positive correlations of freight flows with population size and per capita GDP, and due to the presence of economies of scale, the resulting freight rates are not necessarily lower in the small UAs.

H3: Shipping downwards is more expensive than upwards

This relationship is mostly valid. Table 2 shows that the coefficients are mostly smaller for upwardflows. As the size of freight flows is controlled, these results suggest the presence of a matching problem where road transport companies find backhaul cargo for large urban areas easier as compared to smaller ones.

H4: The larger the flow, the lower the freight rates

This relationship is statistically significant and can be explained by economiesof-scale in transportation and a higher level of competition between truck companies.

H5: The characteristics of the origin UA have a stronger impact on freight rates than the characteristics of destination UA

This relationship is statistically significant. This may be related to the business characteristics in Japan, a country where shippers usually assume the transport costs until the establishment of the consignee (Cost, Insurance, and Freight). These variables are critical in determining freight rates.

Conclusion

Freight transport remains essential for urban growth and development in Japan, as well as in other countries. In this paper, we aimed to establish the impact of the spatial arrangement of freight flows on the ability of shippers to enjoy advantageous freight rates and turn this into a competitive advantage into the space economy. The uneven spatial patterns of freight rates observed in Japan suggest that urban areas are not competing in equal terms to attract and maintain economic activities. Whereas much attention has been paid in the past to flow related aspects, particularly in the context of global trade, considering freight rates emphasises the often-neglected freight advantages of large urban areas. The latter was the core subject of this paper. This paper has analysed, for the first time, the relationship between freight rates and the position of urban areas within the Japanese urban hierarchy. The joint consideration of the size of the urban area and patterns of upward and downward flows provided a valuable framework for understanding inter-urban freight rates. The work has focused on reasons that may lead to freight rate differences and revealed that freight flows and distance largely determine the freight rates between urban areas. Beyond these two sources of explanation, other factors play non-negligible roles.

The differences in the size of the urban areas of origin and destination also influence freight rates, and hence, shipping cargo from small to a large urban area is cheaper than vice versa. This means that the firms located in small urban areas may benefit from lower freight rates when shipping cargo to other urban areas. Conversely, large urban areas may suffer from higher inter-urban freight rates. When there is a wide population gap between the urban areas of origin and destination, there is also a wide gap between the front haul and backhaul freight rates. This confirms the results of previous works and highlights the importance of efficiency issues in truck transport.

Finally, other characteristics such as the economic performance of urban areas of origin and destination, measured by their GDP per capita, play a role in the formation of freight rates. The characteristics of the origin UA turned to be more important than those of the destination UA. This could be a regional specificity since Japanese shippers usually include transport costs in the price of the goods they sell (Cost, Insurance, and Freight). The application of this empirical framework to other regional contexts such the US or France should provide more evidence to improve to our understanding of the determinants of freight rates.

The observed differences in intra-urban freight rates may have implications for the logistical policies of shippers2 . They suggest, on one hand, that shippers sending their cargo to other urban areas may be able to balance some of the intra-urban rates which can be particularly high in large urban areas. On the other hand, this compensation may be harder to achieve for shippers with a narrow (intra-urban) scope. Public authorities can decide on compensating shippers oriented to the intra-urban market for their potentially higher transport costs. This suggests the necessity for incorporating the spatial scope of firms' freight flows in the urban freight policies.

Figures

  possibly a counterintuitive, is related to a relative specialization of prefectures within Tokyo MA in freight flows of different scope. While Tokyo prefecture polarizes most of the -short-distance -flows of the neighbouring areas, Yokohama appears to be distant prefectures.Based on the former maps and the definition of the Major Metropolitan Areas (MA) of the Statistics Bureau of Japan, data on freight movements were aggregated in five hierarchical levels. The first two levels (1 and 2) contain the three MAs of Tokyo, Osaka, and Nagoya. Suburban prefectures have been included when most of their municipalities belonged to one of the three Major Metropolitan Areas, whose definition rely on commuting patterns. A third level (3) is defined with the other prefectures containing core MAs of more than 2 million people: Fukuoka, Hiroshima, Shizuoka, and Miyagi. Additionally, all the other prefectures have been assumed to constitute another two groups (4 and 5) corresponding to the least intensively-urbanised levels of the hierarchy. Hokkaido and Okinawa, which are the islands in the far North and South of the country, were excluded from our analysis. The latter have very specific freight patterns resulting from their population size, surface, peripheralityand lack of direct truck (road) connections with the two largest islands. Figure3presents the population of the prefectures in the five hierarchical levels, and the map in Figure4indicates their location.

Figure 1 .

 1 Figure 1. Main road transport flows. Source: Authors. Data source: RCMS

  1 shows the complete results. The sample size is 17390, and the estimations include fixed effects in time and commodity. Robust standard errors are clustered at pairs of the origin-destination prefecture. The number of stars indicates the statistical significance at p<0.01, ** p<0.05, * and p<0.1.Table 3.:Horizontal freight flows and freight rates (The origin UA and the destination UA belong to the same hierarchical level)

Table 1 .

 1 Summary statistics of freight flows and rates by direction between UA

	Tables
			Log of freight flow			Log of freight rates
	Movements of freight
		Mean	Std. Dev.	Freq.	Mean	Std. Dev.	Freq.
	From 1 to 2	5.34	2.16	2,099	3.74	0.85	2,099
	From 1 to 3	5.68	1.99	1,284	3.72	0.87	1,284
	From 1 to 4	5.84	2.29	2,738	4.05	0.91	2,738
	From 1 to 5	3.87	2.06	4,842	3.95	0.94	4,842
	From 2 to 1	5.82	1.99	2,099	3.65	0.76	2,099
	From 2 to 3	5.46	2.09	2,043	3.65	0.78	2,043
	From 2 to 4	4.70	2.09	3,980	3.76	0.79	3,980
	From 2 to 5	4.12	2.22	8,049	4.14	0.92	8,049
	From 3 to 1	5.68	2.06	1,284	3.61	0.95	1,284
	From 3 to 2	4.99	2.30	2,043	3.73	0.91	2,043
	From 3 to 4	4.75	2.24	2,362	3.74	0.85	2,362
	From 3 to 5	4.05	2.52	4,652	3.98	0.94	4,652
	From 4 to 1	5.89	2.45	2,738	3.93	0.91	2,738
	From 4 to 2	4.67	2.28	3,980	3.65	0.88	3,980
	From 4 to 3	4.83	2.23	2,362	3.66	0.93	2,362
	From 4 to 5	3.21	2.43	8,475	3.94	0.97	8,475
	From 5 to 1	4.16	2.27	4,842	3.67	0.97	4,842
	From 5 to 2	3.96	2.58	8,049	3.99	1.00	8,049
	From 5 to 3	4.04	2.48	4,652	3.88	0.99	4,652
	From 5 to 4	3.00	2.50	8,475	3.96	1.01	8,475
	Total	4.26	2.48	81,048	3.88	0.95	81,048
	Within 1	9.07	2.48	528	5.41	1.25	528
	Within 2	8.60	2.55	881	5.17	1.24	881
	Within 3	9.15	2.12	526	4.82	1.11	526
	Within 4	8.24	2.46	1,114	4.95	1.21	1,114
	Within 5	7.43	2.56	2,310	5.24	1.31	2,310
	Total	8.12	2.58	5,359	5.14	1.27	5,359

Table 2 .

