Knowledge that Transforms

MUCH APPLIED ECONOMETRIC work is based on the correlation and regression of ratio variables which have the same denominator. The denominator generally deflates the various sets of measurements in order to make them comparable. In certain cases deflation is a way of obtaining efficient estimators. Briggs [1] has studied the effect of errors in the deflating variable on the correlation between ratios. The effect of errors in the deflating variable on a scatter diagram of measurements on ratio variables is to displace each representative point along a ray from the origin passing through the representative point of the error-free measurement. This suggests that with error in the deflating variable the ordinary least squares (OLS) estimators of a bivariate regression are biased toward indicating a relationship of proportionality between the ratio variables. It can be demonstrated that this conjecture is generally valid for multiple linear regression with error in the deflator. In most cases in which deflation is used, it is reasonable to suppose that the deflator is a random variable distributed independently of the ratio variables; in this case the conditional expectation of the undeflated independent variables is proportional to the value of the deflator. Under this assumption it can be established that when there is error in the deflator the estimators of the slopes of the regression are inconsistent unless (i) the ratio regression has zero intercept, or (ii) the mean of each of the independent variables is zero, or (iii) the error in the deflator is systematic (i.e., the error term has zero variance). The estimator of the intercept may be inconsistent even when the estimators of the slopes are consistent; for the intercept estimator to be consistent it is necessary that either (i) the intercept

[Two principal questions are treated: (i) Which equilibrium conditions (or, which types of factor demand equations) based on the neoclassical single-capital-good model are unchanged when there are many different capital goods, only one of which is used at any one time? (ii) Are there any "pseudo" productions functions (of "capital" and labor) which correctly describe behavior by profit-rate maximizing entrepreneurs in the many-capital-goods model? A new surrogate production model is developed to resolve these questions. It is shown, inter alia, that if one wishes to predict changes in labor and value capital requirements in response to changes in factor prices, the neoclassical marginal rate of substitution relationship can be justified as the basis for the econometric specification.]

IN TESTING HYPOTHESES on the coefficients of a linear regression model with stochastic regressors it is well known that the usual t test and F test are applicable if the stochastic regressors are statistically independent of the disturbances [3, p. 268; 5, pp. 27-28]. Also, there are cases in which economic hypotheses can be stated in terms of the independence of stochastic regressors and disturbances, the best known examples being the current versus the permanent income hypotheses and the recursiveness hypothesis in a simultaneous equations model. Therefore, it is desirable to develop a procedure that can be used to test the hypothesis that the stochastic regressors and disturbances are independent. In this paper, we examine four alternative tests of independence between the stochastic regressors and disturbances. In the rest of this section we specify the stochastic model and state the hypotheses to be tested. In Section 2 we present two finite sample tests. In Section 3 two alternative asymptotic tests are given and asymptotic power functions of all four tests are examined. In Section 4 we give examples of applications of the test in econometrics. We consider the following linear model:

This paper examines the possible explanations for the changes in output, capital, and labor input of a sample of manufacturing plants over a number of years. Apart from the scale of operation, these changes could be attributed to three causes: technology diffusion, substitution, and improvements in X-efficiency. The empirical findings indicate that a diffusion model modified to incorporate X-efficiency improvements provides the best explanation. This suggests the need for a new approach to the specification of production

EXPERIMENT DESIGN THEORY for regression analysis is becoming important in econometric work, most notably in the context of negative income tax [1] and other subsidy experiments (such as housing and health subsidy experiments being planned). The usual regression design model requires the experimenter to specify the functional form of the behavioral equation under investigation. An apparent difficulty is that the experimenter does not know the true functional form. This paper suggests new procedures for handling the difficulty. The procedures were stimulated by work in planning the New Jersey negative tax experiment. To the planners of the New Jersey experiment, the relevant statistical design literature was not applicable, cookbook fashion, because the practical design guidelines were constructed for simpler situations. However, by combining ingredients from the statistical literature, the New Jersey experimenters were able to define a well-behaved mathematical programming model whose solution would tailor a design to their situation [3]. (The references [2 and 4] provide a useful entry to the relevant statistical literature.) The new procedures suggested here build on the New Jersey design model, which is reviewed in Section 2. Though the exposition runs in terms of subsidy experiments, the material is more generally applicable.

[The economic theory of individual choice most frequently assumes that individual preferences are weak orders; this implies, among other things, a virtually perfect discriminating power on the part of individual decision makers. R. D. Luce's theory of semiorders generalizes the weak order concept to allow imperfect discrimination when choices are close. This paper examines the demand implications of the semiorder axioms and states conditions on demand that are necessary and sufficient for the revealed ordering to be a semiorder.]

[The preliminary test estimator (or predictor) is studied in the context of linear normal regression models. The estimator (or predictor) obtained after the preliminary test is known to be inadmissible with respect to squared error loss under certain assumptions. Nevertheless, it is still widely used in practical application of regression analysis, particularly in econometrics. The object of the present paper is to tabulate the optimal significance points in the preliminary test for practical use. The optimality is based on the minimax regret principle. It is shown that if, as is usual, we take the significance point equal to the 5 per cent point or 10 per cent point, the risk is extremely large for some parameter value. The optimal significance point of the preliminary t test decreases slightly as the degrees of freedom increase,but it is nearly constant; i.e., it lies between 1.370 to 1.380 if d.f. is greater than 6.]

THE MAIN PURPOSE of this paper is to investigate properties of production possibility sets when technology sets are neo-classical. By neo-classical technology we mean (i) externalities in production are absent and (ii) nonproducible commodities or primary factors are fixed in their supply. Production possibility sets are defined to be those derived from technology sets when constraints on the supply of nonproducible commodities are added. Our model is a fairly general one where, in particular, intermediate commodities and joint products are allowed. Of course, individual technology sets will provide us with enough information when we are only interested in individual behavior. In such a case, we may not need the concept of production possibility sets. But when we are concerned with more global pictures of an economy and when the supply of nonproducible commodities is assumed to be fixed, then production possibility sets can provide us with a nice summary of production sectors and it is possible to obtain more qualitative information from our models. In the next section, we shall describe our model and give the main assumptions. Section 3 will be devoted to a characterization of production possibility sets which turns out to be a generalization of the well-known nonsubstitution theorem of Samuelson. Three applications of the result in Section 3 will be discussed in Section 4. In Section 5, we shall show that when technology sets satisfy a condition called the weak indispensability of nonproducible commodities, then production possibility sets have the desirable properties of closedness and boundedness.