Implementable rules for international monetary policy

coordination∗

Michael B. Devereux Charles Engel Giovanni Lombardo

University of British Columbia University of Wisconsin Bank for International Settlements

October 31, 2019

Abstract

While economic and financial integration can increase welfare, it can also complicate the policy

problem, bringing about new trade-offs or magnifying the existing ones. These policy challenges

can be particularly severe in the presence of large (gross) capital flows, e.g. for emerging market

economies. Having a quantitative assessment of these trade-offs is key for the design of effective

policy interventions. Using a Core-Periphery open-economy DSGE model with financial and nominal

frictions, we offer a quantitative assessment of the implied trade-offs and of operational policy tar-

geting rules that can bring about the highest global welfare. These rules need to trade off domestic

inflation variability with foreign factors and financial imbalances. We suggest a novel approach, based

on the SVAR literature, that can be used to represent targeting rules in rich models.

Keywords: Monetary policy; International Spillovers; Cooperation; Targeting Rules; Capital Flows;

Emerging Economies.

JEL code: E4; E5; F4; F5; G1.

∗This paper was prepared for the 19th Jacques Polak Annual Research Conference on “International Spillovers and

Cooperation”; Washington, D.C., November 1-2 2018. We thank Steve Wu and Nikhil Patel and the anonymous referees

for useful comments and suggestions, and Emese Kuruc and Burcu Erik for collecting the data. The views expressed in this

paper do not necessarily reflect the views of the Bank for International Settlements.

1

1 Introduction

What are the key dimensions that monetary policymakers should take into account in a financially

integrated world? In principle, international financial integration should provide countries with more

efficient means to finance growth, and effective ways to diversify their portfolios.1 While this should

improve welfare and thus facilitate the policy problem (by reducing the number of inefficiencies), the

recent international financial turmoil and the ensuing commentary emphasizes the downside of financial

globalization, pointing to an increased vulnerability to foreign shocks, particularly for emerging economies,

and thus to an increased complexity of the monetary policy problem (e.g. Rey, 2016 and Obstfeld, 2017).

A substantial literature has analyzed the nature of monetary policy in face of multiple distortions

in goods markets and domestic and international financial markets (see citations below). But there are

fewer papers that provide practical guidance for the policy-maker on the type of rules that should guide

monetary policy when the policy environment is constrained by these types of distortions. This paper

aims to address this question.

As an initial reference point, we focus on a modeling framework developed in Banerjee et al. (2016)

(BDL), which compares the international propagation of shocks under different monetary policy regimes

in an environment with nominal rigidities and multiple financial frictions in domestic and international

capital markets. That study finds that simple Taylor-type rules – traditionally deemed appropriate

when the key policy tradeoff stems from nominal rigidities (see e.g. Woodford, 2001) – perform quite

poorly in comparison to fully optimal rules (cooperative or non-cooperative) that take into account the

structure of international capital flows and financial frictions. But that paper does not elaborate on the

key dimensions that monetary policymakers should take into account when setting monetary policy in

financially integrated economies. That is the question addressed in the current paper.

In particular, we aim to provide more precise policy recommendations concerning the set of variables

that should guide monetary policy decisions in integrated economies, beyond traditional inflation and

output indicators. A large literature has discussed interest rate rules for open economies within models

that do not feature a prominent role for salient international capital movements, financial intermediation

and financial frictions.2 Some papers discuss the role of financial integration, but either in small-open-

economy models (e.g. Moron and Winkelried, 2005 and Garcia et al., 2011), or abstracting from the

strategic policy dimensions and thus not using welfare-based optimal policies as benchmarks. Most of

the focus in this literature has been on the role that the exchange rate should play in policy rules. Our

focus is rather on the role that financial factors, ranging from credit spreads to leverage and international

capital mobility, should play in informing monetary policy decisions. In addition, our aim in this paper

is to characterize monetary policy in terms of ‘targeting rules’ rather than instrument rules. Svensson

1The empirical evidence on these effects remains ambiguous. Prasad et al. (2007) found little support for this theoreticalprediction, although they point to confounding factors (governance, lack of regulation etc.) as a key source of meagreempirical evidence on the benefits of globalization.

2See for example Ball (1999), Taylor (2001), Laxton and Pesenti (2003), Kollmann (2002), Leitemo and Soderstrom(2005), Batini et al. (2003), Devereux and Engel (2003), Adolfson (2007), Svensson (2000), Devereux et al. (2006), Kirsanovaet al. (2006), Wollmershauser (2006), Galı and Monacelli (2005), Pavasuthipaisit (2010)

1

(2010) argues that targeting rules are more robust than instrument rules, and moreover, in practice,

monetary authorities do focus on targets (such as two percent inflation), and set instruments to achieve

these targets.

We use the model developed by BDL, which features standard nominal rigidities alongside financial

frictions and international financial interdependence. The first dimension gives rise to the traditional

inflation stabilization incentives, while the second provides incentives to stabilize credit spreads, as well

as to mitigate the negative consequences of international financial spillovers.

BDL have shown that in this model the non-cooperative optimal monetary policies imply responses

to shocks that are quite similar to those produced by cooperative policies. On the contrary, “standard”

Taylor-type policy rules, responding only to domestic inflation and output, generate allocations that

appear quite different from the optimal ones. BDL argue that taking the financial dimension explicitly

into account – not done by simple Taylor-type rules – can considerably improve outcomes. These authors,

though, do not compute the actual operational rules that would formally describe to which extent the

financial dimensions should be taken into consideration. Our paper extends the results obtained by BDL

by providing exactly these explicit operational rules emphasizing the role of financial frictions in shaping

the policy tradeoff. We adopt the definition of “simplicity” proposed by Giannoni and Woodford (2017,

p. 57), which is both precise and intuitive: A simple rule should i) exclude Lagrange multipliers; ii) have

a small number of target variables; iii) have a small number of lags; and iv) be independent of the exact

instrument chosen.

Optimal policy plans in theoretical models, and a fortiori in the real world, cannot be always easily

represented by simple rules. In some cases, exact simple rules might not exist at all. We thus look for

approximated simple rules with the properties indicated above that can bring about allocations that are

as close as possible to the truly optimal policies.

One way to achieve our goal would be to search for the parameter values of simple rules that maximize

the objective of the cooperative policymakers. While this avenue has been pursued in the literature, it is

not without problems and turns out to be unfeasible in our case.3 We argue that a practical alternative

strategy can be borrowed from the empirical macroeconomic literature, by gauging a simple, albeit

approximate, description of optimal monetary policy rules through the lens of SVARs. This approach

has the appeal that it uses the same tools and language used in recent econometric studies where monetary

policy is shown to respond to financial factors (e.g. Brunnermeier et al., 2017). By treating the DSGE

model as the data generating process, and by using a novel extension of recent SVAR identification

techniques, we isolate targeting rules for monetary policy that closely replicate the optimal monetary

policy outcomes derived in BDL. These rules indicate prominent roles for non-traditional factors (such

3In the context of our model, two issues make this strategy impractical. First, even assuming that each country followsa three-parameter Taylor-type rule (where the interest rate responds to the lagged interest rate, the inflation rate andoutput growth) the optimization algorithm converges to singularity points of the welfare function, with the latter assumingunreasonably large values: close to singularity points, the accuracy of the second-order approximation is bound to be verypoor. Arbitrarily constraining the admissible range of the parameters leads to corner solutions. Second, to keep computationtimes within hours instead of days (on a 12 cores 2.9 GHz Intel i9 HP workstation) the numerical search of the second-orderaccurate welfare maximum has to be reduced to a small number of parameters (around 3× 2), compared to the simple rulewe discuss in this paper (26× 2). Using the methodology described below considerably reduces the computational burden.

2

as credit spreads) in the description of optimal monetary policy.

The rest of the paper is organized as follows. Section 2 presents a simple example of our approach

to identifying targeting rules using the well-known two-equation linear New Keynesian model. Section 3

gives a brief outline of the model, essentially taken from BDL. Section 4 develops a quantitative analysis

of the model, while section 5, the core of the paper, explicates our approach to deriving optimal, simple

targeting rules and derives these rules. Finally, section 6 offers some conclusions.

2 Example: Recovering rules in the New-Keynesian model

In this section we provide a stylized example of how we aim to approximate optimal policies through

operational targeting rules.4

Consider the optimal policy problem in a variant of the canonical closed-economy New-Keynesian

(NK) model (Woodford, 2003). To illustrate the point at issue, we augment the canonical NK model

with (external) consumption habits and working capital (e.g. Christiano et al., 2005). The role of these

assumptions will appear evident in the derivation of the policy problem.

This simple model (in linearized form) consists of a consumption Euler equation (translated in terms

of output gap xt) and a Phillips curve for inflation (πt), i.e.

Etxt+1 = (1 + h)xt − hxt−1 + αEt (it − πt+1 − i?t ) (2.1)

πt = βEtπt+1 + κ (xt + νt) + ρit (2.2)

where it is the nominal interest rate, i?t is the real natural rate of interest (i.e. a convolution of distur-

bances, including productivity shocks), xt is the output gap, πt is the inflation rate, νt is a cost-push

shock, β ∈ (0, 1) is the households’ time-preference factor, α > 0 is the intertemporal elasticity of substi-

tution, κ > 0 is a coefficient involving a measure of price rigidity, the discount factor, ρ > 0 parametrizes

the effect of working capital, and h ∈ (0, 1) measures the importance of consumption habits. To ease our

illustration, we assume that all shocks are mean-zero, unit-variance iid stochastic processes.

In order to close the model we must specify the behaviour of the monetary authority, as inflation (or

equivalently the nominal interest rate) is not pinned down by the decentralized behavioral equations. For

simplicity we describe the loss function of the monetary authority as

Lt = Et1

2

∞∑i=0

βi[(πt+i − π?t+i

)2+ λxx

2t+i

](2.3)

where a π?t is the inflation target. For the sake of illustration, we assume that the inflation target is a

stochastic process (a policy preference shock).

Minimizing equation (2.3) in terms of πt, xt and it, subject to equations (2.1) and (2.2) yields the

following first order conditions (where φj ; j = 1, 2 are Lagrange multipliers),

4This section summarizes the key insights, relevant for our analysis, of Giannoni and Woodford (2003a,b) and of theSVAR literature (e.g. see Rubio-Ramirez et al., 2010, for a recent survey).

3

π : πt − π?t − αβ−1φ1,t−1 − φ2,t + φ2,t−1 = 0 (2.4a)

x : λxxt + (1 + h)φ1,t − hβEtφ1,t+1 − β−1φ1,t−1 + κφ2,t = 0 (2.4b)

i : αφ1,t + ρφ2,t = 0. (2.4c)

This system can be further simplified as

π :πt − π?t −α

ρφ1,t +

(α

ρ− αβ−1

)φ1,t−1 = 0 (2.5)

x :φ1,t =ρ

β (ρ (1 + h) + κα)φ1,t−1 +

hβρ

(ρ (1 + h) + κα)Etφ1,t+1 −

λxρ

(ρ (1 + h) + κα)xt (2.6)

In the special case of ρ = 0, i.e. the canonical NK model, rearranging these equations would yield the

well known optimal targeting rule for this model, i.e.

πt = −λxκ

(xt − xt−1) + π?t (2.7)

In general however, it might be the case that such simple representation is not feasible, e.g. when

ρ 6= 0 in our example.

Even in this case though, a further simplification is feasible if h = 0. In this case we could still

eliminate the Lagrange multipliers, expressing (2.6) as an infinite sum of lagged output gaps,5 i.e.

φ1,t = −∞∑j=0

(ρ

β (ρ+ κα)

)jλxρ

(ρ+ κα)xt−j (2.8)

By replacing this in equation (2.5) we get a “simple” rule that excludes Lagrange multipliers, i.e.

πt − π?t +

∞∑j=0

(ρ

β (ρ+ κα)

)jλxρ

(ρ+ κα)

(α

ρxt−j −

(α

ρ− αβ−1

)xt−1−j

)= 0 (2.9)

One obvious drawback of this simplified representation of the optimal policy is that it involves an infi-

nite sum. In practice though, a relevant question is how many lags are necessary in order to approximate

the optimal rule sufficiently well.6

Finally, if ρ > 0 and h > 0, the simple backward iteration will not eliminate the multipliers. In this

case, a practical question is to what extent the optimal rule can be approximated by a simpler rule that

omits the multipliers.

We can think of various ways in which this question could be answered. First, one could search for the

simple rule that yields the highest cooperative welfare using the second-order approximation of the DSGE

model. Second, one could represent the candidate target variables as a VAR of order p and identify the

simple policy rule by matching IRFs produced by the model under the fully optimal cooperative policy.

5This is obviously possible only if certain parameter restrictions are satisfied, so that the sum converges. This would bethe case for small enough values of ρ in our example.

6Beyond this simple model, even eliminating all the Lagrange multipliers could leave us with a rule involving a verylarge number of variables. One further dimension of approximation would then consist of replacing some of the endogenousvariables too. In this case, the accuracy of the approximation would inform us about which variables play a more importantrole in the rule (at the selected lag length).

