Ebook Money Demand and Macroeconomic Stability Revisited
The conduct of monetary policy is known to affect the determination of the price level and, under non-neutrality, the real equilibrium allocation. Recent studies to this line of research, mainly focus on policy regimes summarized by interest rate feedback rules, such as Benhabib et al. (2001a, 2001b, 2003) or Carlstrom and Fuerst (2001),4 while previous contributions to this literature have primarily considered monetary policy regimes that are characterized by constant money growth (see, e.g., Obstfeld and Rogoff, 1983, Matsuyama, 1990, 1991, or Matheny, 1998). Correspondingly, researchers nowadays pay less attention to the role of monetary aggregates and increasingly employ money demand specifications that allow to neglect money for the analysis of equilibrium determination (see Dupor, 2001, Woodford, 2003, or Carlstrom and Fuerst, 2004).
In this paper we (re-)assess the role of money for the determination of the price level, and for uniqueness and stability of equilibrium sequences. In particular, we examine the case where the evolution of monetary aggregates is non-negligible due to real balance effects, which typically characterize households’ consumption behavior when transaction services of money are modelled in an explicit way. The classical dichotomy is invalid under this assumption, which might contribute to the determination of the price level under flexible prices, as shown by Patinkin (1949, 1965). We find that uniqueness of the price level under interest rate policy crucially relies on whether the stock of money held at the beginning of the period or at the end of the period is assumed to provide transaction services. In the latter case, a rational expectations equilibrium is consistent with any initial price level and, thus, with multiple price level sequences. If, however, beginning of-period money relates to households’ transactions, then a rational expectations equilibrium is associated with a unique price level sequence (nominal determinacy, as defined by Benhabib et al., 2001). A rational expectations equilibrium can further be uniquely determined (real determinacy), if interest rates are set contingent on current inflation rate. Then, real money becomes a relevant predetermined state variable, which implies that interest rate policy should be passive to avoid explosive or oscillatory equilibrium sequences. When end-of-period money is assumed to provide transaction services, real balance effects turn out to be (almost) negligible for equilibrium determination, and the principles for real determinacy in cashless economies (see Woodford, 2003) apply.
There are a variety of means to induce demand for money, i.e., a non-interest bearing government liability, in general equilibrium models. Most of them, for example, cash-in advance constraints (Clower, 1967), real resource costs of transactions (Feenstra, 1986), or shopping time specifications (McCallum and Goodfriend, 1987), refer to the transaction role of money. An alternative way to induce households to hold a positive amount of money is to assume that money enters the utility (MIU) function, which originates in Sidrauski’s (1967) seminal paper. This is probably the most widely applied approach to money demand in the recent literature on monetary policy analysis (see, e.g., Woodford, 2003), and is often viewed as being closely related to the aforementioned specifications. In fact, Brock (1974) and Feenstra (1986) have shown that assuming MIU can be equivalent to the more explicit specifications of transaction frictions. However, for an exact equivalence, real balances and consumption should enter the utility function in a non-separable way. While this property is commonly neglected, since real balance effects are typically found to be very small (see, e.g., Lucas, 2000, or Ireland, 2003), we show that this can have substantial consequences for equilibrium determination, which under sticky prices does not rely on the magnitude of the real balance effect.
We develop a discrete time dynamic general equilibrium model, where money enters a non separable utility function and prices are either completely flexible or set in a staggered way. We apply two different assumptions about the particular stock of money that enters the utility function, either the stock of money held at the beginning or at the end of the period. The former assumption corresponds to Svensson’s (1985) cash-in-advance specification, where the goods market opens before the asset market, and is, for example, applied in Woodford (1990), McCallum and Nelson (1999), or Lucas (2000). The second assumption can be interpreted as a short-cut for a specification where households can always adjust their money holdings in accordance with their current transactions. It avoids Hahn’s (1965) paradox in finite horizon general equilibrium models and is now widely applied in infinite horizon models (see, e.g., Woodford, 2003).
We focus on the role of money demand and monetary policy rules for the determination of locally stable equilibrium sequences at the steady state. It turns out that the unique determination of the price level relates (under completely flexible prices) to the property of real balances to serve as a relevant state variable. For a rational expectations equilibrium to be characterized by this property, beginning-of-period money has to enter the utility function. On the contrary, real balances never serve as a relevant state variable if end-of-period money provides utility. Thus, both versions substantially differ with regard to the role of money held by households at the beginning of each period. In the former version, beginning-of-period real balances restrict household’s current consumption expenditures. In the latter version, households adjust their end-of-period money holdings in accordance with their current consumption expenditures. Hence, beginning-of-period real balances are then determined by the previous period consumption decision such that the causality is reversed. For the beginning-of-period value of real balances to be, actually, relevant for the determination of a rational expectations equilibrium, there must further exist a unique price level sequence consistent with equilibrium. Put differently, unless there is a uniquely determined price level, there are multiple real values for the beginning-of-period stock of money, which are consistent with a rational expectations equilibrium.
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