Week-9

Received: 19 June 2018 | Revised: 28 December 2018 | Accepted: 3 January 2019 DOI: 10.1111/infi.12345

O R I G I N A L A R T I C L E

The global factor in neutral policy rates: Some implications for exchange rates, monetary policy, and policy coordination

Richard Clarida1,2*

1Department of Economics, Columbia University, New York City, New York 2Board of Governors of the Federal Reserve System, Washington, DC

Correspondence Richard Clarida, Board of Governors of the Federal Reserve System, 20 Street and Constitution Avenue, NW, Washington, DC 20551. Email: [email protected]

Abstract

This paper highlights some of the theoretical and

practical implications for monetary policy and exchange

rates that derive specifically from the presence of a

global general equilibrium factor embedded in neutral

real policy rates in open economies. Using a standard

two‐country Dynamic Stochastic General Equilibrium (DSGE) model, we derive a structural decomposition in

which the nominal exchange rate is a function of the

expected present value of future neutral real interest rate

differentials plus a business cycle factor and a purchas-

ing power parity (PPP) factor. Country‐specific “r*” shocks in general require optimal monetary policy to

pass these through to the policy rate, but such shocks

will also have exchange rate implications, with an

expected decline in the path of the real neutral policy

rate reflected in a depreciation of the nominal exchange

rate. We document a novel empirical regularity between

the equilibrium error in the Vector Error Correction

Model (VECM) representation of the empirical Holston,

Laubach, and Williams (HLW) four‐country r* model and the value of the nominal trade weighted dollar. In

fact, the correlation between the dollar and the 12‐ quarter lag of the HLW equilibrium error is estimated to

International Finance. 2019;22:2–19. wileyonlinelibrary.com/journal/infi © 2019 John Wiley & Sons Ltd | 2

*The views expressed in this article are those of the author and do not necessarily reflect the position of the Board of Governors of the Federal Reserve System or the Federal Reserve System.

be 0.7. Global shocks to r* under optimal policy require

no exchange rate adjustment because passing though r*

shocks to policy rates “does all the work” of maintaining global equilibrium. We also study a richer model with

international spillovers so that in theory there can be

gains to international policy cooperation. In this richer

model, we obtain a similar decomposition for the

nominal exchange rate, but with the added feature that

r* in each country is a function of global productivity

and business cycle factors even if these factors are

themselves independent across countries. We argue that

in practice, there could well be significant costs to

central bank communication and credibility under a

regime of formal policy cooperation, but that gains to

policy coordination could be substantial given that r*s

are correlated across countries.

1 | INTRODUCTION

Over the past 25 years, best‐practice monetary policy has been implemented with reference to interest rate feedback rules that include as inputs estimates of potential output and the real policy rate—consistent with price stability. Before the global financial crisis and reflecting the justly deserved influence of Taylor (1993), it was common in policy simulations (Henderson & McKibbin, 1993) and in empirical work (Clarida, Galí, & Gertler [CGG], 1998, 2000) to make the simplifying assumption that r* is constant. However, it has long been appreciated (Friedman, 1968; Wicksell, 1898) that r* can be time‐varying and in particular, the theoretical analysis of monetary policy rules in Woodford (2003) and CGG (1999, 2002)—among many others—has emphasized that shocks to r* should be reflected in policy rates set by central banks seeking to keep the economy as close as possible to the benchmark of a flexible price equilibrium. Since the global financial crisis, estimated and projected future declines in neutral real policy rates (Hamilton, Ethan, Hatzius, & West, 2016; Holston, Laubach, & Williams [HLW], 2017; Laubach & Williams, 2003) relative to the precrisis experience have become an important consideration in the conduct of monetary policy and the communication of forward guidance at the Fed and some other major central banks (Haldane, 2015; Yellen, 2017).

The focus of this paper is on highlighting some of the theoretical and practical implications for monetary policy and foreign exchange rates that derive specifically from the presence of a global factor—predicted in theory and estimated in practice—embedded in neutral real policy rates in open economies.

After reviewing in Section 2 some of the existing empirical evidence on the presence of a global factor in neutral policy rates, we present in Section 3 a simple two‐country model (based on Clarida, 2014; Galí & Monacelli, 2005) to help illustrate several points about how shocks to neutral policy rates might impact monetary policy and exchange rates. We show that in this model, the short‐run neutral real policy rate in each country will be a function of expected productivity growth in that country, so that if there is a common factor across countries in

3 | CLARIDA

productivity growth, there will be a factor in neutral policy rates. If countries are adjusting policy in response to common, global neutral real rate shocks, this will obviously impart a positive correlation in policy even in the absence of policy cooperation or coordination. As for exchange rates, we derive a novel decomposition for the (log) nominal exchange rate as the sum of a price level term, and business cycle term, and a term which is the present value of expected future neutral real policy rate differentials, with a decline in the expected future neutral policy rate below its long‐run level associated with a depreciation of the exchange rate today. By contrast, in this model exchange rates do not need to adjust to the global component in neutral policy rates, realized or expected. In response to a global shock, a common global decline in real policy rates can “do all the work” to generate global aggregate demand in line with aggregate supply.

The main contribution of the paper is in Section 4, in which we study a more general specification (based on CGG, 2002) of the two‐country model in which there are international spillovers that can lead, in theory, to gains to international policy cooperation. We argue, however, that in practice, credible policy cooperation may be difficult to implement and communicate because in this model it would bind countries to set local policy rates based on an index of global inflation. Moreover, in this model with international spillovers, the neutral real policy rate in each country will depend on expected productivity growth in all countries (and potentially also on global business cycle factors) even if there is no common factor in country productivity growth. As a result, there may be significant gains to policy coordination which are achievable in practice in the noncooperative equilibrium, where again optimal policy can be written as a Taylor‐type rule.