 2 Upward and downward freight flows and freight rates

	Dependent variable	Class	Class	Downward	Upward		Difference
	Freight flows	1	2	-1.271	***	-0.645	***	-0.626 *
		1	3	0		0.086		-0.086
		1	4	0.205		0.445	**	-0.240
		1	5	-0.168		0.306		-0.474 ***
		2	3	0.552	***	0.012		0.540 ***
		2	4	0.504	***	0.503	**	0.001
		2	5	0.485	**	0.399		0.086
		3	4	1.053	***	1.181	***	-0.128
		3	5	1.063	***	1.141	***	-0.078
		4	5	1.097	***	0.849	***	0.248 ***
		Log of population (origin)		1.537	***
		Log of population (dest.)		1.671	***
		Log of per capita GDP (origin)		0.476	*
		Log of per capita GDP (dest.)		-1.022	*
	Freight rates	1	2	-0.271	***	-0.283	***	-0.012
		1	3	0		-0.127		-0.127
		1	4	0.17	***	0.014		-0.156 *
		1	5	-0.002		-0.296	***	-0.294 ***
		2	3	-0.183	***	-0.167	**	0.016
		2	4	-0.16	***	-0.314	***	-0.154 ***
		2	5	0.038		-0.237	***	-0.275 ***
		3	4	-0.049		-0.145	*	-0.096
		3	5	0.031		-0.12		-0.151 **
		4	5	-0.123	*	-0.177	**	-0.054
		Log of population (origin)		0.041	*
		Log of population (dest.)		0.134	***
		Log of per capita GDP (origin)		0.408	***
		Log of per capita GDP (dest.

  Robust standard errors clustered by each prefecture are shown in parentheses. The number of stars indicates the statistical significance at *** p<0.01, ** p<0.05, * and p<0.1.

		**	-0.097	-0.845
		(0.226)	(0.185)	(0.902)
	Class dummy: 3	1.192***	-0.327*	-1.200
		(0.208)	(0.168)	(0.833)
	Class dummy: 4	1.123***	-0.296	-1.674**
		(0.260)	(0.221)	(0.787)
	Class dummy: 5	1.048***	-0.125	-0.896
		(0.352)	(0.267)	(0.744)
	Log of population	1.352***	0.125	0.134
		(0.171)	(0.141)	(0.139)
	Log of per capita GDP	0.297	1.315***	1.316***
		(0.450)	(0.351)	(0.355)
	Constant	-14.181***	-4.399	-3.708
		(4.093)	(2.859)	(3.102)
	Year fixed effects	Yes	Yes	Yes
	Commodity fixed effects	Yes	Yes	Yes
	Observations	1,003	1,003	1,003
	R-squared	0.708	0.494	0.496
	Notes:

Table 4 .

 4 Inter-freight market: Freight flows and freight rates (ratio) Robust standard errors are clustered at pairs of the origin-destination prefecture. The Appendix presents detailed results. The number of stars indicates the statistical significance at *** p<0.01, ** p<0.05, * and p<0.1.

		(1)	(2)
		Ratio of freight rates	Ratio of freight rates
	Ratio of log of freight flow	-0.229***	-0.229***
		(0.005)	(0.005)
	Class dummy: 2	0.141	0.094
		(0.151)	(0.162)
	Class dummy: 3	-0.169	-0.261
		(0.134)	(0.193)
	Class dummy: 4	-0.774*	-0.835*
		(0.429)	(0.438)
	Class dummy: 5	-1.113**	-1.066*
		(0.556)	(0.558)
	Road distance		-0.009
			(0.012)
	Ratio of log of population	-0.439	-0.440
		(0.369)	(0.369)
	Ratio of log of per capita GDP	-0.438*	-0.437*
		(0.241)	(0.241)
	Constant	1.098*	1.068*
		(0.567)	(0.568)
	Origin fixed effects	Yes	Yes
	Destination fixed effects	Yes	Yes
	Year fixed effects	Yes	Yes
	Commodity fixed effects	Yes	Yes
	Observations	11,379	11,379
	R-squared	0.269	0.269
	Notes:

The authors are thankful to the reviewer who has raised this important point.


Pierre Levasseur
email: pierre.levasseur@inrae.fr.

School starting age and nutritional outcomes: Evidence from Brazil

Recent studies reported that the age of primary school enrolment is a major driver of educational achievement and adult income, but its impacts on childhood health and nutrition remain largely unknown, particularly in developing countries where childhood stunting and overweight coexist. In Brazil, children are supposed to enrol in primary school the year they turn 6. Using a database of middle school students in Brazil based on a 2015 survey, I implemented an instrumental variables strategy using quasi-exogenous variations in the students' birthdates to isolate the impact of late primary school enrolment (i.e., older than 6 when enrolled) on height-forage and body mass-for-age indicators. Overall, late enrolment has protective effects against hazardous weight gain (-0.14 z-score unit) but significantly increases the risk of moderate stunting (by 1.5% points). Heterogeneity in family backgrounds may explain these results. Indeed, delayed school enrolment is particularly detrimental for the nutritional status of students from underprivileged settings. In terms of public policy, rather than changing school starting age, this study highlights the importance of focusing on pathways to fight both stunting and overweight conditions in Brazilian children.

Introduction

School starting age is considered as an important instrument of public policy to improve the aggregated level of human capital and promote a country's economic development [START_REF] Ryu | Starting early and staying longer: the effects of a Brazilian primary schooling reform on student performance[END_REF]. While the great majority of studies focused on the effects of delayed school enrolment on educational attainment and mental health outcomes, I propose to analyse its impacts on health and nutritional outcomes.

