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Stationary Equilibrium in a Market for Durable Assets

Econometrica 1985 53(4), 783
[This paper presents a dynamic model of consumer trading on the primary, secondary, and scrap markets for a stochastically deteriorating durable good in a stationary economy with perfect information and no transaction costs. We explicitly model the trading process by tracking each durable from its "birth" in the primary market, through its sequence of owners in the secondary market, until its "death" in the scrap market. We prove that a stationary equilibrium tests, characterize the distribution of consumer holdings of durables, and show that equilibrium asset prices are shadow prices to a particular regenerative optimal stopping problem. We show that each heterogeneous agent equilibrium is observationally equivalent to a homogeneous agent equilibrium. We derive a differential equation for equilibrium rental rates, and a functional equation which links rental rates to asset prices. These equations show precisely how the structure of durable prices and rental rates embody the functional form and population distribution of preferences and the technological characteristics of durable goods.]

The Variability of Aggregate Demand with (S, s) Inventory Policies

Econometrica 1985 53(6), 1395
This paper develops a general theory of the aggregate implications of (S, s) inventory policies. It is shown that (S, s) policies add to the variability of demand, with the variance of orders exceeding the variance of sales. Overall, the (S, s) theory contradicts the widely held notion that retail inventories act as a buffer, protecting manufacturers from fluctuating sales. In 1951, Arrow, Harris, and Marschak [3] introduced the (S, s) form of inventory policy. The policies are designed for retailers of finished goods, who face economies of scale when placing orders with their suppliers. To pursue an (S, s) inventory policy, the retailer establishes a lower stock point s, and an upper stock point S. No order is placed until inventories fall to s or below, whereupon they are restored to the maximum of S. A general proof of the optimality of these (S, s) inventory policies was provided by Scarf [13]. At the microeconomic level, the model has been extensively investigated. Formulae are available to compute optimal policies (e.g., Ehrhardt [6]), and these policies are xidely used in industry (e.g., Schwartz (ed.) [14]). In addition, the model has been extended to increasingly complex demand environments (e.g., Karlin and Fabens [11]). In contrast, little is known about the macroeconomic implications of (S, s) policies. Several recent papers have begun to correct this deficiency. Akerlof has suggested that pursuit of constant threshold money holding policies of the (S, s) variety might be responsible for the observed low short-run income elasticity of the demand for money (Akerlof [1] and Akerlof and Milbourne [2]). In the operations research literature, Ehrhardt, Schultz, and Wagner [7] analyzed the demand environment of a wholesaler supplying several retailers. They required that the distinct retailers have independent sales, ruling out the analysis of common factors in sales. Finally, simulation results of Blinder [4] suggested a role for the (S, s) model in understanding retail sector inventories. However the theoretical difficulties with the model remained unresolved. Blinder commented: If firms have a technology that makes the S, s rule optimal, aggregation across firms is inherently difficult. Indeed it is precisely this difficulty which has prevented the S, s model from being used in empirical work to date (Blinder [4, p. 459]). In this paper we present a general theory of the aggregate implications of (S, s) policies. Our central finding is that (S, s) policies add to the variability of demand, with the variance of orders exceeding the variance of sales. This result holds even in the presence of common factors in retail sales. In addition, a close connection

A Sequential Solution to the Public Goods Problem

Econometrica 1985 53(1), 77
[Much attention has been devoted recently to the problem of implementing an optimal provision of public goods with imperfect information about preferences. The literature studies mechanisms with individual agents directly revealing information about their preferences, and focuses on two types of truthful equilibria: dominant strategy and Bayesian-Nash. We introduce "Stackelberg" mechanisms with truth-telling a dominant strategy for all agents but the first. The first agent plays "before" the other maximizing his expected utility on the assumption that others will reveal their true preferences. We present sufficient conditions for the construction of Stacekelberg mechanisms which yield an efficient provision of public goods, balance the budget, and induce every participant to reveal their true preferences. These results strengthen and extend the known results of the Bayesian-Nash approach.]

Bayesian Econometrics

Econometrica 1985 53(2), 253
[The widespread use of prior information in formulating, estimating, and using econometric models is reviewed. Attempts to avoid the use of prior information by formulating multivariate statistical VAR and ARMA time series models for economic time series data have resulted in heavily over-parametrized models. A simple demand, supply, and entry model is presented to contrast models utilizing prior information provided by economic theory and other sources with multivariate statistical time series models. Formal Bayesian methods for incorporating prior information in econometric estimation, testing, and prediction are presented. A number of published applied Bayesian studies are cited in which Bayesian methods have proved to be effective. It is concluded that wise use of the Bayesian approach will produce improved econometric results.]