Section 5 provides some concluding remarks.

2 | A QUICK REVIEW OF THE EMPIRICAL EVIDENCE

As the motivation for this paper is the phenomenon of a time‐varying global factor in neutral real interest rates, it seems worthwhile at the outset to provide some evidence that these rates are time‐varying and that they appear correlated across countries. Similar to another input to monetary policy analysis—potential output—the neutral real policy rate is both time‐varying and unobservable and thus must be inferred from data. Laubach and Williams (2003), and more recently HLW (2017), have developed and implemented a widely cited methodology for estimating neutral real policy rates. The latter paper is especially useful for our purposes because it consistently applies a common Laubach and Williams' methodology to estimate neutral real policy rates in the United States, the United Kingdom, Canada, and the Eurozone. Other papers—for example Hamilton et al. (2016), King and Low (2014), Rachel and Smith (2015), and IMF (2013)—provide estimates that are also consistent with the presence of a global factor in time‐varying neutral real interest rates (see also inflation report in Bank of England, 2018, p. 39).

Figure 1 displays the HLW estimates of rt ⁎ for the United States, the United Kingdom,

Europe, and Canada as of July 2016. For all four countries, estimates for recent years are well below those in the 1990s and in the years preceding the global financial crisis. It is also interesting to note that for all countries, in the decade or so before the Global Financial Crisis (GFC), the estimates are clustered around 2%, which of course is the assumed constant value for r* in the original Taylor rule. Figure 2 compares the HLW estimates of the US r* with the 1‐year

CLARIDA | 4

Treasury Inflation Protected Securities (TIPS) yield 4 years forward as calculated by the Federal Reserve.

As the HLW econometric approach uses no data on TIPS yields or forwards, so the alignment between the two series is noteworthy. That said, as shown in Figure 3, there is a

-1

0

1

2

3

4

US r* UK r*

Time

CAN r* EUR r*

HLW Es�mates of r*

FIGURE 1 Holston, Laubach, and Williams' estimates of r* [Color figure can be viewed at wileyonlinelibrary.com]

-2

-1

0

1

2

3

4

5

US r*

US TIPS 1y4y Fwd

Time

FIGURE 2 Holston, Laubach, and Williams' r* and TIPS implied forward [Color figure can be viewed at wileyonlinelibrary.com]

5 | CLARIDA

much looser relationship between forward real yields in the United Kingdom (as calculated by the Bank of England) and the HLW estimates of r* for the United Kingdom.

Finally, to get a sense of the comovement among the four neutral real policy rates, we plot the estimated r*t for the United States versus a weighted average of the rt

⁎ estimates for the other three countries, with the weights equal to (minus) the estimated cointegrating vector coefficients reported in HLW (2017). The difference between these two series is the equilibrium error in the VECM representation of the HLW system (since HLW normalize the US coefficient in the cointegrating vector to unity).

3 | A SIMPLE MODEL OF OPTIMAL MONETARY POLICY AND EXCHANGE RATE DETERMINATION WITH r* SHOCKS

We begin with a tractable two‐country version of the Galí and Monacelli (2005) and Clarida (2014) Dynamic Stochastic General Equilibrium (DSGE) model of optimal monetary policy and exchange rate determination extended to allow for global as well as country‐specific stocks to rt

⁎. In this model, rt

⁎ shocks are driven by common as well as country‐specific shocks to home and foreign expected productivity growth. To focus on the main points, and without loss of generality, we assume in this section the “foreign” country operates always at its supply‐determined level of output, rt

⁎ shocks are driven by common as well as country‐specific shocks to home and foreign expected productivity growth. To focus on the main points, and without loss of generality, we assume in this section the “foreign” country operates always at its supply determined level of output

A AY = N = = Ȳt F

t F

t F

t F

t F and that foreign monetary policy is such that the price of foreign output is

constant and equal to 1. We also normalize the nonsupply of labor in the home and foreign country to 1. By contrast, in the home country, “cost push” shocks in the presence of nominal rigidities can cause output and labor demand to deviate from its flexible price supply‐determined level of output so that AY = A X = ȲXt t

F t t t t. In this model, aggregate home productivity is the product of a

common global factor At F and a home‐country‐specific factor At. The home “output gap,” denoted

-2

-1

0

1

2

3

4

5

UK r*

UK Linker 1y5y Fwd

Time

FIGURE 3 Holston, Laubach, and Williams' r* and implied linker forward [Color figure can be viewed at wileyonlinelibrary.com]

CLARIDA | 6

Xt, is endogenous and will be solved for as a function of shocks and the monetary policy rule. An overstrike over a variable indicates its level in a flexible price equilibrium. In the model of this section, with our parameter choices, the flexible price level of output in each country is just equal to the exogenous level of productivity in that country.

Home utility takes the form U C V N b C b C ϕ N( ) − ( ) = ln + (1 − ) ln − (1 + )t t H t F t t ϕ

, , −1 1+ ,

where Ct = (CH,t) b (CF,t)

1–b and Nt is home labor supply and b ≥ 0.5. These preferences feature an intertemporal elasticity of substitution 1/σ equal to 1 and a Cobb–Douglas aggregator for consumption. Households maximize a discounted sum of expected utility subject to a sequence of budget constraints:

P C E M D W N D T+ { } = + − + Γ,t t t t t t t t t t t cpi

, +1 +1

where Mt,t + 1 is a nominal stochastic discount factor, Wt is the money wage, Dt is the distribution paid on securities brought into date t, Tt is lump sum tax collection, and Гt is the distribution of profits earned by producers of intermediate inputs. Foreign preferences and budget constraints are symmetric.

