Interaction terms in panel data

Stephan Yan

Join Date: Jul 2019
Posts: 17

Interaction terms in panel data

08 Jul 2019, 05:52

Dear all,

I am currently working on my master thesis : i am analyzing the link between board gender diversity and firm performance. My sample consists of 264 firms from the S&P500 over the 2006-2012 period.

I am using Stata/SE 15.1 and for the regression i am using reghdfe

my model is the following one :
firm value= B0 + B1[%WomenOnBoard] + B2[control variables] + Year fixed effects*Industry fixed effects + Firm fixed effects + e

My problem is when I want to see how the firms reacted during the subprime crisis and outside the crisis. Therefore, i added interaction terms and worked with dummy variables (Crisis and PostCrisis)
Crisis = 1 when year = 2008 & 2009, 0 otherwise and PostCrisis when year = 2010, 2011, 2012 and 0 otherwise.

firm value= B0 + B1[%women*Crisis] + B1[%women*Post_Crisis] + B3[control variables] + Year fixed effects * Industry Fixed effects + Firm fixed effects + e

Code:

. reghdfe Q c.WOMENONBOARD_w#i.Crisis c.WOMENONBOARD_w#i.PostCrisis BOARDSIZE_w FIRMSIZELNAT_w CASHHO
> LDINGSCHEAT_w LEVV_w, absorb(i.DataYearFiscal#SIC_group FIRM) vce(cluster FIRM)
(MWFE estimator converged in 2 iterations)
note: 1.PostCrisis#c.WOMENONBOARD_w omitted because of collinearity

HDFE Linear regression                            Number of obs   =      1,848
Absorbing 2 HDFE groups                           F(   7,    263) =      17.15
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.8905
                                                  Adj R-squared   =     0.8701
                                                  Within R-sq.    =     0.2031
Number of clusters (FIRM)    =        264         Root MSE        =     0.1537

                                                (Std. Err. adjusted for 264 clusters in FIRM)
---------------------------------------------------------------------------------------------
                            |               Robust
                          Q |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
    Crisis#c.WOMENONBOARD_w |
                         0  |  -.1269574   .1403645    -0.90   0.367    -.4033387    .1494238
                         1  |  -.1456752   .2077467    -0.70   0.484    -.5547336    .2633831
                            |
PostCrisis#c.WOMENONBOARD_w |
                         0  |   .1364259   .1710807     0.80   0.426    -.2004364    .4732881
                         1  |          0  (omitted)
                            |
                BOARDSIZE_w |  -.0001824   .0042915    -0.04   0.966    -.0086325    .0082676
             FIRMSIZELNAT_w |  -.3358434   .0323371   -10.39   0.000    -.3995159   -.2721709
        CASHHOLDINGSCHEAT_w |   .2864215   .1309255     2.19   0.030     .0286258    .5442171
                     LEVV_w |   .0014819   .0013261     1.12   0.265    -.0011292    .0040929
                      _cons |   3.758162   .3072915    12.23   0.000     3.153097    4.363227
---------------------------------------------------------------------------------------------

Absorbed degrees of freedom:
--------------------------------------------------------------------+
                Absorbed FE | Categories  - Redundant  = Num. Coefs |
----------------------------+---------------------------------------|
   DataYearFiscal#SIC_group |        21           0          21     |
                       FIRM |       264         264           0    *|
--------------------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

The problem is that i get an omitted coefficient, how should i deal with it ?

Someone recommended me to do a difference in differences, so i wrote the following code :

Code:

. reghdfe Q c.WOMENONBOARD_w##i.Crisis  BOARDSIZE_w FIRMSIZELNAT_w CASHHOLDINGSCHEAT_w LEVV_w, absorb
> (i.DataYearFiscal#SIC_group FIRM) vce(cluster FIRM)
note: 1bn.Crisis is probably collinear with the fixed effects (all partialled-out values are close to
>  zero; tol = 1.0e-09)
(MWFE estimator converged in 2 iterations)
note: 1.Crisis omitted because of collinearity

HDFE Linear regression                            Number of obs   =      1,848
Absorbing 2 HDFE groups                           F(   6,    263) =      19.36
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.8904
                                                  Adj R-squared   =     0.8700
                                                  Within R-sq.    =     0.2023
Number of clusters (FIRM)    =        264         Root MSE        =     0.1537

