Bounds on Price Setting
I illustrate that the equilibria of games with strategic complementarities may be of little predictive value if the players have non-compact action sets. Motivated by this observation, I study a class of macroeconomic models in which all firms can costlessly choose any price at each date from a compact interval (indexed to last period’s price level). I prove three results that are valid for any such compact interval. First, given any allocation, there is a (possibly time-dependent) specification of monetary and fiscal policy that implies that allocation is part of an equilibrium. Second, given any specification of monetary and fiscal policy in which the former is time invariant and the latter is Ricardian (in the sense of Woodford (1995)), there is a sequence of equilibria in which consumption converges to zero on a date-by-date basis. These first two results suggest that standard macroeconomic models without pricing bounds (be they sticky or flex price) provide a false degree of confidence in long-run macroeconomic stability and undue faith in the long-run irrelevance of monetary policy. The paper’s final result constructs a non-Ricardian nominal framework (in which the long-run growth rate of nominal government liabilities is sufficiently high) that pins down a unique stable real outcome as an equilibrium.