Both the recent literature on production function identification and a considerable body of other empirical work on firm expansion assume a Cobb-Douglas production function. Under this assumption, all technical differences are Hicks neutral. I provide evidence from US manufacturing plants against Cobb-Douglas and present an alternative production function that better fits the data. A Cobb Douglas production function has two empirical implications that I show do not hold in the data: a constant cost share of capital and strong comovement in labor productivity and capital productivity (revenue per unit of capital). Within four digit industries, differences in cost shares of capital are persistent over time. Both the capital share and labor productivity increase with revenue, but capital productivity does not. A CES production function with labor augmenting differences and an elasticity of substitution between labor and capital less than one can account for these facts. To identify the labor capital elasticity, I use variation in wages across local labor markets. Since the capital cost to labor cost ratio falls with local area wages, I strongly reject Cobb-Douglas: capital and labor are complements. Now productivity differences are no longer neutral, which has implications on how productivity affects firms' decisions to expand or contract. Non neutral technical improvements will result in higher stocks of capital but not necessarily more hiring of labor. Specifying the correct form of the production function is more generally important for empirical work, as I demonstrate by applying my methodology to address questions of misallocation of capital.
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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 Cyclicality of Productivity Dispersion
May 2011
Working Paper Number:
CES-11-15
Using plant-level data, I show that the dispersion of total factor productivity in U.S. durable manufacturing is greater in recessions than in booms. This cyclical property of productivity dispersion is much less pronounced in non-durable manufacturing. In durables, this phenomenon primarily reflects a relatively higher share of unproductive firms in a recession. In order to interpret these findings, I construct a business cycle model where production in durables requires a fixed input. In a boom, when the market price of this fixed input is high, only more productive firms enter and only more productive incumbents survive, which results in a more compressed productivity distribution. The resulting higher average productivity in durables endogenously translates into a lower average relative price of durables. Additionally, my model is consistent with the following business cycle facts: procyclical entry, procyclical aggregate total factor productivity, more procyclicality in durable than non-durable output, procyclical employment and countercyclicality in the relative price of durables and the cross section of stock returns.
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Are We Undercounting Reallocation's Contribution to Growth?
January 2013
Working Paper Number:
CES-13-55R
There has been a strong surge in aggregate productivity growth in India since 1990, following
significant economic reforms. Three recent studies have used two distinct methodologies to decompose the sources of growth, and all conclude that it has been driven by within-plant increases in technical efficiency and not between-plant reallocation of inputs. Given the nature of the reforms, where many barriers to input reallocation were removed, this finding has surprised researchers and been dubbed 'India's Mysterious Manufacturing Miracle.' In this paper, we show that the methodologies used may artificially understate the extent of reallocation. One approach, using growth in value added, counts all reallocation growth arising from the movement of intermediate inputs as technical efficiency growth. The second approach, using the Olley-Pakes decomposition, uses estimates of plant-level total factor productivity (TFP) as a proxy for the marginal product of inputs. However, in equilibrium, TFP and the marginal product of inputs are unrelated. Using microdata on manufacturing from five countries ' India, the U.S., Chile, Colombia, and Slovenia ' we show that both approaches significantly understate the true
role of reallocation in economic growth. In particular, reallocation of materials is responsible for over half of aggregate Indian manufacturing productivity growth since 2000, substantially larger than either the contribution of primary inputs or the change in the covariance of productivity and size.
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Has toughness of local competition declined?
May 2022
Working Paper Number:
CES-22-13
Recent evidence on rm-level markups and concentration raises a concern that market
competition has declined in the U.S. over the last few decades. Since measuring competition is difficult, methodologies used to arrive at these findings have merits but also raise technical concerns which question the validity of these results. Given the significance of documenting how competition has changed, I contribute to this literature by studying a different measure of competition. Specifically, I estimate the toughness of local competition over time. To derive this estimate, I use a generalized monopolistic competition model with variable markups. This model generates insights that allows me to measure competition as the sensitivity of weighted-average markup to changes in the number of competitors using directly observable variables. Compared to firm-level markups estimation, this method relaxes the need to estimate production functions. I then use confidential Census data to estimate toughness of local competition from 1997 to 2016, which shows that local competition has decreased in non-tradable industries on average in the U.S. during this time period.
