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  • Hyungsik Roger Moon (a1) and Frank Schorfheide (a2)

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.

Corresponding author
Address correspondence to: Hyungsik Roger Moon, Department of Economics, University of Southern California, KAP 300, University Park Campus, Los Angeles, CA 90089, USA; e-mail:
Or address correspondence to: Frank Schorfheide, Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104, USA; e-mail:
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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