                                            (Std. Err. adjusted for 264 clusters in FIRM)
-----------------------------------------------------------------------------------------
                        |               Robust
                      Q |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
         WOMENONBOARD_w |  -.0734974   .1215175    -0.60   0.546    -.3127683    .1657736
               1.Crisis |          0  (omitted)
                        |
Crisis#c.WOMENONBOARD_w |
                     1  |   .0650714   .0907979     0.72   0.474    -.1137119    .2438547
                        |
            BOARDSIZE_w |   .0000317   .0043224     0.01   0.994    -.0084793    .0085427
         FIRMSIZELNAT_w |  -.3352275   .0325952   -10.28   0.000    -.3994084   -.2710467
    CASHHOLDINGSCHEAT_w |    .293405   .1303574     2.25   0.025     .0367281    .5500819
                 LEVV_w |   .0014913   .0013221     1.13   0.260     -.001112    .0040946
                  _cons |   3.748505   .3097566    12.10   0.000     3.138586    4.358423
-----------------------------------------------------------------------------------------

Absorbed degrees of freedom:
--------------------------------------------------------------------+
                Absorbed FE | Categories  - Redundant  = Num. Coefs |
----------------------------+---------------------------------------|
   DataYearFiscal#SIC_group |        21           0          21     |
                       FIRM |       264         264           0    *|
--------------------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

I also created another variable that divide WOMENONBOARD_w in quartile, as an independent variable for gender diversity (in order to see the impact of the top vs bottom quartile)

Code:

. reghdfe Q i.quart##i.Crisis  BOARDSIZE_w FIRMSIZELNAT_w CASHHOLDINGSCHEAT_w LEVV_w, absorb(i.DataYe
> arFiscal#SIC_group FIRM) vce(cluster FIRM)
note: 1bn.Crisis is probably collinear with the fixed effects (all partialled-out values are close to
>  zero; tol = 1.0e-09)
(MWFE estimator converged in 2 iterations)
note: 1.Crisis omitted because of collinearity

HDFE Linear regression                            Number of obs   =      1,848
Absorbing 2 HDFE groups                           F(  10,    263) =      13.52
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.8909
                                                  Adj R-squared   =     0.8702
                                                  Within R-sq.    =     0.2054
Number of clusters (FIRM)    =        264         Root MSE        =     0.1536

                                        (Std. Err. adjusted for 264 clusters in FIRM)
-------------------------------------------------------------------------------------
                    |               Robust
                  Q |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
              quart |
                 2  |   .0034021    .021553     0.16   0.875    -.0390362    .0458405
                 3  |  -.0131702   .0222317    -0.59   0.554     -.056945    .0306046
                 4  |  -.0298918   .0262545    -1.14   0.256    -.0815876     .021804
                    |
           1.Crisis |          0  (omitted)
                    |
       quart#Crisis |
               2 1  |   .0278492   .0246207     1.13   0.259    -.0206295     .076328
               3 1  |   .0252918   .0217393     1.16   0.246    -.0175134     .068097
               4 1  |   .0058297   .0234859     0.25   0.804    -.0404146     .052074
                    |
        BOARDSIZE_w |  -.0005533   .0043108    -0.13   0.898    -.0090414    .0079347
     FIRMSIZELNAT_w |  -.3349989   .0320547   -10.45   0.000    -.3981154   -.2718824
CASHHOLDINGSCHEAT_w |    .284658   .1298826     2.19   0.029      .028916       .5404
             LEVV_w |   .0014533   .0013958     1.04   0.299     -.001295    .0042016
              _cons |   3.750724   .3039763    12.34   0.000     3.152187     4.34926
-------------------------------------------------------------------------------------

Absorbed degrees of freedom:
--------------------------------------------------------------------+
                Absorbed FE | Categories  - Redundant  = Num. Coefs |
----------------------------+---------------------------------------|
   DataYearFiscal#SIC_group |        21           0          21     |
                       FIRM |       264         264           0    *|
--------------------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

Is diff-and-diffs a better option, however there is still an omitted coefficient ? and i am not sure about how to interpret the results?

Thanks in advance for your precious help.
Stephan YAN

Last edited by Stephan Yan; 08 Jul 2019, 06:02.

