Multinomial logit or xtreg?

[Luke Brown]

Good morning users!
I have an issue and I hope you could help me: I have a panel dataset, I am interested to study how people adjust their risk aversion during financial crisis. I have a categorical variable (riskavers) which can have three different values (1=not taking any financial risk, 2=willing to take a medium risk, 3=willing to take a great risk). However, I do not know which model can capture better its relationship with the dummy variable "crisis". Here I posted a multinomial logit regression (even though I am not completely sure I can use it in a panel dataset as a pooled estimation) and the xtreg command. Can you please help me to decide which one is better or if I should use another one?
Thank you so much
Luke Brown

xtreg riskavers hhsex age educ race logsaving crisis logincome, vce(cluster YY1)

Random-effects GLS regression                   Number of obs      =     31879
Group variable: YY1                             Number of groups   =      6551

R-sq:  within  = 0.2245                         Obs per group: min =         1
       between = 0.2259                                        avg =       4.9
       overall = 0.2260                                        max =         6

                                                Wald chi2(7)       =  11592.78
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

                                 (Std. Err. adjusted for 6551 clusters in YY1)
------------------------------------------------------------------------------
             |               Robust
   riskavers |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       hhsex |  -.0983859    .007495   -13.13   0.000    -.1130758    -.083696
         age |  -.0046486   .0001839   -25.27   0.000     -.005009   -.0042881
        educ |   .0414245   .0010909    37.97   0.000     .0392863    .0435627
        race |  -.0267025   .0031038    -8.60   0.000    -.0327859   -.0206191
   logsaving |   .0056858   .0005938     9.57   0.000     .0045219    .0068497
      crisis |  -.0392017   .0055675    -7.04   0.000    -.0501137   -.0282897
   logincome |   .0899202   .0021053    42.71   0.000     .0857939    .0940464
       _cons |   .6533855   .0272177    24.01   0.000     .6000397    .7067313
-------------+----------------------------------------------------------------
     sigma_u |  .05883202
     sigma_e |  .48710283
         rho |  .01437794   (fraction of variance due to u_i)
------------------------------------------------------------------------------

 mlogit riskavers hhsex age educ race logsaving crisis logincome, baseoutcome(1) vce(cluster YY1)

Iteration 0:   log pseudolikelihood = -26224.432  
Iteration 1:   log pseudolikelihood =  -21636.01  
Iteration 2:   log pseudolikelihood = -21376.921  
Iteration 3:   log pseudolikelihood = -21374.942  
Iteration 4:   log pseudolikelihood = -21374.941  

Multinomial logistic regression                   Number of obs   =      31879
                                                  Wald chi2(14)   =    5973.95
                                                  Prob > chi2     =     0.0000
Log pseudolikelihood = -21374.941                 Pseudo R2       =     0.1849

                                 (Std. Err. adjusted for 6551 clusters in YY1)
------------------------------------------------------------------------------
             |               Robust
   riskavers |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |  (base outcome)
-------------+----------------------------------------------------------------
2            |
       hhsex |  -.3511427   .0340069   -10.33   0.000     -.417795   -.2844904
         age |   -.020097   .0008849   -22.71   0.000    -.0218314   -.0183627
        educ |   .2007731   .0058042    34.59   0.000      .189397    .2121492
        race |   -.173934   .0142654   -12.19   0.000    -.2018938   -.1459743
   logsaving |   .0406524   .0033108    12.28   0.000     .0341633    .0471415
      crisis |  -.2012526   .0283804    -7.09   0.000    -.2568771   -.1456281
   logincome |   .5681068    .015723    36.13   0.000     .5372903    .5989234
       _cons |   -6.04118     .18116   -33.35   0.000    -6.396247   -5.686113
-------------+----------------------------------------------------------------
3            |
       hhsex |  -.3277998   .0828562    -3.96   0.000    -.4901949   -.1654046
         age |  -.0365087   .0021477   -17.00   0.000    -.0407182   -.0322993
        educ |   .1516283   .0124127    12.22   0.000     .1272998    .1759568
        race |  -.0236554    .026387    -0.90   0.370    -.0753731    .0280622
   logsaving |  -.0086072   .0064052    -1.34   0.179    -.0211612    .0039468
      crisis |   -.183439   .0579029    -3.17   0.002    -.2969265   -.0699515
   logincome |   .7799633   .0246435    31.65   0.000     .7316628    .8282637
       _cons |   -9.82149   .2998162   -32.76   0.000    -10.40912   -9.233861
------------------------------------------------------------------------------

