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Power laws in productivity and firm size are well documented empirical regularities. As they are upper right‐tail phenomena, this paper shows that assuming asymptotic power functions for various model primitives (such as demand and firm heterogeneity) are sufficient for matching these regularities. This greatly relaxes the functional‐form restrictions in economic modeling and can be beneficial in certain contexts. We demonstrate this in a modified Melitz (2003) model, which embeds an innovation mechanism so as to endogenize the productivity distribution and generate both of the above‐mentioned power laws. We also investigate the model's welfare implications with regard to innovation by conducting a quantitative analysis of the welfare gains from trade.

Significance Socioeconomic attributes of cities (e.g., wages, education, industrial diversity, and crime) exhibit strong correlations with city size, as measured by population. It has thus been a major research objective to characterize and explain city-size distributions. Whereas city-size distributions are known to exhibit power laws at the country level, we find that they exhibit strikingly similar power laws when examined along a spatial hierarchy of regions within a country. Such a high degree of similarity could not be obtained if city sizes were generated by a random (growth) process. The fact that this regularity emerges along spatial dimensions in a recursive manner suggests the existence of spatial fractal structures. However, such estimated common power laws differ markedly across countries., City-size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from China, France, Germany, India, Japan, and the United States, we first document that large cities are significantly more spaced out than would be expected by chance alone. We next construct spatial hierarchies for countries by first partitioning geographic space using a given number of their largest cities as cell centers and then continuing this partitioning procedure within each cell recursively. We find that city-size distributions in different parts of these spatial hierarchies exhibit power laws that are, again, far more similar than would be expected by chance alone—suggesting the existence of a spatial fractal structure.

This article reviews interrelated power-law phenomena in geography and trade. Given the empirical evidence on the gravity equation in trade flows across countries and regions, its theoretical underpinnings are reviewed. The gravity equation amounts to saying that trade flows follow a power law in distance (or geographic barriers). It is concluded that in the environment with firm heterogeneity, the power law in firm size is the key condition for the gravity equation to arise. A distribution is said to follow a power law if its tail probability follows a power function in the distribution’s right tail. The second part of this article reviews the literature that provides the microfoundation for the power law in firm size and reviews how this power law (in firm size) may be related to the power laws in other distributions (in incomes, firm productivity and city size).

This paper studies optimal containment policy for combating a pandemic in an open- economy context. It does so via quantitative analyses using a model that incorporates a standard epidemiological compartmental model in a multi-country, multi-sector Ricardian model of international trade with full-fledged input-output linkages. We devise a novel approach in computing optimal national policies in the long run, and contrast these policies with a baseline in which countries maintain their current policies until vaccine availability. The welfare gains under optimal policies are asymmetric as the gains for the set of countries which should tighten up the containment measures are much larger than those which should relax. We also find that the welfare implications of optimal policies in open economies differ significantly from those in closed ones.

The household registration system (hukou system) in China has hampered rural-urban migration by posing large migration friction. The system has been gradually relaxed in the past few decades, but the reforms have been differential in city size. We find a striking contrast in migration patterns between years 2005 and 2015; rural people tended to move more to large cities in 2005, but more to small- and medium-sized cities in 2015. We calibrate a spatial quantitative model to the world economy in both years with China divided into rural, mega-city, and other-city regions. We find that alternative urbanization policies that are not differential and that are more laissez-faire substantially improve national welfare, in magnitudes that are comparable to the welfare gains from the trade liberalization that China has put in place in the past.

This paper studies the effect of foreign direct investment (FDI) on industrial agglomeration.Using the differential effects of FDI deregulation in 2002 in China on different industries, we find that FDI actually affects industrial agglomeration negatively. This result is somewhat counter-intuitive, as the conventional wisdom tends to suggest that FDI attracts domestic firms to cluster for various agglomeration benefits, in particular technology spillovers. To reconcile our empirical findings and the conventional wisdom, we develop a theory of FDI and agglomeration based on two counter-veiling forces. Technology diffusion from FDI attracts domestic firms to cluster, but fiercer competition drives firms away. Which force dominates depends on the scale of the economy. When the economy is sufficiently large, FDI discourages agglomeration. We find various evidence on this competition mechanism.

This chapter provides a review of the link between central place theory and the power laws for cities. A theory of city size distribution is proposed via a central place hierarchy a la Christaller (1933) either as an equilibrium results or an optimal allocation. Under a central place hierarchy, it is shown that a power law for cities emerges if the underlying heterogeneity in economies of scale across good is regularly varying. Furthermore, we show that an optimal allocation of cities conforms with a central place hierarchy if the underlying heterogeneity in economies of scale across good is a power function.

This paper provides a quantitative analysis of gains from trade in a model with head-to-head competition using Chinese firm-level data from Economic Censuses in 1995 and 2004. We find a significant reduction in trade cost during this period, and total gains from such improved openness during this period is 7.1%. The gains are decomposed into a Ricardian component and two pro-competitive ones. The pro-competitive effects account for 20% of the total gains. Moreover, the total gains from trade are 13 − 31% larger than what would result from the formula provided by ACR ( Arkolakis et al., 2012 ), which nests a class of important trade models, but without pro-competitive effects. We find that head-to-head competition is the key reason behind the larger gains, as trade flows do not reflect all of the effects via markups in an event of trade liberalization.

