Panel Data with Continuous Response and a Binary Explanatory Variable

[George Val]

Dear all,
I am testing whether a FamilyCEO among family firms performs better than an external CEO. My financial data was collected for each year in 2018-2022, and then I manually indentified binary governance variables for the year 2022, such as FamilyCEO or Active Board Control. Thus, my explanatory variable is a binary timestatic, while my response variable, which controls for firm performance (Return on Assets), is a percentage metric that changes over time.
Further controls, such as LnSales, are also time variant whitin each company.

The variable of interest, is binary and time static, and thus is ommitied from xtreg, fe.

When I run a Hausmann, Fixed Effects is always implied. Although Fixed Effects predict well the time variant variables, the variable of interest is not in the model!

I am assuming, that I can not speculative choose Random Effects just so i can present some coefficients which I understand will be biased and unreliable, after Hausman always suggests Fixed Effects with p value of 0.

I have gone through so much bibliography, like Richard Williams, University of Notre Dame summaries of Paul Allison’s book, Fixed Effects Regression Models for Categorical Data, but I have not found anything that describes my problem. Firstly I belived that Mixed effects will be my solution, but I realized its just Random Effects, which Hausman rejects. Then Conditional Logit/ Fixed Effects Logit Models chapter of Richard Williams, gave me some hope to tackle my problem with xtlogit, fe or clogit , group(id). These commands result in this error though: outcome does not vary in any group.

I would appriciate any help or guidance with this!

Results:

A is id for companies.

. . xtset A Year

Panel variable: A (strongly balanced)
Time variable: Year, 2018 to 2022
Delta: 1 unit

. . xtreg ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, fe
note: FamilyCEO omitted because of collinearity.
note: Listed omitted because of collinearity.

Fixed-effects (within) regression Number of obs = 2,713
Group variable: A Number of groups = 552

R-squared: Obs per group:
Within = 0.1477 min = 2
Between = 0.0008 avg = 4.9
Overall = 0.0018 max = 5

F(4,2157) = 93.42
corr(u_i, Xb) = -0.6824 Prob > F = 0.0000

------------------------------------------------------------------------------
ROAEbitda | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
FamilyCEO | 0 (omitted)
LnAssets | .00912 .0073177 1.25 0.213 -.0052304 .0234704
Leverage | .0010998 .0016542 0.66 0.506 -.0021443 .0043439
LnSales | .0547579 .0031807 17.22 0.000 .0485203 .0609955
LnFirmAge | .018173 .0169342 1.07 0.283 -.015036 .0513821
Listed | 0 (omitted)
_cons | -.6031131 .063925 -9.43 0.000 -.7284741 -.4777521
-------------+----------------------------------------------------------------
sigma_u | .11107798
sigma_e | .0578294
rho | .78675418 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(551, 2157) = 8.35 Prob > F = 0.0000

. . estimates store fe

. . quietly xtreg ROAEbitda FamilyCEO LnAssets LnLiabilities Leverage LnSales LnFirmAge Listed, re

.
. . estimates store re

.
. . hausman fe re

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference Std. err.
-------------+----------------------------------------------------------------
LnAssets | .00912 -.0262048 .0353248 .0064722
Leverage | .0010998 .0012577 -.0001579 .0009204
LnSales | .0547579 .0395582 .0151997 .0018378
LnFirmAge | .018173 -.0081283 .0263014 .015901
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 174.02
Prob > chi2 = 0.0000

.
. . xtlogit ROAEbitda i.FamilyCEO LnAssets LnLiabilities Leverage LnSales LnFirmAge i.Listed i.Year , fe
outcome does not vary in any group
r(2000);

If you need more data or regression results, let me know and I will upload it here.

[Clyde Schechter]

No matter how you try to get around this you will fail: it is mathematically impossible to estimate the effects of a time-invariant variable using a fixed-effects analysis. It's linear algebra, and there's no getting around it, no matter what Hausman or anybody else says. Probably your best bet with this data is to use OLS regression instead.

