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A Problem on Rankings by Committees

Econometrica 1976 44(2), 241
[We consider how large a committee must be before it is possible to achieve simultaneously any two rankings of m alternatives by two seemingly consistent procedures.]

Prior Information on the Coefficients when the Disturbance Covariance Matrix is Unknown

Econometrica 1976 44(4), 725
usefulness of prior information. Viewed broadly, this theme has encompassed such diverse topics as the estimation of a system of simultaneous structural equations, the specification and estimation of distributed lags, and the formal integration of stochastic prior and sample information through Bayes' theorem. Without exception, the results have encouraged the incorporation of further prior information into our statistical procedures, in the sense that the judicious use of such information has produced unambiguously better estimators. That this need not be the case in a typical linear regression application is thus somewhat surprising and constitutes the topic of this paper. Here, we develop the relationship between the specification of the deterministic and the stochastic components of a linear model and show that whenever the covariance structure of the disturbance process is effectively misspecified,2 one can no longer justify the use of prior information about the deterministic part of the model. If the error covariance matrix differs substantively from that required by the Gauss-Markov theorem, the imposition of correct linear restrictions on the regression coefficients leads to less efficient estimators of some estimable functions of the parameters.3 Prior information can hurt! We begin by introducing notation and examining the efficiency of least squares estimators in linear models with varying amounts of prior information. An application of the theory of regular pencils then produces the main results (Section 3), practical implications are drawn in Section 4, and we conclude with an application (Section 5).

Personal Taxation and Portfolio Composition: An Econometric Analysis

Econometrica 1976 44(4), 631
[Although the theory of taxation and portfolio choice has been extensively developed, the current paper begins the econometric study of this subject. The research analyzes the composition of portfolios of 1,799 households in a sample in which high income individuals are greatly overrepresented. The results show that the personal income tax has a very powerful effect on individuals' demands for portfolio assets after adjusting for the effects of net worth, age, sex, and the ratio of human to nonhuman capital.]

The Identification and Parameterization of Armax and State Space Forms

Econometrica 1976 44(4), 713
[It is known that there is a one-to-one correspondence between stationary ARMAX and state space models. In order to estimate these it is necessary first to identify and further, having identified, to choose parameters. This paper discusses the properties a system of identification and parameterization might be desired to have in relation to various examples of identification. It also constructs a (known) canonical state space form (identification) out of the constants needed to specify the corresponding ARMAX form. It is argued that what is here called "simple identification" will be the best basis for identification even though some structures cannot be identified in this manner.]

Estimation of the Earnings Profile from Optimal Human Capital Accumulation

Econometrica 1976 44(6), 1223
[This paper considers an income maximizing life cycle model of human capital accumulation with the objective of simultaneous estimation of the parameters of the model from observations of the age-earnings profile. The earnings profile, which is a solution to the optimal control problem, is nonlinear and therefore was estimated by nonlinear least squares. The parameter estimates are all quite precise (in the standard error sense) and seem to be intuitively reasonable. The results given here suggest that optimal control models can be verified by direct estimation of the solution.]

Taxes in a Labor Supply Model with Joint Wage-Hours Determination

Econometrica 1976 44(3), 485
PAYROLL AND PROGRESSIVE INCOME taxes play an enormous role in the American fiscal system. It is therefore of some importance to know the extent to which they influence work incentives. The purpose of this study is to present some econometric evidence on the effects of taxes on married women, a group of growing importance in the American labor force.2 A testable model of labor supply is developed which permits statistical estimation of a coefficient of tax perception. Unlike previous models of labor supply, it allows for the possibility that the wage may depend on the number of hours worked. Contrary to much of the literature, the results of this paper strongly suggest that marginal tax rates do have an important impact on labor force behavior. This section reviews briefly the past thought on this problem. Section 2 develops a model to explain work decisions when an individual faces a whole set of wagehour combinations, rather than a given wage independent of the number of hours he works. In Section 3 this model is modified to permit an explicit test of whether or not taxes affect individuals' labor supply decisions. Estimation problems are discussed at length, and the empirical results are presented. A concluding section contains a summary and suggestions for future research.