We consider a regression in which one of the observed variables is a proxy for some unobserved variable. Given a lower bound for the correlation between the proxy and the unobserved true variable for which it substitutes, we derive intervals in which the coefficients of the unobserved true regression must lie, regardless of any other correlations involving unobserved variables or disturbances. We present a simple solution for the important special case in which only the signs of the coefficients are of concern and one seeks the smallest correlation between the proxy and the true variable that guarantees the correctness of the signs of the coefficients in the proxy regression. We also present an algorithm for extending these results to the multiple-proxy problem. ATTEMPrS TO CONFRONT economic theories with data are often hampered by the problem that some of the relevant variables are unavailable or even unobservable. In the case of regression models it is customary to substitute proxies for the unavailable variables. Though the coefficients in the proxy regression will not coincide with those in the regression of the dependent variable on the explanatory variables, it is clear by continuity that the differences will be small if each proxy is sufficiently highly correlated with the unobserved true variable for which it substitutes, even if its error is correlated with other errors or variables. Moreover, in many instances the theory predicts not the magnitudes but only the signs of the regression coefficients. Correct inferences will then be drawn from the model provided that the pairwise correlations between the proxies and the true variables are high enough to guarantee that the signs of the regression coefficients would be unchanged if the proxies were replaced by the true variables. In applications econometricians can generally assess those pairwise correlations subjectively, but how high do they need to be? In this paper we present a complete answer to this question when only one variable is a proxy, and describe an algorithm for determining the required correlations when there are several proxies. The effects of proxy variables have been extensively studied in the special case of errors-in-variables (EIV), in which the differences between the proxies and the corresponding true variables (the errors) are independent of the true variables, of each other, and of the disturbances in the true regression. We require no such independence. In the EIV case it is sometimes possible to guarantee correctness of the signs of the coefficients even without prior information about the variances of the measurement errors. For example, if the coefficient vector from the direct regression and the coefficient vectors from the reverse regressions (as one varies the left-side variable) all lie in the same orthant, then the coefficient vector in the true regression must also lie in that orthant (see

A general model of arbitrator behavior in conventional and final-offer arbitration is developed that is based on an underlying notion of an appropriate award in a particular case. This appropriate award is defined as a function of the facts of the case independently of the offers of the parties. In conventional arbitration the arbitration award is argued to be a function of both the offers of the parties and the appropriate award. The weight that the arbitrator puts on the appropriate award relative to the offers is hypothesized to be a function of the quality of the offers as measured by the difference between the offers. In final-offer arbitration itis argued that the arbitrator chooses the offer that is closest to the appropriate award.The model is implemented empirically using data gathered from practicing arbitrators regarding their decisions in twenty-five hypothetical cases. The estimates of the general model strongly support the characterizations of arbitrator behavior in the two schemes. No substantial differences were found in the determination of the appropriate award implicit in the conventional arbitration decisions and the determination of the appropriate award implicitin the final-offer decisions.

A general model of arbitrator behavior in conventional and final-offer arbitration is developed that is based on an underlying notion of an appropriate award in a particular case. This appropriate award is defined as a function of the facts of the case independently of the offers of the parties. In conventional arbitration the arbitration award is argued to be a function of both the offers of the parties and the appropriate award. The weight that the arbitrator puts on the appropriate award relative to the offers is hypothesized to be a function of the quality of the offers as measured by the difference between the offers. In final-offer arbitration it is argued that the arbitrator chooses the offer that is closest to the appropriate award. The model is implemented empirically using data gathered from practicing arbitrators regarding their decisions in twenty-five hypothetical cases. The estimates of the general model strongly support the characterizations of arbitrator behavior in the two schemes. In addition, no substantial differences were found in the determination of the appropriate award implicit in conventional arbitration decisions and the determination of the appropriate award implicit in the final-offer decisions.

[We consider an economy in which agents may or may not communicate with each other. Coalitions can form only between linked agents. We consider two cases: agents must communicate directly to be in the same coalition or in the second case indirectly. We consider the communication to be random. The economy may then be represented by a stochastic graph; the admissible coalitions are then stochastic and thus so is the core of an economy. We demonstrate that if the probability that agents are linked with each other does not tend to zero too fast as this number increases, then the probability that a coalition will form and block any non-Walrasian allocation tends to one, as the number of agents goes to infinity.]

On considere des equations autoregressives a variables exogenes et un terme de bruit blanc normal, ce qui generalise les modeles dynamiques etudies precedemment