fmgmm: Fully-Modified GMM Estimator

In COINT: Unit Root Tests with Structural Breaks and Fully-Modified Estimators

Fully-Modified GMM Estimator

Description

Computes the Kitamura-Phillips (1997) Fully-Modified GMM estimator for single equation and multivariate cointegrated regression models.

Usage

fmgmm(y,x,z,v,ker_fun="parzen",aband=0,times=5) 

Arguments

y	The data of dependent variable(s) in a regression.
x	The data of independent variables in a regression.
z	Instruments
v	Number of autocovariance terms to compute the spectrum at frequency zero, default=15.
ker_fun	Set kernel function to one of the available kernels, default="parzen". See section details below.
aband	Whether to activate the automatic bandwidth selection. aband=1. To activate. aband=0. Do not activate.The default.
times	Number of iteration to compute GMM residuals, default =5.

Details

1. Like FMOLS, fmgmm allows both single equation and multivariate system of equations. The multvariate case is a system that many dependent variables to common Xs.
2. Available kernels. Technical details are referred to Brillinger (1981,P.55)
"parzen"=Parzen kernel
"bartlett"=Bartlett kernel
"dchlet"= Dirichlet kernel
"mdchlet"= Modified Dirichlet kernel
"tukham"=Tukey-Hamming kernel
"tukhan"=Tukey-Hanning kernel
"cauchy"=Cauchy kernel
"bohman"=Bohman kernel
"reisz"=Riesz,Bochner kernel
"gw"= Gauss-Weierstrass kernel
"qs"= Andrews (1991) Quadratic-Spectral

These kernels are written for FM procedures, technically different from those used in pp and kpss tests.

3. Andrews (1991) has developed data based (or automatic) bandwidth procedures for computing the spectrum. COINT implements these procedures for the Parzen, Bartlette, Tukey-Hamming, and the Quadratic-Spectral kernels. When aband is active, COINT ignores the value you specify for the band-width parameter and automatically substitutes the data-based value.
4. The aim of the AR(1) filter is to flatten the spectrum of residual around the zero frequency, thereby making it easier to estimate the true spectrum by simple averaging of the periodogram.

Value

beta	Coefficient estimates.
stderr	Standard error of the residuals.
tstat	t-statistics of parameter estimates.
vcov	Variance-covariance matrix for the parameter estimates.
lromega	long-run variance-covariance matrix of residuals.
s1	The first statistic for testing validity of overidentifying restrictions.
s2	The second statistic for testing validity of overidentifying restrictions.
pvalue	The p-value for s1+s2.
fit	The fitted values, or conditional mean, of the regression.
resid	GMM residuals.

Author(s)

Ho Tsung-wu <[e-mail]>, College of Management, National Taiwan Normal University.

References

Kitamura, Y. and P. C. B. Phillips (1997) Fully-Modified IV, GIVE and GMM Estimation with Possibly Nonstationary Regressors and Instruments. Journal of Econometrics, 80, 85-123.

Examples

data(macro)

y=macro[-1,c(1,4)]
x=macro[-1,c(2,3)]
z=as.matrix(na.omit(diff(macro))) #IV

out=fmgmm(y,x,z,v=15,ker_fun="parzen")
out$beta
out$vcov
out$stderr
out$tstat #t-ratio
tail(out$fit)
tail(out$resid)

COINT documentation built on Sept. 9, 2025, 5:51 p.m.