A better solution, if feasible, is to get a new data set where FamilyCEO actually changes over time within firms. Then you can use a fixed effects model.

[George Val]

Thanks for the quick response!!
So, you are implying that not even Random Effects model could be used? When I run xtreg, re I get a FamilyCEO coefficient, but I am not sure how much I can rely on it.
How would a standard OLS approach work with my variables that have observations throughout the years?

[Clyde Schechter]

How would a standard OLS approach work with my variables that have observations throughout the years?

regress ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, vce(cluster A)

So, you are implying that not even Random Effects model could be used? When I run xtreg, re I get a FamilyCEO coefficient, but I am not sure how much I can rely on it.

I wouldn't rely on a pure random effects regression here. Another approach you might consider, is -xthybrid-, available from SSC. It estimates a correlated random effects model, and it separately reports within-group and between-group effects for each variable. (There will be no within-group effect reported for FamilyCEO, because within-group effects cannot be estimated when there is no within-group variation. But you can use the between group coefficient of FamilyCEO.)

[George Val]

The xthybrid is quite intersting for my case indeed.

How would you choose between xthybrid and standard OLS?

variables such LnAssets stay almost the same across regress; xtreg, re; xthybrid (Within Variation coefficient), which confuses me further!!

the xthybrid command give me this error:
The variable 'FamilyCEO' does not vary sufficiently within clusters
and will not be used to create additional regressors.
[~0% of the total variance in 'FamilyCEO' is within clusters]

Could I define FamilyCEO to vary between clusters instead within?


Here i upload a table showing all results of the following commands.

regress ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, vce(cluster A)
xtset A Year
xtreg ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, fe vce(cluster A)
xtreg ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, re vce(cluster A)
xtreg ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, mle vce(cluster A)
xthybrid ROAEbitda FamilyCEO LnAssets Leverage LnFirmAge Listed, cluster(A)

(1) (2) (3) (4) (5)
ROAEbitda ROAEbitda ROAEbitda ROAEbitda ROAEbitda

main

FamilyCEO 0.00505 0 0.0102 0.0103
(0.65) (.) (1.30) (1.30)

LnAssets -0.0290*** 0.00912 -0.0301*** -0.0300***
(-7.21) (0.61) (-5.80) (-5.89)

Leverage 0.000221 0.00110 0.000830 0.000839
(0.12) (0.71) (0.54) (0.54)

LnSales 0.0309*** 0.0548*** 0.0445*** 0.0447***
(9.74) (5.75) (8.43) (8.10)

LnFirmAge -0.0145 0.0182 -0.00615 -0.00598
(-1.72) (0.63) (-0.67) (-0.67)

Listed -0.0147 0 -0.0448*** -0.0454***
(-1.09) (.) (-3.49) (-3.59)

R__FamilyCEO -0.00122
(-0.15)

R__Listed 0.00684
(0.43)

W__LnAssets 0.0433***
(5.79)

W__Leverage 0.000295
(0.17)

W__LnFirmAge 0.0336
(1.86)

B__LnAssets -0.00869**
(-2.94)

B__Leverage -0.000627
(-0.29)

B__LnFirmAge -0.0200***
(-3.34)

_cons 0.130** -0.603*** -0.0254 -0.0285 0.254***
(3.02) (-4.18) (-0.52) (-0.64) (7.80)

sigma_u
_cons 0.0712***
(13.26)

sigma_e
_cons 0.0589***
(20.92)

var(_cons[~)
_cons 0.00496***
(14.36)

var(e.ROAE~)
_cons 0.00380***
(32.91)

N 2713 2713 2713 2713 2716

[Clyde Schechter]

Your output is all misaligned and unreadable. Please repost it from your results window or log file, enclosing it within code delimiters, so it can be easily read.

Also, when posting back, indicate which model is (1), which is (2), etc.

