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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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Are All Trade Protection Policies Created Equal? Empirical Evidence for Nonequivalent Market Power Effects of Tariffs and Quotas
September 2010
Working Paper Number:
CES-10-27
The steel industry has been protected by a wide variety of trade policies, both tariff- and quota-based, over the past decades. This extensive heterogeneity in trade protection provides the opportunity to examine the well-established theoretical literature predicting nonequivalent effects of tariffs and quotas on domestic firms' market power. Robust to a variety of empirical specifications with U.S. Census data on the population of U.S. steel plants from 1967-2002, we find evidence for significant market power effects for binding quota-based protection, but not for tariff-based protection. There is only weak evidence that antidumping protection increases market power.
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Employer-to-Employer Flows in the United States: Estimates Using Linked Employer-Employee Data
September 2010
Working Paper Number:
CES-10-26
We use administrative data linking workers and firms to study employer-to-employer flows. After discussing how to identify such flows in quarterly data, we investigate their basic empirical patterns. We find that the pace of employer-to-employer flows is high, representing about 4 percent of employment and 30 percent of separations each quarter. The pace of employer-to-employer flows is highly procyclical, and varies systematically across worker, job and employer characteristics. Our findings regarding job tenure and earnings dynamics suggest that for those workers moving directly to new jobs, the new jobs are generally better jobs; however, this pattern is highly procyclical. There are rich patterns in terms of origin and destination of industries. We find somewhat surprisingly that more than half of the workers making employer-to-employer transitions switch even broadly-defined industries (NAICS supersectors).
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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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National Estimates of Gross Employment and Job Flows from the Quarterly Workforce Indicators with Demographic and Industry Detail
June 2010
Working Paper Number:
CES-10-11
The Quarterly Workforce Indicators (QWI) are local labor market data produced and released every quarter by the United States Census Bureau. Unlike any other local labor market series produced in the U.S. or the rest of the world, the QWI measure employment flows for workers (accession and separations), jobs (creations and destructions) and earnings for demographic subgroups (age and gender), economic industry (NAICS industry groups), detailed geography (block (experimental), county, Core- Based Statistical Area, and Workforce Investment Area), and ownership (private, all) with fully interacted publication tables. The current QWI data cover 47 states, about 98% of the private workforce in those states, and about 92% of all private employment in the entire economy. State participation is sufficiently extensive to permit us to present the first national estimates constructed from these data. We focus on worker, job, and excess (churning) reallocation rates, rather than on levels of the basic variables. This permits comparison to existing series from the Job Openings and Labor Turnover Survey and the Business Employment Dynamics Series from the Bureau of Labor Statistics. The national estimates from the QWI are an important enhancement to existing series because they include demographic and industry detail for both worker and job flow data compiled from underlying micro-data that have been integrated at the job and establishment levels by the Longitudinal Employer-Household Dynamics Program at the Census Bureau. The estimates presented herein were compiled exclusively from public-use data series and are available for download.
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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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Building New Plants or Entering by Acquisition? Estimation of an Entry Model for the U.S. Cement Industry
April 2010
Working Paper Number:
CES-10-08
In many industries, firms usually have two choices when expanding into new markets: They can either build a new plant (greenfield entry) or they can acquire an existing incumbent. The U.S. cement industry is a clear example. For this industry, I study the effect of two policies on the entry behavior and industry equilibrium: An asymmetric environmental policy that creates barriers to greenfield entry and a policy that creates barriers to entry by acquisition (like an antitrust policy). In the U.S. cement industry, the comparative advantage (e.g., TFP or size) of entrants versus incumbents and the regulatory entry barriers are important factors that determine the means of expansion. To model this industry, I use a perfect information static entry game. To estimate the supply and demand primitives of my model, I apply a recent estimator of discrete games to a rich database of the U.S. Census of Manufactures for the years 1963-2002. In my counterfactual analyses, I find that a less favorable environment for mergers during the Reagan-Bush administration would decrease the acquired plants by 70% and increase the new plants by 20%. Also, I find that the Clean Air Act Amendments of 1990 increased the number of acquisitions by 7.8%. Furthermore, my simulations suggest that regulations that create barriers to greenfield entry are less favorable in terms of welfare than regulations that create barriers to entry by acquisition. Finally, I demonstrate how my parameter estimates change when I apply the traditional approach in the entry literature where entry by acquisition is not considered, and when using a simple OLS estimation.
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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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Testing for Factor Price Equality in the Presence of Unobserved Factor Quality Diferences
August 2009
Working Paper Number:
CES-09-22
We develop a method for identifying departures from relative factor price equality across regions that is valid under general assumptions about production, markets and factors. Application of this method to the United States reveals substantial and increasing deviations in relative skilled wages across labor markets in both 1972 and 1992. These deviations vary systematically with labor markets .industry structure both in the cross section and over time.
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Understanding Earnings Instability: How Important are Employment Fluctuations and Job Changes?
August 2009
Working Paper Number:
CES-09-20
Using three panel datasets (the matched CPS, the SIPP, and the newly available Longitudinal Employment and Household Dynamics (LEHD) data), we examine trends in male earnings instability in recent decades. In contrast to several papers that find a recent upward trend in earnings instability using the PSID data, we find that earnings instability has been remarkably stable in the 1990s and the 2000s. We find that job changing rates remained relatively constant casting doubt on the importance of labor market 'churning.' We find some evidence that earnings instability increased among job stayers which lends credence to the view that greater reliance on incentive pay increased instability of worker pay. We also find an offsetting decrease in earnings instability among job changers due largely to declining unemployment associated with job changes. One caveat to our findings is that we focus on men who have positive earnings in two adjacent years and thus ignore men who exit the labor force or re-enter after an extended period. Preliminary investigation suggests that ignoring these transitions understates the rise in earnings instability over the past two decades.
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