An Estimation of the Nonlinear Philips Curve in Colombia

As originally drawn and estimated by professor Phillips, the Phillips curve is a curve indeed, not a straight line as often thought. Following Laxton, et. al. (1999) we estimate a convex Phillips curve and model the NAIRU as a variable that is unobserved. Using Colombian data, we provide confidence bands for the NAIRU and report estimated sacrifice ratios. Using the unobserved components methodology along with the Kalman filter, we find evidence in favor of a nonlinear Phillips curve and no evidence against a NAIRU that is constant. This latter finding is explained by the high level of uncertainty in the estimation of the NAIRU. Nonlinearity implies that the sacrifice ratio increases with unemployment, in other words, the cost of decreasing inflation is higher the higher the unemployment rate.