Knowledge that Transforms

Thomas W. Epps, Mary Lee Epps, The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis, Econometrica, Vol. 44, No. 2 (Mar., 1976), pp. 305-321

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).

[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.]

[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.]

[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.]

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.

In a multiplicative model it is usual to assume that the logarithm of the disturbance variable is normally distributed with unknown variance a2 and with a mean which is either zero or - la2 according to the viewpoint taken of the object of the model. It is shown that, for each of several estimation criteria, the two assumptions lead to precisely the same point estimators of the exponents of the explanatory variables in the model and of the conditional mean, median, and mode of the dependent variable for specified values of the explanatory variables. An improved form is also given of the estimator of the conditional mean proposed by Teekens and Koerts [8]. A MULTIPLICATIVE MODEL is one in which a dependent variable is hypothesized to be proportional to the product of powers (unknown) of two or more explanatory variables. Such models arise in many areas; an important example of such a model in econometrics is the Cobb-Douglas production function. Observations will deviate from the theoretical model because of the presence of a disturbance variable. It is customary to include this variable as a multiplicative factor in the model and to assume that its logarithm is normally distributed with a mean which may be either zero or minus half its variance, the choice being dependent upon the viewpoint taken regarding the purpose of the model. We show that the choice does not affect the standard point estimators of the exponents (elasticities) of the explanatory variables in the model nor the standard estimators, including that proposed by Teekens and Koerts [8], of the conditional mean, median, and mode of the dependent variable.

[The static aspect of the Le Chatelier-Samuelson principle in the local version is fully characterized in an extremum formulation with differing systems of auxiliary constraints. The local characterization results in an interesting finding. With the systems of effective constraints which restrict only as man involved variables as the number of constraints, the variations of an extremum system, as consequences of changes in parametric indices of exogeneous conditions, will be only quantitative. With the systems of effective constraints which restrict more or all the involved variables, however, the consequential variations will be qualitative as well as quantitative. Necessary and sufficient conditions are investigated for constrained saddle points to exhibit a generalized Le Chatelier-Samuelson principle. An economic argument along the lines of demand theory is that the generalized principle among constrained demands is established if and only if the Jacobian of the constrained demands with effective constraints exhibits a dominant complementarity for the new constraint with its coefficients non-negative. The Marshallian conjectures about short run and long run are extensively discussed and rigorously proved with the results.]