Regarding uncertainty about estimates of the natural rate, a classic reference is Douglas Staiger, James H. Stock, and Mark W. Watson (1997), “How Precise Are Estimates of the Natural Rate of Unemployment?” in Christina D. Romer and  -5has likely played a role in flattening the Phillips curve.
But a flatter Phillips curve makes it harder to assess whether movements in inflation reflect the cyclical position of the economy or other influences. Second, what would be the consequences for inflation if unemployment were to run well below the natural rate for an extended period?