All countries have administrative birthdate cut-offs for school enrolment, providing a quasi-experimental design that makes it possible to statistically compare children who start school younger (around age 5.5) with their counterparts who start 1 year older (around age 6.5) [START_REF] Angrist | Does compulsory school attendance affect schooling and earnings?[END_REF]. Using the quasi-random variation in school starting age induced by birthdate, the labour economics literature emphasized the positive effects of delayed school enrolment on educational achievement and labour market outcomes, at least for wealthy countries [START_REF] Bedard | The persistence of early childhood maturity: international evidence of long-run age effects[END_REF][START_REF] Datar | Does delaying kindergarten entrance give children a head start?[END_REF][START_REF] Mcewan | The benefits of delayed primary school enrollment discontinuity estimates using exact birth dates[END_REF]. 1 In addition to showing greater readiness for learning and integrating into the school environment, older children are less vulnerable to negative school externalities (e.g. social stigmatization, peer effects) than their younger counterparts [START_REF] Black | Too young to leave the nest? The effects of school starting age[END_REF][START_REF] Stipek | At what age should children enter kindergarten? A question for policy makers and parents[END_REF].

Research in health economics considered mental health as a potential mediator in the relationship between school starting age and socioeconomic success. Indeed, several studies found that delayed school enrolment reduces the risk of behavioural problems such as inattention, hyperactivity, and other disruptive behaviours [START_REF] Balestra | Summer-born struggle: the effect of school starting age on health, education, and work[END_REF][START_REF] Dee | Teen drinking and educational attainment: evidence from two-sample instrumental variables estimates[END_REF][START_REF] Dee | The gift of time? School starting age and mental health[END_REF][START_REF] Mühlenweg | Effects of age at school entry (ASE) on the development of non-cognitive skills: evidence from psychometric data[END_REF]. However, the impact of school starting age on other health dimensions such as physical health and nutrition remains largely unknown and understudied [START_REF] Bahrs | Unlucky to be young? The long-term effects of school starting age on smoking behavior and health[END_REF].

Although several studies analysed the effect of school exposure on childhood obesity, namely when junk food is available in school [START_REF] Anderson | Reading, writing, and refreshments are school finances contributing to children's obesity?[END_REF][START_REF] Schanzenbach | Do school lunches contribute to childhood obesity?[END_REF], limited research has focused on the nutritional consequences of school starting age. To my knowledge, [START_REF] Anderson | Is being in school better? The impact of school on children's BMI when starting age is endogenous[END_REF], [START_REF] Zhang | Does early school entry prevent obesity among adolescent girls?[END_REF], and [START_REF] Chang | The role of formal schooling on weight in young children[END_REF] were the first to compare weight outcomes between early-and late-enrolled students in the US. [START_REF] Mak | Does School Starting Age Matter? The Impact of School on Childhood Obesity, Diet and Time Use in Australia[END_REF] applied a similar approach to the Australian context. However, each study reported different findings. While [START_REF] Zhang | Does early school entry prevent obesity among adolescent girls?[END_REF] and [START_REF] Chang | The role of formal schooling on weight in young children[END_REF] found a higher risk of being obese among late-enrolled girls and boys, respectively, Mak (2018) observed a higher risk of being obese among early-enrolled students (especially for girls), and [START_REF] Anderson | Is being in school better? The impact of school on children's BMI when starting age is endogenous[END_REF] found no significant weight gap between early and delayed enrolments (independent of gender). Given this uncertainty in the nutritional impact of school starting age, more research is needed to understand how delaying school entrance may affect childhood bodyweight. The results are expected to be even more variable in poorer countries where stunting often persists and childhood overweight dramatically increases [START_REF] Doak | Overweight and underweight coexist within households in Brazil, China and Russia[END_REF]. In fact, late school enrolment systematically delays the exposure to (often free) school meals and may make children dependent on (risky) family feeding behaviours longer [START_REF] Thibault | Prevalence and factors associated with overweight and obesity in French primary-school children[END_REF]; this is relevant in terms of calorie intake and nutrient quality and diversity, especially in underprivileged settings [START_REF] Anderson | Is being in school better? The impact of school on children's BMI when starting age is endogenous[END_REF]. In line with this issue, [START_REF] Horta | Consuming school meals improves Brazilian children's diets according to their social vulnerability risk[END_REF] reported in poor Brazilian areas higher consumption of fruit and vegetables versus lower consumption of ultra-processed food and soft drinks among children who usually receive school meals compared to children who do not (usually) use school food services.2 Malnourishment in young childhood significantly impairs physical and mental growth and may contribute to poor lifelong health. In Ghana, [START_REF] Gelli | A school meals program implemented at scale in ghana increases height-for-age during midchildhood in girls and in children from poor households: a cluster randomized trial[END_REF] showed that receiving school meals decreased the risk of stunting by significantly increasing the average height-for-age of primary school children aged between 5 and 8, especially in households living below the poverty line. In rural South Africa, a school program that provides free school meals was shown to reduce both the stunting and overweight rates among children aged from 6 to 12 [START_REF] Graham | Double trouble: Addressing stunting and obesity via school nutrition[END_REF].

Late school enrolment is also likely to increase childcare expenditure, which may directly impair household food security. In such cases, early school attendance would act as a social protection for underprivileged families by alleviating household food pressures [START_REF] Bakhshinyan | Assessing poverty alleviation through social protection: school meals and family benefits in a middle-income country[END_REF]. Likewise, the literature suggests that a child's school enrolment increases his/her mother's employment, especially for single mothers who then do not have to provide constant care for younger children [START_REF] Gelbach | Public schooling for young children and maternal labor supply[END_REF][START_REF] Berlinski | The effect of a large expansion of pre-primary school facilities on preschool attendance and maternal employment[END_REF]. Hence, in addition to incurring extra childcare costs, late school enrolment is likely to delay parental employment and reduce family incomes over a period. Such transitory constraints could make underprivileged households highly vulnerable to food insecurity episodes, which may impact the child's nutritional status and growth [START_REF] Leete | The effect of income shocks on food insufficiency[END_REF].