Up to log linearization, a Euler equation will characterize the equilibrium relationship between the log consumption index (relative to its level in a nonstochastic steady state so that any constant rate of time preference differences out), consumer price index (CPI) inflation, and the one period nominal interest rate Rt:

c E c R E= { } − ( − π ).t t t t t t+1 +1 cpi

With our assumptions on preferences, trade will be balanced period by period (Cole & Obstfeld, 1991) and goods market equilibrium will imply bA A X b S A A A X+ (1 − ) =t

F t t t t

F t F

t t, where St is the equilibrium terms of trade (home good price of foreign good) and b ≥ 1/2 is the expenditure share on locally produced output. This implies St = AtXt or in logs st = at + xt so that the log of the equilibrium terms of trade is equal to the home‐country‐specific factor in productivity at plus the log of the home “output gap” xt. We assume the law of one price and producer currency pricing so that the log nominal exchange rate satisfies et = st + pt, where pt is the log of the price of home output. To see this, note that St = Et/Pt, since we assume producer currency pricing, the law of one price, and the foreign currency price of the foreign good is constant and equal to 1. We have

b Δsπ = π + (1− )t t t+1 cpi

+1 +1 with πt+1 = pt+1 – pt. From balanced trade and goods market equilibrium C b b A A X S= ( ) (1− )t b b t

F t t t

b1− −1

Substituting out for ct and using the definition of CPI and the equilibrium condition for the terms of trade, we obtain a Euler equation in terms of the domestic output gap and the neutral real interest rate:

x E x R E p p r= – { – ( − ) – },t t t t t t tt +1 +1 ⁎

(1)

where r E Δa E Δa= +t t t F

t t ⁎

+1 +1 is the ex ante real interest rate in the home country that maintains the home output gap at zero. We have E ar = ΔF tt t +1

F⁎ period by period, π = 0t F period

by period, rR = Ft F

t

⁎

period by period, and AY =t F

t F period by period. We assume that at is an

autocorrelated deviation of the log level of home productivity from the log level of global productivity at

F which may itself possess a unit root. Note that under this stationarity assumption at + EtΣi = 1,∞Δat+i = 0 if the unconditional mean of at is 0.

7 | CLARIDA

Home firms will set prices as a markup over marginal cost—which is proportional to the real product wage scaled by productivity—in a staggered fashion a la Calvo (Calvo, 1983). With our assumption on preferences, and letting δ = (1 – F)(1 – βF)/F with (1 – F) the fraction of firms that reset prices each period, inflation in the price of home goods will be given by

p p βE p p λx u− = ( − ) + + ,t t t t t t t−1 +1 (2)

where ut is a—possibly autocorrelated—shock to the wage markup and λ = (1 + ϕ)δ. The nominal exchange rate must be consistent with asset market equilibrium, goods market

equilibrium, and long‐run purchasing power parity (which will hold in this model in expectation in the long run under our assumptions on productivity and preferences). A structural equation which characterizes the equilibrium exchange rate in terms of endogenous variables can be written as

∑ ∞

e p x E r r= + − ( − ),t t t t i

t i t i F

=0

+ ⁎

+

⁎

(3)

where r r E Δa− =t F

t t ⁎

t +1 ⁎

is the neutral real rate differential between the home country and the foreign country. Thus the log nominal exchange rate can be decomposed into the sum of a PPP component, a business cycle component, and a (forward‐looking) r* component. Equivalently, persistent but transitory deviations from PPP are the sum of a business cycle component and an r* component. The nominal exchange rate today will reflect the entire expected future time path of the country‐specific component in the neutral real interest rate but in equilibrium does not adjust to the global component in the neutral policy rate. In particular, if today the neutral real rate at home is expected in the future to lie below the neutral real rate abroad, the nominal exchange rate today must weaken relative to domestic prices given the state of the business cycle xt. Figure 5 depicts the empirical relationship between the nominal trade weighted dollar and the equilibrium error calculated using the parameters reported in HLW (2017) and shown in Figure 4. As shown in Figure 6, the equilibrium error appears to lead the trade weighted dollar by about 12 quarters. The simple correlation between the TW dollar and the VECM error lagged 12 quarters is 0.70.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

HW_r*_US

HLW_r*_index_UK,EZ,CA

Equilibrium Error in HLW VECM

Time

FIGURE 4 Equilibrium error in the Holston, Laubach, and Williams' VECM representation [Color figure can be viewed at wileyonlinelibrary.com]

CLARIDA | 8

Notice that structural exchange rate Equation (3) holds in any equilibrium regardless of how the rest of the model is closed. To close the model, we need to take a stand on monetary policy and the central bank objective function, so we can pin down domestic inflation and the output gap. There are two ways to do this. We can just assume that the objective function is quadratic in inflation and the output gap with an arbitrary relative weight α on stabilizing home output at its natural level a a+t

F t. Or, as was derived in CGG (2002) and Galí and Monacelli (2005), we

can follow Woodford (2003) and solve for α—and thus the optimal policy rule—as a function of deep parameters. So for a policymaker who wants to maximize an objective function proportional to ∑

∞ W E β α x= − [π + ]H

t t

t t0 =0 2 2 subject to the Phillips curve and the Euler and

taking Etπt+1 as given, the first‐order condition will be x λ α= −( / )πt t, which is of the same

65

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75

80

85

90

95

100

105

110

115

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

US TWD

HLW Equilibrium Error

Time

FIGURE 5 US TWD versus Holston, Laubach, and Williams' VECM error [Color figure can be viewed at wileyonlinelibrary.com]

65

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85

90

95

100

105

110

115

-1.00

-0.80

-0.60

-0.40

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0.60

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1.00

US TWD

VECM Equilibrium Error lead by 12 q

Time

FIGURE 6 US TWD versus Holston, Laubach, and Williams' VECM error lead by 12 quarters [Color figure can be viewed at wileyonlinelibrary.com]

