compare the coefficients of the independent variable between two subgroup regressions

[Alice Yang]

Hi again,

I'm encountering a problem using -chowtest-. I'm running two xtreg regressions with firm and year F.E., one subsample with high dummy ==1, the other with high dummy ==0. I'm using -chowtest- because -suest- doesn't support -xtreg-, so I can't use -test- or -lincom- afterwards.

chowtest y x cotrols i.firm i.year, group(high)

I get the following error message

maxvar too small
    You have attempted to use an interaction with too many levels or attempted to fit a model with too
    many variables.  You need to increase maxvar; it is currently 5000.  Use set maxvar; see help 
    maxvar.

    If you are using factor variables and included an interaction that has lots of missing cells, try
    set emptycells drop to reduce the required matrix size; see help set emptycells.

    If you are using factor variables, you might have accidentally treated a continuous variable as a
    categorical, resulting in lots of categories.  Use the c. operator on such variables.
r(907);

I think what stata means "too many levels" is that I control for firm F.E., and indeed if I delete i.firm, it works. With the two-way F.E. model, I need both firm and year F.E., I wonder what can I do to make it work? Thanks!

[Carlo Lazzaro]

Alice:
while it's true that -suest- does not support -xtreg, fe-, you may want to consider -sureg-, using -regress- with -i.panelvar- and -i.year- in addition to ther predictors and invoking -cluster()- just before typing -sureg-:

use "https://www.stata-press.com/data/r17/nlswork.dta"
. regress ln_wage i.idcode i.year c.age##c.age if idcode<=20 & nev_mar==0 & year>=70

      Source |       SS           df       MS      Number of obs   =       131
-------------+----------------------------------   F(30, 100)      =      7.75
       Model |  17.9319848        30  .597732825   Prob > F        =    0.0000
    Residual |  7.71722779       100  .077172278   R-squared       =    0.6991
-------------+----------------------------------   Adj R-squared   =    0.6089
       Total |  25.6492125       130  .197301635   Root MSE        =     .2778

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      idcode |
          2  |  -.3985991   .1162129    -3.43   0.001    -.6291622   -.1680361
          4  |  -2.153039   .8993956    -2.39   0.019    -3.937414    -.368664
          5  |  -2.115848   .9026901    -2.34   0.021     -3.90676   -.3249368
          6  |  -1.949703    .748923    -2.60   0.011    -3.435545   -.4638616
          7  |  -1.601565    .398199    -4.02   0.000    -2.391581   -.8115498
          9  |   .0267441   .1231572     0.22   0.829    -.2175963    .2710845
         10  |  -.7165237   .1445676    -4.96   0.000    -1.003342   -.4297056
         12  |  -.5660006   .5844716    -0.97   0.335    -1.725576    .5935743
         13  |  -1.197846   .5912625    -2.03   0.045    -2.370894   -.0247985
         14  |  -1.393738   .5844716    -2.38   0.019    -2.553313   -.2341635
         15  |  -.6671047   .4498168    -1.48   0.141    -1.559528     .225319
         16  |  -.9542889   .4674196    -2.04   0.044    -1.881636   -.0269416
         17  |  -.8061581   .4731089    -1.70   0.091    -1.744793    .1324766
         18  |  -1.761373   .4848091    -3.63   0.000     -2.72322   -.7995251
         19  |  -1.198246   .4639306    -2.58   0.011    -2.118671   -.2778205
         20  |  -1.057955   .4505725    -2.35   0.021    -1.951878   -.1640323
             |
        year |
         71  |  -.3846318   .2400682    -1.60   0.112    -.8609202    .0916566
         72  |  -.6422765   .3389681    -1.89   0.061     -1.31478    .0302266
         73  |  -.9147847   .4531278    -2.02   0.046    -1.813777   -.0157921
         75  |  -1.637065    .744296    -2.20   0.030    -3.113727    -.160403
         77  |  -2.468558   1.034075    -2.39   0.019    -4.520133   -.4169825
         78  |  -2.718327   1.182146    -2.30   0.024    -5.063671   -.3729843
         80  |  -3.497179   1.475272    -2.37   0.020    -6.424078    -.570281
         82  |   -4.19537   1.769693    -2.37   0.020    -7.706391     -.68435
         83  |  -4.282855   1.916492    -2.23   0.028     -8.08512   -.4805904
         85  |  -4.744166   2.209252    -2.15   0.034    -9.127259   -.3610736
         87  |  -5.472591   2.504624    -2.18   0.031    -10.44169    -.503488
         88  |  -5.770168   2.746684    -2.10   0.038    -11.21951    -.320824
             |
         age |   .5584909   .1664175     3.36   0.001     .2283232    .8886585
             |
 c.age#c.age |  -.0036283   .0011315    -3.21   0.002    -.0058731   -.0013835
             |
       _cons |  -7.288003   2.913776    -2.50   0.014    -13.06885   -1.507155
------------------------------------------------------------------------------

. est store model1

. regress ln_wage i.idcode i.year c.age##c.age if idcode<=20 & nev_mar==1 & year>=70
note: age omitted because of collinearity.

