# Mathematics Tutors

 Subject Mathematics Due By (Pacific Time) 11/12/2017 12:00 am

Consider the following wage equation:
lnwi = β0 + β1edui + β2expi + β3exp2i + β4femalei + εi (1)

Where lnwi is individual i’s log wage, edui measures individual i’s years of completed education, and expi measures individual i’s years of experience, and femalei is a dummy variable indicating whether individual i is a female. εi is an unobserved error term. The R2 = 0.283. You estimate regression (1) on a sample of male and female workers in the their 30s and living and working in the UK. The sample size is 453. You obtain the following estimates:

 Coefficient Estimate Standard error β0 0.0473 0.0112 β1 0.0818 0.0052 β2 0.0721 0.0074 β3 -0.00207 0.000293 β4 -0.155 0.0521

[5 marks] Interpret each of the OLS estimates.

[6 marks] Can you reject the hypothesis that education has a positive effect on wages?

[6 marks] Test the hypothesis that being female has a statistically significant effect on wages.

[6 marks] Can you reject the claim that the returns to experience are linear? Be explicit about the hypothesis that you need to test this question.

[5 marks] Calculate the ceteris paribus effect of 5 extra years of schooling on wages.
[9 marks] Interpret the R2 of the regression and test the overall significance of the model.

You now obtain data on these workers’ scores on an achievement test and add this variable to the regression. You estimate regressions (2) and (3) as follows:

lnwi = β0 + β1edui + β2expi + β3exp2i + β4femalei + β5testi + εi (2)

edui = γ0 + γ1testi + ui (3)

Where testi is the worker’s score on an achievement test (measured in percentile rank) administered as part of the survey. You are given the following coefficient estimates with the R2 of estimation for model

(2) being 0.293:

[10 marks] Compare the standard error of β1 in model (2) with that of model (1) and explain possible reasons for this change.

[10 marks] Under which assumptions can you interpret the coefficient β1 as the causal effect of education on wages? Be specific about the assumption and explain in words what it means.

[8 marks] Is the information provided about the estimates of regressions (2) and (3) sufficient for you to explain why the coefficient on education is different between regression (1) and regression (2)?

[8 marks] Is either one of the log wage regressions likely to provide a good indication of the causal effect of education on wages? Use the information above to construct part of your response.

[7 marks] We now control for the seniority by adding the variable tenure to our multiple regression model. Where tenure is the number of years with the same employer. Use an F-test to test whether the inclusion of the additional variables has improved the model, i.e. comparing model 4 with model 1.

lnwi = β0 + β1edui + β2expi + β3exp2i + β4femalei + β5testi + β6tenurei + εi (4) The R2 from this regression is 0.360.

 Coefficient Estimate Standard error β1 0.06834 0.0032 γ1 0.1031 0.02378

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