# Interpreting Labour Economics regression model

Instrumental variables (2SLS) regression
Number of obs = 603

F( 5, 597) = 41.96

Prob > F = 0.0000

R-squared = 0.1386

Root MSE = .26523

         |
logwage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

higher |   .2566441   .1030163     2.49   0.013     .0543257    .4589625
age |  -.0054228   .0055142    -0.98   0.326    -.0162524    .0054068
age2 |   .0000223   .0000675     0.33   0.741    -.0001103    .0001549
urban    |   .2587201   .0304102     8.51   0.000     .1989962    .3184441
rural |  -.0207374   .0296745    -0.70   0.485    -.0790164    .0375417
_cons |   2.370127   .1065349    22.25   0.000     2.160899    2.579356


Instrumented: higher

## Instruments: age age2 metropolitan rural father_educated

I am doing an assignment titled does expansion of higher education improve the earnings? The case of Russia

Regression has been run as shown above, the regression model is based on the widely used Mincer Model with minor modification and proxy to it.

Can anyone of you who are kind enough to assist in term of what do you think of the model and its output? And how would you interpret the output?

• You might want to use the robust option to calculate heteroscedasticity robust standard errors. People with little schooling tend to have less variance in their earnings than those with lots of education, so the error variance is not going to be constant. Also the rural dummy can be problematic because the choice of living in cities is potentially endogenous.
– Andy
Apr 22, 2014 at 9:21

I suppose that higher stands for years of schooling. If this is the case, what you are doing is correcting for the endogeneity problem likely to affect the variable higher. That is, a variable is said to be endogenous when it is likely to be correlated with unobserved factors in the error term. Therefore you are instrumenting it by doing a 2 stages estimation. That is, your Stata command implicitly did the following:

1) It regressed higher on all the exogenous regressors plus the instrument father_education. That is, you assume that having more years of schooling depends on the education of father's. By doing this, you clean your endogenous variable of the endogeneity problem.

2) It runs your original regression using the instrumented (fitted values of the) variable higher as regressor, in place of the original one.

By doing this, the coefficient on higher is now a consistent estimator of the true parameter. The interpretation of the results must account for the fact your dependent variable is in logs, while higher is not. Therefore, a year more of schooling increases (on average) the wage by exp(.2566441)= 1.292585 = 29% and this effect is statistically significant, since p-value<0.05.

Note that this is true as long (1) there is a statistically significant relationship between higher and father_educ (you can test this by verifying that the coefficient on father_educ in the first stage is statistically significant (and positive)), (2) the instrument father_educ is not correlated with the error term.

• I don't think your interpretation of the coefficients is correct. The Mincer equation is a log-linear model, so the coefficients are semi-elasticities but you are calculating elasticities by exponentiating them. So in this case a schooling coefficient of .2566 translates into approximately 25.66% higher earnings for an additional year of education.
– Andy
Apr 22, 2014 at 9:17
• Whops. I made a mistake in the writing, still for the percentage change I have to take the exp(), since the dependent variable is in logs, the independent is not. exp(.2566441)= 1.292585 = 29% increase
– Bob
Apr 22, 2014 at 9:24
• Exactly. Also my quick approximation by multiplying the coefficient with 100 was poor because this only holds roughly for $\beta < |0.1|$
– Andy
Apr 22, 2014 at 9:54
• However, I think that your reasoning was not completely wrong. Indeed, a log variation, i.e. a log difference, is an approximation of a percentage change. Therefore, 0.2566 translates in a % change of the dependent variable due to a UNITARY change in the independent variable X. The exp() transformation should change the interpretation in a percentage change in y due to a PERCENTAGE change in X. Am I right ?
– Bob
Apr 22, 2014 at 9:57
• Hi all, thanks for your guidance and advice. Yes, I did run robustness test for that. Thanks for your reminder. May I know why would it be the case where age which is supposedly to be positive is now negative while age2 is now positive and is totally the opposite of what it normally was. What can we infer from there then? Any thought?
– Lee
Apr 22, 2014 at 13:28