The aim of this study is to fill the literature gap on the potential impacts of school starting age on stunting and body mass indicators in the context of a developing country. Based on a rich and recent survey targeting a large sample of Brazilian middle school children (aged 11-15), I implement an instrumental variables (IV) strategy using assumed exogenous variations in birthdate to isolate the impacts of delayed school enrolment. To measure stunting and body mass indicators, I adjust the objective measurements of height and weight collected by the survey's trained staff for age and gender. The focus on Brazilian middle school children makes this work highly original since the potential effects of school starting age on nutritional outcomes are particularly uncertain in the context of developing countries, where child stunting and overweight often coexist [START_REF] Doak | Overweight and underweight coexist within households in Brazil, China and Russia[END_REF].

Overall, the results show that early enrolment increases the ageadjusted body mass index (BMI-for-age) and the risk of being overweight, especially for boys. These findings echo previous studies that reported a protective effect of delayed enrolment against weight gain [START_REF] Mak | Does School Starting Age Matter? The Impact of School on Childhood Obesity, Diet and Time Use in Australia[END_REF], educational failure, and mental health disorders [START_REF] Black | Too young to leave the nest? The effects of school starting age[END_REF][START_REF] Mcewan | The benefits of delayed primary school enrollment discontinuity estimates using exact birth dates[END_REF]. However, this protective effect may only concern children from privileged family backgrounds. I find that late enrolment reduces BMI-for-age and height-for-age and increases stunting, especially among individuals from underprivileged backgrounds. In contrast, late-enrolled children from privileged background are less likely to be underweight or overweight and have no stunting risks. Several factors may explain this socioeconomic heterogeneity in the nutritional effect of school starting age. First, early enrolment can have health benefits for children from underprivileged background insofar as delayed enrolments may involve extra costs related to longer childcare and parental unemployment (e.g. reducing household food insecurity). Likewise, one can assume that late enrolment delays access to free and dietetic school meals and hence impairs child growth in underprivileged households because of potential nutritional deficiencies.

The rest of the article is organized as follows. Section 2 describes the Brazilian education system. In Section 3, I describe the data and methods. The results are presented in Section 4, and finally, in Section 5, I conclude and provide public policy recommendations.

The Brazilian education system

The Brazilian education system is divided into three school levels: preschool (three grades), elementary school (including five grades of primary school and four grades of middle school) and high school (three grades). Preschool education is entirely optional and rarely free in Brazil. Only primary school and middle school are free and compulsory. In 2006, reform n • 11.274/2006 changed the age of primary school enrolment by adding one grade and advancing the age of primary school enrolment to 6 years old. Before the 2006 reform, compulsory school ranged from age 7-14 (including four grades of primary school and four grades of middle school). Brazilian states had until 2010 to comply; but most Brazilian schools already did so by 2007 [START_REF] Ryu | Starting early and staying longer: the effects of a Brazilian primary schooling reform on student performance[END_REF].

In Brazil, the school year generally lasts from February to December (July is free for half-year holidays and January is free for annual holidays). Since 2006, Brazilian children are eligible for first enrolment in primary school if they turn 6 before March 31 of the same year (Fig. 1). 3This national rule creates a 1-year difference between children born in April (who start school at 6 years old and 10 months) and children born in March (who start school at 5 years old and 10 months). However, the reality is not so clear cut: many Brazilian states continued to choose their own cut-off date for primary school entry and did not uniformly apply the federal date of March 31. According to [START_REF] Ryu | Starting early and staying longer: the effects of a Brazilian primary schooling reform on student performance[END_REF], most of states selected a cut-off date between February and April.

Data and methods

Data

The data were from the second sample of PeNSE 2015 (National Survey of Student Health). Designed by the Brazilian Institute of Geography and Statistics (Portuguese acronym IBGE) and the Health Ministry and supported by the Education Ministry, this was the third crosssectional survey (the two first were conducted in 2009 and 2012). The sample included 371 public and private schools and more than 16,000 students aged from 11 to 19, but it is only representative of the Brazilian population aged from 13 to 17 [START_REF] Oliveira | Características da Pesquisa Nacional de Saúde do Escolar -PeNSE[END_REF]. The survey was directly administered to students in the form of a numerical questionnaire and provides a wealth of information on birthdate (month and year of birth), 4 health-related events and behaviours, as well as about family backgrounds such as owned assets and maternal education. In addition, it provides clinical data such as the height and weight of individuals (measured by professionals using standard equipment in a dedicated session). 5 To exclude children not eligible by the 2006 ′ s educational reform (which changed the compulsory age of primary school entry), I focused on middle school children who were at least 6 years old in 2006 (eligible to the reform), i.e. those who were born from 2000 to 2004 and were between 11 and 15 years old in 2015.

Model

Let consider the following structural linear model:

Y i = β 0 + β 1 LateEnrollment i + β 2 X i + ε i
Y i refers to nutritional and health outcomes of an individual i, including: (i) the body mass index (BMI) adjusted for age and gender using the World Health Organization (WHO, 2006) correction (z-score), 6 (ii) the BMI clinical classification directly measured by the survey staff using the [START_REF] Who | WHO child growth standards: length/height for age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age, methods and development. WHO Child Growth Standards: Length/Height for Age, Weight-for-Age, Weight-for-Length, Weight-for-Height and Body Mass Index-for-Age, Methods and Development[END_REF] correction (e.g. overweight, and underweight dummies), 7 (iii) the height-for-age (z-score), and (iv) a dummy of moderate stunting (equal to 1 if height-for-age < -2 z-scores, 0 otherwise). In the literature, BMI is considered a short-term indicator of nutritional status since weight depends to a great extent on current food consumption and lifestyle [START_REF] Thomas | How does mother's education affect child height?[END_REF]. In contrast, height-for-age is considered a long-term indicator of health status since physical growth strongly reflects nutritional deprivation and maternal risk behaviours from gestation to early childhood [START_REF] Thomas | How does mother's education affect child height?[END_REF].

X i refers to the observed characteristics of an individual i. In accordance with the existing literature analysing the socio-environmental causes of child nutritional statuses (e.g. [START_REF] Pongou | Household and community socioeconomic and environmental determinants of child nutritional status in Cameroon[END_REF], I control for individual and family characteristics. At the individual level, I take standard demographic factors into account: gender and race (white, black, Asian, mixed, or Amerindian). At the household level, I control for socio-demographic factors including household size, a household wealth index summing owned assets (as a proxy of family income), 8 and the mother's education level. Finally, I include school fixed effects and birth month fixed effects interacted with where the school is located in Brazil (North, North-East, South-East, South or Centre-West) to neutralize area-and time-specific heterogeneity (e.g. cultural, geographical, and climate heterogeneity).

