Including time fixed effects in a first differences model

[YH jordaan]

Hello everyone.

I have a question regarding including time fixed effects in a (cross section fixed effects) model where all variables are specified in differences:

So what is the case here: I have 2 models:
- model (1) which includes a quarterly differenced dependent variable, an lagged independent variable, quarterly differenced company specific control variables (which thus differs between companies and over time) and time series control variables specified in first differences as well (for instance the federal funds rate, gdp, infaltion etc which are the same for companies but change over time).

- model (2) which is the same as model (1) except that model (2) includes time fixed effects and thus excludes all the time serie variables.

The problem is that my variable of interest is changing in significance between the models. In model (1) it is significant, in model (2) it is not. Regardles of the change in significance, I wonder if the inclusion of time fixed effects (which are time dummies ofcourse) in a model where almost every variable is specified in first differenced values, is correct? In model (1) all time serie variables are specified in first differences as well, while in model (2) when including time fixed effects these time fixed effects are specified in level values. Can this lead to problems and thus maybe explain the change in significance of my variable of interest?

If so, is there a solution for this? I thought about including the difference in time fixed effects instead of the time fixed effects but how can I do this?

Below I provide the regression output of the two models. Note that Hqualitybank is my variable of interest. Crisidummy, fedfundchange tedspreadchange and changeinflation are time series variables.

Model (1)

. areg marketliq L.Hqualitybank Hbank_Crisis  Dsize Dnim  Dracr Dloanstoassets Ddepositsloans L.Crisisdummy changefe
> dfund changetedspread changeinflation,absorb(gvkey) r

Linear regression, absorbing indicators           Number of obs   =       3466
                                                  F(  11,   3346) =      15.77
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.1672
                                                  Adj R-squared   =     0.1375
                                                  Root MSE        =     0.0161

---------------------------------------------------------------------------------
                |               Robust
      marketliq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
   Hqualitybank |
            L1. |  -.0020248   .0011106    -1.82   0.068    -.0042023    .0001527
                |
   Hbank_Crisis |   .0015005   .0017691     0.85   0.396    -.0019681    .0049692
          Dsize |   .0403292   .0092174     4.38   0.000     .0222568    .0584015
           Dnim |  -.0006059    .001441    -0.42   0.674    -.0034312    .0022194
          Dracr |   .0010526   .0005251     2.00   0.045     .0000231    .0020822
 Dloanstoassets |  -.1695018   .0248656    -6.82   0.000    -.2182552   -.1207485
 Ddepositsloans |   .0132289   .0026041     5.08   0.000     .0081231    .0183346
                |
    Crisisdummy |
            L1. |   .0004759   .0012866     0.37   0.711    -.0020466    .0029984
                |
  changefedfund |   -.000846    .000841    -1.01   0.314    -.0024949    .0008028
changetedspread |  -.0000108   .0009142    -0.01   0.991    -.0018033    .0017817
changeinflation |   .0008102   .0008076     1.00   0.316    -.0007732    .0023937
          _cons |  -.0006858   .0009363    -0.73   0.464    -.0025216      .00115
----------------+----------------------------------------------------------------
          gvkey |   absorbed                                     (109 categories)

Model (2)

areg marketliq L.Hqualitybank  Dsize Dnim  Dracr Dloanstoassets Ddepositsloans i.datum,absorb(gvkey) r

Linear regression, absorbing indicators           Number of obs   =       3520
                                                  F(  60,   3351) =       5.93
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.1970
                                                  Adj R-squared   =     0.1568
                                                  Root MSE        =     0.0159

