Chapter 18: Omitted Variable Bias
In this chapter we discuss the consequences of not including an independent variable that actually does belong in the model. We revisit our discussion in Chapter 13 about the role of the error term in the classical econometric model. There we argue that the error term typically accounts for, among other things, the influence of omitted variables on the dependent variable. The term omitted variable refers to any variable not included as an independent variable in the regression that might influence the dependent variable. In Chapter 13 we point out that, so long as the omitted variables are uncorrelated with the included independent variables, OLS regression will produce unbiased estimates. In this chapter we focus on the issue of omitted variables and highlight the very real danger that omitted variables are in fact correlated with the included independent variables.When that happens, OLS regression generally produces biased and inconsistent estimates, which accounts for the name omitted variable bias.
The chapter begins, in the next section, by emphasizing the importance of the issue of omitted variable bias and tying the problem directly to the fact that economists generally have data from an observational study rather than a controlled experiment. We then split the work into three parts.
First, Section 18.3 uses cooked data from the skiing example to develop an
intuitive understanding of omitted variable bias. Next, in Section 18.4 we
work with real data. In this case, the true parameter values are unknown.
By seeing how parameter estimates change when additional X variables are included
in the regression, however, we will be able to detect strong evidence of omitted
variable bias. The fixed X’s assumption of the classical econometric
model is hard to reconcile with a view of omitted X’s that vary from
one sample to the next. Therefore, in Section 18.5 we consider a new data
generation process, the random X’s model, which does away with the assumption
of fixed X’s in favor of random X’s. This new DGP is used to investigate
omitted variable bias in samples of varying sizes from a given population.
We show that the bias stays constant as the sample size increases.