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Greater data availability has been coupled with developments in statistical theory and economic theory to allow more elaborate and complicated models to be entertained. These include factor models, DSGE models, restricted vector autoregressions, and non-linear models.
In this paper we discuss recent advances in modeling and estimating dynamic factor demand models, and review the use of such models in analyzing the production structure, the determinants of variable and quasi-fixed factors, and productivity growth. The paper also discusses the traditional approach to productivity analysis based on the Divisia index number methodology. Both approaches may be seen as being complementary. The conventional index number approach will measure the rate of technical change correctly if certain assumptions about the underlying technology of the firm and output and input markets hold. The approach is appealing in that it can be easily implemented. However, if the underlying assumptions do not hold, then the conventional index number approach will, in general, yield biased estimates of technical change. The econometric approach based on general dynamic factor demand models allows for a careful testing of various features of a postulated model. Furthermore it not only provides a framework to estimate technical change, but can also yield a rich set of critical information on the structure of production, the dynamics of investment in physical and R&D capital, the effects of spillovers, the depreciation rate of capital, the impact of taxes, expectations, etc. The paper provides both a review of recent methodology developed for the specification and estimation of dynamic factor demand models, as well as a review of recent applications. The paper also explores in terms of a Monte Carlo study how estimates of important characteristics of the production process can be affected by model misspecification. The study suggests that characteristics of the production structure such as scale and technical change are sensitive to model misspecification, and that adopting a simple specification for reasons of convenience may result in serious biases
The empirical analysis of the economic interactions between factors of production, output and corresponding prices has received much attention over the last two decades. Most contributions in this area have agreed on the neoclassical principle of a representative optimizing firm and typically use theory-based structural equation models (SEM). A popular alternative to SEM is given by the vector autoregression (VAR) methodology. The most recent attempts to link the SEM approach with VAR analysis in the area of factor demands concentrate on single-equation models, whereas no effort has been devoted to compare these alternative approaches when a firm is assumed to face a multi-factor technology and to decide simultaneously the optimal quantity for each input. This paper bridges this gap. First, we illustrate how the SEM and the VAR approaches can both represent valid alternatives to model systems of dynamic factor demands. Second, we show how to apply both methodologies to estimate dynamic factor demands derived from a cost-minimizing capital-labour-energy-materials (KLEM) technology with adjustment costs (ADC) on the quasi-fixed capital factor. Third, we explain how to use both models to calculate some widely accepted indicators of the production structure of an economic sector, such as price and quantity elasticities, and alternative measures of ADC. In particular, we propose and discuss some theoretical and empirical justifications of the differences between observed elasticities, measures of ADC, and the assumption of exogeneity of output and/or input prices. Finally, we offer some suggestions for the applied researcher.
Prucha and Nadiri (1982,1986,1988) introduced a methodology to estimate systems of dynamic factor demand that allows for considerable flexibility in both the choice of the functional form of the technology and the expectation formation process. This paper applies this methodology to estimate the production structure, and the demand for labor, materials, capital and R & D by the U.S. Bell System. The paper provides estimates for short-, intermediate- and long-run price and output elasticities of the inputs, as well as estimates on the rate of return on capital and R & D. The paper also discusses the issue of the measurement of technical change if the firm is in temporary rather than long-run equilibrium and the technology is not assumed to be linear homogeneous The paper provides estimates for input and output based technical change as well as for returns to scale. Furthermore, the paper gives a decomposition of the traditional measure of total factor productivity growth.