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From |
<Erkki.Vihriala@bof.fi> |

To |
<statalist@hsphsun2.harvard.edu> |

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

Date |
Wed, 1 Aug 2012 13:22:17 +0000 |

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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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