Hypothesis testing between regression coefficients

Yatharth Garg

Join Date: Mar 2021

Posts: 61
#1

Hypothesis testing between regression coefficients

21 May 2021, 03:25

Hi everyone! So I created this regression table using the following commands

Code:

areg logincome logurbanisation Occupation Gender Age Marital Status Time if CASTE==n [aweight=weight], absorb(STATEID) cluster(STATE_DISTID)

While n is[1,2,3,4] depending on the category (Brahmin, Upper Caste, OBC or Dalit). I need to test whether the coefficients of log(urbanisation) are statistically different from each other. Hence, H0: B(Brahmin)=B(Dalit); H1: B(Brahmin)!= B(Dalit) for example. Is there a way for STATA to perform these tests? If not, how do I go ahead with this analysis? Thank you in advance!
Tags: None
Joro Kolev

Join Date: Aug 2018

Posts: 3047
#2

21 May 2021, 03:48

See this thread here https://www.statalist.org/forums/for...ion-subsamples
in post #3 I explain how you can do what you want to do.
Comment
Yatharth Garg

Join Date: Mar 2021

Posts: 61
#3

21 May 2021, 08:31

Hi Mr Kolev, thank you very much for the help. I ran a similar code as in the thread on post #3.
However, I found that -areg- is not supported by -suest-. Could you please suggest another solution?
Also, the dependent variables in each regression is logincome, the only thing that varies is "if CASTE=n"

Adding to this, my actual null hypothesis would be:
H0: B(Brahmin)=B(Upper Caste)=B(OBC)=B(Dalits)
HI: if not

Last edited by Yatharth Garg; 21 May 2021, 08:38.
Comment
Joro Kolev

Join Date: Aug 2018

Posts: 3047
#4

21 May 2021, 08:35

You did not read my post #3 at the above mentioned thread.

The point of the post is that -regress- has an undocumented option -absorb- so you can fit the same model you re fitting now through -areg-, but through -regress-.

Originally posted by Yatharth Garg View Post

Hi Mr Kolev, thank you very much for the help. I ran a similar code as in the thread on post #3.
However, I found that -areg- is not supported by -suest-. Could you please suggest another solution?
Also, the dependent variables in each regression is logincome, the only thing that varies is "if CASTE=n"
Comment
Yatharth Garg

Join Date: Mar 2021

Posts: 61
#5

21 May 2021, 08:44

Apologies, I tried running the same model with -regress-. However, STATA returns that option absorb() is not allowed, r(198). Please advise!

I have also made an edit to my post #3

Originally posted by Yatharth Garg View Post

Adding to this, my actual null hypothesis would be:
H0: B(Brahmin)=B(Upper Caste)=B(OBC)=B(Dalits)
HI: if not
Comment

Joro Kolev

Join Date: Aug 2018
Posts: 3047

21 May 2021, 09:00

This is interesting, which Stata are you using?

Under Stata 15.1 this works:

Code:

. sysuse auto, clear
(1978 Automobile Data)

. areg price mpg headroom, absorb(rep)

Linear regression, absorbing indicators         Number of obs     =         69
Absorbed variable: rep78                        No. of categories =          5
                                                F(   2,     62)   =      10.60
                                                Prob > F          =     0.0001
                                                R-squared         =     0.2657
                                                Adj R-squared     =     0.1946
                                                Root MSE          =  2613.7617

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -297.1542   65.40836    -4.54   0.000    -427.9037   -166.4048
    headroom |  -334.6746   426.4413    -0.78   0.436    -1187.119    517.7695
       _cons |   13476.44    2201.67     6.12   0.000     9075.361    17877.51
------------------------------------------------------------------------------
F test of absorbed indicators: F(4, 62) = 1.093               Prob > F = 0.368

. regress price mpg headroom, absorb(rep)

Linear regression, absorbing indicators         Number of obs     =         69
                                                F(2, 62)          =      10.60
                                                Prob > F          =     0.0001
                                                R-squared         =     0.2657
                                                Adj R-squared     =     0.1946
                                                Root MSE          =     2613.8

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -297.1542   65.40836    -4.54   0.000    -427.9037   -166.4048
    headroom |  -334.6746   426.4413    -0.78   0.436    -1187.119    517.7695
       _cons |   13476.44    2201.67     6.12   0.000     9075.361    17877.51
------------------------------------------------------------------------------

.

Originally posted by Yatharth Garg View Post

Apologies, I tried running the same model with -regress-. However, STATA returns that option absorb() is not allowed, r(198). Please advise!

