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Schmitt-Grohe, Stephanie; Martin Uribe,. "Policy implications of the New Keynesian Phillips curve." Economic Quarterly. Federal Reserve Bank of Richmond. 2008. HighBeam Research. 19 Oct. 2018 <https://www.highbeam.com>.
Schmitt-Grohe, Stephanie; Martin Uribe,. "Policy implications of the New Keynesian Phillips curve." Economic Quarterly. 2008. HighBeam Research. (October 19, 2018). https://www.highbeam.com/doc/1G1-206162978.html
Schmitt-Grohe, Stephanie; Martin Uribe,. "Policy implications of the New Keynesian Phillips curve." Economic Quarterly. Federal Reserve Bank of Richmond. 2008. Retrieved October 19, 2018 from HighBeam Research: https://www.highbeam.com/doc/1G1-206162978.html
The theoretical framework within which optimal monetary policy was studied before the arrival of the New Keynesian Phillips curve (NKPC), but after economists had become comfortable using dynamic, optimizing, general equilibrium models and a welfare-maximizing criterion for policy analysis, was one in which the central source of nominal nonneutrality was a demand for money. At center stage in this literature was the role of money as a medium of exchange (as in cash-in-advance models, money-in-the-utility-function models, or shopping-time models) or as a store of value (as in overlapping-generations models). In the context of this family of models a robust prescription for the optimal conduct of monetary policy is to set nominal interest rates to zero at all times and under all circumstances. This policy implication, however, found no fertile ground in the boardrooms of central banks around the world, where the optimality of zero nominal rates was dismissed as a theoretical oddity, with little relevance for actual central banking. Thus, theory and practice of monetary policy were largely disconnected.
The early 1990s witnessed a profound shift in monetary economics away from viewing the role of money primarily as a medium of exchange and toward viewing money--sometimes exclusively--as a unit of account. A key insight was that the mere assumption that product prices are quoted in units of fiat money can give rise to a theory of price level determination, even if money is physically nonexistent and even if fiscal policy is irrelevant for price level determination. (1) This theoretical development was appealing to those who regard modern payment systems as operating increasingly cashlessly. At the same time, nominal rigidities in the form of sluggish adjustment of product and factor prices gained prominence among academic economists. The incorporation of sticky prices into dynamic stochastic general equilibrium models gave rise to a policy tradeoff between output and inflation stabilization that came to be known as the New Keynesian Phillips curve.
The inessential role that money balances play in the New Keynesian literature, along with the observed actual conduct of monetary policy in the United States and elsewhere over the past 30 years, naturally shifted theoretical interest away from money growth rate rules and toward interest rate rules: In the work of academic monetary economists, Milton Friedman's celebrated k-percent growth path for the money supply gave way to Taylor's equally influential interest rate feedback rule.
In this article, we survey recent advancements in the theory of optimal monetary policy in models with a New Keynesian Phillips curve. Our survey identifies a number of important lessons for the conduct of monetary policy. First, optimal monetary policy is characterized by near price stability. This policy implication is diametrically different from the one that obtains in models in which the only nominal friction is a transactions demand for money. Second, simple interest rate feedback rules that respond aggressively to price inflation deliver near-optimal equilibrium allocations. Third, interest rate rules that respond to deviations of output from trend may carry significant welfare costs. Taken together, lessons one through three call for the adherence to an inflation targeting objective. Fourth, the zero bound on nominal interest rates does not appear to be a significant obstacle for the actual implementation of low and stable inflation. Finally, product price stability emerges as the overriding goal of monetary policy even in environments where not only goods prices but also factor prices are sticky.
Before elaborating on the policy implications of the NKPC, we provide some perspective by presenting a brief account of the state of the literature on optimal monetary policy before the advent of the New Keynesian revolution.
1. OPTIMAL MONETARY POLICY PRE-NKPC
Within the pre-NKPC framework, under quite general conditions, optimal monetary policy calls for a zero opportunity cost of holding money, a result known as the Friedman rule. In fiat money economies in which assets used for transactions purposes do not earn interest, the opportunity cost of holding money equals the nominal interest rate. Therefore, in the class of models commonly used for policy analysis before the emergence of the NKPC, the optimal monetary policy prescribed that the riskless nominal interest rate--the return on federal funds, say--be set at zero at all times.
