Translog Specification Research Articles

Additive General Error Models for Production, Cost, and Derived Demand or Share Systems

Many empirical studies of production specify a deterministic model of the firm, derive the implied behavioral equations (input demand or share system), and then embed this system in a stochastic framework by tacking on linear error terms. In contrast, this paper proposes general error models (GEMs) in which the error specification is an integral part of the optimization model. These models are the statistical embodiment of Stigler's view that apparent observed inefficiencies reflect the investigator's ignorance of the true optimization problem. Additive GEMs are proposed and interpreted. Specification tests indicate that a translog additive GEM is superior to the standard translog specification.

The role of energy in production functions for southern European economies

Using 32-yr data for five southern European economies, we investigate the role of energy in their production function. Based on input-output and other econometric tests, we conclude that by incorporating energy in the production function as a factor-input, specification errors are avoided. We find energy and capital to be substitutes with each other. The use of flexible translog specification allows the derivation of elasticity estimates in a two-output, three-input framework and fits the data well.

DUALITY AND ELASTICITIES OF SUBSTITUTION I: THEORETICAL CONSIDERATIONS

ABSTRACT An alternative approach to the estimation of functional specifications from physical input data, involves estimation of factor share equations from cost data. This is done by using the duality that exists between the production function and the cost function along the expansion path. The basic dual input definition of elasticity of substitution renders a number of alternative concepts possible. The Allen, Morishima and Shadow measures are particularly useful. Although specific production functions frequently embody assumptions that may have important disadvantages with respect to the substitutability of inputs, the translog specification represents relaxations of these maintained hypotheses. The translog functional specification is thus the production function of choice for empirical estimation of elasticities of substitution between input pairs when little information about the production process other than cost data, is available.

Demand for Electricity of Small Nonresidential Customers under Time-Of-Use (TOU) Pricing

After the oil crisis of 1973, the California Public Utilities Commission (CPUC) in 1976 ordered Pacific Gas and Electric Company (PGandE) to charge its large nonresidential customers with monthly billing demand of over 4000 kilowatts (kW) mandatory time-of-use rates. Using a translog (TLOG) specification attributable to Christensen, Jorgenson, and Lau (1973), Chung and Aigner (1981) estimate the electricity demand price elasticities by time-of-use for 64 of these customers in 13 Standard Industrial Classification (SIC) code groups. Own-price elasticity estimates are generally around -0.1 and at times can be as high as -0.5, or they have the wrong sign. Cross-price elasticity estimates indicate that electricity usages by time-of-use are mostly substitutes. However, the estimated price responsiveness typically is larger than observed usages (see below and the section, Experimental Design and Data). Moreover, positive own-price elasticity estimates, though not statistically significant, raise further doubts about the validity of empirical results.

Regional dimensions of factor and fuel substitution in U.S. manufacturing

This paper analyzes the regional responses to price increases in U.S. manufacturing in the form of fuel and factor substitution. A translog specification of a production process with eight inputs organized into a two stage optimization process — optimizing the mix of four fuels that constitute the energy input and then optimizing the input mix of physical capital, working capital, labor and aggregate energy — is used. Sectoral and regional variations in factor and fuel substitutions as evident from econometric estimation of the model at the level of 50 states and four census regions are discussed and interpreted.

Economies of Scale and Economies of Scope in Multiproduct Financial Institutions: A Study of British Columbia Credit Unions

ABSTRACTThis paper investigates the production technology facing computerized credit unions in Canada. A full system of translog cost equations is estimated in order to test for economies of scale, economies of scope, and other production characteristics in a multiproduct context. The regression results indicate that most of the credit unions in our sample experience significant increasing returns to scale as they expand their level of output. There is also evidence of cost complementarity or economies of scope in their mortgage and other lending activities. As a result, legislation which limits the ability of credit unions to grow and diversify will likely raise the operating costs of this important group of financial institutions. Additional structural tests of the most general translog specification suggest that none of the restrictive production conditions commonly imposed by other researchers using Cobb‐Douglas and CES specifications provide a valid representation of credit union technology. The results of many earlier studies are therefore open to question.

Money balances as factor inputs: An empirical evidence based on translog specification

This is a first attempt to analyze the way money balances (under both definitions) interact with the primary factors in Greek technology. Using a two-output, three-input translog cost specification, we reject the traditional functions as being inappropriate in explaining the production process. It is found that money balances are substitutes for labor and complements to capital services, while value-added is not produced by the primary inputs exclusively. A number of policy implications have emerged and are stated.

