Estimation of nonlinear DSGE models through Laplace based solutions
提出一种基于拉普拉斯变换的非线性DSGE模型求解方法，得到闭式似然函数，无需线性化或模拟即可估计模型。用美国数据估计新古典增长模型，发现非线性异方差模型表现更好，且货币政策冲击是经济不确定性变化的主因。
This paper proposes a novel Laplace-based solution to non-linear DSGE models that has a closed-form likelihood. We implicitly use a non-linear approximation to the policy function that is invertible with respect to the shocks, implying that in the approximation the shocks can be recovered uniquely from some of the control variables. Using perturbation methods and a Lagrange inversion formula, we are able to calculate the derivatives of the likelihood and construct the Laplace based solution. In contrast with previous likelihood-based approaches, the method used here requires neither the introduction of linear shocks nor simulation to evaluate the likelihood. Using US data, we estimate linear and nonlinear variants of a well-known neoclassical growth model with and without time-varying variances. We find that a nonlinear heteroscedastic model has a much better empirical performance. Furthermore, our models allow us to ascertain that the monetary policy shock causes most of the time changes in economic uncertainty.