Hi
I am running an income regression in Stata 12.
Due to the non-linear relationship between income and its determinants I use the logarithm of income in the OLS regression, therefore the predicted values (lsincome) are also in logarithmic form. I need to transform these back into non-logarithmic form, and at first I used a simple formula:
However, I found out that the residuals need to be normally distributed for this to work, and mine are NOT. I read about Duan's smearing estimator here: https://davegiles.blogspot.com/2014/12/s.html, which is supposed to work even if the residuals are not normally distributed. My question is how do I implement this in Stata?
Many thanks
Stella
I am running an income regression in Stata 12.
Due to the non-linear relationship between income and its determinants I use the logarithm of income in the OLS regression, therefore the predicted values (lsincome) are also in logarithmic form. I need to transform these back into non-logarithmic form, and at first I used a simple formula:
Code:
reg logincome i.educ age age2 married male black hispan1 speakengwell i.occ state1-state51 if choice == 1 & empstat == 1 , nocons robust scalar RMSE = e(rmse) predict lsincome, xb gen predincome = exp(lsincome)*exp(RMSE^2/2)
Many thanks
Stella
Code:
* Example generated by -dataex-. To install: ssc install dataex clear input long serial float logincome byte(educ age) float age2 byte(married male black) float hispan1 byte speakengwell float occ 27 10.985292 5 28 784 0 0 1 0 1 18 32 10.778956 3 33 1089 0 1 0 0 1 24 46 9.998797 5 28 784 0 1 0 0 1 5 53 11.112448 5 31 961 0 0 0 0 1 5 54 10.859 4 35 1225 0 0 0 0 1 10 58 9.1049795 4 30 900 1 0 0 0 1 15 64 10.819778 4 34 1156 1 1 1 0 1 23 77 9.392662 5 27 729 0 0 0 0 1 10 80 10.83958 5 31 961 1 0 0 0 1 12 89 9.714746 3 20 400 0 0 1 0 1 19 109 8.556414 3 24 576 0 1 1 0 1 15 110 9.480368 4 19 361 0 1 0 0 1 23 133 9.350102 3 26 676 0 0 1 0 1 8 134 10.596635 5 30 900 1 0 0 0 1 12 142 10.22557 5 27 729 0 0 0 0 1 10 159 10.819778 3 31 961 1 1 0 0 1 23 161 10.37349 3 31 961 1 1 0 0 1 23 175 9.852194 4 27 729 0 1 1 0 1 24 180 10.404263 3 25 625 1 1 0 0 1 23 184 10.714417 3 35 1225 0 0 0 1 0 19 188 9.952278 5 29 841 0 1 0 0 1 24 196 9.836279 4 24 576 0 0 1 0 1 12 200 10.596635 4 23 529 1 1 0 0 1 19 201 10.308952 4 34 1156 0 1 1 0 1 24 215 10.23996 3 30 900 1 1 1 0 1 14 249 10.714417 5 28 784 1 1 0 0 1 4 257 9.546813 6 24 576 0 1 0 0 1 19 272 9.903487 3 34 1156 1 0 0 0 1 24 286 10.071963 4 30 900 0 0 1 0 1 13 294 10.714417 3 26 676 1 1 0 0 1 25 314 9.615806 4 33 1089 1 0 0 0 1 18 326 12.25009 5 27 729 0 0 0 0 1 2 332 10.341743 4 23 529 0 1 0 0 1 4 339 9.680344 4 25 625 0 1 0 0 1 19 358 9.574984 3 35 1225 0 1 0 0 1 17 359 10.911446 5 32 1024 1 0 0 0 1 12 361 10.778956 5 26 676 1 0 0 0 1 12 376 10.819778 5 34 1156 0 1 0 0 1 21 378 9.952278 3 25 625 0 1 1 0 1 24 380 10.23996 4 28 784 0 1 1 0 1 14 382 10.04325 4 30 900 1 1 0 0 1 19 387 10.04325 3 35 1225 1 1 0 0 1 24 399 10.518673 4 25 625 0 1 1 0 1 14 403 10.460242 3 32 1024 0 0 1 0 1 13 406 9.615806 4 35 1225 0 0 1 0 1 19 407 9.472705 5 30 900 0 0 0 0 1 10 417 10.23996 5 29 841 1 1 0 0 1 25 431 8.006368 5 25 625 0 0 1 0 1 15 434 10.341743 4 22 484 1 1 1 0 1 19 446 10.434115 5 34 1156 0 0 0 0 1 19 456 9.1049795 3 33 1089 1 0 1 0 1 18 469 10.668956 5 25 625 1 1 0 0 1 19 474 9.798127 5 31 961 0 0 0 0 1 19 476 9.903487 5 27 729 1 1 0 0 1 25 479 11.0021 3 33 1089 1 1 0 0 1 23 484 10.308952 3 23 529 1 1 0 0 1 11 490 10.859 5 28 784 0 1 0 0 1 18 491 10.819778 3 