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Growing Oligopolies, Prices, Output, and Productivity
November 2018
Working Paper Number:
CES-18-48
American industries have grown more concentrated over the last forty years. In the absence of productivity innovation, this should lead to price hikes and output reductions, decreasing consumer welfare. Using public data from 1972-2012, I use price data to disentangle revenue from output. Difference-in-difference estimates show that industry concentration increases are positively correlated to productivity and real output growth, uncorrelated with price changes and overall payroll, and negatively correlated with labor's revenue share. I rationalize these results in a simple model of competition. Productive industries (with growing oligopolists) expand real output and hold down prices, raising consumer welfare, while maintaining or reducing their workforces, lowering labor's share of output.
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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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Misallocation or Mismeasurement?
February 2020
Working Paper Number:
CES-20-07
The ratio of revenue to inputs differs greatly across plants within countries such as the U.S. and India. Such gaps may reflect misallocation which hinders aggregate productivity. But differences in measured average products need not reflect differences in true marginal products. We propose a way to estimate the gaps in true marginal products in the presence of measurement error. Our method exploits how revenue growth is less sensitive to input growth when a plant's average products are overstated by measurement error. For Indian manufacturing from 1985'2013, our correction lowers potential gains from reallocation by 20%. For the U.S. the effect is even more dramatic, reducing potential gains by 60% and eliminating 2/3 of a severe downward trend in allocative efficiency over 1978'2013.
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Wage Dynamics along the Life-Cycle of Manufacturing Plants
August 2011
Working Paper Number:
CES-11-24R
This paper explores the evolution of average wage paid to employees along the life-cycle of a manufacturing plant in U.S. Average wage starts out low for a new plant and increases along with labor productivity, as the plant survives and ages. As a plant experiences productivity decline and approaches exit, average wage falls, but more slowly than it rises in the case of surviving new plants. Moreover, average wage declines slower than productivity does in failing plants, while it rises relatively faster as productivity increases in surviving new plants. These empirical regularities are studied in a dynamic model of labor quality and quantity choice by plants, where labor quality is reflected in wages. The model's parameters are estimated to assess the costs a plant incurs as it alters its labor quality and quantity in response to changes in its productivity over its life-cycle.
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The Dynamics of Plant-Level Productivity in U.S. Manufacturing
July 2006
Working Paper Number:
CES-06-20
Using a unique database that covers the entire U.S. manufacturing sector from 1976 until 1999, we estimate plant-level total factor productivity for a large number of plants. We characterize time series properties of plant-level idiosyncratic shocks to productivity, taking into account aggregate manufacturing-sector shocks and industry-level shocks. Plant-level heterogeneity and shocks are a key determinant of the cross-sectional variations in output. We compare the persistence and volatility of the idiosyncratic plant-level shocks to those of aggregate productivity shocks estimated from aggregate data. We find that the persistence of plant level shocks is surprisingly low-we estimate an average autocorrelation of the plantspecific productivity shock of only 0.37 to 0.41 on an annual basis. Finally, we find that estimates of the persistence of productivity shocks from aggregate data have a large upward bias. Estimates of the persistence of productivity shocks in the same data aggregated to the industry level produce autocorrelation estimates ranging from 0.80 to 0.91 on an annual basis. The results are robust to the inclusion of various measures of lumpiness in investment and job flows, different weighting methods, and different measures of the plants' capital stocks.
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Older and Slower: The Startup Deficit's Lasting Effects on Aggregate Productivity Growth
June 2018
Working Paper Number:
CES-18-29
We investigate the link between declining firm entry, aging incumbent firms and sluggish U.S. productivity growth. We provide a dynamic decomposition framework to characterize the contributions to industry productivity growth across the firm age distribution and apply this framework to the newly developed Revenue-enhanced Longitudinal Business Database (ReLBD). Overall, several key findings emerge: (i) the relationship between firm age and productivity growth is downward sloping and convex; (ii) the magnitudes are substantial and significant but fade quickly, with nearly 2/3 of the effect disappearing after five years and nearly the entire effect disappearing after ten; (iii) the higher productivity growth of young firms is driven nearly exclusively by the forces of selection and reallocation. Our results suggest a cumulative drag on aggregate productivity of 3.1% since 1980. Using an instrumental variables strategy we find a consistent pattern across states/MSAs in the U.S. The patterns are broadly consistent with a standard model of firm dynamics with monopolistic competition.
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