In the early literature, a demand for money is motivated in a variety of ways, including a cash-in-advance constraint (Lucas 1982), money in the utility function (Sidrauski 1967), a shopping-time technology (Kimbrough 1986), or a transactions-cost technology (Feenstra 1986). Regardless of how a demand for money is introduced, the intuition for why the Friedman rule is optimal in this class of model is straightforward: A zero nominal interest rate maximizes holdings of a good--real money balances--that has a negligible production cost. Another reason why the Friedman rule is optimal is that a positive interest rate can distort the efficient allocation of resources. For instance, in the cash-in-advance model with cash and credit goods, a positive interest rate distorts the allocation of private spending across these two types of goods. In models in which money ameliorates transaction costs or decreases shopping time, a positive interest rate introduces a wedge in the consumption-leisure choice.
To illustrate the optimality of the Friedman rule, we augment a neoclassical model with a transaction technology that is decreasing in real money holdings and increasing in consumption spending. Specifically, consider an economy populated by a large number of identical households. Each household has preferences defined over processes of consumption and leisure and described by the utility function
[E.sub.0][[infinity].summation over (t = 0)][[beta].sup.t]] U ([c.sub.t], [h.sub.t]), (1)
where [c.sub.t] denotes consumption, [h.sub.t] denotes labor effort, [beta] [member of] (0,1) denotes the subjective discount factor, and [E.sub.0] denotes the mathematical expectation operator conditional on information available in period 0. The single period utility function, U, is assumed to be increasing in consumption, decreasing in effort, and strictly concave.
Final goods are produced using a production function, [z.sub.t] F([h.sub.t]), that takes labor, [h.sub.t], as the only factor input and is subject to an exogenous productivity shock, [z.sub.t],.
A demand for real balances is introduced into the model by assuming that money holdings, denoted [M.sub.t], facilitate consumption purchases. Specifically, consumption purchases are subject to a proportional transaction cost, s([[upsilon].sub.t]), that is decreasing in the household's money-to-consumption ratio, or consumption-based money velocity,
[[upsilon].sub.t] = [[[P.sub.t][c.sub.t]]/[M.sub.t]], (2)
where [P.sub.t] denotes the nominal price of the consumption good in period t. The transaction cost function, s([upsilon]), satisfies the following assumptions: (a) s([upsilon]) is nonnegative and twice continuously differentiable; (b) there exists a level of velocity, [[upsilon].bar]] > 0, to which we refer as the satiation level of money, such that s(v) = s'([[upsilon].bar]]) = 0; (c) (upsilon] - [[upsilon].bar]])s'(upsilon]) > 0 for [upsilon] [not equal to] [upsilon]; and (d) 2s'([upsilon]) + [upsilon]s"([upsilon]) > 0 for all ([upsilon] [greater than or equal to]; [upsilon]. Assumption (b) ensures that the Friedman rule (i.e., a zero nominal interest rate) need not be associated with an infinite demand for money. It also implies that both the transaction cost and the distortion it introduces vanish when the nominal interest rate is zero. Assumption (c) guarantees that in equilibrium money velocity is always greater than or equal to the satiation level. Assumption (d) ensures that the demand for money is decreasing in the nominal interest rate.
Households are assumed have access to risk-free pure discount bonds, denoted [B.sub.t]. These bonds are assumed to carry a gross nominal interest rate of [R.sub.t] when held from period t to period t + 1. The flow budget constraint of the household in period t is then given by
[P.sub.t][c.sub.t] [1 + s ([upsilon].sub.t])] + [P.sub.t][[tau].sub.t.sup.L] + [M.sub.t] + [[B.sub.t]/[R.sub.t]] = [M.sub.[t-1]] + [B.sub.[t-1]] + [P.sub.t][Z.sub.t] F([h.sub.t]), (3)
where [[tau].sub.t.sup.L] denotes real lump sum taxes. In addition, it is assumed that the household is subject to a borrowing limit that prevents it from engaging in Ponzi-type schemes. The government is assumed to follow a fiscal policy whereby it rebates any seigniorage income it receives from the creation of money in a lump sum fashion to households.
