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  • Checking fixed effects modeling

    Hi,

    My question is only partly related to stata but I would really appreciate any help here.

    Research goal:
    I am researching the effect of the Chief Financial Officers influence in a company on the companys acquisitions. This managerial influence is also referred to as "managerial power" in the management literature. My goal is to research how the managerial power of a CFO impacts certain characteristics of acquisitions made by the company.

    Sample:
    My sample consists of around 4,300 Acquisitions announced from U.S. companies between 1996 and 2018 made by 1,380 unique acquirors (firms). For each acquisition I have data on the CFO that was in place while the deal was announced.

    I implemented four variables that are used for proxying a managers influence in the acquiring company (reflecting the four dimensions of managerial power introduced by Finkelstein (1992)1).
    Those variables are:
    1. Pay Slice: Compensation of the CFO relative to the sum of compensation of the 5 highest paid managers in the company.
    2. M&A Experience: Number of Deals the CFO was involved in other companies up to 10 years before the deal announcement.
    3. Number of Boardseats: Number of Boards the CFO sits on during the deal announcement (excluding the boardseat he may holds in the acquiring firm)
    4. Ownership: Shares owned by the CFO relative to shares owned by all managers of the company (in percentage)
    One of my dependend variables is the cumulative abnormal return (CAR) around the time of the acquisition announcement as a measure of investor reactions to a given acquisition.

    I am controlling for effects suggested in the literature which include Deal characteristics (Payment method, Deal value...), Acquiror characteristics (Free Cash Flow, Size (Market value)...) as well as for other CFO characteristics (Age, Gender, tenure...).

    Example of my data (due to dataex variable limits I only include a subset of variables):

