Estimation of Conditional Moment Restrictions without Assuming Parameter Identifiability

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 are projected along the exponential Fourier series. The objective function is based on the resulting Fourier coefficients, from which a consistent estimator can be easily obtained. 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 a conventional GMM method. Our simulations confirm that the proposed consistent estimator compares favorably with that of Domı́nguez and Lobato (2004, Econometrica) in terms of bias, standard error and mean squared error. JEL classification: C12, C22