I use Stata version 16 and have confusing outcomes for regressions that use almost the same variables, only with one differing binary variable and related interaction term.
The interaction term with the binary variable for being a family firm is omitted. When performing the same regression with another binary variable for instance being a young firm, it is not omitted.
I think it is necessary to explain the variable construction so the text is pretty long.
I research whether family firms are more oriented towards digital orientation, which is measured by the amount of digital terms in an annual report. And if more digital terms in the annual report have an impact on the performance of a firm in one particular year.
So I have two types of regressions.
The firm observations are over 10 years and 30 different industries.
First, I want to explain the background of variable construction before showing the regressions.
The binary variable for being a family firm is iFFF_PU.
With further information, I created binary variables indicating if a firm is young or for family firms if the firm is run by a successor or the founder (SUCCESSION_second_or_later). Later, I perform all regressions with these different types of binary variables respectively.
I used textual analysis and counted the frequency of digital words. The total amount of frequencies of digital words in a report is shown in the variable Digital_Terms in Stata. Another variable shows the total amount of words in an annual report, named wordcount.
So, I calculated a quotient when dividing Digital_Terms by wordcount. That quotient indicated the digital orientation for one specific firm observation. That variable is named Digital_Terms_rel. I winsorized the variable and created Digital_Terms_rel_W99.
Next, I created a binary variable that shows the digital maturity, digital_mature_above_mean.
I compare the maturity degree by industry and year. So, I create a mean by industry and year as shown in the code below. The three last lines are repeated for each industry.
Code:
generate digital_mature_above_mean=. bysort industry year : egen digital_median_industry1=median (Digital_Terms_rel_W99) if industry==1 replace digital_mature_above_mean=1 if industry==1 & Digital_Terms_rel_W99>=digital_mean_industry1 & digital_mean_industry1!=0 replace digital_mature_above_mean=0 if industry==1 & Digital_Terms_rel_W99<digital_mean_industry1
Furthermore, I winsorized (W99) the control variables and the performance measure ROCE that is used in the second regression (ROCE_PSM_W99).
I created interaction terms for iFFF_PU*digital_mature_above_mean = Digital_mature_FFF.
And for SUCCESSION_second_or_later*digital_mature_above_me an = Digital_mature_second.
In the regressions, I apply fixed effects and use a cluster on the firm level (DSCD_group). I assume that this might be part of the problem with the omitted interaction term.
Now, I want to explain the issue with the interaction term in the regression.
The first regression tells me if family firms use more digital terms in the annual report. There, the family firm variable is not omitted as seen below.
The second regression with the problem follows afterward. The last regression is the same type as the second regression with another binary variable.
In the second regression, the variable iFFF_PU is omitted, together with the interaction term Digital_mature_FFF for iFFF_PU*digital_mature_above_mean.
Interestingly, no variables are omitted in the second regression, when performing it with other binary variables instead of iFFF_PU and Digital_mature_FFF. For instance, SUCCESSION_second_or_later and Digital_mature_second. So I am not sure what is the problem.
As well, the second regression works when not including a binary variable and interaction term and just looking at ROCE and digital maturity.
But I would like to include the effect of being a family firm as an interaction term.
First regression:
Code:
xtreg digital_mature_above_mean iFFF_PU LOGASSETS_W99 RD_TOTALASSETS_W99 LEVERAGE_W99 log_age_W99 i.year, fe vce(cluster DSCD_group)
/*
Fixed-effects (within) regression Number of obs = 6,076
Group variable: DSCD_group Number of groups = 1,509
R-sq: Obs per group:
within = 0.0094 min = 1
between = 0.0031 avg = 4.0
overall = 0.0069 max = 10
F(14,1508) = 2.04
corr(u_i, Xb) = -0.2917 Prob > F = 0.0127
(Std. Err. adjusted for 1,509 clusters in DSCD_group)
------------------------------------------------------------------------------------
| Robust
digital_mature~ean | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------------+----------------------------------------------------------------
iFFF_PU | .1243809 .0588633 2.11 0.035 .0089182 .2398436
LOGASSETS_W99 | .0192579 .0205871 0.94 0.350 -.0211244 .0596402
RD_TOTALASSETS_W99 | .5236466 .2057576 2.54 0.011 .1200451 .927248
LEVERAGE_W99 | -.1882404 .0771609 -2.44 0.015 -.3395945 -.0368863
