Estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments

Shih-Hsun Hsu () and Chung-Ming Kuan ()

Journal of Econometrics, 2011, vol. 165, issue 1, 87-99

Abstract: A well-known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments. In this paper, we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability. These unconditional moments depend on the “instruments” generated from a “generically comprehensively revealing” function, and they are further projected along the exponential Fourier series. The objective function is based on the resulting Fourier coefficients, from which an estimator can be easily computed. A novel feature of our method is that the full continuum of unconditional moments is incorporated into each Fourier coefficient. We show that, when the number of Fourier coefficients in the objective function grows at a proper rate, the proposed estimator is consistent and asymptotically normally distributed. An efficient estimator is also readily obtained via the conventional two-step GMM method. Our simulations confirm that the proposed estimator compares favorably with that of Domínguez and Lobato (2004, Econometrica) in terms of bias, standard error, and mean squared error.

Keywords: Conditional moment restrictions; Fourier coefficients; Generically comprehensive revealing function; Global identifiability; GMM (search for similar items in EconPapers)
JEL-codes: C12 C22 (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:165:y:2011:i:1:p:87-99

DOI: 10.1016/j.jeconom.2011.05.008

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