Difference between vce(robust) and vce(cluster ind) in cross-sectional model

[Nguyen Ha]

Dear Statalisters,

I have a question regarding the use of vce(robust) or vce(cluster ind) for my cross-sectional model. My dataset is small, with 116 observations.
The variable I concerned about is the dummy variable and it's only significant in the last case. There are differences in SE when I use vce(robust) or vce(cluster ind).
I want to ask if it's right if I use vce(cluster ind) in this model and I hope I could understand why there are big changes in my model.
I attached the code here with 3 model: OLS, vce(robust), vce(cluster ind).
Thank you so much.

Best regards,
Ha Nguyen

. reg Y dummy X1 size cash age2 analyst mbratio

      Source |       SS           df       MS      Number of obs   =       116
-------------+----------------------------------   F(7, 108)       =      2.43
       Model |  393.729615         7  56.2470879   Prob > F        =    0.0237
    Residual |  2499.90356       108  23.1472552   R-squared       =    0.1361
-------------+----------------------------------   Adj R-squared   =    0.0801
       Total |  2893.63317       115  25.1620276   Root MSE        =    4.8112

------------------------------------------------------------------------------
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       dummy |  -1.449351   .9828503    -1.47   0.143     -3.39753    .4988292
          X1 |   .0673247    .028259     2.38   0.019     .0113104     .123339
        size |  -.8122102    .400049    -2.03   0.045    -1.605177   -.0192437
        cash |  -15.73149   8.188105    -1.92   0.057    -31.96174    .4987515
        age2 |   .9146657   .4920407     1.86   0.066    -.0606444    1.889976
     analyst |   .0638981   .6261884     0.10   0.919    -1.177316    1.305112
     mbratio |  -.2066817   .2757556    -0.75   0.455    -.7532772    .3399137
       _cons |   14.04019   8.693411     1.62   0.109    -3.191661    31.27204


. reg Y dummy X1 size cash age2 analyst mbratio ,robust

Linear regression                               Number of obs     =        116
                                                F(7, 108)         =       1.84
                                                Prob > F          =     0.0870
                                                R-squared         =     0.1361
                                                Root MSE          =     4.8112

------------------------------------------------------------------------------
             |               Robust
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       dummy |  -1.449351   1.007996    -1.44   0.153    -3.447374    .5486733
          X1 |   .0673247   .0248537     2.71   0.008     .0180604     .116589
        size |  -.8122102   .3700793    -2.19   0.030    -1.545772   -.0786489
        cash |  -15.73149   9.472885    -1.66   0.100     -34.5084     3.04541
        age2 |   .9146657    .615406     1.49   0.140    -.3051757    2.134507
     analyst |   .0638981   .3762059     0.17   0.865    -.6818073    .8096035
     mbratio |  -.2066817   .1959103    -1.05   0.294    -.5950099    .1816464
       _cons |   14.04019   7.764501     1.81   0.073    -1.350401    29.43078
------------------------------------------------------------------------------

reg Y dummy X1 size cash age2 analyst mbratio , vce(cluster ind)

Linear regression                               Number of obs     =        116
                                                F(7, 13)          =      27.17
                                                Prob > F          =     0.0000
                                                R-squared         =     0.1361
                                                Root MSE          =     4.8112

                                   (Std. Err. adjusted for 14 clusters in ind)
------------------------------------------------------------------------------
             |               Robust
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       dummy |  -1.449351   .6598815    -2.20   0.047    -2.874938   -.0237631
          X1 |   .0673247    .021427     3.14   0.008     .0210345    .1136149
        size |  -.8122102   .2410903    -3.37   0.005    -1.333054   -.2913664
        cash |  -15.73149   3.602049    -4.37   0.001    -23.51325    -7.94974
        age2 |   .9146657   .3727299     2.45   0.029     .1094317      1.7199
     analyst |   .0638981    .221543     0.29   0.778    -.4147165    .5425127
     mbratio |  -.2066817   .1792627    -1.15   0.270    -.5939553    .1805919
       _cons |   14.04019   4.305863     3.26   0.006     4.737936    23.34244
------------------------------------------------------------------------------

[Felix Stips]

Often clustered SE's are larger than robust SE's. This makes me wondering, what is the "ind" variable you use? If ind is a variable for each individual (?), then clustering on this variable does not really make sense. In any case, the decision whether to cluster should be based on how your data is grouped. This might give you good insight for that decision
http://cameron.econ.ucdavis.edu/rese...5_February.pdf
https://arxiv.org/abs/1710.02926

[Nguyen Ha]

Dear Felix,
Thank you so much for your reply.
I cluster them by industry using a 2-digit NAICS code. I have 13 industries in total.

Often clustered SE's are larger than robust SE's. This makes me wondering, what is the "ind" variable you use? If ind is a variable for each individual (?), then clustering on this variable does not really make sense. In any case, the decision whether to cluster should be based on how your data is grouped. This might give you good insight for that decision
http://cameron.econ.ucdavis.edu/rese...5_February.pdf
https://arxiv.org/abs/1710.02926

[Andrew Musau]

You do not have enough industries to cluster at the industry level. For your question, -robust- option in regress implements Huber-White standard errors, and is be equivalent to clustering at the observation level.

reg Y dummy X1 size cash age2 analyst mbratio ,robust
gen obs_no=_n
reg Y dummy X1 size cash age2 analyst mbratio , cluster(obs_no)

[Nguyen Ha]

Dear Andrew,
Thank you so much for your reply. Could I ask you why the model doesn't have enough industries? How many are sufficient?
In this case, the use of vce cluster industry is wrong?
Thank you.

You do not have enough industries to cluster at the industry level. For your question, -robust- option in regress implements Huber-White standard errors, and is be equivalent to clustering at the observation level.

[Andrew Musau]

When you cluster your standard errors, you assume that observations within a cluster are correlated, but are uncorrelated with observations in other clusters. Effectively, each cluster is an observation. The cluster robust justification relies on \(N \rightarrow \infty\), so one rule-of thumb often used is that you need at least 30 clusters. In your case, 14 industries are just too few.