Marjorie B. McElroy

The Empirical Content of Nash- Bargained Household Behavior

In households whose allocation decisions can be represented as Nash-bargained household decisions, extrahousehold environmental parameters (EEPs) serve as pure shifters of the threat points. The comparative statics of changes in demands due to changes in these EEPs are given. These are incorporated into a comprehensive statement of the empirical content of Nash-bargained household behavior, including a Nash generalization of Bartens (1966) fundamental matrix equation of the theory of consumer demand. Estimation and data requirements are discussed along with nested testing of the following structure: the neoclassical model is nested in the Nash-bargained model which, in turn, is nested in an unrestricted model of household demands. Emphasized throughout is the enriched menu of explanatory variables for demand analysis provided by the Nash model, as well as the models ability to jointly analyze (i) household formation and (ii) intrahousehold allocation decisions.

Goodness of fit for seemingly unrelated regressions : Glahn's R2y.x and Hooper's r2

This paper presents a measure of goodness of fit for Zellners seemingly unrelated regressions. The measure is a monotonic transform of the appropriate (asymptotic) F-statistic, is bounded on [0, 1] and is maximized by Zellners estimation technique. Glahns composite correlation coefficient is shown to be a special case of this measure. It is also compared to Hoopers squared trace correlation coefficient. All three measures as well as some additional asymptotic summary test statistics are calculated for the two-equation example of Zellner. The applicability of the latter test statistics seems not to be recognized in applied work.

THE JOINT DETERMINATION OF HOUSEHOLD MEMBERSHIP AND MARKET WORK - THE CASE OF YOUNG MEN

Except in special cases, market work and household membership are jointly chosen. A Nash bargaining model of family behavior is used to specify stochastic structural relationships (two indirect utility functions and a market and a reservation wage function) that jointly determine work, consumption, and household membership. The maximum likelihood estimates of the implied trinomial probit model differ sharply from those obtained when either market work or household membership is taken as exogenous. This application to white male youths from the National Longitudinal Surveys shows the insurance function of families: parents insure their sons against poor market opportunities.

Arbitrage Pricing Theory as a Restricted Nonlinear Multivariate Regression Model Iterated Nonlinear Seemingly Unrelated Regression Estimates

By replacing the unknown random factors of factor analysis with observed macroeconomic variables, the arbitrage pricing theory (APT) is recast as a multivariate nonlinear regression model with across-equation restrictions. An explicit theoretical justification for the inclusion of an arbitrary, well-diversified market index is given. Using monthly returns on 70 stocks, iterated nonlinear seemingly unrelated regression techniques are employed to obtain joint estimates of asset sensitivities and their associated APT risk “prices.” Without the assumption of normally distributed errors, these estimators are strongly consistent and asymptotically normal. With the additional assumption of normal errors, they are also full-information maximum likelihood estimators. Classical asymptotic nonlinear nested hypothesis tests are supportive of the APT with measured macroeconomic factors.

Two estimators for the apt model when factors are measured

Abstract Non-linear SUR and ITSUR techniques are proposed for the estimation of the APT and the CAPM when the factors are observed. These techniques estimate all of the parameters of the model simultaneously and directly impose the models non-linear parameter restrictions.

Weaker MSE criteria and tests for linear restrictions in regression models with non-spherical disturbances

Abstract This paper extend, in an asymptotic sense, the strong and the weaker mean square error criteria and corresponding tests to linear models with non-spherical disturbances where the error covariance matrix is unknown but a consistent estimator for it is available. The mean square error tests of Toro-Vizcorrondo and Wallace (1968) and Wallace (1972) test for the superiority of restricted over unrestricted linear estimators in a least squares context. This generalization of these tests makes them available for use with GLS, Zellners SUR, 2SLS, 3SLS, tests of over identification, and so forth.

The residual market factor, the APT, and mean-variance efficiency

The rapidly increasing volume of both published and unpublished work on the arbitrage pricing theory (APT) of Ross (1976) has given rise to a number of misunderstandings at the interface of theoretical and econometric work. In this article we extend the theoretical structure of our previous work (McElroy and Burmeister, 1985, 1988; Burmeister and McElroy, 1987, 1988) to provide a broad yet rigorous framework both for econometric estimation and for better economic interpretation of new empirical results.We begin with the case where allK factors are observed, and then present the second case ofK−1≡J observed APT factors and one unobserved factor, theresidual market factor introduced in McElroy and Burmeister (1985). The economic interpretations for equivalent specifications of this model are discussed, and we enumerate several immediate payoffs to these specifications.The main new results are concerned with the sometimes intricate relationships among APT models withK factors and APT models withK factors that are constrained to satisfy mean-variance efficiency restrictions. These results are not only of theoretical interest, but more importantly they provide the basis for econometric estimation and testing of nested hypotheses. These econometric issues are discussed in detail.