st: Panel cointegration: mixed messages from -xtwest- and dols-estimation

[<Erkki.Vihriala@bof.fi>]

Dear all,

I am trying to estimate a cointegrating relationship between the real exchange rate and various explanatory variables using a panel of 21 countries. 

As a first test, according to -xtunitroot- the individual series are integrated.

I proceed to use -xtwest- (from http://ideas.repec.org/c/boc/bocode/s456941.html) to test whether there exists a cointegrating relationship between the real exchange rate and the explanatory variables. The results are strongly against cointegration (I use the constant-option to account for the fixed effects across panels):

-----------------------------------------------------------------------
xtwest reer_n prodd tot ggc nfa, lags(1 2) constant

Calculating Westerlund ECM panel cointegration tests..........

Results for H0: no cointegration
With 21 series and 4 covariates
Average AIC selected lag length: 1.9
Average AIC selected lead length: 0

-----------------------------------------------+
 Statistic |   Value   |  Z-value  |  P-value  |
-----------+-----------+-----------+-----------|
     Gt    |   -1.448  |    4.786  |   1.000   |
     Ga    |   -1.583  |    6.802  |   1.000   |
     Pt    |   -7.777  |    1.909  |   0.972   |
     Pa    |   -4.535  |    2.883  |   0.998   |
-------------------------------------------------------------------------

However, when testing for cointegration between the real exchange rate and individual explanatory variables, the null of no cointegration is strongly rejected for all regressors (below an example):
---------------------------------------------------------------------
xtwest reer_n prodd, lags(1 2) constant

Calculating Westerlund ECM panel cointegration tests..........

Results for H0: no cointegration
With 21 series and 1 covariate
Average AIC selected lag length: 1.1
Average AIC selected lead length: 0

-----------------------------------------------+
 Statistic |   Value   |  Z-value  |  P-value  |
-----------+-----------+-----------+-----------|
     Gt    |   -2.680  |   -4.602  |   0.000   |
     Ga    |  -10.558  |   -2.876  |   0.002   |
     Pt    |  -12.161  |   -5.559  |   0.000   |
     Pa    |  -11.008  |   -6.996  |   0.000   |
-----------------------------------------------+
--------------------------------------------------------------------

First question: how can these conflicting findings be reconciled? (ie. strong evidence of cointegration between the real exchange rate and each individual regressor but no evidence for cointegration between the real exchange rate and the set of regressors as whole)

My second question concerns the DOLS methodology for estimating the cointegrating relationship. Having found evidence for cointegration between reer_n and prodd above, I try to quantify the relationship by running a fixed effects regression accounting for the serial correlation due to the non-stationarity of the data:

---------------------------------------------------------------------------------
xtreg reer_n prodd L(-1/1).d.prodd, fe vce(cluster ctyno)

Fixed-effects (within) regression               Number of obs      =       546
Group variable: ctyno                           Number of groups   =        21

R-sq:  within  = 0.0004                         Obs per group: min =        26
       between = 0.3121                                        avg =      26.0
       overall = 0.0685                                        max =        26

                                                F(4,20)            =      0.24
corr(u_i, Xb)  = 0.3880                         Prob > F           =    0.9094

                                 (Std. Err. adjusted for 21 clusters in ctyno)
------------------------------------------------------------------------------
             |               Robust
      reer_n |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       prodd |
         --. |   .0134293    .050966     0.26   0.795    -.0928838    .1197424
         FD. |  -.0590749   .3185506    -0.19   0.855    -.7235597    .6054099
         D1. |   .1095792   .2710577     0.40   0.690    -.4558372    .6749957
         LD. |   .0374103   .3480491     0.11   0.915    -.6886073    .7634279
             |
       _cons |   4.258699   .0074655   570.45   0.000     4.243126    4.274272
-------------+----------------------------------------------------------------
     sigma_u |  .20670244
     sigma_e |  .25992447
         rho |  .38740778   (fraction of variance due to u_i)
----------------------------------------------------------------------------------
The coefficient on prodd is statistically insignificant as is the case for ALL other explanatory variables when changing the regressor in the  fe-specification (using the regressors that were found to be cointegrated with reer_n by the -xtwest- command).

How can it be reconciled that on the one hand xtwest finds strong evidence of a cointegrating relationship between reer_n and prodd but on the other hand the cointegrating coefficient in the -xtreg- regression is statistically insignificant?
 

Kind regards,

Erkki Vihriälä

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