LateEnrollment i refers to the enrollment status, which, for each grade, distinguishes younger peers (early enrollment) from older peers (late enrollment). In Brazil, the school year generally starts in February and ends in December. Assuming that the school year starts in February for all Brazilian middle schools, this means that a child born at the beginning of February would start primary school around age 6, a child born between February and the cut-off date (oscillating between March and April depending on states and municipalities) would start before age 6 (i. e. around age 5.5), but a child born after the cut-off date will start primary school 1 year older (i.e. around age 6.5). The state-and municipalspecific administrative rules for primary school enrolment create a fuzzy discontinuity in the birth month distribution by introducing a 1-year gap in primary school enrolment between children born before and after the cut-off date. Since the exact cut-off date is unknown for each school of the sample, I use a calculation to proxy school starting age and distinguish between early and late enrolment based on the age of children when school started (i.e. assuming February as school year starting date). Specifically, using reported birthdate (in month and year) and information on the grade of each individual i in 2015, I attribute the value 0 if a child was born after February f years ago (i.e. younger than 6 years old when enrolled in primary school), and the value 1 if a child was born before February f years ago (i.e. older than 6 years old when enrolled in primary school). f is the theoretical number of years between birth and a given school grade (i.e. the expected age of a child for each school grade based on the administrative rule). In Brazil, f takes the values 11, 12, 13, and 14 for grades 6, 7, 8, and 9 of primary school (i.e. middle school), respectively. Fig. 1 clearly illustrates how each individual in the database is classified between early enrolment (=0) and late enrolment (=1). Table 1 lists the number of observations for both enrolment statuses, and Fig. 2 shows the density functions for each Source: PeNSE 2015, Sample 2.

5 This is not the case for the first sample of PeNSE 2015, which included more than 100,000 students in the final grade of middle school (9 • ano do ensenino basico).

6 Before z-score adjustment, individual BMI was obtained dividing weight (kg) by squared height (m). 7 The adjusted childhood underweight and overweight thresholds correspond to a standard adult equivalent (i.e. <18.5 for underweight status and >25 kg/ m 2 for overweight status). 8 The wealth index is a 5-score index summing the five following assets if owned by household: home landline, a personal mobile phone, home computer, Internet access at home, and a car owned by the household.

grade. 9

Identification strategy

In the study context, the identification of causal effects involves notable statistical complications. More specifically, endogeneity bias may influence the relationship between school starting age and nutritional outcomes. Indeed, parents might voluntarily delay school enrolment of weak children (e.g. suffering from specific illness or characterized by a lower height-for-age or lower weight-for-age). For instance, [START_REF] Alderman | Preschool nutrition and subsequent schooling attainment: longitudinal evidence from Tanzania[END_REF] observed that stunted children in Tanzania have a higher probability of delayed enrolment than healthy children. Such an endogeneity problem would tend to overstate the positive effect of school starting age on stunting and underweight because there is a potential overrepresentation of stunted and underweight children who enrolled school older.

Statistically speaking, it could be possible to use the 1-year jump between children born in March and April of the same year to identify the effects of a delayed school start on nutritional indicators. Unfortunately, although most of states chose between February and April as cut-off date [START_REF] Ryu | Starting early and staying longer: the effects of a Brazilian primary schooling reform on student performance[END_REF], the fuzzy allocation of early-and late-enrolled children across states makes the use of a regression discontinuity design impossible. Hence, to deal with potential endogeneity problems, I opt for a two-stage least squares estimator based on an IV approach inspired by [START_REF] Bedard | The persistence of early childhood maturity: international evidence of long-run age effects[END_REF] and [START_REF] Angrist | Does compulsory school attendance affect schooling and earnings?[END_REF]. More specifically, I use birthdate (month and year) as an exogenous determinant of school starting age (early versus late enrolments), which is relative to grade information and the school cut-off date. Theoretically, the birthdate is a good instrument to neutralize the suspected endogeneity caused by the parental decision to delay school entry of weak children. Indeed, one can assume a quasi-random distribution of birthdate in pre-existing nutritional status (before school enrolment) and the parental decision to delay school entry, so there is no direct link between birthdate and current nutritional status. More formally, the two-step IV model is formulated as follows:

{ Y i = δ 0 + δ 1 LateEnrollment i + δ 2 X i + ∂ i with LateEnrollment i = γ 0 + γ 1 IV i + γ 2 X i + u i }
As modelled above, a first-stage estimation is used to introduce fitted values of enrolment status ( LateEnrollment i ) uncorrelated with residuals (∂ i ) in a second-stage equation. Such an IV strategy relies on the introduction of instruments in first-stage estimates, which must be strong predictors of enrolment status (relevance condition) but uncorrelated with residuals (exclusion restriction condition). In other words, if the selected instruments meet both conditions, δ 1 refers to the effect of exogenous variations in delayed enrolment on nutritional outcomes. Like [START_REF] Bedard | The persistence of early childhood maturity: international evidence of long-run age effects[END_REF], I use birthdate data to instrument enrolment status measured in dummies of birth month per year. There are 12 birth months per year, and the sample includes children born from 2000 to 2004 (a 5-year period), corresponding to 60 birth month dummies.

The first validity condition for an instrument is to be a strong predictor of the assumed endogenous regressor, i.e. delayed school enrolment. [START_REF] Bound | Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak[END_REF] questioned the strength of birth season as an 9 Obviously, schools and parents do not systematically meet the Brazilian rule of primary school starting age. As shown in Table 1, there are more lateenrolled students in the sample since this group is likely to include students whose parents (intentionally or not) delayed school enrollment. Moreover, since I use a calculation to proxy school starting age and distinguish early/late enrollments (there is no information about actual school starting age), some students are mechanically misclassified: all students who repeated a grade are classified into the late enrollment group, and the few students who skipped a grade are presumably included in the early enrollment group. This fuzzy allocation of early-and late-enrolled students in the sample justifies the use of twostep IV regressions. To check for the robustness of the results against these misclassification errors, I ran non-reported estimates restricting the sample to students who have the correct age for the correct grade (hence excluding students who repeated or skipped a grade). Similar results were obtained.

