Semiparametric binary regression models under shape constraints with an application to Indian schooling data
We consider estimation of the regression function in a semiparametric binary regression model defined through an appropriate link function (with emphasis on the logistic link) using likelihood-ratio based inversion. The dichotomous response variable [Delta] is influenced by a set of covariates that can be partitioned as (X,Z) where Z (real valued) is the covariate of primary interest and X (vector valued) denotes a set of control variables. For any fixed X, the conditional probability of the event of interest ([Delta]=1) is assumed to be a non-decreasing function of Z. The effect of the control variables is captured by a regression parameter [beta]. We show that the baseline conditional probability function (corresponding to X=0) can be estimated by isotonic regression procedures and develop a likelihood ratio based method for constructing asymptotic confidence intervals for the conditional probability function (the regression function) that avoids the need to estimate nuisance parameters. Interestingly enough, the calibration of the likelihood ratio based confidence sets for the regression function no longer involves the usual [chi]2 quantiles, but those of the distribution of a new random variable that can be characterized as a functional of convex minorants of Brownian motion with quadratic drift. Confidence sets for the regression parameter [beta] can however be constructed using asymptotically [chi]2 likelihood ratio statistics. The finite sample performance of the methods are assessed via a simulation study. The techniques of the paper are applied to data sets on primary school attendance among children belonging to different socio-economic groups in rural India.
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- P. Groeneboom & G. Jongbloed, 2003. "Density estimation in the uniform deconvolution model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 136-157.
- Handa, Sudhanshu, 2002. "Raising primary school enrolment in developing countries: The relative importance of supply and demand," Journal of Development Economics, Elsevier, vol. 69(1), pages 103-128, October.
- Magnac, Thierry & Maurin, Eric, 2003.
"Identification and Information in Monotone Binary Models,"
IDEI Working Papers
180, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2004.
- Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
- Thierry Magnac & Eric Maurin, 2007. "Identification and Information in Monotone Binary Models," Post-Print halshs-00754218, HAL.
- Thierry Magnac & Eric Maurin, 2008.
"Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data,"
- Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 835-864.
- Thierry Magnac & Eric Maurin, 2004. "Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data," Working Papers 2004-11, Centre de Recherche en Economie et Statistique.
- Magnac, Thierry & Maurin, Eric, 2004. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," IDEI Working Papers 280, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jan 2005.
- Jean Drèze & Geeta Gandhi Kingdon, 2001.
"School Participation in Rural India,"
Review of Development Economics,
Wiley Blackwell, vol. 5(1), pages 1-24, 02.
- Jean Dreze & Geeta Gandhi Kingdon, 1999. "School Participation in Rural India," Working papers 69, Centre for Development Economics, Delhi School of Economics.
- Jean Drèze & Geeta Gandhi Kingdon, 1999. "School Participation in Rural India," STICERD - Development Economics Papers - From 2008 this series has been superseded by Economic Organisation and Public Policy Discussion Papers 18, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Jean Dreze & Geeta Gandhi Kingdon, 1999. "School participation in rural India," LSE Research Online Documents on Economics 6666, London School of Economics and Political Science, LSE Library.
- Banerjee Moulinath & Wellner Jon A., 2005. "Score Statistics for Current Status Data: Comparisons with Likelihood Ratio and Wald Statistics," The International Journal of Biostatistics, De Gruyter, vol. 1(1), pages 1-29, August.
- Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
- Lavy, Victor, 1996. "School supply constraints and children's educational outcomes in rural Ghana," Journal of Development Economics, Elsevier, vol. 51(2), pages 291-314, December.
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