Knowledge that Transforms

[This paper deals with two single-equation estimators in a set of simultaneous linear stochastic equations--namely, ordinary least squares (OLS) and two-stage least squares (2SLS). Under the assumption that all predetermined variables in the model are exogenous, necessary and sufficient conditions are obtained for the existence of even moments of the above estimators. It is shown that for the general case with an arbitrary number of included endogenous variables, even moments of the 2SLS estimator are finite if and only if the order is less than K2 - G1 + 1. Furthermore, even moments of the OLS estimator exist if and only if the order is less than N - K1 - G1 + 1, where N is the sample size, G1 + 1 is the number of included endogenous variables, K1 and K2 respectively are the number of included and excluded exogenous variables in the equation to be estimated.]

IN THEIR ARTICLE [5], Liu and Breen propose a new estimator of the large-sample asymptotic covariance matrix for the limited information maximum likelihood estimator in simultaneous equations, and express surprise that their estimator is different from the estimator proposed by Chernoff and Divinsky [1]. Additionally, they question the interpretation of a statistic used in the past to test over-identifying restrictions.

IN THEIR PAPER [1] with the above title, Blattberg and Sargent have suggested a method for estimating regression parameters when disturbances are generated by a symmetric stable law. This procedure was originally suggested by John Wise [4]. Wise arrived at this estimator by confining attention to the class of linear unbiased estimators and minimizing the scale parameter. He also suggested that his procedure might be considered as a generalization of the classical least squares procedure which fails when the second moments of the disturbances do not exist. Blattberg and Sargent have compared various estimators by using simulated data. The main purpose of this note is to show that the procedure suggested by Wise and Blattberg and Sargent has an optimal property, namely that it yields an estimator that has minimum mean absolute error among the class of all linear unbiased estimators. The model is the well-known linear regression model given by

[In this paper we give necessary and sufficient conditions such that a decision maker who operates in a world in which finitely many states of nature can occur has an increasing, strictly concave utility function U(.) and a subjective probability measure P(.) and such that he chooses among acts with uncertain outcomes according to the expected value of U(.) (with respect to P(.)) which they offer him.]

[In this paper, the authors develop a simultaneous equation model of birth rates composed of four estimated equations. This work differs from past research in that it considers the simultaneous relationship between birth rates and income and includes the cost of fertility as an explanatory factor. This cost is measured by the female labor participation rate under the assumption that income foregone due to fertility is a significant opportunity cost.]

[The purpose of this paper is to investigate the structure of the class of market excess demand functions which can be generated by aggregating individual utility maximizing behavior. Among the results are: (i) in a region of the relative price domain an arbitrary polynomial function can be generated as an excess demand function for a particular commodity, and (ii) for any p in the relative price domain, a given configuration of excess demands and rates of change in excess demand can be generated at p if and only if it is consistent with Walras' Law.]