Cobb-Douglas Specification Research Articles

Indeterminacy with almost constant returns to scale: capital-labor substitution matters

This paper shows, in the benchmark one-sector Ramsey model, that indeterminacy and sunspots may occur when externalities are small, provided that capital and labor are more substitutable than in the usual Cobb-Douglas specification. Key to the results are the general formulations of both preferences and technology that we consider. In particular, indeterminacy is shown to occur under almost constant returns to scale provided that both concavity of utility for consumption is small enough and labor supply is close to indivisible. An important implication of the results is that, when labor supply is positively sloped, indeterminacy does not necessarily require the equilibrium wage-hours locus to be upward sloping.

Public and Private Capital Productivity Puzzle: A Nonparametric Approach

Is public expenditure productive? Is there a shortfall or excess in public capital investment? We address these old issues in light of new econometric tools. It is argued that the Cobb-Douglas specification that ignores nonlinearity inherent in the functional relationship of the production technology causes incorrect estimates of input elasticities. To avoid possible model misspecification, we use Li-Racine generalized kernel estimation. This procedure is used to estimate the returns to private capital, employment, and public capital in gross state product from a panel of 48 states for 17 years. In contrast to previous studies, we find that the return to public capital is positive and significantly different from zero.

Biased Technical Change and Capital-Labour Substitution in Finland, 1902-2003

The paper argues that a Cobb-Douglas specification may be a reasonable description of the Finnish aggregate production function when a sufficiently long time period (the 20th century) is considered. It is, however, a misleading description of the production technology for the post-WWII period. Controlling for biased technical change, the elasticity of substitution is significantly below one, close to 0.5, during 1945-2003. Given that similar results have been obtained for the U.S. economy, the analysis shows that the value of the elasticity of substitution cannot be dependent on some specific structure of economic institutions but is likely to reflect more general aspects of technology and production.

Technological spillovers and patterns of growth with sector-specific R&D

This paper studies a two-sector model of endogenous technical change in which expansion of each production sector is associated with sector-specific R&D investment. It is shown that the pattern of growth is sensitive to the specification of intersectoral technological spillover as well as to the preference structure. If technological spillovers and preferences of consumers are represented by CES functional forms, the balanced-growth equilibrium may not exhibit a well-behaved saddle-point property: it is possible that the balanced-growth path is locally indeterminate or unstable. In addition, a slight modification of technological spillover effects easily yields multiple balanced-growth paths. In contrast, Cobb–Douglas specifications present a unique and determinate balanced-growth path.

Regional Variation and Cereal Production in India

This paper analyzes the agricultural scenario in India by estimating a system of production functions for five major cereal crops (such as wheat, rice, maize, bajra and jowar), using a Translog specification instead of the more commonly used Cobb-Douglas (CD) specification. Our estimation methodology employs a Seemingly Unrelated Regressions in a panel data set up, which allows for cross equation correlation. We use district level data for 13 major states from 1966-1967 to 1994-1995. We examine the inter-regional heterogeneity using four kinds of dummy variables, viz. District dummy, state dummy, production function dummy and agro-ecological dummy. The result indicates presence of non-linear effects of various inputs on the yields. Our results show the significance of regional differences in terms of production system and agro-ecological climates.

The specification of the aggregate production function in the presence of inefficiency

In this paper we consider the impact of the specification of production technology on technical efficiency. We reject the Cobb-Douglas specification of aggregate production in favour of a more general translog form. However, the effect of functional form on the measured efficiency terms is actually quite small. Both of these results are robust to the adjustment of labour to account for years of schooling.

An estimation of US industry-level capital–labor substitution elasticities: support for Cobb–Douglas

A key parameter that determines the distributional impacts of a policy shift in general equilibrium models is the elasticity of substitution between capital and labor. Despite the importance of this parameter in applied modeling, its identification continues to pose a challenge. Given the structure of most growth models, we posit that the true relationship between capital and labor is likely to be close to Cobb–Douglas. Using a rich new data set from the Bureau of Economic Analysis (BEA), we estimate substitution elasticities for 28 industries that cover the entire economy, and provide an indication of the long- and short-run ranges of those estimates. We fail to reject the Cobb–Douglas specification in 20 of the 28 industries. These findings lend support to the Cobb–Douglas specification as a transparent starting point in simulation analysis.

An Estimation of Industry-Level Capital-Labor Substitution Elasticities for U.S. Production: An Argument for Cobb-Douglas

A key parameter that determines the distributional impacts of a policy shift in general equilibrium simulations is the elasticity of substitution between capital and labor. Using a rich new data set by the Bureau of Economic Analysis, we estimate substitution elasticities for 28 industries and provide an indication of the long- and short-run estimates. Given the structure of most growth models, we posit that the relationship between capital and labor is likely to be close to Cobb-Douglas. Our findings lend support to the Cobb-Douglas specification as a transparent starting point in simulation analysis.

