8. The table below (taken from table 2.3 in Mastering Metrics) reports estimates

Question

8. The table below (taken from table 2.3 in Mastering Metrics) reports estimates of the effect of attending a private college or university on log earnings (earnings logged). Each column shows coefficients from a regression of log earning on a dummy for attending a private institution and controls (if applicable) ran on 14,238 individuals who attended college. Standard errors are reported in parentheses below the coefficient. The effect of private school on No Selection Controls Selection Controls Private school 0.212 0.034 0.031 0.152 (0.060) (0.057) (0.062) (0.062) 0.051 (0.008) Own SAT ÷ 100 0.036 (0.006) Average SAT score of schools applied ÷100 0.082 (0.024) (0.022) 0.110 0.071 0.062 (0.013) (0.011) Sent 2 applications Sent 3 applications 0.093 0.079 (0.021) (0.019) Sent 4 plus applications 0.139 024 0.127 023 Can this Interpret coefficient on Private School estimated in column (1). estimate be interpreted as a causal effect? Explain why or why not. a) What happens to the coefficient on Private school when Own SAT score divided by 100 is controlled for in the model (Column (2)) b) c) In columns (3) and (4), selection controls are added to the models (Average SAT score of schools applied to, and dummies for the number of schools applied to). Why are these controls particularly important to add to the model? d) What do columns (3) and (4) suggest about the effect of attending private school on earnings? (Hint: Are the coefficients statistically significant at the 5%7)

Explanation / Answer

a)

The increase of one unit of Private School will led to increase in 0.212 of logged earnings.

We see that after including other variables in the model, the coefficient of variable Private school decreases and also not significant (no significant effect on logged earnings in Col (3) and (4)). So, this estimate cannot be interpreted as a causal effect.

b)

The coefficient on Private school is reduced to 0.152.

Critical values of t at 5% signinficance level and df = n - 2 = 14238-2 = 14236 is 1.96

Test statistic for coefficient on Private school = Coefficient / SE = 0.152 / 0.057 = 2.67

Test statistic for coefficient on Own SAT = Coefficient / SE = 0.051 / 0.008 = 6.375

As, both test statistics are greater than critical value (1.96), both variables Private school and Own SAT are significant.

So, the coefficient on Private school is reduced from 0.212 to 0.152 but still Private school is significant variable in the model.

c.

Better Average SAT scores may led to better logged earnings.

Multiple applications sent led to better chances of attending Private schools and hence better logged earnings.

As, we can think that Average SAT scores and Multiple applications sent may affect the logged earnings, they have been included in the model.

d)

For Col (3),

Critical values of t at 5% signinficance level and df = n - 2 = 14238-2 = 14236 is 1.96

Test statistic for coefficient on Private school = Coefficient / SE = 0.034 / 0.062 = 0.548

As, the test statistics are less than critical value (1.96), the coefficient of variable Private school is not significant and hence it has no significant effect on logged earnings.

For Col (4),

Test statistic for coefficient on Private school = Coefficient / SE = 0.031 / 0.062 = 0.5

As, the test statistics are less than critical value (1.96), the coefficient of variable Private school is not significant and hence it has no significant effect on logged earnings.

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