Question

You have been given data on wages (Yi) for the population who are enrolled in a degree program, you also have data that tells you whether each individual has a bachelor degree (Di) (ie the population is made up of college drop outs and college graduates). You regress wages (measured in dollars per hour) on the education (BA degree) dummy variable and get the following population regression function log(Yi)=1.06 +0.52D.

1. Consider the model as a descriptive model, interpret the estimated slop coefficient in this context.
2. Suppouse there was a national test conducted yesterday. Blake got information about test scores for each individual (x₂). He added the test score as a control variable and he got these results log(Yi)=0.80+0.45D+0.04x_2. What can you tell about the causal effect of obtaining a BA degree?

Answer 1

A. The estimated slope coeffieicent is 0.52. This means that if an individual has a BA degree (D=1), the logarithm of the hourly wage in dollars increases by 0.52 compared to an individual who has no BA degree, (D=0).

B. In the revised model, if an individual has a BA degree (D=1), the logarithm of the hourly wage in dollars increases by 0.45 compared to an individual who has no BA degree, (D=0). The causal effect of obtaining a BA degree reduces, in presence of the additional variable test score (x2).