[Jeff Wooldridge]

With a balanced panel, you should get the same estimates using xtreg, fe and xthybrid on the variables they have in common -- that is, all variables that change across time. In economics, the hybrid approach is called the Mundlak approach, after a 1978 Econometrica paper. It is also a good way to obtain a robust version of the Hausman test. The usual Hausman test is not robust to serial correlation/heteroskedasticity.

Is your panel balanced? If so, xthybrid simply includes the time average of each time-varying variable in a pooled OLS regression. So this gives a very easy way to to choose between POLS and xthybrid. I show their equivalence in my 2019 Journal of Econometrics paper on Correlated Random Effects approaches -- which is yet another name for the "hybrid" approach.

[George Val]

Thank you all for you answers, have been prooved really insightfu!. I hope my supervisor will infact support these models and not stick to simple OLS...

Since i have to submit the following Friday, I need to have reliable results as soon as possible... Maybe the safe solution, if nothing works, would be to drop observations this way: drop all ROAEbitda time variables expect ROAEbitda2022 and then actually run simple reg with 2022 data for all previously time variant variables.

I reallty want to keep a good analysis that utilizes as many variables as possible so I wish this won't be the case, otherwise I would not have gone through 908 firms data, to manually collect all my key variables (FamilyOwnership, FamilyCEO, ActiveBoardControl, CEOinBoard, OtherFamilyonBoard, FamilyinBoardnotCEO, TotalBoardMembers, NumberofShareholders)... This research has a personal connection with myself, so I need to really find reliable and robust results.

My data Balance

. xtset A Year
Panel variable: A (strongly balanced)
Time variable: Year, 2018 to 2022
Delta: 1 unit

Here is the table following these commands.

regress ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, vce(cluster A)
estimates store model1

xtset A Year

xtreg ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, fe vce(cluster A)
estimates store model2

xtreg ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, re vce(cluster A)
estimates store model3

xtreg ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, mle vce(cluster A)
estimates store model4

xthybrid ROAEbitda FamilyCEO LnAssets Leverage LnFirmAge Listed, cluster(A)
estimates store model5

--------------------------------------------------------------------------------------------
                      (1)             (2)             (3)             (4)             (5)  
                ROAEbitda       ROAEbitda       ROAEbitda       ROAEbitda       ROAEbitda  
--------------------------------------------------------------------------------------------
main                                                                                        
FamilyCEO         0.00510               0         0.00983         0.00989                  
                   (0.66)             (.)          (1.24)          (1.24)                  

LnAssets          -0.0286***      0.00910         -0.0285***      -0.0284***                
                  (-7.32)          (0.69)         (-5.47)         (-5.60)                  

Leverage        0.0000238        0.000698        0.000470        0.000472                  
                   (0.02)          (0.88)          (0.47)          (0.47)                  

LnSales            0.0302***       0.0521***       0.0427***       0.0428***                
                   (9.63)          (5.36)          (7.69)          (7.43)                  

LnFirmAge         -0.0147          0.0191        -0.00645        -0.00634                  
                  (-1.78)          (0.71)         (-0.71)         (-0.72)                  

Listed            -0.0146               0         -0.0449***      -0.0453***                
                  (-1.10)             (.)         (-3.50)         (-3.57)                  

R__FamilyCEO                                                                     -0.00106  
                                                                                  (-0.13)  

R__Listed                                                                         0.00671  
                                                                                   (0.42)  

W__LnAssets                                                                        0.0389***
                                                                                   (5.59)  

W__Leverage                                                                      0.000281  
                                                                                   (0.21)  

W__LnFirmAge                                                                       0.0372*  
                                                                                   (2.17)  

B__LnAssets                                                                      -0.00863**
                                                                                  (-2.94)  

B__Leverage                                                                     -0.000767  
                                                                                  (-0.34)  

B__LnFirmAge                                                                      -0.0200***
                                                                                  (-3.35)  

