Knowledge that Transforms

[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.

Generalizing the Sharpe-Lintner capital asset pricing model, Dieffenbach [4] presents a model of securities markets in a private enterprise economy in a multiperiod competitive equilibrium with uncertainty. Risk premiums on securities depend on the covariances of holding period returns with the return on the market portfolio and with a multiperiod cost-of-living index. This paper develops a quantitative theory of that relationship suitable for empirical estimation and testing. Whether the Arrow-Pratt relative risk aversion of a representative investor is greater or less than one is important in the theory; the empirical results for the United States suggest that this value exceeds one. A theoretical and empirical application of the theory to the term structure of United States Treasury securities concludes the paper. Mean observed returns are consistent with theoretical predictions for medium and long term securities, but the differences of mean observed returns among bills of different maturities exceed the theoretical predictions.

[A one-way expected utility representation has the expected utility of one probability measure greater than the expected utility of another probability measure whenever the first is preferred to the second. It requires preferences to be acyclic but not necessarily transitive, and does not require indifference to be transitive. Preference axioms which are sufficient for one-way expected utility for sets of simple probability measures have been presented before (see [8]). This paper uses additional axioms to extend the one-way representation to sets of discrete and more general probability measures.]

The relationship between Pareto optimal (0s) and revenue maximizing (Or) tolls is examined for queuing models that permit balking. When customers have the same value for waiting time, Q, =Or provided the entrepreneur can impose a simple two-part tariff. With heterogeneous values for waiting time, Or can be greater than, equal to, or less than H,. Expanding the number of servers and charging multi-part tariffs are shown to be alternative methods for segmenting the market, and the welfare implications of these two strategies are explored.