I have also made an edit to my post #3

Comment

Joro Kolev

Join Date: Aug 2018
Posts: 3047

21 May 2021, 09:04

Still tell me which Stata you are using, I am interested under which version the above does not work, but you can also try this:

Code:

. _regress price mpg headroom if fore, absorb(rep)

Linear regression, absorbing indicators         Number of obs     =         21
                                                F(2, 16)          =       4.75
                                                Prob > F          =     0.0240
                                                R-squared         =     0.4071
                                                Adj R-squared     =     0.2589
                                                Root MSE          =       1912

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -210.8535   70.52512    -2.99   0.009    -360.3601   -61.34696
    headroom |  -66.90347   974.0123    -0.07   0.946    -2131.717     1997.91
       _cons |   11573.76   2762.907     4.19   0.001     5716.661    17430.86
------------------------------------------------------------------------------

. est sto fore

. _regress price mpg headroom if !fore, absorb(rep)

Linear regression, absorbing indicators         Number of obs     =         48
                                                F(2, 41)          =       8.90
                                                Prob > F          =     0.0006
                                                R-squared         =     0.3306
                                                Adj R-squared     =     0.2326
                                                Root MSE          =     2793.5

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -473.0364   114.3748    -4.14   0.000    -704.0209   -242.0519
    headroom |   -535.417   536.7575    -1.00   0.324    -1619.421    548.5868
       _cons |   17129.81   3365.443     5.09   0.000     10333.16    23926.46
------------------------------------------------------------------------------

. est sto domestic

. suest fore domestic

Simultaneous results for fore, domestic

                                                Number of obs     =         69

--------------------------------------------------------------------------------
               |               Robust
               |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
fore_mean      |
           mpg |  -210.8535   80.27714    -2.63   0.009    -368.1939   -53.51323
      headroom |  -66.90347   567.3178    -0.12   0.906    -1178.826    1045.019
         _cons |   11573.76   2523.328     4.59   0.000      6628.13     16519.4
---------------+----------------------------------------------------------------
fore_lnvar     |
         _cons |   15.11185   .2678884    56.41   0.000      14.5868     15.6369
---------------+----------------------------------------------------------------
domestic_mean  |
           mpg |  -473.0364   155.7149    -3.04   0.002     -778.232   -167.8408
      headroom |   -535.417   421.3216    -1.27   0.204    -1361.192    290.3583
         _cons |   17129.81   4012.619     4.27   0.000     9265.223     24994.4
---------------+----------------------------------------------------------------
domestic_lnvar |
         _cons |    15.8701   .2955829    53.69   0.000     15.29077    16.44943
--------------------------------------------------------------------------------

. test [fore_mean]mpg=[domestic_mean]mpg

 ( 1)  [fore_mean]mpg - [domestic_mean]mpg = 0

           chi2(  1) =    2.24
         Prob > chi2 =    0.1345

.

Comment

Yatharth Garg

Join Date: Mar 2021

Posts: 61
#8

21 May 2021, 09:17

I am using STATA 13.1, which explains why I am unable to use the method you have suggested.
From your post #7, I tried using -_regress- instead, but it returns the same error. Would you suggest a different approach?
Comment
Joro Kolev

Join Date: Aug 2018

Posts: 3047
#9

21 May 2021, 09:58

Then you need to do what Clyde suggests in #2 on the same thread: https://www.statalist.org/forums/for...ion-subsamples

Read factor variables to understand what this does:

Code:

help fvvarlist

Originally posted by Yatharth Garg View Post

I am using STATA 13.1, which explains why I am unable to use the method you have suggested.
From your post #7, I tried using -_regress- instead, but it returns the same error. Would you suggest a different approach?
Comment
Yatharth Garg

Join Date: Mar 2021

Posts: 61
#10

21 May 2021, 14:02

Thank you for your help, I really appreciate it.

Code:

areg logdefincome i.CASTE##(c.(logurbanisation) i.(OCCUPATION RO_3 RO5 mar time)), absorb(STATEID) cluster(STATE_DISTID)

Apologies, I overlooked something. It is working, thanks again.

Last edited by Yatharth Garg; 21 May 2021, 14:13. Reason: Issue resolved
Comment
Yatharth Garg

Join Date: Mar 2021

Posts: 61
#11

21 May 2021, 14:23

Code:

test (CASTE#c.logurbanisation)Forward Caste 2 = (CASTE#c.logurbanisation) OBC 3 =(CASTE#c.logurbanisation) Dalit 4

I ran this code but it is returning an error unknown - function (), r(133). Also, I think to avoid collinearity STATA is not including all values of CASTE. It has 4 values- Brahmin, Upper Caste, OBC and Dalit. But to test my hypothesis, I will need the coefficients for each caste group.
Comment
Yatharth Garg

Join Date: Mar 2021

Posts: 61
#12

22 May 2021, 06:37

Hi Joro, so I updated STATA to 16.1. And I am trying to run code you have suggested before, but I am still receiving this error, r(184), options absorb and cluster with different variables may not be combined.

