This article surveys the development of nonparametric models and methods for estimation of choice models with nonlinear budget sets.The discussion focuses on the budget set regression, that is, the conditional expectation of a choice variable given the budget set.Utility maximization in a nonparametric model with general heterogeneity reduces the curse of dimensionality in this regression.Empirical results using this regression are different from maximum likelihood and give informative inference.The article also considers the information provided by kink probabilities for nonparametric utility with general heterogeneity.Instrumental variable estimation and the evidence it provides of heterogeneity in preferences are also discussed.

FIML is shown to be an instrumental variables estimator where the instruments embody all the over-identifying a priori restrictions. FIML is compared to the two alternative estimators 3SLS and full information instrumental variables. 3SLS differs from FIML in not using all a priori restrictions in forming the instruments. The full information instrumental variables estimator when iterated to convergence yields the FIML estimate. For the case of nonlinearity in the parameters a nonlinear 3SLS and a nonlinear full information instrumental variables estimator are proposed. Both estimators are asymptotically efficient. THIS PAPER UNDERTAKES an investigation of asymptotically efficient estimators for linear and nonlinear simultaneous equation econometric models. By using an instrumental variable approach the equivalence of previously proposed linear estimators to full information maximum likelihood (FIML) follows in a straightforward manner, and a class of new estimators which includes a nonlinear three stage least squares estimator (NL3SLS) and nonlinear full information instrumental variables estimator are proposed and shown to be asymptotically equivalent to FIML. First, an instrumental variable interpretation of FIML is developed by investigating the first order conditions for the maximum of the likelihood function without first concentrating the likelihood function. The essential difference between 3SLS and FIML then becomes evident. The difference between the two estimators is first that FIML uses all over-identifying restrictions in forming the instruments while 3SLS ignores some of these restrictions. Also, FIML uses an estimate of the covariance matrix in forming the instruments which is consistent in the sample with the parameter estimates. Thus the instruments used by FIML are mutually consistent with the parameter estimates in the given sample, while for other estimators the instruments are consistent with the parameter estimates only asymptotically. While this difference in forming the instruments is of no importance asymptotically as is known by the earlier results of Sargan [10] and Rothenberg and Leenders [9], in finite samples there seems to be no reason for not using all known prior information. The use of the a priori restrictions gives a more useful criterion than Dhrymes' [3] recent interpretations of a difference in purging the endogenous variables since all other proposed estimators can be shown to be equivalent by simply proving asymptotic equivalence of the instruments used to those instruments used by the FIML estimator. Then using the instrumental variable interpretation, a relation between FIML and the class of estimators recently proposed by Dhrymes [2], Lyttkens [5, 6], and Brundy and Jorgenson [1] is established. The full information instrumental