[Clyde Schechter]

Well, I would not typically be inclined to use a multinomial model for this outcome variable because it ignores the fact that these categories are clearly ordered. Unless the context is one in which you might expect a difference in a predictor variable to be associated with some arbitrary re-shuffling of the proportions of these risk aversion categories, I'd be more inclined to think of this as an ordinal outcome, which would then lead me to consider a choice between -xtreg- and -xtologit-. Either way I'd be modeling whether a difference in a predictor is associated with increased or decreased risk aversion as a whole. As for the choice between -xtreg- and -xtologit- that would depend on whether or not it makes sense to think of the four categories of risk aversion are, conceptually, equally spaced. (That is, is the conceptual difference between 1 and 2, the same as the difference between 2 and 3 and between 3 and 4?)

If you really are in a context where the ordered property of your outcome is not relevant and you expect arbitrary reshufflings of risk aversion categories in association with your predictors, then you might be criticized for using -mlogit- because it is not a panel data estimator. You can, however, emulate a panel-data version of -mlogit- in -gsem-. See the example in the -gsem- chapter of the PDF documentation that comes with your Stata installation.

[Linh Nguyen]

Clyde Schechter:

[SEM], example 37g , page 372:

gsem (i.insure <- i.nonwhite), mlogit

In page 374:

We could have gotten identical results from Stata’s mlogit command for both this example and
the previous one. To fit the first example, we would have typed
      . mlogit insure i.nonwhite

It means that -mlogit- in -gsem- has coefficients as identical as -mlogit- has. If so, why do we need run - mlogit - in - gsem - for panel data?

Could you please explain it to me?

[Maarten Buis]

That example had nothing to do with panel data. It just showed how to estimate a mlogit for non-panel data with gsem, nothing more, nothing less. If you are interested in a multinomial logit for panel data you need to look at example 41g.

[Linh Nguyen]

Maarten Buis : Thanks for your suggestion. Following Ex. 41g, I have a code:

xtset id year
.....
eststo clear
eststo: gsem (1.decision <- mis_mbm1 tan1 ebitda1 size1 lev1 term1 russel1 reit_spread1 M1[id]) ///
             (2.decision <- mis_mbm1 tan1 ebitda1 size1 lev1 term1 russel1 reit_spread1 M2[id]) ///
             (3.decision <- mis_mbm1 tan1 ebitda1 size1 lev1 term1 russel1 reit_spread1 M3[id]) ///
             (4.decision <- mis_mbm1 tan1 ebitda1 size1 lev1 term1 russel1 reit_spread1 M4[id]) ///
             (5.decision <- mis_mbm1 tan1 ebitda1 size1 lev1 term1 russel1 reit_spread1 M5[id]),mlogit

My sample has 230 firms with 2,013 firm-year observations. I have run this code from yesterday, but it hasn't finished (about 20 hours). Do you know how I can speed up this task?

[Linh Nguyen]

Hi,

I find an example from do-file of help femlogit (user-written command) of Klaus Pforr. He conducts three multinomial logistic model regression (pooled, random effects and fixed effect) for panel data. Hence, I share it with anyone who begins to look for information about the multinomial logistic model for panel data like me.

* pooled
mlogit choice rldist2 rldist3 inflation yr92 male age manual, const(1/3) b(1) vce(cluster serialno)

* random effects
gsem (2.choice <- rldist2 rldist3 inflation yr92 male age manual M1[serialno]) ///
     (3.choice <- rldist2 rldist3 inflation yr92 male age manual M2[serialno]), mlogit const(4/6)

* fixed effects
femlogit choice rldist2 rldist3 inflation yr92, group(serialno) const(1/3) b(1)

Note:
- for detail, you should download these files from femlogit.
- femlogit and gsem are "efficient" for only a small sample (i.e small N). If you have a large sample, you should take a vacation when running these commands

[Carlo Lazzaro]

As far as the original post is concerned, the almost negligible -rho- value seems to cast some doubts on the appropriateness of -xtreg- in this instance.