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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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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Measuring Cross-Country Differences in Misallocation
January 2016
Working Paper Number:
CES-16-50R
We describe differences between the commonly used version of the U.S. Census of Manufactures available at the RDCs and what establishments themselves report. The originally reported data has substantially more dispersion in measured establishment productivity. Measured allocative efficiency is substantially higher in the cleaned data than the raw data: 4x higher in 2002, 20x in 2007, and 80x in 2012. Many of the important editing strategies at the Census, including industry analysts' manual edits and edits using tax records, are infeasible in non-U.S. datasets. We describe a new Bayesian approach for editing and imputation that can be used across contexts.
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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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Misallocation and Manufacturing TFP in China and India
February 2009
Working Paper Number:
CES-09-04
Resource misallocation can lower aggregate total factor productivity (TFP). We use micro data on manufacturing establishments to quantify the potential extent of misallocation in China and India compared to the U.S. Compared to the U.S., we measure sizable gaps in marginal products of labor and capital across plants within narrowly-defined industries in China and India. When capital and labor are hypothetically reallocated to equalize marginal products to the extent observed in the U.S., we calculate manufacturing TFP gains of 30-50% in China and 40-60% in India.
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Missing Growth from Creative Destruction
April 2018
Working Paper Number:
CES-18-18
Statistical agencies typically impute inflation for disappearing products based on surviving products, which may result in overstated inflation and understated growth. Using U.S. Census data, we apply two ways of assessing the magnitude of 'missing growth' for private nonfarm businesses from 1983'2013. The first approach exploits information on the market share of surviving plants. The second approach applies indirect inference to firm-level data. We find: (i) missing growth from imputation is substantial ' at least 0.6 percentage points per year; and (ii) most of the missing growth is due to creative destruction (as opposed to new varieties).
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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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Beyond Cobb-Douglas: Estimation of a CES Production Function with Factor Augmenting Technology
February 2011
Working Paper Number:
CES-11-05
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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The Life Cycle of Plants in India and Mexico
September 2012
Working Paper Number:
CES-12-20
In the U.S., the average 40 year old plant employs almost eight times as many workers as the typical plant five years or younger. In contrast, surviving Indian plants exhibit little growth in terms of either employment or output. Mexico is intermediate to India and the U.S. in these respects: the average 40 year old Mexican plant employs twice as many workers as an average new plant. This pattern holds across many industries and for formal and informal establishments alike. The divergence in plant dynamics suggests lower investments by Indian and Mexican plants in process efficiency, quality, and in accessing markets at home and abroad. In simple GE models, we find that the difference in life cycle dynamics could lower aggregate manufacturing productivity on the order of 25% in India and Mexico relative to the U.S.
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Grouped Variation in Factor Shares: An Application to Misallocation
August 2022
Working Paper Number:
CES-22-33
A striking feature of micro-level plant data is the presence of significant variation in factor cost shares across plants within an industry. We develop a methodology to decompose cost shares into idiosyncratic and group-specific components. In particular, we carry out a cluster analysis to recover the number and membership of groups using breaks in the dispersion of factor cost shares across plants. We apply our methodology to Chilean plant-level data and find that group-specific variation accounts for approximately one-third of the variation in factor shares across firms. We also study the implications ofthese groups in cost shares on the gains from eliminating misallocation. We place bounds on their importance and find that ignoring them can overstate the gains from eliminating misallocation by up to one-third.
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The Impact of Plant-Level Resource Reallocations and Technical Progress on U.S. Macroeconomic Growth
December 2009
Working Paper Number:
CES-09-43
We build up from the plant level an "aggregate(d) Solow residual" by estimating every U.S. manufacturing plant's contribution to the change in aggregate final demand between 1976 and 1996. We decompose these contributions into plant-level resource reallocations and plant-level technical efficiency changes. We allow for 459 different production technologies, one for each 4- digit SIC code. Our framework uses the Petrin and Levinsohn (2008) definition of aggregate productivity growth, which aggregates plant-level changes to changes in aggregate final demand in the presence of imperfect competition and other distortions and frictions. On average, we find that aggregate reallocation made a larger contribution than aggregate technical efficiency growth. Our estimates of the contribution of reallocation range from 1:7% to2:1% per year, while our estimates of the average contribution of aggregate technical efficiency growth range from 0:2% to 0:6% per year. In terms of cyclicality, the aggregate technical efficiency component has a standard deviation that is roughly 50% to 100% larger than that of aggregate total reallocation, pointing to an important role for technical efficiency in macroeconomic fluctuations. Aggregate reallocation is negative in only 3 of the 20 years of our sample, suggesting that the movement of inputs to more highly valued activities on average plays a stabilizing role in manufacturing growth.
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