33 1089 0 1 0 0 1 23 498 10.518673 5 23 529 0 0 0 0 1 19 500 9.472705 3 28 784 1 0 0 0 1 18 538 10.878047 4 28 784 0 1 0 0 1 4 562 11.03489 6 35 1225 1 0 0 0 1 1 564 10.586837 4 25 625 0 1 0 0 1 23 586 7.244227 4 21 441 0 0 1 0 1 24 594 11.440354 4 35 1225 1 1 0 0 1 19 598 9.903487 1 31 961 1 1 0 1 0 21 599 11.0021 4 33 1089 1 1 0 0 1 14 609 9.740969 4 34 1156 0 0 1 0 1 13 610 11.326596 3 34 1156 1 1 0 0 1 1 625 10.596635 5 24 576 0 0 0 0 1 9 627 8.881836 4 33 1089 0 0 0 0 1 18 635 10.596635 5 31 961 1 0 0 0 1 12 652 10.341743 5 30 900 0 1 0 0 0 3 659 10.553205 6 32 1024 0 0 0 0 1 10 662 10.434115 4 27 729 0 1 0 0 1 23 663 10.165852 5 30 900 1 0 0 0 1 11 675 9.769957 4 21 441 0 1 0 0 1 25 687 10.292146 4 34 1156 0 0 1 0 1 19 699 10.491274 5 26 676 1 1 0 0 1 3 703 10.621327 5 25 625 0 0 0 0 1 18 712 11.571195 6 29 841 0 0 0 0 1 9 720 10.89859 5 29 841 1 1 0 0 1 12 734 10.91509 3 31 961 1 1 0 1 0 1 738 9.952278 3 21 441 0 1 0 0 1 26 742 7.937375 5 34 1156 1 0 0 0 1 10 745 10.714417 4 24 576 0 1 0 0 1 24 769 10.714417 5 33 1089 1 0 1 0 1 12 783 9.667766 5 27 729 1 0 0 0 1 19 792 11.512925 3 32 1024 0 1 1 0 1 24 799 10.668956 5 27 729 1 1 0 0 1 4 809 10.308952 3 30 900 0 0 1 0 1 13 811 9.409191 1 34 1156 0 0 1 0 1 18 816 10.308952 6 34 1156 1 0 0 0 1 5 820 10.08581 4 27 729 0 1 0 0 1 1 833 9.126959 4 34 1156 0 0 1 0 1 13 858 10.12663 4 31 961 1 1 0 0 1 16 872 7.17012 4 34 1156 1 0 0 0 1 19 874 10.08581 4 33 1089 1 1 0 0 1 24 877 11.711777 6 28 784 1 0 0 0 1 12 901 10.106428 5 24 576 1 1 0 0 1 18 end label values educ educ label def educ 1 "No high school", modify label def educ 3 "High school graduate", modify label def educ 4 "Some college", modify label def educ 5 "College graduate", modify label def educ 6 "Post graduate", modify label values age AGE label def AGE 19 "19", modify label def AGE 20 "20", modify label def AGE 21 "21", modify label def AGE 22 "22", modify label def AGE 23 "23", modify label def AGE 24 "24", modify label def AGE 25 "25", modify label def AGE 26 "26", modify label def AGE 27 "27", modify label def AGE 28 "28", modify label def AGE 29 "29", modify label def AGE 30 "30", modify label def AGE 31 "31", modify label def AGE 32 "32", modify label def AGE 33 "33", modify label def AGE 34 "34", modify label def AGE 35 "35", modify label values occ occ label def occ 1 "Management, Business, Science, and Arts", modify label def occ 2 "Business Operations Specialists", modify label def occ 3 "Financial Specialists", modify label def occ 4 "Computer and Mathematical", modify label def occ 5 "Architecture and Engineering", modify label def occ 8 "Community and Social Services", modify label def occ 9 "Legal", modify label def occ 10 "Education, Training, and Library", modify label def occ 11 "Arts, Design, Entertainment, Sports, and Media", modify label def occ 12 "Healthcare Practitioners and Technicians", modify label def occ 13 "Healthcare Support", modify label def occ 14 "Protective Service", modify label def occ 15 "Food Preparation and Serving", modify label def occ 16 "Building and Grounds Cleaning and Maintenance", modify label def occ 17 "Personal Care and Service", modify label def occ 18 "Sales and Related", modify label def occ 19 "Office and Administrative Support", modify label def occ 21 "Construction", modify label def occ 23 "Installation, Maintenance, and Repair", modify label def occ 24 "Production", modify label def occ 25 "Transportation and Material Moving", modify label def occ 26 "Military Specific", modify