--------------------------------------------------------------------------------
               |               Robust
     marketliq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
  Hqualitybank |
           L1. |  -.0011879   .0010839    -1.10   0.273    -.0033132    .0009373
               |
         Dsize |   .0407307   .0093138     4.37   0.000     .0224694    .0589919
          Dnim |  -.0006563    .001413    -0.46   0.642    -.0034268    .0021142
         Dracr |   .0010838   .0005156     2.10   0.036     .0000729    .0020947
Dloanstoassets |  -.1695913    .025276    -6.71   0.000    -.2191492   -.1200334
Ddepositsloans |   .0130058   .0025313     5.14   0.000     .0080427    .0179689
               |
         datum |
          166  |  -.0030757   .0025847    -1.19   0.234    -.0081435    .0019921
          167  |  -.0021623   .0022103    -0.98   0.328    -.0064959    .0021713
          168  |  -.0121513   .0027694    -4.39   0.000    -.0175812   -.0067213
          169  |  -.0002611   .0016995    -0.15   0.878    -.0035933     .003071
          170  |   -.005769   .0023909    -2.41   0.016    -.0104568   -.0010813
          171  |  -.0066018   .0022936    -2.88   0.004    -.0110989   -.0021047
          172  |  -.0074842   .0020371    -3.67   0.000    -.0114783   -.0034902
          173  |  -.0041743   .0020196    -2.07   0.039    -.0081341   -.0002145
          174  |   -.005192   .0022203    -2.34   0.019    -.0095452   -.0008388
          175  |  -.0034753   .0019002    -1.83   0.068     -.007201    .0002504
          176  |  -.0057363   .0019598    -2.93   0.003    -.0095788   -.0018938
          177  |  -.0027455   .0022995    -1.19   0.233     -.007254     .001763
          178  |  -.0038011   .0020494    -1.85   0.064    -.0078193    .0002172
          179  |   -.010387   .0029895    -3.47   0.001    -.0162485   -.0045255
          180  |  -.0029657    .001898    -1.56   0.118     -.006687    .0007557
          181  |  -.0028134   .0019581    -1.44   0.151    -.0066525    .0010258
          182  |  -.0029773    .001826    -1.63   0.103    -.0065574    .0006028
          183  |  -.0030122   .0021308    -1.41   0.158      -.00719    .0011657
          184  |  -.0043154    .001977    -2.18   0.029    -.0081917   -.0004391
          185  |  -.0026042   .0017746    -1.47   0.142    -.0060836    .0008753
          186  |  -.0036521   .0020552    -1.78   0.076    -.0076816    .0003774
          187  |  -.0031441   .0020323    -1.55   0.122    -.0071288    .0008407
          188  |  -.0047417    .002174    -2.18   0.029    -.0090042   -.0004793
          189  |  -.0014614   .0016814    -0.87   0.385    -.0047581    .0018353
          190  |  -.0043103   .0020354    -2.12   0.034    -.0083011   -.0003196
          191  |  -.0044737    .002333    -1.92   0.055     -.009048    .0001005
          192  |  -.0024166   .0019312    -1.25   0.211    -.0062031    .0013698
          193  |   -.003139   .0020809    -1.51   0.132    -.0072191     .000941
          194  |   .0012382   .0027618     0.45   0.654    -.0041768    .0066533
          195  |   .0005749   .0039964     0.14   0.886    -.0072608    .0084105
          196  |  -.0006183   .0037055    -0.17   0.867    -.0078835    .0066469
          197  |  -.0089042   .0027313    -3.26   0.001    -.0142594   -.0035489
          198  |  -.0039918   .0033183    -1.20   0.229    -.0104979    .0025143
          199  |   .0003562   .0027968     0.13   0.899    -.0051274    .0058398
          200  |  -.0011279   .0026736    -0.42   0.673    -.0063699    .0041141
          201  |  -.0073056   .0031635    -2.31   0.021    -.0135081    -.001103
          202  |  -.0075308    .002753    -2.74   0.006    -.0129285   -.0021332
          203  |  -.0050696   .0032805    -1.55   0.122    -.0115015    .0013624
          204  |   .0018842   .0031378     0.60   0.548     -.004268    .0080364
          205  |  -.0008211   .0029858    -0.28   0.783    -.0066752     .005033
          206  |   -.005311   .0034661    -1.53   0.126    -.0121069     .001485
          207  |   -.006523   .0034758    -1.88   0.061     -.013338     .000292
          208  |  -.0075814   .0029472    -2.57   0.010    -.0133598    -.001803
          209  |   .0003005   .0024702     0.12   0.903    -.0045428    .0051438
          210  |  -.0064785   .0020873    -3.10   0.002     -.010571    -.002386
          211  |   .0023475   .0024646     0.95   0.341    -.0024848    .0071797
          212  |  -.0058786    .002446    -2.40   0.016    -.0106743   -.0010829
          213  |  -.0002821   .0025935    -0.11   0.913    -.0053672    .0048029
          214  |    .004341   .0024769     1.75   0.080    -.0005153    .0091973
          215  |  -.0042247   .0023808    -1.77   0.076    -.0088926    .0004432
          216  |  -.0009571   .0026356    -0.36   0.717    -.0061246    .0042105
          217  |  -.0058652   .0023668    -2.48   0.013    -.0105058   -.0012246
          218  |  -.0014492   .0023614    -0.61   0.539    -.0060791    .0031807
          219  |   -.001878   .0024527    -0.77   0.444    -.0066869     .002931
               |
         _cons |    .003573   .0014693     2.43   0.015     .0006922    .0064538
---------------+----------------------------------------------------------------
         gvkey |   absorbed                                     (109 categories)

