Are New Keynesian Models Useful When Trend Inflation is Not Low?

The equilibrium in the standard New Keynesian (NK) model with Calvo-pricing becomes explosive at low levels of trend inflation (between 4 to 7 percent). Even halfway before that threshold, optimal prices, price dispersion and costs rise fast to very large levels, and output plummets. We show that the root of these issues is not Calvo pricing as commonly assumed, but rather the popular Dixit-Stiglitz demand structure in NK models. Considering models with general firms' demand functions, we provide two important results: (i) regardless of the price setting behavior, i.e. timeor state-dependent, marginal costs rapidly increasing with trend inflation is a direct consequence of demand functions that fast rise at low relative prices; and (ii) under Calvo pricing, the condition for NK models to always have a stable equilibrium, independently of the level of trend inflation, is that the demand function does not increase unboundedly as relative prices decrease. The Dixit-Stiglitz demand structure fails to satisfy the latter condition. We then propose a model with price wedges to augment any existing demand structure and make them in line with those conditions. Using Dixit-Stiglitz and Kimball-demand aggregators, we show that the generalized NK model with price wedges allows price dispersion to rise slowly with trend inflation and avoids output plummeting to zero. In addition, the implied demand function with price wedges has relatively superior properties, better aligned with the micro and macro evidence.