This paper evaluates the accuracy of a set of techniques that approximate the solution of continuous-time DSGE models. Using the neoclassical growth model I compare linear-quadratic, perturbation and projection methods. All techniques are applied to the HJB equation and the optimality conditions...

The unconditional expectation of social welfare is often used to assess alternative macroeconomic policy rules in applied quantative research. It is shown that it is generally possible to derive a linear-quadratic problem that approximates the exact non-linear porblem where the unconditional...

The unconditional expectation of social welfare is often used to assess alternative macroeconomic policy rules in applied quantitative research. This paper provides a detailed analysis of such policies. It sets out the unconditionally optimal (UO) policy problem and derives an LQ version of that...

The unconditional expectation of social welfare is often used to assess alternative macroeconomic policy rules in applied quantitative research. It is shown that it is generally possible to derive a linear-quadratic problem that approximates the exact non-linear problem where the unconditional...

We examine the linear-quadratic (LQ) approximation of non-linear stochastic dynamic optimization problems in macroeconomics, in particular for monetary policy. We make four main contributions: first, we draw attention to a general Hamiltonian framework for LQ approximation due to Magill (1977)....

We examine the linear-quadratic (LQ) approximation of non-linear stochastic dynamic optimization problems in macroeconomics, in particular for monetary policy. We make four main contributions: first, we draw attention to a general Hamiltonian framework for LQ approximation due to Magill (1977)....

We prove the generality of the methodology proposed in Benigno and Woodford (2006). We show that, even in the presence of a distorted steady state, it is always possible and relatively simple to obtain a purely quadratic approximation to the welfare measure. We also show that, in order to do so,...