      Source |       SS           df       MS      Number of obs   =        37
-------------+----------------------------------   F(22, 14)       =     14.33
       Model |  1.92554289        22  .087524677   Prob > F        =    0.0000
    Residual |  .085521053        14  .006108647   R-squared       =    0.9575
-------------+----------------------------------   Adj R-squared   =    0.8906
       Total |  2.01106394        36  .055862887   Root MSE        =    .07816

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      idcode |
          3  |   .2483247   .8863086     0.28   0.783    -1.652618    2.149268
          4  |    1.02995   .8623204     1.19   0.252    -.8195433    2.879443
          5  |   .5474355   .8863086     0.62   0.547    -1.353507    2.448378
          9  |   .1263577   .0960831     1.32   0.210      -.07972    .3324354
         10  |   .0511744   .0982263     0.52   0.611    -.1595002    .2618489
         16  |   .5789633   .3893933     1.49   0.159    -.2562023    1.414129
         17  |   .5835921   .4089031     1.43   0.175    -.2934178    1.460602
         19  |   .6367364   .4089031     1.56   0.142    -.2402735    1.513746
         20  |   .6474642   .4059241     1.60   0.133    -.2231565    1.518085
             |
        year |
         71  |   .0966576   .1510702     0.64   0.533    -.2273557    .4206709
         72  |   .1935223    .308364     0.63   0.540    -.4678528    .8548974
         73  |   .2529087   .4907068     0.52   0.614    -.7995526     1.30537
         75  |   .0950733   .8557801     0.11   0.913    -1.740392    1.930539
         77  |   .4103127    1.28329     0.32   0.754     -2.34207    3.162695
         78  |   .4022728   1.496635     0.27   0.792     -2.80769    3.612236
         80  |   .4962802    1.94397     0.26   0.802    -3.673121    4.665681
         82  |   .6470116   2.418671     0.27   0.793    -4.540522    5.834545
         83  |    .713633   2.666252     0.27   0.793     -5.00491    6.432176
         85  |   .9464119   3.181843     0.30   0.770    -5.877962    7.770786
         87  |   .8637048   3.724644     0.23   0.820    -7.124861    8.852271
         88  |   1.014173   4.006242     0.25   0.804    -7.578361    9.606707
             |
         age |          0  (omitted)
             |
 c.age#c.age |  -.0007645   .0033937    -0.23   0.825    -.0080433    .0065142
             |
       _cons |   1.698924   1.102326     1.54   0.146    -.6653304    4.063179
------------------------------------------------------------------------------

. est store model2

. suest model1 model2, cluster()

