Some economists believe that in the long run,the unemployment rate is independent of the inflation rate and so the Phillips curve becomes a vertical line.

This is the concept of the vertical long-run Philips curve, which suggests that there is no trade-off between inflation and unemployment in the long run. Instead, the only factor that affects the unemployment rate is the natural rate of unemployment, which is determined by non-monetary factors such as demographics, technology, and labor market institutions. Therefore, changes in the inflation rate do not have a long-term impact on the unemployment rate. However, this does not mean that there is no short-term trade-off between inflation and unemployment, which is captured by the downward-sloping short-run Phillips curve.