4

Within this approach two alternative ways could be pursued in principle. The first consists of using

the theoretical state-space solution of the model to generate the approximated VAR(p). The second

consists of estimating the VAR(p) using simulated data from the DSGE model under the fully optimal

cooperative policies, and then identify the monetary policies in the same way as done in the empirical

SVAR literature (e.g. Rubio-Ramirez et al., 2010). We follow the latter approach. In doing so we are

mindful of the potential pitfalls of representing a DSGE model by a finite order VAR that omits a number

of state variables (see for example Fernandez-Villaverde et al., 2007 and Ravenna, 2007). This said, we

adopt a heuristic approach consisting of estimating a small-dimension VAR that includes only candidate

target variables, and assessing its performance against the true (model) impulse responses. 7

The SVAR that we seek to estimate is thus

A0zt = A1zt−1 + εt (2.10)

where z′t = [πt, xt, it] and ε′t = [νt, π?t , i

?t ]. If equation (2.10) approximates the dynamics of the true zt

sufficiently well, then the second equation in (2.10), corresponding to the policy shock, must be the policy

rule (Leeper et al., 1996).

We can estimate a reduced-form version of (2.10), i.e.

zt = Azt−1 + ut (2.11)

where E(utu′t) = Σu. The SVAR (2.10) is recovered, and the policy rule identified, if there is a matrix

C = A−10 such that ut = Cεt and, thus, Σu = C ′C. In this paper we use IRFs matching to identify a

monetary policy shock, and thus to find C as explained further below.

Finally, as mentioned above, in this paper we are not comparing the relative efficiency of alternative

solution methods: our paper is not primarily a methodological contribution. But our argument, which

is developed at length below, is that this method is simple, computationally parsimonious (relative to

direct optimization of simple rules), and seems to work well in the application we pursue.

3 The Model

Our results are structured around the two country core-periphery model developed by BDL.8 We denote

the periphery economy (sometimes called the Emerging Market Economy, or EME) with the superscript

‘e’ and the center country (sometimes called the Advanced Economy, or AE) with the superscript ‘c’.

The schemata for our model is described in Figure 1.

In both countries there are households, leveraged financial intermediaries (banks),9 capital goods

7We also note that although DSGE models cannot always be represented by finite order VARS, this is the approximationemployed in empirical work. In addition, if the real world data corresponds to the model, then the misspecification shouldapply both to the data and the simulations generated by the model (see Cogley and Nason, 1995). In our case, the ‘data’corresponds to the simulations from the model under the optimal rule, which can then be compared to that generated usingthe estimated targeting rule.

8More details about this model can be found in Banerjee et al. (2015). The whole list of equation is provided in AppendixE.

9In the remainder of the paper, to simplify the discussion, we will refer to capital goods financiers in both the center

5

producers, production firms, and a monetary authority. There is also a global capital market for one-

period risk free bonds. The key difference between the two countries is that the center country banks

borrow exclusively from local households, while the periphery country banks can borrow from local

households, up to a limit,10 and from the foreign global financiers. Banks in both countries finance

local intermediate goods producers who need to purchase capital from capital goods producers. To this

purpose, firms sell to banks securities whose return is contingent on the return on capital (as in Gertler and

Karadi, 2011). This set-up is equivalent to banks trading directly in physical capital: an interpretation

we maintain in the rest of the paper for the sake of parsimony.

There are two levels of agency constraints; global banks must satisfy a net worth constraint in order

to be funded by their domestic depositors, and local EME banks in turn must have enough capital in

order to receive loans from global banks and domestic depositors. In both countries, the intermediate-

goods firms use capital and labour to produce differentiated goods, which are sold to retailers. Retailers

are monopolistically competitive and sell to final consumers, subject to a constraint on their ability

to adjust prices. This set of assumptions constitutes the minimum arrangement whereby capital flows

from advanced economies to EMEs have a distinct directional pattern, financial frictions act to magnify

capital-flow spillovers, and (due to sticky prices) the monetary policy regime may have real consequences

for the nature of spillovers and economic fluctuations.

The emerging country is essentially a mirror image of the center country, except that households in

the emerging country cannot fully finance local banks, but instead engage in inter-temporal consumption

smoothing through the purchase and sale of center currency denominated nominal bonds.11 Banks in

the emerging market use their own capital and financing from global financiers to make loans to local

entrepreneurs. The net worth constraints on banks in both the emerging market and center countries are

motivated along the lines of Gertler and Karadi (2011).

The goal of monetary policymakers is to respond to domestic and foreign shocks in order to maximize

welfare of the domestic households. This amounts to reducing the welfare losses emerging from two

frictions: nominal rigidities and agency problems in the financial sector.

3.1 The Emerging Market Economy (EME)

A fraction n of the world’s households live in the emerging economy. Households consume, work, trade in

foreign and (partially) in domestic financial assets, and act separately as bankers. A banker member of

and peripheral countries as banks. It should be noted however that the key thing that distinguishes them is that they makelevered investments, and are subject to contract-enforcement constraints. In this view, they need not be literally banks inthe strict sense.

10This assumption is meant to capture the feature that within-country financial intermediation between savers andinvestors is more difficult in EMEs than in advanced economies (see e.g. Mendoza et al., 2009). The assumption emphasizesthe strong influence that core-country financial conditions exert on EME financial markets. As discussed below EMEdomestic deposits act mainly to reduce the financial spillover but don’t alter the qualitative properties of the cross-bordertransmission channel. Therefore, in the main results we assume that domestic deposits in EME are constrained to be zero.See also Cuadra and Nuguer (2018).

11We assume that the market for center country nominal bonds is frictionless. Adding additional frictions that limitthe ability of emerging market households to invest in center country nominal bonds would just exacerbate the impact offinancial frictions that are explored below.

6

a household has probability θ of continuing as a banker, upon which she will accumulate net worth, and

a probability 1 − θ of exiting to the status of a consuming working household member, upon which all

net worth will be deposited to her household’s account. In every period, non-bank household members

are randomly assigned to be bankers so as to keep the population of bankers constant.

EME households have limited access to the local financial market. In particular they can deposit

in local financial intermediaries up to an exogenous fraction of total bank liabilities: a limit necessary

to ensure “financial dependence” of the EME. Households can also trade in international bonds (Bet )

with foreign agents. These bonds can be thought of as T-bills of the core country (rebated directly

to core-country households), deposits at core-country financial intermediaries, or simply bonds traded

directly with core-country households. Under the assumptions of our model these three alternatives are

equivalent.12

Households in the EME have preferences over (per capita) consumption Cet and labor Het supply given

by:

E0

∞∑t=0)

βt

(Ce(1−σ)t

1− σ− H

e(1+ψ)t

1 + ψ

)

where consumption is broken down further into consumption of home (Cee,t) and foreign (Cec,t) baskets as

Cet =

(ve

1ηC

e η−1η

e,t + (1− ve)1ηC

e η−1η

c,t

) ηη−1

Here η > 0 is the elasticity of substitution between home and foreign goods, ve ≥ n indicates the presence

of home bias in preferences,13 and we assume in addition that within each basket, goods are differentiated

and within country elasticities of substitution are σp > 1.

The price index for EME households is

P et =(veP 1−η

e,t + (1− ve)P 1−ηc,t

) 11−η

.

Then the household budget constraint is described as follows

P et Cet + StP

ct B

et + P et D

et = P etW

et H

et + Πe

t +R∗t−1StPct−1B

et−1 +Ret−1P

et−1Dt−1.

Households purchase dollar (center country) denominated debt (Bet ), paying the gross nominal return

R∗t−1, and local-currency deposits (Det ), paying the gross nominal return Ret−1. St is the nominal exchange

rate (price of center country currency). They consume home and foreign goods. W et is the real wage, and

Πet represents profits earned from banks and firms, net of new capital infusion into new banks. Households

have the standard Euler and labor supply conditions described by the following first-order conditions

12In particular we are not assuming a special role for government debt, nor asymmetries in the degree to which thecontract between depositors and core-country banks can be enforced.

13Home bias is adjusted to take into account of country size. In particular, for a given degree of openness x ≤ 1,ve = 1− x(1− n), and a similar transformation for the center country home bias parameter.

7

Bet : EtΛet+1|t

R∗tπet+1

St+1

St= 1 (3.1)

Det : EtΛ

et+1|t

Retπet+1

= 1 (3.2)

Het :

W et

P et= Ceσt Heψ

t (3.3)

where Λet|t−1 ≡ β(

CetCet−1

)−σ, and πet+1 ≡

P et+1

P et.

Given two-stage budgeting, it is straightforward (and omitted here) to break down consumption

expenditure of households into home and foreign consumption baskets (see Appendix E for the full list

of equations).

3.1.1 Capital goods producers

Capital producing firms in the EME buy back the old capital from banks at price Qet (in units of the

consumption aggregator) and produce new capital from the final good in the EME economy subject to

the following adjustment cost function:

Γ(Iet , I

et−1

)≡ ζ

(IetIet−1

− 1

)2

Iet

where Iet represents investment in terms of the EME aggregator good.

EME banks then finish the capital goods and rent them to intermediate goods producers.14

Ket = Iet + (1− δ)Ke

t−1

where Ket is the capital stock in production.

3.1.2 EME banks

EME banks begin with some bequeathed net worth from their household, and continue to operate with

probability θ. The net-worth value of the fraction 1− θ of discontinued banks is paid to households lump

sum. We also follow Gertler and Karadi (2011) in the nature of the incentive constraint. Ex ante, EME

banks have an incentive to abscond with borrowed funds before the investment is made. Consequently,

conditional on their net worth, their leverage must be limited by a constraint that ensures that they have

no incentive to abscond.

At the end of time t, a bank i that survives has net worth given by Nei,t in terms the EME good. It can

use this net worth, in addition to debt raised from the global bank, to invest in physical capital at price

Qet in the amount Kei,t+1. Banks liabilities consists of local-currency domestic deposits and loans from

14Equivalently, we could assume that the bank provides risky loans to intermediate goods producers, who use the fundsto purchase capital. The only risk of this loan concerns the (real) gross return on the underlying capital stock.

8

the global bank denominated in center country currency. In real terms (in terms of the center country

CPI), we denote this debt as V ei,t. Thus, EME bank i′s balance sheet is given by

Nei,t +RERtV

ei,t +De

i,t = QetKi,t (3.4)

where RERt =StP

ct

P etis the real exchange rate.

Bank i′s net worth is the difference between the return on previous investment and its gross debt

payments to the global bank and the local depositors.

Nei,t = Rek,tQ

et−1K

ei,t−1 −RERt

Rv,t−1

πctV ei,t−1 −

Ret−1

πetDet−1 (3.5)

where Rv,t−1 is the nominal interest rate received by the global bank, πct ≡P ctP ct−1

is core-country inflation

and Rek,t is the gross return on capital defined below.

Once the bank has made the investment, at the beginning of period t+ 1 its return is realized.

Because it has the ability to abscond with the proceeds of the loan and its existing net worth, the

loan from the global bank must be structured so that the EME bank’s continuation value from making

the investment exceeds the value of absconding. Following Gertler and Karadi (2011), we assume that

the latter value is κet times the value of existing capital ( κet is a random variable, and represents the

stochastic degree of the agency problem). Hence denoting the bank’s value function by Jei,t, it must be

the case that

Jei,t ≥ κetQetKei,t. (3.6)

This is the incentive compatibility constraint faced by the bank.

Since the cost of international funds in equilibrium will be higher than the cost of domestic funds,

due to the intermediation layer and the existence of international arbitrage opportunities for households,

EME banks would always choose to finance themselves locally. To avoid this corner solution we impose

that domestic deposits cannot be larger than a fraction ψD−1ψD

of total liabilities, with ψD ≥ 1 being an

exogenous parameter. In equilibrium EME banks will always be at the constraint, i.e.

Dei,t = (ψD − 1)RERtV

ei,t (3.7)

The problem for an EME bank at time t is described as follows:

Jei,t = max[Kei,t,V

ei,t,D

ei,t]EtΛ

et+1|t

[(1− θ)Ne

i,t+1 + θJei,t+1

](3.8)

subject to equations (3.4), (3.6) and (3.7).

The full set of first order conditions for this problem are set out in Appendix E.

The evolution of net worth averaged across all EME banks, taking account that banks exit with

probability 1 − θ, and that new banks receive infusions of cash from households at rate δT times the

9

existing value of capital, can be written as:

∫Nei,tdi = Ne

t = θ

[(Rek,t −

RERtRERt−1

Rv,t−1

ψD

)Qet−1K

et−1 +

RERtRERt−1

Rv,t−1

ψDNet−1

]+ δTQ

etK

et−1, (3.9)

where Rv,t−1 =

(Rv,t−1

πct+Ret−1

πet(ψD − 1)

).

