Semiparametric Estimation of Latent Variable Asset Pricing Models

This paper studies semi-parametric identification and estimation of the stochastic discount factor in consumption-based asset pricing models with latent state variables. The measurement equations for consumption and dividend shares are specified non-parametrically to allow for robust updating of the Markovian states describing the aggregate growth distribution. For the special case of affine state dynamics and polynomial approximation of the measurement equations, we derive rank conditions for identification, tractable filtering algorithms for likelihood estimation, and closed-form expressions for risk premia and return volatility. Empirically, we find sizable non-linearities and interactions in the impact of shocks to expected growth and volatility on the consumption share and the discount factor, that help explain the divergence between macroeconomic and stock market volatility