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Minimum Distance Estimation Of Nonstationary Time Series Models

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  • Moon, Hyungsik Roger
  • Schorfheide, Frank

Abstract

This paper analyzes the limit distribution of minimum distance (MD) estimators for nonstationary time series models that involve nonlinear parameter restrictions. A rotation for the restricted parameter space is constructed to separate the components of the MD estimator that converge at different rates. We derive regularity conditions for the restriction function that are easier to verify than the stochastic equicontinuity conditions that arise from direct estimation of the restricted parameters. The sequence of matrices that is used to weigh the discrepancy between the unrestricted estimates and the restriction function is allowed to have a stochastic limit. For MD estimators based on unrestricted estimators with a mixed normal asymptotic distribution the optimal weight matrix is derived and a goodness-of-fit test is proposed. Our estimation theory is illustrated in the context of a permanent-income model and a present-value model.

Suggested Citation

  • Moon, Hyungsik Roger & Schorfheide, Frank, 2002. "Minimum Distance Estimation Of Nonstationary Time Series Models," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1385-1407, December.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:06:p:1385-1407_18
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    Cited by:

    1. Castro, Luciano de & Galvao, Antonio F. & Kim, Jeong Yeol & Montes-Rojas, Gabriel & Olmo, Jose, 2022. "Experiments on portfolio selection: A comparison between quantile preferences and expected utility decision models," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 97(C).
    2. Leandro M. Magnusson & Sophocles Mavroeidis, 2010. "Identification‐Robust Minimum Distance Estimation of the New Keynesian Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(2‐3), pages 465-481, March.
    3. Considine, Timothy J., 2018. "Estimating concave substitution possibilities with non-stationary data using the dynamic linear logit demand model," Economic Modelling, Elsevier, vol. 72(C), pages 22-30.
    4. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    5. Galvao, Antonio F. & Wang, Liang, 2015. "Efficient minimum distance estimator for quantile regression fixed effects panel data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 1-26.
    6. Marco Del Negro & Frank Schorfheide, 2004. "Priors from General Equilibrium Models for VARS," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 643-673, May.

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