Simultaneous results for model1, model2                    Number of obs = 168

------------------------------------------------------------------------------
             |               Robust
             | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
model1_mean  |
      idcode |
          2  |  -.3985991   .1096519    -3.64   0.000     -.613513   -.1836853
          4  |  -2.153039    1.05238    -2.05   0.041    -4.215666   -.0904124
          5  |  -2.115848    1.03228    -2.05   0.040     -4.13908   -.0926169
          6  |  -1.949703   .8678963    -2.25   0.025    -3.650749   -.2486579
          7  |  -1.601565   .5637183    -2.84   0.004    -2.706433   -.4966976
          9  |   .0267441   .1029155     0.26   0.795    -.1749666    .2284548
         10  |  -.7165237   .1376904    -5.20   0.000    -.9863919   -.4466555
         12  |  -.5660006   .6201784    -0.91   0.361    -1.781528    .6495267
         13  |  -1.197846    .675193    -1.77   0.076      -2.5212    .1255074
         14  |  -1.393738   .6189753    -2.25   0.024    -2.606908   -.1805692
         15  |  -.6671047    .510464    -1.31   0.191    -1.667596    .3333862
         16  |  -.9542889   .5254206    -1.82   0.069    -1.984094    .0755166
         17  |  -.8061581   .5201381    -1.55   0.121     -1.82561    .2132939
         18  |  -1.761373   .5318271    -3.31   0.001    -2.803734   -.7190106
         19  |  -1.198246   .5243101    -2.29   0.022    -2.225874   -.1706167
         20  |  -1.057955   .5064651    -2.09   0.037    -2.050609   -.0653019
             |
        year |
         71  |  -.3846318   .2663293    -1.44   0.149    -.9066277     .137364
         72  |  -.6422765   .3893245    -1.65   0.099    -1.405339    .1207856
         73  |  -.9147847   .5399805    -1.69   0.090    -1.973127    .1435576
         75  |  -1.637065   .8949692    -1.83   0.067    -3.391172    .1170422
         77  |  -2.468558   1.240131    -1.99   0.047    -4.899169   -.0379463
         78  |  -2.718327   1.415795    -1.92   0.055    -5.493234    .0565792
         80  |  -3.497179   1.761567    -1.99   0.047    -6.949787   -.0445724
         82  |   -4.19537   2.107863    -1.99   0.047    -8.326705   -.0640354
         83  |  -4.282855   2.278382    -1.88   0.060    -8.748402     .182691
         85  |  -4.744166   2.609252    -1.82   0.069    -9.858206     .369873
         87  |  -5.472591   3.005303    -1.82   0.069    -11.36288    .4176946
         88  |  -5.770168   3.246711    -1.78   0.076     -12.1336    .5932698
             |
         age |   .5584909   .1880901     2.97   0.003      .189841    .9271407
             |
 c.age#c.age |  -.0036283   .0011017    -3.29   0.001    -.0057877    -.001469
             |
       _cons |  -7.288003   3.300552    -2.21   0.027    -13.75697   -.8190393
-------------+----------------------------------------------------------------
model1_lnvar |
       _cons |  -2.561715   .1597886   -16.03   0.000    -2.874895   -2.248535
-------------+----------------------------------------------------------------
model2_mean  |
      idcode |
          3  |   .2483247   .7219233     0.34   0.731    -1.166619    1.663268
          4  |    1.02995   .7106266     1.45   0.147    -.3628526    2.422752
          5  |   .5474355   .7220786     0.76   0.448    -.8678126    1.962684
          9  |   .1263577   .0629834     2.01   0.045     .0029125    .2498029
         10  |   .0511744   .0339501     1.51   0.132    -.0153667    .1177154
         16  |   .5789633   .3086062     1.88   0.061    -.0258937     1.18382
         17  |   .5835921   .3278443     1.78   0.075    -.0589709    1.226155
         19  |   .6367364   .3258607     1.95   0.051    -.0019389    1.275412
         20  |   .6474642   .3222265     2.01   0.045     .0159119    1.279017
             |
        year |
         71  |   .0966576   .1326032     0.73   0.466    -.1632399    .3565551
         72  |   .1935223   .2654824     0.73   0.466    -.3268137    .7138583
         73  |   .2529087    .415236     0.61   0.542     -.560939    1.066756
         75  |   .0950733   .6845416     0.14   0.890    -1.246604     1.43675
         77  |   .4103127   1.075616     0.38   0.703    -1.697857    2.518482
         78  |   .4022728   1.253203     0.32   0.748     -2.05396    2.858505
         80  |   .4962802   1.625338     0.31   0.760    -2.689325    3.681885
         82  |   .6470116   2.020067     0.32   0.749    -3.312247     4.60627
         83  |    .713633   2.225899     0.32   0.749    -3.649048    5.076314
         85  |   .9464119   2.654492     0.36   0.721    -4.256297     6.14912
         87  |   .8637048   3.105654     0.28   0.781    -5.223266    6.950675
         88  |   1.014173   3.339698     0.30   0.761    -5.531514     7.55986
             |
         age |          0  (omitted)
             |
 c.age#c.age |  -.0007645   .0028199    -0.27   0.786    -.0062915    .0047625
             |
       _cons |   1.698924   .9136627     1.86   0.063    -.0918218     3.48967
-------------+----------------------------------------------------------------
model2_lnvar |
       _cons |   -5.09805   .1517883   -33.59   0.000     -5.39555    -4.80055
------------------------------------------------------------------------------


. test [model1_mean]c.age#c.age=[model2_mean]c.age#c.age

 ( 1)  [model1_mean]c.age#c.age - [model2_mean]c.age#c.age = 0

           chi2(  1) =    0.89
         Prob > chi2 =    0.3442

.

[Alice Yang]

Hi Carlo,

Thanks a lot for your help. I have a new problem now. My code

reg y i.x controls i.firm i.year if high==1
est store model1

reg y i.x controls i.firm i.year if high==0
est store model2

suest model1 model2, cluster()

test [model1_mean]x = [model2_mean]x

x is a dummy variable, so as high. Then I get this error message

firm: factor variable base category conflict
r(198);

Can you spot anything wrong here? Thanks!

