Censored and Truncated Data

Both censored and truncated data involve a lack of information about a random variable and occur in the context of quantitative analysis of data, when one is using that variable either to estimate a population mean (or other population parameters) or as the dependent variable in a regression analysis. The key distinction between them is whether one has information about missing values. With censored data, one observes some information about the missing data, either in the form of a range of values that they might fall into or in the form of the knowledge that they are missing. With truncated data, one has no information about the existence or value of missing observations. The difference in the structure of information for two types of data determines how one approaches censored or truncated data, whether in the context of a single random variable or as a dependent variable in a regression analysis. This entry discusses the consequences of this kind of missing data for regression analysis and sample selection.

Concerns about censoring and truncation abound in empirical analysis. They can occur either through the structure of data-gathering efforts or through legal requirements. Historically, researchers relied on assumptions about the distribution of the variable to adjust the estimates to account for truncation or censoring. These concerns are just as important when censored or truncated variables [Page 211]are the dependent variables in regression analyses. Scholars have long worried about the consequences of processes such as self-selection for the validity of their regression results, since they often result in biased and inconsistent coefficient estimates. While estimators to correct for censoring and truncation have been around for more than 3 decades, researchers have worried about their sensitivity to distributional assumptions and model specification. While recent work attempts to relax some of these critical assumptions and diagnose sensitivity issues, researchers have also extended previous work by designing estimators for a greater variety of data.