Linearization and Higher-Order Approximations: How Good are They?

Abstract

The standard procedure for analyzing transitional dynamics in non-linear macro models has been to employ linear approximations. Recently quadratic approximations have been explored. This paper examines the accuracy of these and higher-order approximations in an endogenous growth model with public capital, thereby extending the work done in the current literature on the neoclassical growth model. We find that significant errors may persist in computed transition paths and welfare even after resorting to approximations as high as fourth order. Moreover, the accuracy of approximations may not increase monotonically with the increase in the order of approximation. Also, as in the previous literature, we find that achieving acceptable levels of accuracy when computing the welfare consequences of a policy change typically requires a higher order approximation than attaining similar levels of accuracy in the computation of the transition path: typically an increase in order of approximation by one is sufficient.