Tags: None

Carlo Lazzaro

Join Date: Apr 2014

Posts: 17134
#2

08 Jul 2019, 09:29

Stephan:
the text

note: 1bn.Crisis is probably collinear with the fixed effects

that appears above the outcome table of the community-contributed command -reghdfe- is enlightening.
There's nothing you can do about that but change specification and/or go for a more parsimonious regression model.

Kind regards,
Carlo
(StataNow 18.5)
Comment

Stephan Yan

Join Date: Jul 2019
Posts: 17

09 Jul 2019, 02:26

Dear Carlo,

Thanks a lot for your reply. I am kind of blocked right now because of this.

Could you please let me know your thoughts about the following code, when i add WOMENONBOARD_w first without interaction :

Code:

. reghdfe TOBINSQ_w WOMENONBOARD_w c.WOMENONBOARD_w#i.Crisis c.WOMENONBOARD_w#i
> .PostCrisis BOARDSIZE_w FIRMSIZELNAT_w CASHHOLDINGSCHEAT_w SHORTTERMDEBT_w, a
> bsorb(DataYearFiscal#SIC_group FIRM) vce(cluster FIRM)
(MWFE estimator converged in 2 iterations)

HDFE Linear regression                            Number of obs   =      1,848
Absorbing 2 HDFE groups                           F(   7,    263) =      10.61
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.8561
                                                  Adj R-squared   =     0.8292
                                                  Within R-sq.    =     0.1921
Number of clusters (FIRM)    =        264         Root MSE        =     0.4225

                                 (Std. Err. adjusted for 264 clusters in FIRM)
------------------------------------------------------------------------------
             |               Robust
   TOBINSQ_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
WOMENONBOA~w |  -.0871378   .4252178    -0.20   0.838    -.9244024    .7501267
             |
      Crisis#|
          c. |
WOMENONBOA~w |
          1  |  -.2535019   .4152572    -0.61   0.542    -1.071154      .56415
             |
  PostCrisis#|
          c. |
WOMENONBOA~w |
          1  |   -.435717   .4757029    -0.92   0.361    -1.372388     .500954
             |
 BOARDSIZE_w |  -.0025521   .0113192    -0.23   0.822    -.0248398    .0197356
FIRMSIZELN~w |  -.8818711   .1114986    -7.91   0.000    -1.101415   -.6623276
CASHHOLDIN~w |   .8404231   .4231541     1.99   0.048     .0072221    1.673624
SHORTTERMD~w |  -.0078469   .0023438    -3.35   0.001    -.0124619    -.003232
       _cons |   10.35951   1.071377     9.67   0.000     8.249945    12.46908
------------------------------------------------------------------------------

Absorbed degrees of freedom:
--------------------------------------------------------------------+
                Absorbed FE | Categories  - Redundant  = Num. Coefs |
----------------------------+---------------------------------------|
   DataYearFiscal#SIC_group |        21           0          21     |
                       FIRM |       264         264           0    *|
--------------------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

Thanks in advance!

Stephan

Comment

Carlo Lazzaro

Join Date: Apr 2014

Posts: 17134
#4

09 Jul 2019, 02:52

Stephan:
with a sky-rocketing R-sq and most of your coefficients far from statistical significance, you may have a quasi-extreme multicollinearity problem.
Check the correlations of your predictors and see what happens if you switch to a more parsimonious model.

Last edited by Carlo Lazzaro; 09 Jul 2019, 03:43.

Kind regards,
Carlo
(StataNow 18.5)
Comment

Stephan Yan

Join Date: Jul 2019
Posts: 17

09 Jul 2019, 03:41

Dear Carlo,

I check the correlations between the different variables, however, i think it's quite OK?

Code:

             | TOBINS~w ROANIA~w WOMENO~w BOARDS~w FIRMSI~w CASHHO~w SHORTT~w
-------------+---------------------------------------------------------------
   TOBINSQ_w |   1.0000
   ROANIAT_w |   0.4869   1.0000
WOMENONBOA~w |  -0.0098   0.0371   1.0000
 BOARDSIZE_w |  -0.1977  -0.0310   0.1860   1.0000
  FIRMSIZE_w |  -0.3781  -0.1205   0.1779   0.4172   1.0000
CASHHOLDIN~w |   0.4951   0.1944  -0.1064  -0.2468  -0.2736   1.0000
SHORTTERMD~w |   0.0107  -0.0057  -0.0014   0.0569  -0.0740   0.0339   1.0000

I tried numerous things but always have some problems of collinearity because of the fixed effects. Would you mind to tell me what can be a more parsimonious model?