The term in square brackets on the right hand side of equation (3.9) captures the increase in net

worth due to surviving banks, given their average return on investment. The second term represents the

“start-up” financing given to newly created banks by households.

3.2 Firms

A first set of competitive firms hire labour and capital to produce intermediate goods. The representative

EME firm has production function given by:

Y et = AetHe(1−α)t K

e(α)t−1

Given this, then we can define the aggregate return on investment for EME banks (averaging across

idiosyncratic returns) as

Rek,t =Rezt + (1− δ)Qet

Qet−1

where Rzt is the rental rate on capital and δ is the depreciation rate on capital.

The representative EME firm chooses labour and capital so as to minimize costs, yielding the following

efficient demands for factors

MCe,t(1− α)AetHe(−α)t K

e(α)t−1 = W e

rt (3.10)

MCe,tαAetH

e(1−α)t K

e(α−1)t−1 = Rezt (3.11)

where MCe,t is the real marginal cost of production. Intermediate-goods firms sell their output at the

marginal cost.

A second set of firms purchase intermediate goods, re-brand them at no additional costs and sell the

differentiated goods in monopolistically competitive markets. This set of firms sets prices infrequently a

la Calvo (1983), which implies the following specification for the PPI rate of inflation πPPIe,t in the EME:

π∗i,e,t =σp

σp − 1

Fe,tGe,t

πPPIe,t (3.12)

Fe,t = Ye,tMCe,t + Et[βςΛet,t+1π

PPIe,t+1

ηFe,t+1

](3.13)

Ge,t = Ye,tPe,t + Et[βςΛet,t+1π

PPIe,t+1

−(1−η)Ge,t+1

](3.14)

πPPIe,t1−η = ς + (1− ς)

(π∗i,e,t

)1−η(3.15)

10

where π∗i,e,t denotes the inflation rate of newly adjusted goods prices, Fe,t and Ge,t are implicitly defined,

andσpσp−1 represents the optimal static markup of price over marginal cost.

3.3 Center country (AE)

Except for banks, the center country sectors are identical to the peripheral country. Banks differ instead

both in terms of funding and investments.

3.3.1 Center country banks

A representative global bank j has a balance sheet constraint given by

V ej,t +QctKcj,t = N c

j,t +Dcj,t (3.16)

where V ej,t is investment in the EME bank, and QctKcj,t is investment in the center country capital stock.

N cj,t is the bank’s net worth, and Dc

j,t are deposits received from domestic households. All variables are

denominated in real terms, (in terms of the center country CPI).

The global bank’s value function can then be written as:

Jcj,t = Et maxKcj,t+1,V

ej,t,D

cj,t

Λct+1|t[(1− θ)N c

j,t+1 + θJcj,t+1

](3.17)

where

N cj,t+1 +

Rctπct+1

Dcj,t = Rck,t+1Q

ctK

cj,t +

Rv,tπct+1

V ej,t. (3.18)

Here, Λct+1|t is the stochastic discount factor for center country households, Rv,t is, as described above,

the return on the global bank’s loans to the EME bank, and Rct is the nominal interest rate paid to

domestic depositors.

The bank faces the no-absconding constraint:

Jj,t ≥ κct(V ej,t +Qc,tK

cj,t

)(3.19)

where, as in the EME case, κct measures the degree of the agency problem, and as before we assume it is

subject to exogenous shocks.

The full set of first order conditions for the global bank are discussed in detail in Appendix E.2. As

in the case of the EME banks, we can describe the dynamics of net worth for the global banking system

by averaging across surviving banks, and including the ‘start-up’ funding provided by center country

households. We then get the following law of motion for net worth

N ct = θ

((Rck,t −

Rct−1

πct

)Qct−1K

ct−1 +

(Rv,t−1

πct−Rct−1

πct

)n

1− nV et−1 +

Rct−1

πctN ct−1

)+ δTQ

ctK

ct−1. (3.20)

where we have used the fact that∫V ej,tdj = n

1−nVet .

Again, the details of the production firms and price adjustment in the center country are identical to

11

those of the EME economy.

3.4 Exogenous shocks

We consider three different types of exogenous shocks per country: TFP, financial and policy shocks. All

shocks are modeled as autoregressive processes of order one.

3.5 Monetary policy

We use various characterizations of monetary policy, depending on our specific objective. As a baseline

for the description of the properties of our model, we assume that central banks in each country follow

an interest rate rule similar to those used in estimated DSGE models (see in particular Del Negro et al.,

2013), i.e.

logRj,t = λr,j logRj,t−1 + (1− λr,j)

(λπ,j

4

3∑i=0

log

(πjt−i

πjss

)+λy,j

4log

(Y jt

Y jt−3

))+ εjr,t : j = e, c,

(3.21)

where εjr,t is a monetary policy shock. Note that the use of (3.21) is not put forward as one contender

in a ‘horse-race’ between alternative monetary rules. As noted above, we are primarily interested in

characterizing optimal monetary targeting rules, while (3.21) is an instrument rule. Certainly we could

think of extended versions of (3.21) incorporating financial variables that would more approximate an

optimal cooperative (or non-cooperative) monetary policy. But we use (3.21) simply as a baseline for

comparison, showing what outcomes would look like if monetary policy ignored financial constraints.

For the policy exercises we first derive the optimal cooperative and non-cooperative policies as dis-

cussed further below, and then derive simple targeting rules that can approximate the fully optimal rules

sufficiently well.

3.5.1 Optimal monetary policies

Following BDL we consider two alternative optimal policy regimes: i) Optimal policy under cooperation;

and ii) Optimal policy under non-cooperation (Nash equilibrium). Only after confirming that under

our calibration, as in BDL, the Nash and cooperative policies generate very similar responses of the

economies to shocks, we will focus our analysis on the derivation of simple approximately optimal rules

under cooperation.

The non-cooperative frameworks require an explicit definition of policy instruments. The “Taylor-

rule” framework consists of setting the nominal interest rate in response to a subset of variables. The

optimal non-cooperative framework cannot be set in terms of policy rates, for reasons akin to the “indeter-

minacy” of Sargent and Wallace (1975).15 We focus on the case in which PPI inflation is the instrument

of the non-cooperative game.

15See for example , and the discussion in Blake and Westaway (1995) and Coenen et al. (2009).

12

The two optimal-policy frameworks can be defined more precisely as follows:

Definition 1 (Cooperative policy problem). Under the cooperative policy (CP ) problem both policymak-

ers choose the vector of all endogenous variables Θt excluding the policy “instruments”, and the policy

instruments πPPI,et and πPPI,ct in order to solve the following problem

WCP,0 ≡ maxΘt,π

PPI,et ,πPPI,ct

[nWc0 + (1− n)We

0 ] , (3.22)

subject to

EtF(

Θt+1,Θt,Θt−1, πPPI,et+1 , πPPI,ct+1 , πPPI,et , πPPI,ct , πPPI,et−1 , πPPI,ct−1 ,Φt+1,Φt,Φt−1; γ

)= 0, (3.23)

where households’ welfare is defined as

Wj0 = E0

∞∑t=0

βt

(Cj(1−σ)t

1− σ− H

j(1+ψ)t

1 + ψ

), (3.24)

where Ct is consumption, Ht is labor, β ∈ (0, 1) is the discount factor (common across countries and

shared by policymakers), ψ > 0 and σ > 0 are preference parameters, Φt, is the vector of all exogenous

shocks, γ is the parameter measuring the importance (loading) of the exogenous shocks in the model (γ = 0

implies that the model is deterministic), and F (·) is the set of equations representing all the private sector

resource constraints, the public-sector constraints, and all first-order conditions solving the private sector

optimization problems.

Furthermore, the policymaker is subject to the “timeless-perspective” constraint, which defines the

t = 0 range of possible policy interventions (see Benigno and Woodford, 2012).

Denoting by the conformable vector Γt the vector of Lagrange multipliers on the constraint (3.23),

the first order conditions of this problem can be defined as

EtP(

Θt+1,Θt,Θt−1, πPPI,et+1 , πPPI,ct+1 , πPPI,et , πPPI,ct , πPPI,et−1 , πPPI,ct−1 ,Φt+1,Φt,Φt−1,Γt+1,Γt,Γt−1; γ

)= 0,

(3.25)

We can then state the following:

Definition 2 (Cooperative Equilibrium). The cooperative equilibrium is the set of endogenous variables

(quantities and relative prices) and policy instruments, such that given any exogenous process Φt equations

(3.23) and (3.25) are jointly satisfied ∀t.

The (open-loop) non-cooperative policy problem can be defined as follows:

Definition 3 (Non-cooperative policy problem). Under the non-cooperative policy (NP ) problem , each

policymaker chooses independently all endogenous variables and her own instrument in order to solve the

following problem

WjNP,0 ≡ max

Θt,πPPI,jt

Wj0 : j = e, c, (3.26)

13

subject to

EtF(

Θt+1,Θt,Θt−1, πPPI,et+1 , πPPI,ct+1 , πPPI,et , πPPI,ct , πPPI,et−1 , πPPI,ct−1 ,Φt+1,Φt,Φt−1; γ

)= 0. (3.27)

Furthermore, the policymaker is subject to the “timeless-perspective” constraint, which defines the

t = 0 range of possible policy interventions.

The first order conditions of this problem can be defined as

EtPj(

Θt+1,Θt,Θt−1, πPPI,et+1 , πPPI,ct+1 , πPPI,et , πPPI,ct , πPPI,et−1 , πPPI,ct−1 ,Φt+1,Φt,Φt−1,Γ

jt+1,Γ

jt ,Γ

jt−1; γ

)= 0,

(3.28)

where Γjt is a vector of Lagrange multipliers related to the constrained maximization problem of the j

policymaker, where j = e, c.

We can then state the following definition:

Definition 4 (Nash Equilibrium). The non-cooperative (Nash) equilibrium is the set of endogenous

variables (quantities and relative prices) and policy instruments, such that, for any exogenous process Φt,

equations (3.27) and (3.28), both for j = e and j = c, are jointly satisfied ∀t.

4 Quantitative analysis

4.1 Parameterization

The structural parameters of the model are fixed at values prevailing in the related literature and reported

in Table A.1. Most of our analysis is independent of the relative standard deviation of the exogenous

shocks, as we are seeking to approximate the optimal policy, which is invariant to the relative exogenous

volatility. That being said, in order to assess whether the relative magnitude and volatility of the

endogenous variables of our model is commensurate to their empirical counterparts, we estimate the

standard deviations of the exogenous processes (for given structural parameters) using an SMM approach.

In particular we estimate the standard deviations using data for the US ( as representative of an AE)

and the median of a set of 16 Emerging Market Economies. As shown in Appendix B conditional on the

estimated standard deviations, our model can deliver second moments for the key macro aggregates that

are in the ballpark of the empirical counterparts.

In the main analysis we restrict the EME local deposits to zero. In this way we can emphasize the

role of global capital markets for EMEs financial conditions. As shown in Appendix F, introducing local

deposits would reduce the elasticity of EME spreads to AE spreads (since, mechanically, the latter take

a smaller share of the cost of EME banks’ liabilities). In principle we could have allowed for some local

deposits and worsen the agency problem between EME and AE banks at the same time (through κe,t

and/or a differentiated κc,t for cross-border loans). We opted for keeping the agency problem symmetric

across countries.

14

4.2 Spillovers and monetary policy trade-offs

We have assumed that policymakers aim to maximize households’ welfare, nationally or globally depend-

ing on the cooperative regime. This amounts to tackling inefficiency wedges that drive a gap between

the efficient allocation and the actual equilibrium.

There are four kinds of inefficiencies in our model. First, prices do not adjust efficiently to shocks.

A price-dispersion wedge ensues, which is the classical inefficiency in New-Keynesian models. Second,

financial markets are imperfect, generating a wedge between the policy rate and the cost of capital:

the credit spread. Third, households’ risk sharing is incomplete, creating a wedge between households’

marginal utilities across countries. Fourth, international goods markets are not perfectly competitive,

creating a demand externality, and thus a wedge between the actual allocation and the distribution of

global demand that is optimal from a social planner point of view. When all these wedges are closed,

there is no further role for monetary policy. Of these wedges, nominal rigidities play a crucial role, since

in their absence monetary policy would have no traction, except for its effect on nominal debt contracts.

To gain intuition on how these wedges affect the economy, we compare the response to shocks of

the inefficiency-ridden economy with the response of the frictionless economy: essentially captured by an

international real business cycle model. When nominal rigidities are present, the response of the economy

to shocks depends on policy. In this case our benchmark is a NK model with only price rigidities and a

simple rule that links the nominal rate to current inflation.

4.2.1 Flexible prices: The effect of financial frictions

Figure 2 shows the response of a TFP shock in AE, with and without financial frictions (circled- and

dashed-line respectively). Relative to a standard IRBC, in this economy there is still a round-about

of funds to finance EME’s capital. This round-about is frictionless, so that it does not constitute an

incentive for a social planner to change allocations. Upon the TFP shock AE’s GDP increases while

EME’s GDP contracts. Real rates (i.e. the policy rate with constant inflation) fall in both countries.