instrument in the study context of [START_REF] Angrist | Does compulsory school attendance affect schooling and earnings?[END_REF]. However, the first-stage estimates run here are not affected by such a weakness problem. As shown in first-stage estimates reported in Table 2, each birth month dummy has a significant effect on the probability of delayed enrolment in primary school (at the 1% level), and F-statistics and partial R-square values on excluded instruments are both high. According to [START_REF] Bound | Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak[END_REF], both latter indicators are useful to assess the strength of an instrument. 10 Second, to be valid, IV estimates must comply with the exclusion restriction condition. It means that variations in enrolment status induced by birthdate variations are uncorrelated with unobserved variations in health and nutritional outcomes. Unfortunately, the exclusion restriction assumption is not directly testable and always remains debatable. This assumption could be violated if children born at different times have higher or lower unobserved height-for-age or BMIfor-age. For instance, ethnicity-specific seasonality in conception behaviours might be a concern [START_REF] Buckles | Season of birth and later outcomes: old questions, new answers[END_REF], especially in a country like Brazil where racial segregation is still common [START_REF] Dressler | Culture, socioeconomic status, and physical and mental health in Brazil[END_REF]. Likewise, as highlighted by [START_REF] Buckles | Season of birth and later outcomes: old questions, new answers[END_REF], since family backgrounds are highly correlated to season-of-birth and later outcomes, there is a risk that birthdate does not satisfy the exclusion restriction condition. For example, numerous families are likely to have a certain conception experience and might thus schedule the pregnancy to limit negative externalities such as affecting career plans. To limit this potential source of bias associated with racial and family backgrounds, I control the estimates (everything being equal) for race, family composition, and socioeconomic backgrounds. In addition, I systematically include school fixed effects and birth month fixed effects interacted with regions to alleviate potential direct correlations between the instruments (birthdate) and current nutritional outcomes.

Another potential concern that might violate the exclusion restriction condition relies on parental manipulation of conception or birthdate, with a view to intentionally delay the future school enrolment of their children 6 years later (i.e. which could bias first-stage estimates). Brazil has one of the highest rates of caesarean-section (C-section) births in the world, representing half of all deliveries in the country [START_REF] Boerma | Global epidemiology of use of and disparities in caesarean sections[END_REF]. The authors observed that the C-section rates in Brazil are the highest among mothers with high education levels. However, even if informed and educated parents can theoretically manipulate childbirth by controlling conception periods and/or opting for assisted deliveries (e.g. scheduling a C-section), it is unlikely they would intentionally schedule births to delay future school enrolment and maximize the child's educational success (expecting a readiness effect for example). Using a large database from Chile, which has a similar C-section rate, [START_REF] Mcewan | The benefits of delayed primary school enrollment discontinuity estimates using exact birth dates[END_REF] found no evidence of birthdate manipulation near the enrolment cut-off. Notwithstanding the presumed absence of birth manipulation, I checked for continuity of the birth month distribution around the administrative cut-off that separates early-and late-enrolled students in Brazil. I found no evidence of birth manipulation in the data. 11

Results

Descriptive statistics

The restricted sample includes more than 9000 middle school students aged between 11 and 15 (born after 2000) classified as early or late enrolment in primary school according to their birthdate and grade information (Table 1). Table 3 presents the sample means for all observed characteristics used in this study, according to enrolment status. It is worth noting that overweight children are now common in Brazil, with around 29% of the sample (middle school students aged from 11 to 15) classified as overweight in 2015. Underweight status is less prevalent but persists marginally (around 3%), and height-for-age in z-scores is positive but close to 0, suggesting a small proportion of stunting in Brazil (around 1% in the sample). Table 3 shows notable differences across school enrolment status. Both BMI-for-age and heightfor-age are higher among early-enrolled students (relatively younger than their grade peers) compared to later-enrolled students (relatively older than their grade peers). As explained earlier, the overrepresentation of children with lower height-for-age and BMI-for-age among later-enrolled students might be due to endogeneity in the relationship between enrolment status and health status. Indeed, some parents might prefer to keep their children with poor health (being smaller and thinner on average) at home longer, consequently delaying school entry. As shown in Table 3, Black and Mixed children born to mothers with low education are more likely to enrol later. In theory, the overrepresentation of initially healthier students from privileged households in the early enrolment group is likely to bias the effects of late enrolment on BMI-for-age and height-for-age. For this reason, multivariate estimates coupled with an IV strategy is used in the following section.

IV estimates

Table 4 lists IV estimates of the impacts of late enrolment (vs. early enrolment) on nutritional outcomes. In column 1, the whole sample is regressed. Gender-specific estimates are given in columns 2 and 3. In columns 4 and 5, I test for a heterogeneous effect based on the mother's education, distinguishing little education (if the mother did not go beyond middle school) from higher educational level (if the mother at least attended high school). Complete Table 4 is available in Table A1 in Online Appendix.

Overall, Table 4 shows that late-enrolled children have lower BMIfor-age than their peers who enrolled younger, per 0.14 z-score unit. Table 4 clearly reveals gender-specific effects regarding BMI-for-age, highlighting a stronger impact among boys (a reduction of 0.21 zscore unit for BMI-for-age and a reduction of overweight risk by 5.9% points). Moreover, I also detected a heterogeneous effect according to family backgrounds. Delayed enrolment increases the probability of being classified as normal weight among students with educated mothers (i.e. reducing the risks of underweight and overweight).

In contrast, Table 4 shows a negative effect of late enrolment on height-for-age (-0.30 z-score unit), which significantly increases the risk of moderate stunting by 1.5% points. Even if gender-specific results are unclear, there is clear heterogeneity according to family background. Among students with low-educated mothers, late enrolment significantly increases the risk of stunting by 4.9% points and height-forage by 0.74 z-score unit, while respective fitted coefficients are significantly lower among students with educated mothers.

Conclusion

This article analysed the impact of delayed school enrolment on nutritional and health statuses some years later, considering both stunting and excess weight indicators. Specifically, to assess the impact of late enrolments on BMI-for-age and height-for-age among a sample of 10 Given the presence of students and/or Brazilian states that did not comply with the law (regarding the cut-off date for school entry), the prediction is not perfect: fitted coefficients of birth month dummies are different from 1.0 that would be obtained with perfect compliance with the law. 11 A [START_REF] Mccrary | Manipulation of the running variable in the regression discontinuity design: a density test[END_REF] test revealed no significant distribution gap near the cut-off, indicating that the model is not biased by manipulation problems. Similarly, the Frandsen (2017) manipulation test, which is appropriate for discrete running variables, showed no significant gap regarding birth month around the cut-off (p-value = 0.779). middle school students aged between 11 and 15, I implemented IV estimates based on the quasi-randomness of birthdate that determines school starting age in Brazil.

