On a General Computer Algorithm for the Analysis of Models with Limited Dependent Variables

Several econometric models for the analysis of relationships with limited dependent variables have been proposed, including the probit, Tobit, two-limit probit, ordered discrete, and friction models. Widespread application of these methods has been hampered by the lack of suitable computer programs. This paper provides a concise survey of the various models; suggests a general functional model under which they may be formulated and analyzed; reviews the analytic problems and the similarities and dissimilarities of the models; and outlines the appropriate and necessary methods of analysis including, but not limited to, estimation. It is thus intended to serve as a guide for users of the various models, for the preparation of suitable computer programs, for the users of those programs; and, more specifically, for the users of the program package utilizing the functional model as implemented on the NBER TROLL system.

Analysis of Qualitative Variables

A variety of qualitative dependent variable models are surveyed with attention focused on the computational aspects of their analysis. The models covered include single equation dichotomous models; single equation polychotomous models with unordered, ordered, and sequential variables; and simultaneous equation models. Care is taken to illucidate the nature of the suggested "full information" and "limited information" approaches to the simultaneous equation models and the formulation of recursive and causal chain models.

The Effect of and a Test for Misspecification in the Censored-Normal Model

It is well-known that ordinary least-squares will produce inconsistent estimates of the regression parameters if the dependent variable is censored or truncated. Maximum likelihood estimation with a normality assumption on Tobit and other limited dependent variable models is being employed with increasing frequency to avoid this inconsistency. It is not so commonly acknowledged, however, that such estimates lack robustness : The assumptions required of these models are quite strong and any violation, such as heteroscedasticity or nonnormality, may result in an asymptotic bias as severe as in the naive OLS formulations. But to recognize the potential inconsistency in the face of misspecification without a test for and solution to such misspecification is of little use. The purpose of this paper is to examine the nature of the inconsistency and to suggest a general test for misspecification

A Note on 'Experimental Auction Markets and the Walrasian Hypothesis'

This note serves to correct an erroneous inference regarding price dynamics and to graphically illustrate the importance of model specification in the context of a very simple and fascinating structure. In an earlier JPE article, Vernon Smith concluded that excess supply by itself was an unreliable predictor of the speed of price adjustment. On the basis of regression procedures applied to experimental data he found that the potential rent to be captured exerts the dominant influence. Two alternative statistical procedures, a Tobit specification and a nonparametric test, dramatically deny this inference. Excess supply dominates excess rent as a predictor of the rate of adjustment, but in fact neither Hypothesis adequately captures the random behavior of price movement

Censored Regression Models with Unobserved Stochastic Censoring Thresholds

The "Tobit" model is a useful tool for estimation of regression models with a truncated or limited dependent variable, but it requires a threshold which is either a known constant or an observable and independent variable. The model presented here extends the Tobit model to the censored case where the threshold is an unobserved and not necessarily independent random variable. Maximum likelihood procedures can be employed for joint estimation of both the primary regression equation and the parameters of the distribution of that random threshold. The appropriate likelihood function is derived, the conditions necessary for identification are revealed, and the particular estimation difficulties are discussed. The model is illustrated by an application to the determination of a housewife's value of time.

In Search of Scientific Regulation: The UHF Allocation Experiment

This paper reports the results of one attempt to introduce an objective, quantitative, scientific mechanism for making allocational regulatory decisions. The case is the allocation of UHF television stations among cities by the Federal Communications Commission. The mechanism is an experiment which is designed to reveal the preferences of the subjects with respect to alternative allocations. Pilot experiments were performed on FCC staff, the purposes of which were to refine the experimental design and instructions and to provide data for comparing different specifications of the final estimated equation. Participating in the final experiment were six FCC commissioners, nine members of the Commission's congressional oversight committee, and eleven members of the staffs of both groups. Data collected from these experiments have been fitted to theoretical stochastic models of qualitative choice behavior to obtain estimates of allocation preferences as a function of market characteristics. These preference functions are then used (a) to check the coherence of preferences across individuals; (b) to examine differences in policy objectives between congressional oversight committees and the regulatory agency; (c) to determine whether individual preferences can be aggregated into a social decision function with normatively compelling properties, such as consistency with individual preferences or majority-rule equilibrium; and (d) to test the sensitivity of committee decisions to voting institutions and alternative agendas

Specification Errors in Limited Dependent Variable Models

A preliminary investigation of two specification error problems in truncated dependent variable models is reported. It is shown that heteroscedasticity in a tobit model results in biased estimates when the model is misspecified. This differs from the OLS model where estimates are still consistent though inefficient. The second problem examined is aggregation. An appropriate nonlinear least squares regression model is derived for situations when the micro-level model fits a tobit framework but only aggregate data are available.

A Note on 'Experimental Auction Markets and the Walrasian Hypothesis'

This note serves to correct an erroneous inference regarding price dynamics and to graphically illustrate the importance of model specification in the context of a very simple and fascinating structure. In an earlier JPE article, Vernon Smith concluded that excess supply by itself was an unreliable predictor of the speed of price adjustment. On the basis of regression procedures applied to experimental data he found that the potential rent to be captured exerts the dominant influence. Two alternative statistical procedures, a Tobit specification and a nonparametric test, dramatically deny this inference. Excess supply dominates excess rent as a predictor of the rate of adjustment, but in fact neither Hypothesis adequately captures the random behavior of price movement

The Effect of and a Test for Misspecification in the Censored-Normal Model

It is well-known that ordinary least-squares will produce inconsistent estimates of the regression parameters if the dependent variable is censored or truncated. Maximum likelihood estimation with a normality assumption on Tobit and other limited dependent variable models is being employed with increasing frequency to avoid this inconsistency. It is not so commonly acknowledged, however, that such estimates lack robustness : The assumptions required of these models are quite strong and any violation, such as heteroscedasticity or nonnormality, may result in an asymptotic bias as severe as in the naive OLS formulations. But to recognize the potential inconsistency in the face of misspecification without a test for and solution to such misspecification is of little use. The purpose of this paper is to examine the nature of the inconsistency and to suggest a general test for misspecification