9 | CLARIDA

form as in CGG (1999). Since under optimal policy the output gap will be linear in domestic inflation, the equilibrium rate of inflation under optimal policy will satisfy

βE λ α uπ = {π } − ( / )π +t t t t t+1 2 . Solving forward and assuming u ρu ε= +t t t−1 , we obtain

βρ λ α uπ = (1 − + / )t t 2 −1

or πt = ψut. The optimal policy rule given α is obtained by substituting the first‐order condition into the Euler equation and using equilibrium dynamics for inflation. The system can be written as follows:

⎛ ⎝⎜

⎞ ⎠⎟R r

λ ρ

αρ E= + 1 +

(1 − ) π ,t t tt

⁎ +1

R r= ,t F

t F⁎

(4)

⎜ ⎟ ⎛ ⎝

⎞ ⎠ ∑

∞

e p α λ

α ψu E r r= +

− − ( − ),t t t t

i

t i t i F

−1

=0

+ ⁎

+

⁎

with r E Δa E Δa r E Δa= + , =t t t F

t t t F

t F

t ⁎ ⁎ and Etπt+1 = ρψut and pt−1 = Σi = 1,∞ψut – i. Thus optimal

policy in the open economy can be written as a forward‐looking Taylor rule with a time‐varying neutral real interest rate. The time‐varying neutral real interest rate is, in turn, the sum of a global component and a country‐specific component. Also notice that above we focus on an equilibrium with inflation proportional to the exogenous cost push shock ut. As is well known, there are other equilibria in this class of DSGE models which feature speculative hyperinflation, and this would be true even if we were to append a standard utility of real balances into the objective function (see, e.g., Kocherlakota & Phelan, 1999, for an insightful discussion of this issue).

Notice that in this setup, under optimal monetary policy, there is a clean distinction between impact of neutral rate shocks (driven by forecastable changes in productivity growth) and cost push shocks. Under optimal policy, neutral rate shocks should be reflected one for one in policy rates and will result in equilibrium adjustments in nominal exchange rate. These adjustments in policy rates and exchange rate are sufficient to keep the economy at its flexible price equilibrium even in the presence of nominal rigidities. Cost push shocks, by contrast, create a tradeoff between stabilizing output and inflation. Under optimal policy, the central bank follows a forward‐looking Taylor rule and raises the nominal interest rate by more than the rise in expected inflation. This optimal policy depresses output below the flexible price level so as to stabilize expected inflation. The optimal policy will also have implications for the nominal exchange which will be discussed below. Note that cost push shocks have no effect on the neutral policy rate unless those shocks are themselves correlated with productivity shocks.

These three equations illustrate several points about neutral real rate shocks in open economies under flexible exchange rates that are worth noting.

1. The neutral real policy rate in the open economy will in general be a function of global as well local factors such as the rate of current and expected future potential growth. If countries are adjusting policy in response to common, global neutral real rate shocks, this

CLARIDA | 10

will obviously impart a positive correlation in policy even in the absence policy coordination or cooperation.

2. In this model with the parameter assumption we have made on the intertemporal elasticity of substitution, there is no gain to policy cooperation so that the Nash best response policy rules which here take the form of Taylor‐type rules—lead to the maximum level global welfare that can be obtained under discretion.

3. The exchange rate is an asset price that will reflect, in part, expectations of the future time path of the country‐specific component of the neutral policy rate, with a decline in the expected future neutral policy rate below its long‐run level associated with a depreciation of the exchange rate today.

4. However, exchange rate depreciation in the face of a persistent country‐specific r* shock is not a “beggar thy neighbor” policy in either motive or realization. In this simple model, trade is balanced period by period and so the exchange rate adjustment that occurs is required to maintain goods market equilibrium with balanced trade and not to generate a trade surplus.

5. Exchange rate adjustment to a persistent country‐specific r* shock is required because expectations that future home neutral rates will remain below neutral rates in the rest of the world are coincident with expectations that home productivity and output are and will remain elevated relative to their long‐run levels, and this elevated supply requires a weaker nominal exchange rate and a worsening terms of trade as well as a lower neutral policy rate to generate the level and allocation of global aggregate demand to clear the home and world

goods market. In symbols ∞E Σ r a=i t H

tt =1, ⁎

. 6. By contrast, at least under optimal policy, exchange rates do not need to adjust to the global

component in neutral policy rates, realized or expected. In response to a global shock, a common global decline in real policy rates can “do all the work” to generate global aggregate demand in line with aggregate supply.

7. This may look like, but is not, a globally inefficient “currency war” defined as a “race to the bottom” in policy rates as countries seek to avoid home currency appreciation as other countries cut interest rates.

An interesting feature of these models which finds a great deal of empirical support and is discussed extensively in CGG (2002), Clarida and Waldman (2008), Krugman, Obstfeld, and Melitz (2011), and Clarida (2014) is the “bad news good news” result that, with an inflation targeting central bank, a shock that pushes inflation above target can trigger the expectation of a policy rate path that results in an appreciation of the nominal exchange rate today even though in the long run the exchange rate must (in expectation) depreciate to return to PPP. In our model, bad news for inflation resulting from a positive cost push shock to ut will appreciate the nominal exchange rate today if α—the welfare weight on output stabilization—is less than λ —the slope of the Phillips curve:

⎜ ⎟ ⎛ ⎝

⎞ ⎠ ∑

∞

e p α λ

α ψu E r r= +

− − ( − ).t t t t

i

t i t i F

−1

=0

+ ⁎

+

⁎

(5)

A “cost push” shock ut will increase domestic inflation and under optimal policy induce the central bank to raise the nominal interest rate by more than expected inflation. The rise in the ex ante real interest rate will cause st to fall and this, along with the rise in the real interest rate

11 | CLARIDA

itself, will reduce demand for home output. In the “bad news good news” case the equilibrium decline in st is larger in absolute value than is the equilibrium rise in inflation, and this can only be accomplished via an appreciation of the nominal exchange rate. More broadly, the equilibrium nominal exchange rate in this model must possess a unit root even though shocks are stationary and our Cole–Obstfeld equilibrium replicates the complete market allocation. The nominal exchange rate must possess a unit root because time‐consistent monetary policy cannot deliver a stationary price level, only a stationary rate of inflation (CGG, 2002; Woodford, 2003). The unit root in the nominal exchange rate is required to produce a stationary equilibrium terms of trade given that optimal monetary policy produces unit root in the price level.

