Partially Adaptive Estimation of Interval Censored Regression Models

Several valuable data sources, including the census and National Longitudinal Survey of Youth, include data measured using interval responses. Many empirical studies attempt estimation by assuming the data correspond to the interval midpoints and then use OLS or maximum likelihood assuming normality. Stata performs maximum likelihood estimates (MLE) under the assumption of normality, allowing for intra-group variation. In the presence of heteroskedasticity or distributional misspecification, these estimates are inconsistent. In this paper we focus on an estimation procedure that helps prevent distributional misspecification for interval censored data. We explore the application of partially adaptive estimation, which builds on the MLE framework with families of flexible parametric probability density functions which include the normal as a limiting case. These methods are used to estimate determinants associated with household expenditures based on US Census data. Monte Carlo Simulations are performed to compare the relative efficiency of the different methods of estimation. We find that the flexible nature of our proposed partially adaptive estimation technique significantly reduces estimator bias and improves efficiency in the presence of distributional misspecification.