Solving models with external habit

"Habit utility has been the focus of a large and growing body of literature in financial economics. This study investigates ways of accurately and efficiently solving the Campbell and Cochrane (1999) external habit model. Solutions for this model based on a grid of values for the state variable are shown to converge as the grid becomes increasingly fine. Convergence is substantially faster if the price-dividend ratio is computed as a series of 'zero-coupon equity' claims rather than as the fixed-point of the Euler equation. Fitting the model to the term structure as well as to equity moments (as in Wachter (2005)) also results in faster convergence"--National Bureau of Economic Research web site.