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Part A

If a statistical table does not give an entry for the appropriate number(s) of degrees of freedom, then use the closest number(s) of degrees of freedom available.

EARNINGS = current hourly earnings in $

S = years of schooling

EXP = total out-of-school work experience in years

IQ = IQ score, standardized to have a mean of 0, and a standard deviation of 1

MALE = gender of respondent (1 if male, 0 otherwise)

ETHBLACK = African-American (1 if African-American, 0 otherwise)

ETHHISP = Hispanic (1 if Hispanic, 0 otherwise)

AGE = age in years

Note: The dataset is available on cuLearn.

a) Obtain basic summary statistics for the dataset using the STATA “summarize” command, and then copy and paste the output into your assignment.

b) i) What is the variance of the number of years of schooling?

ii) How many males are included in the sample?

iii) How many African-Americans are included in the sample?

iv) How many Hispanics are included in the sample?

c) Compute the correlation matrix for the subset of non-dummy variables in the dataset using the STATA “correlate” command, and then copy and paste the output into your assignment.

d) Identify the two simple correlation coefficients in the correlation matrix from part c) that exceed 0.5 in absolute value. Provide a rationale for the signs of these two simple correlation coefficients. HINT: In answering this question, it may be useful to reflect upon the summary statistics from part a).

With this in mind, Professor B sets up the following very basic dummy variable model, which includes both an intercept and a slope dummy variable

a) Using the data in the Earnings.dta dataset, together with an appropriate set of STATA commands, estimate this model, and then copy and paste the output into your assignment. Be sure to include ALL of your STATA commands in this output.

b) Report your regression results in the standard format of equation (7.8) on p. 199.

c) Carefully interpret the real-world meaning of the four parameter estimates.

d) Are the four parameter estimates individually statistically significant? Explain.

e) Use an F-test to test whether gender has an overall impact (whether on the intercept or on the slope or on both) on current hourly earnings. Be sure to follow the detailed steps outlined on pp. 142-144, including the provision of a clear statement of the relevant null and alternative hypotheses, the use of the general F-statistic formula given in equation (5.10), and a clear explanation of whether you should reject or not reject the null hypothesis and why.

Moreover, Professor C believes that IQ has a non-linear impact on current hourly earnings, rather than a linear impact. With this in mind, Professor C specifies the following extended version of Professor B’s model

a) Using the data in the Earnings.dta dataset, together with an appropriate set of STATA commands, estimate this model, and then copy and paste the output into your assignment. Be sure to include ALL of your STATA commands in this output.

b) Report your regression results in the standard format of equation (7.8) on p. 199.

c) Use an F-test to test whether IQ has an overall impact (this will necessarily be a joint test) on current hourly earnings in the context of this model. Be sure to follow the detailed steps outlined on pp. 142-144, including the provision of a clear statement of the relevant null and alternative hypotheses, the use of the general F-statistic formula given in equation (5.10), and a clear explanation of whether you should reject or not reject the null hypothesis and why.

d) Using your regression results, determine the (estimated) impact of a one unit, that is, a one standard deviation, increase in IQ on current hourly earnings (holding gender and the number of years of schooling constant). Think carefully about your answer.

But, on the other hand, he has always had a certain fascination with logarithms, so he specifies the following semi-log model

where the variable lnEarnings is the natural logarithm of the variable Earnings.

a) Using the data in the Earnings.dta dataset, together with an appropriate set of STATA commands, estimate this model, and then copy and paste the output into your assignment. Be sure to include ALL of your STATA commands in this output.

b) Report your regression results in the standard format of equation (7.8) on p. 199.

c) Carefully interpret the real-world meaning of the four slope parameter estimates.

However she can live with intercept dummy variables. So, Professor Eclectic decides to specify a model involving the regression of EARNINGS on all the other variables available in the original data set.

a) Using the data in the Earnings.dta dataset, estimate this model with STATA, and then copy and paste the output into your assignment.

b) Use your knowledge of econometrics to evaluate the quality of this model, concentrating in particular on the various issues raised in Chapter 6.

c) How might this model be improved? Explain.

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