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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Jean Dreze & Geeta Gandhi Kingdon, 1999. "School Participation in Rural India," Working papers 69, Centre for Development Economics, Delhi School of Economics.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:149:y:2009:i:2:p:101-117. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.