Confidence intervals around statistical estimates of the natural rate are routinely estimated to be quite wide, reflecting both uncertainty about the correct model specification as well as uncertainty about the parameter estimates given the model.
The canonical paper by 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 David H. Romer, eds., Reducing Inflation: Motivation and Strategy (Chicago: University of Chicago Press) puts the 95 percent confidence interval at 1-1/2 percentage points on either side of the point estimate. 2.