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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.
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
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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