XTGLS2 - Estimate General GLS for Pooled, Fixed-effects and First-difference models in large N, small T panel data

[Manh Hoang Ba]

Thanks to Prof. Kit Baum, xtgls2 package are now available on SSC. You can install them from SSC by entering the following command into Stata:

ssc install xtgls2

xtgls2 helps STATA users estimate General GLS for Pooled, Fixed-effects, First-differences models, as described in Kiefer (1980) and Wooldridge (2002, 2010).
In which, the error covariance matrix has an arbitrary form within panels (allowing for heteroskedasticity over time periods and arbitrary serial correlations) and this structure is identical across panels.
It is possible to relax these assumptions, i.e. to allow for heteroskedasticity across panels, by using Arellano (1987) standard errors. xtgls2 does this using the cluster(varname) option with varname = panel variables.
For any comments about the command, please send to [email protected]
Examples:

. webuse abdata, clear

. xtbalance, range(1980 1984)

(498 observations deleted due to out of range)

(358 observations deleted due to discontinues)

. xtgls2 n l(1/2).w c.(k ys)##c.(k ys) i.ind i.year, c(c) fd nocons cl(id) igls nolo

Convergenced after 30 iterations

First-difference Generalized Least Squares (FDGLS) regression

Error covariance structure
     Time series:     Heteroskedasticity and serial correlation
     Cross-section:   Homoskedasticity

Estimated covariances:    3                     Number of obs     =         70
R-squared:                                      Number of groups  =         35
     Within   =  0.0096                         Time periods      =          2
     Between  =  0.0004                         Wald chi2(9)      =     91.594
     Overall  =  0.0004                         Prob > chi2       =     0.0000

                                    (Std. err. adjusted for 35 clusters in id)
------------------------------------------------------------------------------
             |               Robust
           n | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
           w |
         L1. |   .4604677   .1173617     3.92   0.000      .230443    .6904925
         L2. |   .1945558   .2115014     0.92   0.358    -.2199794     .609091
             |
           k |   2.538793   1.366328     1.86   0.063    -.1391604    5.216747
          ys |  -28.17702   30.72851    -0.92   0.359    -88.40379    32.04975
             |
     c.k#c.k |   -.103131   .0643289    -1.60   0.109    -.2292133    .0229513
             |
    c.k#c.ys |  -.4682237   .2880477    -1.63   0.104    -1.032787    .0963393
             |
   c.ys#c.ys |   2.904299   3.291465     0.88   0.378    -3.546854    9.355452
             |
        year |
       1982  |  -.0318849   .0522636    -0.61   0.542    -.1343197    .0705499
       1983  |  -.0247939   .0231626    -1.07   0.284    -.0701917     .020604
------------------------------------------------------------------------------

[Jeff Wooldridge]

This looks like a command I’ve been waiting for! I’d prefer the syntax for the choice of variance estimator to be vce(robust) as well as vce(cluster cid). In the former case, inference is robust to what I call “system heteroskedasticity,” which arises from estimating a constant T x T variance covariance matrix that’s not also the conditional var-cov matrix. That’s a separate issue from clustering. Hopefully the current command does what I want if you use cluster(id) where id is the panel id.

[Manh Hoang Ba]

This looks like a command I’ve been waiting for! I’d prefer the syntax for the choice of variance estimator to be vce(robust) as well as vce(cluster cid). In the former case, inference is robust to what I call “system heteroskedasticity,” which arises from estimating a constant T x T variance covariance matrix that’s not also the conditional var-cov matrix. That’s a separate issue from clustering. Hopefully the current command does what I want if you use cluster(id) where id is the panel id.

Hi prof. Jeffrey Wooldridge,

xtgls2 with the cluster(panel_var) option does indeed compute standard errors that are robust to “system heteroskedasticity”, as you prefer.

Specifically, the formula for computing robust standard errors can be found in Wooldridge (2010):

• Pooled GLS: formula (7.52) on page 172
• FEGLS: formula in chapter 10, on page 314
• FDGSL: similar to FEGLS and PGLS but with first-different transformed data.

The Pooled GLS estimation results with robust standard errors from xtgls2 can be compared with the corresponding output from EViews, with the declaration GLS weights = Period SUR and Covariance method = White period (no d.f. correction).

Thank you so much and wish you a good day.

[Manh Hoang Ba]

Update for xtgls2 and xttest4 command

xttest4 performs Kézdi (2003) test for heteroskedasticity in fixed effects models.
Version 1.3 for xtgls2 can be installed by downloading the .ado and .sthlp files attached to this comment.

The latest versions of these commands can be found at my github address: ManhHB94 (Manh Hoang Ba)

Any comments are welcome.