Why Mundlak and Fixed effect regression coefficient are not exactly same

[Junaid Ahmed]

Dear Statalist,

I have any issue regarding comparing the fixed-effect model and mundlak effect in controlling the means of time-variant variables as additional regressors.
Here are the results. I am wondering why the coefficient of fixed and random effect is slightly different. Might it be due to missing data?

thanks and regards,

 xtreg lremit $xlist0 i.year, vce(cluster pairid) fe

note: comlang_off omitted because of collinearity
note: colony omitted because of collinearity
note: contig omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =      1102
Group variable: pairid                          Number of groups   =       271

R-sq:  within  = 0.1197                         Obs per group: min =         1
       between = 0.5477                                        avg =       4.1
       overall = 0.5723                                        max =         7

                                                F(10,270)          =      5.71
corr(u_i, Xb)  = 0.0948                         Prob > F           =    0.0000

                               (Std. Err. adjusted for 271 clusters in pairid)
------------------------------------------------------------------------------
             |               Robust
      lremit |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lgdpc |   .4199601   .1413403     2.97   0.003      .141691    .6982293
   lgdpc_hos |   .2482984   .3412649     0.73   0.467    -.4235802    .9201771
      lcost2 |  -.1912492   .0978837    -1.95   0.052    -.3839617    .0014632
     lmig_st |   .3740764   .1592843     2.35   0.020     .0604792    .6876735
 comlang_off |          0  (omitted)
      colony |          0  (omitted)
      contig |          0  (omitted)
             |
        year |
       2012  |   .0043988   .0190377     0.23   0.817    -.0330823      .04188
       2013  |  -.0265595   .0471652    -0.56   0.574    -.1194178    .0662988
       2014  |  -.0332107   .0542274    -0.61   0.541    -.1399731    .0735516
       2015  |   .1402847    .055213     2.54   0.012     .0315819    .2489875
       2016  |   .0661839   .0598106     1.11   0.269    -.0515705    .1839384
       2017  |   .0920051   .0592864     1.55   0.122    -.0247174    .2087276
             |
       _cons |  -6.884898   5.217741    -1.32   0.188    -17.15753    3.387733
-------------+----------------------------------------------------------------
     sigma_u |  1.2156288
     sigma_e |  .34090766
         rho |  .92708901   (fraction of variance due to u_i)
------------------------------------------------------------------------------ 

Mundlak Effect results

 xtreg lremit $xlist0 $vlist0 i.year, vce(cluster pairid) 

Random-effects GLS regression                   Number of obs      =      1102
Group variable: pairid                          Number of groups   =       271

R-sq:  within  = 0.1197                         Obs per group: min =         1
       between = 0.6579                                        avg =       4.1
       overall = 0.6785                                        max =         7

                                                Wald chi2(17)      =    847.77
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

                                 (Std. Err. adjusted for 271 clusters in pairid)
--------------------------------------------------------------------------------
               |               Robust
        lremit |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
         lgdpc |   .4439019   .1406352     3.16   0.002     .1682619    .7195418
     lgdpc_hos |   .2524156   .3360553     0.75   0.453    -.4062407    .9110718
        lcost2 |  -.2028169   .0977656    -2.07   0.038    -.3944339   -.0111998
       lmig_st |   .3689689   .1583542     2.33   0.020     .0586004    .6793375
   comlang_off |   .0681932   .1503237     0.45   0.650    -.2264358    .3628223
        colony |   -.135961   .1806898    -0.75   0.452    -.4901066    .2181845
        contig |   .0056654   .3514274     0.02   0.987    -.6831196    .6944504
    lgdpc_mean |  -.1943218   .1454022    -1.34   0.181    -.4793049    .0906614
lgdpc_hos_mean |  -.0928574     .34678    -0.27   0.789    -.7725336    .5868189
   lcost2_mean |  -.3658746   .2326023    -1.57   0.116    -.8217667    .0900174
  lmig_st_mean |    .399029   .1679837     2.38   0.018     .0697869     .728271
               |
          year |
         2012  |   .0038119   .0192994     0.20   0.843    -.0340142    .0416381
         2013  |    -.02782   .0471031    -0.59   0.555    -.1201403    .0645004
         2014  |  -.0348137   .0541059    -0.64   0.520    -.1408593    .0712318
         2015  |   .1384236   .0552425     2.51   0.012     .0301503     .246697
         2016  |   .0623224   .0595451     1.05   0.295    -.0543839    .1790286
         2017  |    .089855   .0592783     1.52   0.130    -.0263284    .2060383
               |
         _cons |  -7.467168   .8463628    -8.82   0.000    -9.126009   -5.808328
---------------+----------------------------------------------------------------
       sigma_u |  1.0303308
       sigma_e |  .34090766
           rho |  .90132614   (fraction of variance due to u_i)
------------------------------------------------------------------------------- 

