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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.
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참고문헌 (10)
참고문헌 신청
Chan, N. H / 1988 / Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes / Annals of Statistics 16 : 367 ~ 401
Engle, R.F / 1987 / Co-integration And Error Correction: Representation, Estimation, and Testing / Econometrica 55 : 251 ~ 276
Gordin, M.I. / 1969 / The Central Limit Theorem for Stationary Processes / Soviet Mathematics-Doklady 10 : 1174 ~ 1176
Hansen, L.P. / 1982 / Large Sample Properties of Generalized Method of Moments Estimators / Econometrica 50 : 1029 ~ 1054
Herrndorf, N. / 1984 / A Functional Central Limit Theorem For Weakly Dependent Sequences of Random Variables / The Annals of Probability 12 : 141 ~ 153
Engle, R.F / 1987 / Co-integration And Error Correction: Representation, Estimation, and Testing / Econometrica 55 : 251 ~ 276
Gordin, M.I. / 1969 / The Central Limit Theorem for Stationary Processes / Soviet Mathematics-Doklady 10 : 1174 ~ 1176
Hansen, L.P. / 1982 / Large Sample Properties of Generalized Method of Moments Estimators / Econometrica 50 : 1029 ~ 1054
Herrndorf, N. / 1984 / A Functional Central Limit Theorem For Weakly Dependent Sequences of Random Variables / The Annals of Probability 12 : 141 ~ 153
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