Timing and real indeterminacy in monetary models

Abstract

An increasingly common approach to the theoretical analysis of monetary policy is to ensure that a proposed policy does not introduce real indeterminacy and thus sunspot fluctuations into the model economy. Policy is typically conducted in terms of directives for the nominal interest rate. This paper uses a discrete-time money-in-the-utility function model to demonstrate how seemingly minor modifications in the trading environment result in dramatic differences in the policy restrictions needed to ensure real determinacy. These differences arise because of the differing pricing equations for the nominal interest rate.ABSTRACT: An increasingly common approach to the theoretical analysis of monetary policy is to ensure that a proposed policy does not introduce real indeterminacy and thus sunspot fluctuations into the model economy. Policy is typically conducted in terms of directives for the nominal interest rate. This paper uses a discrete-time money-in-theutility function model to demonstrate how seemingly minor modifications in the trading environment result in dramatic differences in the policy restrictions needed to ensure real determinacy. These differences arise because of the differing pricing equations for the nominal interest rate.The views stated herein are those of the authors and not necessarily those of the Federal Reserve Bank of Cleveland or those of the Board of Governors of the Federal Reserve System.

Interest rate policy, debt, and indeterminacy with distortionary taxation

“…where L þ 140 is the reaction coefficient of the central bank to inflation, and the constant R=p ðLþ1Þ ensures that the policy rule is steady-state neutral (as in Carlstrom and Fuerst, 2001). Of course, more complicated and thus more descriptively realistic settings for interest rate policy could be devised.…”

“…Kerr and King (1996), Clarida et al (2000), Carlstrom and Fuerst (2001), Woodford (2001). The relevance of asset dynamics in this context has been analyzed by Dupor (2001) and Carlstrom and Fuerst (2005) in models with capital accumulation.…”

Can money matter for interest rate policy?

“…Such shopping time function can, for example, be found in Brock (1974) or in Ljungqvist and Sargent (2000). Assuming that the end-ofperiod stock of money provides transaction services rather accords to a 'cash-when-I'm-done' concept (see Carlstrom and Fuerst, 2001) than to a cash-in-advance assumption, since M jt is the amount of money that is held by household j when it leaves the goods market. This assumption, which ensures that a positive amount of money is held even in a finite horizon framework (see, e.g., Buiter, 2002), is now widely applied in the literature.…”

“…This specification can often be found in related contributions (see, e.g., Carlstrom and Fuerst, 2001). The loss function (19) is then again an approximation of households' welfare (see Woodford, 2003a).…”

“…We follow Carlstrom and Fuerst (2001) and consider cash balances, which consist of the beginning-of-period stock of money and the gross return from bond holdings minus the amount invested in a new bond portfolio plus government transfers:…”