Thanks!

Stephan

Comment

Carlo Lazzaro

Join Date: Apr 2014

Posts: 17134
#6

09 Jul 2019, 03:47

Stephan:
what does -estat vce, corr- give you back?
By a more parsimonious model I meant a regression model with less predictors (provided that it still gives a fair and true view of the data generating process).

Kind regards,
Carlo
(StataNow 18.5)
Comment

Stephan Yan

Join Date: Jul 2019
Posts: 17

09 Jul 2019, 09:06

Dear Carlo,

Code:

. reghdfe TOBINSQ_w c.WOMENONBOARD_w#i.Crisis c.WOMENONBOARD_w#i.PostCrisis BOA
> RDSIZE_w FIRMSIZE_w CASHHOLDINGS_w SHORTTERMDEBT_w, absorb(DataYearFiscal#SIC
> _group FIRM) vce(cluster FIRM)
(MWFE estimator converged in 2 iterations)
note: 1.PostCrisis#c.WOMENONBOARD_w omitted because of collinearity

HDFE Linear regression                            Number of obs   =      1,848
Absorbing 2 HDFE groups                           F(   7,    263) =      10.61
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.8561
                                                  Adj R-squared   =     0.8292
                                                  Within R-sq.    =     0.1921
Number of clusters (FIRM)    =        264         Root MSE        =     0.4225

                                 (Std. Err. adjusted for 264 clusters in FIRM)
------------------------------------------------------------------------------
             |               Robust
   TOBINSQ_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      Crisis#|
          c. |
WOMENONBOA~w |
          0  |  -.5228548   .3804043    -1.37   0.170     -1.27188    .2261707
          1  |  -.7763567   .6504735    -1.19   0.234    -2.057155     .504442
             |
  PostCrisis#|
          c. |
WOMENONBOA~w |
          0  |    .435717   .4757029     0.92   0.361     -.500954    1.372388
          1  |          0  (omitted)
             |
 BOARDSIZE_w |  -.0025521   .0113192    -0.23   0.822    -.0248398    .0197356
  FIRMSIZE_w |  -.8818711   .1114986    -7.91   0.000    -1.101415   -.6623276
CASHHOLDIN~w |   .8404231   .4231541     1.99   0.048     .0072221    1.673624
SHORTTERMD~w |  -.0078469   .0023438    -3.35   0.001    -.0124619    -.003232
       _cons |   10.35951   1.071377     9.67   0.000     8.249945    12.46908
------------------------------------------------------------------------------

Absorbed degrees of freedom:
--------------------------------------------------------------------+
                Absorbed FE | Categories  - Redundant  = Num. Coefs |
----------------------------+---------------------------------------|
   DataYearFiscal#SIC_group |        21           0          21     |
                       FIRM |       264         264           0    *|
--------------------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

For the previous regression, i get:

Code:

. estat vce

Covariance matrix of coefficients of reghdfe model

             |  0b.Crisis#   1.Crisis# 0b.PostC~s# 1o.PostC~s#            
        e(V) | c.WOMENO~w  c.WOMENO~w  c.WOMENO~w  co.WOMEN~w  BOARDSIZ~w
-------------+------------------------------------------------------------
   0b.Crisis#|                                                            
c.WOMENONB~w |   .1447074                                                 
    1.Crisis#|                                                            
c.WOMENONB~w |  .19769233   .42311581                                     
0b.PostCri~s#|                                                            
c.WOMENONB~w | -.09509523  -.25005608   .22629328                         
1o.PostCri~s#|                                                            
co.WOMENON~w |          0           0           0           0             
 BOARDSIZE_w |  .00013524    .0001201  -.00025518           0   .00012812
  FIRMSIZE_w |   .0070345   .00982347   -.0062822           0  -.00007262
CASHHOLDIN~w |  .00566851    .0052027  -.01885119           0    .0013513
SHORTTERMD~w |  1.309e-06   .00003569  -.00005993           0  -6.570e-06
       _cons | -.08600488  -.11510554   .06761209           0  -.00089015

             |                                                
        e(V) | FIRMSIZE_w  CASHHOLD~w  SHORTTER~w       _cons
-------------+------------------------------------------------
  FIRMSIZE_w |  .01243193                                     
CASHHOLDIN~w |  .00003358   .17905942                         
SHORTTERMD~w |  .00004342  -4.507e-06   5.493e-06             
       _cons | -.11816794  -.03771396  -.00033798   1.1478481

and

Code:

