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
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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ARE FIXED EFFECTS FIXED? Persistence in Plant Level Productivity
May 1996
Working Paper Number:
CES-96-03
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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The Life Cycles of Industrial Plants
October 2001
Working Paper Number:
CES-01-10
The paper presents a dynamic programming model with multiple classes of capital goods to explain capital expenditures on existing plants over their lives. The empirical specification shows that the path of capital expenditures is explained by (a) complementarities between old and new capital goods, (b) the age of plants, (c) an index that captures the rate of technical change and (d) the labor intensiveness of a plant when it is newly born. The model is tested with Census data for roughly 6,000 manufacturing plants that were born after 1972.
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Modelling Technical Progress And Total Factor Productivity: A Plant Level Example
October 1988
Working Paper Number:
CES-88-04
Shifts in the production frontier occur because of changes in technology. A model of how a firm learns to use the new technology, or how it adapts from the first production frontier to the second, is suggested. Two different adaptation paths are embodied in a translog cost function and its attendant cost share equations. The paths are the traditional linear time trend and a learning curve. The model is estimated using establishment level data from a non-regulated industry that underwent a technological shift in the time period covered by the data. The learning curve resulted in more plausible estimates of technical progress and total factor productivity growth patterns. A significant finding is that, at the establishment level, all inputs appear to be substitutes.
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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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Long-Run Expectations And Capacity
April 1988
Working Paper Number:
CES-88-01
In this paper, we argue at a general level, that recent economic models of capacity and of its utilization are deficient because they do not adequately take into account firms' long-run expectations about conditions which are pertinent to their investment decisions, i.e., their decisions about altering productive capacity. We argue that the problem with these models is that they rely on the two conventional definitions of capacity which ignore these long-run expectations. Accordingly, we propose a third definition of capacity which incorporates these expectations and, thereby, corrects the problem. Furthermore, we argue that a correct, empirical analysis with the proposed definition -- indeed, any credible analysis of capacity or its utilization -- must take into account the demand for the output produced by the firms being studied. Finally, we apply the definition to clarify the meaning of surveys of capacity and, thus, show how it can be used to improve future surveys of capacity.
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Productivity Races II: The Issue of Capital Measurement
January 1997
Working Paper Number:
CES-97-03
This paper explores the role of capital measurement in determining the productivity of individual textile plants. In addition to gross book value of capital, we experiment with a perpetual inventory measure of capital and implicit (estimated) deflator associated with the age of the plant. Following the methodology of the earlier paper (Productivity Races I), we find that measures of productivity constructed from different measures of capital are highly correlated. Further, their association with alternative measures of economic performance is approximately the same. Nevertheless, the perpetual inventory measure of capital -- the most desirable measure from a theoretical perspective -- does consistently outperform the other two measures.
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An Option-Value Approach to Technology in U.S. Maufacturing: Evidence from Plant-Level Data
July 2000
Working Paper Number:
CES-00-12
Numerous empirical studies have examined the role of firm and industry heterogeneity in the decision to adopt new technologies using a Net Present Value framework. However, as suggested by the recently developed option-value theory, these studies may have overlooked the role of investment reversibility and uncertainty as important determinants of technology adoption. Using the option-value investment model as my underlying theoretical framework, I examine how these two factors affect the decision to adopt three advanced manufacturing technologies. My results support the option-value model's prediction that plants operating in industries facing higher investment reversibility and lower degrees of demand and technological uncertainty are more likely to adopt advanced manufacturing technologies.
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The Impact of Vintage and Survival on Productivity: Evidence from Cohorts of U.S. Manufacturing Plants
May 2000
Working Paper Number:
CES-00-06
This paper examines the evolution of productivity in U.S. manufacturing plants from 1963 to 1992. We define a 'vintage effect' as the change in productivity of recent cohorts of new plants relative to earlier cohorts of new plants, and a 'survival effect' as the change in productivity of a particular cohort of surviving plants as it ages. The data show that both factors contribute to industry productivity growth, but play offsetting roles in determining a cohort's relative position in the productivity distribution. Recent cohorts enter with significantly higher productivity than earlier entrants did, while surviving cohorts show significant increases in productivity as they age. These two effects roughly offset each other, however, so there is a rough convergence in productivity across cohorts in 1992 and 1987. (JEL Code: D24, L6)
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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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