Firms’ money demand and monetary policy

Standard New Keynesian models for monetary policy analysis are ‘cashless’. When the nominal interest rate is the central bank's operating instrument, the LM equation is endogenous and, it is argued, can be ignored. The modern theoretical and quantitative debate on the importance of money for monetary policy conduct, however, overlooks firms’ money demand. Working in an otherwise canonical New Keynesian setup, we show that macroeconomic dynamics are critically affected by the firms’ money demand choice. Under the conventional Taylor‐rule framework, we prove that equilibrium determinacy may require either an active interest rate policy, overreacting to inflation, or a passive interest rate policy, underreacting to inflation, depending on the elasticity of production with respect to cash balances. We then develop a numerical analysis to evaluate our theoretical results. We find that macroeconomic stability is more likely to occur under an active, but not overly aggressive, monetary policy stance. We also examine the dynamic effects of forward‐looking feedback rules. We show that, in this policy regime, indeterminacy is likely to be induced by both active and passive rules, even for relatively low productivity effects of money.     

Friedman's Money Supply Rule vs. Optimal Interest Rate Policy

Using New Keynesian models, we compare Friedman's k‐percent money supply rule to optimal interest rate setting, with respect to determinacy, stability under learning and optimality. First we review the recent literature: open‐loop interest rate rules are subject to indeterminacy and instability problems, but a properly chosen expectations‐based rule yields determinacy and stability under learning, and implements optimal policy. We show that Friedman's rule also can generate equilibria that are determinate and stable under learning. However, computing the mean quadratic welfare loss, we find for calibrated models that Friedman's rule performs poorly when compared to the optimal interest rate rule.     

Superneutrality, indeterminacy and endogenous growth

In this paper, we explore the possibility of having money as a source of indeterminacy in endogenous growth models. We adopt the simple Ak model of endogenous growth to be the main analytical vehicle whose balanced growth paths do not display local indeterminacy. Money is introduced via either a general cash-in-advance (CIA) constraint or a pecuniary transactions costs (PTC) technology. It is shown that local indeterminacy of the dynamics is due to the presence of an intertemporal substitution effect on capital accumulation that works against and dominates the conventional inflation effect of Tobin [1965, Money and economical growth. Econometrica 33(4), Part 2, 671]. If money is growth-rate superneutral, then the intertemporal substitution effect is absent so that local indeterminacy cannot occur. Finally, the strength of the intertemporal substitution effect depends positively on the intertemporal elasticity of substitution in consumption.     

Investment and interest rate policy: a discrete time analysis

This paper analyzes the restrictions necessary to ensure that the interest rate policy rule used by the central bank does not introduce local real indeterminacy into the economy. It conducts the analysis in a Calvo-style sticky price model. A key innovation is to add investment spending to the analysis. In this environment, local real indeterminacy is much more likely. In particular, all forward-looking interest rate rules are subject to real indeterminacy.     

Fiscal Rules,Interest Payments on Debt,and the Irrelevance of the Taylor Principle

We show that in New Keynesian models with non‐neutral government debt, the Taylor principle ceases to be relevant for equilibrium determinacy if the government follows a fiscal rule of levying taxes in proportion to its interest payments on existing debt. This is in contrast with previous studies, which typically have assumed that taxes respond to the level of debt, and have found either a confirmation or reversal of the Taylor principle depending on the feedback from debt to taxes. We find, instead, that the equilibrium effect of the interest rate on debt is crucial for determinacy. If, as in our model, taxes are raised in response to debt interest payments, the range of indeterminacy monotonically decreases with the fiscal feedback parameter. When interest payments are completely tax‐financed, indeterminacy is ruled out without any restrictions on monetary policy.     

(In)determinacy, increasing returns, and the optimality of the Friedman rule in an endogenously growing open economy

This paper sets up a monetary endogenous growth model with Benhabib–Farmer production externalities for an open economy, and then uses it to investigate the possibility of indeterminacy. Moreover, the paper examines how the monetary authorities will set its optimal anchor of the money growth rate from the viewpoint of welfare maximization. Several main findings emerge from the analysis. First, when investment does not involve adjustment costs, the monetary equilibrium is locally determinate regardless of the strength of the labor externality and the extent of world capital market imperfections. Second, in the presence of investment adjustment costs, the monetary equilibrium may exhibit indeterminacy when the aggregate increasing returns-to-scale in production is sufficiently strong. Third, in the presence of world capital market imperfections, the Friedman rule of a zero nominal interest rate fails to be optimal. Fourth, in the face of perfect world capital markets, the optimal nominal money growth rate is maintained at the rate that is conformable to the Friedman rule, regardless of whether investment involves adjustment costs or not.     