Financial frictions alter this picture particularly for the EME. Credit spreads in the center country

fall, thanks to the positive development in asset prices. The ensuing fall in the cost of capital generates a

further boost in aggregate activity (only marginally for AE). The international financial interdependence

implies an easing of the financial condition in EME too, and due to the double-layer of financial friction

this easing is even stronger than in the center country. Net worth reflects this improvement across the

border (net worth is irrelevant absent financial frictions). As a consequence of the lower cost of funds,

GDP in the EME increases considerably and persistently (after the second quarter) instead of contracting,

despite a stronger appreciation of the real exchange rate.

Figure 3 shows the response of the two economies to a pure (contractionary) financial shock (a

positive κ shock) in the AE. The first noticeable effect of this shock is the co-movement across countries.

GDP falls in both countries, although more gradually in the EME. When financial markets are integrated

and and there are financial frictions, financial shocks can generate synchronized responses across countries.

15

The co-movement of credit spreads (the gaps between the return on capital and domestic policy rates) is

the main driver of these business cycle co-movements. The fall in GDP in the EME is larger than that

in the AE (the origin of the shock). This is mostly due to the differences in the size of the two countries.

What should policy do in this case? To reproduce the frictionless allocation, in response to TFP

(financial) shocks policymakers should counter the fall (increase) in credit spreads , e.g. by generating

a relatively more contractionary (expansionary) path of real rates. Under flexible prices this could still

be achieved to some extent by exploiting the fact that debt contracts are nominal: the ex-post value of

debt repayments depends on inflation and on the real exchange rate. Under sticky prices, the traction of

monetary policy is much stronger, but policymakers must now confront the price-dispersion wedge too.

We turn to this case in the next section.

4.3 The optimal cooperative and non-cooperative policy

We begin by solving for the optimal monetary policies, and for reference comparing them with the baseline

policy represented by the Taylor rule (3.21). Figure 4 shows the response of the world economy to the TFP

shock in the center country, under three different monetary policy regimes: Cooperation (dashed line);

Nash (solid line); and Taylor rule (circled line). The responses under cooperative and non-cooperative

policies are relatively similar compared to those under the Taylor rule (though less so on impact). The

Taylor rule generates too little expansion across countries, especially beyond the first quarter. On the

contrary, the optimal policies engineer a larger contraction in spreads that stimulates production. In

particular, the real rate in the center country falls persistently (nominal rate minus CPI inflation). This

induces less volatility in inflation in AE than under Taylor. In EME, the opposite is true. On impact the

cooperative policy brings about more cross-country production switching, and only in the medium term

engineers an expansion of production.

In line with the results of BDL, Figure 4 shows that the baseline Taylor rule does not come sufficiently

close to replicating the optimal response to the TFP shock, either the optimal cooperative solution or

the non-cooperative (Nash) solution. This then raises the key question of the present paper - how

to characterize an operational monetary policy rule which is implied by the optimal policy outcomes

described above? As noted in section 2, there are a number of alternative approaches we could follow in

characterizing optimal rules within this model. In the next section, we outline our method for deriving

simple optimal targeting rule.

5 Identification of simple optimal policy rules

We have seen that simple Taylor rules imply adjustments to shocks that are considerably different from

those implied by the cooperative allocation. On the contrary, the non-cooperative optimal policies do

comparatively better. It is reasonable thus to believe that the simple Taylor rule performs poorly because

it neglects important dimensions of our relatively more complex model. In particular the baseline Taylor

16

rule does not react to variables that are better indicators of the financial inefficiency wedge and of

international spillovers. We thus want to look for operational rules that mimic as close as possible either

the cooperative or the non-cooperative policies, i.e. rules that generate IRFs very close to those obtained

under optimal policies.

In searching for simple good approximations to the truly optimal policies we apply two main criteria.

First the rules should strike a balance between limiting the number of variables and lags involved in the

rule on the one hand, and approximation error on the other. Second, following Giannoni and Woodford

(2017), we wish to characterize the optimal policy in terms of market allocations and prices only, i.e.

excluding the Lagrange multipliers of the policy problem. Self-evidently, a practical rule for monetary

policy implementation should include only economically observable variables that are available to the

policy-maker in real time.

Deriving simple (approximately optimal) rules analytically is not feasible in our model. One alterna-

tive would be to assume that policy is conducted using simple linear feedback (or instrument) rules on

a subset of variables, and then choose the coefficients of the rules by maximizing an objective function

(e.g. global welfare or country specific welfare). This is the strategy commonly used in the literature

(e.g. Coenen et al., 2009). A practical drawback of this approach is that without prior knowledge of the

number of variables and lags necessary to yield good results, experimentation can be very computation-

ally intensive.16 Moreover, as argued above, our primary objective in this paper is to identify monetary

policy in the form of targeting rules, which involve trade-offs between alternative variables that policy

makers should make as part of an optimal policy. In this model, a targeting rule would involve trade-offs

among a relatively large number of variables, including lags. Iterating over parameters of this trade-off to

obtain an optimal rule would be computationally infeasible. As a result, we follow an alternative route.

In particular we follow a strategy inspired by the empirical monetary macroeconomics literature. The

VAR literature (e.g. Sims, 1980, and Sims, 1998, Leeper et al., 1996) tells us that identifying monetary

policy shocks amounts to identifying the structural policy equation for monetary policy. Furthermore,

we know that identification can be achieved (among other approaches) by sign restrictions on IRFs (e.g

Uhlig, 2001, Canova and De-Nicolo, 2002, Baumeister and Hamilton, 2015, and Rubio-Ramirez et al.

(2010)). Our strategy for identifying optimal monetary policy builds on these insights. In particular we

treat our model as the data generating process (DGP) and simulate long series for a subset of variables.

We then estimate the VAR on the simulated data, where the structural policy equation is identified by

matching the VAR response to a monetary policy shock with the response implied by the DSGE model

under optimal (cooperative or non-cooperative) policy. On practical grounds, this approach allows us

to consider various policy specifications (i.e. number of variables and lags) relatively more quickly. One

additional advantage of this method is that it uses the same lens through which we read empirical data.

In principle we could estimate the same VAR on our simulated data and on real-world data and compare

the implied policy rules. We leave this as an extension for future research.

16Note that with this approach the model would have to be evaluated (to second order) for each draw of the parameters.

17

To summarize our procedure (detailed in Appendix C), we use the DSGE under optimal policy

(cooperative or not) as our DGP. We draw 800000 realizations for each variable (dropping the first 10%)

when all shocks are active. We then estimate a VAR(p) in 9 variables (see below for a description), where

we set p=2 for the sake of parsimony.17

We then identify a policy shock for each country. In this regard it is important to note that under

the optimal policy, typically there would not be policy shocks. We add policy shocks to the first order

conditions with respect to domestic (PPI/GDP) inflation. In particular we assume that the FOCs of the

policymakers with respect to domestic PPI inflation are affected by random fluctuations.18 This choice is

motivated on technical grounds, but it is consistent with the idea that a policymaker that would be prone

to random deviations from a Taylor rule, could be prone to random deviations from any rule, optimal or

not.19

The identification of the shock is achieved by minimizing the distance between the IRFs generated by

our DGP and those generated by our DSGE when policy is conducted following our approximated rules.

We note again that the primary motive for including these shocks is not to identify the shock itself, but

the optimal systematic targeting rule that is implied by forcing the response to the shock in the estimated

VAR to be identical to that in the simulated DSGE model. Without an independent policy shock, this

identification would not be possible using the SVAR methodology.

Our aim is to summarize optimal policies by sufficiently simple rules. In pursuing this goal, we have

to strike a balance between simplicity and accuracy. On the one hand, omitting variables from the policy

rule can result in a deterioration of accuracy, and thus in welfare losses. On the other hand, including too

many variables (and lags) can reduce our ability to provide an economic rationale supporting the policy

prescription.

We start with a baseline subset of 9 variables: GDP, producer price index (PPI/GDP) inflation, real

exchange rate (RERt), credit spreads (Rj,k,t+1 − Rj,t, j = e, c), and the two TFP shocks (Ae,t and

Ac,t), i.e.

xt = [Ye,t, Yc,t, πPPIe,t , πPPIc,t , RERt, spreade,t, spreadc,t, Ae,t, Ac,t] (5.1)

This selection of variables is inspired by the literature on optimal policies in open economies, as well

as the need to be parsimonious. Corsetti et al. (2010), for example, show that in a two-country model

the loss function of the policymakers would depend on domestic and foreign output, domestic and foreign

inflation, the terms of trade, and a measure related to capital market inefficiency. We then consider

possible extensions (e.g. including state variables) and assess how large is the improvement in accuracy.

The policy rules that we back out with this approach may not be unique. This is because there might

be other (combinations of) variables perfectly collinear with the variables that we use in the estimation.

This problem is shared by theoretical optimal policy rules too. One related additional complication, in

17To gain intuition on the sources of approximation error, we study cases with p > 2.18More precisely in those equations inflation appears as πi,GDP,t + εRi,t; i = e, c, where εRi,t is an i.i.d. shock.19See also Leeper et al. (1996, p. 12).

18

the estimation-based approach, consists of the need to ensure stochastic non-singularity of the VAR. This

means that we cannot estimate a VAR with more variables than exogenous driving shocks in the DGP.

Our baseline set of variables does not include interest rates. It is well known that optimal (Ramsey)

policies cannot always be represented as interest rate rules: their general form is a targeting rule (Svens-

son, 2010). As shown by Giannoni and Woodford (2003a) in a linear-quadratic context, the optimal

targeting rule will display variables that appear in the objective (loss) function, together with the La-

grange multipliers associated to the policy constraints. This implies that optimal rules might not display

the interest rate explicitly (pure targeting rules a la Giannoni and Woodford, 2003b). A further problem

that can arise by approximating optimal rules with simple interest rate rules relates to implementability

and the existence of saddle-path (i.e. unique) equilibria. To the extent that the inferred rule is an ap-

proximation of the optimal rule, it might fail to generate uniqueness of equilibria. While this problem

can in principle be solved (e.g. aiming for higher accuracy of the approximation), we avoid the issue

altogether by resorting to pure targeting rules.

Inclusion of exogenous shocks

Optimal targeting rules establish relationships between “gaps” or efficiency wedges and other variables

(e.g. Lagrange multipliers). This is immediately evident in the linear-quadratic approach (e.g. Benigno

and Woodford, 2011) or in general when the reduced-form policy objective function is derived from the

equilibrium conditions of the model (e.g. Woodford, 2003 or Corsetti et al., 2010). This means that

targeting rules depend both on endogenous variables and exogenous shocks, i.e. equilibrium outcomes

under the “natural”, frictionless allocations. For example, in the basic New-Keynesian model, driven by

TFP shocks only, the optimal targeting rule relates inflation to the output gap (and its lag), where the

gap is the distance between output under sticky prices and output under flexible prices. Backing out this

policy rule in a VAR would be difficult. The VAR should contain three variables: inflation, output and

TFP. Yet there is only one shock, so that stochastic singularity could emerge.20 Adding measurement

errors would be of little help, as it would introduce serially correlated errors in the VAR.

In view of this constraint we consider alternative policy specifications, under different assumptions

concerning the “observability” of exogenous shocks. We limit this analysis to the two key shocks of

interest in our study: TFP and financial shocks.

5.1 Identification of optimal cooperative policies

Before describing optimal cooperative policies approximated by simple rules, it is important to stress

that under cooperation, and in contrast to the non-cooperative case, we cannot associate one rule to e.g.

the EM country and the other rule to the AE country. While each country implements it’s mandate with

“error”, both share the same objective, and this is reflected by their systematic response to endogenous

20Whether it emerges in practice depends on the correct specification of the lag structure too. In the basic New-Keynesianmodel inflation and output depends only on current TFP so that perfect multicollinearity would make estimation of thetree variable VAR impossible.

19

variables and exogenous shocks. This said, we label rules by country name for convenience.

5.1.1 Using TFP shocks in the VAR

We now assume that that policymakers act cooperatively, up to idiosyncratic shocks to their decision

rules. As described above, we estimate pure targeting rules for both countries using the 9 variable VAR as

described above. Note in particular that the VAR includes TFP shocks, but no other exogenous shocks.

Under the assumption that the DGP for the true model is driven by cooperative policy-making, the

identified approximate policy rules can be derived separately for the emerging economy and the advanced

economy. The rules take the following form:

9∑i=1

2∑j=0

γijxi,t−j = 0 (5.2)

where xi,t−j represents the variable i evaluated at time t − j, and γij is the estimated targeting rule

coefficient. In the following tables, we list the coefficients, where per normalization the coefficient on

contemporaneous PPI inflation is unity.

