Knowledge that Transforms

Develops a specification error test sensitive to negelected heterogeneity, which is viewed as causing parameter variation, by deriving a score test of the hypothesis that parameters have zero variance. The test turns out to be the Information Matrix test and is a useful diagnostic for researchers using cross-sectional or longitudinal data to estimate models of individual economic agents behavior. -from Author specification error neglected heterogeneity parameter variation Information Matrix test

This paper examines the implications of imposing a weak aggregation condition on inequality indices, so that the overall inequality value can be computed from information concerning the size, mean, and inequality value of each population subgroup. It is shown that such decomposable inequality measures must be monotonic transformations of additively decomposable indices. The general functional form of decomposable indices is derived without assuming that the measures are differentiable. The analysis is suitable for extension to the many other kinds of indices for which a similar relationship between the overall index value and subaggregates is desirable.

This paper investigates the performances of dynamic econometric models in relationship to their size. More precisely, the central issue addressed in this paper is whether there exists a procedure that systematically associates with every large-scale model a small-scale model that constitutes a reasonably good approximation of the large-scale model. Such a procedure is shown to exist for both endogenous and exogenous variables. This result is applied to show that a model with approximately twenty endogenous and four hundred exogenous variables can do almost as well as the current models with thousands of variables. This result also implies that a necessary condition for small models of twenty to thirty variables to perform satisfactorily is that only regular patterns of variations for the exogenous variables be considered. THE DEVELOPMENT OF HIGH-SPEED POWERFUL COMPUTERS has enabled econometricians and model makers to design operational large-scale models, the idea being that the complexity of reality is better described by models with the largest feasible number of unknowns and equations than by smaller size models. Nevertheless, the costs involved in operating large-scale models combined with their intrinsic complexity has led many econometricians to favor, when dealing with specific questions, the use of smaller size models which can be operated with comparatively less difficulties. This paper investigates the relationships that can be established between the size of a dynamic econometric model, i.e. the number of its endogenous and exogenous variables, and its accuracy through time. This paper also addresses another question related to the general theme of the size of econometric models, namely the existence of procedures that can systematically associate with every large-scale model a small-scale model that provides a reasonably good approximation of the large-scale model. An important feature of the analysis developed in this paper is the focus put on the local point of view and on the consequences that can be derived from the local approach. Local here means that only the behavior of the model in small neighborhoods of suitably chosen points belonging to some, possibly largedimensional, Euclidean space is considered. Though the validity of the local point of view might be questioned when dealing with the most general problems, it seems to be particularly well-suited to the current practice of econometric modelling. The strength and the main interest of the local point of view is that it enables one to define concepts of approximation up to arbitrary orders that apply to econometric models, approximations being taken here in a sense that is

A WELL DEVELOPED EXACT STATISTICAL THEORY exists for hypothesis testing in the normal linear regression model when the errors are independent and homoscedastic. In the more general case where the error covariance matrix is nonscalar and depends on a set of unknown parameters, exact analysis is difficult and reliance is usually placed on asymptotic approximations for large sample size n. In this paper, higher-order asymptotic expansions are developed for comparing the size and power of some common procedures for testing linear hypotheses on the regression coefficients in a class of generalized normal linear models. The class investigated is essentially the same as in Breusch [4] and Magnus [6] and includes many of the examples of heteroscedasticity and autocorrelation discussed in the literature. We assume simply that the regressors are nonrandom and that the error covariance matrix is a smooth function of a few parameters that can be efficiently estimated by maximum likelihood. Tests based on the Wald, likelihood ratio, and Lagrange multiplier principles are considered. These principles lead to three tests which, though distinct in finite samples, are locally asymptotically equivalent and share certain asymptotic optimality properties. Of course, there are infinitely many other tests that are asymptotically equivalent to the ones examined here. Although the techniques of this paper can be applied to any of them, our results concern only the tests arising from the three traditional principles. We show that, to a second order of approximation under local alternatives, the likelihood ratio test statistic is a simple average of the Wald statistic and the Lagrange multiplier statistic. When the null hypothesis is one dimensional, the three tests are, to second order, equally powerful; that is, after the critical regions are adjusted so that the tests have (to order n - i) the same size, the local power functions differ by terms of smaller order than n -. When the null hypothesis contains more than one

[This paper investigates the exact sampling distribution of the least squares estimator of β in the model y"t = @m + @by"t"-"1 + @u"t where the @u"t are independently N(0, @s extasciicircum2). The distribution is calculated for the case where y"0 is a known constant and where y"0 is a random variable. Given y"0 is a constant we prove a small @s asymptotic result and compute the exact powers of nonsimilar tests of the random-walk hypothesis β = 1 and of the stability hypothesis β = 0.9. The exact powers of a test of the stability hypothesis are calculated for the case where y"0 is random. The accuracy of the standard normal approximation is examined for both start-up regimes.]

[I examine the effects of price discrimination on the equilibrium prices, number of firms, and level of total surplus in a monopolistically competitive market. The main finding is that uniform pricing is more (less) efficient than is price discrimination when the purchases made by the consumers who are discriminated against constitute a small (large) proportion of the total purchases.]