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  • #1

    Comparing regression coefficients across regression models

    Dear Stata Users,

    I am trying to test the difference between the coefficients across two regression models. I noted that suest option if frequently adopted to compare coefficients (https://stats.oarc.ucla.edu/stata/co...s-using-suest/). Unfortunately, I am using FE estimators and suest option is not available on FE models.

    However, several papers also use simple t-tests to compare coefficients. Generally, I use the t-test to test differences among the means of two variables.
    However, I do not know how to apply the test to compare the coefficients of specific independent variables included in my models. Any suggestion would be greatly appreciated.

    Thank you in advance for your support,
    Nicola
    Tags: None
  • #2
    This is not clear. Do the regressions involve the same set of variables? Please show the exact commands that you ran.

    Unfortunately, I am using FE estimators and suest option is not available on FE models.
    suest places restrictions on the estimator, not the model. So if you were to estimate the models using regress, adding the fixed effects as indicators, you may use suest. The issue is that the fixed effects dimension(s) may be too large to allow this, in which case you need to find alternative means. But without more information, it is difficult to advise you.
    Last edited by Andrew Musau; 30 Dec 2023, 13:45.
    • 1 like

    Comment

    • #3
      Nicola:
      Andrew pointed you out in the right direction.
      I shamelessly follow his guidance in the following toy-example (with a negligible number of fixed effect):
      Code:
      . use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. regress ln_wage i.idcode i.year age if idcode<=3

      Source |       SS           df       MS      Number of obs   =        39
-------------+----------------------------------   F(17, 21)       =      2.68
       Model |  3.54194923        17  .208349955   Prob > F        =    0.0171
    Residual |  1.63378973        21  .077799511   R-squared       =    0.6843
-------------+----------------------------------   Adj R-squared   =    0.4288
       Total |  5.17573896        38  .136203657   Root MSE        =    .27893

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      idcode |
          2  |  -.3898423     .11632    -3.35   0.003     -.631743   -.1479415
          3  |  -2.247118   2.111457    -1.06   0.299    -6.638133    2.143897
             |
        year |
         69  |  -.0920902   .5314565    -0.17   0.864    -1.197315    1.013134
         70  |  -.8648493    .779214    -1.11   0.280    -2.485314    .7556149
         71  |  -1.248506    1.09967    -1.14   0.269    -3.535396    1.038383
         72  |   -1.39387   1.443494    -0.97   0.345    -4.395779     1.60804
         73  |  -1.520276    1.79214    -0.85   0.406    -5.247236    2.206684
         75  |  -2.049717   2.495803    -0.82   0.421    -7.240024     3.14059
         77  |  -2.657565   3.203292    -0.83   0.416    -9.319175    4.004045
         78  |  -2.751196   3.557758    -0.77   0.448    -10.14996    4.647567
         80  |  -3.324016   4.267534    -0.78   0.445    -12.19884    5.550808
         82  |  -4.027975   4.983977    -0.81   0.428    -14.39272    6.336774
         83  |  -4.207353   5.333467    -0.79   0.439     -15.2989    6.884199
         85  |  -4.730657   6.044586    -0.78   0.443    -17.30106    7.839747
         87  |  -5.407995   6.755956    -0.80   0.432    -19.45777    8.641785
         88  |  -5.901929   7.348904    -0.80   0.431    -21.18481    9.380954
             |
         age |   .3010572   .3561559     0.85   0.407    -.4396095    1.041724
       _cons |  -2.882579   5.734884    -0.50   0.620    -14.80892    9.043766
------------------------------------------------------------------------------

. estimate store A

. regress ln_wage i.idcode i.year c.age##c.age if idcode<=3

      Source |       SS           df       MS      Number of obs   =        39
-------------+----------------------------------   F(18, 20)       =      4.86
       Model |  4.21278813        18  .234043785   Prob > F        =    0.0005
    Residual |  .962950828        20  .048147541   R-squared       =    0.8139
-------------+----------------------------------   Adj R-squared   =    0.6465
       Total |  5.17573896        38  .136203657   Root MSE        =    .21943

