All entries for Friday 02 November 2007

November 02, 2007

ec902– Should we get married?

The last bit of excercise sheet 2, which we could not cover in some classes, asked you to estimate this model.

$ln%28w%29%3D%5Calpha%7E%2B%7E%5Cbeta_1%7Eln%28%5Cexp%29%7E%2B%7E%5Cbeta_2%7EFemale%7E%2B%7E%5Cbeta_3%7EMarried%7E%2B%7E%5Cbeta_4%7E%28Married*Female%29%7E%2B%7E%5Cvarepsilon%3CBR%3E$

Note that  $%26nbsp%3BMarried*Female%3D1%7E$if and only if the individual is BOTH female AND married.

How do we interpret $%7E%5Cbeta_4%7E$?

Well, we know that, ignoring whether a person is married or not, the effect of being female is the coefficient on the female binary variable, that is $%7E%5Cbeta_2%7E$. But if that person is also married then overall effect of being female becomes $%7E%5Cbeta_2%7E%2B%7E%5Cbeta_4%7E$.

Therefore, the ln(w) of a female differs by $%7E%5Cbeta_2%7E$from that of a man and the difference becomes $%7E%5Cbeta_2%7E%2B%7E%5Cbeta_4%7E$if the female is also married.

Therefore $%7E%5Cbeta_4%7E$measures the additional effect of being married for a female. In other words, it measures whether the gender wage differential changes depending on whether the female is married or not.

Clearly, you can also interpret this focusing on the $%26nbsp%3BMarried%7E$variable. In that case, the interpretation becomes: $%7E%5Cbeta_4%7E$measures the additional effect of being female for a married person. In other words, it measures whether the "marriage wage differential" changes depending on whether the married person is female or not.

Because our dependent variable is ln(w), the coefficient on these dummies can all be interpreted as approximate percentage changes. So, for example, suppose that we find that $%7E%5Cbeta_2%7E$, the coefficient on Female, is $%26nbsp%3B-0.07%7E$. That means that females on average earn approximately 7% $%28%3D%7E%5Cbeta_2%7E*%7E100%29%7E$less than males.

Note: because BOTH the experience variable and the dependent variable are in logs, the coefficient $%7E%5Cbeta_1%7E$on ln(exp) is an elasticity as we showed in the class. Therefore the interpretation is that when experience changes by 1%, the wage (our dependent variable) changes by $%7E%5Cbeta_1%7E%25%7E$. No need to transform the coefficient in this case.

November 2007

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