. corr
(obs=1,848)

             |     FIRM DataYe~l WOMENO~w    quart DFEMALES WOMENO~Y TOBINS~w
-------------+---------------------------------------------------------------
        FIRM |   1.0000
DataYearFi~l |   0.0000   1.0000
WOMENONBOA~w |   0.0819   0.1407   1.0000
       quart |   0.0860   0.1399   0.8997   1.0000
    DFEMALES |   0.0240   0.0710   0.5869   0.4116   1.0000
WOMENONBOA~Y |   0.0983   0.0189   0.7584   0.8645   0.3331   1.0000
   TOBINSQ_w |  -0.0305  -0.1324  -0.0098   0.0273  -0.0152   0.0022   1.0000
ANNUALRETU~w |   0.0128   0.0621  -0.0345  -0.0275  -0.0071  -0.0377   0.0897
   ROANIAT_w |   0.0128  -0.0176   0.0371   0.0454   0.0346   0.0324   0.4869
 BOARDSIZE_w |  -0.0558   0.0525   0.1860   0.1282   0.3013   0.1332  -0.1977
  FIRMSIZE_w |  -0.0625   0.1145   0.1779   0.1453   0.1706   0.1521  -0.3781
CASHHOLDIN~w |  -0.0317   0.0576  -0.1064  -0.0600  -0.0997  -0.0861   0.4951
BOOKTOMARK~w |   0.0445   0.0599  -0.0384  -0.0625  -0.0427  -0.0489  -0.6579
SHORTTERMD~w |   0.0465  -0.0372  -0.0014   0.0009   0.0113  -0.0145   0.0107
LONGTERMDE~w |   0.0354  -0.0339  -0.0118   0.0014   0.0033  -0.0232   0.0234
   SIC_group |   0.0248   0.0000   0.0167   0.0293   0.0399  -0.0177   0.0722
      Crisis |  -0.0000  -0.1581  -0.0160  -0.0172   0.0109   0.0003  -0.1321
  PostCrisis |   0.0000   0.8660   0.1141   0.1146   0.0536   0.0103  -0.0661
   PreCrisis |   0.0000  -0.7906  -0.1090  -0.1083  -0.0697  -0.0116   0.2045

             | ANNUAL~w ROANIA~w BOARDS~w FIRMSI~w CASHHO~w BOOKTO~w SHORTT~w
-------------+---------------------------------------------------------------
ANNUALRETU~w |   1.0000
   ROANIAT_w |   0.0636   1.0000
 BOARDSIZE_w |  -0.0153  -0.0310   1.0000
  FIRMSIZE_w |  -0.0277  -0.1205   0.4172   1.0000
CASHHOLDIN~w |   0.0590   0.1944  -0.2468  -0.2736   1.0000
BOOKTOMARK~w |  -0.1500  -0.4364   0.0639   0.2290  -0.3134   1.0000
SHORTTERMD~w |  -0.0444  -0.0057   0.0569  -0.0740   0.0339  -0.0129   1.0000
LONGTERMDE~w |  -0.0520  -0.0162   0.0558  -0.1041   0.0151  -0.0159   0.7823
   SIC_group |  -0.0529  -0.0227  -0.0568  -0.0568   0.0557  -0.0630  -0.0161
      Crisis |   0.0600  -0.1439  -0.0116  -0.0301  -0.0102   0.1571   0.1121
  PostCrisis |  -0.0091   0.0482   0.0448   0.1021   0.0563  -0.0009  -0.0630
   PreCrisis |  -0.0501   0.0911  -0.0374  -0.0817  -0.0515  -0.1562  -0.0432

             | LONGTE~w SIC_gr~p   Crisis PostCr~s PreCri~s
-------------+---------------------------------------------
LONGTERMDE~w |   1.0000
   SIC_group |  -0.0083   1.0000
      Crisis |   0.1398  -0.0000   1.0000
  PostCrisis |  -0.0687  -0.0000  -0.5477   1.0000
   PreCrisis |  -0.0646   0.0000  -0.4000  -0.5477   1.0000

