In this paper we introduce a general method for estimating
semiparametrically the different components in separable models. The
family of separable models is quite popular in economic research
because this structure offers clear interpretation, has straightforward
economic consequences, and is often justified by theory. This family is
also of statistical interest because it allows us to estimate
high-dimensional complexity semiparametrically without running into the
curse of dimensionality. We consider even the case when multiple
indices appear in the objective function; thus we can estimate models
that are typical in economic analysis, such as those that contain
limited dependent variables. The idea of the new method is mainly based
on a generalized profile likelihood approach. Although this requires
some hypotheses on the conditional error distribution, it yields a
quite general usable method with low computational costs but high
accuracy even for small samples. We give estimation procedures and
provide some asymptotic theory. Implementation is discussed;
simulations and an application demonstrate its feasibility and good
finite-sample behavior.This research was
financially supported by Dirección General de Investigación
del Ministerio de Ciencia y Tecnología under research grants
BEC2001-1121 and BEC2001-1270; Dirección General de Enseñanza
Superior del Ministerio de Educación y Ciencia under Subprograma de
estancias de investigadores españoles en centros de
investigación españoles y extranjeros, ref. PR2000-0096; and
by the Danish Social Science Research fund. We also thank M. Delgado, O.
Linton, two anonymous referees, and all participants of the working group
STAPH on functional statistics in Toulouse, the activities of which are
available on line at
http://www.lsp.upstlse.fr/Fp/Ferraty/staph.html.