Overriding Hausman Test for Fixed vs Random Effects

[Kimara Saldanha]

Hi there,

I am using Stata 14 and am investigating whether bribery affects investment decisions at the firm level, using panel data looking at 25,000+ firms over 3 years. I plan on including firm fixed effects such as size, age, Industry amongst others.

Upon running the Hausman test to see if I should use FE or RE, the test informed me that I should be using FE. However, the FE model does not allow me to include a Country dummy (time-invariant) in my regression - is this a sufficient enough reason for justifying overriding the test and using RE.

Many thanks in advance!


Kimara

[Carlo Lazzaro]

Kimara:
no, it is not, as the results of your inference under -re- would be probably biased (with extent and direction that you cannot forecast).

[Rose Simmons]

Carlo Lazzaro please may I ask you a similar question?

I have a panel dataset with 13 waves (N is 2976) and my dataset involves questionnaire responses from individuals.

. xtdes

    hhid:  6, 21, ..., 89972                                 n =       2976
    year:  2004, 2005, ..., 2016                             T =         13
           Delta(year) = 1 unit
           Span(year)  = 13 periods
           (hhid*year uniquely identifies each observation)

Distribution of T_i:   min      5%     25%       50%       75%     95%     max
                         1       1       1         3         7      13      13

     Freq.  Percent    Cum. |  Pattern
 ---------------------------+---------------
      224      7.53    7.53 |  ...........11
      206      6.92   14.45 |  1111111111111
      166      5.58   20.03 |  ............1
      145      4.87   24.90 |  1............
       94      3.16   28.06 |  ..........111
       81      2.72   30.78 |  ..........1..
       77      2.59   33.37 |  .1...........
       72      2.42   35.79 |  11...........
       62      2.08   37.87 |  ......1......
     1849     62.13  100.00 | (other patterns)
 ---------------------------+---------------
     2976    100.00         |  XXXXXXXXXXXXX

The dependent variable is binary, measuring an individual's ability to save (saving=1 if individual indicated an ability to save; 0 otherwise).
As -saving- is binary, I should be using nonlinear methods (either xtprobit or xtlogit).
When I run -xtlogit, fe-, I lose many observations. This concerns me, as I believe many individuals are being dropped out because they have responded yes to -saving- in all waves they participated in, or no in all waves.
It also drops my -male- binary variable, which would be better kept in for my analysis.

. xtlogit saving $xlist $controllist i.year, fe vce(cluster hhid) nolog
vcetype 'cluster' not allowed
r(198);

. xtlogit saving $xlist $controllist i.year, fe nolog
note: multiple positive outcomes within groups encountered.
note: 1,260 groups (2,748 obs) dropped because of all positive or
      all negative outcomes.
note: male omitted because of no within-group variance.
--Break--
r(1);

I think using a FE estimator would cause a bias in my results because it may drop all individuals who count as -saving=1- or -saving=0- in all waves. As -saving- is my key dependent variable of interest, I think this is cause for concern so I should use RE instead. But would this then also be a source of bias?

I would be grateful if you could please advise on this

Many thanks

[Carlo Lazzaro]

Rose:
plase do not address me your queries, as this one is not my forum. Thanks.
The main problem there seems to rest with your data structure: no statistical magic can do the trick.
Choosing between -re- and -fe- is a matter of -hausman- (with default standard errors) and previous examples in your research field.

[Rose Simmons]

Apologies

I have tried to run the Hausman test but -xtlogit, fe- is taking a very long time with my data - I have left Stata running for 3 hours and it had not returned an outcome

. xtlogit saving $xlist $controllist i.year, fe nolog
note: multiple positive outcomes within groups encountered.
note: 1,260 groups (2,748 obs) dropped because of all positive or
      all negative outcomes.
note: male omitted because of no within-group variance.
--Break--
r(1);

.
. est store fe
last estimation results not found, nothing to store
r(301);

.
. xtlogit saving $xlist $controllist i.year, re nolog

Random-effects logistic regression              Number of obs     =      5,255
Group variable: hhid                            Number of groups  =      1,722

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        3.1
                                                              max =         13