Even if i am doing the regression without any control variables i get :

Code:

. reghdfe TOBINSQ_w c.WOMENONBOARD_w#i.Crisis c.WOMENONBOARD_w#i.PostCrisis, ab
> sorb(DataYearFiscal#SIC_group FIRM) vce(cluster FIRM)
(MWFE estimator converged in 2 iterations)
note: 1.PostCrisis#c.WOMENONBOARD_w omitted because of collinearity

HDFE Linear regression                            Number of obs   =      1,848
Absorbing 2 HDFE groups                           F(   3,    263) =       0.36
Statistics robust to heteroskedasticity           Prob > F        =     0.7785
                                                  R-squared       =     0.8222
                                                  Adj R-squared   =     0.7894
                                                  Within R-sq.    =     0.0016
Number of clusters (FIRM)    =        264         Root MSE        =     0.4690

                                 (Std. Err. adjusted for 264 clusters in FIRM)
------------------------------------------------------------------------------
             |               Robust
   TOBINSQ_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      Crisis#|
          c. |
WOMENONBOA~w |
          0  |  -.4524542   .4439628    -1.02   0.309    -1.326628    .4217198
          1  |  -.6340484   .7302119    -0.87   0.386    -2.071854    .8037571
             |
  PostCrisis#|
          c. |
WOMENONBOA~w |
          0  |   .3615238   .5365096     0.67   0.501    -.6948771    1.417925
          1  |          0  (omitted)
             |
       _cons |   2.042188   .0589208    34.66   0.000     1.926171    2.158204
------------------------------------------------------------------------------

Absorbed degrees of freedom:
--------------------------------------------------------------------+
                Absorbed FE | Categories  - Redundant  = Num. Coefs |
----------------------------+---------------------------------------|
   DataYearFiscal#SIC_group |        21           0          21     |
                       FIRM |       264         264           0    *|
--------------------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

.

Please let me know if you have any advice, i don't know how to fix this problem as i need to include fixed effects.
I have different independent variables to account for the women on board, i tried each of these variables (quart, dfemales, womenonboard_w, womenonboard_dummy).

Thanks Carlo!

Stephan

Comment

Carlo Lazzaro

Join Date: Apr 2014

Posts: 17134
#8

09 Jul 2019, 09:50

Stephan:
what does -estat vce, corr- give you back?

Kind regards,
Carlo
(StataNow 18.5)
Comment

Stephan Yan

Join Date: Jul 2019
Posts: 17

10 Jul 2019, 02:52

Dear Carlo,

Here it is

Code:

. estat vce, corr

Correlation matrix of coefficients of reghdfe model

             | 0b.Cri~s# 1.Crisis# 0b.Pos~s# 1o.Pos~s#                                        
        e(V) | c.WOME~w  c.WOME~w  c.WOME~w  co.WOM~w  BOARDS~w  FIRMSI~w  CASHHO~w  SHORTT~w
-------------+--------------------------------------------------------------------------------
   0b.Crisis#|                                                                                
c.WOMENONB~w |   1.0000                                                                       
    1.Crisis#|                                                                                
c.WOMENONB~w |   0.7989    1.0000                                                             
0b.PostCri~s#|                                                                                
c.WOMENONB~w |  -0.5255   -0.8081    1.0000                                                   
1o.PostCri~s#|                                                                                
co.WOMENON~w |        .         .         .         .                                         
 BOARDSIZE_w |   0.0314    0.0163   -0.0474         .    1.0000                               
  FIRMSIZE_w |   0.1659    0.1354   -0.1184         .   -0.0575    1.0000                     
CASHHOLDIN~w |   0.0352    0.0189   -0.0936         .    0.2821    0.0007    1.0000           
SHORTTERMD~w |   0.0015    0.0234   -0.0538         .   -0.2476    0.1661   -0.0045    1.0000
       _cons |  -0.2110   -0.1652    0.1327         .   -0.0734   -0.9892   -0.0832   -0.1346

             |          
        e(V) |    _cons
-------------+----------
       _cons |   1.0000

Comment

Carlo Lazzaro

Join Date: Apr 2014
Posts: 17134

#10

10 Jul 2019, 06:44

Stephan:
those in red show sign of quasi-extreme multicollinearity.

