# **1 Introduction**

Though the significance of public infrastructure in economic development is well established, how to efficiently allocate different types of infrastructure projects to meet development needs remains an important research and policy question. There is an urgent need to understand how different infrastructure networks interact and evolve over space. How much can fiscally constrained governments improve economic welfare by investing across different infrastructure types? How large are the economic gains of coordinating infrastructure investments in different regions? Should national governments prioritize coordination between different sectoral infrastructure planning agencies?

To answer these questions, we build a novel multi-sector spatial equilibrium model in which the evolution of public infrastructure is endogenously determined by a government that invests in the quality of public capital to maximize welfare. We study two types of public infrastructure—the electricity and road transportation networks—in a concurrent setting to assess the extent of misallocation and spatial complementarities in infrastructure provision.

The endogeneity of infrastructure investment is important because economic activity and the different infrastructure networks affect one another, which can lead to biased estimates in reduced-form settings. Improvements in public infrastructure can also have spillover effects that amplify the aggregate impact on economic activity. Moreover, public infrastructure investments are not randomly allocated in space and could be the result of the own interests of the government, such as political alignment or ethnic favoritism (Cadot et al., 2006; Brollo and Nannicini, 2012; Burgess et al., 2015).

In our model, the economy comprises a fixed set of microregions in which three sectors— agriculture, manufacturing, and services—produce tradeable varieties of final consumption goods.<sup>1</sup> The three sectors produce output using labor (which is freely mobile) and electricity as inputs.<sup>2</sup> Total factor productivities (TFPs) are partly determined endogenously by the equilibrium values of the population and the quality of the electricity flow (see, e.g., FisherVanden et al. (2015), Allcott et al. (2016) and Fried and Lagakos (2023)). This TFP impact of electricity indirectly affects the marginal cost of production and reduces the price at which firms in a particular location sell their products. Transportation improvements also reduce the cost of shipping goods. However, due to network spillovers, road improvements affect all locations that ship goods through affected routes. Additionally, infrastructure quality shapes the population distribution through its impact on wages.

The quantitative analysis focuses on the Brazilian spatial distribution of economic activity, public roads, and electricity supply quality in the year 2010. First, we ask how the spatial

> 1The Brazilian Institute of Geography and Statistics (IBGE) defines a microregion as a set of municipalities that are comparable in terms of social characteristics, geography, and production structure.

> 2Banerjee et al. (2020) argue that mobility of production factors is key for determining the benefits of infrastructure investments. Nevertheless, free mobility is not crucial for our results, as Appendix H shows.

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