Least Square Dummy Variable (LSDV) in Stata

[Sara Harsha]

I am working on a panel of 59 banks picked from 12 countries. My time period spans from 2009 till 2015. My objective is to figure out which determinants impact profit of banks. My dependent variable is therefore profit which takes the abbreviation 'nim' in my commands which I have pasted below. All other variables are explanatory variables. Country names represent country dummies.
I now need to perform 'Least Square Dummy Variables (LSDV) ' on this panel data. I have learnt from various textbooks that 'LSDV' is the other name for 'fixed effect estimation'. I need to know which of the following three commands performs LSDV in my panel data.

Command # 1:

. xtreg nim nir cr lta otoi nlta ooiti eata car bm inf pcgg cpi Nigeria SriLanka Bangladesh India Kenya M
> alaysia Egypt Philippines China Turkey Thailand,fe
note: Nigeria omitted because of collinearity
note: SriLanka omitted because of collinearity
note: Bangladesh omitted because of collinearity
note: India omitted because of collinearity
note: Malaysia omitted because of collinearity
note: Egypt omitted because of collinearity
note: Philippines omitted because of collinearity
note: China omitted because of collinearity
note: Turkey omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =       413
Group variable: id                              Number of groups   =        59

R-sq:  within  = 0.3481                         Obs per group: min =         7
       between = 0.1971                                        avg =       7.0
       overall = 0.2147                                        max =         7

                                                F(14,340)          =     12.97
corr(u_i, Xb)  = -0.0951                        Prob > F           =    0.0000

------------------------------------------------------------------------------
         nim |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         nir |   .0163953    .011685     1.40   0.161    -.0065888    .0393794
          cr |   .0016437   .0009959     1.65   0.100    -.0003151    .0036026
         lta |  -1.106441   .3945453    -2.80   0.005    -1.882498   -.3303838
        otoi |  -.0455696   .0052323    -8.71   0.000    -.0558613   -.0352779
        nlta |  -.0029255   .0072428    -0.40   0.687    -.0171718    .0113208
       ooiti |  -.0466676   .0053673    -8.69   0.000    -.0572249   -.0361104
        eata |  -.0176386   .0077747    -2.27   0.024    -.0329313    -.002346
         car |   .0168051   .0165491     1.02   0.311    -.0157464    .0493566
          bm |   .0007851   .0075308     0.10   0.917    -.0140277    .0155978
         inf |   .0199149   .0167545     1.19   0.235    -.0130407    .0528705
        pcgg |  -.0425883   .0169323    -2.52   0.012    -.0758936   -.0092829
         cpi |  -.0125125   .0130406    -0.96   0.338     -.038163    .0131379
     Nigeria |          0  (omitted)
    SriLanka |          0  (omitted)
  Bangladesh |          0  (omitted)
       India |          0  (omitted)
       Kenya |   .9214237   .7084233     1.30   0.194    -.4720206    2.314868
    Malaysia |          0  (omitted)
       Egypt |          0  (omitted)
 Philippines |          0  (omitted)
       China |          0  (omitted)
      Turkey |          0  (omitted)
    Thailand |  -.8381735   .6967971    -1.20   0.230     -2.20875    .5324025
       _cons |   14.05015   1.784493     7.87   0.000     10.54011    17.56019
-------------+----------------------------------------------------------------
     sigma_u |  1.7229017
     sigma_e |  .63462076
         rho |  .88053173   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(58, 340) =    23.04             Prob > F = 0.0000

.

Command # 2:

. xtreg nim nir cr lta otoi nlta ooiti eata car bm inf pcgg cpi Nigeria SriLanka Bangladesh India Kenya M
> alaysia Egypt Philippines China Turkey Thailand

Random-effects GLS regression                   Number of obs      =       413
Group variable: id                              Number of groups   =        59

R-sq:  within  = 0.3348                         Obs per group: min =         7
       between = 0.7206                                        avg =       7.0
       overall = 0.6728                                        max =         7

