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Article Excerpt
CONSUMPTION HABITS ARE a key component in modern New Keynesian business cycle models. (1) They are relied on to explain movements in aggregate consumption data and to generate the "hump-shaped" impulse responses widely recognized to characterize the responses of output and consumption to demand and supply shocks. With consumption habits there is complementarity between consumption in successive periods, the household utility function is time inseparable, and the marginal rate of substitution between consumption today and consumption at any point in the future depends on the path consumption is expected to take in the interim. Although consumption habit formation appears useful empirically, there appears to be little consensus on how habit formation should be modeled. Thus, while McCallum and Nelson (1999), Amato and Laubach (2004), and Christiano, Eichenbaum, and Evans (2005) assume that the habit formation is internal to households, Smets and Wouters (2003) and Ravn, Schmitt-Grohe, and Uribe (2006) assume that the habit formation is external. Similarly, where Fuhrer (2000), McCallum and Nelson (1999), and Amato and Laubach (2004) assume that it is consumption relative to the habit stock that enters utility (multiplicative habits), Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2003) assume that what matters is the difference between consumption and the habit stock (additive habits). (2)
In light of the host of different ways that habit formation can be modeled, I examine whether the particular modeling choice has material consequences for the business cycle properties of a standard New Keynesian model. To this end, I present a New Keynesian business cycle model, typical of those used to analyze monetary policy, and I derive the consumption Euler equations that arise from different modeling assumptions regarding habit formation. I consider both internal and external habit formation and both multiplicative and additive functional forms and, for a popular class of utility functions, find, surprisingly, that to a log-linear approximation whether habits are additive or multiplicative, internal or external, appears largely unimportant for business cycle behavior. This is not to say that different approaches to modeling consumption habits are innocuous more generally. It is well known, for example, that in the absence of an optimally designed consumption tax, the competitive equilibrium is Pareto inefficient when the habit formation is external. Moreover, due to the effect it has on a firm's pricing decision, the choice of additive or multiplicative habits can have important implications when habits are modeled at the goods level (Ravn, Schmitt-Grohe, and Uribe 2006). In addition, Abel (1990) has shown that asset prices, and the magnitude of the equity premium, depend on how habit formation is introduced.
Habit formation has been used to explain a (Granger) causal relationship from high growth to a high saving rate (Carroll, Overland, and Weil 2000), why recessions are so feared despite their short durations (Campbell and Cochrane 1999), and as a mechanism to capture the inertial, humped-shaped, impulse responses for output that are generated by structural VAR models (Fuhrer 2000). Habit formation has also been used to help understand why current accounts are so volatile (Gruber 2004), to explain why exchange rate pegs tend to be associated with rising consumption and appreciating real exchange rates (Uribe 2002), and, because it breaks the link between the coefficient of relative risk aversion and the (inverse) elasticity of intertemporal substitution, to study the equity premium puzzle (Abel 1990, Constantinides 1990, Campbell and Cochrane 1999). Consumption habits are also attractive because they improve the characteristics of real business cycle models (Boldrin, Christiano, and Fisher 2001) and because they make consumption endogenously persistent, an important feature of estimated consumption Euler equations.
The remainder of the paper is structured as follows. In the following section, the model describing household behavior is outlined and estimable first-order conditions are presented and discussed. Section 2 shows that, to a log-linear approximation, the consumption Euler equations with additive habits encompass those with multiplicative habits. Section 3 uses an estimated New Keynesian model to compare the business cycle properties of internal and external habits. Section 4 concludes.
1. HOUSEHOLDS
The representative household maximizes a utility function defined over consumption, real money balances, and labor. Households are infinitely lived, they rent their labor to firms in a perfectly competitive market, and they transfer wealth through time either by purchasing one-period nominal bonds or by holding nominal money balances. With [c.sub.t] denoting household consumption, [m.sub.t] denoting household nominal money balances, [l.sub.t] denoting household labor supply, [P.sub.t] denoting the aggregate price level, and [H.sub.t] denoting the habit stock, the representative...
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