The results indicate that delayed school entrance may affect both BMI-for-age and height-for-age indicators some years later. More importantly, they clearly highlight heterogeneous effects according to social backgrounds. Indeed, significant harmful effects were found among children from socially deprived backgrounds, for whom delayed enrolment was associated with lower height-for-age and BMI-for-age and higher risk of stunting. In contrast, delayed enrolment tends to have protective effects for children with more educated mothers, reducing the risks of being underweight and overweight (but not significantly increasing the risk of stunting).

Several reasons may explain these nutritional inequalities associated with school starting age. Delaying school enrolment may incur higher costs that make the family more vulnerable to economic shocks, for instance by increasing childcare expenditures and limiting parental employment and earnings [START_REF] Mcewan | The benefits of delayed primary school enrollment discontinuity estimates using exact birth dates[END_REF]. These economic shocks could have led to food deprivations and nutritional deficiencies in the past, thereby impairing children's physical and intellectual growth. Another explanation could be the longer exposure of late-enrolled students to (nutritionally poor) family meals and delayed access to dietetic school meals, as evidenced in the literature on nutrition [START_REF] Gelli | A school meals program implemented at scale in ghana increases height-for-age during midchildhood in girls and in children from poor households: a cluster randomized trial[END_REF][START_REF] Horta | Consuming school meals improves Brazilian children's diets according to their social vulnerability risk[END_REF]. Indeed, early school enrolment implies earlier access to free school meals, which is likely to offset family food deprivations during child growth and reduce the risks of unhealthy food intakes [START_REF] Von Hippel | The effect of school on overweight in childhood: gain in body mass index during the school year and during summer vacation[END_REF][START_REF] Anderson | Is being in school better? The impact of school on children's BMI when starting age is endogenous[END_REF].

The results also emphasized gender-specific trends. I found that younger enrolment in primary school (i.e. before 6 years old) significantly increases BMI-for-age and the risk of childhood overweight, especially for boys, which is consistent with the literature reporting beneficial impacts of late enrolment on educational outcomes among boys. In Chile, [START_REF] Mcewan | The benefits of delayed primary school enrollment discontinuity estimates using exact birth dates[END_REF] found higher risks of repeating first grade due to early enrolment among boys compared to girls. Citing works in psychology [START_REF] Stipek | At what age should children enter kindergarten? A question for policy makers and parents[END_REF], the authors speculated that boys of the same age might be less mature and less ready to absorb school contents than girls. The emotions associated with educational failure potentially affects nutrition and health outcomes by changing feeding behaviours [START_REF] Goldston | Reading problems, psychiatric disorders, and functional impairment from mid-to late adolescence[END_REF][START_REF] Gustafsson | School, learning and mental health: a systematic review[END_REF]. Hence, one can assume that the hazardous weight gain of early-enrolled boys in Brazil is partly driven by mental issues generated by increased educational failures. Furthermore, higher vulnerability of early-enrolled students to negative school externalities such as bullying [START_REF] Black | Too young to leave the nest? The effects of school starting age[END_REF] may also explain their weight gain, increasing the risk of suffering from mental health troubles and nutritional disorders [START_REF] Bauman | Associations among bullying, cyberbullying, and suicide in high school students[END_REF]. In summary, this study emphasized the ambiguous impact of school starting age on health and nutritional outcomes in developing countries such as Brazil. Globally, there are notable nutritional benefits for enrolling later, probably thanks to greater readiness for absorbing school content, higher maturity to manage knowledge tests, and lower sensitivity to negative school externalities such as bullying. However, late enrolment may have several hidden costs for underprivileged students (e.g. higher childcare expenditures, longer mother unemployment, delayed exposure to school meals), which makes many Brazilian families highly vulnerable to economic shocks and food insecurity with children more prone to nutritional deprivation during growth.

The strong heterogeneity in nutritional issues that characterizes Brazilian schools renders the school enrolment policy inefficient. For instance, introducing a delay in primary school enrolment will probably disadvantage lower social groups. Hence, decision makers should act directly by providing free school meals, anti-bullying and anti-obesity campaigns, and social protection programs for poor families with young children. Future research should focus on empirically identifying effective transmission pathways. Likewise, additional investigations aiming to replicate this research using different databases are needed to test the generalization and robustness of the results. The main limitation is the lack of data about exact school starting age (leading to the calculation of a proxy based on some debatable assumptions). Specifically, the results could be affected by misclassification issues, since students who repeated a grade are misclassified as being late-enrolled. Hence, the inclusion of grade repeaters into the late enrolment group might overstate the harmful nutritional effects observed among underprivileged students, assuming that grade retention is correlated with poor child health.

Fig. 1 .

 1 Fig. 1. Late versus early primary school enrolment in Brazil (theoretical age for a cut-off date of March 31 and a school year starting on February 1). Source: The author's analyses.

Fig. 2 .

 2 Fig. 2. Density functions of birthdate across enrolment status for each grade. Notes: The Y-line represents a kernel density function of students per grade. The X-line represents birthdate, in month per year centred on the cut-off that splits early and late enrolment in school (i.e. February). For instance, value 1 refers to February 2004, value 11 refers to December of 2004, value 12 to January of 2003, up to value 60 that refers to January 1999. Source: PeNSE 2015, Sample 2.

Table 1

 1 Sample distribution across school grades (frequencies).

	Grade	Late enrolment	Early enrolment	Total
	Middle school (6th grade)	1943	577	2520
	Middle school (7th grade)	2196	740	2936
	Middle school (8th grade)	1386	1033	2419
	Middle school (9th grade)	751	671	1422
	Total	6276	3021	9297