I have ran the following two versions of the codes:

Code:

regress logdefincome logurbanisation RO_3 RO5 mar time if CASTE==1 [aweight=weight], absorb(STATEID) cluster(STATE_DISTID) _regress logdefincome logurbanisation RO_3 RO5 mar time if CASTE==1 [aweight=weight], absorb(STATEID) cluster(STATE_DISTID)

But I am receiving the same error message while doing these. What could be the problem here?
Comment

Joro Kolev

Join Date: Aug 2018
Posts: 3047

#13

22 May 2021, 09:58

Can you run the following code, and show exactly what you typed and exactly what Stata returned like I am doing below?

Code:

. regress price mpg headroom if fore, absorb(rep)

Linear regression, absorbing indicators         Number of obs     =         21
                                                F(2, 16)          =       4.75
                                                Prob > F          =     0.0240
                                                R-squared         =     0.4071
                                                Adj R-squared     =     0.2589
                                                Root MSE          =       1912

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -210.8535   70.52512    -2.99   0.009    -360.3601   -61.34696
    headroom |  -66.90347   974.0123    -0.07   0.946    -2131.717     1997.91
       _cons |   11573.76   2762.907     4.19   0.001     5716.661    17430.86
------------------------------------------------------------------------------

. est sto fore

. regress price mpg headroom if !fore, absorb(rep)

Linear regression, absorbing indicators         Number of obs     =         48
                                                F(2, 41)          =       8.90
                                                Prob > F          =     0.0006
                                                R-squared         =     0.3306
                                                Adj R-squared     =     0.2326
                                                Root MSE          =     2793.5

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -473.0364   114.3748    -4.14   0.000    -704.0209   -242.0519
    headroom |   -535.417   536.7575    -1.00   0.324    -1619.421    548.5868
       _cons |   17129.81   3365.443     5.09   0.000     10333.16    23926.46
------------------------------------------------------------------------------

. est sto domestic

. suest fore domestic, cluster(rep)

Simultaneous results for fore, domestic

                                                Number of obs     =         69

                                    (Std. Err. adjusted for 5 clusters in rep78)
--------------------------------------------------------------------------------
               |               Robust
               |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
fore_mean      |
           mpg |  -210.8535   25.53476    -8.26   0.000    -260.9007   -160.8063
      headroom |  -66.90347   718.5178    -0.09   0.926    -1475.172    1341.365
         _cons |   11573.76   2049.311     5.65   0.000     7557.186    15590.34
---------------+----------------------------------------------------------------
fore_lnvar     |
         _cons |   15.11185   .1825798    82.77   0.000       14.754     15.4697
---------------+----------------------------------------------------------------
domestic_mean  |
           mpg |  -473.0364   196.1553    -2.41   0.016    -857.4938   -88.57902
      headroom |   -535.417   348.7937    -1.54   0.125     -1219.04    148.2062
         _cons |   17129.81   4629.365     3.70   0.000     8056.423     26203.2
---------------+----------------------------------------------------------------
domestic_lnvar |
         _cons |    15.8701   .1212165   130.92   0.000     15.63252    16.10768
--------------------------------------------------------------------------------

. test [fore_mean]mpg=[domestic_mean]mpg

 ( 1)  [fore_mean]mpg - [domestic_mean]mpg = 0

           chi2(  1) =    1.75
         Prob > chi2 =    0.1862

.

Comment

Yatharth Garg

Join Date: Mar 2021
Posts: 61

#14

22 May 2021, 10:27

Hi, Thank you I am able to get these results now. I overlooked that I could use "cluster()" with suest. These are my results:
I just wanted to confirm another doubt. Is this test known as chow test? Is it also applicable for regression models for different groups (CASTE) within the same panel dataset (two time periods)??

