[This paper is concerned with the estimation of a system of simultaneous linear differential equations that involves predetermined variables. The system is replaced by a discrete approximation that is most conveniently handled in the frequency domain. Our method of estimation is nonlinear least squares. We state conditions under which the estimators will have asymptotically desirable properties. The most notable of these is an aliasing condition on the predetermined variables.]
Silvey [10]. For a model with nonstochastic regressors we show that a systematic inequality relation exists among the test statistics; namely, the value of the Wald statistic is greater than or equal to that of the LR statistic which, in turn, is greater than or equal to that of the LM statistic. When the null hypothesis is true, we find that the Wald, LR, and LM test statistics have identical limiting chi-square distributions. Since for a large sample test the three procedures employ the same critical region, the inequality relation among the test statistics implies that there exists a significance level such that the tests will produce conflicting inferences. These results are parallel to those obtained by Berndt and Savin [2] in the context of a multivariate regression model with independent disturbance vectors. We also consider the Wald and LR tests for a model with a lagged dependent variable. In this case the Wald statistic is not the same as in the nonstochastic regressor case with the result that the inequality between the Wald and LR test statistics no longer holds. We conclude the paper with an empirical example which illustrates the relation among the test statistics.
[This paper investigates the justification for the competitive assumption that consumers will act as price takers by considering the utility gain an individual can achieve by manipulating price formation through the use of non-competitive behavior. Although announcing one's competitive demand is generally not a best replay against the excess demand of the rest of the economy, we show that, as the number of consumers becomes large, the gain any one can achieve acting monopolistically goes to zero if the increase in numbers comes through replication or if the sequence of economies converges to an economy at which the equilibrium price correspondence is continuous.]
DISCUSSIONS OF IDENTIFICATION of parameters in simultaneous equation econometric models almost invariably assume that data are in the form of aggregative time series, i.e., only one measurement of each variable is available in each time period. This note shows that parameters in a model which is underidentified by the usual rank and order criteria at the aggregative level may be identified when disaggregated data aie available. The argument is presented in terms of a traditional textbook example of an underidentified model which consists of a demand and a supply function for a single commodity that are linear in price, and a market clearing equilibrium equation.
[Global necessary conditions are obtained for a discrete capital version of the putty-clay model first introduced by Johansen [7]. Convergence of the optimal solution to a steady state is discussed for concave utilities. Also, the role of obsolescence is analyzed when utility is linear]
IN A RECENT PAPER Cargill and Meyer [1] use Monte Carlo simulations to examine the behavior of some distributed lag estimators when the lag structure is misspecified. The authors hold that it is not easy to compare the Almon polynomial lag method and OLS analytically if the restrictions imposed by the Almon procedure are not correct. It is our intention to derive analytical expressions for the bias in the Almon estimator. We postulate a linear distributed lag model
THE STABILITY PROPERTIES of a competitive economy are well known-at least under the artificial tatonnement assumption which avoids the problem of who changes prices. This note demonstrates that similar, if not stronger, properties carry over to a monopolistic economywhere price formation is completely explained by the independent optimizing behavior of individual agents. The discussion may be interpreted as that of monopoly as the opposite polar case to that of competition or, equivalently, as that of the stability of the concept of equilibrium presented in an earlier paper [1]. Price adjustment is by individuals, following [3 and 4], through their perceived demand curves, following [2 and 5]. There are n commodities (the last being a numeraire) identified by ownership: agent i is endowed with one unit of commodity i and no other commodity. Each agent (i) chooses a price pi ) 0 for his commodity and a consumption x' e R% , so that a state of the economy is an array (p1. p, x . x), or (p, X). Given some existing state (p, X) each agent (i) first chooses pi to maximize his expected income pixi, where xi is his expected sales, given by his perceived linear demand curve (with negative slope one, say) xi(pi) = x-i + Pi - pi; here Xi = I 5i is the existing aggregate demand. Taking account of the constraint xi < 1 this gives