_cons               0.134**        -0.578***      -0.0225         -0.0247           0.253***
                   (3.24)         (-4.24)         (-0.46)         (-0.55)          (7.84)  
--------------------------------------------------------------------------------------------
sigma_u                                                                                    
_cons                                                              0.0711***                
                                                                  (13.21)                  
--------------------------------------------------------------------------------------------
sigma_e                                                                                    
_cons                                                              0.0586***                
                                                                  (21.01)                  
--------------------------------------------------------------------------------------------
var(_cons[~)                                                                                
_cons                                                                             0.00497***
                                                                                  (14.41)  
--------------------------------------------------------------------------------------------
var(e.ROAE~)                                                                                
_cons                                                                             0.00373***
                                                                                  (33.23)  
--------------------------------------------------------------------------------------------
N                    2760            2760            2760            2760            2760  
--------------------------------------------------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001

Thank you all for you answers
Have a great day wherever you are!

[George Val]

I found some interesting? results:

I created a new dofile that only keeps variables from 2022.

after the following code I got the coefficients of the simple OLS regrresion from a dataset containing only 2022 variables. They do not seem very off from model (1) in the previous table of panel data analysis.

regress ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed, vce(cluster A)
regress ROAEbitda FamilyCEO LnAssets Leverage LnSales LnFirmAge Listed

--------------------------------------------
                      (1)             (2)  
             ROAEbit~2022    ROAEbit~2022  
--------------------------------------------
FamilyCEO         0.00585         0.00585  
                   (0.63)          (0.58)  

LnAssets          -0.0275***      -0.0275***
                  (-4.24)         (-4.56)  

Leverage2022     -0.00254        -0.00254  
                  (-1.01)         (-0.81)  

LnSales            0.0291***       0.0291***
                   (4.83)          (4.67)  

LnFirmAge         -0.0226**       -0.0226**
                  (-2.62)         (-2.69)  

Listed            -0.0269         -0.0269  
                  (-1.55)         (-1.30)  

_cons               0.172***        0.172***
                   (3.45)          (3.64)  
--------------------------------------------
N                     542             542  
--------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001

What are you recommendations on what I should follow

[Jeff Wooldridge]

Reducing the panel data set to a single cross section doesn't make much sense. I don't know why you'd drop the year dummy variables in a panel data analysis. Data analysis should be done as objectively as possible. You shouldn't choose the model/estimation based on what you want to be true.

To keep the FamilyCEO variable in the analysis and to account for time trends, xthybrid is the most robust if you put back in the time dummies. It gets you "close" to two-way FE but keeps in FamilyCEO. The hybrid IS pooled OLS with added variables: the within firm averages of every variable that changes across time.

[Jeff Wooldridge]

You might interact FamilyCEO with some of the variables that change across time to see if something interesting emerges there.

[George Val]

Reducing the panel data set to a single cross section doesn't make much sense. I don't know why you'd drop the year dummy variables in a panel data analysis.

I would do this so I can actually tests my hypothesis. If there was no method to test the effect of a binary on time variant variables between diffrent companies, then I would have to test this effect only for one year across companies.

I will look xthybrid further. Are there any model fit tests for this or should I explain the choice of the model intutivly ? Are there any post estimation checks to ensure reliability and robustness?

Lastly, when I run this code, FamilyCEO 's coefficient is not the between effects one. Is there another way to specify the model and control FamilyCEo only for between effects?

. xthybrid ROAEbitda FamilyCEO LnAssets Leverage LnFirmAge Listed, cluster(A)

The variable 'FamilyCEO' does not vary sufficiently within clusters
and will not be used to create additional regressors.
[~0% of the total variance in 'FamilyCEO' is within clusters]
The variable 'Listed' does not vary sufficiently within clusters
and will not be used to create additional regressors.
[~0% of the total variance in 'Listed' is within clusters]

Hybrid model. Family: gaussian. Link: identity.

