st: Best test to detect trends in panel data

[Kim Peeters <kimpeeters84@yahoo.com>]

Hi all,

I want to test whether  panel data variable Y exhibits a trend or not. My unbalanced panel
data contains 415 clusters and information is available for maximum 10 periods.
I have fitted a fixed-effects linear regression model for
panel data. The dependent variable is Y and the independent variable is the
ascending number of periods of which we have information given that Y is not
missing. Clustered standard errors are used.

. xtreg Y period, fe vce(cluster ID)
Fixed-effects (within) regression               Number of obs      =      2985
Group variable: ID                           Number of
groups   =       415
R-sq:  within  = 0.0020                         Obs per group: min =         1
       between =
0.0103                                        avg =       7.4
       overall =
0.0002                                        max =        10
                                                F(1,414)           =      2.52
corr(u_i, Xb)  =
-0.0776                        Prob > F           =    0.1132
                                (Std. Err.
adjusted for 415 clusters in ID)
------------------------------------------------------------------------------
             |               Robust
          Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      period |   .0007806   .0004918     1.59   0.113     -.000186    .0017472
       _cons |   .0451458    .002337    19.32   0.000     .0405531    .0497385
-------------+----------------------------------------------------------------
     sigma_u |  .04562405  sigma_e |  .04797833  rho |  .47486404  
------------------------------------------------------------------------------ 

The coefficient turns out to be not significant, rejecting
the hypothesis that the variable Y is rising over time. I also performed a
Panel-data unit-root test (Fisher-type test):

. xtunitroot fisher Y, dfuller lags(0)
could not compute test for panel 294, 298, 320, 389
Fisher-type unit-root test for Y
Based on augmented Dickey-Fuller tests
------------------------------------------------------
Ho: All panels contain unit roots           Number of panels       =    415
Ha: At least one panel is stationary        Avg. number of periods =   7.39
AR parameter: Panel-specific                Asymptotics: T -> Infinity
Panel means:  Included
Time trend:   Not
included
Drift term:   Not
included                  ADF
regressions: 0 lags
------------------------------------------------------------------------------
                                  Statistic      p-value
------------------------------------------------------------------------------
 Inverse chi-squared(898)  P      2963.7733       0.0000
 Inverse normal            Z       -15.6396       0.0000
 Inverse logit t(2049)     L*      -29.6490       0.0000
 Modified inv. chi-squared Pm       48.7449       0.0000
------------------------------------------------------------------------------
 P statistic requires
number of panels to be finite.
 Other statistics are
suitable for finite or infinite number of panels.
------------------------------------------------------------------------------

Again, we find that no evidence of a trend. However, in the
panel unit root test the alternative hypothesis is: At least one panel is stationary.

My question is: which statistical test suits my purpose
better, i.e. detecting a trend in a panel data variable. 

PS. I have also fitted an areg model (areg Y period, absorb(ID) vce(cluster ID)) and the coefficient of the independent variable period is also not significant.

Thank you for any advice you can provide,
Kim 

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