    Code:
    * Example generated by -dataex-. For more info, type help dataex
    clear
    input long(Acq_ID CFO_ID) str26 CFO_Name byte(CFO_Age CFO_MBA) float CFO_PaySlice byte CFO_No_Boardseats int CFO_Tenure byte CFO_No_Deals str52 Acq_Name int(Deal_Announced Deal_Year_Ann) double Deal_Value float(CFO_Perc_Own_Dir Acq_CAR_1_1_ES2)
      19966 206565 "Jeff Campbell"     61 1  .2097557 2 2638 0 "McKesson Corp"                                18800 2011   90000000 12.200355  -.02181801
       6908  32837 "Larry Carter"      78 0 .18803322 0  477 0 "Cisco Systems Inc"                            13261 1996 4833530000  .9654859  -.00428218
      82823  56737 "Bob Dykes"         73 0 .23726204 1  722 6 "Verifone Systems Inc"                         18506 2010    9000000  7.022498   -.0419592
    1715277 206147 "John Austin"       60 0 .20607075 0  528 0 "The Chefs' Warehouse Inc"                     19703 2013   29900000 2.1689453  -.00999988
      19839 334420 "Joyce Schuldt"     54 0 .14923082 0    5 0 "Maverick Tube Corp"                           16579 2005  1.860e+08         0   .04028475
       2621 334012 "Paul Reilly"       65 0  .1490617 0  521 0 "Arrow Electronics Inc"                        17078 2006   80000000  75.45046  .010976512
      30738 141599 "Brian McKeon"      59 1  .1580198 1 1286 4 "Timberland Co"                                16747 2005   82000000  4.217062  .025647774
    1979174 482279 "Randy Broaddrick"  44 0  .2631579 0  157 3 "Ring Energy Inc"                              19761 2014    6450000 2.2242737           .
      25116 321843 "Dennis Klaeser"    64 1  .1742429 1  744 0 "PrivateBancorp Inc"                           16540 2005   64000000 .59503466   .06500283
    1064229 360075 "James Budge"       56 0   .250058 0 1938 5 "Rovi Corp"                                    18618 2010  741761000 10.470184 -.006451557
     806647 507495 "Cesar Ribeiro"     52 0 .26558557 0 1121 0 "Lincoln Educational Services Corp"            17923 2009    3000000  .8498709   -.0029008
       7637 322193 "Gary Haroian"      70 0 .04092294 0   80 0 "Concord Communications Inc"                   14629 2000  104391000  12.99716   -.2070821
      32498 206690 "Dana Evan"         63 0   .199771 0 1836 1 "Verisign Inc"                                 16812 2006   30000000 11.331512  .016551858
      30437 206292 "Greg Beecher"      64 0  .2313652 1 1292 1 "Teradyne Inc"                                 18884 2011  5.800e+08  4.894503   .00418798
        428  33484 "Tom Freyman"       67 0 .14662687 0  844 0 "Abbott Laboratories"                          15910 2003  1.600e+08   5.97643   -.0427234
       4081 532517 "Kevin Riley"       62 0  .2105263 0  355 0 "Berkshire Hills Bancorp Inc"                  18618 2010  114915000  8.721497  .001181409
      29943 321145 "Craig Cohen"       63 0  .3952577 0  782 0 "TALX Corp"                                    15147 2001   12100000 3.8284714 -.002068691
      21553 205616 "Steve Krablin"     71 0 .15972222 0 1536 7 "National-Oilwell Inc"                         14685 2000  328136000 1.2829663   .05274526
       5860 320196 "Martin Durant III" 69 0  .1481551 0 2119 0 "Carmike Cinemas Inc"                          16545 2005   66000000 2.0207245           .
      30483 343439 "Joseph Abell III"  67 1 .15521003 0 1773 0 "TETRA Technologies Inc"                       16869 2006   50000000         0   .04393317
      29526 203470 "Mike Lehman"       72 0  .1679528 0 2029 0 "Sun Microsystems Inc"                         14479 1999  545053000 .14703006  -.06867583
      21585  60411 "Lewis Holland"     78 0 .12717396 0  701 0 "National Commerce Bancorp, Memphis,Tennessee" 14367 1999   78251000 1.7000953  .028819654
        324  34064 "Neal Arnold"       61 1 .09556917 0  197 0 "Fifth Third Bancorp"                          14411 1999 2120738000         0  -.06448339
     122662 346602 "Kevin Phillips"    61 0  .1666305 0 1450 0 "ManTech International Corp"                   18252 2009  2.420e+08  19.83208   .05128356
       3169 537867 "Kevin O'Shea"      56 1  .2171365 1 1189 0 "AvalonBay Communities Inc"                    21063 2017   76800000   2.75876 -.005469032
    1941706 457702 "Mark Wetzel"       63 1  .2186312 0  112 3 "Aviv REIT Inc"                                19785 2014   48500000 .05218355  .028736543
     937594  44196 "Byron Pollitt Jr"  70 1 .23381294 0 1057 3 "Visa Inc"                                     18667 2011  1.900e+08  7.633737  .015262982
      13057 497919 "Tim Gallagher"     60 1  .1641626 0 1094 0 "Genesee & Wyoming Inc"                        17651 2008   97000000  5.313417 -.033886403
      14372  36363 "Dave Zwiener"      67 1  .2044825 1  288 0 "The Hartford Financial Services Group Inc"    13803 1997  184722000  6.702297  .015409133
     755706 509385 "Judy Bjornaas"     59 1 .28308672 0  700 0 "NCI Inc"                                      17344 2007   64800000 2.5869734 -.005903121
    end
    format %tdDD/NN/CCYY Deal_Announced
    format Deal_Value %15.0fc
    Data preparation:
    I prepared the data for panel data analysis using