This paper discusses the effect of income inequality on selection and aggregate productivity in a general equilibrium model with non-homothetic preferences. It shows the existence of a negative relationship between the number and quantity of products consumed by an income group and the earnings of other income groups. It also highlights the negative effect of a mean-preserving spread of income on aggregate productivity through the softening of firms’ selection. This effect is however mitigated in the presence of international trade. In a quantitative analysis, it is shown that an excessively large mean-preserving spread of income may harm the rich as it raises firms’ markups on their purchases. This is contrary to the general belief that income inequality benefits the rich.

This paper explores whether and how corruption and competition-for-promotion motives affect urban land supply in the People's Republic of China. Conditional on demand-side factors, we find that corruption is highly correlated with an increase in land supply. The corruption effects are strongest for commercial land, followed by residential land, and then industrial land. To shed light on the competition motives among prefectural leaders, we examine how the number of years in office affects land supply and distinguish among different hypotheses. Our empirical results show robust rising trends in land sales. These results are consistent with the hypothesis that among prefectural leaders the impatience and anxiety in later years from not being promoted may contribute to an increase in land sales revenue in later years. We also find that prefectural leaders may aim for more land sales revenue over their first few years in office instead of seeking higher revenue in their first 1–2 years.

This paper develops an index of allocative efficiency that depends upon the distribution of mark-ups across goods and is separable from an index of standard Ricardian gains from trade. It determines how changes in trade frictions affect allocative efficiency in an oligopoly model of international trade, decomposing the effect into the cost-change channel and the price-change channel. Formulas are derived shedding light on the signs and magnitudes of the two channels. In symmetric country models, trade tends to increase allocative efficiency through the cost-change channel, yielding a welfare benefit beyond productive efficiency gains. In contrast, the price-change channel has ambiguous effects on allocative efficiency.

Central place theory is a key building block of economic geography and an empirically plausible description of city systems. This paper provides a rationale for central place theory via a dynamic programming formulation of the social planner's problem of city hierarchy. We show that there must be one and only one immediate smaller city between two neighboring larger-sized cities in any optimal solution. If the fixed cost of setting up a city is a power function, then the immediate smaller city will be located in the middle, confirming the locational pattern suggested by Christaller [4] . We also show that the solution can be approximated by iterating the mapping defined by the dynamic programming problem. The main characterization results apply to a general hierarchical problem with recursive divisions.

This paper proposes a theory of competition and customization. When firms allocate their production to both custom-made and standardized products, the fraction of sales from the former will increase in the face of increased competition. Recent surveys conducted by the World Bank on Chinese firms provide a rare direct measure of customization that allows us to test the above-mentioned prediction. We find empirical results consistent with the prediction.

The fundamental law of highway congestion states that when congested, the travel speed on an expanded expressway reverts to its previous level before the capacity expansion. In this paper, we propose a theory that generalizes this statement and finds that if there exists a coverage effect, that is, the effect of longer road length on traffic conditional on capacity, then the new equilibrium travel speed could be lower than its previous level. Given the fundamental law, the theory predicts that the elasticity of traffic to road capacity is at least 1. We estimate this elasticity for national expressways in Japan and test this prediction. Using the planned national expressway extension as an exogenous source of variation for capacity expansion, we obtain elasticity estimates ranging between 1.24 and 1.34, consistent with the prediction of our theory. We further investigate the sources of the larger-than-unity elasticity and find that the coverage effect plays a critical role, compared with the effect due to lane expansion.

We develop a model of trade and agglomeration that incorporates trade in both intermediate goods and final goods and allows all firms to choose their locations. There are two types of labor: skilled labor, which is mobile, and unskilled labor, which is immobile. Upon choosing its factory site, a final goods firm that is managed by skilled labor can produce these goods using local unskilled labor and a variety of intermediate goods produced by productivity-heterogeneous producers. We characterize world equilibrium and establish the conditions under which industrial agglomeration arises as a stable equilibrium outcome. We show that when the unskilled labor force is small, the role played by the selection of intermediate firms becomes less important, and trade liberalization induces dispersion. When the unskilled labor force is large and the selection effect becomes influential, trade liberalization can generate non-monotonic effects on industrial agglomeration. The dispersion effect of trade liberalization arises when unskilled labor–intermediate input complementarity matters to firm selection to a greater degree. When this is the case, trade liberalization may induce less selective firm entry and cause average productivity to fall.

This paper proposes a theory of city size distribution via a hierarchy approach rather than the popular random growth process. It does so by formalizing central place theory using an equilibrium entry model and specifying the conditions under which city size distribution follows a power law. Central place theory describes the way in which a hierarchical city system with difierent layers of cities serving difierently sized market areas is formed from a uniformly populated space. The force driving the city size difierences in this model is the heterogeneity in economies of scale across goods. The city size distribution under a central place hierarchy exhibits a power law if the distribution of scale economies is regularly varying, which is a general class that encompasses many well-known, commonly used distributions. This model is also consistent with a power law for flrms and a number-average-size rule, which is the log-linear relationship between the number and average size of the cities in which an industry is located.

This paper studies whether changes in the exchange rate aect a country's export structure, using an arguably exogenous sudden appreciation of renminbi on July 21, 2005 as the main source of identi…cation. Employing combined regression discontinuity and dierence-in-dierences approach, we show that China's export structure became more similar to that of the developed countries after the currency appreciation. We also …nd that the majority of the appreciation eect comes from the inter-…rm resource reallocation rather than the inter-region or intra-…rm resource reallocation.

It is an empirically plausible description of cities and is route to explain empirical regularities in city size distribution and industrial locations. This paper formalizes central place hierarchy by providing a rationale for it via a social planner's problem. The optimal city hierarchy is then compared with the equilibrium city hierarchy in Hsu (2008).