Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T06:58:47.570Z Has data issue: false hasContentIssue false

MOMENT-BASED INFERENCE WITH STRATIFIED DATA

Published online by Cambridge University Press:  30 April 2010

Gautam Tripathi*
Affiliation:
University of Connecticut
*
*Address correspondence to Gautam Tripathi, Department of Economics, University of Connecticut-Storrs, 341 Mansfield Road, Unit 1063, Storrs, CT 06269; e-mail: gautam.tripathi@uconn.edu.

Abstract

Many data sets used by economists and other social scientists are collected by stratified sampling. The sampling scheme used to collect the data induces a probability distribution on the observed sample that differs from the target or underlying distribution for which inference is to be made. If this effect is not taken into account, subsequent statistical inference can be seriously biased. This paper shows how to do efficient semiparametric inference in moment restriction models when data from the target population are collected by three widely used sampling schemes: variable probability sampling, multinomial sampling, and standard stratified sampling.

Type
ARTICLES
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.)

References

REFERENCES

Bickel, P., Klassen, C., Ritov, Y., & Wellner, J. (1993) Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins Press.Google Scholar
Bickel, P.J. & Ritov, J. (1991) Large sample theory of estimation in biased sampling regression models. Annals of Statistics 19, 797816.CrossRefGoogle Scholar
Brown, B.W. & Newey, W.K. (1998) Efficient semiparametric estimation of expectations. Econometrica 66, 453464.CrossRefGoogle Scholar
Brown, B.W. & Newey, W.K. (2002) GMM, efficient bootstrapping, and improved inference. Journal of Business and Economic Statistics 20, 507517.Google Scholar
Butler, J. (2000) Efficiency results of MLE and GMM estimation with sampling weights. Journal of Econometrics 96, 2537.Google Scholar
Cosslett, S. (1981a) Efficient estimation of discrete choice models. In Manski, C.F. & McFadden, D. (eds.), Structural Analysis of Discrete Data with Econometric Applications, pp. 51111. MIT Press.Google Scholar
Cosslett, S. (1981b) Maximum likelihood estimation for choice-based samples. Econometrica 49, 12891316.CrossRefGoogle Scholar
Cosslett, S. (1993) Estimation from endogenously stratified samples. In Maddala, G., Rao, C., & Vinod, H. (eds.), Handbook of Statistics, pp. 143. Elsevier Science.Google Scholar
DeMets, D. & Halperin, M. (1977) Estimation of a simple regression coefficient in samples arising from a subsampling procedure. Biometrics 33, 4756.Google Scholar
Devereux, P. & Tripathi, G. (2009) Optimally combining censored and uncensored datasets. Journal of Econometrics 151, 1732.Google Scholar
DuMouchel, W.H. & Duncan, G.J. (1983) Using sample survey weights in multiple regression analysis of stratified samples. Journal of the American Statistical Association 78, 535543.Google Scholar
Efromovich, S. (2004) Distribution estimation for biased data. Journal of Statistical Planning and Inference 124, 143.CrossRefGoogle Scholar
El-Barmi, H. & Rothmann, M. (1998) Nonparametric estimation in selection biased models in the presence of estimating equations. Nonparametric Statistics 9, 381399.Google Scholar
Fisher, N.I., Hall, P., Jing, B.-Y., & Wood, A.T. (1996) Improved pivotal methods for constructing confidence regions with directional data. Journal of the American Statistical Association 91, 10621070.Google Scholar
Harville, D.A. (1997) Matrix Algebra from a Statistician’s Perspective. Springer-Verlag.CrossRefGoogle Scholar
Hausman, J.A. & Wise, D.A. (1981) Stratification on endogenous variables and estimation: The Gary income maintenance experiment. In Manski, C.F. & McFadden, D. (eds.), Structural Analysis of Discrete Data with Econometric Applications, pp. 365391. MIT Press.Google Scholar
Hellerstein, J. & Imbens, G.W. (1999) Imposing moment restrictions from auxiliary data by weighting. Review of Economics and Statistics 81, 114.Google Scholar
Holt, D., Smith, T., & Winter, P. (1980) Regression analysis of data from complex surveys. Journal of The Royal Statistical Society, Series A 143, 474487.CrossRefGoogle Scholar
