Estimates of production functions suffer from an omitted variable problem; plant quality is an omitted variable that is likely to be correlated with variable inputs. One approach is to capture differences in plant qualities through plant specific intercepts, i.e., to estimate a fixed effects model. For this technique to work, it is necessary that differences in plant quality are more or less fixed; if the "fixed effects" erode over time, such a procedure becomes problematic, especially when working with long panels. In this paper, a standard fixed effects model, extended to allow for serial correlation in the error term, is applied to a 16-year panel of textile plants. This parametric approach strongly accepts the hypothesis of fixed effects. They account for about one-third of the variation in productivity. A simple non-parametric approach, however, concludes that differences in plant qualities erode over time, that is plant qualities f-mix. Monte Carlo results demonstrate that this discrepancy comes from the parametric approach imposing an overly restrictive functional form on the data; if there were fixed effects of the magnitude measured, one would reject the hypothesis of f-mixing. For textiles, at least, the functional form of a fixed effects model appears to generate misleading conclusions. A more flexible functional form is estimated. The "fixed" effects actually have a half life of approximately 10 to 20 years, and they account for about one-half the variation in productivity.
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Whittling Away At Productivity Dispersion
March 1995
Working Paper Number:
CES-95-05
In any time period, in any industry, plant productivity levels differ widely and this dispersion is persistent. This paper explores the sources of this dispersion and their relative magnitudes in the textile industry. Plants that are measured as being more productive but pay higher wages are not necessarily more profitable; wage dispersion can account for approximately 15 percent of productivity dispersion. A plant that is highly productive today may not be as productive tomorrow. I develop a new method for measuring ex-ante dispersion and the percentage of dispersion "explained" by mean reversion. Mean reversion accounts for as much as one half the observed productivity dispersion. A portion of the dispersion, however, appears to reflect real quality differences between plants; plants that are measured as being more productive expand faster and are less likely to exit.
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Technology Locks, Creative Destruction And Non-Convergence In Productivity Levels
April 1995
Working Paper Number:
CES-95-06
This paper presents a simple solution to a new model that seeks to explain the distribution of plants across productivity levels within an industry, and empirically confirms some key predictions using the U.S. textile industry. In the model, plants are locked into a given productivity level, until they exit or retool. Convex costs of adjustment captures the fact that more productive plants expand faster. Provided there is technical change, productivity levels do not converge; the model achieves persistent dispersion in productivity levels within the context of a distortion free competitive equilibrium. The equilibrium, however, is rather turbulent; plants continually come on line with the cutting edge technology, gradually expand and finally exit or retool when they cease to recover their variable costs. The more productive plants create jobs, while the less productive destroy them. The model establishes a close link between productivity growth and dispersion in productivity levels; more rapid productivity growth leads to more widespread dispersion. This prediction is empirically confirmed. Additionally, the model provides an explanation for S-shaped diffusion.
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Whittling Away At Productivity Dispersion Futher Notes: Persistent Dispersion or Measurement Error?
November 1996
Working Paper Number:
CES-96-11
This note considers several hypotheses regarding measurement error as a source of observed cross-sectional dispersion in plant-level productivity in the US textile industry. The hypotheses that reporting error and/or price rigidity in either materials and/or output account for a substantial portion of the observed dispersion in productivity are consistent with the data. Similarly, the hypothesis that transitory product niches or fashion effects lead to differential markups and consequently dispersion in observed productivity is consistent with the data. The hypothesis that transfer pricing problems lead to persistent differences in plant-level productivity, in contrast, does not appear to be consistent with the data. Finally, the hypothesis that some plants have permanent product niches that lead to dispersion in observed productivity does not appear to be consistent with data. In order to avoid imposing a strong functional form on the data, this note follows a non-parametric methodology developed in the early paper.
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Productivity Dispersion and Plant Selection in the Ready-Mix Concrete Industry
September 2011
Working Paper Number:
CES-11-25
This paper presents a quantitative model of productivity dispersion to explain why inefficient producers are slowly selected out of the ready-mix concrete industry. Measured productivity dispersion between the 10th and 90th percentile falls from a 4 to 1 difference using OLS, to a 2 to 1 difference using a control function. Due to volatile productivity and high sunk entry costs, a dynamic oligopoly model shows that to rationalize small gaps in exit rates between high and low productivity plants, a plant in the top quintile must produce 1.5 times more than a plant in the bottom quintile.
