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
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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.
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).
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
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
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
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.
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)