When firms make decisions about which product to manufacture at a more disaggregated level than observed in the data, measured firm productivity will reflect both true differences in productivity and non-random decisions about which products to manufacture. This paper examines a model of industry equilibrium where firms endogenously sort across products. We use the model to characterize the direction and magnitude of the resulting bias in productivity and to trace the implications for evaluating the aggregate effects of policy reforms such as industry deregulation. The endogenous sorting of firms across products provides a new source of reallocation and leads to biased measures of deregulation's impact on firm and aggregate productivity.
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Product Choice and Product Switching
October 2005
Working Paper Number:
CES-05-22
This paper develops a model of endogenous product selection within industries by firms. The model is motivated by new evidence we present on the prevalence and importance of product changing activity by U.S. manufacturers. Three-fifths of continuing firms alter their product mix within an industry every five years, and added and dropped products account for a substantial portion of firm output. In the model, firms make decisions about both industry entry and product choice. Product choice is shaped by the interaction of heterogeneous firm characteristics and diverse product attributes. Changes in market conditions within an industry result in simultaneous adjustment along a number of margins, including both entry/exit and product choice.
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Multi-Product Firms and Product Switching
August 2008
Working Paper Number:
CES-08-24
This paper examines the frequency, pervasiveness and determinants of product switching by U.S. manufacturing firms. We find that one-half of firms alter their mix of five-digit SIC products every five years, that product switching is correlated with both firm- and firm-product attributes, and that product adding and dropping induce large changes in firm scope. The behavior we observe is consistent with a natural generalization of existing theories of industry dynamics that incorporates endogenous product selection within firms. Our findings suggest that product switching contributes to a reallocation of resources within firms towards their most efficient use.
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Firms' Exporting Behavior under Quality Constraints
May 2009
Working Paper Number:
CES-09-13
We develop a model of international trade with export quality requirements and two dimensions of firm heterogeneity. In addition to "productivity", firms are also heterogeneous in their "caliber" {the ability to produce quality using fewer fixed inputs. Compared to singleattribute models of firm heterogeneity emphasizing either productivity or the ability to produce quality, our model provides a more nuanced characterization of firms' exporting behavior. In particular, it explains the empirical fact that firm size is not monotonically related with export status: there are small firms that export and large firms that only operate in the domestic market. The model also delivers novel testable predictions. Conditional on size, exporters are predicted to sell products of higher quality and at higher prices, pay higher wages and use capital more intensively. These predictions, although apparently intuitive, cannot be derived from singleattribute models of firm heterogeneity as they imply no variation in export status after size is controlled for. We find strong support for the predictions of our model in manufacturing establishment datasets for India, the U.S., Chile, and Colombia.
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Multi-Product Firms and Trade Liberalization
August 2009
Working Paper Number:
CES-09-21
This paper develops a general equilibrium model of international trade that features selection across firms, products and countries. Firms' export decisions depend on a combination of firm 'productivity' and firm-product-country 'consumer tastes', both of which are stochastic and unknown prior to the payment of a sunk cost of entry. Higher-productivity firms export a wider range of products to a larger set of countries than lower-productivity firms. Trade liberalization induces endogenous reallocations of resources that foster productivity growth both within and across firms. Empirically, we find key implications of the model to be consistent with U.S. trade data.
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IPO Waves, Product Market Competition, and the Going Public Decision: Theory and Evidence
March 2012
Working Paper Number:
CES-12-07
We develop a new rationale for IPO waves based on product market considerations. Two firms, with differing productivity levels, compete in an industry with a significant probability of a positive productivity shock. Going public, though costly, not only allows a firm to raise external capital cheaply, but also enables it to grab market share from its private competitors. We solve for the decision of each firm to go public versus remain private, and the optimal timing of going public. In equilibrium, even firms with sufficient internal capital to fund their new investment may go public, driven by the possibility of their product market competitors going public. IPO waves may arise in equilibrium even in industries which do not experience a productivity shock. Our model predicts that firms going public during an IPO wave will have lower productivity and post-IPO profitability but larger cash holdings than those going public off the wave; it makes similar predictions for firms going public later versus earlier in an IPO wave. We empirically test and find support for these predictions.
