Knowledge that Transforms

This paper utilizes asymptotic expansions of the Edgeworth type to investigate alternative forms of the Wald test of nonlinear restrictions. Some formulae for the asymptotic expansion of the distribution of the Wald statistic are provided for a general case that should include most econometric applications. When specialized to the simple cases that have been studied recently in the literature, these formulae are found to explain rather well the discrepancies in sampling behavior that have been observed by other authors. It is further shown how the corrections delivered by Edgeworth expansions may be used to find transformations of the restrictions which accelerate convergence to the asymptotic distribution.

The authors analyze the substitution bias in Laspeyres-type price indexes, using 101 c ommodities. They construct the tightest theoretical bounds on the cos t-of-living index using nonparametric methods and also construct supe rlative price indexes. Using nonparametric methods, the authors find homothetic preferences are consistent with the data. Sensitivity test s indicate that this result is not vacuous. Under this hypothesis, th e bias is between 0.22 and 0.14 percent per year. Superlative indexes imply a bias of about 0.18 percent. This estimate is somewhat larger than found in earlier studies. Commodity aggregation is found to be a major contributor to measured substitution bias. Copyright 1988 by The Econometric Society.

In this paper we extend Varian's (1984) nonparametric production analysis to situations when the set of observed output, input, and price data is not consistent with profit maximization for at least one firm. In such cases, Varian's results imply that no production possibility set containing all observations can rationalize the observed data. We identify each firm whose performance, given the prices faced by it, may be found consistent with profit maximization relative to some production possibility set containing all observed output-input vectors. We show that the set 4' of all such firms can itself be weaklv rationalized in the sense that there exists a (closed, convex, and monotone) production possibility set that contains all the observations, and relative to which the performance of all the firms in the set 8O is consistent with profit maximization given their respective prices. By definition, firms not included in this largest set d of efficient observations unambiguously deviate from profit maximizing behavior for any production possibility set containing all observations. We follow Farrell (1957) and analyze these deviations into technical and allocative efficiency measures, considering as admissible all closed, convex, and monotone production possibility sets relative to which the performance of each firm in the set g remains consistent with profit maximization. We then describe nonparametric methods for determining the tightest upper and lower bounds on the technical, allocative, and aggregate efficiency measures evaluated relative to all such admissible production possibility sets. It is seen that the tightest upper bound on the technical efficiency measure is the same as the value computed by the nonparametric efficiency evaluation technique known as data envelopment analysis, thus establishing a link between this literature in management science/operations research and the nonparametric production analysis in economics.

Recently, attention has been given to a model of two-person bargaining in which the parties alternate making of fers and there is uncertainty about the valuation of one party. The p urpose of the analysis has been to identify delay to agreement with a screening process, where agents with relatively lower valuations dis tinguish themselves by waiting longer to settle. The authors point ou t a fundamental difficulty with this program by demonstrating that th e assumptions used in the literature allow for delay only in so far a s the time between offers is significant. Copyright 1988 by The Econometric Society.

In this paper, household is modeled as a two-member collectivity taking Pareto-efficient decisions. The consequences of this assumption are analyze d in a three-good model, in which only total consumption and each mem ber's labor supply are observable. If the agents are assumed egoistic (i.e., they are only concerned with their own leisure and consumptio n), it is possible to derive falsifiable conditions upon household la bor supplies from both a parametric and a nonparametric viewpoint. If , alternatively, agents are altruistic, restrictions obtain in the no nparametric context; useful interpretation stems from the comparison with the characterization of aggregate demand for a private-good econ omy. Copyright 1988 by The Econometric Society.

A VIEW STILL WIDELY HELD among economists is that given the objective of maximizing a Paretian social welfare function-rationing of private goods is inferior to transfers and subsidies. Hence, existing rationing, e.g. in housing programs involving rent regulation, subsidized medical treatment to needy individuals, distribution of day care for children according to need, etc., is often interpreted as a reflection of paternalistic objectives on the part of the government or simply as bad policy; see Tobin (1970). The purpose of this paper is to challenge the general validity of this conventional wisdom in the context of a traditional model of public sector pricing supplemented by an anonymous rationing scheme which affects individuals' consumption patterns significantly. As is often the case, a government cannot achieve distributional equity (i.e., situations where the social value of marginal utility of income is equal for all individuals) by means of taxes and transfers because the use of these instruments is subject to various constraints. This is a common feature of many taxation models; cf. Atkinson and Stiglitz (1980). From a purely technical point of view, there is scope for improving on social welfare in such situations by means of other measures such as rationing. But, since the use of rationing as well as taxes and transfers is likely to be restricted by the same underlying factors, e.g. information about consumers' preferences and endowments or administrative costs, it may be questioned whether rationing qualifies as an efficient policy instrument. The type of rationing considered in this paper is stochastic rationing; when prices are set at levels which generate excess demand, some of the potential consumers are randomly barred from the markets entirely so that demand equals supply. From the point of view of implementation, such a rationing scheme has the desirable property of not requiring the government to have information about preferences and endowments at the individual consumer level; nor is extensive administration required. Another interesting aspect of such a scheme is that, in a sense, it represents a lower bound on rationing schemes since, in most cases, actual rationing can be based on some information about consumers. Therefore, if there are cases where a market-clearing equilibrium can be improved upon by reducing prices below market-clearing levels combined with elimination of excess demand by means of stochastic rationing, the argument for rationing as a potentially efficient policy tool is in fact fairly strong. In this paper we show that such cases do exist. We also indicate that stochastic rationing may still be efficient even in situations where prices can be highly differentiated among different groups of individuals, e.g. income groups. We conclude that the absence of costless redistribution of income, which indeed seems to be consistent with real-world situations, is crucial for the results. Two kinds of policy changes are considered. The first involves eliminating a marginal excess demand by means of rationing. In the model in this paper, there is a continuum of consumers. Therefore, while such a marginal rationing affects some consumers in a nonmarginal fashion, it only affects an infinitesimal group of consumers. Hence, it only

This paper presents a theory of equilibrium asset pricing that generalizes the recent work of G. Connor (1984). Th e model extends Connor's results to more general sets of asset return s and consumer preferences; introduces production; and provides a fra mework for analyzing exact and approximate equilibrium asset pricing. The other major contribution of the paper is the introduction of geo metric arguments that exploit the properties of induced preferences o ver assets. This method of analyzing asset pricing provides an intuit ively appealing way of analyzing equilibrium asset pricing theories. Copyright 1988 by The Econometric Society.

The Helpman-Razin model of international trade under uncertainty is extended to allow for country-specific productivi ty shocks. It is shown that, for the multiple-sector multiple-factor case, there exists a set of interesting sufficient conditions under w hich it is possible to predict the pattern of international trade in securities, goods, and factor content on the basis of cross-country d ifferences in factor endowments. It is shown that, under these circum stances, some well-known empirical tests have to be modified. Copyright 1988 by The Econometric Society.