Table 1: EM targeting rule: TFP shocks in VAR

Variable t t-1 t-2GDP EME 0.724 -1.34 0.6GDP AE 0.002 0.263 -0.251Spread EME -0.008 0.006 -0.001Spread AE -0.175 0.157 -0.04PPI Infl. EME 1 4.23 -2.59PPI Infl. AE 1.04 -2.31 1.21Real Exch. Rate 0.048 0.037 -0.088TFP EME -0.765 1.35 -0.558TFP AE 0.226 -0.488 0.263

Table 2: AE targeting rule: TFP shocks in VAR

Variable t t-1 t-2GDP EME 0 0.029 -0.028GDP AE 0.022 0.016 -0.037Spread EME 0 0.001 0Spread AE -0.016 0.024 -0.006PPI Infl. EME 0.023 -0.166 0.134PPI Infl. AE 1 -0.845 0.283Real Exch. Rate 0.002 -0.005 0.003TFP EME 0.001 -0.029 0.026TFP AE 0.027 -0.08 0.053

While these rules are somewhat arbitrary, as discussed earlier they are inspired by the optimal target

rules of simpler models. They are history dependent, and functions of variables relevant for the inefficiency

wedges (except for the shock).

20

Relative to the simple targeting rules of New Keynesian open economy models, the estimated rules

here give a role to financial variables; the interest rate spreads for both countries appear in the rules of

both countries. In addition, the rules indicate an important interaction between the advanced economy

country and the emerging economy. For instance, inflation in the AE country should react to changes

in GDP, spreads, and TFP shocks in the emerging markets, and a similar interdependence characterizes

the targeting rule for the emerging economy.

Targeting rules inform us about the trade-off faced by policymakers and thus on the implied optimal

sacrifice ratio. For example equation (2.7) tells us that a positive output growth must be accompanied

by inflation falling below its target. To gain intuition along this perspective Figures 5 and 6 displays

the coefficients of the approximated rules (1 and 2) respectively. In particular, these figures relate

the weighted average of three quarters of domestic inflation to the normalized coefficients of the other

variables appearing in the targeting rule.21 To improve readability, shaded areas represent different

groups of variables.

Under this specification of the simple rule, the graphs suggest that the trade-off between PPI inflation

and spreads is very weak, while the major source of trade-off is between domestic and foreign inflation.

We then compare the response of the economy to TFP shocks: the truly optimal cooperative policy

implied by the simulated model, and the “estimated” optimal cooperative policy. For comparison pur-

poses, we add the response of the economy under the baseline, non-optimized Taylor rule. Figures 7 and

8 show the impulse responses for a subset of variables: seven target variables plus net-worth in the two

economies.

We see that in the response to TFP shocks in the advanced economy, the simple targeting rule delivers

responses that are very close, if not identical, to those produced by the fully optimal rule. GDP rises in

the advanced economy, but falls in the emerging market, which experiences a significant real exchange

rate appreciation. Spreads fall in both countries, as does PPI inflation, and net worth rises. Clearly, the

targeting rules outlined above capture very closely the responses of the true optimal policy.

5.1.2 Controlling simultaneously for TFP and financial shocks in the VAR

Including only TFP shocks in the simple rule might be insufficient to capture factors affecting natural

rates. In this subsection we include in the simple rule (i.e. in the VAR) two types of shocks that are of

particular interest in our analysis, TFP shocks and financial shocks. In order to maintain the number

of shocks equal to the number of variables in the VAR we have to trade-off the inclusion of two sets of

shocks with the omission of two other variables. Since we are interested in particular on the trade-off

between price stability and and stabilization of credit spreads we omit GDP from this scenario.22

Figures 9 and 10 show again the same information graphically. Contrary to the previous case, in

21This is obtained rewriting the targeting rule asa1π

PPI,jt + a2π

PPI,jt−1 + a3π

PPI,jt−2

a1 + a2 + a3=

1

a1 + a2 + a3(rest of terms),

where j = e, c and where a1...3 are the coefficients on inflation.22As argued above, these rules are not unique as linear combination of other variables could perfectly proxy some of the

variables included in the rule.

21

Table 3: EME targeting rule: Financial and TFP shocks in VAR

Variable t t-1 t-2Spread EME -0.072 0.047 0.022Spread AE -0.131 0.348 -0.199PPI Infl. EME 1 -0.426 0.02PPI Infl. AE 0.122 -0.072 0.024Real Exch. Rate 0.036 -0.034 -0.002TFP EME -0.021 0.021 0.001TFP AE 0.023 -0.008 -0.006Fin. Shock EME 0.038 -0.027 -0.012Fin. Shock AE 0.06 -0.174 0.106

Table 4: AE targeting rule: Financial and TFP shocks in VAR

Variable t t-1 t-2Spread EME -0.089 0.242 -0.145Spread AE -0.44 0.855 -0.412PPI Infl. EME 0.061 -0.093 0.031PPI Infl. AE 1 -0.405 0.068Real Exch. Rate -0.003 -0.005 0.013TFP EME 0.001 0.006 -0.009TFP AE -0.018 0.05 -0.013Fin. Shock EME 0.05 -0.136 0.083Fin. Shock AE 0.232 -0.468 0.229

which the VAR included only TFP shocks, now spreads play a more important role.

Figures 11 and 12 compare the responses to TFP shocks in AE and EM respectively, under three sets

of rules: the approximated rules, the fully optimal cooperative policy, and (as benchmark) the ad-hoc

Taylor rule. Figures 13 and 14 display the policy comparison under financial shocks in AE and EM

respectively. All four cases display a very tight match between the approximated rules and the fully

optimal rules.

To gain further intuition on what the optimal cooperative monetary policy does, we compare it with

strict PPI inflation targeting (IT): πPPI,et = πPPI,ct = 0, a subcase of the simple rule (5.2). Figures 15

to 18 show this comparison for TFP and financial shocks in the two economies, respectively. From this

comparison we find a number of interesting results. First, when the shock originates in the center country,

strict inflation targeting generates responses to TFP and financial shocks that are markedly different from

the optimal ones. In particular, in response to a TFP shock in the center country, spreads are allowed to

fall too much under IT than under optimal policies, which boosts output in both economies more than

it would be optimal. Under the optimal (simple) rule, the milder fall in spreads, can be traded off with

a larger fall in inflation. If the TFP shock originates in the EME, the particular policy regime is less

important for real allocations. This is partially explained by the smaller size of the EME country, and

partially by the smaller amplification that the EME financial channel exerts globally: The AE financial

block has direct global effects through the dependence of EME banks on AE loans.

Moving to financial shocks (Figure 18) we observe a relatively similar constellation of effects (note the

different scale of vertical axis across countries). A special feature of financial shocks, relative to TFP, is

22

that the domestic spread responds to the domestic financial shock in a way that is virtually independent

of two policy regimes (optimal and IT). This is not true for the response of the domestic spread to foreign

financial shocks, especially for the EME spread: fully stabilizing inflation comes at the cost of more

volatile spreads.

Finally, comparing the response to an AE’s TFP shocks under IT, cooperative and estimated rule,

when the banks’ ICC is not binding, shows that the optimal cooperative policy is not particularly far from

strict inflation targeting.23 This exercise corroborates our finding that monetary policymakers confronted

with inefficient capital flows need to trade-off price stability with the stabilization of credit spreads.

6 Conclusion

Our paper addresses the question of how practical rules for monetary policy can be characterized in

financially integrated economies, with multiple conflicting distortions, so as to maximize welfare. We

contribute to the recent literature on the international dimensions of monetary policy by providing more

insights concerning simple, implementable rules that can best approximate fully optimal, but complex,

rules. Financial factors are a key channels through which shocks and policies propagate across countries

above and beyond exchange rates. The latter have been shown to provide little additional usefulness in

designing monetary policies for open economies. International capital flows (and the associated credit

spreads) are more likely to play an independent role in shaping the response of economies to shocks. Our

results indicate that (relatively) simple targeting rules for monetary policy can replicate welfare based

optimal monetary policy very closely. These targeting rules differ considerably from commonly described

rules for New Keynesian open economy models, and in particular contain non-traditional variables, such

as credit spreads. These results are consistent with the basic economic principle that are widely discussed

in the related literature: Targeting rules display relationships among efficiency wedges that matter for

policymakers, i.e. the “gap” variables that would appear in the loss-function of the policymaker. With

sufficiently simple models, the policy objective can be expressed analytically in terms of these gaps, and

simple rules can be explicitly and exactly derived. More in general, the richer, and presumably the

more interesting are the features of the model, the less likely might be that explicit simple rules can be

derived analytically. This is the case of our model. One practical contribution of our paper is to show

that we could still provide more economic intuition on the policy tradeoffs by approximating the truly

optimal rule using regression methods. In particular we point out that SVAR methods have been used

to identify policy in the real world, where less information is available to the econometrician than it is

available to the modeler. By exploiting those insights we show that relatively simple rules, that trade off

inflation volatility and spread volatility, can bring about allocations very similar to those produced by

more complex optimal policies. Our paper can be seen as a first step in the direction of simplifying the

communication of policy prescriptions in complex models. One of the appealing features of optimal policy

analysis in New-Keynesian models is its intuitive simplicity. The research agenda to which this paper

23A residual change in the EME spread under these assumptions reflect roundabout flow of funds financing EME’s capital.

23

contributes aims at maximizing communicability while expanding the number of real-world frictions that

policymakers are likely to face.

24

References

Adolfson, M. (2007). Incomplete exchange rate pass-through and simple monetary policy rules. Journal

of International Money and Finance, 26(3):468–494.

Arias, J. E., Caldara, D., and Rubio-Ramırez, J. F. (2018). The systematic component of monetary

policy in SVARs: An agnostic identification procedure. Journal of Monetary Economics.

Ball, L. M. (1999). Policy Rules for Open Economies. In Monetary Policy Rules, pages 127–156. University

of Chicago Press.

Banerjee, R., Devereux, M. B., and Lombardo, G. (2015). Self-Oriented Monetary Policy, Global Financial

Markets and Excess Volatility of International Capital Flows. Working Paper 21737, National Bureau

of Economic Research.

Banerjee, R., Devereux, M. B., and Lombardo, G. (2016). Self-oriented monetary policy, global finan-

cial markets and excess volatility of international capital flows. Journal of International Money and

Finance, 68:275–297.

Batini, N., Harrison, R., and Millard, S. P. (2003). Monetary policy rules for an open economy. Journal

of Economic Dynamics and Control, 27(11-12):2059–2094.

Baumeister, C. and Hamilton, J. D. (2015). Sign Restrictions, Structural Vector Autoregressions, and

Useful Prior Information. Econometrica, 83(5):1963–1999.

Benigno, P. and Woodford, M. (2011). Linear-Quadratic Approximation of Optimal Policy Problems.

Journal of Economic Theory.

Benigno, P. and Woodford, M. (2012). Linear-quadratic approximation of optimal policy problems.

Journal of Economic Theory, 147(1):1–42.

Blake, A. P. and Westaway, P. F. (1995). Time Consistent Policymaking: The Infinite Horizon Linear-

Quadratic Case.

Brunnermeier, M., Palia, D., Sastry, K. A., and Sims, C. A. (2017). Feedbacks: Financial markets and

economic activity. Mimeo.

Caballero, J., Fernandez, A., and Park, J. (2019). On corporate borrowing, credit spreads and eco-

nomic activity in emerging economies: An empirical investigation. Journal of International Economics,

118:160–178.

Calvo, G. A. (1983). Staggered Prices in a Utility-Maximizing Framework. Journal of Monetary Eco-

nomics, 12:383–398.

Canova, F. and De-Nicolo, G. (2002). Monetary Disturbances Matter for Business Fluctuations in the

G-7. Journal of Monetary Economics, 49:1131–1159.

25

Christiano, L. J., Eichenbaum, M., and Evans, C. (2005). Nominal Rigidities and the Dynamic Effects

of a Shock to Monetary Policy. Journal of Political Economy, 113:1–45.

Coenen, G., Lombardo, G., Smets, F., and Straub, R. (2009). International Transmission and Monetary

Policy Coordination. In Gali, J. and Gertler, M., editors, International Dimensions of Monetary Policy.

University Of Chicago Press, Chicago.

Cogley, T. and Nason, J. M. (1995). Output Dynamics in Real-Business-Cycle Models. In American

Economic Review, volume 85, pages 492–511.

Corsetti, G., Dedola, L., and Leduc, S. (2010). Optimal Monetary Policy in Open Economies. In

Friedman, B. M. and Woodford, M., editors, Handbook of Monetary Economics, volume 3 of Handbook

of Monetary Economics, pages 861–933. Elsevier.

Cuadra, G. and Nuguer, V. (2018). Risky banks and macro-prudential policy for emerging economies.

Review of Economic Dynamics, 30:125–144.

Del Negro, M., Eusepi, S., Giannoni, M. P., Sbordone, A. M., Tambalotti, A., Cocci, M., Hasegawa, R.,

and Linder, M. H. (2013). The FRBNY DSGE model. FRBNY, Staff Report No647.

Devereux, M. B. and Engel, C. (2003). Monetary Policy in the Open Economy Revisited: Price Setting

and Exchange-Rate Flexibility. Review of Economic Studies, 70(4):765–783.

