Abstract:
While incomplete models are desirable due to their robustness to misspecification, they
cannot be used to conduct full information exercises i.e. counterfactual experiments and
predictions. Moreover, the performance of the corresponding GMM estimators is fragile
in small samples. To deal with both issues, we propose the use of an auxiliary conditional
model for the observables f(X|Z, '), where the equilibrium conditions E(m(X, #)|Z) = 0
are imposed on f(X|Z, ') using information projections, and (#, ') are estimated jointly.
We provide the asymptotic theory for parameter estimates for a general set of conditional
projection densities, under correct and local misspecification of f(X|Z, '). In either cases,
efficiency gains are significant. We provide simulation evidence for the Mean Squared
Error (MSE) both under the case of local and fixed density misspecification and apply
the method to the prototypical stochastic growth model. Moreover, we illustrate that
given (#ˆ, 'ˆ) it is now feasible to do counterfactual experiments without explicitly solving
for the equilibrium law of motion.

Key Words:
Incomplete models, Information projections, Small Samples, Shrinkage