This paper provides a consistent and asymptotically normal estimator for the intercept of a semiparametrically estimated sample selection model. The estimator uses a decreasingly small fraction of all observations as the sample size goes to infinity, as in Heckman (1990). In the semiparametrics literature, estimation of the intercept has typically been subsumed in the nonparametric sample selection bias correction term. The estimation of the intercept, however, is important from an economic perspective. For instance, it permits one to determine the "wage gap" between unionized and nonunionized workers, decompose the wage differential between different socioeconomic groups (e.g. male-female and black--white), and evaluate the net benefits of a social programme.

In the literature on the empirical distribution of foreign exchange rates there is now consensus that exchange rate yields are fat-tailed. Three problems, however, persist: (1) Which class of distribution functions is most appropriate? (2) Are the parameters of the distribution invariant over subperiods? (3) What are the effects of aggregation over time on the distribution? In this paper we employ extreme value theory to shed new light on these questions. We apply the theoretical results to EMS data.*We wish to thank Laurens de Haan for his invaluable theoretical insights. Guido Imbens, Peter Schotman, an anonymous referee and the editors of this journal provided valuable comments. Ieko Sevinga provided able research assistance. We profited from presentations given at Brown University, the University of Zurich and the European Economic Association meetings 1988. The major part of this work was conducted while all three authors were at Erasmus University Rotterdam.'The survey by Boothe and Glassman gives the state of the art in modelling the exchange rate yield distribution. Therefore we deem it unnecessary to provide an exegesis of the existing literature. Rather, for each issue we discuss, we refer to the corresponding discussion in Boothe and Glassman. Thus, the reader should bear in mind that this is not a critique, but a continuation. Our approach, though, is quite novel. 0022-1996/90/%03.50 0 1990-Elsevier Science Publishers B.V. (North-Holland) J.I.E. D

We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on "identification at infinity" which leads to non-standard convergence rate. Andrews and Schafgans (1998) derived asymptotic results for a smoothed version of the estimator. We examine the optimal bandwidth selection for the estimators and derive asymptotic MSE rates under a wide class of distributional assumptions. We also provide some comparisons of the estimators and practical guidelines.

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