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st: dfuller test statistic

From   Skipper Seabold <>
Subject   st: dfuller test statistic
Date   Wed, 16 Jun 2010 15:14:32 -0400


In Stata 11, when I do

webuse lutkepohl2
dfuller ln_inc, lags(4) regress

The reported test-statistic for a unit root is just the t-statistic on
the lagged ln_inc.  However, the Hamilton textbook and MacKinnon
(1994) recommend that when lagged values of the difference are
included that the appropriate test statistic is

Z = (T/(1-sum(coefficients on lagged differences))) * (coefficient on
lagged level - 1)

where T is the number of observations (not including lags).

Is this just a recommendation?  Is the single t-statistic valid to
test, and if so are the regression surface results of MacKinnon (1994)
with no lagged differences valid for this specification?


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