[Andrew Musau]

I have encountered this situation before. A trick is to clone the categorical variables that trigger the error and use the cloned variables in the second estimation. #2 of https://www.statalist.org/forums/for...t-time-periods illustrates.

[Alice Yang]

Hi Andrew,

Thanks for your trick, it works well!

[Alice Yang]

hello again,

It's been a while since I asked this question, I have another problem now. When I use the following code

reg y i.x controls i.firm i.year if high==1
est store model1

gen FIRM = firm

reg y i.x controls i.FIRM i.year if high==0
est store model2

suest model1 model2, cluster()

test [model1_mean]x = [model2_mean]x

I got this error message

[x] not found
r(111);

If I use i.x, then

i:  operator invalid
r(198);

I don't know why x is not found, it is used in estimating model1 and model2, so what's wrong here? x is a dummy variable.

Thanks a lot for any advice!

[Carlo Lazzaro]

Alice:
I cannot replicate your problem:

. sysuse auto
(1978 automobile data)


. regress price mpg trunk if foreign==0

      Source |       SS           df       MS      Number of obs   =        52
-------------+----------------------------------   F(2, 49)        =      8.42
       Model |   125089266         2    62544633   Prob > F        =    0.0007
    Residual |   364105535        49   7430725.2   R-squared       =    0.2557
-------------+----------------------------------   Adj R-squared   =    0.2253
       Total |   489194801        51  9592054.92   Root MSE        =    2725.9

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |   -307.292   107.8128    -2.85   0.006      -523.95   -90.63405
       trunk |   36.35242   118.7538     0.31   0.761    -202.2924    274.9972
       _cons |   11628.88   3572.654     3.25   0.002     4449.364     18808.4
------------------------------------------------------------------------------

. estimate store foreign_0

. regress price mpg trunk if foreign==1

      Source |       SS           df       MS      Number of obs   =        22
-------------+----------------------------------   F(2, 19)        =      7.30
       Model |  62721024.2         2  31360512.1   Prob > F        =    0.0044
    Residual |  81642188.6        19  4296957.29   R-squared       =    0.4345
-------------+----------------------------------   Adj R-squared   =    0.3749
       Total |   144363213        21   6874438.7   Root MSE        =    2072.9

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -232.7421   70.27696    -3.31   0.004    -379.8335   -85.65075
       trunk |   158.6694   144.4289     1.10   0.286    -143.6237    460.9625
       _cons |   10340.07   2692.813     3.84   0.001     4703.943    15976.19
------------------------------------------------------------------------------

. estimate store foreign_1

. suest foreign_0 foreign_1 , cluster()

Simultaneous results for foreign_0, foreign_1               Number of obs = 74

---------------------------------------------------------------------------------
                |               Robust
                | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
foreign_0_mean  |
            mpg |   -307.292   111.5024    -2.76   0.006    -525.8328   -88.75125
          trunk |   36.35242   89.39376     0.41   0.684    -138.8561     211.561
          _cons |   11628.88   3479.299     3.34   0.001     4809.581    18448.18
----------------+----------------------------------------------------------------
foreign_0_lnvar |
          _cons |   15.82113   .2967708    53.31   0.000     15.23947    16.40279
----------------+----------------------------------------------------------------
foreign_1_mean  |
            mpg |  -232.7421   73.49488    -3.17   0.002    -376.7894   -88.69479
          trunk |   158.6694   119.9163     1.32   0.186    -76.36216     393.701
          _cons |   10340.07   2334.061     4.43   0.000     5765.389    14914.74
----------------+----------------------------------------------------------------
foreign_1_lnvar |
          _cons |   15.27342   .2284388    66.86   0.000     14.82569    15.72115
---------------------------------------------------------------------------------

. test [foreign_0_mean]mpg = [foreign_1_mean]mpg

 ( 1)  [foreign_0_mean]mpg - [foreign_1_mean]mpg = 0

           chi2(  1) =    0.31
         Prob > chi2 =    0.5767

.

