Knowledge that Transforms

THE EFFECTS OF COMMODITY PRICE STABILIZATION on an individual consumer's welfare has been controversial ever since the issue was first analyzed by Waugh [15]. The early approach of Waugh, which was based explicitly on expected consumer's surplus and ignored the production side of the economy, has since been generalized in several respects. For instance, Turnovsky, Shalit, and Schmitz (hereafter T-S-S) [14] have suggested an approach that utilizes the indirect utility function of a single individual. By focusing on a single consumer and comparing risk-no risk situations where prices are random variables, they derive interesting and useful results that express conditions for the desirability of price stabilization in terms of the familiar Arrow-Pratt measure of relative risk aversion, price and income elasticities, and budget shares. Although the approach of T-S-S provides useful information about an individual's preference for or against price stability, it does not provide information about a group of heterogeneous consumers' preference for price stability. The approach of T-S-S also assumes that perfect price stabilization is possible; indeed, in many cases government policy may serve to partially stabilize prices, but not perfectly stabilize prices.2 Thus the analysis of T-S-S does not address comparisons of risk-risk situations (the comparisons of unstable versus partially stabilized prices) nor comparisons when there are heterogeneous individuals. Recently, Newbery and Stiglitz [9, 10] have used stochastic dominance rules to analyze mean preserving partial price stabilization schemes. The purpose of the present note is to extend the T-S-S and Newbery-Stiglitz analysis by providing comparisons of partial price stabilization policies that affect multiple prices in non-mean preserving ways. Since an excellent survey of the stabilization literature appears in Newbery and Stiglitz [10], we proceed with the results of our analysis.

This paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices. In this model, asset prices and their stochastic properties are determined endogenously. One principal result is a partial differential equation which asset prices must satisfy. The solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy. IN THIS PAPER, we develop a general equilibrium asset pricing model for use in applied research. An important feature of the model is its integration of real and financial markets. Among other things, the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables. The model is fully consistent with rational expectations and maximizing behavior on the part of all agents. Our framework is general enough to include many of the fundamental forces affecting asset markets, yet it is tractable enough to be specialized easily to produce specific testable results. Furthermore, the model can be extended in a number of straightforward ways. Consequently, it is well suited to a wide variety of applications. For example, in a companion paper, Cox, Ingersoll, and Ross [7], we use the model to develop a theory of the term structure of interest rates. Many studies have been concerned with various aspects of asset pricing under uncertainty. The most relevant to our work are the important papers on intertemporal asset pricing by Merton [19] and Lucas [16]. Working in a continuous time framework, Merton derives a relationship among the equilibrium expected rates of return on assets. He shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model. Lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes. The random output of these processes is exogenously determined and perishable. Assets are defined as claims to all or a part of the output of a process, and the equilibrium determines the asset prices. Our theory draws on some elements of both of these papers. Like Merton, we formulate our model in continuous time and make full use of the analytical tractability that this affords. The economic structure of our model is somewhat similar to that of Lucas. However, we include both endogenous production and

[It is shown that if an iterative price mechanism depends only upon a finite amount of information from the market as given by the aggregate excess demand function, then this mechanism cannot always be effective. That is, there are pure exchange economies where this mechanism will not find a price equilibrium. This statement already holds in the case of two commodities. The approach used to reach this conclusion extends to other iterative systems used to determine the zeros of a function.]

This paper derives the exact finite sample distribution of the two-stage generalized least squares (GLS) estimator in a multivariate linear model with general linear parameter restrictions. This includes the seemingly unrelated regression (SUR) model as a special case and generalizes presently known exact results for the latter system. The usual classical assumptions are made concerning nonrandom exogenous variables and normally distributed errors. The theoretical results of this paper are made possible by the author's development of a matrix fractional calculus. This operator calculus is the main theoretical tool of the paper and may be used to solve a wide range of other unsolved problems in econometric distribution theory. IN THE EARLY 1960's Zellner [10] developed a two-stage GLS estimator for the coefficients in a linear multivariate system that is now popularly known as the SUR model. This two-stage procedure has since been used in many empirical applications. GLS also forms the basis of other commonly used estimators both in linear models with heteroscedastic or autocorrelated errors and in simultaneous equation systems where it leads to three stage least squares (3SLS). In spite of extensive research and perhaps surprisingly in view of the popularity of GLS methods in empirical work, the exact finite sample distribution of the SUR estimator is known only in highly specialized cases. These cases effectively restrict attention to two equation systems and models with orthogonal regressors [2]. Existing distribution theory is even more limited in the case of other commonly used GLS estimators, such as the two-stage estimator in linear models with heteroscedastic errors. Here, only low order moment formulae are known and then only in the simplest two sample setting. The research underlying the present paper is motivated by the deficiencies outlined above. Our initial object of study was the exact distribution of the SUR estimator in the general case. But the methods we have developed open the way to an exact distribution theory for econometric estimators in a much wider setting than the SUR model. The present paper will derive the exact finite sample distribution of the two-stage GLS estimator in the multivariate linear model subject to general linear parameter restrictions. This generalizes all presently known distribution theory for the SUR model itself. Two important specializations of our results will be illustrated in detail: the unrestricted multivariate linear model; and the Zellner model with pairwise orthogonal regressors. The analytical results reported here are made possible by the introduction of a fractional matrix calculus. This calculus is developed in terms of the action of

[This paper considers a repeated principal agent relationship where the principal is risk neutral, the agent is risk averse, the principal can borrow or save at a fixed interest rate, and the agent discounts future consumption. It is shown that memory plays a very strong role in every Pareto-optimal contract. Sufficient conditions for Pareto-optimal contracts to exhibit rising or falling wages are identified. Finally, it is shown that the restriction of the agent's access to credit is necessary to achieve a Pareto-optimal outcome. In particular, under every Pareto-optimal contract for every outcome of every period the agent would choose to save some of his wage if he could.]

[In this paper we consider the computation of an equilibrium in a pure exchange economy with a block diagonal pattern. Such a structure appears in, e.g., international trade models. Utilizing the block diagonal pattern, the full equilibrium problem is reformulated as a problem on the product space of several lower-dimensional price-simplices. Some numerical results show the usefulness of this method.]

Expected value maximizing sequential search rules can be expressed in terms of reservation values. In search with learning the reservation value at any stage of the search is unknown until that stage is reached. Thus calculating ex ante (and subsequent) probabilities of search duration and the offer accepted is difficult if these probabilities are expressed in terms of reservation values. This paper shows, for a wide class of learning procedures, how re-expressing these probabilities in terms of fixed points allows their direct calculation and, thereby, calculation of the expected value of adaptive search. Examples and comparative statics results are presented.

[A dynamic model of insider trading with sequential auctions, structured to resemble a sequential equilibrium, is used to examine the informational content of prices, the liquidity characteristics of a speculative market, and the value of private information to an insider. The model has three kinds of traders: a single risk neutral insider, random noise traders, and competitive risk neutral market makers. The insider makes positive profits by exploiting his monopoly power optimally in a dynamic context, where noise trading provides camouflage which conceals his trading from market makers. As the time interval between auctions goes to zero, a limiting model of continuous trading is obtained. In this equilibrium, prices follow Brownian motion, the depth of the market is constant over time, and all private information is incorporated into prices by the end of trading.]