Code:

. reg logdefincome logurbanisation OCCUPATION RO_3 RO5 mar time if CASTE==1 [aweight=weight], absorb(STATEID)
(sum of wgt is 15,905,197.516266)

Linear regression, absorbing indicators         Number of obs     =      3,545
                                                F(6, 3508)        =     145.46
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2806
                                                Adj R-squared     =     0.2733
                                                Root MSE          =     .85863

---------------------------------------------------------------------------------
   logdefincome |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
logurbanisation |   .2391378   .0245798     9.73   0.000     .1909457      .28733
     OCCUPATION |  -.0124496   .0004776   -26.07   0.000     -.013386   -.0115132
           RO_3 |  -.0233625   .0422432    -0.55   0.580    -.1061861    .0594612
            RO5 |   .0033383   .0013873     2.41   0.016     .0006184    .0060582
            mar |   .0452835   .0426309     1.06   0.288    -.0383004    .1288674
           time |   .1676947   .0296392     5.66   0.000     .1095828    .2258066
          _cons |   11.88449   .0702837   169.09   0.000     11.74668    12.02229
---------------------------------------------------------------------------------

. est sto Brahmin

. reg logdefincome logurbanisation OCCUPATION RO_3 RO5 mar time if CASTE==2 [aweight=weight], absorb(STATEID)
(sum of wgt is 54,320,713.348907)

Linear regression, absorbing indicators         Number of obs     =     11,398
                                                F(6, 11361)       =     444.65
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2719
                                                Adj R-squared     =     0.2696
                                                Root MSE          =     .86149

---------------------------------------------------------------------------------
   logdefincome |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
logurbanisation |   .2580549    .014159    18.23   0.000     .2303008     .285809
     OCCUPATION |  -.0126262   .0002914   -43.33   0.000    -.0131974   -.0120549
           RO_3 |   .2005149   .0204225     9.82   0.000     .1604832    .2405466
            RO5 |   .0022378   .0007984     2.80   0.005     .0006728    .0038028
            mar |  -.1343825   .0247072    -5.44   0.000    -.1828129    -.085952
           time |   .2353157   .0167395    14.06   0.000     .2025035     .268128
          _cons |   11.72298   .0398381   294.27   0.000      11.6449    11.80107
---------------------------------------------------------------------------------

. est sto UC

. reg logdefincome logurbanisation OCCUPATION RO_3 RO5 mar time if CASTE==3 [aweight=weight], absorb(STATEID)
(sum of wgt is 164,647,900.89105)

Linear regression, absorbing indicators         Number of obs     =     30,017
                                                F(6, 29980)       =     638.23
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2020
                                                Adj R-squared     =     0.2011
                                                Root MSE          =     .81445

---------------------------------------------------------------------------------
   logdefincome |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
logurbanisation |   .2515227   .0083876    29.99   0.000     .2350827    .2679627
     OCCUPATION |   -.008117   .0002117   -38.34   0.000     -.008532   -.0077021
           RO_3 |   .1855754   .0108907    17.04   0.000     .1642291    .2069216
            RO5 |  -.0011359   .0004454    -2.55   0.011    -.0020089    -.000263
            mar |  -.1450388   .0148359    -9.78   0.000    -.1741178   -.1159597
           time |   .2569152   .0097133    26.45   0.000     .2378768    .2759537
          _cons |   11.29003   .0253479   445.40   0.000     11.24035    11.33971
---------------------------------------------------------------------------------

. est sto OBC

. reg logdefincome logurbanisation OCCUPATION RO_3 RO5 mar time if CASTE==4 [aweight=weight], absorb(STATEID)
(sum of wgt is 137,986,090.04941)

Linear regression, absorbing indicators         Number of obs     =     24,288
                                                F(6, 24253)       =     467.46
                                                Prob > F          =     0.0000
                                                R-squared         =     0.2242
                                                Adj R-squared     =     0.2231
                                                Root MSE          =     .74137

---------------------------------------------------------------------------------
   logdefincome |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
logurbanisation |   .1881318   .0084703    22.21   0.000     .1715295    .2047341
     OCCUPATION |  -.0053109   .0002373   -22.38   0.000     -.005776   -.0048458
           RO_3 |   .1522171   .0107964    14.10   0.000     .1310555    .1733787
            RO5 |  -.0003801   .0004439    -0.86   0.392    -.0012502      .00049
            mar |  -.1621373   .0149063   -10.88   0.000    -.1913545   -.1329201
           time |   .3381171   .0098089    34.47   0.000      .318891    .3573431
          _cons |   10.88021   .0268017   405.95   0.000     10.82768    10.93275
---------------------------------------------------------------------------------

. est sto Dalit

. suest Brahmin UC OBC Dalit, vce(cluster STATE_DISTID)