Devereux, M. B., Lane, P. R., and Xu, J. (2006). Exchange Rates and Monetary Policy in Emerging

Market Economies. Economic Journal, 116(511):478–506.

Favara, G., Gilchrist, S., Lewis, K. F., and Zakrajsek, E. (2016). Updating the Recession Risk and the

Excess Bond Premium. FEDS Notes, (1836).

Fernandez-Villaverde, J., Rubio-Ramırez, J. F., Sargent, T. J., and Watson, M. W. (2007). ABCs (and

Ds) of Understanding VARs. The American Economic Review, 97(3):1021–1026.

Galı, J. and Monacelli, T. (2005). Monetary Policy and Exchange Rate Volatility in a Small Open

Economy. Review of Economic Studies, 72(3):707–734.

Garcia, C. J., Restrepo, J. E., and Roger, S. (2011). How much should inflation targeters care about the

exchange rate? Journal of International Money and Finance, 30(7):1590–1617.

Gertler, M. and Karadi, P. (2011). A Model of Unconventional Monetary Policy. Journal of monetary

Economics, 58(1):17–34.

Gertler, M. and Kiyotaki, N. (2010). Financial Intermediation and Credit Policy in Business Cycle

Analysis. In Friedman, B.M. and Woodford, M., editor, Handbook of Monetary Economics, volume 3,

page 547. North-Holland.

26

Giannoni, M. P. and Woodford, M. (2003a). Optimal Interest-Rate Rules: I. General Theory. Working

Paper 9419, National Bureau of Economic Research.

Giannoni, M. P. and Woodford, M. (2003b). Optimal Interest-Rate Rules: II. Applications. Working

Paper 9420, National Bureau of Economic Research.

Giannoni, M. P. and Woodford, M. (2017). Optimal target criteria for stabilization policy. Journal of

Economic Theory.

Gilchrist, S. and Zakrajsek, E. (2012). Credit Spreads and Business Cycle Fluctuations. American

Economic Review, 102(4):1692–1720.

Golub, G. H. and Van Loan, C. F. (1996). Matrix Computations. Johns Hopkins University Press,

Baltimore, third edition.

Kirsanova, T., Leith, C., and Wren-Lewis, S. (2006). Should central banks target consumer prices or the

exchange rate? The Economic Journal, 116(512).

Kollmann, R. (2002). Monetary Policy Rules in the Open Economy: Effects on Welfare and Business

Cycles. Journal of Monetary Economics, 49(5):989–1015.

Laxton, D. and Pesenti, P. (2003). Monetary Rules for Small, Open, Emerging Economies. Journal of

Monetary Economics, 50(5):1109–1146.

Leeper, E. M., Sims, C. A., Zha, T., Hall, R. E., and Bernanke, B. S. (1996). What Does Monetary

Policy Do? Brookings papers on economic activity, 1996(2):1–78.

Leitemo, K. and Soderstrom, U. (2005). Simple monetary policy rules and exchange rate uncertainty.

Journal of International Money and Finance, 24(3):481–507.

Mendoza, E. G., Quadrini, V., and Rıos-Rull, J. V. (2009). Financial integration, financial development,

and global imbalances. Journal of Political Economy, 117(3):371–416.

Moron, E. and Winkelried, D. (2005). Monetary policy rules for financially vulnerable economies. Journal

of Development economics, 76(1):23–51.

Obstfeld, M. (2017). Two Trilemmas for Monetary Policy. Speech: Bank Negara Malaysia Conference

on “Monetary Policy 2.0?”.

Pavasuthipaisit, R. (2010). Should inflation-targeting central banks respond to exchange rate movements?

Journal of International Money and Finance, 29(3):460–485.

Prasad, E. S., Rogoff, K., Wei, S.-J., and Kose, M. A. (2007). Financial globalization, growth and

volatility in developing countries. In Globalization and poverty, pages 457–516. University of Chicago

Press.

27

Ravenna, F. (2007). Vector autoregressions and reduced form representations of DSGE models. Journal

of Monetary Economics, 54(7):2048–2064.

Rey, H. (2016). International Channels of Transmission of Monetary Policy and the Mundellian Trilemma.

IMF Economic Review, 64(1):6–35.

Rubio-Ramirez, J. F., Waggoner, D. F., and Zha, T. (2010). Structural vector autoregressions: Theory

of identification and algorithms for inference. The Review of Economic Studies, 77(2):665–696.

Sargent, T. J. and Wallace, N. (1975). “Rational” Expectations, the Optimal Monetary Instrument, and

the Optimal Money Supply Rule. Journal of Political Economy, 83(2):241–254.

Scrucca, L. (2013). GA: A Package for Genetic Algorithms in R. Journal of Statistical Software, 53(4):1–

37.

Sims, C. A. (1980). Macroeconomics and Reality. Econometrica: Journal of the Econometric Society,

pages 1–48.

Sims, C. A. (1998). Comment on Glenn Rudebusch’s” Do Measures of Monetary Policy in a VAR Make

Sense?”. International Economic Review, 39(4):933–941.

Svensson, L. (2010). Inflation Taargeting. In Friedman, B. M. and Woodford, M., editors, Handbook of

Monetary Economics, volume 3B, pages 1237–1302. Elsevier.

Svensson, L. E. O. (2000). Open-economy inflation targeting. Journal of international economics,

50(1):155–183.

Taylor, J. B. (2001). The role of the exchange rate in monetary-policy rules. American Economic Review,

91(2):263–267.

Uhlig, H. (2001). What Are the Effects of Monetary Policy on Output? Results from an Agnostic

Identification Procedure. Journal of Monetary Economics, 52(2):381–419.

Uhlig, H. (2005). What Are the Effects of Monetary Policy on Output? Results from an Agnostic

Identification Procedure. Journal of Monetary Economics, 52(2):381–419.

Wollmershauser, T. (2006). Should central banks react to exchange rate movements? An analysis of

the robustness of simple policy rules under exchange rate uncertainty. Journal of Macroeconomics,

28(3):493–519.

Woodford, M. (2001). The Taylor rule and optimal monetary policy. American Economic Review,

91(2):232–237.

Woodford, M. (2003). Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton U.P.,

Princeton, NJ.

28

Xiang, Y., Gubian, S., Suomela, B., and Hoeng, J. (2013). Generalized simulated annealing for global

optimization: the GenSA Package. R Journal, 5(June):13–28.

29

Table A.1: Parameter Values

Description Label ValueEME size n 0.15Discount factor β 0.99Demand elasticity −σp 6Calvo probability ςe = ςc 0.85Premium on NFA position γB -0.001MP response to output λy,e = λy,c 0.5MP response to inflation λπ,e = λπ,c 1.5MP response to lagged rate λr,e = λr,c 0.85Counsumers’ risk aversion σ 1.02ICC parameter κc = κe 0.38

Description Label ValueBanks’ survival rate θ 0.97Share of K in production α 0.3EME home bias νp,e 0.745AE home bias νp,c 0.955Depreciation of K δ 0.025Share of K transferred to new banks δT 0.004Adjustment cost of I ηe = ηc 4Trade elasticity ηp 1.5Inverse Frisch elasticity ψ 2Quarterly inflation objective πe,cobj 1.0062

Appendix

A Parameter values

The values of the key parameters of the model are fixed at values prevailing in the related literature,

with two exceptions. First, it turned out that in order to match the relative volatility of the investment

share, a larger cost of investment than typically used in the literature was needed. We choose a value

that is about twice as large as in the literature. Second, in order to improve the estimation of the VAR

on simulated data we opted for mildly autoregressive exogenous shocks and assigned a value of 0.5 to the

persistence parameter.

B Data moments

All the structural parameters of our model are fixed at values prevailing in the related literature. In order

to ensure that the relative volatility of key variables of the model is commensurate to their empirical

counterpart we estimate the standard deviations of the three key shocks underlying our experiments

(productivity, financial and policy shocks) using an SMM approach. We use various data sources. For US

credit spreads we use the “GZ” spreads computed by Gilchrist and Zakrajsek (2012) (see also the Fed’s

updates of these series; Favara et al., 2016). The standard deviation of these spreads hoovers around 100

basis points, depending on frequency (they are available at monthly and quarterly frequency) and on the

sample period. For EMEs we use similar series constructed by Caballero et al. (2019). The standard

deviations of these variables are reported in Table B.3.

For the remaining macroeconomic variables we built a panel of quarterly data (1990Q1-2019Q2) from

various sources as reported in Table B.2. For comparison, we report also standard deviations for the euro

area, although we use only the U.S. as a representative AE when estimating the shocks. Since interest

rates and inflation display a persistent downward trend we subtract a linear trend from these series before

computing standard deviations. Since EMEs displayed periods of heightened volatility, for robustness we

controlled for outliers, but did not find economically significant differences in the moments of interest.

Since EMEs appear to be more heterogeneous limiting attention to the median (or average) standard

30

deviations would be inappropriate. We thus compute three percentiles (10, 50 and 90%) as well as the

mean and two measures of dispersion (standard deviations and inter-quartile range).

We use this data to estimate the standard deviation of the three sets of shocks. Table B.4 compares

the moments produced by the model at the estimated parameters with the empirical counterparts (the

values of the standard deviations of the structural shocks are shown in Table B.5). Considering that

we estimate 6 parameters using 11 moments (while keeping all other parameters constant) the model

performs relatively well. For the EME, the model generates standard deviations below the 10th percentile

only the real exchange rate and for interest rates, albeit less significantly. Inflation and the policy rate

are also poorly matched for the AE. Fine-tuning the policy rule could further improve on this margin.

Nevertheless, as the main focus of our paper is normative, we consider these results sufficiently satisfactory.

C Identification via IRFs matching

Let us recall that in order to determine the policy equation (rule) in the VAR, we need to identify the

monetary policy shock (Leeper et al., 1996, p. 9).24

We achieve identification by minimizing the distance between the “true” IRFs to a policy shock (based

on the DSGE under optimal policy) and the IRFs to a policy shock obtained from the VAR estimated on

simulated data. Our IRFs matching (IRM) approach can be seen as an extension of the sign-restriction

identification method used in the empirical VAR literature (e.g. Uhlig (2005) and Rubio-Ramirez et al.

(2010)). In this Section we only explain the main differences with respect to the standard sign-restriction

(SR) approach.

Both the IRM and SR approaches start from an estimated VAR equation

yt = Ayt−1 + ut (C.1)

where ut is a vector of reduced form shocks.

Both approaches seek to identify one or more structural shocks (elements) in the vector εt such that

ut = A−10 εt, where the (contemporaneous coefficient) matrix A0 is unknown. The first key step in the

identification amounts to finding the matrix A0. The second step amounts to identifying which element

in εt corresponds to the shock of interest. To this aim, note that a factorization of the covariance matrix

or the residual shocks can be written as

E(utu′t) ≡ Σu = PQQ′P ′ (C.2)

where P is a factorization of Σu, (e.g. Cholesky) and Q is an orthonormal rotation matrix such that

QQ′ = I (e.g. Canova and De-Nicolo, 2002).

Σu offers a set ofn (n+ 1)

2independent parameters, while the matrix A−1

0 ≡ PQ has n2 parameters.

In order to determine the remaining n2 − n (n+ 1)

2parameters we need

n (n− 1)

2restrictions (order

24Recently Arias et al. (2018) exploit this fact to impose identifying restrictions consisting of priors about the way policyresponds to endogenous variables.

31

Table B.2: Data: Standard deviations

R π ∆ logRER ∆ logGDP ∆ log Inv.GDP

EM

Es

Cou

ntr

ies

Chile 4.58 4.72 4.01 1.19 3.79Colombia 5.05 4.85 5.29 0.80 4.03Czechia 2.80 4.73 4.94 0.83 2.80Indonesia 7.20 12.42 10.21 1.64 9.60India 1.83 5.07 2.88 0.76 2.69

Mexico 6.35 7.98 6.09 1.29 2.88Malaysia 1.52 2.67 3.59 1.48 6.94Peru 3.69 27.72 2.06 1.05 3.15Philippines 2.91 4.29 3.77 0.73 6.52Poland 4.79 10.93 5.27 0.62 3.15

Russia 19.57 26.49 7.86 1.66 7.10Thailand 2.54 3.57 4.43 1.95 5.50Turkey 16.49 16.86 7.15 2.86 4.85Taiwan 1.41 3.64 2.37 1.39 2.97South Africa 2.14 3.63 5.99 0.64 2.73

Per

centi

les

10% 1.64 3.59 2.58 0.68 2.7650% 3.69 4.85 4.94 1.19 3.7990% 12.78 22.64 7.57 1.84 7.04

Mom

ents Mean 5.52 9.30 5.06 1.26 4.58

Stdev. 5.39 8.25 2.19 0.61 2.11IQR 3.36 7.71 2.36 0.78 3.08

AE

s

Cou

ntr

ies

United States 1.56 2.36 0.00 0.58 1.16Euro Area 0.94 2.34 3.89 0.57 1.58

Data sources: BIS; Datastream; OECD; Global Financial Data.Note: Not all the data was available in seasonally adjusted form, so we seasonally adjusted all seriesbefore computing moments. Inflation and nominal interest rates were detrended due to the downwardtrend for most of the sample. Maximum sample range: 1990Q1-2019Q2.

