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# st: Testing for serial correlation in small panel samples

 From christina sakali <[email protected]> To statalist <[email protected]> Subject st: Testing for serial correlation in small panel samples Date Tue, 6 Sep 2011 15:22:44 +0300

```Hello all,

I need to test for serial correlation in a panel regression with
individual fixed effects and only 121 observations (11 cross-sections,
11 years).

I have tried to implement the Wooldridge test (xtoserial) and the
results suggest the presence of serial correlation (Results from xtreg
and xtserial are provided below).

However, I read in Drukker (2003, p.168) that this test "is found to
have good size and power properties with samples of moderate size"
(Drukker's experiments contain samples of at least N=500, T=5).
Moreover Drukker (2003, p. 173) mentions that "When the errors are
conditionally heteroscedastic, the test may have less power in the
fixed effects case than in the random effects case in small samples
with low levels of serial correlation".

As a consequence, I was wondering whether Stata supports other
routines for testing for serial correlation which are more appropriate
for smaller samples.

For example is there a way to compute Bhargava's et al. (1982) DW
stat. for panel data or Baltagi's (2001, p.94) LM test for first-order
serial correlation in a fixed effects model?

. xtreg fdi gg trade sec tert trans, fe

Fixed-effects (within) regression               Number of obs      =       121
Group variable (i): panelvar                    Number of groups   =        11

R-sq:  within  = 0.5888                         Obs per group: min =        11
between = 0.0252                                        avg =      11.0
overall = 0.2831                                        max =        11

F(5,105)           =     30.07
corr(u_i, Xb)  = -0.6066                        Prob > F           =    0.0000

------------------------------------------------------------------------------
fdi |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
gg |   1.130961   .3984048     2.84   0.005     .3409984    1.920924
trade |   1.544293   .5143336     3.00   0.003     .5244645    2.564122
sec |   3.217286   1.550775     2.07   0.040     .1423854    6.292187
tert |   4.319199   1.654556     2.61   0.010     1.038521    7.599877
trans |   5.480038   1.828782     3.00   0.003     1.853901    9.106175
_cons |  -15.72257   2.564898    -6.13   0.000    -20.80829   -10.63685
-------------+----------------------------------------------------------------
sigma_u |  .60076209
sigma_e |  .46248795
rho |  .62788568   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0:     F(10, 105) =     6.04             Prob > F = 0.0000

. xtserial fdi gg trade sec tert trans

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
F(  1,      10) =      7.471
Prob > F =      0.0211

.
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```

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