Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-12T18:12:19.742Z Has data issue: false hasContentIssue false
  • English
  • Français

BIAS CORRECTIONS IN TESTING AND ESTIMATING SEMIPARAMETRIC, SINGLE INDEX MODELS

Published online by Cambridge University Press:  17 March 2010

Roger Klein  and
Chan Shen
Get access Rights & Permissions [Opens in a new window]

Abstract

Semiparametric methods are widely employed in applied work where the ability to conduct inferences is important. To establish asymptotic normality for making inferences, bias control mechanisms are often used in implementing semiparametric estimators. The first contribution of this paper is to propose a mechanism that enables us to establish asymptotic normality with regular kernels. In so doing, we argue that the resulting estimator performs very well in finite samples.

Semiparametric models are commonly estimated under a single index assumption. Because the consistency of the estimator critically depends on this assumption being correct, our second objective is to develop a test for it. To ensure that the test statistic has good size and power properties in finite samples, we employ a bias control mechanism similar to that underlying the estimator. Furthermore, we structure the test so that its form adapts to the model under the alternative hypothesis. Monte Carlo results confirm that the bias control and the adaptive feature significantly improve the performance of the test statistic in finite samples.

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1683 - 1718
Copyright
Copyright © Cambridge University Press 2010

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.)

Footnotes

We thank the editor and anonymous referees for helpful comments. Any errors are the sole responsibility of the authors.

References

REFERENCES

Ahn, H. (1997) Semiparametric estimation of a single-index model with nonparametrically generated regressors. Econometric Theory 13, 3–31.10.1017/S0266466600005624CrossRefGoogle Scholar
Andrews, D.W.K. (2003) Tests for parameter instability and structural change with unknown change point: A corrigendum. Econometrica 71, 395–397.CrossRefGoogle Scholar
Bhattacharaya, P.K. (1967) Estimation of a probability density function and its derivatives. Indian Journal of Statistics, Series A 373–383.Google Scholar
Bierens, H.J. (1990) A consistent conditional moment test of functional form. Econometrica 58, 1443–1458.Google Scholar
Climov, D., Delecroix, M., & Simar, L. (2002) Semiparametric estimation in single index Poisson regression: A practical approach. Journal of Applied Statistics 29, 1047–1070.Google Scholar
Delgado, M.A. & Mora, J. (1995) Nonparametric and semiparametric inference with discrete regressors. Econometrica 63, 1477–1484.Google Scholar
Delgado, M.A. & Stengos, T. (1994) Semiparametric specification testing of non-nested econometric models. Review of Economic Studies 61, 291–303.CrossRefGoogle Scholar
Escanciano, J.C. & Song, K. (2007) Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects. PIER Working Paper Archive, 2007.CrossRefGoogle Scholar
Fraga, M. & Martins, O. (2001) Parametric and semiparametric estimation of sample selection models: An empirical application to the female labour force in Portugal. Journal of Applied Econometrics 16, 23–39.Google Scholar
Gerfin, M. (1996) Parametric and Semi-parametric estimation of the binary response model of labor market participation. Journal of Applied Econometrics 11, 321–339.Google Scholar
Gorgens, T. (2000) Semiparametric estimation of single-index transition intensities. Paper presented at Econometric Society World Congress 2000 (Contributed Papers 0596).Google Scholar
Gorgens, T. & Horowitz, J.L. (1999) Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable. Journal of Econometrics 90, 155–191.Google Scholar
Härdle, W. & Mammen, E. (1993) Comparing nonparametric versus parametric regression fits. Annals of Statistics 21(4), 1926–1947.Google Scholar
Härdle, W., Mammen, E., & Müller, M. (1998) Testing parametric versus semiparametric modelling in generalized linear models. Journal of the American Statistical Association 93, 1461–1474.Google Scholar
Härdle, W., Spokoiny, V., & Sperlich, S. (1997) Semiparametric single index versus fixed link function modelling. Annals of Statistics 25, 212–243.Google Scholar
Hoeffding, H. (1963) Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 48, 13–30.CrossRefGoogle Scholar
Honore, B.E. & Powell, J.L. (2005) Pairwise difference estimation of nonlinear models. In Andrews, D.W.K. & Stock, J.H. (eds.), Identification and Inference in Econometric Models. Essays in Honor of Thomas Rothenberg, pp. 520–553. Cambridge University Press.Google Scholar
Horowitz, J.L. & Spokoiny, V.G. (2001) An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599–631.CrossRefGoogle Scholar
Horowitz, J.L. & Härdle, W. (1994) Testing a parametric model against a semiparametric alternative. Econometric Theory 10, 821–848.CrossRefGoogle Scholar
Ichimura, H. (1993) Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. Journal of Econometrics 58, 71–120.Google Scholar
Klein, R.W. (1993) Specification tests for binary choice models based on index quantiles. Journal of Econometrics 59, 343–375.Google Scholar
Klein, R.W., Shen, C., & Vella, F. (2009) Joint Binary Selection and Treatment Models. Manuscript, Rutgers University and Georgetown University.Google Scholar
Klein, R.W. & Sherman, R.P. (2002) Shift restrictions and semiparametric estimation in ordered response models. Econometrica 70, 663–692.CrossRefGoogle Scholar
Klein, R.W. & Spady, R.H. (1993) An efficient semiparametric estimator for binary response models. Econometrica 61, 387–421.CrossRefGoogle Scholar
Newey, W.K. (1985) Maximum likelihood specification testing and conditional moment tests. Econometrica 53, 1047–1070.10.2307/1911011CrossRefGoogle Scholar
Newey, W.K., Hsieh, F., & Robins, J. (2004) Twicing kernels and a small bias property of semiparametric estimators. Econometrica 72, 947–962.Google Scholar
Pakes, A. & Pollard, D. (1989) Simulation and the asymptotics of optimization estimators. Econometrica 57, 1027–1058.Google Scholar
Powell, J.L., Stock, J.H., & Stoker, T.M. (1989) Semiparametric estimation of weighted average derivatives. Econometrica 57, 1403–1430.Google Scholar
Serfling, R.J. (1980) Approximation Theorems of Mathematical Statistics. Wiley.Google Scholar
Shen, C. (2009) Determinants of Healthcare Decisions: Insurance, Utilization and Expenditures. Manuscript, Georgetown University.Google Scholar
Tripathy, G. & Kitamura, Y. (2003) Testing conditional moment restrictions. Annals of Statistics 31, 2059–2095.Google Scholar