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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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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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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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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The Reallocation Myth
April 2018
Working Paper Number:
CES-18-19
There is a widely held view that much of growth in the U.S. can be attributed to reallocation from low to high productivity firms, including from exiting firms to entrants. Declining dynamism ' falling rates of reallocation and entry/exit in the U.S. ' have therefore been tied to the lackluster growth since 2005. We challenge this view. Gaps in the return to resources do not appear to have narrowed, suggesting that allocative efficiency has not improved in the U.S. in recent decades. Reallocation can also matter if it is a byproduct of innovation. However, we present evidence that most
innovation comes from existing firms improving their own products rather than from entrants or fast-growing firms displacing incumbent firms. Length: 26 pages
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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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Evidence for the Effects of Mergers on Market Power and Efficiency
January 2016
Working Paper Number:
CES-16-43
Study of the impact of mergers and acquisitions (M&As) on productivity and market power has been complicated by the difficulty of separating these two effects. We use newly-developed techniques to separately estimate productivity and markups across a wide range of industries using confidential data from the U.S. Census Bureau. Employing a difference-in-differences framework, we find that M&As are associated with increases in average markups, but find little evidence for effects on plant-level productivity. We also examine whether M&As increase efficiency through reallocation of production to more efficient plants or through reductions in administrative operations, but again find little evidence for these channels, on average. The results are robust to a range of approaches to
address the endogeneity of firms' merger decisions.
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Entry Costs Rise with Growth
October 2024
Working Paper Number:
CES-24-63
Over time and across states in the U.S., the number of firms is more closely tied to overall employment than to output per worker. In many models of firm dynamics, trade, and growth with a free entry condition, these facts imply that the costs of creating a new firm increase sharply with productivity growth. This increase in entry costs can stem from the rising cost of labor used in entry and weak or negative knowledge spillovers from prior entry. Our findings suggest that productivity-enhancing policies will not induce firm entry, thereby limiting the total impact of such policies on welfare.
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Global Sourcing and Multinational Activity: A Unified Approach
September 2022
Working Paper Number:
CES-22-36
Multinational firms (MNEs) accounted for 42 percent of US manufacturing employment, 87 percent of US imports, and 84 of US exports in 2007. Despite their disproportionate share of global trade, MNEs' input sourcing and final-good production decisions are often studied separately. Using newly merged data on firms' trade and FDI activity by country, we show that US MNEs are more likely to import not only from the countries in which they have affiliates, but also from other countries within their affiliates' region. We rationalize these patterns in a unified framework in which firms jointly determine the countries in which to produce final goods, and the countries from which to source inputs. The model generates a new source of scale economies that arises because a firm incurs a country specific fixed cost that allows all its assembly plants to source inputs from that country. This shared fixed cost across plants creates interdependencies between firms' assembly and sourcing locations, and leads to non-monotonic responses in third markets to bilateral trade cost changes.
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