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Estimation of ordered response models with sample selection

We introduce two new Stata commands for the estimation of an ordered response model with sample selection. The opsel command uses a standard maximum likelihood (ML) approach to fit a parametric specification of the model where errors are assumed to follow a bivariate Gaussian distribution. The snpopsel command uses the semi-nonparametric (SNP) approach of Gallant and Nychka (1987) to fit a semiparametric specification of the model where the bivariate density function of the errors is approximated by a Hermite polynomial expansion. The snpopsel command extends the set of Stata routines for SNP estimation of discrete response models. Compared to the other SNP estimators, our routine is relatively faster because it is programmed in MATA. In addition, we provide new post-estimation routines to compute linear predictions, predicted probabilities and marginal effects. These improvements are also extended to the set of SNP Stata commands originally written by Stewart (2004) and De Luca (2008). An illustration of the new opsel and snpopsel commands is provided through an empirical application on self-reported health with selectivity due to sample attrition.

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Paper provided by Tor Vergata University, CEIS in its series CEIS Research Paper with number 168.

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Length: 27 pages
Date of creation: 03 Jun 2010
Date of revision: 03 Jun 2010
Handle: RePEc:rtv:ceisrp:168
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  1. John Fitzgerald & Peter Gottschalk & Robert Moffitt, 1998. "An Analysis of Sample Attrition in Panel Data: The Michigan Panel Study of income Dynamics," Economics Working Paper Archive 379, The Johns Hopkins University,Department of Economics.
  2. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
  3. Paul Contoyannis & Andrew M. Jones & Nigel Rice, 2004. "The dynamics of health in the British Household Panel Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(4), pages 473-503.
  4. Mark B. Stewart, 2004. "Semi-nonparametric estimation of extended ordered probit models," Stata Journal, StataCorp LP, vol. 4(1), pages 27-39, March.
  5. Giuseppe De Luca & Franco Peracchi, 2012. "Estimating Engel curves under unit and item nonresponse," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(7), pages 1076-1099, November.
  6. Chen, Songnian & Khan, Shakeeb, 2003. "Semiparametric Estimation Of A Heteroskedastic Sample Selection Model," Econometric Theory, Cambridge University Press, vol. 19(06), pages 1040-1064, December.
  7. Meng, Chun-Lo & Schmidt, Peter, 1985. "On the Cost of Partial Observability in the Bivariate Probit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 71-85, February.
  8. Coppejans, Mark & Gallant, A. Ronald, 2000. "Cross Validated SNP Density Estimates," Working Papers 00-10, Duke University, Department of Economics.
  9. Agar Brugiavini & Tullio Jappelli & Guglielmo Weber, 2002. "The Survey on Health, Aging and Wealth," CSEF Working Papers 86, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  10. Lee, Lung-fei, 1995. "Semiparametric maximum likelihood estimation of polychotomous and sequential choice models," Journal of Econometrics, Elsevier, vol. 65(2), pages 381-428, February.
  11. Stewart, Mark B., 2005. "A comparison of semiparametric estimators for the ordered response model," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 555-573, April.
  12. Cheti Nicoletti & Franco Peracchi, 2005. "Survey response and survey characteristics: microlevel evidence from the European Community Household Panel," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(4), pages 763-781.
  13. Giuseppe De Luca, 2008. "SNP and SML estimation of univariate and bivariate binary-choice models," Stata Journal, StataCorp LP, vol. 8(2), pages 190-220, June.
  14. Roger W. Klein & Robert P. Sherman, 2002. "Shift Restrictions and Semiparametric Estimation in Ordered Response Models," Econometrica, Econometric Society, vol. 70(2), pages 663-691, March.
  15. Coppejans, Mark, 2007. "On efficient estimation of the ordered response model," Journal of Econometrics, Elsevier, vol. 137(2), pages 577-614, April.
  16. Alfonso Miranda & Sophia Rabe-Hesketh, 2006. "Maximum likelihood estimation of endogenous switching and sample selection models for binary, ordinal, and count variables," Stata Journal, StataCorp LP, vol. 6(3), pages 285-308, September.
  17. Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
  18. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
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