On the Estimation of Euler Equations in the Presence of a Potential Regime Shift

The concept of a peso problem is formalized in terms of a linear Euler equation and a non-linear marginal model describing the dynamics of the exogenous variable driving the process. It is shown that, using a threshold autoregressive model as a marginal model, it is possible to produce time-varying peso premia. A Monte Carlo method and a method based on the numerical solution of integral equations are considered as tools for computing conditional future expectations in the marginal model. A Monte Carlo study illustrates the poor performance of the generalized method of moments estimator in small and even relatively large samples. The poor performance is particularly acute in the presence of a peso problem but is also serious in the simple linear case