Section 11 Sample Selection Models

This section will provide a brief overview of models designed to address issues where we do not observe our full outcome data, or the outcome is censored or truncated in some way. In each of these cases, if we only use the standard methods discussed so far in the course, we may end up with biased estimates.

Here is a brief video overview.

Sample	Y	X	Example
Censored	y is known exactly only if some criterion defined in terms of y is met.	x variables are observed for the entire sample, regardless of whether y is observed exactly	If income is measured exactly only if above the poverty line. All other incomes are reported at the poverty line.
Sample Selected	y is observed only if a criteria defined in terms of some other random variable (Z) is met.	the determinants of whether Z =1 are observed for the entire sample, regardless of whether y is observed or not	Survey data with item or unit non-response
Truncated	y is known only if some criterion defined in terms of y is met	x variables are observed only if y is observed	Donations to political campaigns

Here are supplemental resources

• King, Gary. 1998. Unifying political methodology: The likelihood theory of statistical inference. University of Michigan Press. Chapters: 9. Available online through Rutgers libraries.
• Fox, John. Applied Regression and Generalized Linear Models. Excerpts from Chapter 20 (see Canvas)
• The documentation for the sampleSelection package in R is here