The tightenings in 1999 could be interpreted as unwinding the earlier easings, once the factors that motivated the easings had themselves reversed. Of course, every policy action needs to be defended in terms of its contribution in the future to achieving the objectives of monetary policy. In this spirit, I interpreted the tightening moves as preemptive attempts to limit inflation risks.
Why did policymakers tolerate for a while further increases in the output gap, and why did they subsequently become more concerned about the inflation risks from further increases in the output gap? I think the change can be rationalized in terms of my discussion of the case for a nonlinear policy response under uncertainty.