32

Table B.3: Standard deviations of EMEs credit spreads (basis points)

EFI† EFI-NFC†† EMBI†††C

ou

ntr

ies

Brazil 290.8 375.0 303.2Chile 78.2 80.0 52.0Colombia 172.8 193.6 144.1Mexico 166.8 176.3 68.5Malaysia 70.8 70.5 66.4

Peru 291.1 303.8 180.7Philippines 147.4 152.0 152.3Russia 507.2 531.0 846.3Turkey 92.6 520.7 52.7South Africa 317.5 337.8 103.9

Per

centi

les

10% EME 77.5 79.0 52.750% EME 169.8 248.7 124.090% EME 336.4 521.7 357.5

Mom

ents

Mean EME 213.5 274.1 197.0Stdev EME 137.7 167.3 240.8IQR 184.7 207.7 106.7

Data sources: Caballero et al. (2019).

Note: Standard deviations based on quarterly data; sample 1991Q1-2017Q2. IQR=inter-

quartile range.

† External Financial Indicator computed by Caballero et al. (2019).

†† External Financial Indicator computed by Caballero et al. (2019) for non-financial cor-

porations.

††† J.P. Morgan Emerging Markets Bond Spread.

condition).25

The standard SR approach finds the missing restrictions by imposing that the sign of the VAR IRFs

(on impact or over a longer horizon) match the sign of IRFs suggested e.g. by theory. Here is where our

IRM approach differ. We know exactly the value of the IRFs of each variable and for any horizon to a

monetary policy shock: our DGP is the DSGE. We can then obtain the missingn (n− 1)

2restrictions by

minimizing the distance of the VAR IRFs to the “true” IRFs to a monetary policy shock.

Since we have n variables, with h IRFs periods per variable we have n× h IRF-gap points. Then we

need h∗ = n/2− 1/2 periods per variable for an exact identification (i.e. h such that n× h =n (n− 1)

2).

Thus, for example, with 9 variables we can reach exact identification with 4 periods per variable. These

points do not need to be contiguous. For example, with 9 variables, we choose to match the first two

25Although we are only interested in one row of the VAR, we need the full A0 matrix.

33

Table B.4: Model vs Data: Standard deviations (%)

Variables Model Data Data percentiles [10%, 90%]

∆ log(GDP ) EM 1.8 1.2 [0.68, 1.8]∆ log(GDP ) AE 0.51 0.58

∆ log(I

GDP) EM 2.9 3.8 [2.8, 7.0]

∆ log(I

GDP) AE 0.82 1.2

Short term Rate EM 1.3 3.7 [1.6, 12.8]Short term Rate AE 0.59 1.6Spread EM† 1.2 1.7 [0.78, 3.4]Spread AE† 1.2 1Inflation EM 3.9 4.8 [3.6, 22.6]Inflation AE 1.2 2.4∆ log(RER) 1.1 4.9 [2.6, 7.6]

Note: The Data column is obtained using the values in Tables B.2 and B.3.

AE moments are computed using U.S. data.

† EFI.

Table B.5: Estimated standard deviation of shocks (in percent)

Parameter valueσAe 0.17σAc 0.07σRe 0.43σRc 0.14σκe 1.45σκc 0.043

periods together with the fourth and sixth period.

Let’s define the difference between IRFs as

νh ≡ [(x1 − x1) , . . . , (xh − xh)] (C.3)

so that νh is a n× h matrix, xt is the n× 1 vector of VAR IRFs and xt is the n× 1 vector of target IRFs

(i.e. from the DGP). If h = h∗, νh contains exactlyn (n− 1)

2elements: the missing restrictions.

Since an exact solution (νh = 0) is unlikely to exist, due to omitted variables in the VAR, we look for

a solution that minimizes the IRFs gap, i.e.

Q = arg minQ‖Wνh‖N (C.4)

subject to

PP ′ = Σu (C.5)

where ‖·‖N is the N norm of a vector and W is a weighting matrix used to give more prominence to

particular horizons.26 We choose W to penalize sign discrepancies in the first two periods.

The matrix P can be obtained in different ways. The two most common consist of i) the Cholesky

26We consider N =∞ and N = 2.

34

factorization of the estimated variance of the residuals ut, and ii) the spectral decomposition (E (utu′t) =

PDP ′, where P is the eigenvector matrix and D the diagonal eigenvalue matrix). See Rubio-Ramirez

et al. (2010) for details.

We choose the Cholesky factorization, such that the whole set of n2 restrictions would be

restrictions =

arg minQ ‖Wνh‖NP = chol(Σu)

(C.6)

This implies, for example, that the restrictions we are looking for, amount ton (n− 1)

2possible pairwise

rotations of the rows of a Givens (Jacobi) matrix Q, for a given rotation angle θ.

C.1 Using optimization algorithms to match IRFs

A novel methodological contribution of this paper is to use optimization algorithms to find the optimal

rotation matrix in the IRFs matching exercise. By using Givens rotations (Golub and Van Loan, 1996)

we can parametrize the optimization problem (IRFs matching) in terms of the vector of rotation angles θ.

This vector has length nθ ≡n (n− 1)

2, since there are exactly nθ possible permutations of the elements

of the innovation vector, and there is one angle per permutation. The matching function in our case

appears smooth and continuous along each element of θ, but it is highly non-linear moving across angles,

with a large number of local minima. We use a suite of optimization algorithms to find the optimal

rotation matrix. In particular we start the search by using a Simulated Annealing optimization method

(implemented in the GenSA package in R by Xiang et al., 2013), followed by a Genetic Algorithm method

(implemented in the GA package in R by Scrucca, 2013), and refine the search using a gradient-based

method.

D Deterministic steady state

In order to finding the rational-expectation solution of our model using perturbation methods we need

to find the solution of the deterministic steady state of the non-linear model. Most, but not all, of

the variables can be solved recursively. We adopt the following strategy, we search numerically for four

variables — labor supply in both countries (He and Hc), the price index of EME goods relative to EME’s

CPI (P c), and the cost of funds for EME banks Rc — that can satisfy four residual conditions. The

other variables are solved recursively. The omission of the time (t) subscript denotes steady state values.

Let’s start with the EME banks. It is convenient to express the value function of the bank relative

to its net worth. Note that from the vantage point of the banks existing at time t net worth at time t is

total net worth (i.e. Ne sum of surviving banks’ net worth and transfer), while the relevant net worth in

the bank surviving in the future is the surviving banks’ net worth (Nei,t), i.e.

vei,t = EtΛet+1|t

(1− θ)

Nei,t+1

Net+1

+ θNei,t+1

Net

vei,t+1

(D.1)

35

where vei,t =Jei,tNet

.

In the steady state have

vei =β (1− θ) N

ei

Ne

1− βθNei

Ne

(D.2)

where

Ne =θRxe + δeT

1− θ RvψD

Ke (D.3)

where Rxe ≡ Rek −RvψD

, and

Nei =

Ne − δeTKe

θ(D.4)

so that, using equation (D.3) have

Nei

Ne=

1− δeT1− θ Rv

ψDθRxe + δeTθ

=

Rxe + δeTRvψD

(θRxe + δeT )(D.5)

Assuming that the ICC is binding, and using equation (D.3) and (D.2) we can write equation (E.4)

as

κe1− θ Rv

ψDθRxe + δeT

=β (1− θ)Ne

Nei

− βθ(D.6)

and by using equation (D.5) we can further simplify the latter as

κe1− θ Rv

ψDθRxe + δeT

=

(1− θ)β

(Rxe + δeT

RvψD

)

(θRxe + δeT )− βθ

(Rxe + δeT

RvψD

) (D.7)

or

κe

(1− θ Rv

ψD

)β (1− θ)

(θ (1− β)Rxe + δeT

(1− βθ Rv

ψD

))= (θRxe + δeT )

(Rxe + δeT

RvψD

)(D.8)

or

κe

(1− θ Rv

ψD

)β (1− θ)

(θ (1− β)Rxe + δeT

(1− βθ Rv

ψD

))= θRxe2 + δeT

(1 + θ

RvψD

)Rxe + δeT

2 RvψD

(D.9)

36

which is a quadratic equation in the credit spread Rxe with solution

Rxe1,2 =−b±

√b2 − 4ac

2a(D.10)

where

a =θ (D.11)

b =δeT

(1 + θ

RvψD

)−κe

(1− θ Rv

ψD

)β (1− θ)

θ (1− β) (D.12)

c =δeT2 RvψD−κe

(1− θ Rv

ψD

)β (1− θ)

δeT

(1− βθ Rv

ψD

)(D.13)

We can then use equations (E.10) and (E.11) evaluated in the steady state, i.e.

γe = β (1− θ + θJe′i )Rxe

κe, (D.14)

and

Je′i (γe − 1) + β (1− θ + θJe′i )RvψD

= 0, (D.15)

respectively, to obtain a quadratic equation in Je′i , i.e.

θβRxe

κeJe′2i −

(1− (1− θ)βRx

e

κe− θβ Rv

ψD

)Je′i + (1− θ)β Rv

ψD= 0, (D.16)

with solution

Je′i 1,2 =−b±

√b2 − 4ac

2a; (D.17)

where

a =θβRxe

κe(D.18)

b = (1− θ)βRxe

κe+ θβ

RvψD− 1 (D.19)

c = (1− θ)β RvψD

. (D.20)

We can then use equation (D.14) to obtain γe.

So far we have then used 5 equations (E.4), (D.2), (D.5), (D.14), and (D.15), to obtain the 5 variables

vei ,NeiNe , Rxe, Je′i , and γe, given a guess (draw) for Rv.

In order to address the AE banks we need to solve for the level of capital in EME and, thus, the

amount of EME banks’ borrowing.

37

With a guess for P e we can use the CPI indexes to solve for P c and RER, i.e.

RER =

[2v − 1

(1− v)

(v

2v − 1− P 1−η

e

)] 1

1− η(D.21)

and

Pc =

(v

2v − 1− (1− v)

2v − 1RERη−1

) 11−η

(D.22)

Since we have a guess for He too, we can use the firms’ demand for capital to obtain the EME capital

stock

Ke =

(P eα

Rek − (1− δ)

) 11−α

He (D.23)

and

Ne =θRxe + δeT1− θRv

Ke (D.24)

With these we can solve for the steady state EME banks’ borrowing

V e =Ke −Ne

RERψD. (D.25)

The return on AE capital can be easily derived from the arbitrage condition

Rck = Rv. (D.26)

Having guessed a value for Hc we can thus derive the capital stock in AE from firms’ demand for capital

Kc =

(P cα

Rck − 1

) 11−α

Hc. (D.27)

We can now compute the following AE banks’ variables

N c =θ((Rck − β−1

)(V e +Kc)

)+ δTK

c

1− θβ−1(D.28)

N ci =

N c − δTKc

θ(D.29)

and the banks’ value relative to net worth

vc = βN ci

N c[(1− θ) + θvc] , (D.30)

where we have used the fact that R∗ = β−1.

We can then use the FOC of the AE banks with respect to V e and the envelope condition to solve

for Jc′i and γc. Analogously to the EME banks’ problem this entails a quadratic equation:

Jc′i 1,2 =−b±

√b2 − 4ac

2a(D.31)

38

where

a =β

κcθ(Rck −R∗); (D.32)

b =β

κc(1− θ)(Rck −R∗)− (1− βθR∗); (D.33)

c =β(1− θ)R∗; (D.34)

and

γc =β

κc(Rck −R∗) (1− θ + θJci

′) . (D.35)

The rest of the variables can be derived recursively from the steady state version of the respective

equations listed in Appendix E.

The four residual conditions necessary to verify our guesses are EME households’ budget constraint

(E.49), the resource constraints in each economy (E.50) and (E.51), and the ICC constraint of AE banks

(E.21).

E Full list of equations used in the simulation

In this appendix we list all the equations of the model used in the derivation of the numerical results.

For simplicity we omit the expectation operator, with the understanding that expressions involving t+ 1

variables hold in expectation. We start by giving some more details about the derivation of the bank’s first

order conditions, before listing the equations describing households’ and firms’ choices and equilibrium

conditions.

