Is the Phillips Curve Really a Curve? Some Evidence for Canada, the United Kingdom, and the United States

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Abstract
Previous tests for convexity in the Phillips curve have been biased because researchers have employed filtering techniques for the NAIRU that have been fundamentally inconsistent with the existence of convexity. This paper places linear and nonlinear models of the Phillips curve on an equal statistical footing by estimating model-consistent measures of the NAIRU. After imposing plausible restrictions on the variability in the NAIRU we find that the nonlinear model fits the data best. The implications for the macroeconomic policy debate is that policymakers that are unsuccessful in stabilizing the business cycle will induce a higher natural rate of unemployment.
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