Working Papers

[Google Scholar Citations]

Functional Forms for Tractable Economic Models and the Cost Structure of International Trade

August 2018, in collaboration with Glen Weyl

[SSRN PDF - main paper] [SSRN PDF - online appendix] [ArXiv PDF - all in one file]

Resubmitted to the the Journal of Political Economy 

Abstract:We present functional forms allowing a broader range of analytic solutions to common economic equilibrium problems. These can increase the realism of pen-and-paper solutions or speed large-scale numerical solutions as computational subroutines. We use the latter approach to build a tractable heterogeneous firm model of international trade accommodating economies of scale in export and diseconomies of scale in production, providing a natural, unified solution to several puzzles concerning trade costs. We briefly highlight applications in a range of other fields. Our method of generating analytic solutions is a discrete approximation to a logarithmically modified Laplace transform of equilibrium conditions.

Notes: This paper contains numerous new results, but also replaces previous versions "The Average-Marginal Relationship and Tractable Equilibrium Forms", "A Tractable Approach to Pass-Through Patterns" and "Pass-Through and Demand Forms".

Multi-Dimensional Pass-Through, Incidence, and the Welfare Burden of Taxation in Oligopoly

March 2017, in collaboration with Takanori Adachi, preliminary [ArXiv PDF]    [SSRN PDF]

Abstract: This paper studies welfare consequences of unit and ad valorem taxes in oligopoly with general demand, non-constant marginal costs, and a generalized type of competition. We present formulas providing connections between marginal cost of public funds, tax incidence, unit tax pass-through, ad valorem tax pass-through, and other economic quantities of interest. First, in the case of symmetric firms, we show that there exists a simple, empirically relevant set of sufficient statistics for the marginal cost of public funds, namely the pass-through and the industry demand elasticity. Specializing to the case of price or quantity competition, we show how marginal cost of public funds and pass-through are expressed using elasticities and curvatures of demand and inverse demand. These results also apply to symmetric oligopoly with multi-product firms. Second, we present a generalization with the tax revenue function specified as a general function parameterized by a vector of tax parameters. We analyze multi-dimensional pass-through, generalizing the results of Weyl and Fabinger (2013), and show that it is crucial for evaluating welfare changes in response to changes in taxation. Finally, we generalize our results to the case of heterogeneous firms, as well as to the case of changes in both production costs and taxes.

Cities as Solitons: Analytic Solutions to Models of Agglomeration and Related Numerical Approaches

November 2015, this draft is preliminary [SSRN PDF]

Abstract: Economic geography equilibria that represent spontaneous agglomeration in a featureless underlying geographic space have been solved only numerically, and the resulting spatial configurations were symmetric. This paper introduces a method of obtaining analytic solutions to similar models. In the case of continuum space, the multi-city equilibria are again symmetric. However, by working in discrete space it is possible to generate stable equilibria with multiple cities of various population levels and spatial extent, asymmetrically distributed across space. The properties of these equilibria may be understood in terms of deterministic chaos theory. The analytic approach makes it possible to find all equilibria, stable and unstable. There are two qualitative predictions that may be empirically tested: (1) the stability of an isolated city does not depend on its precise position, and (2) if two cities are too close to each other, the configuration becomes unstable and the space between the cities is filled with newcomers, turning the two cities into a megalopolis. In addition, the stable equilibria of the model are compared to population density in northern Chile. It is possible to find equilibria that match the real-world population density profile with correlation of 0.9 or more.

International Influences on Japanese Supply Chains

January 2017, in collaboration with Yoko Shibuya and Mina Taniguchi       [SSRN PDF]

Abstract: This paper investigates the transmission mechanism of Chinese productivity shocks through industry-level and firm-level networks in the Japanese manufacturing sector using an instrumental variable approach. We find that increased Chinese productivity in a particular industry negatively affects Japanese suppliers of Japanese firms in that industry (upstream propagation) and positively affects their Japanese corporate customers (downstream propagation). This is different from the recently studied case of the United States, which did not lead to evidence for downstream propagation of such shocks.

