Consider the following simple linear regression model designed to examine the relationship between earnings and educational attainment: Wagei = β0 + β1Educi + εi (1) where i indexes individuals, W agei is an individual's wage measures in dollars, Educ is the number of years of schooling and ε is a random disturbance term. We would expect, on average, higher levels of education to be associated with higher incomes. However, the simple regression model ignores the fact earnings tend to increase with age, regardless of educational attainment.
Thus, a more appropriate model might be:
Wagei = β0 + β1Educi + β2Agei + εi (2)
where Agei is an individual's age measured in years.
(a) If Corr(Educi , Agei) > 0 and you estimate model (1) when the true model is model (2), will your estimate of β1 be unbiased? Will it be consistent? Provide a detailed explanation.
(b) If Corr(Educi , Agei) > 0 and you estimate model (1) when the true model is model (2), will your estimate of β1 overstate, understate or correctly state the impact of education on earnings in the regression? Why?
(c) If Corr(Educi , Agei) = 0 and you estimate model (1) when the true model is model (2), will your estimate of β1 be unbiased? Will it be consistent? Provide a detailed explanation.
(d1) Finally, suppose Corr(Educi , Agei) = 0 and you estimate model (1) when the true model is model (2). How would the results you obtain from the model?
(d2) differ from the results you would obtain from model (1)
(d3)Specifically, what differences would you expect between the R2 0 s, estimates of β1 and standard errors of βˆ 1 between the two models?

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