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      idcode |
          2  |  -.4183815   .0918256    -4.56   0.000    -.6099263   -.2268366
          3  |   .6579353   1.834332     0.36   0.724    -3.168414    4.484284
             |
        year |
         69  |   .3367906   .4335876     0.78   0.446    -.5676572    1.241238
         70  |   .2089384   .6771373     0.31   0.761    -1.203545    1.621422
         71  |   .3144116   .9610926     0.33   0.747    -1.690392    2.319216
         72  |   .5888124   1.253657     0.47   0.644     -2.02627    3.203894
         73  |   .8912873   1.550825     0.57   0.572    -2.343676    4.126251
         75  |   1.246958   2.152898     0.58   0.569    -3.243908    5.737823
         77  |   1.560689   2.761762     0.57   0.578    -4.200247    7.321624
         78  |   1.941522   3.068213     0.63   0.534    -4.458659    8.341703
         80  |    2.34498   3.684737     0.64   0.532    -5.341247    10.03121
         82  |   2.698954   4.315145     0.63   0.539     -6.30228    11.70019
         83  |   2.994437   4.618087     0.65   0.524    -6.638723     12.6276
         85  |   3.538578   5.245889     0.67   0.508    -7.404154    14.48131
         87  |   3.965153   5.878139     0.67   0.508    -8.296429    16.22674
         88  |    4.40786   6.407149     0.69   0.499    -8.957218    17.77294
             |
         age |   .0773019   .2865219     0.27   0.790    -.5203723    .6749761
             |
 c.age#c.age |  -.0045583   .0012212    -3.73   0.001    -.0071057    -.002011
             |
       _cons |   1.341224   4.651269     0.29   0.776    -8.361153     11.0436
------------------------------------------------------------------------------

. estimate store B

. suest A B

Simultaneous results for A, B                               Number of obs = 39

------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
A_mean       |
      idcode |
          2  |  -.3898423   .0906971    -4.30   0.000    -.5676053   -.2120792
          3  |  -2.247118   .6005261    -3.74   0.000    -3.424128   -1.070109
             |
        year |
         69  |  -.0920902   .1107847    -0.83   0.406    -.3092243    .1250438
         70  |  -.8648493   .2478246    -3.49   0.000    -1.350577   -.3791222
         71  |  -1.248506   .3829516    -3.26   0.001    -1.999078   -.4979351
         72  |   -1.39387   .4097095    -3.40   0.001    -2.196886    -.590854
         73  |  -1.520276   .5202896    -2.92   0.003    -2.540025   -.5005269
         75  |  -2.049717    .758806    -2.70   0.007    -3.536949   -.5624846
         77  |  -2.657565    .970228    -2.74   0.006    -4.559177   -.7559528
         78  |  -2.751196   1.082508    -2.54   0.011    -4.872872   -.6295199
         80  |  -3.324016   1.302378    -2.55   0.011     -5.87663   -.7714024
         82  |  -4.027975   1.530587    -2.63   0.008    -7.027869    -1.02808
         83  |  -4.207353   1.621794    -2.59   0.009    -7.386011   -1.028695
         85  |  -4.730657   1.858014    -2.55   0.011    -8.372297   -1.089018
         87  |  -5.407995   2.062526    -2.62   0.009    -9.450472   -1.365517
         88  |  -5.901929   2.215694    -2.66   0.008    -10.24461   -1.559248
             |
         age |   .3010572   .1107847     2.72   0.007     .0839232    .5181913
       _cons |  -2.882579   1.843797    -1.56   0.118    -6.496356    .7311975
-------------+----------------------------------------------------------------
A_lnvar      |
       _cons |   -2.55362   .1401788   -18.22   0.000    -2.828366   -2.278875
-------------+----------------------------------------------------------------
B_mean       |
      idcode |
          2  |  -.4183815   .0807647    -5.18   0.000    -.5766773   -.2600856
          3  |   .6579353   .6207428     1.06   0.289    -.5586983    1.874569
             |
        year |
         69  |   .3367906   .1004751     3.35   0.001      .139863    .5337182
         70  |   .2089384   .2173278     0.96   0.336    -.2170163     .634893
         71  |   .3144116   .3300279     0.95   0.341    -.3324311    .9612544
         72  |   .5888124    .421578     1.40   0.163    -.2374653     1.41509
         73  |   .8912873   .5188029     1.72   0.086    -.1255477    1.908122
         75  |   1.246958   .7300432     1.71   0.088    -.1839004    2.677816
         77  |   1.560689   .9381513     1.66   0.096     -.278054    3.399431
         78  |   1.941522   1.044322     1.86   0.063    -.1053105    3.988355
         80  |    2.34498   1.262371     1.86   0.063    -.1292219    4.819183
         82  |   2.698954   1.466749     1.84   0.066    -.1758208     5.57373
         83  |   2.994437   1.571986     1.90   0.057    -.0865997    6.075474
         85  |   3.538578   1.819024     1.95   0.052    -.0266442    7.103801
         87  |   3.965153   2.031644     1.95   0.051    -.0167963    7.947103
         88  |    4.40786   2.174655     2.03   0.043     .1456145    8.670106
             |
         age |   .0773019   .0866033     0.89   0.372    -.0924374    .2470412
             |
 c.age#c.age |  -.0045583   .0007208    -6.32   0.000    -.0059712   -.0031455
             |
       _cons |   1.341224   1.443448     0.93   0.353    -1.487882     4.17033
-------------+----------------------------------------------------------------
B_lnvar      |
       _cons |  -3.033485   .1518706   -19.97   0.000    -3.331146   -2.735824
------------------------------------------------------------------------------

