xtreg vs areg in case of clustered std errors.

[YH jordaan]

Hello everyone,

I have a question regarding the following: I use cross section (in my case banks) fixed effects in my regression on panel data. Untill now I have used the areg option for this, with obsorbing at the bank level ( absorb(gvkey) ). When I was talking to my thesis supervisor and told her that I wanted to use both bank fixed effects and cluster standard errors on the bank level, she told me that this is not right as this is doing the same thing twice (Are you guys agree on this??). To test what she said I used both robust and cluster with xtreg, and the results were the same. However, when I use areg absorb(gvkey) robust or areg absorb (gvkey) cluster (gvkey) results do differ. My question is, how can this differ between areg (where the cluster and robust option results in different regression results) and xtreg( where using robust or cluster does not change regression results). I have searched the statalist forum already and read this post: http://www.stata.com/statalist/archi.../msg00596.html . However, I sill dont get why using cluster differs between areg and xtreg.

Here some results:

Areg with robust

. areg mliq L.Hqualitybank Hbank_Crisis  size nim  racr loanstoassets depositsloans L.Crisisdummy fedfund tedspread
> changeinflation,absorb(gvkey) r

Linear regression, absorbing indicators           Number of obs   =       3755
                                                  F(  11,   3615) =      42.87
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.8284
                                                  Adj R-squared   =     0.8218
                                                  Root MSE        =     0.0258

---------------------------------------------------------------------------------
                |               Robust
           mliq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
   Hqualitybank |
            L1. |  -.0048897   .0016137    -3.03   0.002    -.0080536   -.0017258
                |
   Hbank_Crisis |   .0015343   .0027677     0.55   0.579    -.0038921    .0069606
           size |   .0037692   .0016317     2.31   0.021       .00057    .0069684
            nim |  -.0034188    .001323    -2.58   0.010    -.0060127   -.0008249
           racr |   .0016591   .0003786     4.38   0.000     .0009168    .0024014
  loanstoassets |  -.0460795   .0131867    -3.49   0.000    -.0719336   -.0202253
  depositsloans |   .0278637   .0039698     7.02   0.000     .0200803    .0356471
                |
    Crisisdummy |
            L1. |   .0057046   .0017564     3.25   0.001      .002261    .0091483
                |
        fedfund |  -.0014908   .0003294    -4.53   0.000    -.0021365    -.000845
      tedspread |  -.0030266   .0011774    -2.57   0.010    -.0053351   -.0007181
changeinflation |   .0001491   .0014236     0.10   0.917     -.002642    .0029402
          _cons |  -.0023362   .0230833    -0.10   0.919    -.0475939    .0429215
----------------+----------------------------------------------------------------
          gvkey |   absorbed                                     (129 categories)

VS areg with cluster

. areg mliq L.Hqualitybank Hbank_Crisis  size nim  racr loanstoassets depositsloans L.Crisisdummy fedfund tedspread
> changeinflation,absorb(gvkey) cluster(gvkey)

Linear regression, absorbing indicators           Number of obs   =       3755
                                                  F(  11,    128) =       6.64
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.8284
                                                  Adj R-squared   =     0.8218
                                                  Root MSE        =     0.0258

                                   (Std. Err. adjusted for 129 clusters in gvkey)
---------------------------------------------------------------------------------
                |               Robust
           mliq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
   Hqualitybank |
            L1. |  -.0048897   .0041795    -1.17   0.244    -.0131595    .0033802
                |
   Hbank_Crisis |   .0015343   .0045884     0.33   0.739    -.0075447    .0106132
           size |   .0037692   .0048582     0.78   0.439    -.0058435     .013382
            nim |  -.0034188   .0028916    -1.18   0.239    -.0091403    .0023028
           racr |   .0016591   .0009438     1.76   0.081    -.0002084    .0035266
  loanstoassets |  -.0460795   .0374456    -1.23   0.221     -.120172     .028013
  depositsloans |   .0278637   .0115271     2.42   0.017     .0050555    .0506719
                |
    Crisisdummy |
            L1. |   .0057046   .0034413     1.66   0.100    -.0011045    .0125138
                |
        fedfund |  -.0014908    .000876    -1.70   0.091    -.0032241    .0002426
      tedspread |  -.0030266   .0018372    -1.65   0.102    -.0066618    .0006085
changeinflation |   .0001491   .0019137     0.08   0.938    -.0036375    .0039358
          _cons |  -.0023362   .0799416    -0.03   0.977    -.1605142    .1558418
----------------+----------------------------------------------------------------
          gvkey |   absorbed                                     (129 categories)

xtreg with robust

. xtreg mliq L.Hqualitybank Hbank_Crisis  size nim  racr loanstoassets depositsloans L.Crisisdummy fedfund tedspread
>  changeinflation,fe r

Fixed-effects (within) regression               Number of obs      =      3755
Group variable: gvkey                           Number of groups   =       129

R-sq:  within  = 0.2504                         Obs per group: min =         1
       between = 0.2905                                        avg =      29.1
       overall = 0.3465                                        max =        54

                                                F(11,128)          =      6.87
corr(u_i, Xb)  = -0.1019                        Prob > F           =    0.0000