Reputational Effects in Sovereign Default

January 2016, in collaboration with Konstantin Egorov This draft is preliminary. [SSRN PDF]

Abstract: We present a tractable, quantitative model of sovereign borrowing that delivers empirically relevant regularities, such as graduation from default, sovereign debt spreads that may be high for an extended period of time, high debt-to-GDP ratios, and high default rates. The model is an asymmetric-information extension of otherwise standard models of endogenous default on sovereign debt, with borrowing levels determined in equilibrium. Governments could be of different types based on their level of responsibility (cost of default as perceived by the politicians). Only the governments observe their level of responsibility. International investors try to infer the unobserved types based on the history of all observable actions, which gives irresponsible politicians an incentive to choose the same actions as responsible ones would. Governments could tolerate periods of high interest rates without defaulting to signal that they are of better type and to gain good reputation. This leads to lower interest rates during future recessions. For the same reason, even responsible governments should pay at first high interest rates in order to signal their type and thus "graduate from default" afterwards. A calibrated version of the model features these regularities, matches standard business cycle moments, and leads to a more realistic default rate in equilibrium, with parameter values same as in the existing literature.

Revisiting the role of transport costs on spatial market integration in the Philippines

In collaboration with Olivia Quek

Are domestic markets for food staples well integrated across space within a country in developing economies? We study this question in the case of Philippine rice markets. Analyzing the wholesale price of rice in each province over an extended time span, we observe significant and persistent price gaps, even between neighboring provinces where one has a surplus over the other. One possible explanation to this seeming puzzle - which has been highlighted by the existing literature - is informa- tion asymmetry. In contrast with the literature, we do not find empirical support for imperfect information playing a significant role in explaining the price gaps. We build a model of rice trade in the Philippines that seems to capture the features of the observed trade flows well even though it assumes perfect information. Our results indicate that trade costs in- clusive of logistics costs play a large role and are significantly higher than what sea freight tariff schedules would suggest.

Trade and Interdependence in a Spatially Complex World 

[PDF] [Online Appendix]

Abstract: This paper presents an analytic solution framework applicable to a wide variety of general equilibrium international trade models, including those of Krugman (1980), Eaton and Kortum (2002), Anderson and van Wincoop (2003), and Melitz (2003), in multi-location cases. For asymptotically power law trade costs and in the large-space limit, it is shown that there are parameter thresholds where the qualitative behavior of the model economy changes. In the case of the Krugman (1980) model, the relevant parameter is closely related to the elasticity of substitution between different varieties of goods. The geographic reach of economic shocks changes fundamentally when the elasticity crosses a critical threshold: below this point shocks are felt even at long distances, while above it they remain local. The value of the threshold depends on the approximate dimensionality of the spatial conīŦguration. This paper bridges the gap between empirical work on international and intranational trade, which frequently uses data sets involving large numbers of locations, and the theoretical literature, which has analytically examined solutions to the relevant models with realistic trade costs only for the case of very few locations.

Price Dynamics for Durable Goods

In collaboration with Gita Gopinath and Oleg Itskhoki

Some partial results were summarized in my dissertation  [Dissertation] [Durable Goods Chapter]

Abstract: Durable goods producers with market power but without the ability to commit to future pricing policies face a time-inconsistency problem: they would like consumers to believe that in the future prices will be high, while in fact, in subsequent periods they have strong incentives to lower prices in order to increase sales. While this effect has been studied in Industrial Organization literature in partial equilibrium settings, its general equilibrium macroeconomic consequences remained unexplored. We fill this gap in the literature by showing how models of this kind may be solved and what their main implications are. Among other things, we show that "incomplete pass-though" of exchange rates into consumer prices that has been empirically documented naturally arises in models of this kind.

A Multidimensional Envelope Theorem with Endogenous Choice Sets

In collaboration with Glen Weyl

Motivated by the desire to more efficiently encourage the development of new vaccines, Kremer (QJE 1998) analyzed the possibility of encouraging innovation through patent buyouts by the government. Weyl and Tirole (QJE 2012) generalize this analysis by taking into account the heterogeneity in consumers' willingness to pay for different innovations. Our "Multidimensional Envelope Theorem" project provides technical underpinnings for the analysis of models of this kind and provides mathematical results that may be applied more broadly to multidimensional screening problems.

Large Deviation Instabilities in Economic Geography Models

In collaboration with Akira Ishide

Economic geography models are known to exhibit many equilibria. It is not clear, a priori, which ones are the most relevant for the real world. One goal of this project is to analyze the degree of stability of these equilibria under large stochastic disturbances and to identify equlibria that are most likely to occur in reality. An additional goal is to analyze welfare consequences of rare events in which entire towns/cities disappear due to outmigration, with only ghost towns left over (as currently observed in half of Detroit).

Exchange Rate Pass-Through and Global Supply Chains

In collaboration with Ruo Shangguan

In this work, which is still in early stages, we investigate the price dynamics of Chinese exports with focus on the role of imported inputs.

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