Factors substitutability, heterogeneity and endogenous fluctuations in a finance constrained economy

This paper examines the local properties of perfect foresight equilibrium of a finance constrained economy featuring two classes of infinitely-lived agents with heterogeneous general preferences. It is primarily concerned with the conceivability of endogenous fluctuations for large plausible capital-labor elasticities of substitution. It is notably shown that heterogeneity in preferences allows Hopf cycles to be entirely consistent with a wide range of elasticities of substitution including the unitary one (Cobb-Douglas specifications).

A Cross-Country Empirical Investigation of the Aggregate Production Function Specification

Many growth models assume that aggregate output is generated by a Cobb-Douglas production function. In this article we question the empirical relevance of this specification. We use a panel of 82 countries over a 28-year period to estimate a general constant-elasticity-of-substitution (CES) production function specification. We find that for the entire sample of countries we can reject the Cobb-Douglas specification. When we divide our sample of countries up into several subsamples, we find that physical capital and human capital adjusted labor are more substitutable in the richest group of countries and are less substitutable in the poorest group of countries than would be implied by a Cobb-Douglas specification.

Worker-Firm Matching and Unemployment in Transition to a Market Economy: (Why) Are the Czechs More Successful than Others?

In this paper we compare the nature and determinants of outflows from unemployment in the case of the Czech and Slovak Republics, which in early 1990's experienced a process close to a controlled experiment. Overall, our study suggests that the exceptionally low unemployment rate in the Czech Republic as compared to Slovakia and the other Central and East European economies has been brought about principally by (1) a rapid increase in vacancies along with unemployment, resulting in a balanced unemployment-vacancy situation at the aggregate as well as district level, (2) a major part played by vacancies and the newly unemployed in the outflow from unemployment, (3) a matching process with strongly increasing returns to scale throughout (rather than only in parts of) the transition period, and (4) ability to keep the long term unemployed at relatively low levels. Using the framework of matching functions we find that in many years the usual Cobb-Douglas specification and the hypothesis of constant returns to scale are rejected. A translog matching function with weak separability between the existing and newly unemployed is found to be the functional form best supported by the data. Our theoretical analysis also indicates that by not adjusting data for the varying size of districts or regions, previous studies may have generated estimates of the returns to scale of the matching function that were biased toward unity.

Worker-Firm Matching and Unemployment in Transition to a Market Economy: (Why) are the Czechs More Successful than Others?

In this paper we compare the nature and determinants of outflows from unemployment in the case of the Czech and Slovak Republics which in early 1990’s experienced a process close to a controlled experiment. Overall, our study suggests that the exceptionally low unemployment rate in the Czech Republic as compared to Slovakia and the other Central and East European economies has been brought about principally by (1) a rapid increase in vacancies along with unemployment, resulting in a balanced unemployment-vacancy situation at the aggregate as well as district level, (2) a major part played by vacancies and the newly unemployed in the outflow from unemployment, (3) a matching process with strongly increasing returns to scale throughout (rather than only in parts of) the transition period, and (4) ability to keep the long term unemployed at relatively low levels. Using the framework of matching functions we find that in many years the usual Cobb-Douglas specification and the hypothesis of constant returns to scale are rejected. A translog matching function with weak separability between the existing and newly unemployed is found to be the functional form best supported by the data. Our theoretical analysis also indicates that by not adjusting data for the varying size of districts or regions, previous studies may have generated estimates of the returns to scale of the matching function that were biased toward unity.

Teamwork versus delegation — comparison of Japanese and German management styles

Teamwork and delegation as alternative management styles are described in terms of management production functions using Cobb-Douglas specifications; a comparison is made between management systems with teamwork at the top (the German Vorstand system) and at the ground level (Japanese quality circles) as extreme cases.

Information Technology As A Factor Of Production: The Role Of Differences Among Firms

Despite evidence that information technology (IT) has recently become a productive investment for a large cross-section of firms, a number of questions remain. Some of these issues can be addressed by extending the basic production function approach that was applied in earlier work. Specifically, in this short paper we: 1) control for individual firm differences in productivity by employing a ‘firm effects’ specification, 2) consider the more flexible translog specification instead of only the Cobb-Douglas specification, and 3) allow all parameters to vary between various subsectors of the economy. We find that while ‘firm effects’ may account for as much as half of the productivity benefits imputed to IT in earlier studies, the elasticity of IT remains positive and statistically significant. We also find that the estimates of IT elasticity and marginal product are little-changed when the less restrictive translog production function is employed. Finally, we find only limited evidence of differences in IT's marginal product between manufacturing and services and between the ‘measurable’ and ‘unmeasurable’ sectors of the economy. Surprisingly, we find that the marginal product of IT is at least as high in firms that did not grow during 1988–1992 sample period as it is in firms that grew.

