Rolling regression for calculating expected inflation rate.

[Sc Meng]

Dear all,

Suppose I have the following dataset:

clear
input int year double(inf gdp)
1990 5.72458974 3.9071139
1991 6.68398563 9.29407591
1992 8.19824765 14.21616358
1993 15.20220481 13.86757602
1994 20.60060944 13.05215872
1995 13.6705391 10.94922737
1996 6.50109595 9.92837246
1997 1.62216042 9.23076923
1998 -.89258936 7.83761392
1999 -1.26840965 7.66748617
2000 2.06146138 8.49150849
2001 2.04311501 8.33991055
2002 .60485066 9.13064594
2003 2.60544121 10.03560303
2004 6.9543218 10.11122346
2005 3.90263978 11.39577594
2006 3.92791085 12.71947902
2007 7.74917984 14.23138804
2008 7.79180194 9.65428937
2009 -.2105339 9.39981317
2010 6.88114487 10.63614046
2011 8.07559638 9.55091409
2012 2.33512068 7.85962749
2013 2.16101914 7.76861528
2014 .791193 7.29951892
2015 .06269939 6.90531667
2016 1.07275629 6.73667525
2017 3.88416989 6.75700761
2018 2.93333231 6.56697386
end

I'd would like to calculate the expected inflation rate by using the t+1 real inflation rate as the dependent variable(the inf in the dataset) and the t real inflation rate and t real GDP(the gdp in the dataset) growth rate as independent variables. How can I construct my codes to reach this goal?

Note: this regression is based on the thoery of Phillips Curve.

[Sc Meng]

if I change the dataset like this:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int year double(inf gdp) float(inf1 gdp1)
1990  5.72458974   3.9071139          .         .
1991  6.68398563  9.29407591    5.72459  3.907114
1992  8.19824765 14.21616358   6.683986  9.294076
1993 15.20220481 13.86757602   8.198248 14.216164
1994 20.60060944 13.05215872  15.202205 13.867576
1995  13.6705391 10.94922737   20.60061 13.052158
1996  6.50109595  9.92837246   13.67054 10.949227
1997  1.62216042  9.23076923   6.501096  9.928372
1998  -.89258936  7.83761392  1.6221604  9.230769
1999 -1.26840965  7.66748617  -.8925893  7.837614
2000  2.06146138  8.49150849 -1.2684096  7.667486
2001  2.04311501  8.33991055  2.0614614 8.4915085
2002   .60485066  9.13064594   2.043115 8.3399105
2003  2.60544121 10.03560303   .6048506  9.130646
2004   6.9543218 10.11122346   2.605441 10.035603
2005  3.90263978 11.39577594   6.954322 10.111223
2006  3.92791085 12.71947902    3.90264 11.395776
2007  7.74917984 14.23138804   3.927911  12.71948
2008  7.79180194  9.65428937    7.74918 14.231388
2009   -.2105339  9.39981317   7.791802  9.654289
2010  6.88114487 10.63614046  -.2105339  9.399813
2011  8.07559638  9.55091409   6.881145  10.63614
2012  2.33512068  7.85962749   8.075597  9.550914
2013  2.16101914  7.76861528  2.3351207  7.859628
2014     .791193  7.29951892   2.161019  7.768615
2015   .06269939  6.90531667    .791193  7.299519
2016  1.07275629  6.73667525  .06269939  6.905317
2017  3.88416989  6.75700761  1.0727563  6.736675
2018  2.93333231  6.56697386    3.88417  6.757008
end

and use code as following:
Code:

tsset year
rolling,recursive window(1) clear:reg inf inf1 gdp1

I am sure my codes are incorrect but I don't how to make it works.

[Nick Cox]

I am confused. I read your regression as

reg inf L.inf gdp1

and don't understand how rolling enters into it.

[Sc Meng]

I am confused. I read your regression as

reg inf L.inf gdp1

and don't understand how rolling enters into it.

Maybe I misunderstand the code of rolling command.

[Nick Cox]

Sure, I see and saw your code, but it doesn't match your word description,

t+1 real inflation rate as the dependent variable(the inf in the dataset) and the t real inflation rate and t real GDP(the gdp in the dataset) growth rate as independent variable

[Sc Meng]

Sure, I see and saw your code, but it doesn't match your word description,

Yes, that's the main problem. I don't how to use it to reach my purpose. Thanks very much, still.

In terms of "t+1 real inflation rate as the dependent variable(the inf in the dataset) and the t real inflation rate and t real GDP(the gdp in the dataset) growth rate as independent variable", I think I should add information like for each current period we need to regress all the former observations before the period, maybe like:

For 1991's real inflation rate, it needs regression with 1990's real inflation rate and real GDP growth rate.
For 1992's real inflation rate, it needs regression with 1991's and 1990's real inflation rate and real GDP growth rate.
......etc.
And the fitted values are the expected inflation rate I need.

If I do not make mistakes in understanding the method of calculating the expected inflation.

I am so sorry for making you confused.

