Consistent Estimation Of Models Defined By Conditional Moment Restrictions Under Minimal Identifying Conditions

For econometric models defined by conditional moment restrictions, it is well known that the popular estimation methods such as the generalized method of moments and generalized empirical likelihood based on an arbitrary finite number of unconditional moment restrictions implied by the conditional moment restrictions can render inconsistent estimates. To guarantee the estimation consistency, some additional assumptions on these unconditional moment restrictions have to be levied. This paper introduces a simple consistent estimation procedure without assuming identifying conditions on the implied unconditional moment restrictions. This procedure is based on a weighted L2 norm with a unique weighting function, where a full continuum of unconditional moment restrictions is employed. It is quite easy to implement for any dimension of conditioning variables, and no any user-chosen number is required. Furthermore statistical inference is straightforward since the proposed estimator is asymptotically normal. Monte Carlo simulations demonstrate that the new estimator has excellent finite sample properties and outperforms other competitors in the cases we consider.