Is the short-run Phillips curve nonlinear? Empirical evidence for Australia, Sweden and the United States

The Phillips curve has generally been estimated in a linear framework which implies a constant relationship between inflation and unemployment. Lately there have been several studies which claim that the slope of the Phillips curve is a function of macroeconomic conditions and that the relationship is asymmetric. If this is true the assumption of linearity is too restrictive. In this paper linear Phillips curves for Australia, Sweden and the United States are tested for linearity and parameter constancy. The nonlinear alternative is specified as a smooth transition regression model. It turns out that linearity is rejected for both Australia and Sweden while the Phillips curve for the United States is linear.