This is a sequel to an earlier paper by the author, Dhrymes (1990). Using the LRD sample, that paper examined the adequacy of the functional form specifications commonly employed in the literature of US Manufacturing production relations. The "universe" of the investigation was the three digit product group; the basic unit of observation was the plant; the sample consisted of all "large" plants, defined by the criterion that they employ 250 or more workers. The study encompassed three digit product groups in industries 35, 36 and 38, over the period 1972-1986, and reached one major conclusion: if one were to judge the adequacy of a given specification by the parametric compatibility of the estimates of the same parameters, as derived from the various implications of each specification, then the three most popular (production function) specifications, Cobb-Douglas, CES and Translog all fell very wide of the mark. The current paper focuses the investigation on two digit industries (but retains the plant as the basic unit of observation), i.e., our sample consists of all "large" manufacturing plants, in each of Industry 35, 36 and 38, over the period 1972-1986. It first replicates the approach of the earlier paper; the results are basically of the same genre, and for that reason are not reported herein. Second, it examines the extent to which increasing returns to scale characterize production at the two digit level; it is established that returns to scale at the mean, in the case of the translog production function are almost identical to those obtained with the Cobb-Douglas function.1 Finally, it examines the robustness and characteristics of measures of productivity, obtained in the context of an econometric formulation and those obtained by the method of what may be thought of as the "Solow Residual" and generally designated as Total Factor Productivity (TFP). The major finding here is that while there are some differences in productivity behavior as established by these two procedures, by far more important is the aggregation sensitivity of productivity measures. Thus, in the context of a pooled sample, introduction of time effects (generally thought to refer to productivity shifts) are of very marginal consequence. On the other hand, the introduction of four digit industry effects is of appreciable consequence, and this phenomenon is universal, i.e., it is present in industry 35, 36 as well as 38. The suggestion that aggregate productivity behavior may be largely, or partly, an aggregation phenomenon is certainly not a part of the established literature. Another persistent phenomenon uncovered is the extent to which productivity measures for individual plants are volatile, while two digit aggregate measures appear to be stable. These findings clearly calls for further investigation.
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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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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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Productivity Growth Patterns in U.S. Food Manufacturing: Case of Meat Products Industry
March 2004
Working Paper Number:
CES-04-04
A panel constructed from the Census Bureau's Longitudinal Research Database is used to measure total factor productivity growth at the plant-level and analyzes the multifactor bias of technical change for the U.S. meat products industry from 1972 through 1995. For example, addressing TFP growth decomposition for the meat products sub-sector by quartile ranks shows that the technical change effect is the dominant element of TFP growth for the first two quartiles, while the scale effect dominates TFP growth for the higher two quartiles. Throughout the time period, technical change is 1) capital-using; 2) material-saving; 3) labor-using; and, 4) energy-saving and becoming energy-using after 1980. The smaller sized plants are more likely to fluctuate in their productivity rankings; in contrast, large plants are more stable in their productivity rankings. Plant productivity analysis indicate that less than 50% of the plants in the meat industry stay in the same category, indicating considerable movement between productivity rank categories. Investment analysis results strongly indicate that plant-level investments are quite lumpy since a relatively small percent of observations account for a disproportionate share of overall investment. Productivity growth is found to be positively correlated with recent investment spikes for plants with TFP ranking in the middle two quartiles and uncorrelated with firms in the smallest and largest quartiles. Similarly, past TFP growth rates are positively correlated with future investment spikes for firms in the same quartiles. \
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Productivity Growth Patterns in U.S. Food Manufacturing: Case of Dairy Products Industry
May 2004
Working Paper Number:
CES-04-08
A panel constructed from the Census Bureau's Longitudinal Research Database is used to measure total factor productivity growth at the plant-level and analyzes the multifactor bias of technical change at three-digit product group level containing five different four-digit sub-group categories for the U.S. dairy products industry from 1972 through 1995. In the TFP growth decomposition, analyzing the growth and its components according to the quartile ranks show that scale effect is the most significant element of TFP growth except the plants in the third quartile rank where technical change dominates throughout the time periods. The exogenous input bias results show that throughout the time periods, technical change is 1) capital-using; 2) labor-using after 1980; 3) material-saving except 1981-1985 period; and, 4) energy-using except 1981-1985 and 1991-1995 periods. Plant productivity analysis indicate that less than 50% of the plants in the dairy products industry stay in the same category, indicating considerable movement between productivity rank categories. Investment analysis results indicate that plant-level investments are quite lumpy since a relatively small percent of observations account for a disproportionate share of overall investment. Productivity growth is found to be positively correlated with recent investment spikes for plants with TFP ranking in the middle two quartiles and uncorrelated with plants in the smallest and largest quartiles. Similarly, past TFP growth rates present no significant correlation with future investment spikes for plants in any quartile.
