Knowledge that Transforms

THE PRACTICE of pooling cross section data with time series has been found to be very useful in applied econometric work. Frequently, investigators have estimated some parameters from a single cross section sample and have used these estimates as prior restrictions in the time series equation. Tobin's study of demand for food [2] is a classic example of this. Tobin estimated the income elasticity of demand for food from family budget data for 1941 and used this as prior information in the time series equation for demand for food using annual observations from 19131941. This practice of pooling is justified by specifying the equation in a general (microeconomic) form and treating income elasticity as a long run parameter best estimated from cross section data, whereas price elasticity is designated as a short run response. The possibility, however, always exists that the income elasticity estimated from cross section data may not be the appropriate prior restriction for the time series equation. This may be due to reasons of aggregation bias or because of the fact that income may be a proxy for cyclical fluctuations in time series analysis. It is necessary, therefore, to test the validity of such a prior restriction. Maddala [1] has provided a likelihood ratio test for the pooling of a single cross section sample with time series data. Applying his method to Tobin's study, he found that pooling was inappropriate. In this note, we would like to suggest that the Durbin-Watson (DW) statistic may provide the same information. We compare the DW statistic for the restricted equation (i.e., using the cross section information) with that for the unrestricted equation. All other variables are identical, and therefore the statistics are comparable. Since it is well known that misspecification may lead to serial correlation, a drop in the DW statistic for the restricted as against the unrestricted equation is a clear indication that pooling is a specification error. Tobin's equation for demand for food can be written as

This paper is concerned with the problem of estimating demand and supply schedules in disequilibrium markets. The results of Fair and Jaffee are expanded in three ways. (1) Their directional method I is modified to yield consistent estimates. (2) A maximum likelihood alternative to their quantitative method is proposed. (3) The price equation is generalized to be a multivariate, stochastic function, and a method is proposed for estimating demand and supply schedules in this case.

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

Peer Reviewed

[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.