Table 2

 2 First step regressions of late enrolment on instruments and covariates.

	Dependent outcome: Delayed enrolment	Whole sample	Female	Male	Better educated mother	Mother with little education (incl. DKN)
	Male (dummy)	0.020 *			0.023 *	0.045 * **
		(0.010)			(0.013)	(0.010)
	Black (dummy)	0.051 * *	0.080 * **	0.015	0.042 *	0.048 * **
		(0.017)	(0.024)	(0.027)	(0.023)	(0.015)
	Asian (dummy)	0.023	0.022	0.023	0.008	0.048 *
		(0.026)	(0.033)	(0.031)	(0.044)	(0.026)
	Mixed (dummy)	0.011	0.015	0.006	0.011	0.032 * *
		(0.013)	(0.017)	(0.014)	(0.017)	(0.012)
	Amerindian (dummy)	0.008	-0.004	0.026	0.034	0.006
		(0.020)	(0.031)	(0.040)	(0.039)	(0.017)
	Household size (number)	0.003	-0.004	0.008 * *	-0.001	0.010 * **
		(0.003)	(0.006)	(0.003)	(0.005)	(0.002)
	Basic education (dummy)	-0.039 * **	-0.030	-0.054		-0.153 * **
		(0.012)	(0.029)	(0.033)		(0.021)
	High school (dummy)	-0.052 * **	-0.019	-0.081 *
		(0.016)	(0.028)	(0.037)
	University (dummy)	-0.061 * **	-0.078 * *	-0.057	-0.002
		(0.016)	(0.029)	(0.042)	(0.015)
	DKN (dummy)	-0.018	-0.024	-0.013		-0.110 * **
		(0.018)	(0.030)	(0.039)		(0.025)
	Wealth index (5-point score)	-0.014 * **	-0.015 * *	-0.012 * *	-0.021 * *	-0.010 * **
		(0.002)	(0.005)	(0.004)	(0.007)	(0.002)
	Instruments (birthdate)	YES* **	YES* **	YES* **	YES* **	YES* **
	Birth month fixed effects interacted with regions	YES	YES	YES	YES	YES
	School fixed effects	YES	YES	YES	YES	YES
	Constant	0.210 * *	0.329 *	0.196 * *	0.183 * *	0.401 * *
		(0.088)	(0.163)	(0.076)	(0.068)	(0.147)
	Observations	9215	4574	4641	3880	8301
	R-squared	0.575	0.577	0.619	0.623	0.479
	Partial R-squared on excluded instruments	0.391	0.381	0.417	0.413	0.281
	F-statistic on excluded instruments	1108.66	1192.28	604.99	1268.84	491.25
	P-value	0.000	0.000	0.000	0.000	0.000

Notes: Standard errors (in parentheses) are clustered on discrete months. For representativeness, each individual i is weighted using the weight parameter available in PeNSE 2015. Instruments are birth month per year (total 120 dummies), all with significant fitted coefficients. All covariates are included. The group of children with better educated mothers includes children with mothers who attended at least high school. The group of mothers with little education includes children with mothers who have at most a basic education and children who do not know their mother's education level. Significance level: * 10%, * *5%, * ** 1%. Source: PeNSE 2015, Sample 2.

Table 3

 3 Sample means across enrolment status.

		Early enrolment	Late enrolment	All students
	BMI-for-age (z-score)	0.45	0.38	0.40
	Underweight (dummy)	0.03	0.03	0.03
	Overweight (dummy)	0.30	0.28	0.29
	Height-for-age (z-score)	0.45	0.31	0.36
	Stunting (dummy)	0.01	0.01	0.01
	Male (dummy)	0.45	0.54	0.51
	Black (dummy)	0.10	0.15	0.13
	Asian (dummy)	0.05	0.04	0.04
	Mixed (dummy)	0.40	0.43	0.42
	Amerindian (dummy)	0.04	0.04	0.04
	Household size (number)	4.44	4.63	4.56
	Basic education (dummy)	0.20	0.23	0.22
	High school (dummy)	0.22	0.18	0.19
	University (dummy)	0.23	0.15	0.18
	DKN (dummy)	0.32	0.36	0.35
	Wealth index (5-point score)	3.58	3.10	3.26
	Notes: Each individual i is weighted using the weight parameter available in
	PeNSE 2015.
	Source: PeNSE 2015, Sample 2.

Table 4

 4 Impacts of late enrolment (vs. early enrolment) on health and nutritional outcomes (IV estimates). Standard errors (in parentheses) are clustered on discrete months. For representativeness, each individual i is weighted using the weight parameter available in PeNSE 2015. Instruments are birth month per year. All covariates are included. The complete table is available in Table A1 of the Appendix. The group of children with better educated mothers includes children with mothers who attended at least high school. The group of mothers with little education includes children with mothers who have at most a basic education and children who do not know their mother's education level. Significance level: * 10%, * *5%, * ** 1%. Source: PeNSE 2015, Sample 2.

		Whole sample	Male	Female	Better educated mother	Mother with little education (incl. DKN)
	BMI-for-age (z-score)	-0.140 * *	-0.213 *	-0.096	-0.083	-0.167 * **
		(0.071)	(0.118)	(0.076)	(0.073)	(0.048)
		N = 9213	N = 4573	N = 4640	N = 3880	N = 8299
	Underweight (dummy)	0.004	0.024	-0.013	-0.017 * *	0.015
		(0.011)	(0.020)	(0.011)	(0.009)	(0.012)
		N = 9215	N = 4574	N = 4641	N = 3880	N = 8301
	Overweight (dummy)	-0.045	-0.059 *	-0.029	-0.061 * *	-0.031
		(0.028)	(0.033)	(0.030)	(0.027)	(0.028)
		N = 9215	N = 4574	N = 4641	N = 3880	N = 8301
	Height-for-age (z-score)	-0.300 * **	-0.126	-0.474 * **	-0.186 * *	-0.739 * **
		(0.061)	(0.080)	(0.073)	(0.089)	(0.070)
		N = 9212	N = 4571	N = 4641	N = 3879	N = 8299
	Stunting (dummy)	0.015 * **	0.021 * *	0.005	0.003	0.049 * **
		(0.005)	(0.009)	(0.004)	(0.007)	(0.016)
		N = 9212	N = 4571	N = 4641	N = 3879	N = 8299
	Notes:

Similar findings were also observed in wealthy countries. For example, von Hippel et al. (2007) observed a higher increase in young US children weight during summer vacations than during the kindergarten and first-grade school years, suggesting that school exposure has a protective effect against weight gain. Likewise, comparing school meals and packed lunches in English primary schools,[START_REF] Evans | Impact of school lunch type on nutritional quality of English children's diets[END_REF] found that the former are of better nutritional quality, being richer in fibers, folates, proteins, zinc with lower sodium and sugar levels.

Before 2006, students used to start primary education in the calendar year they turned 7.

Unfortunately, exact birth dates are not available in the data.P. Levasseur

Acknowledgements

The database is publicly available online at: https://www.gov.br/sau de/pt-br/assuntos/saude-de-a-a-z/p/pesquisa-nacional-de-saude-do-es colar-pense, Data are anonymous and contain no personal information. The author is responsible for all errors. This study did not benefit from specific funding support. The author has no conflict of interest to declare. This research was supported by the INRAE program Global Food Security (GloFoodS).

Funding sources

This study did not beneficiated from specific funding support.

Conflict of interest statement

The author has no conflict of interest to declare.

Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.ehb.2021.101104.