Knowledge that Transforms

Research Methods/Statistical Methods

This paper investigates the effect of costs of adjustment on the dynamic characteristics of intra-urban resource allocation. The analysis is concentrated on the development pattern of an open city within a system of many cities both in steady-state and in variable-state economies. Competitive equilibrium of the urban system as a whole is also discussed and compared to Pareto optimum allocation. Some of the results that characterize the resource allocation under static analysis are reestablished for the dynamic case as well. But others that follow from comparative statics are shown to be incorrect under the dynamic analysis.

INTRODUCTION THE METHOD OF INSTRUMENTAL VARIABLES (IV), proposed independently by Reiersol [15] and Geary [4], is one of the most useful classes of estimation techniques available to econometricians. The method is particularly useful in the context of errors-in-variables and simultaneous equation problems, and it ineludes ordinary least squares (OLS), two-stage least squares (2SLS) (Klein [9]), three-stage least squares (3SLS) (Madansky [12]) and certain full-information maximum likelihood estimators (Hausman [7]) as special cases. To date, the definitive theoretical treatment of the instrumental variables method is that of Sargan [16]. Important contributions have also been made by Brundy and Jorgenson [!, 2]. However, this work has not established the properties of IV estimators for all of the kinds of data analyzed by economists. Sargan's work is appropriate for data which are stochastic processes of the kind considered by Koopmans, Rubin, and Leipnik 10] in their study of dynami

Quandt and Ramsey have suggested an estimator for normal mixtures and switching regressions, which minimizes a sum of squared differences between empirical and theoretical values of the moment generating function. This paper demonstrates how their estimator can be improved by minimizing a generalized sum of squares rather than an ordinary sum of squares. When this is done, more points of evaluation (moments) are unambiguously better than less. Most of the results presented are also applicable to method of moments estimators in general.

[The matrix weighted average (H = V extasciicircum-1) extasciicircum-1Hb, where H and V are symmetric positive definite matrices and b is a vector, is shown to lie in one ellipsoid if V is bounded from below, V "* @ extless V, another ellipsoid if V is bounded from above, V @ extless V*, and another ellipsoid if V is bounded from above and below, V "*@ extless V @ extless V*. These results are applied to bound the posterior mean vector of the normal linear regression model.]