Measuring Dynamic Marketing Mix Interactions Using Translog Functions

Jagpal et al. (1979) showed, using multiplicative nonhomogeneous (MNH) sales response functions, that current econometric specifications for measuring marketing mix interactions and/or carryover effects may be structurally restrictive, regardless of their predictive usefulness. They concluded that there is a need for more flexible specifications of the sales response function which provide greater consistency with marketing theory and hence allow more effective control of marketing instruments. This paper proposes the transcendental logarithmic (translog) formulation because it is more general than the MNH function. First, we develop the rationale for the translog specification. In the second part of the paper, we estimate a translog advertisingsales model using the monthly Lydia Pinkham data. The translog results are shown to be consistent with marketing theory, to differ significantly from previous analyses of the same data, and to have useful policy implications.

Production functions for general hospitals

After a description of the production structure of the hospital sector in the Netherlands the outputs and the inputs are defined: outputs as weighted admissions, weighted patient days and inter- mediate production and inputs as the number of beds, the number of specialists, the facility-index (a scale index of the composition of the infrastructure of the hospital), drugs (in monetary terms) and the number of staff (subdivided into nurses, paramedical staff and so on). We have estimated three types of models: Cobb-Douglas, CES and the more general translog specification and the characteristics of these are compared. Using data for 110 general acute hospitals, the Cobb-Douglas and translog specifications are estimated by ordinary least squares method; the CES-specification by several methods (OLS and non-linear methods). We conclude that the more general translog specification fits the data better than the Cobb-Douglas or the CES specification. The results are interpreted in terms of the output elasticities, the elasticities of substitution and the scale effects. Thereafter, following Feldstein, we construct indices of productivity, of cost and of input efficiency.

On the bias in flexible functional forms and an essentially unbiased form: The fourier flexible form

The Fourier flexible form and its derived expenditure system are introduced. Subject to smoothness conditions on the consumer's true indirect utility function, the consumer's true expenditure system must be of the Fourier form over the region of interest in an empirical investigation. Arbitrarily accurate finite parameter approximations of the consumer's true expenditure system are obtained by dropping all high-order terms of the Fourier expenditure system past an appropriate truncation point. The resulting finite parametersystem is tractable in empirical studies. The reader who is primarily interested in applications need only read the second and fifth sections. The remainder of the article is concerned with the verification of these claims and an investigation of some aspects of the bias in Translog specifications.

The effects of restricted energy imports: Implications for the economy of a small country

The author presents a theoretical analysis of what may happen to the economy of a small country when there are restrictions on its energy purchases in the international market. Various formulations of the macro production function are presented and in each case expressions are derived for the elasticity of GDP with respect to both energy price and energy quantity. The relative importance of price control and quantity control is discussed. The production functions considered range from a simple model with fixed proportions between labour, capital and energy to a translog specification, which allows for ‘assistance’ and ‘competition’ between inputs. The Appendix gives empirical estimates for the Israeli case.

Energy substitution in the UK, 1948–64

In this paper translog specification is used to investigate the extent of interfuel substitution in the UK during the period 1948–64. The results indicate that relative changes in energy prices had significant effects on energy consumption.

The meaning and measurement of potential output: A comment on the Perloff and Wachter results

Perloff and Wachter have produced an interesting and thought provoking study of the nation’s production frontier. The study is a contribution to the literature both in terms of its conclusions and its technical analysis. The most relevant conclusion is the 1977:4 GNP gap of about $22 billion, which is far below the gap estimated by several other studies. Since recent estimates using a modified version of the methods explained by Rasche and Tatom (1977b, 1977~) indicate a similar gap, 1 will not question this basic conclusion. Instead, 1 would like to focus upon the assumptions, data, and technical analysis used in the study to arrive at this conclusion. The major contributions of the Perloff and Wachter study are (a) the suggested shift in emphasis from a high-employment measure of potential output to a nonaccelerating inflation rate (NIR) measure; (b) the relatively successful use of a production function approach to such measures; (c) the use of the translog specification of the function as well as the inclusion of cyclically sensitive production function parameters; and (d) the evidence provided in support of recent “low” estimates of potential output as opposed to “high” estimates offered in other studies. The first contribution is the most novel aspect of the paper and deserves comment before the more technical aspects are taken up.