The distinction between the price level and inflation is crucial, see Ball and Mankiw (1994) or Chadha and Prasad (1994) for classical arguments why de-trended price level may appear counter-cyclical. Simply put, the de-trended price level becomes countercyclical exactly in the case if inflation follows the cycle in output positively and with a lag. Since both output and price level are non-stationary, researchers who detrend both series fall into a trap and must recover their negative comovement, as in Cooley and Ohanian (1991) for instance. Further, the data starting in the 1990’s are influenced by the inflation targeting regimes, which have starkly different implications than a price level targeting with a drift. Under inflation targeting, the changes in the price level are permanent, bygones are bygones. Inflation targeting central bank cares about deviation of inflation from its target.