    Code:
    xtset Acq_ID
    
    xtsum CFO_PaySlice CFO_No_Boardseats CFO_No_Deals CFO_Perc_Own_Dir
    
    Variable         |      Mean   Std. dev.       Min        Max |    Observations
    -----------------+--------------------------------------------+----------------
    CFO_Pa~e overall |  .2030756   .0961471          0   3.606383 |     N =    4348
             between |             .1157044          0   3.606383 |     n =    1380
             within  |             .0484867   -.108415   1.262201 | T-bar = 3.15072
                     |                                            |
    CFO_No~s overall |  .3199172   .7994125          0         14 |     N =    4348
             between |             .6833354          0          6 |     n =    1380
             within  |             .4903563  -2.537226   11.90325 | T-bar = 3.15072
                     |                                            |
    CFO_No~s overall |  .9544618   2.452258          0         29 |     N =    4348
             between |             2.163101          0         21 |     n =    1380
             within  |             1.409748  -10.64554    24.7878 | T-bar = 3.15072
                     |                                            |
    CFO_Pe~r overall |  5.382116   6.925948          0        100 |     N =    4348
             between |             6.745748          0        100 |     n =    1380
             within  |             4.065572  -30.33086   43.11768 | T-bar = 3.15072
    Question 1:
    I did not include a -timevar- as this would reduce my sample due to duplicates (there are acquirors that announced more than one dear in a given year) and I am not planning to use time series commands


    Most paper that are related to my research question make use of industry and year fixed effects in their analysis. As to my understanding it's not possible to use the fe approach when the key explanatory variables are constant across time as the fe will wipe out those variables. How is it possible however, that stata calculates coefficients for those variables that are constant over time like for example the gender variable?

    I am wondering why there isn't any problem with this code for example:
    Code:
    xtreg Acq_CAR_1_1_ES2 CFO_Gender, fe
    My empirical model looks like this:

    Code:
    xtreg Acq_CAR_1_1_ES2 CFO_PaySlice CFO_No_Boardseats CFO_No_Deals CFO_Perc_Own_Dir Deal_Controls Acquiror_Controls CFO_Controls i.Deal_Year_Ann, fe (vce cluster Acq_ID)
    Question 2:
    I would really appreciate if the model specification looks alright considering my data structure. I included firm fixed effects (and not industry) because when implementing firm fixed effects it also control for differences across industries as a firm is typically within the same industry across time. Would you agree with this argumentation?

    The output when running the regression on my overall sample is:
    Code:
    . xtreg Acq_CAR_1_1_ES2 CFO_PaySlice CFO_No_Boardsitze CFO_No_Deals CFO_Perc_Own_Dir CFO_Board CFO_Age CFO_Gender CFO_MBA CFO_CPA CFO_Tenure Deal_Value Targ_Listed Deal_Structure Deal_No_Bidders Deal_Div_FF12 Acq_MktValue A
    > cq_Leverage Acq_ROA Acq_Cash_holdings Acq_TobinsQ Acq_FCF Acq_No_Deals i.Deal_Year_Ann, fe vce(cluster Acq_ID)
    
    Fixed-effects (within) regression               Number of obs     =      2,521
    Group variable: Acq_ID                          Number of groups  =        980
    
    R-squared:                                      Obs per group:
         Within  = 0.0467                                         min =          1
         Between = 0.0063                                         avg =        2.6
         Overall = 0.0220                                         max =         75
    
                                                    F(39,979)         =          .
    corr(u_i, Xb) = -0.1598                         Prob > F          =          .
    
