Daniel Primont

On testing separability restrictions with flexible functional forms

Abstract In this paper, we examine the implications of imposing separability on the translog and three other flexible forms. Our results imply that the Berndt-Christensen ‘nonlinear’ test for weak separability tests not only for weak separability, but also imposes a restrictive structure on the macro and micro functions for all currently known ‘flexible’ functional forms. For example, testing for weak separability using the translog as an exact form is in fact equivalent to testing for a hybrid of strong (additive) separability and homothetic weak separability with Cobb-Douglas aggregator functions. Our results show that these ‘flexible’ functional forms are ‘separability-inflexible’. That is, they are not capable of providing a second-order approximation to an arbitrary weakly separable function in any neighbourhood of a given point.

Stochastic estimation of firm technology, inefficiency, and productivity growth using shadow cost and distance functions

It is well-known that a firms technology, allocative efficiency, technical efficiency, and productivity growth can be estimated using a shadow cost system, comprised of a shadow cost function and its share equations, whose arguments are outputs and shadow input prices (prices internal to the firm). We provide a dual characterization to estimate these measures using a shadow distance system. This system is comprised of a shadow distance function, expressed in terms of shadow input quantities and output quantities, plus the first-order conditions from the cost-minimization problem. An advantage of the distance system over the cost system is that we obtain direct estimates of input inefficiency with the former, but indirect estimates with the latter. We also show how to express cost function derivatives in terms of distance function derivatives, which allows calculation of returns to scale and price elasticities of demand from the estimated distance system. Using panel data on US electric utilities, we estimate both systems and find a strong similarity between their associated measures.

Efficiency measures for multiplant firms

Previous studies of output-based efficiency measures make no distinction between plant data and firm data. In this paper two new efficiency measures are proposed and characterized in the context of multiplant firms. An empirical example is given to illustrate the two measures.

Stochastic Estimation of Firm Inefficiency Using Distance Functions

Econometric estimation of allocative and technical efficiency has frequently been carried out using a shadow cost function and its associated share or demand equations. Since the problem is formulated in terms of shadow prices, the effect of allocative inefficiency on input usage must be computed indirectly from input share or demand equations. As an alternative approach, we derive and estimate an input shadow distance system comprising the dual shadow input distance function and the price equations derived from the shadow cost minimization problem. Estimated shadow quantities provide direct estimates of the effect of allocative inefficiency on input usage. One can also easily calculate firm- and time-varying technical inefficiency by decomposing the residuals. We also compute returns to scale and the cost savings obtained by eliminating both types of inefficiency. Our approach is illustrated using a panel of U.S. railroads.

A Distance Function Approach to Multioutput Technologies

Most empirical production studies which exploit the principles of duality theory do so by estimating a firms cost function. An interesting exception is a recent paper by Kim [5] which appeared in this Journal. Kim estimated an indirect production function and argued that such an approach might have econometric advantages over the cost function approach. However, any arguments for an indirect production function approach would appear to lose their force when the firms under study produce several outputs. In fact, both the direct and indirect production functions are inappropriate models in this case. In this paper, we consider four ways to represent a multioutput technology, namely the output distance function, the input distance function, the indirect output distance function, and the cost function. While these four representations have already been introduced in the literature by Shephard [6; 7] and Fare [3], we relate them to each other in new ways, i.e., we present some duality theorems. We also show that the output distance function and the indirect output distance function are natural multioutput generalizations of the concepts of a production function and an indirect production function.

Luenberger Productivity Indicators: Aggregation Across Firms

Two methods of aggregating Luenberger productivity indicators across firms are considered. One method makes use of some rather implausible allocative efficiency assumptions. The second method, a superlative index number approach, relies on more palatable assumptions and is judged to be the more promising of the two methods.

Economic Analysis of Production Price Indexes

Preface 1. Introduction 2. Principles of price and quantity measurement: ouputs 3. Comparative statics: outputs 4. Principles of price and quantity measurement: inputs 5. Comparative statics: inputs 6. Aggregation Appendix References.

Homothetic non-parametric production models

Abstract A test for homotheticity in the context of non-parametric production models is proposed. We also show how a homothetic piece-wise linear technology can be constructed from an observed input—output data set.

Efficiency Measures for Multiplant Firms with Limited Data

Measures of technical efficiency typically require data on outputs and inputs measured in physical units. However, in many applications such data may be difficult or costly to obtain. Examples of this problem include: (a) Firms which only report financial data, i.e., outputs and inputs measured in money units. (b) Multiproduct firms which only report total revenue for an extensive product line. (c) Firms which only report total cost.

Index numbers and consistency in aggregation

Abstract This paper is an analysis of the concept of consistency in aggregation. This is the conjunction of three requirements: (i) for any given partition of the variables, two-stage aggregation is consistent, (ii) that each subaggregate and the overall aggregate have the same functional form, and (iii) that all partitions of the variables are feasible. We show that in the scalar case this results in a quasi-additive functional form. The generalization to many attributes is however shown to lead to few restrictions.