关于算法:3SMFE4统计算法分析

3SMFE4 LM Statistical Methods in Finance and Economics
Additional Tasks for Year 4 and PGT students
This will be assessed as 10% of course mark.
__
Before you work on this additional task sheet, please make sure you read the following information:

1. Download the data; attach your R code to your solution.
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).
   __
   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”

4. .Less than 1st grade
5. .1st,2nd,3rd,or 4th grade
6. .5th or 6th grade
7. .7th and 8th grade
8. .9th grade
9. .10th grade
10. .11th grade
11. .12th grade no diploma
12. .High school graduate – high school diploma or equivalent
13. .Some college but no degree
14. .Associate degree in college – occupation/vocation program
15. .Associate degree in college – academic program
16. .Bachelor’s degree (for example: BA,AB,BS)
17. .Master’s degree (for example:MA,MS,MENG,MED,MSW, MBA)
18. .Professional school degree (for example: MD,DDS,DVM,LLB,JD)

19. .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

20. 2 –
    Using the data in cps4_small.csv answer the following questions. Provide R code to support your
    answer.
21. 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 
22. 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.
23. Plot the residuals from part (1) against MARRIED. Is there evidence of heteroskedasticity?
24. 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.
25. 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.
26. 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.
27. Plot the least squares residuals against EDUC and against EXPER. What do they suggest?
28. 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?
29. 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.
30. 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.
31. 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.
32. 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.
33. Find a 95% forecast interval for the wage of a married worker with 18 years of education and
34. years of experience. Ignore the uncertainty and sampling error.
35. Are you happy about the above model? Do you have any other ideas to improve the model?