Does the labour share of income drive inflation?

Woodford (2001) has presented evidence that the new-Keynesian Phillips curve fits the empirical behavior of inflation well when the labor income share is used as a driving variable, but fits poorly when deterministically detrended output is used. He concludes that the output gap - the deviation between actual and potential output - is better captured by the labor income share, in turn implying that central banks should raise interest rates in response to increases in the labor share. We show that the empirical evidence generally suggests that the labor share version of the new-Keynesian Phillips curve is a very poor model of price inflation. We conclude that there is little reason to view the labor income share as a good measure of the output gap, or as an appropriate variable for incorporation in a monetary policy rule.