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We propose a method that reconciles two popular approaches to structuralestimation and inference: Using a complete - yet approximate model versusimposing a set of credible behavioral conditions. This is done by distortingthe approximate model to satisfy these conditions. We provide the asymptotictheory and Monte Carlo evidence, and illustrate that counterfactual experimentsare possible. We apply the methodology to the model of long run risks inaggregate consumption (Bansal and Yaron, 2004), where the complete model isgenerated using the Campbell and Shiller (1988) approximation. Using US data,we investigate the empirical importance of the neglected non-linearity. We findthat distorting the model to satisfy the non-linear equilibrium condition isstrongly preferred by the data while the quality of the approximation is yetanother reason for the downward bias to estimates of the intertemporalelasticity of substitution and the upward bias in risk aversion.

Equilibrium Restrictions and Approximate Models -- With an application to Pricing Macroeconomic Risk