                                        (Std. err. adjusted for 980 clusters in Acq_ID)
    -----------------------------------------------------------------------------------
                      |               Robust
      Acq_CAR_1_1_ES2 | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
    ------------------+----------------------------------------------------------------
         CFO_PaySlice |   .0036156   .0254389     0.14   0.887    -.0463055    .0535366
    CFO_No_Boardsitze |  -.0006362   .0025143    -0.25   0.800    -.0055702    .0042978
         CFO_No_Deals |  -.0000699   .0007644    -0.09   0.927    -.0015699    .0014301
     CFO_Perc_Own_Dir |  -.0005353   .0002961    -1.81   0.071    -.0011164    .0000459
            CFO_Board |   .0262056   .0120205     2.18   0.029     .0026167    .0497944
              CFO_Age |  -.0005674   .0004353    -1.30   0.193    -.0014216    .0002869
           CFO_Gender |  -.0005629   .0078833    -0.07   0.943    -.0160331    .0149072
              CFO_MBA |  -.0086922   .0055608    -1.56   0.118    -.0196047    .0022204
              CFO_CPA |   .0046285   .0050339     0.92   0.358    -.0052499    .0145069
           CFO_Tenure |   3.32e-07   1.99e-06     0.17   0.867    -3.57e-06    4.24e-06
           Deal_Value |  -1.70e-12   6.34e-13    -2.68   0.008    -2.94e-12   -4.53e-13
          Targ_Listed |  -.0104142   .0054327    -1.92   0.056    -.0210753    .0002469
       Deal_Structure |   .0006119   .0008242     0.74   0.458    -.0010056    .0022294
      Deal_No_Bidders |   .0299449   .0194579     1.54   0.124    -.0082391    .0681289
        Deal_Div_FF12 |   .0023041   .0043431     0.53   0.596    -.0062189     .010827
         Acq_MktValue |   5.68e-11   6.87e-11     0.83   0.408    -7.80e-11    1.92e-10
         Acq_Leverage |   .0235281   .0299002     0.79   0.432    -.0351479     .082204
              Acq_ROA |   .1052179   .0336337     3.13   0.002     .0392154    .1712204
    Acq_Cash_holdings |   .0232797   .0233957     1.00   0.320    -.0226318    .0691912
          Acq_TobinsQ |  -.0010224   .0003921    -2.61   0.009    -.0017919   -.0002528
              Acq_FCF |  -.0411013   .0447207    -0.92   0.358    -.1288608    .0466582
         Acq_No_Deals |  -.0001504   .0002632    -0.57   0.568    -.0006669    .0003661
                      |
        Deal_Year_Ann |
                2000  |  -.0283307   .0143435    -1.98   0.049    -.0564783   -.0001832
                2001  |  -.0085731   .0176251    -0.49   0.627    -.0431604    .0260142
                2002  |  -.0059201    .015401    -0.38   0.701    -.0361429    .0243027
                2003  |  -.0119448   .0164911    -0.72   0.469    -.0443068    .0204173
                2004  |  -.0040144   .0137251    -0.29   0.770    -.0309485    .0229196
                2005  |  -.0053451   .0140514    -0.38   0.704    -.0329194    .0222292
                2006  |  -.0147642   .0145507    -1.01   0.311    -.0433183    .0137899
                2007  |   .0001967   .0152248     0.01   0.990    -.0296803    .0300736
                2008  |  -.0152089   .0165615    -0.92   0.359     -.047709    .0172912
                2009  |   .0012625   .0148922     0.08   0.932    -.0279617    .0304868
                2010  |   .0052353   .0150384     0.35   0.728     -.024276    .0347466
                2011  |   .0000944   .0145346     0.01   0.995    -.0284282     .028617
                2012  |   .0047204   .0153463     0.31   0.758     -.025395    .0348357
                2013  |  -.0011319   .0164663    -0.07   0.945    -.0334452    .0311814
                2014  |   .0024371   .0160913     0.15   0.880    -.0291404    .0340146
                2015  |  -.0097286   .0167224    -0.58   0.561    -.0425445    .0230873
                2016  |  -.0118784   .0159008    -0.75   0.455    -.0430819    .0193251
                2017  |  -.0066215   .0158199    -0.42   0.676    -.0376664    .0244234
                2018  |   -.009364   .0179147    -0.52   0.601    -.0445197    .0257917
                      |
                _cons |  -.0052567   .0402274    -0.13   0.896    -.0841987    .0736852
    ------------------+----------------------------------------------------------------
              sigma_u |  .06233286
              sigma_e |  .06280384
                  rho |   .4962363   (fraction of variance due to u_i)
    -----------------------------------------------------------------------------------
    Question 3:
    Accordingly, there doesn't seem to be an effect on either of the power variables on the CAR. Before moving on with my research I just want to make sure whether there could be a fundamental problem with the model causing the potential effects to be insignificant.
    If you made it up to this point and read the entire post: Thank you very much!

    Kind regards

    _____________________________________
    1 https://www.jstor.org/stable/256485
    Last edited by Marc Pelow; 02 Mar 2022, 09:37.