[Rich Goldstein]

is "x" an actual variable in your data or is, e.g., a local (which would call for slightly different syntax)

[Carlo Lazzaro]

Alice:
as an aside to Rich's helpful insight, owing Andrew Musau so much as usual, I applied his astute trick while elaborating on my previous example:

. sysuse auto.dta
(1978 automobile data)

. clonevar new_rep78=rep78
(5 missing values generated)

.  regress price mpg trunk i.rep78 if foreign==0

      Source |       SS           df       MS      Number of obs   =        48
-------------+----------------------------------   F(6, 41)        =      3.13
       Model |   150261808         6  25043634.7   Prob > F        =    0.0128
    Residual |   327705889        41  7992826.55   R-squared       =    0.3144
-------------+----------------------------------   Adj R-squared   =    0.2140
       Total |   477967697        47  10169525.5   Root MSE        =    2827.2

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |  -421.9874   133.0415    -3.17   0.003    -690.6701   -153.3046
       trunk |   4.537399   137.4309     0.03   0.974    -273.0099    282.0847
             |
       rep78 |
          2  |   584.1071   2346.868     0.25   0.805    -4155.489    5323.704
          3  |   1166.417   2234.737     0.52   0.605    -3346.725     5679.56
          4  |    201.588   2406.236     0.08   0.934    -4657.904     5061.08
          5  |   4277.323   3225.064     1.33   0.192    -2235.824    10790.47
             |
       _cons |   13387.67   4145.464     3.23   0.002     5015.732     21759.6
------------------------------------------------------------------------------

. estimate store foreign_0

.  regress price mpg trunk i.new_rep78 if foreign==1

      Source |       SS           df       MS      Number of obs   =        21
-------------+----------------------------------   F(4, 16)        =      3.28
       Model |    44485047         4  11121261.8   Prob > F        =    0.0381
    Residual |  54170307.5        16  3385644.22   R-squared       =    0.4509
-------------+----------------------------------   Adj R-squared   =    0.3136
       Total |  98655354.6        20  4932767.73   Root MSE        =      1840

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         mpg |   -197.077   67.44553    -2.92   0.010    -340.0551   -54.09885
       trunk |   151.8929   134.1417     1.13   0.274    -132.4748    436.2607
             |
   new_rep78 |
          4  |   2043.128   1255.692     1.63   0.123    -618.8201    4705.076
          5  |   2122.739   1242.792     1.71   0.107    -511.8621     4757.34
             |
       _cons |   7553.783   2712.066     2.79   0.013      1804.46    13303.11
------------------------------------------------------------------------------

. estimate store foreign_1

. suest foreign_0 foreign_1, cluster()

Simultaneous results for foreign_0, foreign_1               Number of obs = 69

---------------------------------------------------------------------------------
                |               Robust
                | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
foreign_0_mean  |
            mpg |  -421.9874   126.1393    -3.35   0.001    -669.2159   -174.7588
          trunk |   4.537399   103.6611     0.04   0.965    -198.6347    207.7095
                |
          rep78 |
             2  |   584.1071    1237.14     0.47   0.637    -1840.643    3008.858
             3  |   1166.417   1165.787     1.00   0.317    -1118.484    3451.319
             4  |    201.588   1080.791     0.19   0.852    -1916.724      2319.9
             5  |   4277.323   1760.797     2.43   0.015     826.2246    7728.422
                |
          _cons |   13387.67   3371.028     3.97   0.000     6780.573    19994.76
----------------+----------------------------------------------------------------
foreign_0_lnvar |
          _cons |   15.89406   .2851599    55.74   0.000     15.33515    16.45296
----------------+----------------------------------------------------------------
foreign_1_mean  |
            mpg |   -197.077   66.48022    -2.96   0.003    -327.3758   -66.77815
          trunk |   151.8929   94.27177     1.61   0.107    -32.87633    336.6622
                |
      new_rep78 |
             4  |   2043.128   948.4507     2.15   0.031     184.1986    3902.057
             5  |   2122.739   1040.569     2.04   0.041     83.26023    4162.218
                |
          _cons |   7553.783   2156.595     3.50   0.000     3326.934    11780.63
----------------+----------------------------------------------------------------
foreign_1_lnvar |
          _cons |   15.03505   .2229259    67.44   0.000     14.59813    15.47198
---------------------------------------------------------------------------------

. test [foreign_0_mean]2.rep78 = [foreign_1_mean]4.new_rep78

 ( 1)  [foreign_0_mean]2.rep78 - [foreign_1_mean]4.new_rep78 = 0

           chi2(  1) =    0.88
         Prob > chi2 =    0.3493

As far as your second error message is concerned, I tried to replicate it via:

. test [foreign_0_mean]i.rep78 = [foreign_1_mean]i.new_rep78
i:  operator invalid
r(198);

This error message makes sense as Stata cannot understand which levels of te categorical variable I'm going to compare.

[Alice Yang]

Hi Carlo,

My bad... I've spelt the independent variable wrong, that's why stata says the variable is not found... For simplicity, I use x to represent the dummy independent variable, the actual variable is of another name. Sorry for causing any confusion, and thanks a lot for your help!