E.1 EME banks

There is an infinite number of identical banks indexed by the subscript i. The representative EME bank’s

optimal value is

Jei,t = max[Kei,t+1,V

ei,t,D

ei,t]EtΛ

et+1|t

[(1− θ)Ne

i,t+1 + θJei,t+1

], (E.1)

where

Nei,t = Rek,tQ

et−1K

ei,t−1 −RERt

Rv,t−1

πctV ei,t−1 −

Ret−1

πetDei,t−1, (E.2)

subject to the balance sheet

Nei,t +RERtV

ei,t +De

i,t = QetKi,t, (E.3)

and incentive compatibility constraint

Jei,t ≥ κetQetKei,t. (E.4)

39

Domestic deposit constraint

Dei,t ≤ (ψD − 1)RERtV

ei,t (E.5)

where ψD ≥ 1. Since Et

(RERt+1

RERt

Rv,tπct+1

− Retπet+1

)≥ 0 – which is due to the presence of credit spreads in

combination to the international asset pricing condition of the households – then the constraint (E.5) is

always binding and we can rewrite the balance sheet equation E.3 as

Nei,t + ψDRERtV

ei,t = QetKi,t, (E.6)

and the net-worth equation E.2

Nei,t = Rek,tQ

et−1K

ei,t−1 − Rv,t−1RERtV

ei,t−1, (E.7)

where Rv,t−1 =

(Rv,t−1

πct+Ret−1

πet(ψD − 1)

)Using equation (E.6) to replace V ei,t in equation (E.7) yields

Nei,t+1 =

(Rek,t+1 −

RERt+1

RERt

Rv,tψD

)QetK

ei,t +

RERt+1

RERt

Rv,tψD

Net . (E.8)

And aggregating across banks yields∫Nei,t+1di = Ne

t+1 = θ

((Rek,t+1 −

RERt+1

RERt

Rv,tψD

)QetK

et +

RERt+1

RERt

Rv,tψD

Net

)+ δTQ

et+1K

et . (E.9)

The first order conditions with respect to Kei,t is

Kei,t : EtΩ

et+1|t

(Rek,t+1 −

RERt+1

RERt

Rv,tψD

)Qet −Qetκe,tγet = 0, (E.10)

the envelope condition is

Nei,t : −Je′i,t (1− γet ) + EtΩ

ei,t+1|t

RERt+1

RERt

Rv,tψD

= 0, (E.11)

and the complementary slackness conditions is

γet ≥ 0;(Jei,t − κetQetKe

i,t

)γet = 0; (E.12)

where Ωei,t+1|t ≡ Λt+1|t[(1− θ) + θJe′i,t+1

]is the discount factor of the bank, and γet is the multiplier

associated to the constraint (E.4).27

27Gertler and Kiyotaki (2010) and Gertler and Karadi (2011) show that under the assumption underlying the bank

problem, the value function Jjt , j = e, c, is linear in net-worth. This allows aggregation across agents and implies that

Je′i,t = Je

i,tNei,t.

40

E.2 AE banks

There is an infinite number of identical banks indexed by the subscript j. The AE representative bank’s

value function is

Jcj,t = Et maxKcj,t+1,V

ej,t,D

ct

Λct+1|t[(1− θ)N c

j,t+1 + θJcj,t+1

], (E.13)

subject to the balance sheet constraint

n

1− nV ej,t +QctK

cj,t = N c

j,t +Dct , (E.14)

and the incentive compatibility constraint

Jj,t ≥ κct(

n

1− nV ej,t +Qc,tK

cj,t

); (E.15)

were the net worth is defined as

N cj,t+1 = Rck,t+1Q

ctK

cj,t +

Rv,tπct+1

n

1− nV ej,t −

Rctπct+1

Dcj,t. (E.16)

Using equation (E.14) to eliminate deposits Dcj,t from equation (E.16) we obtain

N cj,t+1 =

(Rck,t+1 −

Rctπct+1

)QctK

cj,t +

(Rv,tπct+1

− Rctπct+1

)n

1− nV ej,t +

Rctπct+1

N cj,t. (E.17)

The first order conditions of the banks’ problem are

Kcj,t : Ωcj,t+1|t

(Rck,t+1 −

Rctπct+1

)Qct −Qctκc,tγct = 0 (E.18)

V cj,t : Ωcj,t+1|t

(Rv,tπct+1

− Rctπct+1

)− κc,tγct = 0 (E.19)

the envelope condition is

N cj,t : −Jc′j,t (1− γct ) + EtΩ

cj,t+1|t

RERt+1

RERt

Rctπct+1

= 0, (E.20)

and the complementary slackness conditions is

γct ≥ 0;

[Jcj,t − κct

(QctK

cj,t +

n

1− nV ej,t

)]γct = 0; (E.21)

where the notation is symmetric to that used for the EME bank.

E.3 Households and firms

Households preferences:

(E.22)Uet =

((Cet )

1−σ

1− σ− χ (He

t )1+ψ

1 + ψ

)

(E.23)U ct

((Cct )

1−σ

1− σ− χ (Hc

t )1+ψ

1 + ψ

)

41

Price dispersion measures:

(E.24)(∆et ) = ς

(∆et−1

) ( πPPI,et

πPPI,eχπ

)σp+ (1− ς)

(Π∗,et

)(−σp)

(E.25)(∆ct) = ς

(∆ct−1

) ( πPPI,ct

πPPI,cχπ

)σp+ (1− ς)

(Π∗,ct

)(−σp)

where χπ = 0, 1 is a Boolean parameter capturing price indexation to steady state inflation. In the

reported simulation it takes the value 1.

Optimal price set by price-changing firms:

(E.26)(Π∗,et

)=

(F et )

(Get )

(E.27)(Π∗,ct

)=

(F ct )

(Gct)

where

(E.28)(F et ) = (Y et ) (MCet ) + ς(

Λet+1|t

) ( πPPI,et+1

πPPI,eχπ

)σp (F et+1

)

(E.29)(F ct ) = (Y ct ) (MCct ) + ς(

Λct+1|t

) ( πPPI,ct+1

πPPI,cχπ

)σp (F ct+1

)

(E.30)(Get ) =(Y et ) (P et )

σpσp−1

+ ς(

Λet+1|t

) ( πPPI,et+1

πPPI,eχπ

)σp−1 (Get+1

)

(E.31)(Gct) =(Y ct ) (P ct )

σpσp−1

+ ς(

Λct+1|t

) ( πPPI,ct+1

πPPI,cχπ

)σp−1 (Gct+1

)where MC is the marginal cost.

Relative PPI price dynamics:

(E.32)1 = ς

(πPPI,et

πPPI,eχπ

)σp−1

+ (1− ς)(Π∗,et

)1−σp

(E.33)1 = ς

(πPPI,ct

πPPI,cχπ

)σp−1

+ (1− ς)(Π∗,ct

)1−σpEuler equation for foreign bonds:

(E.34)

(Λet+1|t) (R∗t )

(πct+1)(RERt+1)

(RERt)− 1 = 0

Consumption Euler equation for EME

(E.35)(Ret )

(Λet+1|t

)(πet+1

) = 1

42

Centre country consumption Euler equation:

(E.36)

(Λct+1|t

)(R∗t )(

πct+1

) − 1 = 0

Gross return on capital:

(E.37)(Rk,et

) (Qet−1

)=(

(MCet ) (Aet ) α (Het )

1−α (Ket−1

)α−1+ (1− δ) (Qet )

)

(E.38)(Rk,ct

) (Qct−1

)=(α (MCct ) (Act) (Hc

t )1−α (

Kct−1

)α−1+ (1− δ) (Qct)

)Aggregate price indexes (in units of consumption aggregator):

(E.39)1 = νe (P et )1−ηp + (1− νe) ((P ct ) (RERt))

1−ηp

(E.40)1 = νc (P ct )1−ηp + (1− νc)

((P et )

(RERt)

)1−ηp

CPI inflation measures:(E.41)(P et ) (πet ) =

(P et−1

) (πPPI,et

)

(E.42)(P ct ) (πct ) =(P ct−1

) (πPPI,ct

)Labor market clearing condition:

(E.43)(Aet ) (MCet ) (1− α) (Het )

(−α) (Ket−1

)α(Cet )

(−σ)= χ (He

t )ψ

(E.44)(Act) (MCct ) (1− α) (Hct )

(−α) (Kct−1

)α(Cct )

(−σ)= χ (Hc

t )ψ

Accumulation law for capital:

(E.45)(Ket ) =

((Iet ) +

(Ket−1

)(1− δ)

)(E.46)(Kc

t ) =((Ict ) + (1− δ)

(Kct−1

))Investment Euler equations:

(E.47)(Qet ) = 1 +η

2

((Iet )(Iet−1

) − 1

)2

+

((Iet )(Iet−1

) − 1

)(Iet ) η(Iet−1

) − (Λet+1|t

)η

((Iet+1

)(Iet )

)2 ((Iet+1

)(Iet )

− 1

)

(E.48)(Qct) = 1 +η

2

((Ict )(Ict−1

) − 1

)2

+

((Ict )(Ict−1

) − 1

)(Ict ) η(Ict−1

) − (Λct+1|t

)η

((Ict+1

)(Ict )

)2 ((Ict+1

)(Ict )

− 1

)Aggregate budget constraint for EME households:

(E.49)

(Cet ) +Bet (RERt) = (Y et ) (P et )−(Ket−1

)α(He

t )1−α

(MCet ) (Aet ) α

+ (Qet ) (Iet )− (Iet )

1 +η

2

((Iet )(Iet−1

) − 1

)2

+ (1− θ) Nei,t −

(Ket−1

)(Qet ) δT + (RERt)

(R∗t−1

)(πct )

Bet−1

43

Goods market clearing conditions:

(E.50)(Ket−1

)α(Aet ) (He

t )1−α

= (∆et ) (Y et )

(E.51)(Kct−1

)α(Act) (Hc

t )1−α

= (∆ct) (Y ct )

Aggregate demand for domestic and foreign goods:

(E.52)

(Y et ) = νe (P et )(−ηp)

(Cet ) + (Iet )

1 +η

2

((Iet )(Iet−1

) − 1

)2

+ (1− νc) 1− nn

((P et )

(RERt)

)(−ηp)(Cct ) + (Ict )

1 +η

2

((Ict )(Ict−1

) − 1

)2

(E.53)

(Y ct ) =

(Cet ) + (Iet )

1 +η

2

((Iet )(Iet−1

) − 1

)2+

(1− νe) n

1− n((P ct ) (RERt))

(−ηp)

+

(Cct ) + (Ict )

1 +η

2

((Ict )(Ict−1

) − 1

)2 νc (P ct )

(−ηp)

F Different degrees of financial dependence

In the main text we have assumed that the EME banks cannot borrow domestically. This assumption

aims to maximize the degree of financial dependence of the periphery country. Allowing for domestic

deposits reduces the cost of borrowing for EME banks, as the deposit rate lies below the cost of cross-

border loans. Figures 19 and 20 compare the response of a subset of variables to TFP and financial

shocks in the center country under two scenarios: i) no domestic deposits, and ii) liabilities equally

split between domestic and foreign loans. Importantly, this comparison is performed using the baseline

parameter values, and in particular using the baseline severity of the agency problem. As it is apparent

from the figures, the degree of financial dependence is virtually irrelevant for the larger economy (AE).

On the other hand, and as expected, the EME is more insulated from foreign shocks when it can use

domestic funds to finance banks and thus production.

44

Figure 1: The two-country world

45

Figure 2: Flexible prices: AE TFP shock

46

Figure 3: Flexible preices: Financial shock

47

Figure 4: TFP shock: Alternative policy regimes

48

Figure 5: Normalized coefficients of EM targeting rule 1: VAR controlling for TFP shocks.

49

Figure 6: Normalized coefficients of AE targeting rule 2: VAR controlling for TFP shocks.

50

Figure 7: Responses under truly optimal and approximated policies, controlling for TFP shocks in VAR:TFP shock in AE.

51

Figure 8: Responses under truly optimal and approximated policies, controlling for TFP shocks in VAR:TFP shock in EM.

52

Figure 9: Coefficients of EM targeting rule 3: VAR controlling for TFP and financial shocks.

53

Figure 10: Coefficients of AE targeting rule 4: VAR controlling for TFP and financial shocks.

54

Figure 11: Responses under truly optimal and approximated policies, controlling for TFP and financialshocks in VAR: TFP shock in AE.

55

Figure 12: Responses under truly optimal and approximated policies, controlling for TFP and financialshocks in VAR: TFP shock in EM.

56

Figure 13: Responses under truly optimal and approximated policies, controlling for TFP and financialshocks in VAR: Financial shock in AE.

57

Figure 14: Responses under truly optimal and approximated policies, controlling for TFP and financialshocks in VAR: Financial shock in EM.

58

Figure 15: Comparison with inflation targeting. Controlling for TFP and financial shocks in VAR: IRFsto a TFP shock in AE.

59

Figure 16: Comparison with inflation targeting. Controlling for TFP and financial shocks in VAR: IRFsto a TFP shock in EM.

60

Figure 17: Comparison with inflation targeting. Controlling for TFP and financial shocks in VAR: IRFsto a Financial shock in AE.

61

Figure 18: Comparison with inflation targeting. Controlling for TFP and financial shocks in VAR: IRFsto a Financial shock in EM.

62

Figure 19: Role of domestic deposits: AE TFP shock

63

Figure 20: Role of domestic deposits: AE financial shock

64