Measurement of dispersion of productivity levels and productivity growth rates across businesses is a key input for answering a variety of important economic questions, such as understanding the allocation of economic inputs across businesses and over time. While item nonresponse is a readily quantifiable issue, we show there is also misreporting by respondents in the Annual Survey of Manufactures (ASM). Aware of these measurement issues, the Census Bureau edits and imputes survey responses before tabulation and dissemination. However, edit and imputation methods that are suitable for publishing aggregate totals may not be suitable for estimating other measures from the microdata. We show that the methods used dramatically affect estimates of productivity dispersion, allocative efficiency, and aggregate productivity growth. Using a Bayesian approach for editing and imputation, we model the joint distributions of all variables needed to estimate these measures, and we quantify the degree of uncertainty in the estimates due to imputations for faulty or missing data.
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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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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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Plant-Level Productivity and Imputation of Missing Data in the Census of Manufactures
January 2011
Working Paper Number:
CES-11-02
In the U.S. Census of Manufactures, the Census Bureau imputes missing values using a combination of mean imputation, ratio imputation, and conditional mean imputation. It is wellknown that imputations based on these methods can result in underestimation of variability and potential bias in multivariate inferences. We show that this appears to be the case for the existing imputations in the Census of Manufactures. We then present an alternative strategy for handling the missing data based on multiple imputation. Specifically, we impute missing values via sequences of classification and regression trees, which offer a computationally straightforward and flexible approach for semi-automatic, large-scale multiple imputation. We also present an approach to evaluating these imputations based on posterior predictive checks. We use the multiple imputations, and the imputations currently employed by the Census Bureau, to estimate production function parameters and productivity dispersions. The results suggest that the two approaches provide quite different answers about productivity.
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Punctuated Entrepreneurship (Among Women)
May 2018
Working Paper Number:
CES-18-26
The gender gap in entrepreneurship may be explained in part by employee non-compete agreements. Exploiting exogenous state-level variation in non-compete policy, I find that women more strictly subject to non-competes are 11-17% more likely to start companies after their employers dissolve. This result is not explained by the incidence of non-competes or lawsuits; however, women face higher relative costs in defending against potential litigation and in returning to paid employment after abandoning their ventures. Thus entrepreneurship among women may be 'punctuated' in that would-be female founders are throttled by non-competes, their potential unleashed only by the failure of their employers.
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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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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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Dispersion in Dispersion: Measuring Establishment-Level Differences in Productivity
April 2018
Working Paper Number:
CES-18-25RR
We describe new experimental productivity statistics, Dispersion Statistics on Productivity (DiSP), jointly developed and published by the Bureau of Labor Statistics (BLS) and the Census Bureau. Productivity measures are critical for understanding economic performance. Official BLS productivity statistics, which are available for major sectors and detailed industries, provide information on the sources of aggregate productivity growth. A large body of research shows that within-industry variation in productivity provides important insights into productivity dynamics. This research reveals large and persistent productivity differences across businesses even within narrowly defined industries. These differences vary across industries and over time and are related to productivity-enhancing reallocation. Dispersion in productivity across businesses can provide information about the nature of competition and frictions within sectors, and about the sources of rising wage inequality across businesses. Because there were no official statistics providing this level of detail, BLS and the Census Bureau partnered to create measures of within-industry productivity dispersion. These measures complement official BLS aggregate and industry-level productivity growth statistics and thereby improve our understanding of the rich productivity dynamics in the U.S. economy. The underlying microdata for these measures are available for use by qualified researchers on approved projects in the Federal Statistical Research Data Center (FSRDC) network. These new statistics confirm the presence of large productivity differences and we hope that these new data products will encourage further research into understanding these differences.
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Simultaneous Edit-Imputation for Continuous Microdata
December 2015
Working Paper Number:
CES-15-44
Many statistical organizations collect data that are expected to satisfy linear constraints; as examples, component variables should sum to total variables, and ratios of pairs of variables should be bounded by expert-specified constants. When reported data violate constraints, organizations identify and replace values potentially in error in a process known as edit-imputation. To date, most approaches separate the error localization and imputation steps, typically using optimization methods to identify the variables to change followed by hot deck imputation. We present an approach that fully integrates editing and imputation for continuous microdata under linear constraints. Our approach relies on a Bayesian hierarchical model that includes (i) a flexible joint probability model for the underlying true values of the data with support only on the set of values that satisfy all editing constraints, (ii) a model for latent indicators of the variables that are in error, and (iii) a model for the reported responses for variables in error. We illustrate the potential advantages of the Bayesian editing approach over existing approaches using simulation studies. We apply the model to edit faulty data from the 2007 U.S. Census of Manufactures. Supplementary materials for this article are available online.
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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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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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