If I am not clear about specific things or have to provide more information; please let me know. I am both quite new to Stata as well making uses of a forum.

Thank you in advance for your help,

YH

[YH jordaan]

What do I have to provide to get responses/feedback on my opening post?

[Nick Cox]

Roughly speaking, if people think they can almost or partially answer your question, they will do so.

Lack of a reply means usually too busy, not interested, don't do that kind of thing, or don't understand what you want.

Advice on bumping (mostly, please don't) in http://www.statalist.org/forums/foru...-similar-topic

[Carlo Lazzaro]

YH (the usual kind reminder about re-registering with real full names applies and adds to Nick's sound remarks) wrote:

Note that Hqualitybank is my variable of interest... In model (1) it is significant, in model (2) it is not...

Although I'm not a significance fan, from the results you posted, it does not seem so (model 1: p=0,068; model 2: p=0.273).

Comparing adjusted R-squared, model #2 seems to perform slightly better that model #1; however, which one is more in line with the recommendations reported in the literature of your research field, I can't say.

[Clyde Schechter]

Echoing Carlo's deprecation of significance testing, notice that in each model, your coefficient for Hqualitybank falls comfortably within the 95% confidence interval of the other, and in absolute terms, the difference in values is pretty small. So, really the two models aren't saying much different about the effect of this variables.

That said, in general, when adding time fixed effects to a model substantially changes the results of a key variable, the implication is that the effect of that variable is confounded with time-based shocks to the outcome variable. (In a smaller data set it could also just mean overfitting of noise, but your data set is large enough to accommodate this many variables without much risk of that.)

[YH jordaan]

Roughly speaking, if people think they can almost or partially answer your question, they will do so.

Lack of a reply means usually too busy, not interested, don't do that kind of thing, or don't understand what you want.

Advice on bumping (mostly, please don't) in http://www.statalist.org/forums/foru...-similar-topic

This is something I completely understand of course. However, because of the fact that in previous topics of me, I failed to present all the complete information, I thought that this was also the case here. That is why I asked this question.

[YH jordaan]

YH (the usual kind reminder about re-registering with real full names applies and adds to Nick's sound remarks) wrote:



Although I'm not a significance fan, from the results you posted, it does not seem so (model 1: p=0,068; model 2: p=0.273).

Comparing adjusted R-squared, model #2 seems to perform slightly better that model #1; however, which one is more in line with the recommendations reported in the literature of your research field, I can't say.

Thanks for your feedback Carlo Lazzaro . YH are the first letters of my first and second name, thats why I registered that way. If I can change this to my full first name and surname, I will do this.

[YH jordaan]

Echoing Carlo's deprecation of significance testing, notice that in each model, your coefficient for Hqualitybank falls comfortably within the 95% confidence interval of the other, and in absolute terms, the difference in values is pretty small. So, really the two models aren't saying much different about the effect of this variables.

That said, in general, when adding time fixed effects to a model substantially changes the results of a key variable, the implication is that the effect of that variable is confounded with time-based shocks to the outcome variable. (In a smaller data set it could also just mean overfitting of noise, but your data set is large enough to accommodate this many variables without much risk of that.)

Thanks Clyde Schechter . Regarding the fact that the two coeficients dont differ much in absolute values you are of course absolutetly right. But at least for me, it was even more surprising that the p-value did change (so) much. In my opinion this was a bit strange and that is why I decided to ask a question about it.

[Carlo Lazzaro]

YH:
I'm perfectly fine with first letters; I was just wondering if I should address you as he or she in future posts.