[Nick Cox]

OK, With rangestat installed

ssc install rangestat

you can do this, The results necessarily conflate artefacts of small sample size and any progressive change in the relationship. You need a minimum of 4 data points to fit 3 parameters too.

* Example generated by -dataex-. To install: ssc install dataex
clear
input int year double(inf gdp) float(inf1 gdp1)
1990  5.72458974   3.9071139          .         .
1991  6.68398563  9.29407591    5.72459  3.907114
1992  8.19824765 14.21616358   6.683986  9.294076
1993 15.20220481 13.86757602   8.198248 14.216164
1994 20.60060944 13.05215872  15.202205 13.867576
1995  13.6705391 10.94922737   20.60061 13.052158
1996  6.50109595  9.92837246   13.67054 10.949227
1997  1.62216042  9.23076923   6.501096  9.928372
1998  -.89258936  7.83761392  1.6221604  9.230769
1999 -1.26840965  7.66748617  -.8925893  7.837614
2000  2.06146138  8.49150849 -1.2684096  7.667486
2001  2.04311501  8.33991055  2.0614614 8.4915085
2002   .60485066  9.13064594   2.043115 8.3399105
2003  2.60544121 10.03560303   .6048506  9.130646
2004   6.9543218 10.11122346   2.605441 10.035603
2005  3.90263978 11.39577594   6.954322 10.111223
2006  3.92791085 12.71947902    3.90264 11.395776
2007  7.74917984 14.23138804   3.927911  12.71948
2008  7.79180194  9.65428937    7.74918 14.231388
2009   -.2105339  9.39981317   7.791802  9.654289
2010  6.88114487 10.63614046  -.2105339  9.399813
2011  8.07559638  9.55091409   6.881145  10.63614
2012  2.33512068  7.85962749   8.075597  9.550914
2013  2.16101914  7.76861528  2.3351207  7.859628
2014     .791193  7.29951892   2.161019  7.768615
2015   .06269939  6.90531667    .791193  7.299519
2016  1.07275629  6.73667525  .06269939  6.905317
2017  3.88416989  6.75700761  1.0727563  6.736675
2018  2.93333231  6.56697386    3.88417  6.757008
end

rangestat (reg) inf inf1 gdp1, interval(year . 0)

format reg_r2-se_cons %4.3f

list reg* b*

     +---------------------------------------------------------+
     | reg_nobs   reg_r2   reg_ad~2   b_inf1   b_gdp1   b_cons |
     |---------------------------------------------------------|
  1. |        .        .          .        .        .        . |
  2. |        1        .          .        .        .        . |
  3. |        2        .          .        .        .        . |
  4. |        3        .          .        .        .        . |
  5. |        4    0.963      0.890    0.951    0.583   -1.860 |
     |---------------------------------------------------------|
  6. |        5    0.735      0.470    0.119    0.990    0.777 |
  7. |        6    0.564      0.274   -0.002    1.091   -0.044 |
  8. |        7    0.471      0.206    0.270    0.933   -2.628 |
  9. |        8    0.545      0.363    0.548    0.758   -4.411 |
 10. |        9    0.631      0.508    0.613    0.739   -5.035 |
     |---------------------------------------------------------|
 11. |       10    0.646      0.545    0.567    0.750   -4.574 |
 12. |       11    0.662      0.577    0.577    0.749   -4.713 |
 13. |       12    0.676      0.605    0.596    0.750   -5.029 |
 14. |       13    0.683      0.620    0.589    0.758   -5.033 |
 15. |       14    0.671      0.611    0.555    0.822   -5.241 |
     |---------------------------------------------------------|
 16. |       15    0.658      0.601    0.552    0.815   -5.358 |
 17. |       16    0.653      0.600    0.579    0.740   -4.919 |
 18. |       17    0.654      0.605    0.565    0.784   -5.218 |
 19. |       18    0.648      0.601    0.584    0.679   -4.393 |
 20. |       19    0.595      0.545    0.540    0.763   -5.354 |
     |---------------------------------------------------------|
 21. |       20    0.557      0.505    0.479    0.806   -5.189 |
 22. |       21    0.558      0.509    0.481    0.809   -5.159 |
 23. |       22    0.541      0.493    0.452    0.864   -5.742 |
 24. |       23    0.549      0.504    0.452    0.863   -5.731 |
 25. |       24    0.562      0.521    0.454    0.880   -5.957 |
     |---------------------------------------------------------|
 26. |       25    0.579      0.540    0.456    0.891   -6.107 |
 27. |       26    0.587      0.551    0.453    0.876   -5.909 |
 28. |       27    0.572      0.537    0.452    0.816   -5.193 |
 29. |       28    0.574      0.540    0.457    0.795   -4.992 |
     +---------------------------------------------------------+

.

[Sc Meng]

OK, With rangestat installed

ssc install rangestat

you can do this, The results necessarily conflate artefacts of small sample size and any progressive change in the relationship. You need a minimum of 4 data points to fit 3 parameters too.

