Knowledge that Transforms

The distribution of personal income is approximated by a two-parameter gamma density function (Pearson Type III). The two parameters may be considered as indicators of scale and of inequality, respectively. Maximum likelihood estimates of the parameters are derived from a random sample using graphical techniques, and a likelihood ratio test for the hypothesis that the inequality parameter is the same for different distributions is presented. The derivation of both the estimates and the test statistic requires computing the arithmetic and geometric means from the sample. An empirical application, including a comparison of the gamma and lognormal distributions to demonstrate the better fit of the gamma, is made to personal income data in the United States for the years 1960 to 1969. Using the gamma density, inequality is shown to decrease when unemployment or inflation decreases, or when the real national product increases.

[In this paper we study the properties of the ordinary least squares estimator ofthe coefficients of linear macor models when the coefficients of linear micro relations are random with identical mean and variance. It is shown that the ordinary least squares estimator is equal to a minimum variance linear unbiased estimator of the coefficients of a linear macro equation obtained by aggregating over all micro relations. Futher, some problems associated with estimating the covariance matrix of the ordinary least squares estimator, using only aggregate data, are indicated.]

Peter Schmidt, The Algebraic Equivalence of the Oberhofer-Kmenta and Theil-Boot Formulae for the Asymptotic Variance of a Characteristic Root of a Dynamic Econometric Model, Econometrica, Vol. 42, No. 3 (May, 1974), pp. 591-592

[This paper contains the formulation of the theoretical restrictions on the labor supply functions of the husband and wife in a model of family labor supply in a manner that makes them readily amenable to test and, if they are not rejected, to imposition onto the data. It also contains an application of the proposed empirical counterparts of the theoretical equations to cross-sectional data from the 1960 U.S. Census of Population.]

[This paper contains a relatively simple proof for the stability of Edgeworthian recontracting. It also applies that proof to a random recontracting process in an economy with a finite number of utility vectors, in which the recontracting process is a Markov chain and all non-core utility vectors correspond to transient states.]

Interstate labor force migration in Venezuela was estimated for 3 groups of migrants classified by their own educational levels. Regional educational levels and education-specific average wages were included as explanatory variables in order to distinguish between the various effects of education on migration and to estimate differences in the response of educated and uneducated migrants to other explanatory variables. The basic model resembled that used in other econometric studies of migration; migration was assumed to be a function of a number of origin and destination state characteristics which were believed likely to represent costs and benefits of living in various states for most persons. Migration rates rather than absolute numbers were the dependent variable. Zellner's regression technique was employed, and appropriate F statistics were used to test the null hypothesis of equal response of migrants to each of the explanatory variables across educational levels. A substantial proportion of the variance in migration rates was explained for each level of education. The results showed that educated members of the labor force in Venezuela are more mobile and also that there are significant differences in the responses of educated and uneducated migrants to variables which reflect the costs and benefits of alternative locations. The educated were less deterred by increased distance and more responsive to wage rates in alternative locations. The educated appear to be more mobile because of their greater access to information and greater incentives to make additional investments in search of better opportunities. Both educated and uneducated migrants are attracted to more populated regions but the elasticity is almost twice as high for the educated. Educational opportunity was found to be an important locational advantage for those who already had attended secondary school. The less educated are less likely to move to states with high educational levels, perhaps because they fear job competition from the educated. Destination unemployment variables were not highly significant for the uneducated. Results of the study indicate that disaggregation of migration by educational levels is necessary for a clear understanding of the complex relationships involved.

[Necessary and sufficient conditions are determined under which a truncated approximation to generalized least squares is more efficient than ordinary least squares. For the general case, the necessary conditions are unlikely to be fulfilled. For a first order Markov model in a second order world, the sufficient conditions are satisfied only when one of the second order roots is very small, and therefore the first order assumption is approximately true. When the class of possible exogenous variables is limited to those typical of economic time series, the sufficient conditions are satisfied for a wider range of cases. Relative efficiencies are computed for a variety of cases.]

This paper considers the asymptotic distribution of forecasts made several time periods in the future. Such forecasts typically arise in the dynamic simulation of an econometric model.

[The economic environment (social output) is treated explicitly as a social choice variable. Individual orderings over the set of environments are derived from maximizing behavior. The influence of each individual on the choice made by society is expressed in terms of a power indice which is itself a function of the prevailing environment. These individual power indices give rise to a power rule which provides a social ordering over the set of environments, with the social choice set under any environment being non-empty. The existence of equilibrium in terms of the power rule is established.]