  • #2
    I am still very interesting in hearing your thoughts and did some extra testing in the meantime
    Hausman test results suggest that re is suitable:
    Code:
    xtreg Acq_CAR_1_1_ES2 CFO_PaySlice CFO_No_Boardsitze CFO_No_Deals CFO_Perc_Own_Dir CFO_Board CFO_Age CFO_Gender CFO_MBA CFO_CPA CFO_Tenure Deal_Value Targ_Listed Deal_Structure Deal_No_Bidders Deal_Div_FF12 Acq_MktValue Acq_Leverage Acq_ROA Acq_Cash_holdings Acq_TobinsQ Acq_FCF Acq_No_Deals, fe
    
    estimates store fixed
    
    xtreg Acq_CAR_1_1_ES2 CFO_PaySlice CFO_No_Boardsitze CFO_No_Deals CFO_Perc_Own_Dir CFO_Board CFO_Age CFO_Gender CFO_MBA CFO_CPA CFO_Tenure Deal_Value Targ_Listed Deal_Structure Deal_No_Bidders Deal_Div_FF12 Acq_MktValue Acq_Leverage Acq_ROA Acq_Cash_holdings Acq_TobinsQ Acq_FCF Acq_No_Deals, re
    
    estimates store random
    
    hausman fixed random
    Result:

    Code:
    Note: the rank of the differenced variance matrix (19) does not equal the number of coefficients being tested (22); be sure this is what you expect, or there may be
            problems computing the test.  Examine the output of your estimators for anything unexpected and possibly consider scaling your variables so that the coefficients
            are on a similar scale.
    
                     ---- Coefficients ----
                 |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
                 |     fixed        random       Difference       Std. err.
    -------------+----------------------------------------------------------------
    CFO_PaySlice |    .0159054     .0106131        .0052923        .0232891
    CFO_No_Boa~e |     .000298    -.0000494        .0003474        .0021693
    CFO_No_Deals |   -.0001977    -.0002787         .000081        .0007793
    CFO_Perc_O~r |   -.0004792    -.0000603        -.000419        .0002545
       CFO_Board |    .0165749     .0060153        .0105596        .0095732
         CFO_Age |   -.0003122     1.08e-06       -.0003133         .000363
      CFO_Gender |   -.0001703     .0039131       -.0040834        .0076443
         CFO_MBA |   -.0079263    -.0054712       -.0024552        .0043982
         CFO_CPA |    .0044388     .0008035        .0036353        .0042589
      CFO_Tenure |    4.87e-07    -9.74e-07        1.46e-06        1.63e-06
      Deal_Value |   -1.73e-12    -1.81e-12        8.50e-14        2.46e-13
     Targ_Listed |   -.0099633    -.0133341        .0033708         .003022
    Deal_Struc~e |    .0005324     .0000302        .0005022         .000482
    Deal_No_Bi~s |    .0273427      .023375        .0039677        .0139876
    Deal_Div_~12 |    .0016818    -.0007084        .0023903        .0029916
    Acq_MktValue |    3.03e-11     3.92e-11       -8.90e-12        3.93e-11
    Acq_Leverage |    .0242551     .0058658        .0183893        .0150745
         Acq_ROA |    .0945742     .0101078        .0844664          .02973
    Acq_Cash_h~s |    .0253062     -.019994        .0453002        .0154538
     Acq_TobinsQ |   -.0015969    -.0013971       -.0001999        .0002147
         Acq_FCF |   -.0285622     .0430743       -.0716365        .0394497
    Acq_No_Deals |   -.0001665    -.0004628        .0002963        .0002478
    ------------------------------------------------------------------------------
                              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(19) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                =  29.33
    Prob > chi2 = 0.0609
    (V_b-V_B is not positive definite)

    In the literature related to my topic, researchers often make use of robust and (firm level) clustered standard errors, so I used:

    Code:
    xtreg Acq_CAR_1_1_ES2 CFO_PaySlice CFO_No_Boardsitze CFO_No_Deals CFO_Perc_Own_Dir CFO_Board CFO_Age CFO_Gender CFO_MBA CFO_CPA CFO_Tenure Deal_Value Targ_Listed Deal_Structure Deal_No_Bidders Deal_Div_FF12 Acq_MktValue Acq_Leverage Acq_ROA Acq_Cash_holdings Acq_TobinsQ Acq_FCF Acq_No_Deals, re
    
    xtoverid, robust cluster(Acq_ID)
    H0 is rejected which suggests that fe is more reasonable:

