We derive tests for the presence of bias from using censored regressors in linear regression analysis. The test follows from the principles of (Hausman) specification tests, and is applicable in situations of exogenous censoring. We apply the test in two substantive empirical applications; the estimation of the effects of financial wealth on household consumption, and the estimation of the impact of foreign denominated debt on firm investment decisions. In each application we find strong rejection of the absence of censoring bias.
We study issues that arise for estimation of a linear model when a regressor is censored. We discuss the efficiency losses from dropping censored observations, and illustrate the losses for bound censoring. We show that the common practice of introducing a dummy variable to `correct for' censoring does not correct bias or improve estimation. We show how censored observations generally have zero semiparametric information, and we discuss implications for estimation. We derive the likelihood function for a parametric model of mixed bound-independent censoring, and apply that model to the estimation of wealth effects on consumption.
We study the bias that arises from using censored regressors in estimation of linear models. We present results on bias in OLS regression estimators with exogenous censoring,
and IV estimators when the censored regressor is endogenous. Bound censoring such as top-and bottom-coding result in expansion bias, or effects that are too large. Independent
random censoring results in bias that varies with the estimation method; attenuation bias in OLS estimators and expansion bias in IV estimators. We note how large biases can
result when there are several regressors, and how that problem is particularly severe when a 0-1 variable is used in place of a continuous regressor.
The above papers update and replace the following two unpublished working papers
We give semiparametric identification and estimation results for econometric models with a regressor that is endogenous, bound censored and selected, called a Tobin regressor. We show how parameter sets are identified, and give generic estimation results as well as results on the construction of confidence sets for inference. The specific procedure uses quantile regression to address censoring, and a control function approach for estimation of the final model. Our procedure is applied to the estimation of the effects on household consumption of changes in housing wealth. Our estimates fall in plausible ranges, significantly above low OLS estimates and high IV estimates that do not account for the Tobin regressor structure.
This chapter covers recent solutions to aggregation problems in three application areas, consumer demand analysis, consumption growth and wealth, and labor participation and wages. Each area involves treatment of heterogeneity and nonlinearity at the individual level. Three types of heterogeneity are highlighted: heterogeneity in individual tastes, heterogeneity in income and wealth risks and heterogeneity in market participation. Work in each area is illustrated using results from empirical data. The overall aim is to present specific models that connect individual behavior with aggregate statistics, as well as discuss the principles for constructing such models.
These introductory lectures on semiparametric methods in econometrics are long overdue for a thorough rewrite and updating. The printed lectures have become hard-to-find, and are posted here in case students find them useful. If you have any comments relevant to updating the lectures, please email them to me at email@example.com, and accept my thanks in advance.