Comparing two Coefficients

[Patrick Johannes]

Hello there,

i have split my sample into two parts and ran a fe regression for both of them.

is it possible to say that one effect ist stroger than the other? can i say that the coefficient of the governance variable in period 2 is stronger than in period 1?

Linear regression                               Number of obs     =      2,088
                                                F(53, 430)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.7361
                                                Root MSE          =     .09705

                                         (Std. Err. adjusted for 431 clusters in company_code)
----------------------------------------------------------------------------------------------
                             |               Robust
         return_volatility_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
            governance_score |  -.0248947   .0150816    -1.65   0.100    -.0545375    .0047481
              company_size_w |  -.0404233   .0086368    -4.68   0.000    -.0573988   -.0234478
            dividend_ratio_w |  -.8944752    .187322    -4.78   0.000    -1.262656   -.5262946
      earnings_smoothing_2_w |  -.0219127   .0050407    -4.35   0.000    -.0318202   -.0120053
                  leverage_w |   .0228574   .0284547     0.80   0.422    -.0330702    .0787849
research_development_ratio_w |   .0840555    .101191     0.83   0.407    -.1148351    .2829461
              sales_growth_w |  -.0268705   .0161192    -1.67   0.096    -.0585527    .0048118
         tangability_ratio_w |   .0415229   .0149298     2.78   0.006     .0121784    .0708674
             turnover_rate_w |   .0268959   .0016942    15.88   0.000      .023566    .0302258
                 blockholder |   .0008572   .0022735     0.38   0.706    -.0036114    .0053257
        trade_union_coverage |  -.0000485   .0004925    -0.10   0.922    -.0010165    .0009196
                  bank_power |    .387277   .0397159     9.75   0.000     .3092155    .4653385
                             |
                       sic_2 |
                         13  |  -.0304118   .0150801    -2.02   0.044    -.0600516    -.000772
                         20  |  -.1392726   .0161967    -8.60   0.000    -.1711072    -.107438
                         21  |  -.1314665   .0323268    -4.07   0.000    -.1950048   -.0679282
                         22  |  -.1170602   .0116354   -10.06   0.000    -.1399296   -.0941908
                         23  |  -.0864256   .0288507    -3.00   0.003    -.1431315   -.0297196
                         24  |  -.0144642   .0172295    -0.84   0.402    -.0483288    .0194003
                         25  |  -.0491051    .014703    -3.34   0.001    -.0780037   -.0202065
                         26  |  -.0932712   .0265203    -3.52   0.000    -.1453966   -.0411457
                         27  |  -.1102874   .0213453    -5.17   0.000    -.1522415   -.0683332
                         28  |  -.1001355   .0143351    -6.99   0.000    -.1283111     -.07196
                         29  |  -.0705352   .0149799    -4.71   0.000    -.0999782   -.0410922
                         30  |  -.0265549   .0369599    -0.72   0.473    -.0991994    .0460896
                         31  |  -.0848841   .0332142    -2.56   0.011    -.1501664   -.0196017
                         32  |   .0024467   .0159965     0.15   0.879    -.0289944    .0338879
                         33  |   .0167423   .0388873     0.43   0.667    -.0596906    .0931752
                         34  |  -.0953966   .0169065    -5.64   0.000    -.1286262    -.062167
                         35  |  -.0498152   .0162776    -3.06   0.002    -.0818087   -.0178216
                         36  |  -.0549001   .0180429    -3.04   0.002    -.0903634   -.0194368
                         37  |  -.0394992   .0181193    -2.18   0.030    -.0751127   -.0038858
                         38  |  -.1142142   .0159051    -7.18   0.000    -.1454755   -.0829528
                         39  |  -.0832297   .0223976    -3.72   0.000    -.1272521   -.0392072
                         50  |  -.1162061    .024314    -4.78   0.000    -.1639952   -.0684169
                         51  |  -.0762255   .0210122    -3.63   0.000     -.117525   -.0349261
                         52  |   -.090609   .0116039    -7.81   0.000    -.1134164   -.0678016
                         53  |  -.1292317   .0149522    -8.64   0.000    -.1586202   -.0998431
                         54  |  -.1221297   .0142309    -8.58   0.000    -.1501005   -.0941589
                         55  |  -.1201868   .0281467    -4.27   0.000     -.175509   -.0648646
                         56  |  -.0906343   .0237194    -3.82   0.000    -.1372546   -.0440139
                         57  |  -.1217428   .0272069    -4.47   0.000    -.1752178   -.0682678
                         58  |  -.1360863   .0194496    -7.00   0.000    -.1743144   -.0978583
                         59  |  -.0626834   .0200505    -3.13   0.002    -.1020925   -.0232742
                         70  |   .0141774   .0388447     0.36   0.715    -.0621716    .0905265
                         72  |  -.0498467   .0193437    -2.58   0.010    -.0878666   -.0118268
                         73  |  -.0595291   .0167802    -3.55   0.000    -.0925105   -.0265477
                         75  |  -.0240225   .0618428    -0.39   0.698    -.1455743    .0975293
                         78  |  -.0734657   .0236273    -3.11   0.002    -.1199051   -.0270264
                         79  |  -.0495513   .0308397    -1.61   0.109    -.1101666     .011064
                         80  |  -.1468875   .0238443    -6.16   0.000    -.1937534   -.1000217
                         82  |  -.0930031   .0181935    -5.11   0.000    -.1287624   -.0572438
                         87  |  -.0597639   .0310283    -1.93   0.055    -.1207499    .0012221
                             |
                        year |
                       2004  |  -.1906044    .014588   -13.07   0.000     -.219277   -.1619318
                       2005  |   -.490761   .0420629   -11.67   0.000    -.5734355   -.4080864
                       2006  |  -.7040922   .0631446   -11.15   0.000    -.8282028   -.5799817
                       2007  |  -.7784349   .0708597   -10.99   0.000    -.9177093   -.6391604
                       2008  |  -.3461531   .0470228    -7.36   0.000    -.4385762   -.2537299
                       2009  |          0  (omitted)
                             |
                       _cons |   -2.18514   .3043332    -7.18   0.000    -2.783305   -1.586974
----------------------------------------------------------------------------------------------

