These advantages are illustrated in Den Haan (2000) for the comovement between
prices and output. Through the use of this procedure, Den Haan is able to question a
class of theoretical models believed to be consistent with empirical findings based on
traditional statistics. Cooley and Ohanian (1991) show that the correlation between prices
and real activity filtered with the HP filter of Hodrick and Prescott (1997) is negative in
the postwar period, which might seem inconsistent with a model in which demand shocks
play a dominant role. However, this empirical finding can be consistent with models of
sticky prices that only have demand shocks. In this type of model, just after a positive
demand shock the price level has not moved very much but the HP-trend level has
already increased considerably — implying that the detrended price observation is
negative. This together with a positive detrended output observation produces a negative
correlation.1 Using VAR forecast errors for prices and output, Den Haan (2000) finds that
the correlation coefficients become negative when the forecast horizon increases;
typically at forecast horizons between one and two years. More importantly, the observed
negative correlation between prices and output VAR forecast errors are shown to be not
consistent with a sticky price model with only demand shocks.