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Micro Data and the Macro Elasticity of Substitution
March 2012
Working Paper Number:
CES-12-05
We estimate the aggregate elasticity of substitution between capital and labor in the US manufacturing sector. We show that the aggregate elasticity of substitution can be expressed as a simple function of plant level structural parameters and sufficient statistics of the distribution of plant input cost shares. We then use plant level data from the Census of Manufactures to construct a local elasticity of substitution at various levels of aggregation. Our approach does not assume the existence of a stable aggregate production function, as we build up our estimate from the cross section of plants at a point in time. Accounting for substitution within and across plants, we find that the aggregate elasticity is substantially below unity at approximately 0.7. Lastly we assess the sources of the bias of aggregate technical change from 1987 to 1997. We find that the labor augmenting character of aggregate technical change is due almost exclusively to labor augmenting productivity growth at the plant level rather than relative growth in capital intensive plants.
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Aggregating From Micro to Macro Patterns of Trade
February 2018
Working Paper Number:
CES-18-10
We develop a new framework for aggregating from micro to macro patterns of trade. We derive price indexes that determine comparative advantage across countries and sectors and the aggregate cost of living. If firms and products are imperfect substitutes, we show that these price indexes depend on variety, average demand/quality and the dispersion of demand/quality-adjusted prices, and are only weakly related to standard empirical measures of average prices, thereby providing insight for elasticity puzzles. Of the cross-section (time-series) variation in comparative advantage, 50 (90) percent is accounted for by variety and average demand/quality, with average prices contributing less than 10 percent.
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Accounting for Trade Patterns
February 2024
Working Paper Number:
CES-24-07
We develop a quantitative framework for decomposing trade patterns. We derive price indexes that determine comparative advantage and the aggregate cost of living. If firms and products are imperfect substitutes, we show that these price indexes depend on variety, average appeal (including quality), and the dispersion of appeal-adjusted prices. We show that they are only weakly related to standard empirical measures of average prices. We find that 40 percent of the cross-section variation in comparative advantage, and 90 percent of the time-series variation, is accounted for by variety and average appeal, with less than 10 percent attributed to average prices.
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Survival of the Best Fit: Competition from Low Wage Countries and the (Uneven) Growth of U.S. Manufacturing Plants
October 2002
Working Paper Number:
CES-02-22
We examine the relationship between import competition from low wage countries and the reallocation of US manufacturing from 1977 to 1997. Both employment and output growth are slower for plants that face higher levels of low wage import competition in their industry. As a result, US manufacturing is reallocated over time towards industries that are more capital and skill intensive. Differential growth is driven by a combination of increased plant failure rates and slower growth of surviving plants. Within industries, low wage import competition has the strongest effects on the least capital and skill intensive plants. Surviving plants that switch industries move into more capital and skill intensive sectors when they face low wage competition.
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Output Market Power and Spatial Misallocation
November 2023
Working Paper Number:
CES-23-57
Most product industries are local. In the U.S., firms selling goods and services to local consumers account for half of total sales and generate more than sixty percent of the nation's jobs. Competition in these industries occurs in local product markets: cities. I propose a theory of such competition in which firms have output market power. Spatial differences in local competition arise endogenously due to the spatial sorting of heterogeneous firms. The ability to charge higher markups induces more productive firms to overvalue locating in larger cities, leading to a misallocation of firms across space. The optimal policy incen tivizes productive firms to relocate to smaller cities, providing a rationale for commonly used place-based policies. I use U.S. Census establishment-level data to estimate markups and to structurally estimate the model. I document a significant heterogeneity in markups for local industries across U.S. cities. Cities in the top decile of the city-size distribution have a fifty percent lower markup than cities in the bottom decile. I use the estimated model to quantify the general equilibrium effects of place-based policies. Policies that remove markups and relocate firms to smaller cities yield sizable aggregate welfare gains.
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