* Example generated by -dataex-. To install: ssc install dataex
clear
input int year double(inf gdp) float(inf1 gdp1)
1990 5.72458974 3.9071139 . .
1991 6.68398563 9.29407591 5.72459 3.907114
1992 8.19824765 14.21616358 6.683986 9.294076
1993 15.20220481 13.86757602 8.198248 14.216164
1994 20.60060944 13.05215872 15.202205 13.867576
1995 13.6705391 10.94922737 20.60061 13.052158
1996 6.50109595 9.92837246 13.67054 10.949227
1997 1.62216042 9.23076923 6.501096 9.928372
1998 -.89258936 7.83761392 1.6221604 9.230769
1999 -1.26840965 7.66748617 -.8925893 7.837614
2000 2.06146138 8.49150849 -1.2684096 7.667486
2001 2.04311501 8.33991055 2.0614614 8.4915085
2002 .60485066 9.13064594 2.043115 8.3399105
2003 2.60544121 10.03560303 .6048506 9.130646
2004 6.9543218 10.11122346 2.605441 10.035603
2005 3.90263978 11.39577594 6.954322 10.111223
2006 3.92791085 12.71947902 3.90264 11.395776
2007 7.74917984 14.23138804 3.927911 12.71948
2008 7.79180194 9.65428937 7.74918 14.231388
2009 -.2105339 9.39981317 7.791802 9.654289
2010 6.88114487 10.63614046 -.2105339 9.399813
2011 8.07559638 9.55091409 6.881145 10.63614
2012 2.33512068 7.85962749 8.075597 9.550914
2013 2.16101914 7.76861528 2.3351207 7.859628
2014 .791193 7.29951892 2.161019 7.768615
2015 .06269939 6.90531667 .791193 7.299519
2016 1.07275629 6.73667525 .06269939 6.905317
2017 3.88416989 6.75700761 1.0727563 6.736675
2018 2.93333231 6.56697386 3.88417 6.757008
end

rangestat (reg) inf inf1 gdp1, interval(year . 0)

format reg_r2-se_cons %4.3f

list reg* b*

+---------------------------------------------------------+
| reg_nobs reg_r2 reg_ad~2 b_inf1 b_gdp1 b_cons |
|---------------------------------------------------------|
1. | . . . . . . |
2. | 1 . . . . . |
3. | 2 . . . . . |
4. | 3 . . . . . |
5. | 4 0.963 0.890 0.951 0.583 -1.860 |
|---------------------------------------------------------|
6. | 5 0.735 0.470 0.119 0.990 0.777 |
7. | 6 0.564 0.274 -0.002 1.091 -0.044 |
8. | 7 0.471 0.206 0.270 0.933 -2.628 |
9. | 8 0.545 0.363 0.548 0.758 -4.411 |
10. | 9 0.631 0.508 0.613 0.739 -5.035 |
|---------------------------------------------------------|
11. | 10 0.646 0.545 0.567 0.750 -4.574 |
12. | 11 0.662 0.577 0.577 0.749 -4.713 |
13. | 12 0.676 0.605 0.596 0.750 -5.029 |
14. | 13 0.683 0.620 0.589 0.758 -5.033 |
15. | 14 0.671 0.611 0.555 0.822 -5.241 |
|---------------------------------------------------------|
16. | 15 0.658 0.601 0.552 0.815 -5.358 |
17. | 16 0.653 0.600 0.579 0.740 -4.919 |
18. | 17 0.654 0.605 0.565 0.784 -5.218 |
19. | 18 0.648 0.601 0.584 0.679 -4.393 |
20. | 19 0.595 0.545 0.540 0.763 -5.354 |
|---------------------------------------------------------|
21. | 20 0.557 0.505 0.479 0.806 -5.189 |
22. | 21 0.558 0.509 0.481 0.809 -5.159 |
23. | 22 0.541 0.493 0.452 0.864 -5.742 |
24. | 23 0.549 0.504 0.452 0.863 -5.731 |
25. | 24 0.562 0.521 0.454 0.880 -5.957 |
|---------------------------------------------------------|
26. | 25 0.579 0.540 0.456 0.891 -6.107 |
27. | 26 0.587 0.551 0.453 0.876 -5.909 |
28. | 27 0.572 0.537 0.452 0.816 -5.193 |
29. | 28 0.574 0.540 0.457 0.795 -4.992 |
+---------------------------------------------------------+

.

Thanks very much, Cox and I need to time digest suggestions from you.

[Attaullah Shah]

This is an example of a recursive window. You may like to try asreg with the recursive option for this.

ssc install asreg
asreg inf inf1 gdp1, window(year 1) recursive

[Sc Meng]

This is an example of a recursive window. You may like to try asreg with the recursive option for this.

ssc install asreg
asreg inf inf1 gdp1, window(year 1) recursive

Thank you very much,Shah.
I have did like this to mactch my needs

asreg inf inf1 gdp, window(year 5) recursive fit

I sincerely appreciate the help from you.