A stationary competitive equilibrium can be shown to be a set of plans {[c.sub.t], [h.sub.t], [[upsilon].sub.t],), satisfying the following three conditions:
[[upsilon].sub.t.sup.2] s' ([[upsilon].sub.t.] = [[[R.sub.t] - 1]/[R.sub.t]], (4)
[[[U.sub.h]([c.sub.t], [h.sub.t])]/[[U.sub.c]([c.sub.t], [h.sub.t])]] = [[[z.sub.t]F'([h.sub.t])]/[1 + s([[upsilon].sub.t.]) + [[upsilon].sub.t.]s'([[upsilon].sub.t.])]], and (5)
[1 + s([[upsilon].sub.t.])][c.sub.t] = [z.sub.t] F'([h.sub.t]), (6)
given monetary policy {[R.sub.t]}, with [R.sub.t] [greater than or equal to] 1, and the exogenous process ([z.sub.t]). The first equilibrium condition can be interpreted as a demand for money or liquidity preference function. Given our maintained assumptions about the transactions technology, s([[upsilon].sub.t]), the implied money demand function is decreasing in the gross nominal interest rate, [R.sub.t]. Further, our assumptions imply that as the interest rate vanishes, or [R.sub.t] approaches unity, the demand for money reaches a finite maximum level given by [c.sub.t]/[[upsilon].bar]). At this level of money demand, households are able to perform transactions costlessly, as the transactions cost, s([upsilon],), becomes nil. The second equilibrium condition shows that a level of money velocity above the satiation level, [[upsilon].bar], or, equivalently, an interest rate greater than zero, introduces a wedge between the marginal rate of substitution of consumption for leisure and the marginal product of labor. This wedge, given by 1 + s([[upsilon].sub.t]) + [[upsilon].sub.t]s'([[upsilon].sub.t]), induces households to move away from consumption and toward leisure. The wedge is increasing in the nominal interest rate, implying that the larger is the nominal interest rate, the more distorted is the consumption-leisure choice. The final equilibrium condition states that a positive interest rate entails a resource loss in the amount of s ([[upsilon].sub.t])[c.sub.t]. This resource loss is increasing in the interest rate and vanishes only when the nominal interest rate equals zero.
We wish to characterize optimal monetary policy under the assumption that the government has the ability to commit to policy announcements. This policy optimality concept is known as Ramsey optimality. In the context of the present model, the Ramsey optimal monetary policy consists in choosing the path of the nominal interest rate that is associated with the competitive equilibrium that yields the highest level of welfare to households. Formally, the Ramsey policy consists in choosing processes [R.sub.t], [c.sub.t], [h.sub.t], and [[upsilon].sub.t] to maximize the household's utility function given in equation (1) subject to the competitive equilibrium conditions given by equations (4) through (6).
When one inspects the three equilibrium conditions above, it is clear that if the policymaker sets the monetary policy instrument, which we take to be the nominal interest rate, such that velocity is at the satiation level, ([[upsilon].sub.t] = [[upsilon].bar]), then the equilibrium conditions become identical to an economy without the money demand friction, i.e., [c.sub.t] = [z.sub.t] F([h.sub.t]) and--[[[U.sub.h]([c.sub.t], [h.sub.t])]/[[U.sub.c]([c.sub.t], [h.sub.t])]] = [z.sub.t] F'([h.sub.t]). Because the real allocation in the absence of the monetary friction is Pareto optimal, the proposed monetary policy must be Ramsey optimal. By a Pareto optimal allocation we mean a feasible real allocation (i.e., one satisfying c, = [z.sub.t] F [[h.sub.t]]) with the property that any other feasible allocation that makes at least one agent better off also makes at least one agent worse off. It follows from equation (4) that setting the nominal interest rate to zero ([R.sup.t] = 1) ensures that v, = v. For this reason, optimal monetary policy takes the form of a zero nominal interest rate at all times.
Under the optimal monetary policy, the rate of change in the aggregate price level varies over time. …
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