Economists are often confronted with the choice between a completely specified, yet approximate model and an incomplete model that only imposes a set of behavioral restrictions that are believed to be true. We offer a reconciliation of these approaches and demonstrate its usefulness for estimation and economic inference. The approximate model , which can be structural or statistical, is distorted such that to satisfy the equilibrium conditionswhich are deemed as credible . We provide the relevant asymptotic theory and supportive simulation evidenceon the MSE performance in small samples. We illustrate that it is feasible to do counterfactual experiments without explicitly solving for the equilibrium law of motion . We apply the methodology to the model of long run risks in aggregate consumption (Bansal and Yaron, 2004), where the auxiliary model is generated using the Campbell and Shiller (1988) approximation. Using US data, we investigate the empirical importance of the neglected non-linearity. We find that the distorted model is strongly preferred by the data and substantially improves the identification of the structural parameters. More importantly, it completely overturns key qualitative predictions of the linear model , such as the absence of endogenous time variation in risk premia and level effects, which is crucial for understanding the link between asset prices and macroeconomic risk .
This paper proposes a reconciliation between two approaches to structural estimation and inference: Using a complete - yet approximate model versus imposing a set of credible behavioral conditions. This is done by distorting the approximate model to satisfy these conditions . We provide the asymptotic theory and Monte Carlo evidence, and illustrate that counterfactual experiments are possible . We apply the methodology to the model of long run risks in aggregate consumption (Bansal and Yaron, 2004), where the complete model is generated using the Campbell and Shiller (1988) approximation. Using US data, we investigate the empirical importance of the neglected non-linearity. We find that distorting the model to satisfy the original equilibrium condition is strongly preferred by the data and substantially improves the identification of the structural parameters. Tilting also restores key qualitative predictions of the non-linear model such as the endogenous time variation in risk premia , a property which is lost with linearization .
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Economists are often confronted with the choice between a completely specified,
This paper proposes a reconciliation between two approaches to structural estimation and inference: Using a complete -
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and an incomplete model that only imposes
versus imposing
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behavioral restrictions that are believed to be true. We offer a reconciliation of these approaches and demonstrate its usefulness for estimation and economic inference. The approximate model , which can be structural or statistical, is distorted such that to satisfy the equilibrium conditionswhich are deemed as credible
credible behavioral conditions. This is done by distorting the approximate model to satisfy these conditions
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relevant
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supportive simulation evidenceon the MSE performance in small samples. We illustrate that it is feasible to do counterfactual experiments without explicitly solving for the equilibrium law of motion
Monte Carlo evidence, and illustrate that counterfactual experiments are possible
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auxiliary
complete
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the distorted model
distorting the model to satisfy the original equilibrium condition
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More importantly, it completely overturns
Tilting also restores
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linear model ,
non-linear model
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absence of
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and level effects, which is crucial for understanding the link between asset prices and macroeconomic risk
, a property which is lost with linearization