+-----------------------------------+
|             Variable |   model    |
|----------------------+------------|
| ROAEbitda            |            |
|         R__FamilyCEO |    -0.0011 |
|            R__Listed |     0.0067 |
|          W__LnAssets |     0.0389 |
|          W__Leverage |     0.0003 |
|         W__LnFirmAge |     0.0372 |
|          B__LnAssets |    -0.0086 |
|          B__Leverage |    -0.0008 |
|         B__LnFirmAge |    -0.0200 |
|                _cons |     0.2532 |
|----------------------+------------|
|         var(_cons[A])|            |
|                _cons |     0.0050 |
|----------------------+------------|
|      var(e.ROAEbitda)|            |
|                _cons |     0.0037 |
|----------------------+------------|
| Statistics           |            |
|                   ll |  3236.8837 |
|                 chi2 |    93.1550 |
|                    p |     0.0000 |
|                  aic | -6451.7675 |
|                  bic | -6386.6146 |
+-----------------------------------+
Level 1: 2760 units. Level 2: 552 units.

Thank you for your time and understanding!

[George Val]

I investigated more the xthybrid command and I studied this

https://www3.nd.edu/~rwilliam/Taiwan2018/Hybrid.pdf

.

I ran two xthybrid commands, but now i used the option use() with time varying variables.

The one has no interaction terms and the second inlcudes them. @Jeff Wooldrifge

I also used the test option, because Williams suggests that

If the assumptions of the random effects model are true, the coefficients for the B_

variables (between-group) should equal the coefficients for the corresponding W_

variables. xthybrid has a test option that lets you test whether or not the assumptions hold

I understand I have to exclude Assets and Firm age? Interactions seem all ok.

A last question would be on how can I justify the use of xthybrid vs xtreg, re in my Thesis? I can well understand why FE would not work but I am not sure yet why Random Effects are not suitable.

My primarily research question is: Family vs External CEO in family firms. I also test for moderating effects of size and industry. Later I also test the effect of Active Control on firm performance, which I define as ROA (%).

xthybrid ROAEbitda FamilyCEO Listed, use (LnAssets Leverage LnFirmAge) cluster( A) test full


-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Model model
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Mixed-effects GLM                               Number of obs     =      2,716
Family: Gaussian
Link:   Identity
Group variable: A                               Number of groups  =        552

                                                Obs per group:
                                                              min =          2
                                                              avg =        4.9
                                                              max =          5

Integration method: mvaghermite                 Integration pts.  =          7

                                                Wald chi2(8)      =      95.94
Log likelihood = 3161.4441                      Prob > chi2       =     0.0000
---------------------------------------------------------------------------------
      ROAEbitda | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
   R__FamilyCEO |  -.0012191   .0078951    -0.15   0.877    -.0166932     .014255
      R__Listed |   .0068469   .0160279     0.43   0.669    -.0245672    .0382611
    W__LnAssets |   .0432721   .0074712     5.79   0.000     .0286287    .0579154
    W__Leverage |   .0002946   .0017625     0.17   0.867    -.0031598     .003749
   W__LnFirmAge |   .0335355   .0180062     1.86   0.063    -.0017559    .0688269
    B__LnAssets |  -.0086935   .0029528    -2.94   0.003    -.0144808   -.0029061
    B__Leverage |  -.0006267    .002152    -0.29   0.771    -.0048446    .0035912
   B__LnFirmAge |  -.0199983   .0059897    -3.34   0.001    -.0317379   -.0082587
          _cons |   .2540493   .0325603     7.80   0.000     .1902324    .3178663
----------------+----------------------------------------------------------------
A               |
      var(_cons)|   .0049634   .0003456                      .0043302    .0056892
----------------+----------------------------------------------------------------
var(e.ROAEbitda)|   .0037993   .0001154                      .0035796    .0040324
---------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 1177.72       Prob >= chibar2 = 0.0000

