Knowledge that Transforms

This paper provides general conditions which ensure consistency and asymptotic normality for the nonlinear least squares estimator. These conditions apply to time-series, cross-section, panel, or experimental data for single equations as well as systems of equations. The regression errors may be serially correlated and/or heteroscedastic. For an important special case, we propose a new covariance matrix estimator which is consistent regardless of the presence of heteroscedasticity or serial correlation of unknown form. We also give some new tests for model misspecification, based on the information matrix testing principle

The essence of selection bias is that we do not observe nonoptimal choices. This applies whether the choice variable is discrete or continuous. This paper extends the selection bias methodology to the case where the choice variable is continuous and the choice set is ordered. The leading practical application of this analysis is the schooling choice problem. Schooling is treated as a continuous choice variable and selectivity corrected rates of return are estimated. The findings suggest selectivity is of considerable importance and support the comparative advantage hypothesis of Willis and Rosen [18].

G. H. Hillier, T. W. Kinal, V. K. Srivastava, On the Moments of Ordinary Least Squares and Instrumental Variables Estimators in a General Structural Equation, Econometrica, Vol. 52, No. 1 (Jan., 1984), pp. 185-202

Reformulating marginal productivity theory by replacing productivity with respect to commodities with productivity with respect to persons and then defining perfectly competitive equilibrium as an allocation at which each person receives the marginal product of his/her contribution called a no-surplus allocation there emerges a competitive theory of price determination. Characterizations of no-surplus allocations are given in models with a nonatomic continuum of agents and an infinite-dimensional commodity space. Comparisons between the no-surplus and Walrasian equilibrium definitions of competitive equilibrium are made and some sufficient conditions are obtained for the existence of a no-surplus allocation.

[This paper develops a general, competitive model of commodity differentiation. The structure analyzed is sufficiently rich to admit the basic structures of many of the common models of commodity differentiation as special cases. Thus, the model provides a unifying framework within which alternative formulations of strategic product choice can be compared. It is shown that competitive equilibria exist under only mild restrictions on the underlying economic structure and vary continuously with endowments. Finally, some results relevant to all models of commodity differentiation featuring price taking consumers are presented. The results are shown to point to some potentially important methodological restrictions.]

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[The lecture investigates some consequences of a frequently observed phenomenon: There are once and for all costs of switching from one good to one of its substitutes. The decision to substitute then is an investment decision. Such substitution costs, in conjunction with problems of oppportunism, have frequently been seen as a reason for vertical integration. Reputation for a fair treatment of customers may enable suppliers to maintain market relations for goods involving substitution costs. A model looks at "competitive distance" between two goods with substitution costs. If future tastes are uncertain the model shows that with low rates of discount or high rates of market growth competitive distance declines as substitution costs rise. It is also shown that competitive distance rises with a rising rate of discount. Given the effectiveness of the reputation mechanism, numerical analysis shows that competitive distance is smaller in most cases with substitution costs than without substitution costs.]

When zero mean measurement error is added to the dependent variable for the nonlimit observations of the censored normal regression model, the conventional maximum likelihood estimator (Tobit) is inconsistent. Correct maximum likelihood estimation appears to be computationally difficult under various specifications for the distribution of the measurement error. Estimators based on either the expectation function or the conditional expectation function for uncensored observations remain consistent in the presence of measurement error. Eight such estimators are examined. The results of a numerical experiment suggest that several of these estimators are substantially more efficient than the conventional maximum likelihood estimator when measurement error exists and that they also will do reasonably well when it does not.

Lung-Fei Lee, Robert H. Porter, Switching Regression Models with Imperfect Sample Separation Information--With an Application on Cartel Stability, Econometrica, Vol. 52, No. 2 (Mar., 1984), pp. 391-418