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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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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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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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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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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Inter Fuel Substitution And Energy Technology Heterogeneity In U.S. Manufacturing
March 1993
Working Paper Number:
CES-93-05
This paper examines the causes of heterogeneity in energy technology across a large set of manufacturing plants. This paper explores how regional and intertemporal variation in energy prices, availability, and volatility influences a plant's energy technology adoption decision. Additionally, plant characteristics, such as size and energy intensity, are shown to greatly impact the energy technology adoption decision. A model of the energy technology adoption is developed and the parameters of the model are estimated using a large, plant-level dataset from the 1985 Manufacturing Energy Consumption Survey (MECS).
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Measuring Plant Level Energy Efficiency and Technical Change in the U.S. Metal-Based Durable Manufacturing Sector Using Stochastic Frontier Analysis
January 2016
Working Paper Number:
CES-16-52
This study analyzes the electric and thermal energy efficiency for five different metal-based durable manufacturing industries in the United States from 1987-2012 at the 3 digit North American Industry Classification System (NAICS) level. Using confidential plant-level data on energy use and production from the quinquennial U.S. Economic Census, a stochastic frontier regression analysis (SFA) is applied in six repeated cross sections for each five year census. The SFA controls for energy prices and climate-driven energy demand (heating degree days - HDD - and cooling degree days - CDD) due to differences in plant level locations, as well as 6-digit NAICS industry effects. A Malmquist index is used to decompose aggregate plant technical change in energy use into indices of efficiency and frontier (best practice) change. Own energy price elasticities range from -.7 to -1.0, with electricity tending to have slightly higher elasticity than fuel. Mean efficiency estimates (100 percent equals best practice level) range from a low of 32 percent (thermal 334 - Computer and Electronic Products) to a high of 86 percent (electricity 332 - Fabricated Metal Products). Electric efficiency is consistently better than thermal efficiency for all NAICS. There is no clear pattern to the decomposition of aggregate technical Thermal change. In some years efficiency improvement dominates; in other years aggregate technical change is driven by improvement in best practice.
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Decomposing Technical Change
May 1991
Working Paper Number:
CES-91-04
A production function is specified with human capital as a separate argument and with embodied technical change proxied by a variable that measures the average vintage of the stock of capital. The coefficients of this production function are estimated with cross section data for roughly 2,150 new manufacturing plants in 41 industries, and for subsets of this sample. The question of interactions between new investment and initial endowments of capital is then examined with data for roughly 1,400 old plants in 15 industries.
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The Energy Efficiency Gap and Energy Price Responsiveness in Food Processing
June 2020
Working Paper Number:
CES-20-18
This paper estimates stochastic frontier energy demand functions with non-public, plant-level data from the U.S. Census Bureau to measure the energy efficiency gap and energy price elasticities in the food processing industry. The estimates are for electricity and fuel use in 4 food processing sectors, based on the disaggregation of this industry used by the National Energy Modeling System Industrial Demand Module. The estimated demand functions control for plant inputs and output, energy prices, and other observables including 6-digit NAICS industry designations. Own price elasticities range from 0.6 to -0.9 with little evidence of fuel/electricity substitution. The magnitude of the efficiency estimates is sensitive to the assumptions but consistently reveal that few plants achieve 100% efficiency. Defining a 'practical level of energy efficiency' as the 95th percentile of the efficiency distributions and averaging across all the models result in a ~20% efficiency gap. However, most of the potential reductions in energy use from closing this efficiency gap are from plants that are 'low hanging fruit'; 13% of the 20% potential reduction in the efficiency gap can be obtained by bringing the lower half of the efficiency distribution up to just the median level of observed performance. New plants do exhibit higher energy efficiency than existing plants which is statistically significant, but the difference is small for most of the industry; ranging from a low of 0.4% to a high of 5.7%.
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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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