. test [A_mean]age=[B_mean]age

 ( 1)  [A_mean]age - [B_mean]age = 0

           chi2(  1) =    7.71
         Prob > chi2 =    0.0055

.
      Last but not least, I do echo Andrew's advice to post what you typed and what Stata gave you back (as per FAQ). Thanks.
      Kind regards,
      Carlo
      (Stata 19.0)
      • 1 like

      Comment

      • #4
        Thank you very much Andrew Musau and Carlo Lazzaro for your repliesYes, the regressions involve the same set of variables. I have tried to use regress and add FE. Suest command gives me back the following warning message: "Code1: factor variable base category conflict". I had a similar issue with Country Dummies. I solved it by creating single dummies by each country (i.e. Country1-Country100) instead of i.Country. I have too many firm Codes to do the same with Code1. Do you know how to solve it?
        Below, I report the output (I Removed the dummies to fit within the character limit).


        Code:
        reg Kim100_w2 l.FGD l.ln_emp l.DEq l.Bize l.CEO_sep l.Firm_Age l.Capex_TA l.GDPgrowth  i.Period country1-country103 sector1-sector12 i.Code1 if F_Control==0 & Match1!=.

Source    SS    df    MS      Number of obs   =    1,513
            F(187, 1325)    =    43.62
Model    266277.871    187    1423.94583   Prob > F        =    0.0000
Residual    43255.7853    1,325    32.6458757   R-squared       =    0.8603
            Adj R-squared   =    0.8405
Total    309533.656    1,512    204.718026   Root MSE        =    5.7137

                
Kim10~2    Coefficient    Std. err.    t    P>t     [95% conf.    interval]
                
FGD    
L1.    .0568314    .0276084    2.06   0.040     .0026705    .1109923
    
ln_emp    
L1.    -1.437617    .4995122    -2.88   0.004    -2.417538    -.4576961
    
DEq    
L1.    -3.41e-07    .0000266    -0.01   0.990    -.0000525    .0000518
    
Bize    
L1.    .4937908    .1176362    4.20   0.000     .2630173    .7245643
    
CEO_sep    
L1.    -1.004342    .5641725    -1.78   0.075     -2.11111    .1024271
    
Firm_Age    
L1.    -.4290541    .1211534    -3.54   0.000    -.6667277    -.1913806
    
Capex_TA    
L1.    .0506036    .0630879    0.80   0.423    -.0731595    .1743667
    
GDPgrowth    
L1.    -.5306111    .1161777    -4.57   0.000    -.7585234    -.3026988
    