[Carlo Lazzaro]

Junaid:
the differences arose beacuse of you perforemd two different models.
Missing vaklues cannot be the reason, as you have the same number of observations (1102) in both regression models.
As an aside, please note that the easiest way to share what you tyoed and what Stata gave you back (as you laudably did) is via CODE delimiters:

#toggle available from the Advanced editor bar

[Junaid Ahmed]

Dear Carlo Lazzaro,

Thanks for it. However, in principles, the coefficient must be same for mundlak and fixed-effect model. As in the gravity model, we are always interested to see the effect of time-invariant variables like distance and common language, so in comparing with FE, we will also use the Mundlak effect model. Please guide.

[Eric de Souza]

Please provide the code for how you calculated the means.

[Junaid Ahmed]

Dear Eric de Souza

bysort home: egen mean_lgdpc=mean(lgdpc)
bysort host: egen mean_gdpc_lhos=mean(lgdpc_hos)
bysort host home: egen mean_lcost2=mean(lcost2)
bysort host home: egen mean_lbtrade=mean(lbtrade)
bysort host home: egen mean_lmig_st=mean(lmig_st)

lgdpc is home specific variable, meaning the recipient of remittances, lgdpc_hos is s host-specific variable, meaning sending country and other variables remittances cost, trade and migrant stock are the bilateral types of variables.

[Eric de Souza]

I think that the difference is arising from the way you calculate the means. The first two egens have a different bysort compared with the last three. I see no other reason.
I have always used the egen command for the Mundlak or CRE model with "non-gravity data in the following way:
. egen experbar = mean(exper), by(nr)
. egen unionbar = mean(union), by(nr)
. egen marriedbar = mean(married), by(nr)

I will be away the rest of the day.

[Jeff Wooldridge]

It’s almost certainly due to missing data. I explain this in my 2019 Journal of Econometrics paper. You should only use the complete cases when generating the time averages. Also, the time averages of the year dummies must be included in the unbalanced case.

[Junaid Ahmed]

Dear Eric de Souza,

The first two is basically the country-specific variable for both home and host, and the last three basically deal with bilateral data, that is why sorted by both host and home.

[Junaid Ahmed]

Dear Jeff Wooldridge,


so you mean dropped the countries with missing information, Do you not think, it will make problems. Also, could you please elaborate "You should only use the complete cases when generating the time averages. Also, the time averages of the year dummies must be included in the unbalanced case". What I understood, that we could also use the average for year dummies when working with unbalanced data. Could you please provide a Stata command for generating the time averages of year dummies.

Thanks

[Jeff Wooldridge]

No, you don't drop the country. You drop any observation (indexed by country and time) where any of the variables -- dependent variable or explanatory variable -- is missing. This is what fixed effects -- or any Stata command -- does. In other words, you must use the same time periods when you compute the time averages, even if you have different time periods available for some variables. It helps to start by creating a selection indicator that is one if and only if you have a complete set of cases. Then, use it in egen.

xtset id year
gen s = (y != .) & (x1 != .) & ... & (xK != .)
egen x1bar = mean(x1) if s, by(id)
egen x2bar = mean(x2) if s, by(id)
egen xKbar = mean(xK) if s, by(id)
egen year2bar = mean(year2) if s, by(id)
egen yearTbar = mean(yearT) if s, by(id)
xtreg y x1 ... xK year2 ... yearT x1bar ... xKbar year2bar ... yearTbar, re vce(cluster id)

[Eric de Souza]

@Jeff Wooldridge.
I had completely forgotten about your paper. I do have a copy of the 2010 version.

[Junaid Ahmed]

Jeff Wooldridge , Thanks a lot, it perfectly works.
Junaid

[Phil Bromiley]

Junaid - you might look at xthybrid and the Mundlak estimator that do this automatically.