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Estimating Capital Efficiency Schedules Within Production Functions
May 1992
Working Paper Number:
CES-92-04
The appropriate method for aggregating capital goods across vintages to produce a single capital stock measure has long been a contentious issue, and the literature covering this topic is quite extensive. This paper presents a methodology that estimates efficiency schedules within a production function, allowing the data to reveal how the efficiency of capital goods evolve as they age. Specifically we insert a parameterized investment stream into the position of a capital variable in a production function, and then estimate the parameters of the production function simultaneously with the parameters of the investment stream. Plant level panel data for a select group of steel plants employing a common technology are used to estimate the model. Our primary finding is that when using a simple Cobb Douglas production function, the estimated efficiency schedules appear to follow a geometric pattern, which is consistent with the estimates of economic depreciation of Hulten and Wykoff (1981). Results from more flexible functional forms produced much less precise and unreliable estimates.
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The Missing Link: Technology, Productivity, and Investment
October 1995
Working Paper Number:
CES-95-12
This paper examines the relationship between productivity, investment, and age for over 14,000 plants in the U.S. manufacturing sector in the 1972-1988 period. Productivity patterns vary significantly due to plant heterogeneity. Productivity first increases and then decreases with respect to plant age, and size and industry are systematically correlated with productivity and productivity growth. However, there is virtually no observable relationship between investment and productivity or productivity growth. Overall, the results indicate that plant heterogeneity and fixed effects are more important determinants of observable productivity patterns than sunk costs or capital reallocation. Key Words: productivity, investment, technical change
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Market Structure and Productivity: A Concrete Example
June 2001
Working Paper Number:
CES-01-06
This paper shows that imperfect output substitutability explains part of the observed persistent plant-level productivity dispersion. Specifically, as substitutability in a market increases, the market's productivity distribution exhibits falling dispersion and higher central tendency. The proposed mechanism behind this result is truncation of the distribution from below as increased substitutability shifts demand to lower-cost plants and drives inefficient plants out of business. In a case study of the ready-mixed concrete industry, I examine the impact of one manifestation of this effect, driven by geographic market segmentation resulting from transport costs. A theoretical foundation is presented characterizing how differences in the density of local demand impact the number of producers and the ability of customers to choose between suppliers, and through this, the equilibrium productivity and output levels across regions. I also introduce a new method of obtaining plant-level productivity estimates that is well suited to this application and avoids potential shortfalls of commonly used procedures. I use these estimates to empirically test the presented theory, and the results support the predictions of the model. Local demand density has a significant influence on the shape of plant-level productivity distributions, and accounts for part of the observed intra-industry variation in productivity, both between and within given market areas.
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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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HOW IMPORTANT ARE SECTORAL SHOCKS
September 2014
Working Paper Number:
CES-14-31
I quantify the contribution of sectoral shocks to business cycle fluctuations in aggregate output. I develop a multi-industry general equilibrium model in which each industry employs the material and capital goods produced by other sectors, and then estimate this model using data on U.S. industries sales, output prices, and input choices. Maximum likelihood estimates indicate that industry-specific shocks account for nearly two-thirds of the volatility of aggregate output, substantially larger than previously assessed. Identification of the relative importance of industry-specific shocks comes primarily from data on industries intermediate input purchases, data that earlier estimations of multi-industry models have ignored.
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Plant Turnover and Demand Fluctuations in the Ready-Mix Concrete Industry
March 2006
Working Paper Number:
CES-06-08
Fluctuations in demand cause some plants to exit a market and other to enter. Would eliminating these 'uctuations reduce plant turnover? A structural model of entry and exit in concentrated markets is estimated for the ready-mix concrete industry, using plant level data from the U.S. Census. The Nested Pseudo-Likelihood algorithm is used to 'nd parameters which rationalize behavior of 'rms involved in repeated competition. Due to high sunk costs, turnover rates would only be reduced by 3% by eliminating demand 'uctuations at the county level, saving around 20 million dollars a year in scrapped capital. However, demand 'uctuations blunt 'rms'incentive to invest, reducing the number of large plants by more than 50%.
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