Code:

. estat vce, corr

Correlation matrix of coefficients of reghdfe model

             | 0b.Cri~s# 1.Crisis# 0b.Pos~s# 1o.Pos~s#                                       
        e(V) | c.WOME~w  c.WOME~w  c.WOME~w  co.WOM~w  BOARDS~w  FIRMSI~w  CASHHO~w  SHORTT~w
-------------+--------------------------------------------------------------------------------
   0b.Crisis#|                                                                               
c.WOMENONB~w |   1.0000                                                                      
    1.Crisis#|                                                                               
c.WOMENONB~w |   0.7989    1.0000                                                            
0b.PostCri~s#|                                                                               
c.WOMENONB~w |  -0.5255   -0.8081    1.0000                                                  
1o.PostCri~s#|                                                                               
co.WOMENON~w |        .         .         .         .                                        
BOARDSIZE_w |   0.0314    0.0163   -0.0474         .    1.0000                              
  FIRMSIZE_w |   0.1659    0.1354   -0.1184         .   -0.0575    1.0000                    
CASHHOLDIN~w |   0.0352    0.0189   -0.0936         .    0.2821    0.0007    1.0000          
SHORTTERMD~w |   0.0015    0.0234   -0.0538         .   -0.2476    0.1661   -0.0045    1.0000
       _cons |  -0.2110   -0.1652    0.1327         .   -0.0734   -0.9892   -0.0832   -0.1346

             |         
        e(V) |    _cons
-------------+----------
       _cons |   1.0000

Kind regards,
Carlo
(StataNow 18.5)

Comment

Stephan Yan

Join Date: Jul 2019

Posts: 17
#11

10 Jul 2019, 09:00

Dear Carlo,

Thanks! I see better now... However, how can i manage to not have multicollinearity, knowing that i want to see the interaction between my independent variable and the crisis/outisde-crisis period ?
What would you recommend?

Thanks a lot for your time and help.

Stephan
Comment
Carlo Lazzaro

Join Date: Apr 2014

Posts: 17134
#12

10 Jul 2019, 10:02

Stephan:
if you want to keep the same regression specification, you will experience the same nuisances.
The only fix is to change your model specification.

Kind regards,
Carlo
(StataNow 18.5)
Comment
Stephan Yan

Join Date: Jul 2019

Posts: 17
#13

18 Jul 2019, 04:21

Dear Carlo,

First of all thanks for your previous answer. I am still trying to find a solution regarding the interaction term indepvar#crisisperiod.

Now i would like to ask your advice regarding the fixed effect in my model:

1) If i am using the following model (time and industry fixed effects, without firm fixed effect) :

reghdfe depvar indepvar somecontrolvariables, absorb(YEAR#SIC_group)

I get a positive and significant coefficient., however the rsquare is low, around 0.16.

2) If i am using the same model and add the firm fixed effect, i get a positive but insignificant coefficient, with a Rsquare of 0.86

reghdfe depvar indepvar somecontrolvariables, absorb(YEAR#SIC_group ID)

3) Now if i am using the same model but only with industry and firm fixed effect (without time fixed effect): I get negative and significant coefficient, with a Rsquare of 0.80

reghdfe depvar indepvar somecontrolvariables, absorb(SIC_group ID)

Knowing that the Rsquare is quite low, should i go for the 2nd or 3rd option ? And do you think it's important to include the time fixed effect knowing that there is the subcrime crisis (Crisis = 2008 & 2009), my sample consist of US firms from S&P500 from 2005-2015 (i extended from 2012 to 2015).

Thanks a lot for your help!

Stephan
Comment
Carlo Lazzaro

Join Date: Apr 2014

Posts: 17134
#14

18 Jul 2019, 04:29

Stephan:
hunting for the modell with "the best" parameters is not that methodologically rewarding. Try to give a fair and true view of the data generating process, instead: for instance, what did other researchers in your field when presented with the same analysis?
Given the subprime crisis, I think it could be wise to add -i.time- among your predictors.

