Estimating Production Functions in Differentiated-Product Industries with Quantity Information and External Instruments, with Nicolás de Roux, Marcela Eslava, and Eric Verhoogen
R&R, Journal of the European Economic Association. Online Appendix, Supplementary Materials. NBER working paper 28323.
This paper highlights shortcomings of standard methods of production-function estimation when quality or variety vary at the firm level and develops a new approach that can be applied in such contexts. We take advantage of input and output quantity data from Colombian producers of rubber and plastic products. Using constant-elasticity-of-substitution aggregators of outputs and material inputs at the firm level, we derive a simple expression showing how quality and variety choices may bias standard estimators. Using real exchange rates and variation in the “bite” of the national minimum wage, we construct external instruments for materials and labor choices to supplement standard internal instruments. We implement a two-step instrumental-variables method, estimating a difference equation to recover the materials and labor coefficients and then a levels equation to recover the capital coefficient. A simple Monte-Carlo simulation illustrates the advantages of our method in a setting with firm-level input-quality differences.
Output Market Power and Spatial Misallocation.
U.S. Census working paper CES-23-57. Media: Marginal Revolution.
Most product industries are local. In the U.S., firms selling goods and services to local consumers account for half of the economy's sales and create over sixty percent of jobs. Competition in these industries occurs in local product markets. I propose a theory of such competition in which firms have output market power and choose where to operate. Spatial differences in local competition arise endogenously due to the spatial sorting of heterogeneous firms. The ability of more productive firms to charge higher markups induces them to overvalue locating in larger markets, leading to firm misallocation across space. The optimal policy is a location-specific output subsidy that eliminates markups, providing a rationale for place-based policies. Moreover, the optimal policy incentivizes productive firms to relocate to smaller markets by eliminating markup dispersion. I use U.S. Census micro-data to estimate the model's parameters and find significant heterogeneity in markups across U.S. markets. Producers in markets in the top decile of the market-size distribution have a fifty percent lower markup than those in the bottom decile. Using the estimated model, I quantify the general equilibrium effects of implementing the optimal policy and find that welfare losses due to output market power are 2.4%. Additionally, this policy increases local productivity in smaller markets by 14%, but decreases local productivity in larger markets by 5%.
(In)formal Growth: Knowledge Dynamics with Learning Segmentation, with Jose M. Quintero.
We investigate how labor informality affects wage dynamics, skill formation, and economic growth. Using longitudinal worker data from Chile, we first document three empirical facts: (i) formal workers earn significantly higher wages than informal workers throughout their life cycle, driven by both a levels effect and a growth effect; (ii) nearly half of the formal-informal wage gap in levels is explained by the sorting of high-skilled workers into formal jobs; and (iii) formal workers experience faster wage growth over time, consistent with learning from higher-skilled peers. Then, to rationalize these findings, we develop a heterogeneous-agent endogenous growth model in which workers choose between formal and informal employment based on current skills, learning opportunities, and labor market regulations. Workers accumulate human capital through interactions with more skilled peers. In equilibrium, more knowledgeable workers sort into the formal sector, and the economy’s growth rate depends on the overall skill distribution and workers’ interaction rates with highly skilled formal peers. Finally, we structurally estimate the model's parameters to quantify the impact of formalization policies. We find that policies that decrease the cost of hiring formal workers are more effective in reducing the size of the informal sector compared to policies that increase the cost of hiring informal workers. However, both policies have adverse effects on economic growth by lowering the quality of interactions among more skilled workers.
Climate Risk in Dynamic Spatial Equilibrium, with Adrien Bilal and Esteban Rossi-Hansberg.
Green Buildings: Aggregate Effects of Housing Carbon Policies, with Olivia Bordeu and Alvaro Contreras Mellado.
