Any help will be appreicated! thank you! Question 4: We are often interested in

Question

Any help will be appreicated! thank you!

Question 4: We are often interested in the effect of education on earnings. So you estimate the fol- lowing regression equation where earnings are monthly earnings and education denotes an individual's total years of education log( earnings) 8.2 + 0.04educationi Part (a): Interpret the coefficient on education (i.e., interpret B1) Your friend says that your model is misspecified because it is not really the years of education that matter, but rather the education credentials that vou receive that matter. You therefore split your education variable into four categories, using an indicator (or dummy variable for each which are indicated in the brackets: (i) high school dropout (dropout), (ii) high school graduate (hsgrad), (iii) college graduate (college), (iv) master's or phd graduate masters). You then estimate the following relationship: log(earnings) = 6.4-0.03dropout, + 0.1 2college, + 0.16masters (0.02) (0.04) Part (b): Why did you omit the dummy variable for high school graduate (hsgrad) from Part (c): Interpret the coefficient on college Part (d): According to the above relationship, what is the expected increase in earnings your regression? that you, a college graduate, would get by doing your master's degree?

Explanation / Answer

Part (a):   The given regression shows the relation between earnings of an individual with the same individual's total years of education. The given relation is logarithmic in nature. First it can be concluded that that is a constant value in the equation (8.2), which shows a basic earnings of an individual, but than a positive addition of earnings, which being with a positive coefficient, progressively adds to the earnings of an individual with his education. The given logarithmic relation also expresses that although the relation with education is incremental, but, with higher the education goes it starts saturating.

Part(b): In the second regression the dummy variable is dropped. Reason is clear from the observation is that the coefficient of dropouot is negative i.e the constant chosen or the standardised constant (6.4) is standardised for a high school graduate. That means if an individual is high school graduate the relation is taken as constant (6.4). But, if an individual is high school dropout then it has a negative relationn i.e. decrement in the earnings.

Part (c): The coefficient of college is positive that is opposite to the high school dropout i.e. if an individual goes for higher education(college) it further adds to the high school graduate's earnings. If we talk about the abstract value of constant, then we found that the coeffient(0.12) is greater than the coefficient used for education in first equation (0.04). Thus differentiating between simple years of education and years of education in college. And the higher the coefficient the Higher the importance (greater addition to earnings).

Part (d): First of all, as the coefficient for master's education is positive and highest among all other coefficient, means the addition to earnings are highest with the master's degree.

And to further calculate the increase in the earnings, one should first of all know the base of the given logarithmic equation (It is log with base 2, 10, e or any other). Than number of years are to put, Then it will become a simple log value can easily be found, using log table etc.

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