Kind regards,
Carlo
(StataNow 18.5)
Comment

Stephan Yan

Join Date: Jul 2019
Posts: 17

#15

18 Jul 2019, 04:43

Thanks for your answer Carlo. Actually a lot of researchers in this topic have been using the same indepvar, control variables as i am using, some included all the fixed effects (time, firm and industry), others only time and firm... And for sure mixed results, some positive link, some others negative or even no relationship between the main indepvar and depvar.

Indeed, it would be better to include the time fixed effects.

Code:

. reghdfe Q2ln_w WOB_w firmsize2_w lev2_w boardsizeln_w, absorb(YEAR#SIC_group)
(MWFE estimator converged in 1 iterations)

HDFE Linear regression                            Number of obs   =      2,473
Absorbing 1 HDFE group                            F(   4,   2436) =      51.22
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.1641
                                                  Adj R-squared   =     0.1517
                                                  Within R-sq.    =     0.0776
                                                  Root MSE        =     0.3696

-------------------------------------------------------------------------------
       Q2ln_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        WOB_w |    .279656   .0900488     3.11   0.002     .1030758    .4562362
  firmsize2_w |   .0915374    .007778    11.77   0.000     .0762852    .1067896
       lev2_w |  -.1555203   .0541967    -2.87   0.004    -.2617968   -.0492438
boardsizeln_w |  -.3623525   .0450892    -8.04   0.000    -.4507697   -.2739353
        _cons |   .5456387   .1081438     5.05   0.000     .3335755     .757702
-------------------------------------------------------------------------------

Absorbed degrees of freedom:
----------------------------------------------------------+
      Absorbed FE | Categories  - Redundant  = Num. Coefs |
------------------+---------------------------------------|
   YEAR#SIC_group |        33           0          33     |
----------------------------------------------------------+

Code:

. reghdfe Q2ln_w WOB_w firmsize2_w lev2_w boardsizeln_w, absorb(YEAR ID)
(dropped 6 singleton observations)
(MWFE estimator converged in 5 iterations)

HDFE Linear regression                            Number of obs   =      2,467
Absorbing 2 HDFE groups                           F(   4,   2201) =     215.67
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.8663
                                                  Adj R-squared   =     0.8502
                                                  Within R-sq.    =     0.2816
                                                  Root MSE        =     0.1552

-------------------------------------------------------------------------------
       Q2ln_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        WOB_w |   .0817731   .0676498     1.21   0.227     -.050891    .2144372
  firmsize2_w |   .3042183   .0106181    28.65   0.000     .2833957    .3250408
       lev2_w |  -.1435866   .0506361    -2.84   0.005    -.2428861   -.0442872
boardsizeln_w |  -.2067144   .0319225    -6.48   0.000    -.2693158   -.1441131
        _cons |  -1.876947   .1216241   -15.43   0.000    -2.115457   -1.638437
-------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
        YEAR |        11           0          11     |
          ID |       252           1         251     |
-----------------------------------------------------+

Code:

 reghdfe Q2ln_w WOB_w_lag firmsize2_w lev2_w boardsizeln_w, absorb(YEAR#SIC_group ID)
(dropped 5 singleton observations)
(MWFE estimator converged in 7 iterations)

HDFE Linear regression                            Number of obs   =      2,152
Absorbing 2 HDFE groups                           F(   4,   1877) =     223.07
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.8865
                                                  Adj R-squared   =     0.8700
                                                  Within R-sq.    =     0.3222
                                                  Root MSE        =     0.1434

-------------------------------------------------------------------------------
       Q2ln_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
    WOB_w_lag |   .0510644    .069537     0.73   0.463    -.0853135    .1874424
  firmsize2_w |   .3262593   .0111245    29.33   0.000     .3044416     .348077
       lev2_w |   -.121698   .0531832    -2.29   0.022    -.2260023   -.0173936
boardsizeln_w |   -.196547   .0327708    -6.00   0.000     -.260818    -.132276
        _cons |  -2.136371   .1260527   -16.95   0.000    -2.383589   -1.889153
-------------------------------------------------------------------------------

Absorbed degrees of freedom:
----------------------------------------------------------+
      Absorbed FE | Categories  - Redundant  = Num. Coefs |
------------------+---------------------------------------|
   YEAR#SIC_group |        30           0          30     |
               ID |       244           3         241     |
----------------------------------------------------------+

.

Given the Rsquare of the first option, i am not sure if i can go with that one, which option do you think is the fairest one ?

Thanks!

Stephan

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