Some effects of regional differentiation on integration in the European community

The main objective of this article is to discuss integration problems concerning regional differentiation and regional disparities in the E.C. countries, by adopting theoretical approaches and indicators for measuring the disparities in regional development policies. To test the relevance of the potentiality factors, the analysis studied the causes of regional disparities which are used in the E.C. studies as the most convenient approach. Turkish G.D.P. variations by regions are examined using the quasiproduction function based on a Cobb-Douglas specification taking into account as a function of activity, infrastructure, industrial employment and agglomeration rates. The results show that these factors are significant for testing the potential theory for a developing area.

Human capital and job levels: Explaining the age-income funnel

In a previous paper on optimal human capital investment [Theeuwes et al. (1985)] we derived earnings functions based on a lifetime wealth maximization assumption. A Cobb-Douglas specification for the human capital production function resulted in a non-linear estimation equation in which earnings were explained as a function of years of experience. In the present paper we re-estimate this model using individual instead of aggregate data and extend the model with job level information as a contribution to the explanation of the age-income funnel. The latter refers to the increasing variance of the age-income distribution for older age brackets. Assignment to job levels over the life cycle contributes significantly to the variance of the ageincome profile.

Banking Costs, Generalized Functional Forms, and Estimation of Economies of Scale and Scope

Recently, researchers have claimed that the primitive Cobb-Douglas production technology captures banking cost functions adequately. These findings rule out scope economies and U-shaped cost curves. The rejection of the generalized flexible form postulated by the above authors is a necessary, but not a sufficient, condition to justify a Cobb-Douglas specification. Using restricted generalized functional forms, the authors find that the composite output Cobb-Douglas specification is an inadequate description of banking cost technology. Translog specifications with multiple products capture the data best, suggesting the presence of both scope and scale economies. Copyright 1989 by Ohio State University Press.

A DIAGRAMMATIC INTRODUCTION TO DISEQUILIBRIUM MACROECONOMICS

A three-commodity model of short-run, non-Walrasian equilibrium is p resented. Without restrictive (e.g., Cobb-Douglas) specifications of utility or production functions, it is possible to obtain definite re sults on uniqueness, stability under short-run quantity adjustment, a nd comparative statics for the model. Much of the analysis can be con ducted through a simple, four-quadrant diagram. Moreover, nonuniquene ss is easily analyzed and the nature of a catastrophic Walrasian equi librium from the non-Walrasian viewpoint is clarified via a study of the stability accompanying this phenomenon. Copyright 1987 by Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research

Production functions and tract rents in Western U.S. surface coal mining

This study introduces the coal tract as an input to a mining production function and reports empirical estimates of surface coal mining technology in the Powder River Basin and Green River/Hams Fork region. Cobb-Douglas and constant elasticity of substitution production functions were estimated for twenty mines using data on capital, labor, and energy inputs from 1982 operations, and data describing tract geological characteristics. Several prominent results appear. The mines exhibit constant returns to scale, and the analysis could not detect any effects of depletion on mining costs across mines at different stages of exploitation. The Cobb-Douglas specification appears to be satisfactory. Using data on flows of capital services rather than simply on capital stocks, surface coal mining in these two regions appears much less capital-intensive than the nationwide estimate for surface coal mining previously offered. Of the geological characteristics considered in the analysis, only remaining reserves appear appropriately viewed as an input to mining. The stripping ratio has a very pronounced, negative effect on production, but it affects the productivity of all inputs rather than having its effects restricted to operating as a tract characteristic. Our methodology permits direct assessment of tract, or royalty, rent, which is almost exactly 12.5% of the value of output. Keeping in mind the limitations of the data base and the statistical nature of the estimate of 12.5%, we suggest that the current federal royalty rate of 12.5%, probably extracts a share of sales revenue very close to the government's `proper' share as owner of the tract. Sensitivity analysis of tract rents for representative mines, using prices, geological characteristics and estimated coefficients from the production function, indicates particular sensitivity to the stripping ratio, much more than to reserve base size.

Discriminating among alternative production functions in Polish industry

Large scale econometric models for both market-type and socialist centrally planned economies generally specify production relationships in the form of an aggregate production function. This paper addresses the problem of specifying the functional form of the production function for a socialist centrally planned economy: Poland. Three production functions, Cobb-Douglas, CES and VES, are estimated and a non-nested test for functional form is performed using a pooled cross section-time series regression technique. The estimates of the Cobb-Douglas specification are slightly superior to those of the CES and VES specifications, but the latter provide important detail for historical analysis and interesting implications for growth.