Money and Prices Under Uncertainty

Abstract

Monetary policy does not suffice to determine the stochastic path of inflation. A "nominal equivalent martingale measure", associated with nominal asset prices, and the initial price level characterize the indeterminacy of monetary equilibria under uncertainty; when prices are flexible, the "nominal equivalent martingale measure" determines the distribution of rates of inflation up to the first moment. Monetary policy sets interest rates or money supplies; fiscal policy is Ricardian or non-Ricardian; asset markets are complete or incomplete;in commodity markets, competition may be imperfect and prices sticky; the asset market opens before or after the commodity market at each date-event. Recursive equilibria under interest rate policy are, also, indeterminate. Indeterminacy, here, does not derive from the stability of a deterministic steady state. Determinacy of the real allocation requires that the asset market be complete, monetary policy set interest rates, prices be flexible and the exchange of assets precede the exchange of commodities.

Anchoring expectations of inflation

“…A recent paper by Adao-Correia-Teles (2010) contains a message similar to that of this paper, showing that controlling the prices of long-term bonds can remove the indeterminacy exhib-ited by Nakajima-Polemarchakis (2005). Their model stays close to the framework of NakajimaPolemarchakis with exogenous states of nature, while we introduce explicitly the agents' expectations as a state variable to be "controlled" in a sense that we make precise.…”

“…The model is close in spirit to the model of Nakajima-Polemarchakis (2005) 2 who showed that if monetary policy consists solely of fixing the short-term interest rate, and fiscal policy is Ricardian, then the equilibrium is indeterminate. In such a setting, at each date, the only attribute of the random inflation at the next period which is determined in equilibrium is its mean which is tied down by the Fisher equation relating the short-term nominal interest rate to the real interest rate and the mean of next period's inflation.…”

“…to offer labor services to firms who convert them into output and pay the agent for the labor services. To incorporate production into the model in the simplest way which at the same time captures the idea that production is influenced by the nominal interest rate set by the monetary authorities, we use the device introduced by Lucas-Stokey (1985) and also used by Polemarchakis-Nakajima (2005). At each date-event ξ ∈ | D an agent has an endowment e h of 'time' which can be used either for leisure (…”

Term structure and forward guidance as instruments of monetary policy

“…To keep the analysis simple we do not go all the way to a New-Keynesian model which has the most realistic description of the feedback between nominal and real variables, adhering instead to the simpler flexible-price model of production introduced by Lucas-Stokey (1987) and used by Schmitt-Grohé-Uribe (2000) and Nakajima-Polemarchakis (2005) to study the indeterminacy of equilibrium when monetary-fiscal policy is Ricardian. This amounts to changing the description of the private sector of the economy in the following way.…”

An Argument for Positive Nominal Interest

“…In an economy of overlapping generations with cash-in-advance constraints, a central bank issues balances in exchange for bonds and distributes its profits, seignorage, as dividends to shareholders Bloise, Drèze, and Polemarchakis (2005), Nakajima and Polemarchakis (2005)). Importantly, shares to the bank are traded in the asset market and the bank is, initially, owned by a finite number of individuals, most simply among those active at the 1 Search theoretic models of monetary economies (Diamond (1984) or Kiyotaki and Wright (1989)) are, evidently, more satisfactory, but the simple cash-in-advance formulation here, as in much of the literature, offers analytical tractability and does not play an otherwise important role in the argument argument.…”