Imbens, G.W. (1992) An efficient method of moments estimator for discrete choice models with choice-based sampling. Econometrica 60, 11871214.CrossRefGoogle Scholar
Imbens, G.W. (1997) One-step estimators for over-identified generalized method of moments models. Review of Economic Studies 64, 359383.CrossRefGoogle Scholar
Imbens, G.W. & Lancaster, T. (1994) Combining micro and macro data in microeconomic models. Review of Economic Studies 61, 655680.Google Scholar
Imbens, G.W. & Lancaster, T. (1996) Efficient estimation and stratified sampling. Journal of Econometrics 74, 289318.Google Scholar
Imbens, G.W., Spady, R.H., & Johnson, P. (1998) Information theoretic approaches to inference in moment condition models. Econometrica 66, 333357.CrossRefGoogle Scholar
Jewell, N.P. (1985) Least squares regression with data arising from stratified samples of the dependent variable. Biometrika 72, 1121.CrossRefGoogle Scholar
Kitamura, Y. (1997) Empirical likelihood methods with weakly dependent processes. Annals of Statistics 25, 20842102.Google Scholar
Kitamura, Y. (2001) Asymptotic optimality of empirical likelihood for testing moment restrictions. Econometrica 69, 16611672.Google Scholar
Kitamura, Y. (2006) Empirical Likelihood Methods in Econometrics: Theory and Practice. Invited symposium on Weak Instruments and Empirical Likelihood at the 9th World Congress of the Econometric Society.Google Scholar
Manski, C.F. & Lerman, S.R. (1977) The estimation of choice probabilities from choice based samples. Econometrica 45, 19771988.CrossRefGoogle Scholar
Manski, C.F. & McFadden, D. (1981) Alternative estimators and sample design for discrete choice analysis. In Manski, C.F. & McFadden, D. (eds.), Structural Analysis of Discrete Data with Econometric Applications, pp. 250. MIT Press.Google Scholar
Nevo, A. (2003) Using weights to adjust for sample selection when auxiliary information is available. Journal of Business and Economic Statistics 21, 4352.CrossRefGoogle Scholar
Newey, W.K. (1990) Semiparametric efficiency bounds. Journal of Applied Econometrics 5, 99135.Google Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In: Engle, R. & McFadden, D. (eds.), Handbook of Econometrics, vol. IV, pp. 21112245. Elsevier Science B.V.CrossRefGoogle Scholar
Newey, W.K. & Smith, R.J. (2004) Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 72, 219255.Google Scholar
Owen, A. (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75, 237249.Google Scholar
Owen, A. (2001) Empirical Likelihood. Chapman and Hall/CRC.Google Scholar
Qin, J. (1993) Empirical likelihood in biased sample problems. Annals of Statistics 21, 11821196.CrossRefGoogle Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood and general estimating equations. Annals of Statistics 22, 300325.Google Scholar
Quesenberry, C.P. & Jewell, N.P. (1986) Regression analysis based on stratified samples. Biometrika 73, 605614.CrossRefGoogle Scholar
Scott, A. & Wild, C. (1986) Fitting logistic models under case-control or choice based sampling. Journal of The Royal Statistical Society, Series B 48, 170182.Google Scholar
Severini, T.A. & Tripathi, G. (2001) A simplified approach to computing efficiency bounds in semiparametric models. Journal of Econometrics 102, 2366.CrossRefGoogle Scholar
Smith, R.J. (1997) Alternative semi-parametric likelihood approaches to generalized method of moments estimation. Economic Journal 107, 503519.CrossRefGoogle Scholar
Smith, R.J. (2005) Weak Instruments and Empirical Likelihood: A Discussion of the Papers by D.W.K. Andrews and J.H. Stock and Y. Kitamura. Invited discussion of the symposium on Weak Instruments and Empirical Likelihood at the 9th World Congress of the Econometric Society.CrossRefGoogle Scholar
Tripathi, G. (2002) Inference in Conditional Moment Restriction Models When There Is Selection Due to Stratification. Manuscript, University of Wisconsin-Madison.Google Scholar
Wooldridge, J.M. (1999) Asymptotic properties of weighted M-estimators for variable probability samples. Econometrica 67, 13851406.Google Scholar
Wooldridge, J.M. (2001) Asymptotic properties of weighted M-estimators for standard stratified samples. Econometric Theory 17, 451470.Google Scholar