Knowledge that Transforms

This paper presents the necessary and sufficient conditions for determining the signs of the solution variables of a system of linear equations based only upon a knowledge of the signs of the coefficient matrix and the signs of the right hand side variables. This problem was initially formulated in economics due to the idea that the signs of an equation's derivatives might have a stronger empirical basis than that of a particular functional form. A new interest in qualitative problems has arisen in connection with the need to develop analytic measures in order to better manage the understanding and use of large, computer-based mathematical systems. The conditions for the qualitative determinancy of nonhomogeneous systems are developed in terms of a small number of necessary conditions which are jointly sufficient. Algorithmic approaches are given for testing a given system for qualitative determinancy. For nonhomogeneous systems algorithms are given for constructing all possible qualitatively determinate systems of a given size. For the homogeneous case conditions are also given for the qualitative invertibility of the (irreducible) coefficient matrix. These conditions are then related to the problem of partially qualitatively determinate systems and the signs in the qualitative inverse of a matrix.

[Differing opinions about the specification of econometric relationships often lead to a situation in which there are competing non-nested models. This paper is concerned with the problem of testing such models. It is first assumed that tests are based upon instrumental variable estimates (so that the models can be alternative versions of an equation in a system). The tests so derived are then specialized to the case in which ordinary least squares is an appropriate estimator.]

This picture is greatly complicated when restrictions on the structural disturbance variances and covariances, (henceforth "covariance restrictions") are allowed.Koopmans Rubin, and Leipnik (1950) recognized the usefulness of such restrictions for identification and demonstrated their equivalence to bilinear restrictions on the coefficients.This work was pursued by Wegge (1965) j Rothenberg (1971), and especially Fisher (1963, 1965), surveyed in Fisher (19-66, Chapters 3 and 4).Structural estimation is also complicated by covariance restrictions: as pointed out by Rothenberg and Leenders (1964), system instrumental variables estimators (3SLS) are asymptotically inefficient when covariance i restrictions are present.Two features of these results are (i) the absence of useful necessary and sufficient conditions for identifiability in the presence of covariance restrictions, and (ii) the disappearance of the link between restrictions required for identification and instrumental variables required for estimation.The problem of incorporating covariance restric- tions Into the theory of identification and estimation is thus Incomplete.In this and a companion paper on estimation (Hausman-Taylor (1981)), we provide a simple, complete, and useful solution to the problem In terms of instrumental variables .In the present paper, we derive necessary and sufficient conditions for identifiability in linear simultaneous equations models subject to linear restrictions on the coefficients and covariances.The result, in practical

[This paper analyzes the optimal capital policy of an entrepreneurial firm whose cost of borrowing depends on its debt-equity ratio. The firm chooses the investment plan that maximizes the entrepreneur's intertemporal utility, given static expectations. It is shown that the rate of investment is closely related to the rate of profit retention. It is also demonstrated that the optimal plan can be approximated by a flexible accelerator model of investment. If expectations prove wrong, the investment behavior of the firm could involve instantaneous debt and capital stock adjustment prior to the operation of the flexible accelerator.]

This paper examines the consequences and detection of model misspecification when using maximum likelihood techniques for estimation and inference. The quasi-maximum likelihood estimator (QMLE) converges to a well defined limit, and may or may not be consistent for particular parameters of interest. Standard tests (Wald, Lagrange Multiplier, or Likelihood Ratio) are invalid in the presence of misspecification, but more general statistics are given which allow inferences to be drawn robustly. The properties of the QMLE and the information matrix are exploited to yield several useful tests for model misspecification.

[The well known result that every finite, strictly deterministic game with perfect information has a unique solution unless the utility functions of the players lie in a low dimensional exception space, is generalized to games containing change moves. Two group decision procedures, "voting by successive proposal and veto" and "voting by repeated veto," are analyzed in this context. The first procedure is efficient, anonymous, and neutral for an arbitrary number n of participants and an arbitrary finite set of alternatives, the second only if n @? 3.]

SINCE ITS INTRODUCTION, the expected utility hypothesis has been widely used in the construction of economic models. More recently, attention has focused on the conditions under which it is possible in principle to recover individual investors' risk preferences from their demand for assets (Dybvig and Polemarchakis [2]). This paper represents a first attempt to recover preferences operationally from data on the actual demand for assets. Numerous difficulties are encountered in attempting to measure preferences toward risk in a real world setting. Preferences are revealed through the choices of an individual. But in an uncertain world, these choices also depend on his expectations of future events. Hence, an immediate problem arises in separating the influences of each on such decisions. Problems can also arise in measuring other variables, such as wealth, which influence choices. Because of these difficulties, efforts to classify and measure an individual's risk preferences have been confined to direct assessments in hypothetical environments (e.g. Kahneman and Tversky [4] and Keeney and Raiffa [5, pp. 203-212]).2 In these studies the authors assumed that stated preferences are accurate indicators of actual behavior. The question remains, however, whether individuals actually behave in the way their assessments predict. The purpose of this note is to make some progress in answering this question. In it an experiment is described which infers an individual's risk preferences from his actual choices in a real world environment. Specifically, the risk aversion of a dealer in U.S. Government securities is assessed directly and then estimated statistically from his actual demand for bills in the weekly Treasury auctions. The distribution of returns used in the analysis are calculated from the forecasts made by the dealer himself. In addition to introducing new procedures for measuring preferences, this study provides insights into the reliability of direct assessments in predicting the actual behavior.

The effects of minimum wage legislation on the employment and wage rates of youth are estimated using a new statistical approach. We find that without the minimum, not only would the percent of out-of-school youth who are employed be 4 to 6 percent higher than it is, but also that these youth would earn more.