log_age_W99 | -.1573416 .0596105 -2.64 0.008 -.2742698 -.0404133
|
year |
2008 | .0099622 .0209893 0.47 0.635 -.0312091 .0511335
2009 | .0279309 .0226848 1.23 0.218 -.0165662 .072428
2010 | .0199412 .022291 0.89 0.371 -.0237835 .0636659
2011 | .0191032 .0255865 0.75 0.455 -.0310857 .069292
2012 | .0358215 .0279123 1.28 0.200 -.0189295 .0905726
2013 | .0447236 .0294185 1.52 0.129 -.0129819 .1024292
2014 | .0462766 .0311215 1.49 0.137 -.0147694 .1073227
2015 | .0495094 .0333949 1.48 0.138 -.015996 .1150148
2016 | .0201235 .0367715 0.55 0.584 -.0520052 .0922522
|
_cons | .5737268 .3168242 1.81 0.070 -.0477361 1.19519
-------------------+----------------------------------------------------------------
sigma_u | .42184424
sigma_e | .33024646
rho | .62001075 (fraction of variance due to u_i)
------------------------------------------------------------------------------------
*/Second regression with omitted variables:
Code:
xtreg ROCE_PSM_W99 digital_mature_above_mean iFFF_PU Digital_mature_FFF LOGASSETS_W99 RD_TOTALASSETS_W99 LEVERAGE_W99 log_age_W99 i.year, fe vce(cluster DSCD_group)
/*
Fixed-effects (within) regression Number of obs = 2,846
Group variable: DSCD_group Number of groups = 491
R-sq: Obs per group:
within = 0.0801 min = 1
between = 0.1123 avg = 5.8
overall = 0.0658 max = 10
F(14,490) = 8.47
corr(u_i, Xb) = -0.4980 Prob > F = 0.0000
(Std. Err. adjusted for 491 clusters in DSCD_group)
-------------------------------------------------------------------------------------------
| Robust
ROCE_PSM_W99 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
digital_mature_above_mean | .0015257 .0068942 0.22 0.825 -.0120201 .0150715
iFFF_PU | 0 (omitted)
Digital_mature_FFF | 0 (omitted)
LOGASSETS_W99 | .0595091 .0213889 2.78 0.006 .0174838 .1015344
RD_TOTALASSETS_W99 | -.1839393 .1770742 -1.04 0.299 -.5318578 .1639791
LEVERAGE_W99 | -.4000058 .0716585 -5.58 0.000 -.5408016 -.2592101
log_age_W99 | -.0119956 .0257857 -0.47 0.642 -.0626598 .0386685
|
year |
2008 | -.0321236 .0130105 -2.47 0.014 -.0576869 -.0065604
2009 | -.0698131 .0109915 -6.35 0.000 -.0914095 -.0482168
2010 | -.0370126 .0101041 -3.66 0.000 -.0568653 -.0171599
2011 | -.0421062 .0105742 -3.98 0.000 -.0628825 -.0213298
2012 | -.0748366 .014759 -5.07 0.000 -.1038353 -.0458379
2013 | -.0823939 .0137447 -5.99 0.000 -.1093998 -.055388
2014 | -.0743612 .0142766 -5.21 0.000 -.1024121 -.0463104
2015 | -.0687012 .0152917 -4.49 0.000 -.0987465 -.0386558
2016 | -.0668769 .0152307 -4.39 0.000 -.0968023 -.0369514
|
_cons | -.4618073 .2551419 -1.81 0.071 -.9631145 .0395
--------------------------+----------------------------------------------------------------
sigma_u | .17623383
sigma_e | .12431114
rho | .66775488 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------------Code:
xtreg ROCE_PSM_W99 digital_mature_above_mean SUCCESSION_second_or_later Digital_mature_second LOGASSETS_W99 RD_TOTALASSETS_W99 LEVERAGE_W99 log_age_W99 i.year, fe vce(cluster DSCD_group)
/*
Fixed-effects (within) regression Number of obs = 2,846
Group variable: DSCD_group Number of groups = 491
R-sq: Obs per group:
within = 0.0807 min = 1
between = 0.1114 avg = 5.8
overall = 0.0642 max = 10
F(16,490) = 7.59
corr(u_i, Xb) = -0.5238 Prob > F = 0.0000
(Std. Err. adjusted for 491 clusters in DSCD_group)
--------------------------------------------------------------------------------------------
| Robust
ROCE_PSM_W99 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
digital_mature_above_mean | -.0038213 .0105641 -0.36 0.718 -.0245779 .0169352
SUCCESSION_second_or_later | .0148595 .0260783 0.57 0.569 -.0363796 .0660986
Digital_mature_second | .0118455 .0118562 1.00 0.318 -.0114499 .0351408
LOGASSETS_W99 | .0602139 .0214728 2.80 0.005 .0180238 .102404
RD_TOTALASSETS_W99 | -.1935052 .1780475 -1.09 0.278 -.543336 .1563256
LEVERAGE_W99 | -.3999631 .071717 -5.58 0.000 -.5408739 -.2590524
log_age_W99 | -.0126539 .0256519 -0.49 0.622 -.0630551 .0377473
|
year |
2008 | -.0322014 .0130127 -2.47 0.014 -.0577689 -.0066338
2009 | -.0700359 .0110284 -6.35 0.000 -.0917046 -.0483671
2010 | -.0374974 .0102 -3.68 0.000 -.0575385 -.0174563
2011 | -.0427666 .010715 -3.99 0.000 -.0638196 -.0217137
2012 | -.0754224 .0148515 -5.08 0.000 -.1046029 -.046242
2013 | -.0834185 .0138344 -6.03 0.000 -.1106006 -.0562364
2014 | -.0756862 .0144859 -5.22 0.000 -.1041484 -.0472241
2015 | -.0702621 .0155296 -4.52 0.000 -.100775 -.0397492
2016 | -.0689003 .0153864 -4.48 0.000 -.0991317 -.0386689
|
_cons | -.4721153 .2569105 -1.84 0.067 -.9768975 .032667
---------------------------+----------------------------------------------------------------
sigma_u | .17777008
sigma_e | .12432234
rho | .67155502 (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------
0 Response to Omitted Variables in Interaction Term - Other Panel Data Regressions with same Procedure without Omitted Variables
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