Tests of the random effects assumption:
  _b[B__LnAssets] = _b[W__LnAssets]; p-value: 0.0000
  _b[B__Leverage] = _b[W__Leverage]; p-value: 0.7405
  _b[B__LnFirmAge] = _b[W__LnFirmAge]; p-value: 0.0048

then I created these interactions:

gen CEO_Asset=FamilyCEO*LnAssets

gen CEO_Lev=FamilyCEO*Leverage

gen CEO_List=FamilyCEO*Listed

gen Age_CEO= FamilyCEO*LnFirmAge

Results of xthybrid with interactions

xthybrid ROAEbitda FamilyCEO Listed, use (LnAssets Leverage LnFirmAge CEO_Asset CEO_Lev CEO_List Age_CEO) cluster(A) test full

The variable 'CEO_List' does not vary sufficiently within clusters
and will not be used to create additional regressors.
[~0% of the total variance in 'CEO_List' is within clusters]

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Model model
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Mixed-effects GLM                               Number of obs     =      2,716
Family: Gaussian
Link:   Identity
Group variable: A                               Number of groups  =        552

                                                Obs per group:
                                                              min =          2
                                                              avg =        4.9
                                                              max =          5

Integration method: mvaghermite                 Integration pts.  =          7

                                                Wald chi2(14)     =     111.58
Log likelihood = 3168.9624                      Prob > chi2       =     0.0000
---------------------------------------------------------------------------------
      ROAEbitda | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
----------------+----------------------------------------------------------------
   R__FamilyCEO |   .1138254   .0710074     1.60   0.109    -.0253466    .2529974
      R__Listed |   .0042638   .0160288     0.27   0.790    -.0271522    .0356797
    W__LnAssets |   .0707354   .0140897     5.02   0.000       .04312    .0983508
    W__Leverage |  -.0261081   .0120863    -2.16   0.031    -.0497968   -.0024194
   W__LnFirmAge |   .0257901   .0346974     0.74   0.457    -.0422157    .0937958
   W__CEO_Asset |  -.0377249    .016639    -2.27   0.023    -.0703367   -.0051132
     W__CEO_Lev |   .0269669   .0122162     2.21   0.027     .0030236    .0509103
     W__Age_CEO |   .0165437   .0406617     0.41   0.684    -.0631519    .0962392
    B__LnAssets |  -.0040593   .0051255    -0.79   0.428    -.0141051    .0059865
    B__Leverage |  -.0230506   .0169901    -1.36   0.175    -.0563506    .0102493
   B__LnFirmAge |  -.0055574   .0125352    -0.44   0.658     -.030126    .0190111
   B__CEO_Asset |  -.0060655   .0059961    -1.01   0.312    -.0178176    .0056866
     B__CEO_Lev |    .022581   .0171285     1.32   0.187    -.0109904    .0561523
     B__Age_CEO |  -.0168626    .014264    -1.18   0.237    -.0448195    .0110942
          _cons |   .1615458   .0643315     2.51   0.012     .0354584    .2876332
----------------+----------------------------------------------------------------
A               |
      var(_cons)|   .0049222   .0003428                      .0042941    .0056422
----------------+----------------------------------------------------------------
var(e.ROAEbitda)|   .0037806   .0001149                       .003562    .0040126
---------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 1174.95       Prob >= chibar2 = 0.0000

Tests of the random effects assumption:
  _b[B__LnAssets] = _b[W__LnAssets]; p-value: 0.0000
  _b[B__Leverage] = _b[W__Leverage]; p-value: 0.8834
  _b[B__LnFirmAge] = _b[W__LnFirmAge]; p-value: 0.3955
  _b[B__CEO_Asset] = _b[W__CEO_Asset]; p-value: 0.0734
  _b[B__CEO_Lev] = _b[W__CEO_Lev]; p-value: 0.8349
  _b[B__Age_CEO] = _b[W__Age_CEO]; p-value: 0.4382