[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.]

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

When charitable contributions are tax deductible, the marginal price of charitable giving in other consumption foregone per dollar of contributions is generally less than unity. Further, if the income tax schedule is a progressive step function, the marginal price of contributions is generally a rising step function of the level of contributions. The problem of estimating a contributions demand function for individuals is therefore complicated by the spurious correlation between the level of contributions and the observed marginal price. We take this econometric problem into account in estimating a contributions demand function using data from the 1972-73 Consumer Expenditure Survey. After comparing our results with those of estimation techniques used by other authors, we provide evidence on the impacts of alternative tax policies on charitable giving using our estimates of the model parameters.

IN THIS PAPER we present a weighted-instrumental-variables estimator that is resistant2 to heavy-tailed errors, aberrant data in either the endogenous or exogenous variables, and certain other model failures. The estimator is analogous to the weighted-least-squares approach to robustness proposed by Krasker and Welsch [21] for ordinary regression. We will discuss the theory that motivated this estimator, derive some of its properties, describe our computational algorithm, and, using an empirical example, illustrate the estimator's utility as a tool for data analysis in structural models. The evolution of robust estimators for simultaneous-equations models has closely resembled the development of robust methods for ordinary regression. In both cases, research focused at first on the well-documented effects of long-tailed error distributions on the classical procedures. For ordinary regression models, statisticians have studied the properties of least-absolute-deviations (LAD) estimators (see Bassett and Koenker [2] and Amemiya [1]) and maximum-likelihood-type estimators (called M-estimators; see Huber [14]). For simultaneous-equations models, LAD can be generalized in several different ways to modify two-stage least squares or instrumental variables; Amemiya [1] has presented these estimators in a unified framework, and Powell [31] has proven their asymptotic normality under weak assumptions. Fair [8] has compared two-stage LAD estimates of a U.S. macroeconomic model with two-stage least squares and full-information maximum likelihood estimates. The M-estimator concept can also be generalized to simultaneous equations. For example, Prucha and Kelejian [32] have considered maximum-likelihood estimation under the assumption that the disturbance vector is multivariate student t. Although LAD and M-estimators maintain a high efficiency when the error distribution is heavy-tailed, they are not robust in the stronger sense of Hampel [10] which, roughly speaking, requires an estimator to have a limited sensitivity to any small fraction of the data.3 LAD and M-estimators fail under this criterion because a single observation whose values for the right-side variables are highly anomalous can have an arbitrarily large effect on LAD estimates or M-estimates, just as on the classical procedures. Consequently, these estimators do not provide insurance against the sort of gross errors that occur in some data sets; nor do they serve as reliable diagnostics for departures from linearity occurring in extreme regions of the space of right-side variables. For linear models, the estimators that satisfy the strong Hampel robustness criterion have become known as bounded-influence estimators. Several such estimators have been