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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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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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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Macro and Micro Dynamics of Productivity: From Devilish Details to Insights
January 2017
Working Paper Number:
CES-17-41R
Researchers use a variety of methods to estimate total factor productivity (TFP) at the firm level and, while these may seem broadly equivalent, how the resulting measures relate to the TFP concept in theoretical models depends on the assumptions about the environment in which firms operate. Interpreting these measures and drawing insights based upon their characteristics thus must take into account these conceptual differences. Absent data on prices and quantities, most methods yield 'revenue productivity' measures. We focus on two broad classes of revenue productivity measures in our examination of the relationship between measured and conceptual TFP (TFPQ). The first measure has been increasingly used as a measure of idiosyncratic distortions and to assess the degree of misallocation. The second measure is, under standard assumptions, a function of funda-
mentals (e.g., TFPQ). Using plant-level U.S. manufacturing data, we find these alternative
measures are (i) highly correlated; (ii) exhibit similar dispersion; and (iii) have similar relationships with growth and survival. These findings raise questions about interpreting the first measure as a measure of idiosyncratic distortions. We also explore the sensitivity of estimates of the contribution of reallocation to aggregate productivity growth to these alternative approaches. We use recently developed structural decompositions of aggregate productivity growth that depend critically on estimates of output versus revenue elasticities. We find alternative approaches all yield a significant contribution of reallocation to
productivity growth (although the quantitative contribution varies across approaches).
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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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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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Productivity Races I: Are Some Productivuty Measures Better Than Others?
January 1997
Working Paper Number:
CES-97-02
In this study we construct twelve different measures of productivity at the plant level and test which measures of productivity are most closely associated with direct measures of economic performance. We first examine how closely correlated these measures are with various measures of profits. We then evaluate the extent to which each productivity measure is associated with lower rates of plant closure and faster plant growth (growth in employment, output, and capital). All measures of productivity considered are credible in the sense that highly productive plants, regardless of measure, are clearly more profitable, less likely to close, and grow faster. Nevertheless, labor productivity and measures of total factor productivity that are based on regression estimates of production functions are better predictors of plant growth and survival than factor share-based measures of total factor productivity (TFP). Measures of productivity that are based on several years of data appear to outperform measures of productivity that are based solely on data from the most recent year.
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RECOVERING THE ITEM-LEVEL EDIT AND IMPUTATION FLAGS IN THE 1977-1997 CENSUSES OF MANUFACTURES
September 2014
Working Paper Number:
CES-14-37
As part of processing the Census of Manufactures, the Census Bureau edits some data items and imputes for missing data and some data that is deemed erroneous. Until recently it was difficult for researchers using the plant-level microdata to determine which data items were changed or imputed during the editing and imputation process, because the edit/imputation processing flags were not available to researchers. This paper describes the process of reconstructing the edit/imputation flags for variables in the 1977, 1982, 1987, 1992, and 1997 Censuses of Manufactures using recently recovered Census Bureau files. Thepaper also reports summary statistics for the percentage of cases that are imputed for key variables. Excluding plants with fewer than 5 employees, imputation rates for several key variables range from 8% to 54% for the manufacturing sector as a whole, and from 1% to 72% at the 2-digit SIC industry level.
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