Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-15T05:59:30.161Z Has data issue: false hasContentIssue false
  • English
  • Français

ESTIMATORS FOR PERSISTENT AND POSSIBLY NONSTATIONARY DATA WITH CLASSICAL PROPERTIES

Published online by Cambridge University Press:  27 April 2012

Yuriy Gorodnichenko ,
Anna Mikusheva  and
Serena Ng
Yuriy Gorodnichenko
Affiliation:
University of California at Berkeley
Anna Mikusheva
Affiliation:
MIT
Serena Ng*
Affiliation:
Columbia University
*
*Address correspondence to Serena Ng, Department of Economics, Columbia University, 420 W. 118 St., New York, NY 10027, USA; e-mail: Serena.Ng@columbia.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a moments-based nonlinear estimator that is $\root \of T $-consistent and uniformly asymptotically normal irrespective of the degree of persistence of the forcing process. These properties hold for linear autoregressive models, linear predictive regressions, and certain nonlinear dynamic models. Asymptotic normality is obtained because the moments are chosen so that the objective function is uniformly bounded in probability and so that a central limit theorem can be applied. Critical values from the normal distribution can be used irrespective of the treatment of the deterministic terms. Simulations show that the estimates are precise and the t-test has good size in the parameter region where the least squares estimates usually yield distorted inference.

Type
Articles
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012 , pp. 1003 - 1036
Copyright
Copyright © Cambridge University Press 2012

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

Abowd, J.M. & Card, D. (1989) On the covariance structure of earnings and hours changes. Econometrica 57, 411–445.CrossRefGoogle Scholar
Altonji, J.G. & Segal, L.M. (1996) Small-sample bias in GMM estimation of covariance structures. Journal of Business & Economic Statistics 14, 353–366.Google Scholar
Canjels, E. & Watson, M.W. (1997) Estimating deterministic trends in the presence of serially correlated errors. Review of Economics and Statistics 79, 184–200.Google Scholar
Chernozhukov, V. & Hong, H. (2003) An MCMC approach to classical estimation. Journal of Econometrics 115, 293–346.Google Scholar
Coibion, O. & Gorodnichenko, Y. (2011) Strategic interaction among heterogeneous price setters in estimated DSGE model. Review of Economics and Statistics 93, 920–940.Google Scholar
Gorodnichenko, Y. & Ng, S. (2010) Estimation of DSGE models when the data are persistent. Journal of Monetary Economics 57, 325–340.Google Scholar
Han, C. & Kim, B. (2011) A GMM interpretation of the paradox in the inverse probability weighting estimation of the average treatment effect on the treated. Economics Letters 110, 163–165.Google Scholar
Han, C., Phillips, P.C.B., & Sul, D. (2011) Uniform asymptotic normality in stationary and unit root autoregression. Econometric Theory 27, 1117–1151.Google Scholar
Jansson, M. & Moreira, M.J. (2006) Optimal inference in regession models with nearly integrated regressors. Econometrica 74, 681–714.Google Scholar
Komunjer, I. & Ng, S. (2011) Dynamic identification of dynamic stochastic general equilibrium models. Econometrica 79, 1995–2032.Google Scholar
Laroque, G. & Salanie, B. (1997) Normal estimators for cointegrating relationships. Economics Letters 55, 185–189.Google Scholar
Mikusheva, A. (2007a) Uniform inference in autoregressive models. Econometrica 75, 1411– 1452.Google Scholar
Mikusheva, A. (2007b) Uniform inference in autoregressive models. Econometrica 75, online supplementary material.Google Scholar
Mikusheva, A. (2012) One dimensional inference in autogressive models with potential presence of a unit root. Econometrica 80, 163–212.Google Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, pp. 2111–2245. North-Holland.Google Scholar
Pesavento, E. & Rossi, B. (2006) Small-sample confidence interevals for multivariate impulse response functions at long horizons. Journal of Applied Econometrics 21, 1135–1155.Google Scholar
Phillips, P.C.B. & Han, C. (2008) Gaussian inference in AR(1) time series with or without a unit root. Econometric Theory 24, 631–650.CrossRefGoogle Scholar
Phillips, P.C.B. & Lee, C.C. (1996) Efficiency gains from quasi-differencing under nonstationarity. In Robinson, P. & Rosenblatt, M. (eds.), Athens Conference on Applied Probability and Time Series, vol. II, Time Series Analysis in Honor of E.J. Hannan, pp. 300–314. Springer.Google Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.Google Scholar
Phillips, P.C.B. & Xiao, Z. (1998) A primer on unit root testing. Journal of Economic Surveys 12, 423–469.CrossRefGoogle Scholar
Pierce, D.A. (1982) The asymptotic effect of substituting estimators for parameters in certain types of statistics. Annals of Statistics 10, 475–478.Google Scholar
Prokhorov, A. & Schmidt, P. (2009) GMM redundancy results for general missing data problem. Journal of Econometrics 151, 47–55.Google Scholar
So, B.S. & Shin, D.W. (1999) Cauchy estimators for autoregressive processes with applications to unit root tests and confidence intervals. Econometric Theory 15, 165–176.CrossRefGoogle Scholar
Uhlig, H. (1999) A Toolkit for analyzing nonlinear dynamic stochastic models easily. In Marimon, R. & Scott, A. (eds.), Computational Methods for the Study of Dynamic Economies, pp. 30–61. Oxford University Press.Google Scholar