                                   (Std. Err. adjusted for 129 clusters in gvkey)
---------------------------------------------------------------------------------
                |               Robust
           mliq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
   Hqualitybank |
            L1. |  -.0048897   .0041074    -1.19   0.236    -.0130169    .0032375
                |
   Hbank_Crisis |   .0015343   .0045093     0.34   0.734    -.0073881    .0104566
           size |   .0037692   .0047744     0.79   0.431    -.0056777    .0132162
            nim |  -.0034188   .0028417    -1.20   0.231    -.0090417    .0022041
           racr |   .0016591   .0009276     1.79   0.076    -.0001762    .0034944
  loanstoassets |  -.0460795   .0367998    -1.25   0.213    -.1188941    .0267351
  depositsloans |   .0278637   .0113282     2.46   0.015     .0054488    .0502786
                |
    Crisisdummy |
            L1. |   .0057046   .0033819     1.69   0.094    -.0009871    .0123963
                |
        fedfund |  -.0014908   .0008609    -1.73   0.086    -.0031942    .0002127
      tedspread |  -.0030266   .0018055    -1.68   0.096    -.0065991    .0005458
changeinflation |   .0001491   .0018807     0.08   0.937    -.0035722    .0038705
          _cons |  -.0023362   .0785628    -0.03   0.976    -.1577861    .1531137
----------------+----------------------------------------------------------------
        sigma_u |  .03901529
        sigma_e |  .02583222
            rho |  .69522501   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

Xtreg with cluster

. xtreg mliq L.Hqualitybank Hbank_Crisis  size nim  racr loanstoassets depositsloans L.Crisisdummy fedfund tedspread
>  changeinflation,fe cluster(gvkey)

Fixed-effects (within) regression               Number of obs      =      3755
Group variable: gvkey                           Number of groups   =       129

R-sq:  within  = 0.2504                         Obs per group: min =         1
       between = 0.2905                                        avg =      29.1
       overall = 0.3465                                        max =        54

                                                F(11,128)          =      6.87
corr(u_i, Xb)  = -0.1019                        Prob > F           =    0.0000

                                   (Std. Err. adjusted for 129 clusters in gvkey)
---------------------------------------------------------------------------------
                |               Robust
           mliq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
   Hqualitybank |
            L1. |  -.0048897   .0041074    -1.19   0.236    -.0130169    .0032375
                |
   Hbank_Crisis |   .0015343   .0045093     0.34   0.734    -.0073881    .0104566
           size |   .0037692   .0047744     0.79   0.431    -.0056777    .0132162
            nim |  -.0034188   .0028417    -1.20   0.231    -.0090417    .0022041
           racr |   .0016591   .0009276     1.79   0.076    -.0001762    .0034944
  loanstoassets |  -.0460795   .0367998    -1.25   0.213    -.1188941    .0267351
  depositsloans |   .0278637   .0113282     2.46   0.015     .0054488    .0502786
                |
    Crisisdummy |
            L1. |   .0057046   .0033819     1.69   0.094    -.0009871    .0123963
                |
        fedfund |  -.0014908   .0008609    -1.73   0.086    -.0031942    .0002127
      tedspread |  -.0030266   .0018055    -1.68   0.096    -.0065991    .0005458
changeinflation |   .0001491   .0018807     0.08   0.937    -.0035722    .0038705
          _cons |  -.0023362   .0785628    -0.03   0.976    -.1577861    .1531137
----------------+----------------------------------------------------------------
        sigma_u |  .03901529
        sigma_e |  .02583222
            rho |  .69522501   (fraction of variance due to u_i)
---------------------------------------------------------------------------------

So question 1) do you agree about the fact that using clustering on the same level as you apply fixed effects is redundant? and question 2) How is it possible that results differ between xtreg and areg when applying clustering?

Thank you in advance for your answers!

Yannick

[Clyde Schechter]

On page 402 of the [XT] manual you will find in the section on options for the FE model,

Specifying vce(robust) is equivalent to specifying vce(cluster panelvar); see xtreg, fe in Methods and formulas.

By contrast -areg- treats -vce(robust)- as simply specifying the robust "sandwich" estimator without automatically incorporating the cluster corrections.

Using a fixed effects model and specifying cluster robust standard errors is not doing the same thing twice. The use of fixed effects accounts for within-cluster correlation of observations by "taking out" a common intercept for each group. But it is not always the case that the resulting residuals are now independent. If intra-group residual correlation remains after fixed effects are included, the additional use of cluster robust vce may be appropriate, if the number of clusters is sufficiently large. (Your 129 clusters is probably fine in this regard.)

[YH jordaan]

On page 402 of the [XT] manual you will find in the section on options for the FE model,


By contrast -areg- treats -vce(robust)- as simply specifying the robust "sandwich" estimator without automatically incorporating the cluster corrections.

Using a fixed effects model and specifying cluster robust standard errors is not doing the same thing twice. The use of fixed effects accounts for within-cluster correlation of observations by "taking out" a common intercept for each group. But it is not always the case that the resulting residuals are now independent. If intra-group residual correlation remains after fixed effects are included, the additional use of cluster robust vce may be appropriate, if the number of clusters is sufficiently large. (Your 129 clusters is probably fine in this regard.)

Thanks for your answer! With respect to the fact that after the use of fixed effects it may be the case that residuals are still not independent: how can I test for this? I know I can test my variables on serial correlation with either the xtcorr or xtserial commands, but you cant apply this on a fixed effects model.

[Clyde Schechter]

Well, one approach might be to -predict- the residuals and then calculate the intra-class correlation with -icc-. But, though I didn't mention it earlier, the cluster robust VCE also deals with issues of heteroskedasticity. So you may want to explore for that as well, in whatever way you normally do that.

[YH jordaan]

Well, one approach might be to -predict- the residuals and then calculate the intra-class correlation with -icc-. But, though I didn't mention it earlier, the cluster robust VCE also deals with issues of heteroskedasticity. So you may want to explore for that as well, in whatever way you normally do that.

I looked into the stata manual and the only thing I see is the application of icc with random or mixed models. Furthermore, when I searched for help icc in stata I got ''No entries found for icc''. Is predicting e and testing e with xtserial equivalent to using icc?

Note: i have stata version 12.

[Clyde Schechter]

I'm not familiar with -xtserial-. It's not an official Stata command, by the way.