An alternative approach for introducing instrumental variables based on ordinary least squares omitted variable bias

Abstract

An alternative approach for introducing instrumental variables in econometrics courses is presented in this article. The method is based on the ordinary least squares omitted variable bias formula. The intuition for the approach capitalizes on students’ understanding and intuition of omitted variables. Thus, if students understand omitted variable bias, they can understand instrumental variables. Furthermore, using omitted variable bias to derive the instrumental variables estimator clearly highlights the critical assumptions of instrumental variables. The author illustrates the proposed method mathematically and discusses the intuition in both simple and multiple regression cases.

Keywords:

• Econometrics
• instrumental variables
• omitted variable bias

JEL Codes:

• A2
• C26

Notes

1 An alternative example is Hill, Griffiths, and Lim (2018), who introduce IV using the solution to the sample moment conditions $\frac{1 }{n}{\sum }_{i=1}^n\left(y_i-{\beta }_0-{\beta }_1{x}_i\right)=0$ and $\frac{1}{n}{\sum }_{i=1}^n{z}_i\left(y_i-{\beta }_0-{\beta }_1{x}_i\right)=0$.

2 Keefer (2021) discusses the estimator as a method for transforming a measured classical confounding variable into a valid instrument. The estimator is shown to perform well, compared to OLS, in simulations, but it is particularly sensitive to weak instruments.