Knowledge that Transforms

This paper derives an asymptotically valid test for first-order autoregressive errors. The test is derived in a simultaneous system of equations context, and allows lagged endogenous variables to be present in the model.

WE CONSIDER THE PROBLEM of estimating the coefficients of the Cobb-Douglas production function when observations are obtained from a cross section of firms. Under the assumptions that the firms operate in competitive markets and maximize actual profits, a stochastic model of production of the firms can be represented

Consider a competitive economy with infinite horizon Ramsey behavior by households, present-value maximizing firms and infinitely many futures markets. If prices adjust according to excess demands, then the economy is locally stable. This is in marked contrast to the saddle-point instability exhibited by the myopic foresight dynamics in models of this genre. It is argued that infinite futures markets are idealizations of actual economic forces.

[The power function of the Durbin-Watson test for first-order serial correlation is examined. The power function depends upon the regression vectors, but useful upper and lower bounds for the power are established. The bounds are obtained from inequalities on the characteristic roots of real non-definite symmetric matrices developed in this article.]

[If two linear models have different sets of explanatory variables and the same variable to be explained, the residual variance of the correct model (S extasciicircum2"n) has a smaller mean value than that of the incorrect one (t extasciicircum2"n). This note shows under fairly general conditions that S extasciicircum2"n extless t extasciicircum2"n will hold with probability arbitrarily close to 1 provided that the sample size n is large enough.]

[This paper examines the determinants of the demand for labor by fourteen two-digit manufacturing industries of India, and in particular the role of factor prices and expectations, to aid understanding of the causes of the low rates of labor absorption in the manufacturing sector. This is done within the framework of neoclassical models of factor demand. A method is suggested for measuring expectations. Our results show that adverse factor prices, long adjustment lags, low output elasticities, and the shift in the industrial structure in favor of the capital goods sector are some of the more important factors responsible for the observed low rates of labor absorption. Finally, some implications of our results for studies relating to labor demand functions in general are discussed.]

[This paper is a study on optimal consumption over time under the assumption of uncertainty about prices and interest rates. A stochastic model has been developed in which present wealth is either consumed or invested in a future commodity and loans. The possibility of lending and borrowing allows the model to capture some of the aspects of a monetary economy, such as the effects of actual or anticipated inflation on optimal plans. Future prices follow a Markovian process. Conditions for the existence of optimal policies are given for concave utility functions in general, but constant elasticity utility functions are studied in greater detail. The case in which the expected value of the discounted stream of utilities is infinite, is also investigated.]

Some economic variables are restricted by an upper and lower limit but are continuous between the two limits. Measurements of such variables are sometimes available in their natural form and sometimes only in the form of three categories where information concerning the middle category is suppressed (unemployed, employed part time, employed full time, for example). Where such a variable is a continuous function of other variables between the two limits, the function can be estimated from data of either sort provided the function and the distribution of errors can be specified. WHEN THE LIMITED dependent variable technique developed by Tobin [3] is extended to provide for cases in which the dependent variable in a regression is subject to both an upper limit and a lower limit, a surprising property of the statistical model emerges.1 Estimates of the regression function can be obtained whether or not the exact values of the dependent variable are known for the nonlimit cases. Provided the functional form can be specified correctly, classification of the dependent variable into upper limit, lower limit, and non-limit observations provides enough information, along with observed values of the independent

Suppose that the coefficients of an input-output matrix, A, are random variables but that we have ascertained their expected values, EA. What will be the relation of the Leontief inverse of EA, (I EA) ', to the expected value of the inverse, E(I A) ? Will one or the other be uniformly greater? We will show that if all coefficients of A are independent, then the expected value of the inverse is uniformly greater than or equal to the inverse of the expected value. If, on the other hand, the column and row sums of the coefficient matrix are fixed, and smaller than one, so that the variables are not independent, then, in the two-by-two case, the opposite is true of the off-diagonal elements.