                                                Wald chi2(23)      =    334.94
corr(u_i, X)   = 0 (assumed)                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
         nim |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         nir |   .0187304   .0115449     1.62   0.105    -.0038972     .041358
          cr |   .0012113   .0009953     1.22   0.224    -.0007396    .0031621
         lta |  -.7070863   .2783553    -2.54   0.011    -1.252653   -.1615198
        otoi |  -.0395627   .0050475    -7.84   0.000    -.0494556   -.0296698
        nlta |    .002645   .0070117     0.38   0.706    -.0110978    .0163877
       ooiti |  -.0439643   .0053437    -8.23   0.000    -.0544377   -.0334908
        eata |  -.0217432   .0078519    -2.77   0.006    -.0371326   -.0063538
         car |   .0230583   .0161679     1.43   0.154    -.0086302    .0547468
          bm |   .0044242   .0077166     0.57   0.566    -.0107001    .0195485
         inf |   .0221639   .0171058     1.30   0.195    -.0113628    .0556907
        pcgg |  -.0461017   .0175316    -2.63   0.009     -.080463   -.0117403
         cpi |   -.021785   .0121113    -1.80   0.072    -.0455228    .0019527
     Nigeria |   3.033168   .5995214     5.06   0.000     1.858128    4.208208
    SriLanka |   .2917484   .5777481     0.50   0.614    -.8406169    1.424114
  Bangladesh |   .2904912   .5843622     0.50   0.619    -.8548377     1.43582
       India |  -.5742879   .5308723    -1.08   0.279    -1.614779    .4662027
       Kenya |   2.126572   .5044502     4.22   0.000     1.137868    3.115277
    Malaysia |  -2.424813   .6493439    -3.73   0.000    -3.697504   -1.152122
       Egypt |  -1.831614   .6096875    -3.00   0.003     -3.02658   -.6366488
 Philippines |  -.6361527    .466915    -1.36   0.173    -1.551289    .2789839
       China |   -1.47036   .8933924    -1.65   0.100    -3.221377    .2806571
      Turkey |   1.160753   .6421596     1.81   0.071    -.0978566    2.419363
    Thailand |  -.3987376   .6466344    -0.62   0.537    -1.666118    .8686425
       _cons |   12.48027   1.468979     8.50   0.000     9.601125    15.35942
-------------+----------------------------------------------------------------
     sigma_u |  .87351738
     sigma_e |  .63462076
         rho |  .65452757   (fraction of variance due to u_i)
------------------------------------------------------------------------------

Command # 3:

 reg nim nir cr lta otoi nlta ooiti eata car bm inf pcgg cpi Nigeria SriLanka Bangladesh India Kenya Mal
> aysia Egypt Philippines China Turkey Thailand

      Source |       SS       df       MS              Number of obs =     413
-------------+------------------------------           F( 23,   389) =   43.16
       Model |  1217.92882    23  52.9534271           Prob > F      =  0.0000
    Residual |  477.245929   389  1.22685329           R-squared     =  0.7185
-------------+------------------------------           Adj R-squared =  0.7018
       Total |  1695.17475   412  4.11450183           Root MSE      =  1.1076

------------------------------------------------------------------------------
         nim |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         nir |   .0244971   .0138858     1.76   0.078    -.0028035    .0517976
          cr |  -.0002709   .0012601    -0.22   0.830    -.0027484    .0022066
         lta |   .0197848   .1800724     0.11   0.913    -.3342522    .3738218
        otoi |  -.0175484   .0053328    -3.29   0.001     -.028033   -.0070637
        nlta |   .0225154   .0078639     2.86   0.004     .0070543    .0379764
       ooiti |  -.0438234   .0069521    -6.30   0.000    -.0574918   -.0301551
        eata |  -.0503858   .0111521    -4.52   0.000    -.0723117   -.0284598
         car |   .0722298   .0180023     4.01   0.000     .0368357    .1076239
          bm |   .0161238   .0127652     1.26   0.207    -.0089736    .0412211
         inf |   .0175698   .0278604     0.63   0.529    -.0372059    .0723456
        pcgg |  -.0524609   .0293188    -1.79   0.074     -.110104    .0051822
         cpi |  -.0428361   .0180001    -2.38   0.018    -.0782257   -.0074465
     Nigeria |    2.65039   .3263086     8.12   0.000     2.008841    3.291939
    SriLanka |   .8536365   .3892656     2.19   0.029     .0883088    1.618964
  Bangladesh |   .8205079   .3720648     2.21   0.028     .0889982    1.552018
       India |  -.3762995   .3591384    -1.05   0.295    -1.082395    .3297957
       Kenya |   2.897395   .3746782     7.73   0.000     2.160747    3.634043
    Malaysia |  -2.140142   .4942142    -4.33   0.000    -3.111807   -1.168477
       Egypt |  -.9467589    .311581    -3.04   0.003    -1.559352   -.3341653
 Philippines |  -.3202755   .2946155    -1.09   0.278    -.8995135    .2589625
       China |  -1.556073   .5554704    -2.80   0.005    -2.648172   -.4639728
      Turkey |   1.475286   .4628376     3.19   0.002     .5653102    2.385263
    Thailand |  -1.002632   .4558766    -2.20   0.028    -1.898923   -.1063418
       _cons |    9.64989   1.527788     6.32   0.000     6.646134    12.65365
------------------------------------------------------------------------------

.