4 | POLICY CORRELATION, GAINS FROM POLICY COORDINATION, BUT POTENTIAL PITFALLS FROM POLICY COOPERATION

Although these are absent in the simple model of Section 3, in general there may be international spillovers to monetary policy that are not fully incorporated in Taylor‐type rules that feedback solely on domestic macroeconomic variables. If so, there can in theory be gains to monetary policy cooperation. By cooperation, we mean that home and foreign central banks set policies that maximize world welfare, even if each central bank would like to run a different policy taking the other central bank's policy as given as in a Nash equilibrium. However, while we observe that national monetary policies are often correlated (eras of global monetary easing; global rate hike cycles), they also appear sometimes to be coordinated (after all, what else are central bankers doing at all those G7, G20, IMF, and Basel meetings?), but rarely (if ever) do major central banks respect a binding commitment to pursue cooperative policies, policies that would differ from noncooperative policies aimed solely at satisfying their objectives for domestic inflation and employment. It has long been well appreciated (Taylor, 1982) that in small‐ or large‐scale open economy macro models, the calibrated gains to international monetary policy cooperation (see, e.g., Obstfeld & Rogoff, 2002) are found to be modest relative to the welfare achieved under a Nash equilibrium in which each country runs a sensible policy taking as given the policy of the other countries. In this section, we will make a somewhat different and less often discussed case against global monetary policy cooperation even in a world of r* shocks. Namely, that in practice, adopting it—or succumbing to it!—could plausibly erode central bank credibility and public support for sound, rules‐based policies. According to this view, the all‐in cost to a regime of policy cooperation could swamp the theoretical benefits, and if so, we should not bemoan the absence of formal monetary policy cooperation, we should celebrate it!

However, and perhaps especially in a world in which there is a common global component in neutral real policy rates across countries, international monetary policy coordination— defined to include the sharing of information and analysis regarding estimates of the unobservable inputs to policy rules such as the equilibrium real rate of interest and potential output as well as the considerations that would govern the timing and trajectory of a baseline policy path as well as trigger deviations from such a path—can enhance the design and effectiveness of baseline policy rules. We will give examples below. But while international monetary policy coordination may enhance the efficiency of a policy rule framework if it is in place, there are reasons to doubt that in practice there are likely to be additional material, reliable, and robust gains that would flow from a formal regime of binding monetary policy

CLARIDA | 12

cooperation, at least among major G7 economies and even including a number of emerging economies with flexible exchange rates and relatively open capital accounts. In such a regime, national monetary policies in each country are constrained to be set so as to jointly maximize world welfare. In these models, as in the earlier literature they build on, there are externalities to monetary policy that create such theoretical gains to cooperation. However, as CGG (2002) and Engel (2009) illustrate in “new Keynesian” models, and as we review below, to achieve the theoretical gains to international monetary policy cooperation, policy rates in each country must be set with reference to an index of inflation deviations from target in both the home and the foreign countries. In words, whereas optimal policy in the absence of cooperation can be implemented with a policy rule that reacts to domestic inflation, output gaps, and the appropriately defined equilibrium—or neutral—real interest rate, a global welfare increasing policy must bind central banks to policy rules that react to foreign as well as domestic inflation, policy rules that they would not chose were they not bound.

In practice, there could be another problem with policy cooperation that is absent from most theoretical discussions. Simply stated, the problem is the threat to the credibility of the central bank, the challenges to central bank communication, and the resulting potential loss of support for its policy actions from the public when the policy choices required by cooperation react not only to home inflation but also to deviations of foreign inflation from target. For example, if home inflation is above target but foreign inflation is below target, the optimal policy rule under cooperation calls for the home (real) policy rate to be lower—more accommodative—than it would be in the absence of cooperation (CGG, 2002). In theoretical models, the commitment to the inflation target is just assumed to be perfect and credible, but in practice credibility appears to be a function of central bank communication and as well the policies actually implemented to push inflation back to target. In practice, central banks could have a hard time maintaining credibility as well as communicating a policy that kept home real interest rates low—or in extreme cases negative—not because home inflation is too low, but because foreign inflation is too low! Or imagine the opposite case, with home inflation below target when foreign inflation is above target. In this case, the optimal policy rule under cooperation calls for the home (real) policy rate to be higher—less accommodative—than it would be in the absence of cooperation, not because home inflation is too high, but because foreign inflation is!

