Difference between reg vce cluster (id) AND reg robust cluster (id)

[Simona Battipaglia]

Hello everyone,

I am using panel data and running a model with the Least Squares Dummy Variables Model (LSDVM).

I have heteroskedasticity and autocorrelation in one of my specifications and only autocorrelation in the others.

However, I am confused about the difference of the following standard errors:
1.

reg Y X1 X2, vce cluster (id)

and

2.

reg Y X1 X2, robust cluster (id)

Is robust cluster (id) to deal with both autocorrelation and heteroskedasticity?
And is vce cluster (id) only to deal with autocorrelation?


Thanks in advance,
Best,
Simona

[Carlo Lazzaro]

Simona:
both codes do the same job:

use "C:\Program Files (x86)\Stata15\ado\base\a\auto.dta"
. reg price mpg trunk, cluster(foreign)

Linear regression                               Number of obs     =         74
                                                F(0, 1)           =          .
                                                Prob > F          =          .
                                                R-squared         =     0.2222
                                                Root MSE          =     2637.6

                                (Std. Err. adjusted for 2 clusters in foreign)
------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -220.1649   45.58852    -4.83   0.130    -799.4219    359.0922
       trunk |   43.55851   9.441408     4.61   0.136    -76.40595     163.523
       _cons |   10254.95   185.7531    55.21   0.012     7894.732    12615.17
------------------------------------------------------------------------------

. reg price mpg trunk, robust cluster (foreign)

Linear regression                               Number of obs     =         74
                                                F(0, 1)           =          .
                                                Prob > F          =          .
                                                R-squared         =     0.2222
                                                Root MSE          =     2637.6

                                (Std. Err. adjusted for 2 clusters in foreign)
------------------------------------------------------------------------------
             |               Robust
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -220.1649   45.58852    -4.83   0.130    -799.4219    359.0922
       trunk |   43.55851   9.441408     4.61   0.136    -76.40595     163.523
       _cons |   10254.95   185.7531    55.21   0.012     7894.732    12615.17
------------------------------------------------------------------------------

For the sake of efficiency, I would go -vce(cluster clusterid)-.
The -robust- option in -regress- offers more ways to deal with heteroskedasticity, but cannot relax the assumption of the independence of observations within the same cluster.

[Simona Battipaglia]

Thank you a lot for the prompt reply.

So I am right in saying that -vce (cluster clusterid)- can deal with heteroskedasticity, serial correlation and also inter-dependence of within-cluster observations?

[Carlo Lazzaro]

Simona:
yes, with the the sidenote that serial correlation is another way to say non-independent observations within the same cluster (ie, panel).

[Simona Battipaglia]

A huge thank you for the elucidation and for your time!

Best regards,
Simona