2-way clustering in OLS regression

[Lukas Motsch]

Hello,

I have a question:

I have a regression with reg x y (several independent variables [GDP, unemployment rate, etc.]), vce (). I would like to clusters by countries and years, but you can not just enter in vce a 2nd variable. How can I cluster the standard error at the country and time level?

Thanks in Advance!

[Andreas Denzer]

Hey,

why don't you generate a new identifier which combines the country and time level information?

For instance your dataset looks like:

obs no. | country | year
1 USA 2003
2 USA 2004
3 USA 2005
4 MEX 2003
5 MEX 2004
6 MEX 2005

Proposal:
gen ni = country + string(year)


and then ... vce(cluster(ni)) ?

[Carlo Lazzaro]

Lukas:
welcome to the list.
You may want something along the following lines:

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


. egen double_cluster=group(idcode year)

. regress ln_wage age i.race, vce(cluster double_cluster)

Linear regression                               Number of obs     =     28,510
                                                F(3, 28509)       =     905.75
                                                Prob > F          =     0.0000
                                                R-squared         =     0.0946
                                                Root MSE          =     .45494

                    (Std. Err. adjusted for 28,510 clusters in double_cluster)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0196731   .0004233    46.48   0.000     .0188435    .0205028
             |
        race |
      black  |  -.1377638   .0059505   -23.15   0.000    -.1494271   -.1261006
      other  |   .0666999   .0284081     2.35   0.019     .0110187    .1223812
             |
       _cons |   1.141686    .012024    94.95   0.000     1.118119    1.165254
------------------------------------------------------------------------------

However, if you have a large N, small T panel dataset, -xtreg- usually outperforms -regress-.

[depado]

If I undertand correctly your point, I would have a look at this nice paper: http://www.nber.org/papers/t0327 (published on JBES)

[Kim Boehm]

Hi Lukas,

I'm not sure, if it fits your approach, but have you thought about using multi-level models? For more information see e.g.

• Good introducty paper: http://onlinelibrary.wiley.com/doi/1...059.x/abstract
• Good video about basics and why to use it: https://www.youtube.com/watch?v=f817HdHJneo
• Example from stata: http://blog.stata.com/2013/02/04/mul...s-of-variance/ and http://blog.stata.com/2013/02/18/mul...itudinal-data/
• What stata manuals describe about the command xtmixed

[River Huang]

It is easy to do that by (ssc install) reghdfe. Please help reghdfe for further usages and examples.

[lal mohan kumar]

Dear Carlo
In the post,

https://www.statalist.org/forums/forum/general-stata-discussion/general/1409000-2-way-clustering-in-ols-regression?p=1409016#post1409016

, as an answer, to

https://www.statalist.org/forums/forum/general-stata-discussion/general/1409000-2-way-clustering-in-ols-regression#post1409000

you have mentioned that for clustering by id code and year one can first create a group which comprises, id and year and then in regress command we can cluster by this group, so the codes as you suggested

use "http://www.stata-press.com/data/r14/nlswork.dta", clear
egen double_cluster=group(idcode year)
regress ln_wage age i.race, vce(cluster double_cluster)

But in the output file it is written as

(Std. Err. adjusted for 28510 clusters in double_cluster)

, since we have unique 28534 cluster but age is missing for 24 observations, we have 28510 observations.
However, this results can also be obtained by using robust option

regress ln_wage age i.race, vce(robust)

Thus can we conclude that under vce(robust) option in regress is similar to clustering both by id -year clusters?
In fact what I have seen is

use "http://www.stata-press.com/data/r14/nlswork.dta", clear
egen double_cluster=group(idcode year)
regress ln_wage age i.race, vce(cluster double_cluster)            // way 1
regress ln_wage age i.race, vce(robust)                                   // way 2
reghdfe ln_wage age i.race, noabsorb cluster(idcode#year)   // way 3

all the three ways give common results

However, for idcode and year clusters, we must try

.reghdfe ln_wage age i.race, noabsorb cluster(idcode year)

and we get the following results

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

. reghdfe ln_wage age i.race, noabsorb cluster(idcode year)
(MWFE estimator converged in 1 iterations)

HDFE Linear regression                            Number of obs   =     28,510
Absorbing 1 HDFE group                            F(   3,     14) =      99.06
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.0946
                                                  Adj R-squared   =     0.0945
Number of clusters (idcode)  =      4,710         Within R-sq.    =     0.0946
Number of clusters (year)    =         15         Root MSE        =     0.4549

                           (Std. Err. adjusted for 15 clusters in idcode year)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0196731   .0014594    13.48   0.000     .0165431    .0228032
             |
        race |
      black  |  -.1377638   .0133762   -10.30   0.000     -.166453   -.1090747
      other  |   .0666999   .0664563     1.00   0.333    -.0758347    .2092346
             |
       _cons |   1.141686   .0456635    25.00   0.000     1.043748    1.239625
------------------------------------------------------------------------------

Where we are simultaneously allowing errors to be correlated for observations in the same idcode and for observations in the same year. Here we have 2 clusters too unlike one in the option vce(idcode#year)

Am I correct?