. 
end of do-file

. do "C:\Users\Paddy\AppData\Local\Temp\STD307c_000000.tmp"

. 
. regress return_volatility_w governance_score company_size_w dividend_ratio_w earnings_smoothing_2_w leverage_w resear
> ch_development_ratio_w sales_growth_w tangability_ratio_w turnover_rate_w blockholder trade_union_coverage bank_power
>  i.sic_2 i.year if year > 2010, vce (cluster company_code)
note: 2019.year omitted because of collinearity

Linear regression                               Number of obs     =      3,134
                                                F(54, 420)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.6752
                                                Root MSE          =     .06619

                                         (Std. Err. adjusted for 421 clusters in company_code)
----------------------------------------------------------------------------------------------
                             |               Robust
         return_volatility_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
            governance_score |  -.0195744   .0086024    -2.28   0.023    -.0364835   -.0026654
              company_size_w |  -.0251767   .0046063    -5.47   0.000    -.0342309   -.0161225
            dividend_ratio_w |  -.6324831   .0940964    -6.72   0.000    -.8174417   -.4475244
      earnings_smoothing_2_w |  -.0057561    .002902    -1.98   0.048    -.0114604   -.0000518
                  leverage_w |   .0344702   .0170789     2.02   0.044     .0008995    .0680409
research_development_ratio_w |   .2468165   .0671307     3.68   0.000     .1148625    .3787705
              sales_growth_w |   .0341093   .0120846     2.82   0.005     .0103555    .0578631
         tangability_ratio_w |   .0181575   .0102887     1.76   0.078    -.0020663    .0383813
             turnover_rate_w |   .0263781   .0017497    15.08   0.000     .0229387    .0298174
                 blockholder |   .0054793   .0015189     3.61   0.000     .0024937    .0084649
        trade_union_coverage |  -.0000215   .0003034    -0.07   0.944    -.0006179    .0005749
                  bank_power |  -.0966771   .0245319    -3.94   0.000    -.1448976   -.0484566
                             |
                       sic_2 |
                         21  |   .0304405   .0172305     1.77   0.078    -.0034283    .0643093
                         22  |  -.0055592   .0282167    -0.20   0.844    -.0610228    .0499044
                         23  |   .0420466   .0417709     1.01   0.315    -.0400596    .1241527
                         24  |   .0224067   .0157591     1.42   0.156    -.0085697    .0533832
                         25  |    .050406   .0108798     4.63   0.000     .0290203    .0717917
                         26  |   -.006852   .0167531    -0.41   0.683    -.0397824    .0260785
                         27  |   .0284892   .0194864     1.46   0.144    -.0098139    .0667923
                         28  |   .0263143   .0120419     2.19   0.029     .0026444    .0499843
                         29  |   .0581011   .0141749     4.10   0.000     .0302385    .0859637
                         30  |   .0381382   .0160436     2.38   0.018     .0066023     .069674
                         31  |   .0727234    .013591     5.35   0.000     .0460085    .0994383
                         32  |   .0307623    .009945     3.09   0.002     .0112141    .0503105
                         33  |   .0098386   .0422816     0.23   0.816    -.0732713    .0929486
                         34  |   .0013414   .0119072     0.11   0.910    -.0220638    .0247465
                         35  |    .038221   .0130557     2.93   0.004     .0125583    .0638836
                         36  |   .0334714    .015186     2.20   0.028     .0036215    .0633213
                         37  |   .0242125   .0139162     1.74   0.083    -.0031415    .0515666
                         38  |  -.0049464   .0118221    -0.42   0.676    -.0281842    .0182913
                         39  |   .0342769   .0152831     2.24   0.025      .004236    .0643178
                         50  |   .0017851   .0166087     0.11   0.914    -.0308614    .0344315
                         51  |   .0551732   .0232763     2.37   0.018     .0094206    .1009257
                         52  |   .0083861   .0131168     0.64   0.523    -.0173966    .0341689
                         53  |  -.0032044    .013684    -0.23   0.815    -.0301021    .0236933
