Knowledge that Transforms

Arthur Lewbel, Constructing Instruments for Regressions With Measurement Error When no Additional Data are Available, with An Application to Patents and R&D, Econometrica, Vol. 65, No. 5 (Sep., 1997), pp. 1201-1213

The authors examine core convergence for economies with a large finite number of agents and an infinite number of commodities. They find a serious disconnection between economies with a large finite number of agents and economies with a continuum of agents: the authors provide examples of nonconvergence of the core for large finite economies in L[superscript 1], a commodity space for which core equivalence holds for continuum economies. In addition, they show that, if preferences exhibit uniformly vanishing marginal utility of consumption at infinity, core convergence is restored.

This paper reports a laboratory experiment that examines price formation in the single call market. The experiment design is intended to enhance the predictive power of the Bayesian Nash equilibrium (BNE) theory for this trading institution. The data support several qualitative implications of the BNE, especially when subjects compete against Nash 'robot' opponents, but subjects' behavior is not as responsive to changes in the pricing rule as the BNE predictions. Offers tend to reveal more of the underlying values and costs than predicted, particularly when subjects are experienced. A simple learning model accounts for several of the deviations from BNE.

The author considers the problem of estimation in a panel data sample selection model, where both the selection and the regression equation of interest contain unobservable individual-specific effects. He proposes a two-step estimation procedure, which 'differences out' the sample selection effect and the unobservable individual effect from the equation of interest. In the first step, the unknown coefficients of the 'selection' equation are consistently estimated. The estimates are then used to estimate the regression equation of interest. The estimator proposed in this paper is shown to be consistent and asymptotically normal. The proposed estimator is shown to be consistent and asymptotically normal. Its finite sample properties are investigated in a small Monte Carlo simulation.

WE WARN OF A CLASS of problems that can occur when inverting confluent characteristic functions (CF's). The term confluence is often used in Mathematics in connection with analysis and/or dynamic (difference, differential, and integral) equations; for example, see the classic text by Whittaker and Watson (1927). A confluence (of singularities) is a joint degeneracy that occurs within a function; here, the CF. When one is dealing with the CF of a k-dimensional variate where k > 1, these joint degeneracies can distort the derivation of the marginal density of some lower-dimensional combination of the k components. The distortions are both analytical and numerical. In this note, we first express the distributional problem in the simplest bivariate case, then clarify it with examples from a simple autoregressive (AR) model. Let R, S be two continuous (for simplicity) variates based on a sample of n observations, with joint CF pn(u,v) =E[euR+ivS], i = , and Pr{S > 0} = 1. The joint density h,jr, s) of R and S is expressed by means of the inversion formula as

The literature on the aggregation of (S, s) policies has ignored the impact of aggregate behavior on the individual's optimization problem. In the case of pricing, the feedback effects are clear. Not only do pricing strategies determine the evolution of the price level, but the evolution of the price level also influences the optimal pricing strategies. In this paper, we provide a consistent treatment of aggregation and optimization. We use this model to analyze three issues in the menu cost pricing literature: the relationship between strategic complementarity and the real effects of money; the relationship between the variance of the money supply and the correlation between money and output; and the relationship between the cost of price adjustment and the size of price adjustment. QUESTIONS CONCERNING THE DYNAMICS of aggregate variables such as prices, employment, investment, and consumption represent the core of business cycle analysis. One striking feature of these variables is the radical difference between properties of these aggregates and the nature of the individual behavior that underlies them. The behavior of a firm's prices, investment and employment, and the behavior of an individual's consumption all involve frictional elements that lead to discrete adjustment at the microeconomic level. Heterogeneity among individuals, however, tends to smooth the behavior of the corresponding aggregates. In recent years, a large body of research has developed to examine the manner in which microeconomic frictions influence aggregate dynamics. One of the centerpieces of this research has been the (S, s) model developed by Arrow, Harris, and Marschak (1951). The key element of this model is the state dependence of individual decisions. Agents act when a state variable crosses some critical threshold which balances the cost and benefits of adjustment. The aggregate implications of this form of microeconomic behavior have been analyzed by Blinder (1981), Caplin (1985), and Mosser (1991) in the context of inventory dynamics; by Caplin and Spulber (1987), Caballero and Engel (1991, 1993), and Caplin and Leahy (1991) in the context of prices; and by Bertola and Caballero (1990), Caballero (1993), and Eberly (1994) in the context of con- sumer durables. One of the most limiting aspects of these models is that they focus exclusively on the impact that microeconomic inertia has on aggregate dynamics. They 1We would like to thank Michael Harrison, loannis Karatzas, John Leahy Sr., Andreu Mas-Colell, a co-editor and four anonymous referees for helpful discussions and comments, and the National Science Foundation and the Sloan Foundation for financial support.

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The authors consider a family of rank tests based on the regression rank score process introduced by C. Gutenbrunner and J. Jureckova (1992) to test the unit root hypothesis in economic time series. In contrast to tests based on least-squares methods, the rank tests are asymptotically Gaussian under the null hypothesis, and have excellent power--particularly under innovation exhibiting heavy tails. These regression rank scores arise as a vector of solutions of the dual form of the linear program required to compute the regression quantile statistics of R. W. Koenker and G. Bassett (1978). For location model, they are simple ranks of the sample observations.

This paper develops a general framework for modeling choice under uncertainty that extends subjective expected utility to include nonseparabilities, state-dependence, and the effect of subjective or ill defined consequences. This is accomplished by not including consequences among the formal primitives. Instead, the effect of consequences is modeled indirectly, through conditional preferences over acts. The main results concern the aggregation of conditional utilities to form an unconditional utility, including the case of additive aggregation. Applications, obtained by further specifying the structure of acts and conditional preferences, include disappointment, regret, and the subjective value of information.