  We provide a new estimation method for conditional moment models via the
martingale difference divergence (MDD).Our MDD-based estimation method is
formed in the framework of a continuum of unconditional moment restrictions.
Unlike the existing estimation methods in this framework, the MDD-based
estimation method adopts a non-integrable weighting function, which could grab
more information from unconditional moment restrictions than the integrable
weighting function to enhance the estimation efficiency. Due to the nature of
shift-invariance in MDD, our MDD-based estimation method can not identify the
intercept parameters. To overcome this identification issue, we further provide
a two-step estimation procedure for the model with intercept parameters. Under
regularity conditions, we establish the asymptotics of the proposed estimators,
which are not only easy-to-implement with analytic asymptotic variances, but
also applicable to time series data with an unspecified form of conditional
heteroskedasticity. Finally, we illustrate the usefulness of the proposed
estimators by simulations and two real examples.
