This paper studies the determinacy of equilibrium in a new Keynesian model with deep habits under different interest rate rules. The main finding is that an interest rate rule satisfying the Taylor principle is no longer a sufficient condition to guarantee determinacy. Including interest rate smoothing and a response to output deviations from steady state significantly enlarges the regions of determinacy. However, under all the simple interest rate rules considered, determinacy is not guaranteed for a very high degree of deep habits. Deep habits give rise to countercyclical markups, which is in line with empirical evidence and makes them an appealing feature in the study of demand shocks. The countercyclicality of markups also leads to multiple equilibria because of self-fulfilling expectations for a high degree of deep habit formation.

This paper investigates how the inclusion of capital in the workhorse new open economy macro model affects its ability to generate volatile and persistent real exchange rates. We show that capital accumulation facilitates intertemporal consumption smoothing and significantly reduces the volatility of the real exchange rate. Nonetheless, monetary and investment-specific technology (IST) shocks still induce more real exchange rate volatility and less consumption comovement than productivity shocks (with or without capital). We find that endogenous persistence is particularly sensitive to the inertia of the monetary policy rule even with persistent exogenous shocks. However, irrespective of whether capital is present, productivity and IST shocks trigger highly persistent real exchange rates, whereas monetary shocks do not. Moreover, we point out that IST shocks tend to generate countercyclical real exchange rates—unlike productivity or monetary shocks—but have the counterfactual effect of also producing excessive investment volatility and countercyclical consumption.

Evidence suggests that durable goods and residential housing are more flexibly priced than nondurables and services. Using a standard sticky price general equilibrium model, Barsky, House, and Kimball [American Economic Review 97(3) (2007), 984–998] demonstrate that if durable goods are flexibly priced and nondurables are sticky, then a monetary contraction leads to an expansion in production in the durable sector. This is wildly at odds with the empirical evidence. This paper demonstrates that if three features are added to the model (sticky nominal wages, housing construction adjustment costs, and habit persistence in consumption), it delivers sectoral implications that are broadly consistent with the data.

Two alternative theories of aggregate supply, both with a New Keynesian “flavor,” are compared. The first assumes that prices are rigid due to the existence of menu costs. The second derives price stickiness endogenously as one equilibrium in an economy with multiple equilibria. In both cases I show that the Ball–Romer concept of real rigidities is essential to explain why monetary policy has real persistent effects. I argue that dynamic menu cost models are determinate because they make special assumptions about the way that money enters the economy. For example, most authors assume either a cash-in-advance constraint or that money enters separably into utility or production functions. Once one moves beyond these special cases, menu cost models that display real rigidity are also likely to display indeterminacy.