[Hong Il Yoo]

I don't quite get what you're asking (admittedly, it's not addressed to me either) but I have a feeling that you may find section 2 of my background paper for -vcemway- useful [Link].

[lal mohan kumar]

Dear Hong
Sorry for being vague. My question was whether we can perform two way clustering with regress command as mentioned in #3. I think those commands in #3 gives only robust standard errors. So I was confused

[Hong Il Yoo]

I assume that #3 refers to:

egen double_cluster=group(idcode year)
regress ln_wage age i.race, vce(cluster double_cluster)

No, these command lines don't apply two-way clustering. They adjust standard errors for one-way clustering on the intersection of -idcode- and -year-. As I summarise in section 2 of the hyperlinked paper, to compute a two-way clustered covariance matrix, you need the covariance matrix that your -regress- command line produces but what it produces is not a two-way clustered covariance matrix itself.

[lal mohan kumar]

Yes, I will check the paper. As an aside I think for two clustering we need to run the command

 
 reghdfe ln_wage age i.race, noabsorb cluster(idcode year)

Am I right?

[Hong Il Yoo]

That works. So does:

vcemway regress ln_wage age i.race, cluster(idcode year)

and

ivreg2 ln_wage age i.race, cluster(idcode year)

where -vcemway- and -ivreg2- are other community-contributed commands.

[lal mohan kumar]

Thank you Hong for the help and those codes They are new to me

[Joro Kolev]

Creating a variable that is the crossing of the panel and the year does not result in double clustering. In fact what this procedure results into, are standard robust variances (robust standard errors). See the demonstration below.

You need command which knows how to double cluster, and some of them were mentioned above, e.g., -ivreg2- knows how to double cluster.

Demonstration that clustering on the crossing of two variables is not double clustering, but simply robust standard errors:

.  webuse nlswork, clear
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. egen notdoubleclustering = group(idcode year)

. reg ln_wage hours age i.race, robust

Linear regression                               Number of obs     =     28,443
                                                F(4, 28438)       =     744.16
                                                Prob > F          =     0.0000
                                                R-squared         =     0.1047
                                                Root MSE          =     .45223

------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       hours |   .0047844   .0003766    12.70   0.000     .0040462    .0055226
         age |   .0197855   .0004204    47.07   0.000     .0189616    .0206094
             |
        race |
      black  |  -.1449203   .0059211   -24.48   0.000    -.1565259   -.1333147
      other  |   .0595309   .0272146     2.19   0.029     .0061889    .1128729
             |
       _cons |    .966118   .0184062    52.49   0.000     .9300409    1.002195
------------------------------------------------------------------------------

. reg ln_wage hours age i.race, robust cluster(notdoubleclustering)

Linear regression                               Number of obs     =     28,443
                                                F(4, 28442)       =     744.16
                                                Prob > F          =     0.0000
                                                R-squared         =     0.1047
                                                Root MSE          =     .45223

               (Std. Err. adjusted for 28,443 clusters in notdoubleclustering)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       hours |   .0047844   .0003766    12.70   0.000     .0040462    .0055226
         age |   .0197855   .0004204    47.07   0.000     .0189616    .0206094
             |
        race |
      black  |  -.1449203   .0059211   -24.48   0.000    -.1565259   -.1333147
      other  |   .0595309   .0272146     2.19   0.029     .0061889    .1128729
             |
       _cons |    .966118   .0184062    52.49   0.000     .9300409    1.002195
------------------------------------------------------------------------------

[Joro Kolev]

Further, these two way clustered standard errors are easy enough to compute manually, if you wish to do so.

Here it it how (I will use as a benchmark the -ivreg2- results which are double clustered), the -erepost- is user written by Ben Jann:

.  webuse nlswork, clear
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. qui: ivreg2 ln_wage hours age i.race, robust cluster(idcode year)

. est sto ivreg2

. qui reg ln_wage hours age i.race, robust cluster(idcode)

. mat Vid = e(V)

. qui reg ln_wage hours age i.race, robust cluster(year)

. mat Vyear = e(V)

. qui reg ln_wage hours age i.race, robust

. mat V =Vid+Vyear-e(V)

. erepost V=V

. est sto manual

. esttab ivreg2 manual, b se mtitles

--------------------------------------------
                      (1)             (2)   
                   ivreg2          manual   
--------------------------------------------
hours             0.00478***      0.00478***
               (0.000856)      (0.000880)   

age                0.0198***       0.0198***
                (0.00141)       (0.00145)   

1.race                  0               0   
                      (.)             (.)   

2.race             -0.145***       -0.145***
                 (0.0128)        (0.0129)   

3.race             0.0595          0.0595   
                 (0.0616)        (0.0619)   

_cons               0.966***        0.966***
                 (0.0389)        (0.0400)   
--------------------------------------------
N                   28443           28443   
--------------------------------------------
Standard errors in parentheses
* p<0.05, ** p<0.01, *** p<0.001

.