Problem with the first command is that iy is omitting my country dummies. I don't want this to happen. I need to know their sign and significance.
Confusion with the second command is that it uses xtreg plus it doesn't use -fe- option.
I read LSDV is simply OLS applied on model that includes country dummies. So, is -xtreg- the right command or is the 3rd command that uses -reg- correct?'

Please reply! Which among these three commands actually perform LSDV in my model?

[Carlo Lazzaro]

Sara:
even though you can get the same result with -areg-, -xtreg,fe- and -regression-, I would go -xtreg, fe-, because it outperforms the clustered standard errors obtained with the other approaches.
The following codes consiser -areg-and -xtreg, fe- (but not -regress-, due to bothering -matsize- issues):

. use "http://www.stata-press.com/data/r14/nlswork.dta", clear
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. areg ln_wage hours i.race, abs( idcode) vce(cluster idcode)
note: 2.race omitted because of collinearity
note: 3.race omitted because of collinearity

Linear regression, absorbing indicators         Number of obs     =     28,467
                                                F(   1,   4709)   =       0.67
                                                Prob > F          =     0.4124
                                                R-squared         =     0.6249
                                                Adj R-squared     =     0.5505
                                                Root MSE          =     0.3204

                             (Std. Err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       hours |   .0004474   .0005458     0.82   0.412    -.0006227    .0015175
             |
        race |
      black  |          0  (omitted)
      other  |          0  (omitted)
             |
       _cons |   1.658941   .0199551    83.13   0.000      1.61982    1.698063
-------------+----------------------------------------------------------------
      idcode |   absorbed                                    (4710 categories)





. xtreg ln_wage hours i.race, fe vce(cluster idcode)
note: 2.race omitted because of collinearity
note: 3.race omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =     28,467
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.0001                                         min =          1
     between = 0.0314                                         avg =        6.0
     overall = 0.0074                                         max =         15

                                                F(1,4709)         =       0.81
corr(u_i, Xb)  = 0.0976                         Prob > F          =     0.3696

                             (Std. Err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       hours |   .0004474   .0004986     0.90   0.370    -.0005301     .001425
             |
        race |
      black  |          0  (omitted)
      other  |          0  (omitted)
             |
       _cons |   1.658941   .0182299    91.00   0.000     1.623202     1.69468
-------------+----------------------------------------------------------------
     sigma_u |   .4229084
     sigma_e |  .32040339
         rho |  .63532952   (fraction of variance due to u_i)
------------------------------------------------------------------------------

[daniel klein]

None of the commands shown here implement the LSDV estimator, when you want bank fixed-effects. The command that does this is

regress nim ... i.id

The results will be identical to those obtained from xtreg with fe option. If countries get omitted because of collinearity then there is probably nothing you can do about it. The reason this does not happen with the two other approaches you have shown is these are not fixed-effects estimators. Here the variances between banks are used to estimate the relationships.

Note that the differences in standard errors between areg and xtreg that Carlo shows, result because of different assumptions about the number of clusters when the sample increases. You need to know which you want.

Best
Daniel

[Sara Harsha]

So many thanks Carlo and Daniel:

Daniel, you mean to say that I must go for the xtreg, fe command and let dummy variables be omitted as it can't be helped. Plus, I don't want to create dummies at bank level but at country level.

[daniel klein]

Assuming that id is a bank identifier, it seems odd you get coefficients for some countries at all. I suppose a bank does not change the country it is located in? In this case there might be a coding error in your data.

Only you can decide which model you want. Think about which variances you want to base your estimates on. If you want to use variances within banks only, thus controlling for any observed and unobserved (time-constant) differences between banks, then you should go with xtreg , fe with banks as panel identifiers. If you want within country effects instead you need to use countries as the panel identifier - or include country indicators like you did in your third approach. This is not clear from your question.

Best
Daniel

[Sara Harsha]

So many thanks, Daniel!

[Taulant Yzellari]

Hey Carlo and Daniel, do you have any suggestions what to do for a panel var model with fixed effect estimation?

[Carlo Lazzaro]

Taulant:
with no detail at all, I would go -xtreg, fe-.

[Taulant Yzellari]

Thank you for your quick reply Carlo. The problem with this method is that it accepts only one dependent variable and I need to insert a vector of dependent variables. I am trying to estimate the panel var model with fixed effects as in

the picture. Thank you in advance

[Carlo Lazzaro]

Taulant:
I'm not familiar with this stuff.
See: https://journals.sagepub.com/doi/pdf...867X1601600314 The Stata Journal (2016) 16, Number 3, pp. 778–804

[Taulant Yzellari]

Yes, I already saw it but it does not offer any possibility for fixed effects with OLS. Thnx anyway!