Knowledge that Transforms

WHEN ESTIMATING REGRESSION MODELS it is very nearly always assumed that the sample is random. The recent literature has begun to deal with the problems which arise when estimating a regression model with samples which may not be random. The most general case in which one only has access to a single nonrandom sample has not been addressed since it is a very imposing problem. The case which has been addressed starts with a random sample but considers the problem of missing values for the dependent variable of a regression. If the determination of which values are to be observed is related to the unobservable error term in the regression, then methods such as ordinary least squares are in general inappropriate. By constructing a joint model which represents both the regression model to be estimated and the process determining when the dependent variable is to be observed, some progress can be made towards taking into account nonrandomness for the observed values of the dependent variable. The actual techniques employed fall into two rough groups, full information maximum likelihood models, and limited information methods which are more easily estimated. In the full information category are two methods. One model combines the probit and the normal regression models, and the other combines the Tobit or limited dependent variable model with the normal regression model. The form of the probit regression model is

[A dynamic noncooperative game in which firms choose output and cost-reducing investment sequences is developed. The sequences exhibit several properties of manufacturing industries. Several steady states exist. Under some reasonable conditions only industry structures in which firms have different market shares can be locally stable steady states. So the model presents one explanation of the source of differences among firms in homogeneous good oligopolies.]

This paper develops a test of the rational expectations hypothesis advanced by Muth [18]. The framework considered here allows for multiperiod expectations of several endogenous variables, with or without lagged exogenous variables. In conventional (linear) models, the hypothesis implies that the expectations are linear in certain relevant variables, and restricts the coefficients of these variables to be certain functions of the parameters in the imbedding model. The test is developed as a test of the validity of these restrictions. The paper also treats the estimation problem in some details, under the alternative hypothesis which is taken as simply the negation of the rational expectations hypothesis.

[This paper is an exploration of the empirical implications for the behavior of consumer-workers of treating unemployment as a constraint on choice rather than the result of it. The consequences of one family member's unemployment for the constrained commodity demand functions and the labor supply functions of other family members are first examined and then the normative interpretation of unemployment's compensation is considered. The final section of the paper contains estimates of a simple set of aggregate labor supply and commodity demand functions that are based on utility maximization and that explicitly recognize the presence of both constrained and unconstrained microeconomic units.]

[This paper presents the theoretical development of bounds tests and exact tests for serial correlation in the context of a simultaneous equation model which are analogous to those developed for single equation models. The powers of the exact tests are estimated and compared using Monte Carlo simulation of a three equation model.]

asymptotic variances of multipliers for nonlinear models. It is used to estimate the uncertainty of the results of eight policy experiments for a particular model. ALTHOUGH MACROECONOMETRIC MOI)ELS are widely used to analyze the effects of alternative government actions on the economy, estimates of the uncertainty of these effects are rarely, if ever, presented. This is, of course, not surprising, since most macroeconometric models are nonlinear. Unlike for linear models, formulas for the asymptotic variances of impact and dynamic multipliers are not known for nonlinear models. ’ It is possible, however, to estimate these variances for nonlinear models by stochastic simulation, and the purpose of this paper is to discuss the method by which this can be done. The method is discussed in Section 2, and results of applying the method to eight policy experiments for the model in Fair [7,10] are presented in Section 3.3 Given the obvious importance of knowing how much confidence to place on the results of any particular policy experiment in a model, it is hoped that this study will stimulate others to obtain uncertainty estimates for their models similar to those presented in Section 3. 2. THE METHOD The. method can be applied to a model that is nonlinear in both variables and coefficients. Let G denote the total number of equations in the model, M the number of stochastic equations, and N the total number of predetermined (both exogenous and lagged endogenous) variables. Assume (for exposition.4 con-venience only) that the model is quarterly, and let the ith equation of the model for quarter t be written: (1) CpdYi,, YGh Zlb, ZN,,

Robert A. Pollak, Terence J. Wales, Comparison of the Quadratic Expenditure System and Translog Demand Systems with Alternative Specifications of Demographic Effects, Econometrica, Vol. 48, No. 3 (Apr., 1980), pp. 595-612

In our previous paper, "Optimal Allocation of Public Goods...," (1977) we presented a mechanism for determining efficient public goods allocations when preferences are unknown and consumers are free to misrepresent their demands for public goods. We proved the basic welfare theorem for this model: If consumers are competitive in markets for private goods and follow Nash behavior in their choice of demands to report to the mechanism, then equilibria will be Pareto optimal. In this paper we show this result is not vacuous by proving that an equilibria will be Pareto optimal. In this paper we show this result is not vacuous by proving that an equilibrium will exist for a wide class of economies. Our conditions are slightly stronger than those required to prove the existence of a Lindahl equilibrium. In order to rule out the possibility of bankruptcy, we assume additionally that at all Pareto optimal allocations, private goods consumption is bounded away from zero.

[In this paper the Le Chatelier principle for a Leontief model due to Samuelson and Morishima is extended to a more general system of nonlinear equations. The global strong version of the principle as well as the weak one is presented without using any determinant theory or calculus. The strong version is concerned with comparative statics when some constraints are relaxed together with changes in parameters. It is also shown that our results are applicable to the system of excess demand functions which satisfy the gross substitute condition.]