While, perhaps for these reasons, we do not have many confirmed sightings of genuine monetary policy cooperation, we do perhaps observe rather more examples of policy coordination. The CGG (2002) model—which is a generalization of the model of Section 3— provides an illustration of the value of policy coordination in the noncooperative Nash equilibrium in a symmetric two‐country model. We now allow for σ > 1 (which is consistent with estimates often reported in the empirical macro literature) but set b = 1/2 so as to focus on the tractable symmetric case. Under these conditions, the Cole–Obstfeld result will still hold, and trade will be balanced period by period. The log nominal exchange rate consistent with goods market equilibrium will satisfy

e p p y y x x= − + ¯ − ¯ + − .t t F t t t

F t t

F (6)

The neutral real interest rate that clears the home goods market at the flexible price level of output conditional on foreign output is given by (see Clarida, 2014; CGG, 2002, for all derivations)

13 | CLARIDA

r σ

E y σ

E y σ

E x= ( + 1)

2 Δ¯ +

( − 1)

2 Δ¯ +

( − 1)

2 Δ .t t t t t

F t t

F⁎ +1 +1 +1

(7)

The neutral real interest rate that clears the foreign goods market at the flexible price level of output conditional on home output is given by

r σ

E y σ

E y σ

E x= ( + 1)

2 Δ¯ +

( − 1)

2 Δ¯ +

( − 1)

2 Δ .t

F t t

F t t t t+1 +1 +1

⁎

(8)

The neutral real rate differential is given by

r r E y y σ

E x x− = (Δ¯ − Δ¯ ) + ( − 1)

2 (Δ − Δ ).t t

F t t t

F t t

F t

⁎ ⁎ +1 +1 +1 +1

(9)

Note that in the special case σ = 1 these equations simplify to their counterparts in Section 3. Under our assumptions that at, ut, and ut

F are stationary with zero mean, the unconditional mean of home output is equal to the mean of foreign output and the unconditional means of the output gaps are zero. It follows that

∑ ∞

e p p σ

x x E r r= − + ( + 1)

2 ( − ) − ( − ).t t t

F t t

F t

i

t i t i F

=0

+ ⁎

+ ⁎ (10)

As in the simpler model of Section 3, we have a structural equation that decomposes the nominal exchange rate into a PPP term, a (relative) business cycle term, and a (forward‐looking) neutral real rate term. Ceteris paribus, it is again the country‐specific component of the home neutral real rate that is reflected in equilibrium nominal exchange rate, with a decline in the neutral rate inducing a depreciation of the nominal exchange rate.

In the simple model of Section 3, the neutral real rate in each country is solely a function of that country's expected rate of potential output growth. However, when there are cross‐country spillovers, this will not be the case and instead, the neutral real rate in each country will in equilibrium be a function of home and foreign productivity growth as well as the home and foreign business cycle factors xt and x

F t. To see this, begin with the equations for flexible price

output at home and abroad derived in CGG (2002):

⎜ ⎟ ⎛ ⎝

⎞ ⎠

⎡ ⎣⎢

⎤ ⎦⎥y

σ φ φ a a

σ y

σ x=

+ 1

2 + (1 + )( + ) +

(1 − )

2 ¯ +

(1 − )

2 ,t t t

F t F

t F

−1

⎜ ⎟ ⎛ ⎝

⎞ ⎠

⎡ ⎣⎢

⎤ ⎦⎥y

σ φ φ a

σ y

σ x=

+ 1

2 + (1 + ) +

(1 − )

2 ¯ +

(1 − )

2 .Ft

F t t t

−1

(11)

These two linear equations can be solved for ȳt and ȳt F each as a function of a a x x, , ,t t

F t t

F. It follows that home and foreign neutral real rates share common global general equilibrium factors per below even if home and foreign productivity are independent:

CLARIDA | 14

r σ

E y a a x x

σ E y a a x x

= ( + 1)

2 Δ¯ (Δ , Δ , Δ , Δ )

+ ( − 1)

2 Δ (Δ , Δ , Δ , Δ ),

t t t t t F

t t F

t t F

t t F

t t F

⁎ +1 +1 +1 +1 +1

+1 +1 +1 +1 +1

r σ

E y a a x x

σ E y a a x x

= ( + 1)

2 Δ¯ (Δ , Δ , Δ , Δ )

+ ( − 1)

2 Δ (Δ , Δ , Δ , Δ ),

t F

t t F

t t F

t t F

t t t t F

t t F

+1 +1 +1 +1 +1

+1 +1 +1 +1 +1

⁎

(12)

which reduce to r E Δa E Δa= + tt t t F

t ⁎ and r E Δa= tt

F t F⁎ in the σ = 1 case. Letting Ψ y y= ¯ − ¯t t t

F

denote the flexible price output differential we have Ψ a x x( , , )t t t F so that the flexible price

output differential is in equilibrium a function of relative home productivity—as in the simpler model of Section 3—as well as the home and foreign output gaps. In sum, regardless of how we close the model, we must have

∑ ∞

e p p σ

x x E r r= − + ( + 1)

2 ( − ) − ( − ),t t t

F t t

F t

i

t i t i F

=0

+ ⁎

+

⁎

with

r r E Ψ a x x σ

E x x− = (Δ , Δ , Δ ) + ( − 1)

2 (Δ − Δ ).t t

F t t t t

F t t

F t

⁎ +1 +1 +1 +1 +1

⁎

(13)

We close the model with a policy rule that is the optimal best response taking the other country's output as given. In the “home” country, CGG (2002) show that the optimal Nash monetary policy rule can be written as a forward‐looking Taylor rule:

⎛ ⎝⎜

⎞ ⎠⎟R r

λ ρ

αρ

σ E= + 1 +

(1 − ) + 1

2 π .t t tt

⁎ +1 (14)

And similarly in the foreign country

⎛ ⎝⎜

⎞ ⎠⎟R r

λ ρ

αρ

σ E= + 1 +

(1 − ) + 1

2 π .Ft t

F t

F t

⁎ +1 (15)

Under the optimal Nash monetary policies we still have

x λ

α x

λ

α = − π and = − π .t t

F t

F t

And so under optimal policy as before π βρ λ α u= (1 − + / )t t2 −1 and π βρ λ α u= (1 − + / )t F

t F2 −1 .

