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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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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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Soft Information and Investment: Evidence from Plant-Level Data
October 2010
Working Paper Number:
CES-10-38R
A reduction in travel time between headquarters and plants makes it easier for headquarters to monitor plants and gather 'soft' information--i.e., information that cannot be transmitted through non-personal means. Using a difference-in-differences methodology, I find that the introduction of new airline routes that reduce the travel time between headquarters and plants leads to an increase in plant-level investment of 8% to 9% and an increase in plants' total factor productivity of 1.3% to 1.4%. Consistent with the notion that a reduction in travel time makes it easier for headquarters to monitor plants and gather soft information, I find that my results are stronger: i) for plants whose headquarters are more time constrained; ii) for plants operating in soft-information industries; iii) during the earlier years of my sample period, when alternative, non-personal, means of monitoring and transmitting information were less developed; iv) for plants where information uncertainty is likely to be greater and soft information is likely to be more valuable, such as smaller plants and peripheral plants operating in industries that are not the firm's main industry.
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Local Environmental Regulation and Plant-Level Productivity
September 2010
Working Paper Number:
CES-10-30R
This paper examines the impact of environmental regulation on the productivity of manufacturing plants in the United States. Establishment-level data from three Censuses of Manufactures are used to estimate 3-factor Cobb-Douglas production functions that include a measure of the stringency of environmental regulation faced by manufacturing plants. In contrast to previous studies, this paper examines effects on plants in all manufacturing industries, not just those in 'dirty' industries. Further, this paper employs spatial-temporal variation in environmental compliance costs to identify effects, using a time-varying county-level index that is based on multiple years of establishment-level data from the Pollution Abatement Costs and Expenditures survey and the Annual Survey of Manufactures. Results suggest that, for the average manufacturing plant, the effect on productivity of being in a county with higher environmental compliance costs is relatively small and often not statistically significant. For the average plant, the main effect of environmental regulation may not be in the spatial and temporal dimensions.
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Entry, Growth, and the Business Environment: A Comparative Analysis of Enterprise Data from the U.S. and Transition Economies
September 2010
Working Paper Number:
CES-10-20
What role does new firm entry play in economic growth? Are entrants and young firms more or less productive than incumbents, and how are their relative productivity dynamics affected by financial constraints and the business environment? This paper uses comprehensive manufacturing firm data from seven economies (United States, Georgia, Hungary, Lithuania, Romania, Russia, and Ukraine) to measure new firm entry and the productivity dynamics of entrants relative to incumbents in the same industries. We contrast hypotheses based on 'leapfrogging,' in which entrants embody superior productivity, with an 'experimentation' approach, in which entrants face uncertainty and incumbents can innovate. The results imply that leapfrogging is typical of early and incomplete transition, but experimentation better characterizes both the US and mature transition economies. Improvements in financial markets and the business environment tend to raise both the entry rate and productivity growth, but they are associated with negative relative productivity of entrants and smaller contributions of reallocation to growth among both entrants and incumbents.
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An Alternative Theory of the Plant Size Distribution with an Application to Trade
May 2010
Working Paper Number:
CES-10-10
There is wide variation in the sizes of manufacturing plants, even within the most narrowly defined industry classifications used by statistical agencies. Standard theories attribute all such size differences to productivity differences. This paper develops an alternative theory in which industries are made up of large plants producing standardized goods and small plants making custom or specialty goods. It uses confidential Census data to estimate the parameters of the model, including estimates of plant counts in the standardized and specialty segments by industry. The estimated model fits the data relatively well compared with estimates based on standard approaches. In particular, the predictions of the model for the impacts of a surge in imports from China are consistent with what happened to U.S. manufacturing industries that experienced such a surge over the period 1997'2007. Large-scale standardized plants were decimated, while small-scale specialty plants were relatively less impacted.
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Plant-Level Responses to Antidumping Duties: Evidence from U.S. Manufacturers
October 2009
Working Paper Number:
CES-09-38R
This paper describes the effects of a temporary increase in tariffs on the performance and behavior of U.S. manufacturers. Using antidumping duties as an example of temporary protection, I compare the responses of protected manufacturers to those predicted by models of trade with heterogeneous firms. I find that apparent increases in revenue productivity associated with antidumping duties are primarily due to increases in prices and mark-ups, as physical productivity falls among protected plants. Moreover, antidumping duties slow the reallocation of resources from less productive to more productive uses by reducing product-switching behavior among protected plants.
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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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The Green Industry: An Examination of Environmental Products Manufacturing
September 2008
Working Paper Number:
CES-08-34
The "green industry" is often noted in discussions of the costs and benefits of environmental policy, and it has been characterized as a unique industry with substantial potential for employment growth, well-paying jobs, and export opportunities. In this paper, we examine the characteristics and recent economic performance of the green industry, using establishment-level data on environmental products manufacturers (EPMs) from the 1995 Survey of Environmental Products and Services, together with data from the Annual Survey of Manufactures and various Census of Manufactures. Results suggest that there are some differences between EPMs and their non-EPM counterparts in the same industry, in terms of employment, employee compensation, exports, and productivity. However, we do not find any evidence that EPMs performed any better than otherwise similar plants, in terms of survival, employment growth, wage growth, and export growth. Our findings offer a more complex and nuanced portrayal of the green industry than is typical, and we suggest that this industry may not be as exceptional as is sometimes maintained.
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The Going Public Decision and the Product Market
July 2008
Working Paper Number:
CES-08-20
At what point in a firm's life should it go public? How do a firm's ex ante product market characteristics relate to its going public decision? Further, what are the implications of a firm going public on its post-IPO operating and product market performance? In this paper, we answer the above questions by conducting the first large sample study of the going public decisions of U.S. firms in the literature. We use the Longitudinal Research Database (LRD) of the U.S. Census Bureau, which covers the entire universe of private and public U.S. manufacturing firms. Our findings can be summarized as follows. First, a private firm's product market characteristics (market share, competition, capital intensity, cash flow riskiness) significantly affect its likelihood of going public. Second, private firms facing less information asymmetry and those with projects that are cheaper for outsiders to evaluate are more likely to go public (consistent with Chemmanur and Fulghieri (1999)). Third, IPOs of firms occur at the peak of their productivity cycle (consistent with Clementi (2002)): the dynamics of total factor productivity (TFP) and sales growth exhibit an inverted U-shaped pattern. Finally, sales, capital expenditures, and other performance variables exhibit a consistently increasing pattern over the years before and after the IPO. The last two findings are consistent with the widely documented post-IPO operating underperformance of firms being due to the real investment effects of a firm going public, and inconsistent with underperformance being solely due to earnings management immediately prior to the IPO.
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