Exogenous Sample Selection and Self-Selection Bias in Regression Models

Exogenous Sample Selection and Self-Selection Bias in Regression Models

This article examines the potential biases that can arise from non-random samples in regression analysis, focusing on two specific scenarios:

1. Crime Reporting on College Campuses

Consider a model relating the annual number of crimes on college campuses ('crime') to student enrollment ('enroll'):

log('crime') = B0 + B1 * log('enroll') + E

This is a constant elasticity model where B1 represents the elasticity of crime with respect to enrollment. Imagine we estimate this model using a sample of colleges. However, this sample is not randomly selected from all colleges in the United States because many schools in 1992 did not report campus crimes. Can we consider this non-reporting as exogenous sample selection?

The answer is no. Exogenous sample selection requires a selection process that's independent of the variables in the model. Here, the failure to report crimes might be linked to the level of crime itself, the campus size, or student socioeconomic status – all factors potentially correlated with the 'crime' variable. Consequently, the sample might not represent all US colleges, leading to biased estimates.

2. PC Ownership and College GPA

Let's consider a model to estimate the impact of personal computer (PC) ownership on college grade point average (GPA):

GPA = B0 + B1 * ('PC') + E

Suppose we estimate this model using a sample of college students who voluntarily participated in a survey about their PC ownership and GPA. Can we assume this sample is randomly selected from the entire college student population?

The answer is again no. Self-selection bias arises when individuals choose to participate in a study based on their characteristics, which are related to the outcome variable. In this case, students opting into the survey might be more likely to own PCs and have higher GPAs than those who don't participate. This non-random selection makes the sample unrepresentative of all college students, potentially leading to biased model estimates.

Conclusion

These examples highlight the importance of understanding potential biases arising from non-random sampling in regression analysis. Exogenous sample selection and self-selection bias can significantly affect the reliability and accuracy of model results. Researchers must carefully consider the potential for such biases and employ appropriate techniques to address them if present.