Ajay Maindiratta

Maximum likelihood estimation of monotone and concave production frontiers

In this paper we bring together the previously separate parametric and nonparametric approaches to production frontier estimation by developing composed error models for maximum likelihood estimation from nonparametrically specified classes of frontiers. This approach avoids the untestable restrictions of parametric functional forms and also provides a statistical foundation for nonparametric frontier estimation. We first examine the single output setting and then extend our formulation to the multiple output setting. The key step in developing the estimation problems is to identify operational constraint sets to ensure estimation from the desired class of frontiers. We also suggest algorithms for solving the resulting constrained likelihood function optimization problems.

A Comparison of DEA and Translog Estimates of Production Frontiers Using Simulated Observations from a Known Technology

Data envelopment analysis (DEA), introduced in Charnes, Cooper, and Rhodes (1978), provides a new approach to the estimation of relative efficiencies of decision making units (DMUs). As described by Banker (1980b) and Banker, Charnes, and Cooper (1984), DEA also encompasses estimation of production frontiers making minimal assumptions—such as convexity—about the production possibility set. DEA may be employed to estimate technical and scale efficiencies as in Banker, Charnes, and Cooper, rates of substitution between inputs as in Banker, Charnes, and Cooper and Charnes, Cooper, and Rhodes (1978), and returns to scale and most productive scale sizes as in Banker (1984) and Banker, Charnes, and Cooper (1984). These estimates of different production characteristics pertain to the efficient production surface, unlike the commonly employed regression techniques which estimate the average production correspondence. In this chapter, we report on the results of a simulation study in which DEA was employed to estimate the production frontier from input and output data randomly generated from a known technology.

Largest size-efficient scale and size efficiencies of decision-making units in data envelopment analysis

Abstract This paper extends the usual DEA analysis, which evaluates input savings that could have been effected by a decision-making unit, given its observed task, to inquire into whether even greater savings would be possible if the task were to be optimally apportioned to a number of smaller units. The notion of size efficiency is introduced to measure this potential for further input reductions, and then compared and contrasted to the extant notion of scale efficiency. The existence of a largest radially size-efficient output scale is established as a ray property of the production frontier. An illustrative application to hospitals is described.

Market Imperfections as the Cause of Accounting Income Smoothing—The Case of Differential Capital Access

We show income smoothing results as a rational equilibrium behavior in a setting where the manager has superior foresight about the firms prospects but faces inferior capital access relative to the owner. Under a legal structure that makes forecast-based compensation impractical and an accounting framework that requires reported income to be consistent, unbiased and cash-flow convergent, we show that the manager reports a composite of the underlying income and his foresight information. Moreover, the reported income will exhibit a lower inter-temporal variance than the underlying income. The extent of smoothing is shown to increase with the accuracy of foresight information.We argue that other market imperfections could also cause income smoothing if the manager is privately better informed about future prospects. As such, this paper supports the view that income smoothing is not always opportunistic but can be induced by the owner to satisfy his need to be informed about the future performance of the firm.

On the Consistency of Maximum Likelihood Estimation of Monotone and Concave Production Frontiers

Banker and Maindiratta (1992) provides a method for the estimation of a stochastic production frontier from the class of all monotone and concave functions. A key aspect of their procedure is that the arguments in the log-likelihood function are the fitted frontier outputs themselves rather than the parameters of some assumed parametric functional form. Estimation from the desired class of functions is ensured by constraining the fitted points to lie on some monotone and concave surface via a set of inequality restrictions. In this paper, we establish that this procedure yields consistent estimates of the fitted outputs and the composed error density function parameters.

Nonparametric tests for optimizing behavior in production: Extensions to unobservable factors and superadditive technology

This paper develops two new nonparametric tests for optimizing behavior in production. The first is a test for consistency of observed data with cost minimization from a superadditive technology. Superadditivity of technology plays a key role in the theory of industry structure and natural monopoly. The second is an extension of Varians profit maximization test. When the data fails Varians test, one possible explanation is technical/allocative inefficiency. However, another possibility is the presence of unobservable, untradeable, and varying endowments of some factor of production. This paper develops a test that allows for such an ordinally measurable factor and notes its correspondence to the Afriat Theorem for utility maximization in demand analysis.