[Estimates of parameters in Tobit and other models for limited, truncated and censored dependent variables are not robust against misspecification. A test of the standard assumptions against a general misspecified alternative in the univariate censored normal model is derived and extended to the Tobit regression case. Computational ease and freedom from specification of a specific alternative hypothesis are primary attractions of the test.]

IN NONLINEAR MODELS the power function is often approximated by asymptotic methods. The most common approach is to consider the asymptotic local power function. The local power function is monotonic and it has essentially the same shape as the power function in the classical normal linear regression model. However, the accuracy of the approximation can be poor at nonlocal alternatives. This note examines the exact powers of the Wald test in the case of a one parameter nonlinear regression model with normal errors. The model is based on the exponential response function f( x, O) = exp( Ox). The results show that the exact power function of the Wald statistic can be nonmonotonic. For selected designs the exact powers of the Wald test first increase and then eventually decline as the distance between the hypothesized and the true values of the parameter increases. The exponential structure appears in many nonlinear models; see Gallant (1975, 1987) and Bates and Watts (1988). This suggests that nonmonotonicity of the Wald test is a feature of a wide class of nonlinear models. Indeed, Nelson and Savin (1988) show that it arises in standard logit, probit, and Tobit models as well. The focus here on the nonlinear regression model is for expository convenience. While the existence of nonmonotonic power is not new, the surprising results are that this phenomenon occurs in very simple nonlinear models and that it can be quite severe. In such cases the asymptotic local power approximation provides a very poor guide to the performance of alternative tests.

Some economic variables are restricted by an upper and lower limit but are continuous between the two limits. Measurements of such variables are sometimes available in their natural form and sometimes only in the form of three categories where information concerning the middle category is suppressed (unemployed, employed part time, employed full time, for example). Where such a variable is a continuous function of other variables between the two limits, the function can be estimated from data of either sort provided the function and the distribution of errors can be specified. WHEN THE LIMITED dependent variable technique developed by Tobin [3] is extended to provide for cases in which the dependent variable in a regression is subject to both an upper limit and a lower limit, a surprising property of the statistical model emerges.1 Estimates of the regression function can be obtained whether or not the exact values of the dependent variable are known for the nonlimit cases. Provided the functional form can be specified correctly, classification of the dependent variable into upper limit, lower limit, and non-limit observations provides enough information, along with observed values of the independent

[The paper presents maximum likelihood methods for estimating four types of disequilibrium models. In each case the model includes three equations: the demand equation, the supply equation, and the condition that quantity observed is the minimum of quantity demanded and quantity supplied. The first model consists of just these equations. In the second model one knows whether one is on the demand function or the supply function by looking at the direction of the change in price. In the third model the price change is assumed to be proportional to excess demand. In the fourth model the price change is a stochastic function of excess demand and possibly other exogenous variables. Some illustrative calculations are presented using the housing starts model considered by Fair and Jaffee in an earlier issue of this journal.]

Andrew F. Daughety, Forrest D. Nelson, An Econometric Analysis of Changes in the Cost and Production Structure of the Trucking Industry, 1953-1982, The Review of Economics and Statistics, Vol. 70, No. 1 (Feb., 1988), pp. 67-75

Results from the Iowa Political Stock Market are analyzed to ascertain how well markets work as aggregators of information. The authors find that the market worked extremely well, dominating opinion polls in forecasting the outcome of the 1988 presidential election, even though traders in the market exhibited substantial amounts of judgment biases. Their explanation is that judgment bias refers to average behavior, while in markets it is marginal traders who influence price. They present evidence that in this market a sufficient number of traders were free of judgment bias so that the market was able to work well. Copyright 1992 by American Economic Association.