15 | CLARIDA

In this more general model, the neutral real interest rate in each country will be a linear function of home and foreign productivity as well as the cost push shocks, and this will be true even if home and foreign productivity are independent (see equation block (12)). Thus, even if there is no global component to productivity, there will in general equilibrium be a global component to the neutral real interest rate because of the cross‐country spillovers that arise when σ is not equal to 1. We illustrate this with a numerical example. Let σ = 3 and ϕ = 1 and solve equation block (11) for home and foreign flexible price output for the case in which home productivity is independent of foreign productivity (so that log productivity at home is equal to at instead of a a+t t

F in equation block (11)). The solutions are

y a x a x y a x a x= 6

8 + 1

8 − 2

8 − 3

8 and =

6

8 + 1

8 − 2

8 − 3

8 ,t t t t

F t F F

t F t

F t t t (16)

which imply that relative flexible price output is simply

y y a a x x¯ − ¯ = − + 1

2 ( − ).t t

F t t

F t t

F (17)

So from Equation (12) we have for these parameters

⎜ ⎟ ⎜

⎟

⎛ ⎝

⎞ ⎠

⎛ ⎝

⎞ ⎠

r E a x a x E a x a

x

= 2 6

8 Δ +

1

8 Δ −

2

8 Δ −

3

8 Δ +

6

8 Δ +

9

8 Δ −

2

8 Δ

− 3

8 Δ ,

t t t t t F

t F

t F t

F t t

t

⁎ +1 +1 +1 +1 +1 +1 +1

+1

which simplifies to

r a a x x= 10

8 Δ +

2

8 Δ +

3

8 Δ −

1

8 Δt t t

F t F

t ⁎

+1 +1 +1 +1 (18)

and symmetrically for the foreign country. So in general, even if home and foreign productivity are uncorrelated, the neutral real rate in each country will be a function of both home and foreign productivity.

The best Nash policy in this two‐country model is a Taylor‐type rule for setting the policy rate as a function of expected home inflation and time‐varying equilibrium home real interest rate which is function of expected home and foreign productivity growth as well as the expected change in home and foreign output gaps. Thus, to the extent the foreign central bank has some comparative advantage in nowcasting (in the rigorous sense of Giannone, Reichlin, & Small, 2008) or forecasting foreign productivity growth and business cycle factors, sharing this information or even pooling these nowcasts with the home central bank could improve its estimate of the home equilibrium real interest rate and thus the effectiveness of its policy rule in meeting its domestic objectives. While in the simple models of Sections 3 and 4 the global drivers of the r*s are assumed to be observed and with known values of the parameters mapping them to neutral policy rates, in practice this is not the case and coordination in such signal extraction efforts could be very valuable.

As discussed above, to achieve the theoretical gains from monetary policy cooperation in these models it no longer suffices for the policymaker to follow an instrument rule based solely on domestic inflation and the neutral real interest rate. Instead, under cooperation the home

CLARIDA | 16

central bank must set the policy rate as a function of home and foreign variables. In its simplest form, this rule can be written as

⎛ ⎝⎜

⎞ ⎠⎟

⎛ ⎝⎜

⎞ ⎠⎟R r

λ ρ

αρ

σ E

σ

σ ϕ

λ ρ

αρ

σ E= + 1 +

(1 − ) + 1

2 π +

− 1

+ 1 + 2

(1 − ) + 1

2 π .t t tt t F

t ⁎

+1 +1 (19)

In sum, not only do the quantitative gains from time‐inconsistent cooperative monetary policy rules appear to be modest, but in addition the policy rules required to implement the cooperative outcome could well be difficult to communicate and to adhere to without sacrificing the credibility of the inflation target and the policy regime itself.

Yet another challenge to implementing in practice the sort of formal binding cooperative equilibrium modeled above is related to the Orphanides (2004) critique of real‐time information and the requirements required to implement some rule‐based policies. For example, the inputs to Equation (16) above include real‐time output gaps in both (all) countries, expected productivity growth in both countries, and the correct measure of inflation in each country. In practice, these inputs are unobservable and time‐varying and must be inferred from data.

5 | CONCLUDING REMARKS

We have reviewed some simple examples based on rigorous models which can (a) generate monetary policy correlation—via the global factor present in each country's equilibrium real interest rate; (b) rationalize the alleged benefits to monetary policy coordination; but (c) provide some intuition for why binding monetary policy cooperation is rare in practice if not in academic papers. The appeal of these models is that they are tractable and admit intuitive closed‐form solutions. That said, the models make assumptions about pricing (producer vs. local), and preferences (Cobb–Douglas and CES that satisfy the Cole–Obstfeld balanced trade conditions) that while common in the literature, are clearly special cases. Further research on the generality of the results in this paper is warranted. We have focused on the global factor in neutral real policy rates and shown how a plausible source of fluctuations in these rates (productivity growth with a global as well as country‐specific component) also can trigger adjustment in the nominal exchange rates. While we have assumed that productivity levels in each are stationary, all the results of this paper go through with nonstationary productivity if home and foreign productivity are cointegrated.

In the models of this paper, a country‐specific shock that pushes the expected path of the home r*t below the foreign r*t requires a depreciation of the home nominal exchange rate to maintain global equilibrium even with balanced trade. By contrast, a common global shock that depresses home and foreign neutral real policy rates equally will have no exchange rate implications. While these models are quite simple and in particular omit important potential additional drivers of neutral real policy rates—such as asset market imperfections and institutional and individual desires to hold safe assets—they are rich enough to shed light on the importance of global general equilibrium considerations in accounting for and inferring shifts in country neutral policy rates. One topic for future research is modeling medium and long horizon forecastable changes in neutral real policy rates as are estimated by HLW. The neutral real rates that we solve for in the models of Sections 3 and 4 are the rates consistent with the stochastic flexible prices equilibrium in these workhorse DSGE models and may be thought

17 | CLARIDA

of a “short run” r*s. In the models of Sections 3 and 4, the unconditional mean of these home and foreign r*s are constant and equal. A worthwhile extension beyond the scope of this paper would be to introduce nonstationary dynamics and or segmented trends (Rappoport & Reichlin, 1989) into relative productivity levels which would allow for a tighter linkage between the HLW econometric methodology and the theoretical modeling of time variation in r*.