Financial market imperfections and monetary policy strategy

In a model with imperfect money, credit and reserve markets, we examine if an inflation-targeting central bank applying the funds rate operating procedure to indirectly control market interest rates also needs a monetary aggregate as policy instrument. We show that if private agents use information extracted from money and financial markets to form inflation expectations and if interest rate pass-through is incomplete, the central bank can use a narrow monetary aggregate and the discount interest rate as independent and complementary policy instruments to reinforce the credibility of its announcements and the role of inflation target as a nominal anchor for inflation expectations. This study shows how a monetary policy strategy combining inflation targeting and monetary targeting can be conceived to guarantee macroeconomic stability and the credibility of monetary policy. Friedman's k-percent money growth rule, which can generate dynamic instability, and two alternative stabilizing feedback monetary targeting rules are examined.     

What to stabilize in the open economy*

We consider the question how “best” to maintain price‐level stability in an open economy, and evaluate three possible policy choices: (a) a constant money growth rate rule; (b) a fixed exchange rate; and (c) a policy of explicit commitment to a price‐level target. In each case we assume that policy is conducted by injecting reserves into or withdrawing reserves from the “banking system.” In evaluating the three regimes, we adopt the criterion that the “best” policy should leave the least scope for indeterminacy and “excessive” economic volatility. In a steady‐state equilibrium, the choice of regime is largely irrelevant; any steady‐state equilibrium under one regime can be duplicated by an appropriate choice of the “control” variable under any other regime. However, we show that the sets of equilibria under the three regimes are dramatically different. When all countries follow the policy of fixing a constant rate of money growth, there are no equilibria displaying endogenously arising volatility and there is no indeterminacy of equilibrium. Under a regime of fixed exchange rates, indeterminacies and endogenously arising fluctuations are impossible if and only if the country with the low “reserve‐to‐deposit” ratio is charged with maintaining the fixed rate. Finally, when one country targets the time path of its price level, under very weak conditions, there will be indeterminacy of equilibrium and endogenously arising volatility driven by expectations.     

TURNPIKE PROPERTIES OF A MONEY‐IN‐THE‐UTILITY‐FUNCTION MODEL*

This study establishes the global stability of a long‐run stationary state in a money‐in‐the‐utility‐function model. The major finding is that the constant money supply rule results in a stable allocation and price system if consumers discount their future utilities sufficiently weakly. Nominal and real interest rates will be in the neighbourhood of the inverse of the consumers’ discount factor β^‐1.     

Global and local determinacy in a one-step forward looking New Keynesian model

In this paper we consider a New Keynesian model for optimal monetary policy in a staggered fashion. We provide the relations of a non linear model of general economic equilibrium, implementing a suitable Taylor-type interest rate rule. We characterize the conditions that guarantee local determinacy and explore conditions under which local bifurcations of the target equilibrium may occur. Afterwards, we argue how local determinacy might be associated with global indeterminacy, providing some numerical examples.     

Wealth in utility,the Taylor principle and determinacy

Wealth in the utility function leads to the discounting to consumer’s Euler equation, enlarging determinacy regions and making it easier for the monetary authority to ensure equilibrium determinacy. We show that a passive policy rule which adjusts nominal interest rate by less than one-for-one in response to the inflation rate is able to rule out equilibrium indeterminacy, if properly specified, due to the presence of the demand channel of the Taylor principle and equilibrium determinacy. Furthermore, the extent to which monetary policy rule can be passive in order to avoid indeterminacy depends critically on the degree of preference over wealth as well as the underlying structures and parameters of the model.     

Debt, liquidity and dynamics

Summary. Money, which provides liquidity, is distinct from debt. The introduction of a bank that issues money in exchange for debt and pays out its profit as dividend to shareholders modifies the model of overlapping generations. The set of equilibrium paths, their dynamic properties, as well as the scope and effectiveness of monetary policy are significantly altered: though low rates of interest are associated with superior steady state allocations, stability of the steady state may require a nominal rate of interest above a certain minimum: without production, a decrease in the nominal rate of interest may result in explosive behavior or convergence to an endogenous cycle, while in an economy with production, an increase in the nominal rate of interest may lead to indeterminacy and fluctuations.Received: 5 October 2004, Revised: 5 November 2004 JEL Classification Numbers: E30, E32, E50, E52.C. Rochon, H.M. Polemarchakis: We thank Jean-Michel Grandmont for helpful comments. Correspondence to: C. RochonThis revised version was published online in May 2005 with a corrected abstract.     