    Code:
    Test of overidentifying restrictions: fixed vs random effects
    Cross-section time-series model: xtreg re  robust cluster(Acq_ID)
    Sargan-Hansen statistic  31.519  Chi-sq(20)   P-value = 0.0487

    Comment


    • #3
      Marc:
      with 980 panels cluster-robust standard errors is the way to go.
      That said, I would go -fe-.
      However, please note that both -hausman- and -xtoverid. outcomes are just a tad above and below the arbitratry 5% watershed.
      Kind regards,
      Carlo
      (StataNow 18.5)

      Comment


      • #4
        Thank you, Carlo!
        Any thoughts on my questions in the first post?

        Comment


        • #5
          Marc:
          Question 1:
          1) you can include -i.time- (which is highly advisable when you go -fe-) even though you do not -xtset- your dataset with a -timevar- .
          Question 2:
          2) just to keep it simple, if your firms do not change -industry- during the timespan your T dimension stretches over, the -fe- machinery would wipe it out. Hence, -i.industry- in or out does not make any difference.
          Question 3:
          3) the substantive issue lies in a within R_sq = 0.0467, which is really low; in addition sigma_u and sigma_e values are really similar, which may mean not a great panel-wise effect (if any). However, it may well be soething usual in your reserach field and/or it may be due to a limited variation in your time-varying predictors.
          Kind regards,
          Carlo
          (StataNow 18.5)

          Comment


          • #6
            What exactly do you mean by "panel-wise" effect? My guess is that - as a result - it may be more advisable to use a non-panel model?
            Is there any specific test I may try to check whether the time variation in my predictors is sufficient?
            Really appreciate your help

            Comment


            • #7
              Marc:
              the panel-wise effect has to do with the -u- component of the error term (see -xtreg- entry, Stata .pdf manual.
              I think a panel model is the right approach; probably your data has too limited variation in time-varying variables.
              You may want to take a look at -xtsum- and see variable within variation.
              Kind regards,
              Carlo
              (StataNow 18.5)

              Comment


              • #8
                Hi Carlo,
                actually I did include the output of xtsum in the original post but I am afraid that the post a bit too long and somehow confusing, sorry. Its shown under Data description part. Is there something like a rule of thumb that helps to evaluate whether the valuation is sufficient?
                One last question: Is there a model that comes to your mind that may work better, given the (potential) time-invariant predictors?

                Comment


                • #9
                  Marc:
                  1) yes, you're right. As per your -xtsum- outcome table, you can see that for some of your predictors the within variation across the T dimension (which is the one to look at when dealing with -fe- specification) is really limited.
                  2) my jerk-knee rejection would point you out to -xtreg,re-. However, if -fe- is the way to go (as it seems from -xtoverid- oucome), -re- is inconsistent and its coefficients unrealiable.
                  Kind regards,
                  Carlo
                  (StataNow 18.5)

                  Comment


                  • #10
                    A low variance of the predictors is not only a problem in panel analysis but also in a regression with cross-sectional data, isn't it?
                    Does the Hausman test or -xtoverid- consider the limited within variance of the predictors in its test decision in any way?
                    In the end it seems that it is a matter of judgement and probably (as you mentioned) also depending on the publications in my research area. There is actually not one publication here that does not apply to fixed effects. Also, not a single paper mentioned the within variance but only the overall R2.

                    Thank you very much for your help

                    Comment


                    • #11
                      Marc:
                      1) yes, but it bites harder with -fe- as it's the within panel variation that matters;
                      2) -xtoverid- adopts a restriction-based approach, that you can find explained in its helpfile;
                      3) go -fe-;
                      4) overall R-sq is less invormative when you go -fe-. However, techical journals nay have different editorial policies about reporting the results of statistical analyses.
                      Kind regards,
                      Carlo
                      (StataNow 18.5)

                      Comment


                      • #12
                        Thank you very much, I really appreciate the effort you put in every single of your answers.

                        Comment

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