ACKNOWLEDGMENTS

This paper was prepared for the Annual BIS Research Conference held June 23, 2017 in Lucerne, Switzerland. The author would like to thank Jordi Galí for sharing his insights on this and related topics.

ORCID

Richard Clarida http://orcid.org/0000-0003-4208-3732

REFERENCES

Bank of England. (2018). Inflation report, August. Calvo, G. A. (1983). Staggered prices in a utility‐maximizing framework. Journal of Monetary Economics, 12,

383–398. Clarida, R. (2014). Monetary policy in open economies: Practical perspectives for pragmatic central bankers.

Journal of Economic Dynamics and Control, 49, 21–30. Clarida, R., Galí, J., & Gertler, M. (1998). Monetary policy rules in practice: Some international evidence.

European Economic Review, 42, 1033–1067. Clarida, R., Galí, J., & Gertler , M. (1999). The science of monetary policy. Journal of Economic Perspectives, 37(4),

1661–1707. Clarida, R., Galí, J., & Gertler, M. (2000). Monetary policy rules and macroeconomic stability: Evidence and some

theory. Quarterly Journal of Economics, 115(1), 147–180. Clarida, R., Galí, J., & Gertler, M. (2002). A simple framework for international monetary policy analysis. Journal

of Monetary Economics, 49, 879–904. Clarida, R., & Waldman, D. (2008). Is bad news about inflation good news for the exchange rate? In J. Campbell,

& Campbell (Eds.), Asset prices and monetary policy (pp. 371–396). Chicago, IL: University of Chicago Press. Cole, H. L., & Obstfeld, M. (1991). Commodity trade and international risk sharing: How much do financial

markets matter? Journal of Monetary Economics, 28, 3–24. Engel, C. (2009). Currency misalignments and optimal monetary policy: A reexamination. National Bureau of

Economic Research, Working Paper 14829. Friedman, M. (1968). The role of monetary policy. The American Economic Review, 58(1), 1–17. Galí, J., & Monacelli, T. (2005). Monetary policy and exchange rate volatility in a small open economy. Review of

Economic Studies, 72, 707–734. Giannone, D., Reichlin, L., & Small, D. (2008). Nowcasting: The real‐time informational content of

macroeconomic data. Journal of Monetary Economics, 55(4), 665–676. Haldane, A. G. (2015). “Stuck”. Speech by chief economist. Bank of England, Open University, Milton Keynes,

June 29. Hamilton, J. D., Ethan, S. H., Hatzius, J., & West, K. D. (2016). The equilibrium real funds rate: Past, present, and

future. IMF Economic Review, 64(4), 660–707. Henderson, D. W., & McKibbin, W. J. (1993). A comparison of some basic monetary policy regimes for open

economies: Implications of different degrees of instrument adjustment and wage persistence. Carnegie‐Rochester conference series on public policy 39, 221–317. Amsterdam: North‐Holland.

CLARIDA | 18

Holston, K., Laubach, T., & Williams, J. C. (2017). Measuring the natural rate of interest: International trends and determinants. Journal of International Economics, 108, S59–S75.

IMF (2013). Dancing together? Spillovers, common shocks, and the role of financial and trade linkages. World Economic Outlook, October, 92‐112.

King, M., & Low, L. (2014). Measuring the “world” real interest rate. National Bureau of Economic Research, Working Paper 19887.

Kocherlakota, N., & Phelan, C. (1999). Explaining the fiscal theory of the price level. Quarterly Review‐Federal Reserve Bank of Minneapolis, 4, 14–23.

Krugman, P., Obstfeld, M., & Melitz, M. (2011). International economics. Upper Saddle River, NJ: Prentice Hall. Laubach, T., & Williams, J. C. (2003). Measuring the natural rate of interest. Review of Economics and Statistics,

85(4), 1063–1070. Obstfeld, M., & K. (2002). Global implications of self‐oriented national monetary rules. Quarterly Journal of

Economics, 117(2), 503–535. Orphanides, A. (2004). Monetary policy rules, macroeconomic stability, and inflation: A view from the trenches.

Journal of Money, Credit and Banking, 36, 151–175. Rachel, L., & Smith, T. (2015). Secular drivers of global real interest rates (Discussion Paper 571). London: Bank

of England. Rappoport, P., & Reichlin, L. (1989). Segmented trends and non‐stationary time series. The Economic Journal,

99(395), 168–177. Taylor, J. B. (1982). Macroeconomic tradeoffs in an international economy with rational expectations. In W.

Hildebrand (Ed.), Advances in economic theory (pp. 235–252). Cambridge, MA: Cambridge University Press. Taylor, J. B. (1993). Macroeconomic policy in a world economy: From econometric design to practical operation.

New York: W. W. Norton. Wicksell, K. (1898). Interest and prices: A study of the causes regulating the value of money, trans. R. F. Kahn.

London: Macmillan. Woodford, M. (2003). Interest and prices: Foundations of a theory of monetary policy. Princeton, NJ: Princeton

University Press. Yellen, J. L. (2017). The economic outlook and the conduct of monetary policy. Speech at the Stanford Institute

for Economic Policy Research, Stanford University, Stanford, California, January 19.

How to cite this article: Clarida R. The global factor in neutral policy rates: Some implications for exchange rates, monetary policy, and policy coordination. International Finance. 2019;22:2–19. https://doi.org/10.1111/infi.12345

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