Discussion W6

Source: https://www.jstor.org/stable/2937954

1.

The research question that the authors are interested in estimating is the causal effect of schooling on earnings. They want to know specifically how an additional year of education impacts wages while also addressing the potential bias caused by unobserved factors.

2.

\[ earnings_i = \beta_0 + \beta_1 \cdot schooling_i + e_i \]

Where:

• earnings = weekly or annual earnings
• schooling = years of completed schooling
• e_i = error term

3.

Running the above naive OLS specification may cause bias because schooling may be endogenous. It could be correlated with other factors in e_i. This leads to bias and possibly reverse causality if higher expected earnings influence educational choices.

4.

1.

First Stage:

\[Schooling_i = \pi_0 + \pi_1 QOB_i + v_i\]

Where QOB is a set of quarter of birth indicators and v_i is the first stage error term.

Second Stage:

\[Earnings_i = \beta_0 + \beta_1 \widehat{Schooling}_i + \varepsilon_i\]

Where schooling_i are the predicted years of schooling from the first stage.

Why Relevant?
Quarter of birth affects the age at which students can legally drop out, making some stay in school longer. This creates variation in schooling unrelated to individual choices.

Why Exogenous?
Quarter of birth is essentially random and unlikely to affect earnings except through its effect on schooling.

2.

An example of when exogenetity could be potentially violated is if quarter of birth is related other factors that affect earnings.