Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T05:52:20.145Z Has data issue: false hasContentIssue false
  • English
  • Français

Efficient IV Estimation in Nonstationary Regression

An Overview and Simulation Study

Published online by Cambridge University Press:  11 February 2009

Yuichi Kitamura  and
Peter C.B. Phillips
Yuichi Kitamura
Affiliation:
University of Minnesota
Peter C.B. Phillips
Affiliation:
Cowles Foundation for Research in Economics Yale University
Get access Rights & Permissions [Opens in a new window]

Abstract

A limit theory for instrumental variables (IV) estimation that allows for possibly nonstationary processes was developed in Kitamura and Phillips (1992, Fully Modified IV, GIVE, and GMM Estimation with Possibly Non-stationary Regressors and Instruments, mimeo, Yale University). This theory covers a case that is important for practitioners, where the nonstationarity of the regressors may not be of full rank, and shows that the fully modified (FM) regression procedure of Phillips and Hansen (1990) is still applicable. FM. versions of the generalized method of moments (GMM) estimator and the generalized instrumental variables estimator (GIVE) were also developed, and these estimators (FM-GMM and FM-GIVE) were designed specifically to take advantage of potential stationarity in the regressors (or unknown linear combinations of them). These estimators were shown to deliver efficiency gains over FM-IV in the estimation of the stationary components of a model.

This paper provides an overview of the FM-IV, FM-GMM, and FM-GIVE procedures and investigates the small sample properties of these estimation procedures by simulations. We compare the following five estimation methods: ordinary least squares, crude (conventional) IV, FM-IV, FM-GMM, and FM-GIVE. Our findings are as follows, (i) In terms of overall performance in both stationary and nonstationary cases, FM-IV is more concentrated and better centered than OLS and crude IV, though it has a higher root mean square error than crude IV due to occasional outliers, (ii) Among FM-IV, FM-GMM, and FM-GIVE, (a) when applied to the stationary coefficients, FM-GIVE generally outperforms FM-IV and FM-GMM by a wide margin, whereas the difference between the latter two is quite small when the AR roots of the stationary processes are rather large; and (b) when applied to the nonstationary coefficients, the three estimators are numerically very close. The performance of the FM-GIVE estimator is generally very encouraging.

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 5 , October 1995 , pp. 1095 - 1130
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.CrossRefGoogle Scholar
Hansen, B.E. & Phillips, P.C.B. (1990) Estimation and inference in models of cointegration: A simulation study. Advances in Econometrics 8, 225–248.Google Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Kitamura, Y. & Phillips, P.C.B. (1992) Fully Modified IV, GIVE, and GMM Estimation with Possibly Non-stationary Regressors and Instruments. Mimeo, Yale University.Google Scholar
Nelson, C.R. & Startz, R. (1990) The distribution of the instrumental variables estimator and its t-ratio when the instrument is a poor one. Journal of Business 63, 125–140.CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1989) Statistical inference in regressions with integrated processes: Part 2. Econometric Theory 5, 95–131.CrossRefGoogle Scholar
Parzen, E. (1957) On consistent estimates of the spectrum of a stationary time series. Annals of Mathematical Statistics 28, 329–348.CrossRefGoogle Scholar
Phillips, P.C.B. (1989) Partially identified econometric models. Econometric Theory 5, 181–240.CrossRefGoogle Scholar
Phillips, P.C.B. (1991) Optimal inference in cointegrated systems. Econometrica 59, 283–306.CrossRefGoogle Scholar
Phillips, P.C.B. & Hansen, B.E. (1990) Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99–125.CrossRefGoogle Scholar
Phillips, P.C.B. & Park, J.Y. (1988) Asymptotic equivalence of ordinary least squares and generalized least squares in regressions with integrated regressors. Journal of the American Statistical Association 83, 111–115.CrossRefGoogle Scholar
Priestley, M.B. (1981) Spectral Analysis and Time Series. London: Academic Press.Google Scholar
Sargan, J.D. (1988) Lectures on Advanced Econometrics. New York: Basil Blackwell.Google Scholar
White, H. (1984) Asymptotic Theory for Econometricians. New York: Academic Press.Google Scholar