The Generalized Method of Moments in the Presence of Nonstationary Variables

다국어 초록 (Multilingual Abstract)

This paper studies the generalized method of moments (GMM) in the presence of nonstationary time series with a unit root. We investigate asymptotic
properties of the GMM estimator in such a situation. It is shown that the GMM estimator
is a consistent estimator regardless of whether or not the model under study contains
nonstationarity. On the other hand, the asymptotic distribution of the GMM estimator is
nonstandard in the presence of nonstationarity. Such nonstandard limiting behavior of
the GMM estimator in the presence of unit roots causes difficulty in statistical inference.
However, under a reasonable condition implied in an equilibrium relation the
asymptotic distribution of the GMM estimator is described by a mixed normal
distribution. The mixed normality of the estimator itself is, in general, not of direct use
for statistical inference. However, the mixed normality of the estimator sometimes
enables us to derive results that are useful for statistical inference. We show that,
under some reasonable conditions, the asymptotic behavior of the J-statistic for testing
the validity of moment restrictions is characterized by a chi-square distribution.

다국어 초록 (Multilingual Abstract)

This paper studies the generalized method of moments (GMM) in the presence of nonstationary time series with a unit root. We investigate asymptotic
properties of the GMM estimator in such a situation. It is shown that the GMM estimator
is a consistent estimator regardless of whether or not the model under study contains
nonstationarity. On the other hand, the asymptotic distribution of the GMM estimator is
nonstandard in the presence of nonstationarity. Such nonstandard limiting behavior of
the GMM estimator in the presence of unit roots causes difficulty in statistical inference.
However, under a reasonable condition implied in an equilibrium relation the
asymptotic distribution of the GMM estimator is described by a mixed normal
distribution. The mixed normality of the estimator itself is, in general, not of direct use
for statistical inference. However, the mixed normality of the estimator sometimes
enables us to derive results that are useful for statistical inference. We show that,
under some reasonable conditions, the asymptotic behavior of the J-statistic for testing
the validity of moment restrictions is characterized by a chi-square distribution.

참고문헌 (Reference)

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