GRADE: UNI: uestion l (28 points): Consider the following results for a wage reg

Question

GRADE: UNI: uestion l (28 points): Consider the following results for a wage regression where lwage is the natural log of average hourly earnings in US dollars, age is in years, female is a binary variable for gender, bachelor is one for someone with bachelor degree and zero otherwise, femxbac and femxage are self explanotary interaction variables Regression 1: le bachelor femxbac, r Linear regression Number of obs = 15316 F( 4,15311) = 861.64 Prob >E R-squared Root MSE = 0 . 0000 = 0.1852 = .50507 lwage I Std. Err [95% Conf. Interval] female | bachelor I femxbac I 0259277 2257049 3980052 1082764 cons 1.708492 0014453 010984 0114889 016584.4 0434411 17.94 0.000 20.55 0.000 34.64 0.000 6.53 0.000 39.33 0.000 0230947 2472348 3754857 075769:1 1.623342 0287606 2041749 4205248 1407838 1.793642 Regression 2: reg lwage female age bachelor femxage, r Linear reqression Number of obs = 15316 F( 4, 15311) - Prob F R-squared Root MSE 840.78 = 0.0000 = 0 . 1848 5052 Robust Std. Err. Lwage Coef [95% Conf. Interval] 3.86 0. 000 16.86 0. 000 53.32 0.000 5.93 0.000 cons 1.481794 .0583113 25.41 0.000 . 331927 .032957 4437149 .0171776 .0859364 0019547 0083212 002895 1634814 0291256 4274044 0228521 1.367497 .5003726 .0367884 . 4600254 0115032 1.596092 bachelor | femxage 2

Explanation / Answer

Here, the variable female will take on the value 1 if the person is a female and it will take on the value 0 if the person is a male. So, the coefficient of the variable ‘female’ in the regression explains the difference in the logarithmic values of wage difference between a female and a male.

That is, we can write,

E [(lwage / female = 1) – (lwage / female = 0)] = - 0.2257049

Similarly, the variable ‘bachelor’ takes on the value 1 if the person possesses a bachelor’s degree and 0 if not. So, it shows the difference between the logarithmic values between a bachelor degree holder and a novice.

So, we can write,

E [(lwage / bachelor = 1) – (lwage / bachelor = 0)] = 0.3980052.

Also the variable ‘femxbac’ explains the combine effect of both the variables ‘female’ and ‘bachelor’; that is, the difference in logarithmic values of wage if female = 1 or 0 and bachelor = 1 or 0.

So, we can write,

E [ {(lwage / female = 1, bachelor = 1) – (lwage / female = 1, bachelor = 0)} – {( lwage / female = 0, bachelor = 1) – ( lwage / female = 0, bachelor = 0)} ] = 0.1082764                 …(i)

From the above expected difference we can write as follows—

E [( lwage / female = 1, bachelor = 1) – ( lwage / female = 0, bachelor = 1)] – E [( lwage / female = 1, bachelor = 0) – ( lwage / female = 0, bachelor = 0)] = 0.1082764                    …(ii)

This means, it is a two variable analysis, where we need to find the following—

E [(lwage / female = 1, bachelor = 1) – (lwage / female = 0, bachelor = 1)]

So, from equation (ii), we can write,

E [(lwage / female = 1, bachelor = 1) – (lwage / female = 0, bachelor = 1)] = 0.1082764 + E [( lwage / female = 1, bachelor = 0) – ( lwage / female = 0, bachelor = 0)]

We cannot know the exact value as the separate values are not given here.

E [{(lwage / female = 1, bachelor = 1) – (lwage / female = 1, bachelor = 0)}] – E [{( lwage / female = 0, bachelor = 1) – ( lwage / female = 0, bachelor = 0)}] = 0.1082764

Here also we cannot get the exact value as the separate values, that means, the difference in the log wage of male participants with and without bachelor degrees is not given.

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