Knowledge that Transforms

[Over half a century ago Frank Graham argued that decreasing costs could justify protection. Although this contention stimulated a huge literature, a correct analysis has never been made. The present paper attempts to fill this gap. It is shown that Graham's case applies to trade between approximately equally-sized economies and that a greater degree of increasing returns actually reduces its likelihood. Furthermore, increasing returns yield a positive analysis nearly completely symmetric to that of Ricardian constant costs. A new analytical tool, the allocation curve, is introduced, with which Marshallian stability is fully analogous to Walrasian instability with offer curves.]

statistics of a linear hypothesis in the standard linear model. These test statistics, which correspond to Wald, likelihood ratio, and Lagrange multiplier tests, are shown to have the same limiting chi-square behavior under mild regularity conditions on design and the distribution of errors. The asymptotic theory of the tests is derived for a large class of error distributions; thus in Huber's [10] terminology we investigate the behavior of the likelihood ratio test under non-standard conditions. The asymptotic efficiency of the 11 tests involves a modest sacrifice of power compared to classical tests in cases of strictly Gaussian errors but may yield large efficiency gains in non-Gaussian situations. The Lagrange multiplier test seems particularly attractive from a computational standpoint. We derive the asymptotic distribution of the three alternative 11 test statistics for a simple linear exclusion hypothesis. Extension of these results to hypotheses of the form R,8 = r is a straightforward exercise. When the density of the error distribution is strictly positive at the median, all three test statistics have the same limiting central x2 behavior at the null and noncentral x2 behavior for local alternatives to the null. When the variance of the error distribution is bounded, analogous results are well known for classical forms of the Wald, likelihood ratio, and Lagrange multipler tests based on least-squares methods. See, for example, Silvey [18] and the discussion in Section 4 below.

[The maximum likelihood approach is used to derive Hausman's specification test. Its asymptotic power is compared with the more conventional test procedures.]

Douglas W. Caves, Laurits R. Christensen, W. Erwin Diewert, The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity, Econometrica, Vol. 50, No. 6 (Nov., 1982), pp. 1393-1414

MANY COMMODITIES can be viewed as bundles of individual attributes for which no explicit markets exist. It is often of interest to estimate structural demand and supply functions for these attributes, but the absence of directly observable attribute prices poses a problem for such estimation. In an influential paper published several years ago, Rosen [3] proposed an estimation procedure to surmount this problem. This procedure has since been used in a number of applications (see, for example, Harrison and Rubinfeld [2] or Witte, et al. [4]). The purpose of this note is to point out certain pitfalls in Rosen's procedure, which, if ignored, could lead to major identification problems. In Section 2 we summarize briefly the key aspects of Rosen's method as it has been applied in the literature. Section 3 discusses the potential problems inherent in this procedure and provides an example. Section 4 concludes with a few suggestions for future research.

For the Tobit model with independent observations, Amemiya [1] has established the strong consistency and asymptotic normality of a stationary point, 9, of the log-likelihood. The likelihood for dependent observations may be computationally intractable, so the behavior of 9 in the presence of serially correlated observations is of interest. Under a relaxation of Amemiya's assumption of independence, we prove that 9 is strongly consistent and asymptotically normal, and give an expression for the limiting covariance matrix.

A PROBLEM OF ESTIMATION that has long confronted many economists is the difficulty of estimating the parameters of equations with limited dependent variables on cross-section time-series (i.e., panel) data. While there are widely available packaged computer programs for estimating either (a) cross-section probit and Tobit models or (b) simple permanent-transitory, random-effects panel models with continuous dependent variables, there are no available computationally feasible methods of combining these two models. This is because the likelihood function that arises in such a combined model contains multivariate normal integrals whose evaluation is quite difficult, if not impossible, with conventional approximation methods. There is a widespread feeling among those working in the area that one possible method of evaluation, the use of quadrature techniques, is in principle possible but is in practice computationally too burdensome to consider (e.g., Albright et al. [2, p. 13]; Hausman and Wise [6, p. 12]). In this note we point out that this is true only of standard quadrature techniques such as trapezoidal integration or its improved variants; Gaussian quadrature, on the other hand, is extremely efficient and is well within the bounds of computational feasibility on modern computers. In what follows, we state the nature of the integrals that need to be evaluated, provide a brief exposition of Gaussian quadrature, and provide a numerical illustration of its use in

[In a portfolio problem with given asset returns, the portfolio efficient set is the set of portfolios chosen by any risk averse agent. Using an approach of Peleg and Yaari [13], we characterize the portfolio efficient set and derive some of its properties. In particular, we show that it may not be convex, proving that a central result of mean variance theory, the efficiency of the market portfolio, does not generalize. Finally, a characterization of the efficiency of several observations gives a version of revealed preference theory for incomplete markets.]

[Experimental studies have shown that the key behavioral assumption of expected utility theory, the so-called "independence axiom," tends to be systematically violated in practice. Such findings would lead us to question the empirical relevance of the large body of literature on the behavior of economic agents under uncertainty which uses expected utility analysis. The first purpose of this paper is to demonstrate that the basic concepts, tools, and results of expected utility analysis do not depend on the independence axiom, but may be derived from the much weaker assumption of smoothness of preferences over alternative probability distributions. The second purpose of the paper is to show that this approach may be used to construct a simple model of preferences which ties together a wide body of observed behavior toward risk, including the Friedman-Savage and Markowitz observations, and both the Allais and St. Petersburg Paradoxes.]