                         54  |   .0099408    .018664     0.53   0.595    -.0267457    .0466273
                         55  |  -.0136201   .0189074    -0.72   0.472     -.050785    .0235449
                         56  |   .0292476   .0178389     1.64   0.102    -.0058171    .0643122
                         57  |   .0104898   .0372296     0.28   0.778    -.0626898    .0836695
                         58  |  -.0067515   .0190734    -0.35   0.724    -.0442427    .0307396
                         59  |   .0356023   .0134419     2.65   0.008     .0091806    .0620239
                         70  |   .0100439   .0273551     0.37   0.714     -.043726    .0638138
                         72  |   .0390487   .0122056     3.20   0.001     .0150571    .0630404
                         73  |   .0164809   .0127765     1.29   0.198    -.0086329    .0415946
                         75  |   .0205875   .0281016     0.73   0.464    -.0346498    .0758248
                         78  |   .0251894   .0122396     2.06   0.040     .0011308    .0492479
                         79  |   .0247439   .0196943     1.26   0.210    -.0139678    .0634556
                         80  |  -.0274531   .0145026    -1.89   0.059    -.0559598    .0010535
                         82  |   .0988074   .0148506     6.65   0.000     .0696166    .1279981
                         87  |   .0399987   .0188036     2.13   0.034     .0030378    .0769596
                             |
                        year |
                       2012  |  -.0734135   .0070246   -10.45   0.000    -.0872213   -.0596057
                       2013  |  -.0924838   .0093868    -9.85   0.000    -.1109348   -.0740328
                       2014  |  -.1007837   .0090648   -11.12   0.000    -.1186018   -.0829656
                       2015  |  -.0743972    .009796    -7.59   0.000    -.0936525   -.0551419
                       2016  |  -.0636849   .0125124    -5.09   0.000    -.0882797   -.0390901
                       2017  |  -.1162378   .0117682    -9.88   0.000    -.1393696    -.093106
                       2018  |  -.0432795   .0077273    -5.60   0.000    -.0584686   -.0280904
                       2019  |          0  (omitted)
                             |
                       _cons |   1.017701   .1710983     5.95   0.000      .681385    1.354016
----------------------------------------------------------------------------------------------

[Felix Bittmann]

One option is to compare the confidence intervals and see if they overlap. If so, the effect is similar. However, in your setup it is probably much better to work with interaction effects. Generate a binary variable that identifies both groups and then run:

reg depvar (var1 var2 var3)##i.groupvar, options

The interaction term of governance and the grouping will tell you exactly the difference of the coefs and make it easy to assess the statistical significance.

[Richard Williams]

Looking at overlapping confidence intervals is problematic. If two 95% CIs overlap, that does NOT mean that the coefficients do not significantly differ at the .05 level. With overlapping CIs, you are looking at whether a high possible value on one coefficient overlaps with a low possible value on another. In other words, to overlap, two unlikely events may have to occur, not just one.

I agree that looking at interaction effects is a better way to go.

You don't necessarily have to interact every variable with group membership. For example, your theory may say that the effect of education may differ by gender, but predict no such differences for other variables.

[Bruce Weaver]

Here is a short article on the issue of overlapping CIs, should anyone need a published article to convince a skeptical boss or supervisor that two independent point estimates can differ significantly, even though their CIs overlap.

• https://www.cmaj.ca/content/166/1/65.full
• https://pubmed.ncbi.nlm.nih.gov/11800251/

[Felix Bittmann]

Both Richard and Bruce are right, thanks for pointing this out, looking at the CIs is problematic and can easily lead to wrong conclusions. I think the only thing that is always valid is that no overlap means a robust significant difference for the given level. Another interesting source for this is https://academic.oup.com/jinsectscie...3/1/34/2577125. But note that this is then a very conservative estimation and the interaction approach is clearly better.