Inflation and Unemployment in General Equilibrium*

When labor is indivisible, there exist efficient outcomes with some agents randomly unemployed, as in Rogerson (1988) . We integrate this idea into the modern theory of monetary exchange, where some trade occurs in centralized markets and some in decentralized markets, as in Lagos and Wright (2005) . This delivers a general equilibrium model of unemployment and money, with explicit microeconomic foundations. We show that the implied relation between inflation and unemployment can be positive or negative, depending on simple preference conditions. Our Phillips curve provides a long‐run, exploitable, trade‐off for monetary policy; it turns out, however, that the optimal policy is the Friedman rule.     

Price rules, wage indexing, and optimal monetary policy

There has been a recent increased interest in a monetary price rule. This paper analyzes the efficiency of such a monetary rule within the context of a rational expectations macro model. We compare the price rule with the standard money rule and interest rate rule. We find that as the supply shock variance approaches zero the price rule dominates both a money and interest rate rule. We then investigate the efficiency of these alternative money rules when we allow wage indexation to the price level.     

Investment,interest rate rules,and equilibrium determinacy

Summary. By adding endogenous investment to a flexible-price, money-in-the-utility-function model, this paper studies the role that physical capital plays in stabilizing the real side of the economy when the monetary authority follows interest-rate feedback rules. We show that with inelastic labor supply equilibrium uniqueness is ensured under both active and passive monetary policies. For the case where money affects both preferences and technology, the uniqueness result remains true under active monetary policy. With endogenous labor supply, the uniqueness result holds again regardless of the stance of monetary policies for the case with separable leisure, but indeterminacy remains likely under both active and passive monetary policies when leisure is nonseparable.Received: 19 December 2001, Revised: 12 May 2003, JEL Classification Numbers: E52, O42.We are grateful to Jess Benhabib and an anonymous referee for helpful comments and suggestions. Correspondence to: C.K. Yip     

Disinflation costs in China and monetary policy regimes

This paper investigates the real effects of a disinflationary policy in China, in which we conduct a disinflation experiment in a medium-scale New Keynesian model. We highlight two key features of China's economy: the relevance of money to monetary policy rules and household inequality. For the former, we consider two monetary policy regimes: an expanded Taylor rule with money and a money supply rule. For the latter, we take into account a share of the population that is limited in its ability to participate in assets markets. Our analysis suggests that a disinflation policy is more costly when the central bank controls the money supply than the case in which the nominal interest rate is the policy instrument. Our results are driven by the different impacts of disinflation on nominal and real interest rates under the two regimes.     

Self-fulfilling patience

This paper explores macroeconomic implications of investment in patience in a standard neoclassical growth model with Becker-Mulligan endogenous time preferences. The endogenous discount rate acts as a new margin for inter-temporal decisions, in addition to the standard margin that hinges on the marginal return of capital. This time preference margin alters the equilibrium dynamics and stability of the neoclassical growth model substantially. When the discount rate is positive, there may exist multiple steady states that are either saddle-point stable or unstable. When the discount rate is negative, the unique steady state is locally indeterminate due to self-fulfilling patience investment. Interestingly, the existence of the local indeterminacy does not need any externality. When the discount rate is zero, various types of bifurcations can happen, leading to rich equilibrium dynamics such as limit cycles and chaos. We show that opening up the closed economy can cause aggregate instability.     

ON DECREASING MARGINAL IMPATIENCE*

One of the most controversial assumptions in endogenous time preference theory is that the degree of impatience is marginally increasing in wealth. We examine the implications of an empirically more relevant specification whereby time preference exhibits decreasing marginal impatience (DMI). With DMI, there are multiple steady‐state non‐satiated and satiated equilibria. In a constant interest rate economy, the non‐satiated steady‐state point is necessarily unstable. In a capital economy with decreasing returns technology, both the non‐satiated and satiated steady‐state points can be saddlepoint stable. The model is used to examine policy implications for the effects of capital taxation and government spending.     

Balanced-budget rules and macroeconomic (in)stability

It has been shown that under perfect competition and constant returns-to-scale, a one-sector real business cycle model may exhibit indeterminacy and sunspots when income tax rates are determined by a balanced-budget rule with a pre-set level of government expenditures. This paper shows that indeterminacy disappears if the government finances endogenous public spending and transfers with fixed income tax rates. Under this type of balanced-budget formulation, the economy exhibits saddle-path stability and equilibrium uniqueness, regardless of the source of government revenue and/or the existence of lump-sum transfers.