Semiparametric binary regression models under shape constraints with an application to Indian schooling data

Abstract

a r t i c l e i n f oArticle history: Available online xxxx JEL classification: C1 Keywords:Convex minorants Likelihood ratio statistic School attendance Semiparametric binary regression a b s t r a c tWe 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 ∆ 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 (∆ = 1) is assumed to be a non-decreasing function of Z . The effect of the control variables is captured by a regression parameter β. 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 χ 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 β can however be constructed using asymptotically χ 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.

Nonparametric and Semiparametric Analysis of Current Status Data Subject to Outcome Misclassification

“…This model is part of a bigger family of semiparametric binary regression models under shape constraints studied by Banerjee, D., and Mishra (2009). Applying those results, the regression coefficient has $\sqrt{n}$ rate of convergence and the likelihood ratio statistic may be used to compute confidence intervals for the regression coefficients.…”

Distribution-free tests of stochastic monotonicity

“…Monotonicity is also an 0304-4076/$ -see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jeconom.2012.02.005 important identification assumption in many nonparametric and semiparametric settings, see Matzkin (1994) for a survey and Aguirregabiria (2010), Banerjee et al (2009), Lewbel and Linton (2007), and Tanaka (2008) for some recent applications. The monotonicity of the intergenerational transition function is also worth testing in the analysis of intergenerational mobility; i.e.…”

An adaptive test of stochastic monotonicity

“…Kasy (2014), Hoderlein, Holzmann, Kasy, and Meister (2016), Chetverikov and Wilhelm (2017), Wilhelm (2017)) and for testing identifying assumptions (e.g. Matzkin (1994), Lewbel and Linton (2007), Banerjee, Mukherjee, and Mishra (2009)). …”