Risk-Sensitive Linear Approximations

I construct risk-sensitive approximations of policy functions of DSGE models around the stochastic steady state and ergodic mean that are linear in the state variables. The method requires only the solution of linear equations using standard perturbation output to construct the approximation and is uniformly more accurate than standard linear approximations. In an application to real business cycles with recursive utility and growth risk, the approximation successfully estimates risk aversion using the Kalman filter, where a standard linear approximation provides no information and alternative methods require computationally intensive procedures such as particle filters. At the posterior mode, the model s market price of risk is brought in line with the postwar US Sharpe ratio without compromising the fit of the macroeconomy.