Consumer's surplus is a widely used tool in applied welfare economics. Both economic theorists and cost benefit analysis often use consumer's surplus despite its somewhat dubious reputation. The basic idea is to evaluate the value to a consumer or his willingness to for a change in price of a good from say pricep? to pricep'. Because price changes affect consumer welfare, an evaluation of this effect is often a key input to public policy decisions. Yet consumer's surplus is probably the most controversial of widely used economic concepts. Both Paul Samuelson and Ian Little conclude that the economics profession would be better off without it. It is my feeling of the situation that substantial agreement exists on the correct quantities to be measured: the amount the consumer would pay or would need to be paid to be just as well off after the price change as he was before the price change. The quantities correspond to John Hicks' compensating variation measures. An alternative measure which takes ex post price change utility as the basis of comparison is Hicks' equivalent variation.' The controversy arises in the measurement of these quantities. The usual measurement procedure is to use the area to the left of the Marshallian (market) demand curve between two price levels. Jules Dupuit originated this measure of welfare change, and Alfred Marshall and Hicks derived appropriate conditions for its use. The primary condition for the area to the left of the demand curve to correspond to the compensating variation is to have constant marginal utility of income. Marshall gave this condition, and if it holds, the same quantity will be derived as the area to the left of the compensated (Hicksian) demand curve. This area to the left of the compensated demand curve is exactly what the compensating variation and equivalent variation measure. Thus the constant marginal utility of income is a sufficient condition for Marshallian consumer's surplus to be equal to Hicks' consumer's surplus. In this case Arnold Harberger's plea to use the welfare triangle as one-half times the product of the price change times the quantity change to measure deadweight loss corresponds to the correct theoretical amount of welfare change. In a recent paper, Robert Willig derives bounds for the percentage difference between the correct measure of either the compensating or equivalent variation and the Marshallian measure derived form the market demand curve. His bounds, which depend on the income elasticity of demand for the single good in the region of price change being considered as well as the proportion of the consumer's income spent on the good, demonstrate that the Marshallian consumer's surplus is often a good approximation to Hicks' consumer's surplus. The fact that the proportion of the consumer's income spent matters as well as the income elasticity was first pointed out by Harold Hotelling. Willig contends that the approximation error will be less than the errors involved in estimating the demand curve. Thus he hopes to remove the need for apology that applied economists often need to give to theorists who remark on the inappropriateness of using Marshallian consumer's surplus to measure welfare change. However, in this paper I show that for the case primarily considered by Willig of a single price change, which is also the situation in which consumer's surplus is often used in applied work, no approximation is necessary. *Professor of economics, Massachusetts Institute of Technology, and research associate, National Bureau of Economic Research. I would like to thank Peter Diamond, Erwin Diewert, Daniel McFadden, Robert Merton, Robert Solow, Hal Varian, Joel Yellin, and the referees for help and comments. Research support from the National Science Foundation is acknowledged. 'The reason that we still have two, rather than one, of Samuelson's six measures of consumer's surplus arises from an index number problem of the correct basis for the welfare comparison. I will give both measures but plan to concentrate on the compensating variation.

An econometric analysis demonstrates that television ratings for NBA games are substantially higher when certain players ('superstars') are involved. Thus, these superstars are quite important for generating revenue, not only for their own teams but for other teams as well. Using the econometric analysis and additional information on attendance and paraphernalia sales, the authors estimate the value of Michael Jordan to the other NBA teams to be approximately $53 million. The positive externality superstars have on other teams can lead to an inefficient distribution of player talent. The authors examine several league policies that might be used to address the externality.

Jerry A. Hausman, David A. Wise; Discontinuous Budget Constraints and Estimation: The Demand for Housing, The Review of Economic Studies, Volume 47, Issue 1, 1

A model of labor supply is formulated which takes explicit account of nonlinearities in the budget set which arise because the net, after-tax wage depends on hours worked. These nonlinearities may lead to a convex budget set due to the effect of progressive marginal tax rates, or they may lead to a nonconvex budget set due to the effect of government transfer programs such as AFDC or a negative income tax. The nonlinearities affect both the marginal wage and the "virtual" nonlabor income which the individual faces. The model is estimated on a sample of prime-age males from the Gary negative income tax experiment.

A model of labor supply is formulated which takes explicit account of nonlinearities in the budget set which arise because the net, after-tax wage depends on hours worked. These nonlinearities may lead to a convex budget set due to the effect of progressive marginal tax rates, or they may lead to a nonconvex budget set due to the effect of government transfer programs such as AFDC or a negative income tax. The nonlinearities affect both the marginal wage and the "virtual" nonlabor income which the individual faces. The model is estimated on a sample of prime-age males from the Gary negative income tax experiment.

Individual heterogeneity is an important source of variation in demand. Allow-ing for general heterogeneity is needed for correct welfare comparisons. We consider general heterogenous demand where preferences and linear budget sets are statis-tically independent. Only the marginal distribution of demand for each price and income is identified from cross-section data where only one price and income is observed for each individual. Thus, objects that depend on varying price and/or income for an indiviual are not generally identified, including average exact con-sumer surplus. We use bounds on income effects to derive relatively simple bounds on the average surplus, including for discrete/continous choice. We also sketch an approach to bounding surplus that does not use income effect bounds. We apply the results to gasoline demand. We find tight bounds for average surplus in this application but wider bounds for average deadweight loss.