Dennis J. Aigner

Formulation and estimation of stochastic frontier production function models

Previous studies of the so-called frontier production function have not utilized an adequate characterization of the disturbance term for such a model. In this paper we provide an appropriate specification, by defining the disturbance term as the sum of symmetric normal and (negative) half-normal random variables. Various aspects of maximum-likelihood estimation for the coefficients of a production function with an additive disturbance term of this sort are then considered.

Statistical Theories of Discrimination in Labor Markets

Examines economic discrimination in labor markets using a stochastic model. Analysis of several types of economic discrimination within the context of competitive market assumptions; Empirical plausibility and implications of the alternative models of economic discrimination; Role of statistical theories in the explanation of labor market discrimination. (Abstract copyright EBSCO.)

Regression with a binary independent variable subject to errors of observation

In a recent study of the socio-economic effects of the disease bilharzia on the population of the Caribbean island of St. Lucia, Weisbrod et al. (1973) make abundant use of regression methods to analyze the various relationships of interest. A common independent variable in their work is a dummy variable that indicates the presence or absence of the disease in the person sampled (the observation unit). The nature of diagnosis for this particular disease is such that if a person is diagnosed as having the disease, he does indeed have it. However, if the diagnosis is negative there is a non-zero probability, q, that he has been diagnosed incorrectly and has the disease. It is the intent of this note to consider the effects of such an independent variable - a binary variable subject td ‘errors of classification’ - in least squares regression. The results of both an analysis of bias in least squares parameter estimates and of the availability of alternative estimators is parallel to the classical case where both the variable and its measurement error are continuous random variables. Many details will not be repeated here in deference to the reader’s familiarity with that subject. The important practical difference between the two cases is that the information needed to obtain consistent (or nearly so) parameter estimates may be more readily available in the discrete case. In the study cited, for instance, extraneous information about q is available from patient medical histories and examination data. The following section of the present article contains a brief exposition of the nature of a discrete ‘classification error’. Previous authors who have treated this material include Neyman (1950), Bross (1954) and Lord and Novick (1968). Sect. 3 then takes up an analysis of the effects of including an independent variable subject to such measure

Latent variable models in econometrics

Publisher Summary This chapter discusses latent variable models in econometrics. The essential characteristic of a latent variable is revealed by the fact that the system of linear structural equations in which it appears cannot be manipulated so as to express the variable as a function of measured variables only. It discusses that for a linear structural equation system to be called “latent variable model,” there is at least one more independent variable than the number of measured variables. Usage of the term “independent” variable as contrasted with “exogenous” variable, the more common phrase in econometrics, includes measurement errors and the equation residuals themselves. In the functional model, the true values of exogenous variables are fixed variates, and therefore, are best thought of as nuisance parameters that may have to be estimated en route to getting consistent estimates of the primary structural parameters of interest. Finally, restrictions on a models covariance structure, which are commonplace in sociometric and psychometric modeling, also serve to aid identification.

MSE dominance of least squares with errors-of-observation

Abstract On a criterion of minimum asymptotic coefficient bias, it has been shown recently [McCallum (1972), Wickens (1972)] that faced with a choice of using or discarding a (perhaps poor) proxy for an otherwise relevant independent variable which appears in a multiple regression model, one should always use the proxy. In this paper the analysis is expanded to consider variance in addition to bias in the criterion function. Our major finding is that although inclusion of the proxy is not a superior strategy unequivocally, it is recommended over a broad range of empirical situations.

On Student Evaluation of Teaching Ability

Student evaluation of instructor performance has become a widespread practice. This paper examines the relationship of both student and course characteristics to student rankings of instructors.

Estimation of Pareto's Law from Grouped Observations

Abstract The problem of estimating the scale parameter in the Pareto distribution from grouped observations is considered. Several estimators—the maximum likelihood estimator and four variants of least squares—are evaluated. Most of these have identical BAN properties but require nonlinear computations. A linearized BAN estimator is constructed, and numerical illustrations are provided.

A random coefficient approach to the estimation of residential end-use load profiles *

Abstract This paper develops some extensions to the statistical approach to the estimation of residential end-use load curves and provides a substantive application of these developments to a sample of households. Importantly, the typical assumption that the coefficients of the appliance dummies are fixed, ignores two important sources of variation: during any particular hour the intensity of use of a particular appliance will vary from household to household; also the dummies indicate only absence or presence of the appliance and do not allow for variations in size or capacity. Our treatment of the coefficients of appliance dummies as random rather than fixed provides a structure for the heteroskedasticity that has been observed in previous studies of this kind. Also included in the analysis is the utilization of other sources of information in particular from direct metering and a sample of diaries. The resultant single equation specifications for individual hours are then pooled and jointly estimated using an SUR structure.

Correcting for Truncation Bias in the Analysis of Experiments in Time-of-Day Pricing of Electricity

This paper applies methods for analyzing data from samples that have been chosen by restricting the target population in discernible ways to date from a 1976 experiment in time-of-day pricing of electricity for residential customers in Arizona. We find that whereas conventional estimation methods lead to the conclusion that the peak price elasticity of demand is larger (in absolute value) than either the corresponding midpeak or offpeak elasticity, once truncation bias is accounted for, the peak elasticity is smaller than the other two. This finding accords with a preliminary analysis of data from Wisconsin, where no such sample truncation was present.

Estimation of time-of-use pricing response in the absence of experimental data: An application of the methodology of data transferability☆

Abstract A random coefficients regression framework is used to characterize the problem of pooling the results of various designed experiments in time-of-use pricing for electricity. The ‘empirical Bayes’ estimation approach fostered by Lindley and Smith provides for the inclusion of prior information on the variance–covariance matrix of regression coefficients across experiments and a means to impute an estimate of price response (in this case the elasticity of substitution) to a region which did not have an experiment. The methodology is illustrated with an application where two experiments that were conducted in Southern California are pooled in order to infer a measure of price response to an example TOU tariff in a large midwestern utility.