Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-24T07:01:32.707Z Has data issue: false hasContentIssue false
  • English
  • Français

SEMIPARAMETRIC ESTIMATION OF SEPARABLE MODELS WITH POSSIBLY LIMITED DEPENDENT VARIABLES

Published online by Cambridge University Press:  24 September 2003

Juan M. Rodríguez-Póo ,
Stefan Sperlich  and
Philippe Vieu
Juan M. Rodríguez-Póo
Affiliation:
Universidad de Cantabria
Stefan Sperlich
Affiliation:
Universidad Carlos III de Madrid
Philippe Vieu
Affiliation:
Université Paul Sabatier
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 6 , December 2003 , pp. 1008 - 1039
Copyright
© 2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ai, C. & X. Chen (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica. 71, 1795–1844.Google Scholar
Amemiya, T. (1985) Advanced Econometrics. Cambridge: Harvard University Press.
Andrews, D.W.K. (1994) Asymptotics for semiparametric econometric models via stochastic equicontinuity. Econometrica 62, 43–72.Google Scholar
Berndt, E.R. & L.R. Christensen (1973) The internal structure of functional relationships: Separability, substitution, and aggregation. Review of Economic Studies 40, 403–410.Google Scholar
Blundell, R. & J.-M. Robin (2000) Latent separability: Grouping goods without weak separability. Econometrica 68, 53–84.Google Scholar
Bosq, D. (1998) Nonparametric Statistics for Stochastic Processes. Lecture Notes in Statistics 110. New York: Springer-Verlag.
Chamberlain, G. (1992) Efficiency bounds for semiparametric regression. Econometrica 60, 567–596.Google Scholar
Deaton, A. & J. Muellbauer (1980) Economics and Consumer Behavior. Cambridge: Cambridge University Press.
Delgado, M.A. & J. Mora (1995) Nonparametric and semiparametric estimation with discrete regressors. Econometrica 63, 1477–1484.Google Scholar
Denny, M. & M. Fuss (1977) The use of approximation analysis to test for separability and the existence of consistent aggregates. American Economic Review 67, 404–418.Google Scholar
Fan, J. (1992) Design-adaptive nonparametric regression. Journal of the American Statistical Association 87, 998–1004.Google Scholar
Fernández, A.I. & J.M. Rodríguez-Poó (1997) Estimation and specifications testing in female labor participation models: Parametric and semiparametric methods. Econometric Reviews 16, 229–248.Google Scholar
Fuss, M., D. McFadden, & Y. Mundlak (1978) A survey of functional forms in the economic analysis of production. In M. Fuss & D. McFadden (eds.), Production Economics: A Dual Approach to Theory and Applications, vol. 1, pp. 219–268.
Goldman, S.M. & H. Uzawa (1964) A note on separability in demand analysis. Econometrica 32, 387–398.Google Scholar
Gronau, R. (1973) The effects of children on the housewife's value of time. Journal of Political Economy 81, S168–S199.Google Scholar
Härdle, W., S. Huet, E. Mammen, & S. Sperlich (2000) Bootstrap Inference in Semiparametric Generalized Additive Models. Working paper 00–70, Universidad Carlos III de Madrid, Spain.
Hastie, T.J. & R.J. Tibshirani (1990) Generalized Additive Models. London: Chapman and Hall.
Heckman, J. (1974) Shadow prices, market wages, and labor supply. Econometrica 42, 679–694.Google Scholar
Horowitz, J. (2001) Nonparametric estimation of a generalized additive model with an unknown link function. Econometrica 69, 499–513.Google Scholar
Ichimura, H. & L.F. Lee (1991) Semiparametric estimation of multiple index models. In W.A. Barnett, J. Powell, & G. Tauchen (eds.), Nonparametric and Semiparametric Methods in Econometrics and Statistics, pp. 3–50. New York: Cambridge University Press.
Klein, R.W. & R.H. Spady (1993) An efficient semiparametric estimator for discrete choice models. Econometrica 61, 387–421.Google Scholar
Lejeune, M. (1985) Estimation non-paramétrique par noyaux: Régression polynomiale mobile. Revue de Statistique Appliquée 33, 43–67.Google Scholar
Leontief, W. (1947a) Introduction to a theory of the internal structure of functional relationships. Econometrica 15, 361–373.Google Scholar
Leontief, W. (1947b) A note to the interrelation of subsets of independent variables of a continuous function with continuous first derivatives. Bulletin of the American Mathematical Society 53, 343–350.Google Scholar
Lewbel, A. & O. Linton (2002) Nonparametric censored and truncated regression. Econometrica 70, 765–779.Google Scholar
Linton, O.B. (1997) Efficient estimation of additive nonparametric regression models. Biometrika 84, 469–474.Google Scholar
Linton, O.B. (2000) Efficient estimation of generalized additive nonparametric regression models. Econometric Theory 16, 502–523.Google Scholar
Linton, O.B. & J.P. Nielsen (1995) A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika 82, 93–101.Google Scholar
Mammen, E., O. Linton, & J.P. Nielsen (1999) The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Annals of Statistics 27, 1443–1490.Google Scholar
McCullagh, P. & J.A. Nelder (1989) Generalized Linear Models. London: Chapman and Hall.
Newey, W.K. (1990) Semiparametric efficiency bounds. Journal of Applied Econometrics 5, 99–135.Google Scholar
Newey, W.K. (1994) The asymptotic variance of semiparametric estimators. Econometrica 62, 1349–1382.Google Scholar
Pinske, J. (2000) Feasible Multivariate Nonparametric Regression Estimation Using Weak Separability. Preprint, University of British Columbia, Canada.
Rodríguez-Póo, J.M., S. Sperlich, & P. Vieu (2000) Semiparametric Estimation of Weak and Strong Separable Models. Discussion paper 00-69, Statistics and Econometrics Series, Universidad Carlos III, Madrid.
Serfling, T. (1980) Approximation Theorems of Mathematical Statistics. New York: Wiley.
Severini, T.A. & J.G. Staniswalis (1994) Quasi-likelihood estimation in semiparametric models. Journal of the American Statistical Association 89, 501–511.Google Scholar
Severini, T.A. & W.W. Wong (1992) Profile likelihood and conditionally parametric models. Annals of Statistics 4, 1768–1802.Google Scholar
Sperlich, S., O. Linton, & W. Härdle (1999) Integration and backfitting methods in additive models: Finite sample properties and comparison. Test 8, 419–458.Google Scholar
Sperlich, S., D. Tjøstheim, & L. Yang (2002) Nonparametric estimation and testing of interaction in additive models. Econometric Theory 18, 197–251.Google Scholar
Staniswalis, J.G. (1989) The kernel estimate of a regression function in likelihood-based models. Journal of the American Statistical Association 84, 276–283.Google Scholar
Stone, C.J. (1985) Additive regression and other nonparametric models. Annals of Statistics 13, 689–705.Google Scholar
Stone, C.J. (1986) The dimensionality reduction principle for generalized additive models. Annals of Statistics 14, 590–606.Google Scholar
Tjøstheim, D. & B.H. Auestad (1994) Nonparametric identification of nonlinear time series: Projections. Journal of the American Statistical Association 89, 1398–1409.Google Scholar