2206_Problem_Set_1

.pdf

School

University of New South Wales *

*We aren’t endorsed by this school

Course

2206

Subject

Economics

Date

Apr 3, 2024

Type

pdf

Pages

5

Uploaded by BarristerThunderMonkey13 on coursehero.com

2206 PROBLEM SET 1 LILY EDWARDS BLASIKIEWICZ - Z5418961 TUTORIAL MONDAY 9:00 Note - I will be rounding all decimals to two decimal places for the final answer, but all computation will use the unrounded values given by STATA. Question 1 Given this output from regressing wage on education, we get the following model: \ Wage = 1 . 57 + 0 . 36 Educ, N = 1260 , R 2 = 0 . 0451 The estimated coefficient c α 1 = 0 . 36 implies that an extra year of education is associated with an increase in that individuals hourly wage by $ 0.36 dollars. Question 2 Using a log-linear model: Date : March 2024. 1
2 LILY EDWARDS BLASIKIEWICZ - Z5418961 TUTORIAL MONDAY 9:00 We predict this model for Wage: \ ln Wage = 0 . 90 + 0 . 06 Educ, N = 1260 , R 2 = 0 . 0708 The estimated coefficient c β 1 = 0 . 06 implies that an extra year of education is associated with an increase in that individuals hourly wage of 6%. Question 3 Linear regression models must be linear in the parameters, hence (a), (c), and (d) are not linear regressions models, whereas (b) is. Question 4 The Zero Conditional Mean assumption in mathematical terms essentially says that the expected value of the error term must have no reliance on any of the independent variables, i.e. E ( U | X i ) = 0. In less mathematical terms, there must be no confounding factors in the error term, else we don’t have an un- biased estimator. If we are to look at model (1), the ZCM assumption assumes that the error term U has no reliance on education. It’s quite easy to see why ZCM may not hold in this case due to the fact that the model explains so little, an example that would violate the ZCM, could be parental income, which has a great effect on the quality of education an individual might receive, as well as the years of study that individual is able to complete. If parental income is low, the child may be less capable of for university or being supported financially, and hence might enter the workforce after completing high school, rather than getting a university degree. This would violate ZCM due to parental income being omitted from the model, and education having some correlation with parental income. If ZCM doesn’t hold, then b ( α 1 ) would be influenced by the omitted variable and would hence be biased.
2206 PROBLEM SET 1 3 Question 5 a. Hence the predicted model is: \ ln Wage = 0 . 37 + 0 . 08 Educ + 0 . 22 Noncog, N = 1260 , R 2 = 0 . 2022 b. The estimated coefficient b γ 1 = 0 . 08 implies that an extra year of education is associated with an increase in that individuals hourly wage by 8%. The estimated coefficient b γ 2 = 0 . 22 implies that one extra non-cognitive skill is associated with an increase in that individuals hourly wage by 22%. c. Evidently considering model (2) has β 1 = 0 . 06 compared to model (3)’s b γ 1 = 0 . 08, shows that model (2) likely had omitted variables, it also shows that too little weight was given to education in the second model when compared to the third model. d. The bias for β 1 is negative, model (2) essentially tells us that education is less important as a factor of hourly wage when there are no other independent variables considered. When you consider non-cognitive skills as well, education matters more. If we average across people with a similar number of non-cognitive skills, education has a higher weight, but when averaging across all the different possible numbers of non-cognitive skills (what model (2) does by only considering education) education happens to matters less, implying a negative bias. We can also check this using the formula E ( ˆ β 1 ) ˆ γ 1 = ˆ γ 2 ˆ δ 1 , we know E ( ˆ β 1 ) ˆ γ 1 = 0 . 0602839 0 . 0758434 which is negative. e. Education and non-cognitive skills are negatively correlated, which we can see from the previous question and the relationship between bias and correlation. E ( ˆ β 1 ) ˆ γ 1 = ˆ γ 2 ˆ δ 1 = 0 . 0155595 = 0 . 2199816 · ˆ δ 1 and hence ˆ δ 1 ≈ − 0 . 07. Question 6 To check whether education is statistically significant at the 1% significance level. We first define the null and alternate hypotheses: H 0 : γ 1 = 0 , H 1 : γ 1 ̸ = 0
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help