) You have obtained a sample of 14,925 individuals from the Current Population S
ID: 3050760 • Letter: #
Question
) You have obtained a sample of 14,925 individuals from the Current Population Survey (CPS) and are interested in the relationship between average hourly earnings and years of education. The regression yields the following result: ˆ ahe= -4.58 + 1.71×educ , R2 = 0.182, SER = 9.30
where ahe and educ are measured in dollars and years respectively.
a. Interpret the coefficients and the regression R2.
b. Is the effect of education on earnings large?
c. Why should education matter in the determination of earnings? Do the results suggest that there is a guarantee for average hourly earnings to rise for everyone as they receive an additional year of education? Do you think that the relationship between education and average hourly earnings is linear?
d. The average years of education in this sample is 13.5 years. What is mean of average hourly earnings in the sample?
e. Interpret the measure SER. What is its unit of measurement.
Explanation / Answer
(a)
A person with one more year of education increases her earnings by $1.71. There is no meaning attached to the intercept, it just determines the height of the regression. The model explains 5 percent of the variation in average
hourly earnings.
(b)
The difference between a high school graduate and a college graduate is four years of education. Hence a
college graduate will earn almost $7 more per hour, on average ($6.84 to be precise). If you assume that there are 2,000 working hours per year, then the average salary difference would be close to $14,000 (actually $13,680).
Depending on how much you have spent for an additional year of education and how much income you have forgone, this does not seem particularly large.
(c)
In general, you would expect to find a positive relationship between years of education and average hourly
earnings. Education is considered investment in human capital. If this were not the case, then it would be a
puzzle as to why there are students in the econometrics course — surely they are not there to just "find
themselves" (which would be quite expensive in most cases). However, if you consider education as an
investment and you wanted to see a return on it, then the relationship will most likely not be linear. For example, a constant percent return would imply an exponential relationship whereby the additional year of education
would bring a larger increase in average hourly earnings at higher levels of education. The results do not suggest that there is a guarantee for earnings to rise for everyone as they become more educated since the regression R2 does not equal 1. Instead the result holds "on average."
(d)
Since BetaSharpHat0 = Yhat - BetaSharpHat1X > Yhat = BetaSharpHat0 + BetaSharpHat1X Substituting the estimates for the slope and the intercept then results in a
mean of average hourly earnings of roughly $18.50
(e)
The typical prediction error is $9.30. Since the measure is related to the deviation of the actual and fitted
values, the unit of measurement must be the same as that of the dependent variable, which is in dollars here.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.