Identification and inference in linear stochastic discount factor models

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"When linear asset pricing models are estimated using excess return data, a normalization of the model must be selected. Several normalizations are equivalent when the model is correctly specified, but the identification conditions differ across normalizations. In practice, some or all of these identification conditions fail statistically when conventional consumption-based models are estimated, and inference is not robust across normalizations. Using asymptotic theory and Monte Carlo simulations, I present evidence that the lack of robustness in qualitative inference across normalizations can be attributed to model misspecification and lack of identification. I propose the use of tests for failure of the rank conditions. Using a calibrated model, I show that these tests are effective in detecting non-identified models"--National Bureau of Economic Research web site.