  Model approximations are common practice when estimating structural or
quasi-structural models. The paper considers the econometric properties of
estimators that utilize projections to reimpose information about the exact
model in the form of conditional moments. The resulting estimator efficiently
combines the information provided by the approximate law of motion and the
moment conditions. The paper develops the corresponding asymptotic theory and
provides simulation evidence that tilting substantially reduces the mean
squared error for parameter estimates. It applies the methodology to pricing
long-run risks in aggregate consumption in the US, whereas the model is solved
using the Campbell and Shiller (1988) approximation. Tilting improves empirical
fit and results suggest that approximation error is a source of upward bias in
estimates of risk aversion and downward bias in the elasticity of intertemporal
substitution.