Period    
2010    -1.08526    .953616    -1.14   0.255    -2.956022    .7855021
2011    2.432828    .9297886    2.62   0.009     .6088093    4.256846
2012    2.688224    .9615374    2.80   0.005     .8019219    4.574525
2013    1.599915    1.007752    1.59   0.113    -.3770496    3.576879
2014    2.491208    1.095078    2.27   0.023     .3429332    4.639483
2015    2.800812    1.198602    2.34   0.020     .4494474    5.152178
2016    2.439761    1.305112    1.87   0.062    -.1205505    5.000072
2017    3.356287    1.415905    2.37   0.018     .5786267    6.133947
2018    3.707957    1.552137    2.39   0.017     .6630416    6.752872
2019    3.440156    1.664568    2.07   0.039     .1746796    6.705632
2020    3.541455    1.785838    1.98   0.048     .0380767    7.044834
    
country1    0    (omitted)
country2    0    (omitted)
country3    -.6832236    3.394753    -0.20   0.841      -7.3429    5.976453
country4    0    (omitted)
country5    0    (omitted)
country6    0    (omitted)
12244    0    (omitted)
    
_cons    40.38754    8.785796    4.60   0.000     23.15195    57.62313


eststo FF0

        Code:
        reg Kim100_w2 l.FGD l.ln_emp l.DEq l.Bize l.CEO_sep l.Firm_Age l.Capex_TA l.GDPgrowth  i.Period country1-country103 sector1-sector12 i.Code1 if  F_Control==0 & Match1!=.

Source    SS    df    MS      Number of obs   =    1,521
            F(194, 1326)    =    60.13
Model    604501.391    194    3115.98655   Prob > F        =    0.0000
Residual    68713.0211    1,326    51.8197746   R-squared       =    0.8979
            Adj R-squared   =    0.8830
Total    673214.412    1,520    442.904219   Root MSE        =    7.1986

                
Kim10~2    Coefficient    Std. err.    t    P>t     [95% conf.    interval]
                
FGD    
L1.    .0075365    .0298193    0.25   0.801    -.0509616    .0660346
    
ln_emp    
L1.    -.4734108    .7783526    -0.61   0.543    -2.000348    1.053526
    
DEq    
L1.    -.0001447    .0003354    -0.43   0.666    -.0008025    .0005132
    
Bize    
L1.    .0979694    .1262105    0.78   0.438    -.1496246    .3455633
    
CEO_sep    
L1.    1.592828    .7508731    2.12   0.034     .1197997    3.065857
    
Firm_Age    
L1.    -.2107377    1.011458    -0.21   0.835    -2.194969    1.773494
    
Capex_TA    
L1.    .3113552    .0999548    3.11   0.002     .1152684    .5074421
    
GDPgrowth    
L1.    -.0366181    .1436555    -0.25   0.799     -.318435    .2451988
    
Period    
2010    -1.11329    1.197386    -0.93   0.353    -3.462267    1.235686
2011    .413681    1.097471    0.38   0.706    -1.739288    2.56665
2012    .6869564    1.075042    0.64   0.523    -1.422011    2.795924
2013    .3675669    1.069122    0.34   0.731    -1.729789    2.464923
2014    1.539048    1.081356    1.42   0.155    -.5823062    3.660403
2015    2.00478    1.103212    1.82   0.069    -.1594513    4.169011
2016    2.597457    1.11329    2.33   0.020     .4134547    4.78146
2017    1.31635    1.0929    1.20   0.229    -.8276509    3.460351
2018    1.89807    1.112924    1.71   0.088    -.2852138    4.081353
2019    4.617067    1.129893    4.09   0.000     2.400495    6.833639
2020    5.537602    1.138261    4.86   0.000     3.304614    7.77059
    
country1    0    (omitted)
country2    -3.164635    3.378161    -0.94   0.349    -9.791758    3.462488
country3    0    (omitted)
country4    0    (omitted)
country5    0    (omitted)
country6    0    (omitted)
country7    0    (omitted)

    
_cons    65.72687    7.744485    8.49   0.000     50.53409    80.91965




eststo FF0



        Code:
        suest FF0 FF1, cluster (Code1)
Code1: factor variable base category conflict
r(198)

        Apart suest command, is there a way to just use a simple t-test to compare coefficients instead of suest?

        Thank you for your precious suggestions,
        All the best,
        N

        Last edited by Nicola Rossi; 02 Jan 2024, 11:48.

        Comment

        • #5
          You can either estimate both models jointly (equivalent to what suest does) or bootstrap the difference. For the former, you would need to duplicate the observations and create a sample dummy. Then interact this dummy with your variables and fixed effects. There are several examples in the forum, e.g., https://www.statalist.org/forums/for...-fixed-effects. Otherwise provide a data example if you cannot make progress.
          • 1 like

          Comment

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