Knowledge that Transforms

A pairwise trading process is formulated subject to conditions of nonnegativity of traders' holdings and quid pro quo. It is shown that that: (i) There is a centralized procedure that achieves the equilibrium allocation for an arbitrary economy. (ii) It is not in general possible to find a decentralized procedure that achieves the equilibrium allocation for an arbitrary economy. (iii) In a monetary economy there is a decentralized procedure that achieves the equilibrium allocation. The usefulness of money is that it allows decentralization of the trading process.

[A two equation model that explains the simultaneous determination of wage and price inflation and their interaction with inflationary expectations (of the adaptive type) and real variables is presented. A dynamic definition of the long run trade off between inflation and unemployment is introduced and applied to the model in order to find conditions under which the model is stable or, in economic terminology, has a long run trade off. The model is then applied to the U.S. economy during the period 1949-1970. It is found that for all speeds of adjustment in expectations between 0 and 1 there is a permanent trade off.]

Aman Ullah, A. L. Nagar, The Exact Mean of the Two-Stage Least Squares Estimator of the Structural Parameters in an Equation Having Three Endogenous Variables, Econometrica, Vol. 42, No. 4 (Jul., 1974), pp. 749-758

In the first section of this paper the overidentifying restrictions on a system of linear simultaneous equations are expressed in terms of restrictions on the reduced form parameters. These restrictions provide the basis of a test of the structure using only the unrestricted reduced form parameter estimates. Under Ho the test proposed is asymptotically equivalent to a likelihood ratio test. The test may be applied as a single equation or complete system procedure and it may be presented as either a x2 or an F statistic. The case is also made here for system overidentification tests rather than single equation procedures, the arguments being drawn from the statistical literature on hypothesis testing by induction. The computational advantages of the present proposals are substantial when compared to FIML based likelihood -ratio tests and Monte Carlo experiments confirm that a system version of the test performs well in large samples. The system version of the test behaves like the FIML likelihood ratio test in large sample situations both under Ho and H1. However, the Monte Carlo studies indicate that both the single equation and system versions of the test perform poorly in small samples. THE AIM OF THIS paper is to investigate the possibility of deciding on the specification of a simultaneous equation model prior to the estimation of the structure. A well established test procedure is suggested which uses OLS estimates of the reduced form parameters; it enables the null hypothesis, that the model specified is not significantly different from the model which generated the sample, to be tested. Because of the one-to-one correspondence between the overidentified structure and the restricted reduced form, it is possible to make inferences about the structure from the observed compatibility of the reduced form restrictions with the sample information. In addition, the reduced form restrictions resulting from a particular equation may be isolated and tested separately, if desired. The principle underlying the test would appear to be due to Wald [17J; namely, that if the null hypothesis is correct and the structure postulated as the maintained hypothesis was responsible for the generation of the observed sample, then the unrestricted reduced form parameter estimates will tend, if the sample size is large enough, to satisfy the reduced form restrictions advanced under the maintained hypothesis. A number of problems relating to identification of linear simultaneous equations make life a little difficult and are discussed subsequently. Now, take the linear structure

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