New tests of the New-Keynesian Phillips curve

Is the observed correlation between current and lagged inflation a function of backward-looking inflation expectations, or do the lags in inflation regressions merely proxy for rational forward-looking expectations, as in the new-Keynesian Phillips curve? Recent research has attempted to answer this question by using instrumental variables techniques to estimate "hybrid" specifications for inflation that allow for effects of lagged and future inflation. We show that these tests of forward-looking behavior have very low power against alternative, but non-nested, backward-looking specifications, and demonstrate that results previously interpreted as evidence for the new-Keynesian model are also consistent with a backward-looking Phillips curve. We develop alternative, more powerful tests, which find a very limited role for forward-looking expectations.