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

► We propose an approach ensuring parameter identifiability in unconditional moments. ► The instruments are generated by GCR functions and projected along Fourier series. ► The objective function for estimation is determined by the Fourier coefficients. ► The proposed estimator is consistent and asymptotically normally distributed. ► An efficient estimator can be easily computed via the two-step GMM method.