# 讲解3SMFE4 LM Statistical Method

3SMFE4 LM Statistical Methods in Finance and Economics
This will be assessed as 10% of course mark.
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2. With R codes and all your solutions including figures together, it should not go more than 9 pages.
3. I am responsible for clarification (NOT responsible for running programs nor explaining results for you).
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The dataset cps4_small.csv contains the following information:
Variables: wage educ exper hrswk married female metro midwest south west black asian

Obs: 1000 observations
wage earnings per hour
educ years of education
exper post education years experience
hrswk usual hours worked per week
married = 1 if married
female = 1 if female
metro = 1 if lives in metropolitan area
midwest = 1 if lives in midwest
south = 1 if lives in south
west = 1 if lives in west
black = 1 if black
asian = 1 if asian
Note on education variable. CPS reports educational attainment by category for numerical
values for "educ"
12 .High school graduate – high school diploma or equivalent
13 .Some college but no degree
14 .Associate degree in college - occupation/vocation program
14 .Associate degree in college - academic program
16 .Bachelor's degree (for example: BA,AB,BS)
18 .Master's degree (for example:MA,MS,MENG,MED,MSW, MBA)
21 .Professional school degree (for example: MD,DDS,DVM,LLB,JD)
21 .Doctorate degree (for example: PHD,EDD)

Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
wage | 1000 20.61566 12.83472 1.97 76.39
educ | 1000 13.799 2.711079 0 21
exper | 1000 26.508 12.85446 2 65
hrswk | 1000 39.952 10.3353 0 90
married | 1000 .581 .4936423 0 1
female | 1000 .514 .5000541 0 1
metro | 1000 .78 .4144536 0 1
midwest | 1000 .24 .4272968 0 1
south | 1000 .296 .4567194 0 1
west | 1000 .24 .4272968 0 1
black | 1000 .112 .3155243 0 1
asian | 1000 .043 .2029586 0 1
- 2 -
Using the data in cps4_small.csv answer the following questions. Provide R code to support your
1. Estimate the following wage equation with least squares and heteroskedasticity-robust
standard errors, and report the results.
ln(WAGE)   EDUC EXPER  EXPER  (EXPER *EDUC) e 5
2
1 2 3 4 
2. Add MARRIED to the equation and re-estimate. Holding education and experience constant,
do married workers get higher wages? Using a 1% significance level, test a null hypothesis
that wages of married workers are less than or equal to those of unmarried workers against
the alternative that wages of married workers are higher.
3. Plot the residuals from part (1) against MARRIED. Is there evidence of heteroskedasticity?
4. Estimate the model in part (1) twice---once using observations on only married workers and
once using observations on only unmarried workers. Use the Goldfeld-Quandt test and a 1%
significance level to test whether the error variances for married and unmarried workers are
different.
5. Find generalized least squares of the model in part (1). Compare the estimates and standard
errors with those obtained in part (1) using traditional OLS with the White’s correction.
6. Find two 95% interval estimates for the marginal effect
E(ln(WAGE))/EDUC
for a worker
with 12 years of education and 25 years of experience. Use the results from part (1) with the
White’s correction for one interval and the results from part (5) GLS results for the other
interval. Comment on any differences.
7. Plot the least squares residuals against EDUC and against EXPER. What do they suggest?
8. Test for heteroskedasticity using a Breusch-Pagan test where the variance depends on EDUC,
EXPER and MARRIED. What do you conclude at a 5% significance level?
9. Estimate a variance function that includes EDUC, EXPER, and MARRIED and use it to
estimate the standard deviation for each observation and list the first ten estimates. Hint:
Don’t take log of EDUC, EXPER, and MARRIED.
10. Find generalized least squares estimates of the wage equation based on findings in (9).
Compare the GLS estimates and standard errors with those obtained from least squares
estimation with heteroskedasticity-robust standard errors.
11. Find two 95% interval estimates for the marginal effect
  E EXPER (ln(WAGE))/
for a worker
with 16 years of education and 20 years of experience. Use least squares with
heteroskedasticity-robust standard errors for one interval and the results from part (10) for the
other. Comment on any difference.
12. Forecast the wage of a married worker with 18 years of education and 16 years of experience.
Use both the natural predictor and the corrected predictor.
13. Find a 95% forecast interval for the wage of a married worker with 18 years of education and
16 years of experience. Ignore the uncertainty and sampling error.
14. Are you happy about the above model? Do you have any other ideas to improve the model?