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(35)     =    1057.45
Log likelihood  = -2292.1537                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
      saving |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        prec |   .0211324   .0261927     0.81   0.420    -.0302044    .0724692
    purchase |  -.0139693   .0214863    -0.65   0.516    -.0560818    .0281431
      retire |   .0123291   .0174498     0.71   0.480    -.0218719      .04653
     bequest |   .0110517   .0156804     0.70   0.481    -.0196813    .0417846
      growth |   .0259308    .023222     1.12   0.264    -.0195834    .0714451
     mediumh |   .4742525    .094876     5.00   0.000      .288299     .660206
       longh |   .3169892   .2595958     1.22   0.222    -.1918092    .8257875
        male |   .4800632   .1637146     2.93   0.003     .1591884    .8009379
         age |  -.0316504   .0283883    -1.11   0.265    -.0872904    .0239896
             |
 c.age#c.age |   .0002376   .0002692     0.88   0.377    -.0002901    .0007653
             |
    incabove |   1.619798   .3629739     4.46   0.000     .9083819    2.331213
    incbelow |  -1.686708   .3078902    -5.48   0.000    -2.290161   -1.083254
    employed |  -.1317712     .19749    -0.67   0.505    -.5188444    .2553021
     retired |  -.1003171   .2025975    -0.50   0.620    -.4974009    .2967666
      health |     .15395   .0758732     2.03   0.042     .0052413    .3026587
      income |   7.59e-06   1.97e-06     3.86   0.000     3.74e-06    .0000115
        risk |  -.0061015    .008453    -0.72   0.470    -.0226691     .010466
 selfcontrol |   .5145004   .0377929    13.61   0.000     .4404276    .5885731
       child |  -.2540876   .0636087    -3.99   0.000    -.3787583   -.1294169
  saving1exp |   2.835128   .1028447    27.57   0.000     2.633556      3.0367
     partner |   -.232524   .1412318    -1.65   0.100    -.5093332    .0442853
         uni |   .3364228   .1421604     2.37   0.018     .0577935    .6150522
       owner |   .2936193   .1315744     2.23   0.026     .0357382    .5515003
             |
        year |
       2005  |  -1.709988   .1857686    -9.20   0.000    -2.074088   -1.345888
       2006  |   -1.89114   .1931469    -9.79   0.000    -2.269701   -1.512579
       2007  |   -1.81953   .1965375    -9.26   0.000    -2.204736   -1.434323
       2008  |  -1.674247   .1851979    -9.04   0.000    -2.037228   -1.311266
       2009  |  -1.538971   .1830974    -8.41   0.000    -1.897835   -1.180106
       2010  |  -1.909524   .1874136   -10.19   0.000    -2.276848     -1.5422
       2011  |  -1.738739   .2346666    -7.41   0.000    -2.198677   -1.278801
       2012  |  -1.469885   .2299633    -6.39   0.000    -1.920604   -1.019165
       2013  |  -1.708581   .2433071    -7.02   0.000    -2.185454   -1.231707
       2014  |  -1.754064   .2234026    -7.85   0.000    -2.191925   -1.316203
       2015  |  -1.544468   .2359341    -6.55   0.000     -2.00689   -1.082045
       2016  |  -1.943985   .2317234    -8.39   0.000    -2.398155   -1.489816
             |
       _cons |  -3.490882   .9049471    -3.86   0.000    -5.264546   -1.717219
-------------+----------------------------------------------------------------
    /lnsig2u |   .2428145    .144787                     -.0409627    .5265918
-------------+----------------------------------------------------------------
     sigma_u |   1.129085   .0817384                       .979727    1.301212
         rho |   .2792806   .0291431                      .2258648    .3397843
------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 141.80                 Prob >= chibar2 = 0.000

.
. est store re

.
. hausman fe re
estimation result fe not found
r(111);

I am unsure of how to proceed. -xtlogit, re- produces an outcome in a couple of minutes, but -xtlogit, fe- will take hours.

Please could someone advise me on the next course of action?
Q1: Should I let Stata run overnight to see if -xtlogit, fe- produces an outcome? Or is it not worth using -xtlogit, fe-, because I can foresee further analysis being complicated by the large amount of time it takes to run?
Q2: Could I use -xtprobit, re- instead? If so, then I think that I would not need to conduct a Hauman test, as there is no -xtprobit, re-.

The literature I am basing my work on is cross-sectional data (I aim for my contribution to the literature to be that I am using panel data methods instead) so unfortunately I cannot say that the literature uses FE or RE.

Thanks in advance

[Carlo Lazzaro]

Rose:
Q1: as you probably have little/no variation for the same panel unit across years, -fe- (which is conditional under -xtlogit-), won't do the trick. That said, -re- specification sounds more rasonable;
Q2: immaterial, as per Q1.

[Rose Simmons]

Thank you Carlo Lazzaro , I will use a RE estimator instead