Interval censored regression with fixed effects

Abstract

This paper considers identification and estimation of a fixed-effects model with an interval-censored dependent variable. In each time period, the researcher observes the interval (with known endpoints) in which the dependent variable lies but not the value of the dependent variable itself. Two versions of the model are considered: a parametric model with logistic errors and a semiparametric model with errors having an unspecified distribution. In both cases, the error disturbances can be heteroskedastic over cross-sectional units as long as they are stationary within a cross-sectional unit; the semiparametric model also allows for serial correlation of the error disturbances. A conditional-logit-type composite likelihood estimator is proposed for the logistic fixed-effects model, and a composite maximum-score-type estimator is proposed for the semiparametric model. In general, the scale of the coefficient parameters is identified by these estimators, meaning that the causal effects of interest are estimated directly in cases where the latent dependent variable is of primary interest (e.g., pure data-coding situations). Monte Carlo simulations and an empirical application to birthweight outcomes illustrate the performance of the parametric estimator.

FIGURE 1

Efficiency of $\widehat{\beta }$ as a function of ${\beta }_0$

FIGURE 2

Histogram of birthweights (in grams)