Simultaneous results for Brahmin, UC, OBC, Dalit

                                                Number of obs     =     69,248

                            (Std. Err. adjusted for 367 clusters in STATE_DISTID)
---------------------------------------------------------------------------------
                |               Robust
                |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
Brahmin_mean    |
logurbanisation |   .2391378   .0761168     3.14   0.002     .0899516     .388324
     OCCUPATION |  -.0124496   .0007918   -15.72   0.000    -.0140016   -.0108977
           RO_3 |  -.0233625   .0556035    -0.42   0.674    -.1323434    .0856185
            RO5 |   .0033383   .0020592     1.62   0.105    -.0006977    .0073743
            mar |   .0452835   .0628542     0.72   0.471    -.0779085    .1684755
           time |   .1676947   .0518206     3.24   0.001     .0661282    .2692612
          _cons |   11.88449   .1462376    81.27   0.000     11.59786    12.17111
----------------+----------------------------------------------------------------
Brahmin_lnvar   |
          _cons |  -.3048372    .049098    -6.21   0.000    -.4010676   -.2086068
----------------+----------------------------------------------------------------
UC_mean         |
logurbanisation |   .2580549   .0830582     3.11   0.002     .0952638     .420846
     OCCUPATION |  -.0126262   .0007136   -17.69   0.000    -.0140247   -.0112276
           RO_3 |   .2005149   .0441338     4.54   0.000     .1140142    .2870156
            RO5 |   .0022378   .0016129     1.39   0.165    -.0009234     .005399
            mar |  -.1343825   .0326064    -4.12   0.000    -.1982898   -.0704751
           time |   .2353157    .053953     4.36   0.000     .1295697    .3410617
          _cons |   11.72298   .1299617    90.20   0.000     11.46826     11.9777
----------------+----------------------------------------------------------------
UC_lnvar        |
          _cons |  -.2981787   .0535308    -5.57   0.000    -.4030972   -.1932602
----------------+----------------------------------------------------------------
OBC_mean        |
logurbanisation |   .2515227   .0626357     4.02   0.000      .128759    .3742864
     OCCUPATION |   -.008117   .0005712   -14.21   0.000    -.0092365   -.0069975
           RO_3 |   .1855754   .0198042     9.37   0.000     .1467598     .224391
            RO5 |  -.0011359   .0008889    -1.28   0.201    -.0028782    .0006063
            mar |  -.1450388   .0282333    -5.14   0.000    -.2003751   -.0897024
           time |   .2569152   .0306815     8.37   0.000     .1967807    .3170498
          _cons |   11.29003   .1190317    94.85   0.000     11.05673    11.52333
----------------+----------------------------------------------------------------
OBC_lnvar       |
          _cons |  -.4104783   .0328025   -12.51   0.000      -.47477   -.3461867
----------------+----------------------------------------------------------------
Dalit_mean      |
logurbanisation |   .1881318   .0805667     2.34   0.020      .030224    .3460396
     OCCUPATION |  -.0053109   .0008276    -6.42   0.000    -.0069329   -.0036889
           RO_3 |   .1522171   .0248261     6.13   0.000     .1035588    .2008754
            RO5 |  -.0003801   .0009132    -0.42   0.677      -.00217    .0014099
            mar |  -.1621373   .0315722    -5.14   0.000    -.2240177   -.1002569
           time |   .3381171   .0401445     8.42   0.000     .2594353    .4167988
          _cons |   10.88021   .1691854    64.31   0.000     10.54862    11.21181
----------------+----------------------------------------------------------------
Dalit_lnvar     |
          _cons |  -.5985151   .0501537   -11.93   0.000    -.6968145   -.5002157
---------------------------------------------------------------------------------

. test [Brahmin_mean]logurbanisation=[UC_mean]logurbanisation=[OBC_mean]logurbanisation=[Dalit_mean]logurbanisation

 ( 1)  [Brahmin_mean]logurbanisation - [UC_mean]logurbanisation = 0
 ( 2)  [Brahmin_mean]logurbanisation - [OBC_mean]logurbanisation = 0
 ( 3)  [Brahmin_mean]logurbanisation - [Dalit_mean]logurbanisation = 0

           chi2(  3) =    1.01
         Prob > chi2 =    0.7987

Last edited by Yatharth Garg; 22 May 2021, 10:29. Reason: Repetition

Comment

Joro Kolev

Join Date: Aug 2018

Posts: 3047
#15

22 May 2021, 12:06

Very good then, so my procedure works under Stata 16 as well.

Yes, this is called a Chow test.

I did not understand this question "Is it also applicable for regression models for different groups (CASTE) within the same panel dataset (two time periods)," the answer is probably Yes, but if you want ask again, and ask specifically what you want to do, and not at such great level of generality.

In general the Chow test of stability of coefficients can be applied to any type of data, including panel data.
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