Suppose that you wish you expand upon the wage model by using a random sample of

Question

Suppose that you wish you expand upon the wage model by using a random sample of people from the Current Population Survey (CPS).

A State your hypothesis as to the effect you believe each of the three explanatory variables education, age, and experience would have on log(wage).

(B) Run an OLS regression of log(wage) on education, age, and experience. Comment on the statistical significance of your included variables and if this matches your hypothesis. Do you see any potential issues with the model as specified that would explain your findings?

C Consider another model regressing wage (in levels) on education and age. Find the 95% confidence interval for the average wage of someone with the average level of education and of the average in the sample. Then, find the 95% prediction interval of the wage of a randomly selected person who happens to have the average level of education and is of the average in the sample. Explain why we would expect these two results to be different.

Hint: this will require several steps. Review the slides and/or the textbook for the necessary steps to calculate these numbers.

D Run another OLS regression of log(wage) on education and age, including a quadratic term for age.Why would we want to include a quadratic version of age in this regression? How do we interpret the impact of age and age squared on log(wage)? Based on your results, at what point is there a change in direction of the impact of age on someone’s wage in this sample?

Hint: create the new variables using the “gen” command

ECreate a new interaction variable education*age and include it in your model from part D. Based on the coefficient estimates (ignoring statistical significance), what is the predicted impact of an additional year of education for someone of the average age in the sample?   

earnings per hour Wage educ years of education age in years age exper experience log(wage) 'wage age 2 agesqr educ age educ age

Explanation / Answer

Solution:

A.

a) Null hypothesis : There is no relationship between the dependent and Independent variable i.e The slope is equal to 0

b) Alternate hypothesis : slope is not equal to 0.

B.

As seen from the regression output, only the variable age is statistically significant as its p value is less then 0.05 or 5%. Also the mutiple R square and adjusted R square is very low, which significes that not much variation is explained by the Independent variable.

C.

Please provide the dataset for further computation.

D.

Adding the square of the variable allows you to model more accurately the effect of age, which may have a non-linear relationship with the independent variable. For instance, the effect of age could be positive up until, say, the age of 50, and then negative thereafter.

Adding the age squared to age, allows you to model the effect a differing ages, rather than assuming the effect is linear for all ages.

E.

Please provide the dataset

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