We use new micro data for 11,520 plants taken from the Census Bureau=s 1991 Manufacturing Energy Consumption Survey (MECS) and 1991 Annual Survey of Manufactures (ASM) to estimate elasticities of substitution between energy and capital. We found that energy and capital are substitutes. We also found that estimates of Allen elasticities of substitution -- which have been used as a standard measure of substitution -- are sensitive to varying data sets and levels of aggregation. In contrast, estimates of Morishima elasticities of substitution -- which are theoretically superior to the Allen elasticities -- are more robust (except when two-digit level data are used). The results support the views that (i) the Morishima elasticity is a better measure of factor substitution and (ii) micro data provide more accurate elasticity estimates than those obtained from aggregate data. Our findings appear to resolve the long-standing conflict among the estimates reported in the many previous studies regarding energy-capital substitution/complementarity.
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Factor Substitution In U.S. Manufacturing: Does Plant Size Matter
April 1998
Working Paper Number:
CES-98-06
We use micro data for 10,412 U.S. manufacturing plants to estimate the degrees of factor substitution by industry and by plant size. We find that (1) capital, labor, energy and materials are substitutes in production, and (2) the degrees of substitution among inputs are quite similar across plant sizes in a majority of industries. Two important implications of these findings are that (1) small plants are typically as flexible as large plants in factor substitution; consequently, economic policies such energy conservation policies that result in rising energy prices would not cause negative effects on either large or small U.S. manufacturing plants; and (2) since energy and capital are found to be substitutes; the 1973 energy crisis is unlikely to be a significant factor contributing to the post 1973 productivity slowdown. of Substitution
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A Flexible Test for Agglomeration Economies in Two U.S. Manufacturing Industries
August 2004
Working Paper Number:
CES-04-14
This paper uses the inverse input demand function framework of Kim (1992) to test for economies of industry and urban size in two U.S. manufacturing sectors of differing technology intensity: farm and garden machinery (SIC 352) and measuring and controlling devices (SIC 382). The inverse input demand framework permits the estimation of the production function jointly with a set of cost shares without the imposition of prior economic restrictions. Tests using plant-level data suggest the presence of population scale (urbanization) economies in the moderate- to low-technology farm and garden machinery sector and industry scale (localization) economies in the higher technology measuring and controlling devices sector. The efficiency and generality of the inverse input demand approach are particularly appropriate for micro-level studies of agglomeration economies where prior assumptions regarding homogeneity and homotheticity are less appropriate.
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Returns to Scale in Small and Large U.S. Manufacturing Establishments
September 1990
Working Paper Number:
CES-90-11
The objective of this study is to assess the possibility of differences in the production technologies between large and small establishments in five selected 4-digit SIC manufacturing industries. We particularly focus on estimating returns to scale and then make interferences regarding the efficiency of small businesses relative to large businesses. Using cross-section data for two census years, 1977 and 1982, we estimate a transcendental logarithmic (translog) production model that provides direct estimates of economies of scale parameters for both small and large establishments. Our primary findings are: (i) there are significant differences in the production technologies between small and large establishments; and (ii) based on the scale parameter estimates, small establishments appear to be as efficient as large establishments under normal economic conditions, suggesting that large size is not a necessary condition for efficient production. However, small establishments seem to be unable to maintain constant returns to scale production during economic recession such as that in 1982.
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Measuring Total Factor Productivity, Technical Change And The Rate Of Returns To Research And Development
May 1991
Working Paper Number:
CES-91-03
Recent research indicates that estimates of the effect of research and development (R&D) on total factor productivity growth are sensitive to different measures of total factor productivity. In this paper, we use establishment level data for the flat glass industry extracted from the Census Bureau's Longitudinal Research Database (LRD) to construct three competing measures of total factor productivity. We then use these measures to estimate the conventional R&D intensity model. Our empirical results support previous finding that the estimated coefficients of the model are sensitive to the measurement of total factor productivity. Also, when using microdata and more detailed modeling, R&D is found to be a significant factor influencing productivity growth. Finally, for the flat glass industry, a specific technical change index capturing the learning-by-doing process appears to be superior to the conventional time trend index.
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The Structure Of Production Technology Productivity And Aggregation Effects
August 1991
Working Paper Number:
CES-91-05
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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Scale Economies and Consolidation in Hog Slaughter
March 2000
Working Paper Number:
CES-00-03
We use establishment based panel data to estimate a cost function which identifies the role of scale economies in hog slaughter consolidation. We find modest by extensive technological scale economies in the 1990s, and they became more important over time. But wages rose sharply with plant size through the 1970s and those wage premiums generated a pecuniary scale diseconomy that largely offset the effects of technological scale economies. The size-wage relation disappeared in the 1980; with growing technological scale economies and disappearing pecuniary diseconomies, large plants realized growing cost advantages over smaller plants, and production shifted to larger plants.
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Energy Prices, Pass-Through, and Incidence in U.S. Manufacturing*
January 2016
Working Paper Number:
CES-16-27
This paper studies how increases in energy input costs for production are split between consumers and producers via changes in product prices (i.e., pass-through). We show that in markets characterized by imperfect competition, marginal cost pass-through, a demand elasticity, and a price-cost markup are suffcient to characterize the relative change in welfare between producers and consumers due to a change in input costs. We and that increases in energy prices lead to higher plant-level marginal costs and output prices but lower markups. This suggests that marginal cost pass-through is incomplete, with estimates centered around 0.7. Our confidence intervals reject both zero pass-through and complete pass-through. We and heterogeneous incidence of changes in input prices across industries, with consumers bearing a smaller share of the burden than standards methods suggest.
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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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Micro Data and the Macro Elasticity of Substitution
March 2012
Working Paper Number:
CES-12-05
We estimate the aggregate elasticity of substitution between capital and labor in the US manufacturing sector. We show that the aggregate elasticity of substitution can be expressed as a simple function of plant level structural parameters and sufficient statistics of the distribution of plant input cost shares. We then use plant level data from the Census of Manufactures to construct a local elasticity of substitution at various levels of aggregation. Our approach does not assume the existence of a stable aggregate production function, as we build up our estimate from the cross section of plants at a point in time. Accounting for substitution within and across plants, we find that the aggregate elasticity is substantially below unity at approximately 0.7. Lastly we assess the sources of the bias of aggregate technical change from 1987 to 1997. We find that the labor augmenting character of aggregate technical change is due almost exclusively to labor augmenting productivity growth at the plant level rather than relative growth in capital intensive plants.
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