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Large Plant Data in the LRD: Selection of a Sample for Estimation
March 1999
Working Paper Number:
CES-99-06
This paper describes preliminary work with the LRD during our tenure at the Census Bureau as participants in the ASA/NSF/Census Research Program. The objective of the work described here were two-fold. First, we wanted to examine the suitableness of these data for the calculation of plant-level productivity indexes, following procedures typically implemented with time series data. Second, we wanted to select a small number of 2-digit industry groups that would be well suited to the estimation of production functions and systems of factor share equations and factor demand forecasting equations with system-wide techniques. This description of our initial work may be useful to other researchers who are interested in the LRD for the analysis of productivity growth and/or the estimation of systems of factor equations, because the specific results reported in this memo suggest that the data are of good quality, or because the nature of the tasks undertaken provides insight into issues that arise in the analysis of longitudinal establishment data.
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Using the Survey of Plant Capacity to Measure Capital Utilization
July 2011
Working Paper Number:
CES-11-19
Most capital in the United States is idle much of the time. By some measures, the average workweek of capital in U.S. manufacturing is as low as 55 hours per 168 hour week. The level and variability of capital utilization has important implications for understanding both the level of production and its cyclical fluctuations. This paper investigates a number of issues relating to aggregation of capital utilization measures from the Survey of Plant Capacity and makes recommendations on expanding and improving the published statistics deriving from the Survey of Plant Capacity. The paper documents a number of facts about properties of capital utilization. First, after growing for decades, capital utilization started to fall in mid 1990s. Second, capital utilization is a useful predictor of changes in capacity utilization and other factors of production. Third, adjustment of productivity measures for variable capital utilization improves statistical and economic properties of these measures. Fourth, the paper constructs weights to aggregate firm level capital utilization rates to industry and economy level, which is the major enhancement to available data.
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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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Decomposing Learning By Doing in New Plants
December 1992
Working Paper Number:
CES-92-16
The paper examines learning by doing in the context of a production function in which the other arguments are labor, human capital, physical capital, and vintage as a proxy for embodied technical change in physical capital. Learning is further decomposed into organization learning, capital learning, and manual task learning. The model is tested with time series and cross section data for various samples of up to 2,150 plants over a 14 year period. Word Perfect Version
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Nature Versus Nurture in the Origins of Highly Productive Businesses: An Exploratory Analysis of U.S. Manufacturing Establishments
September 2011
Working Paper Number:
CES-11-26
This paper investigates the origins of productivity leaders, those that operate close to and help push out the production frontier. Do such businesses emerge as top performers from the very beginning of their lives, for example as the consequence of an outstanding founding idea, technology, or location? Or, at the other extreme, do they appear initially as completely average (or even underperformers) that exhibit gradual improvement as they learn and develop with age? To answer this question we draw upon five decades of U.S. Census of Manufacturing (CM) establishment-level data, tracing the productivity leaders of the most recent CM (2007) back over their observed life spans. We also examine possible industry-level correlates of variation in the extent of nature versus nurture that are suggested by theories of industry dynamics and economic growth.
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Linking Investment Spikes and Productivity Growth: U.S. Food Manufacturing Industry
October 2008
Working Paper Number:
CES-08-36
We investigate the relationship between productivity growth and investment spikes using Census Bureau's plant-level data set for the U.S. food manufacturing industry. We find that productivity growth increases after investment spikes suggesting an efficiency gain or plants' learning effect. However, efficiency and the learning period associated with investment spikes differ among plants' productivity quartile ranks implying the differences in the plants' investment types such as expansionary, replacement or retooling. We find evidence of both convex and non-convex types of adjustment costs where lumpy plant-level investments suggest the possibility of non-convex adjustment costs and hazard estimation results suggest the possibility of convex adjustment costs. The downward sloping hazard can be due to the unobserved heterogeneity across plants such as plants' idiosyncratic obsolescence caused by different R&D capabilities and implies the existence of convex adjustment costs. Food plants frequently invest during their first few years of operation and high productivity plants postpone investing due to high fixed costs.
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