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Federal Reserve Bank of Chicago

Optimal Monetary Policy in an Open
Emerging Market Economy
Tara Iyer

June 2016
WP 2016-06

Optimal Monetary Policy in an Open Emerging Market Economy
Tara Iyer⇤

Abstract
The majority of households across emerging market economies are excluded from the financial
markets and cannot smooth consumption. I analyze the implications of this for optimal monetary
policy and the corresponding choice of domestic versus external nominal anchor in a small open
economy framework with nominal rigidities, aggregate uncertainty, and financial exclusion. I find
that, if set optimally, monetary policy smooths the consumption of financially-excluded agents by
stabilizing their income. Even though CPI inflation targeting approximates optimal monetary policy when financial inclusion is high, targeting the exchange rate is appropriate if financial inclusion
is limited. Nominal exchange rate stability, upon shocks that create trade-offs for monetary policy, directly stabilizes the import component of financially-excluded agents’ consumption baskets,
which smooths their consumption and reduces macroeconomic volatility. This study provides a
counterpoint to Milton Friedman’s long-standing argument for a float.

Keywords Asymmetric Risk-Sharing, Fixed Exchange Rates, Financial Exclusion, Optimal Monetary Policy,
Emerging Market Economies

JEL classification F21, F31, E24, E52, F43

⇤ Department of Economics, University of Oxford. I am grateful to Chris Adam, Jeff Campbell, and Andrea Ferrero,
for many helpful discussions, and to Marco Bassetto, Emmanuel Farhi, James Fenske, Benjamin Friedman, Gita Gopinath,
Alejandro Justiniano, Greg Mankiw, Jing Zhang, and seminar participants at the Federal Reserve Bank of Chicago, for very
useful comments. All errors are my own.

“In developing countries where financial markets are underdeveloped, the poor do not have access to credit and
[are thus restricted to consuming disposable income]... The challenge is how to stabilize output more effectively
and reduce the burden on the poor... Central Banks need to resort to instruments other than the interest rate.”
- The 2014 Global Economic Symposium (GES, 2014)

Introduction

The Global Financial Crisis of 2007-09 led to macroeconomic volatility in many emerging market
economies (EMEs) and, in particular, adversely affected poor agents within these countries (World
Bank, 2009). One significant factor that contributed to the vulnerability of the poor was their inability
to insure against the crisis-related contraction of incomes by drawing on savings held in the financial
markets. The macroeconomic consequences of this are not trivial, as on average, financially-excluded
households constitute 60% of households in EMEs, compared to the corresponding average of under 5% in advanced economies (World Bank, 2015; see Figure 1).1 This was highlighted by the crisis,
which renewed interest in the following interlinked macroeconomic stabilization questions. Can monetary policy be effective while paying attention to financially-excluded agents? Relatedly, should the
supporting nominal anchor be domestic or external?
A major channel in the monetary transmission mechanism, through which nominal interest rate
changes affect the real economy, is the intertemporal optimization by private agents who react to
interest rate surprises by changing their asset portfolios. This channel is considerably restricted in
economies where the majority of households do not hold assets, and the appropriate monetary policy
in this case has been subject to much recent debate in policy circles (summarized in Prasad, 2013 and
IMF, 2015a). To complement the policy discussions, however, the corresponding theoretical analysis
has been fairly limited. I seek to fill in this gap by providing benchmark results on the implications
of limited financial inclusion for optimal monetary policy and the corresponding choice of a nominal
anchor in an open emerging market economy.
The economy in this study is small and open, and specifically of measure zero, as EMEs are typically price takers for tradable goods (Frankel, 2010). Openness further permits a quantitative comparison of domestic versus external nominal anchors in approximating optimal monetary policy. Financially excluded agents fully consume their income each period, as they do not have the economic
means to save and borrow from financial institutions. The Euler Equation does not hold for these
agents, implying that a fraction of the economy cannot insure against shocks through international
risk-sharing arrangements. I characterize the optimal monetary policy for the model in the presence
of distortions caused by monopolistic competition and staggered price setting, and rank simple monetary rules in terms of lowest welfare losses away from the optimum. The implications of different
1 Regional

abbreviations used in Figure 1 are as follows. MENA: Middle East and North Africa. SSA: Sub-Saharan
Africa. ASIA: East, South, and Central Asia. LAC: Latin America and the Caribbean. EUR: Europe. CIS: Commonwealth of
Independent States.

shocks are analyzed, with the focus primarily on adverse supply (or cost-push) shocks. This is of particular interest since over the past few years, cost-push shocks, due to domestic food price volatility
(driven by weather conditions) and fuel input price volatility (driven by world market conditions),
have been predominant in EMEs (Frankel, 2010).

Figure 1: Financial Inclusion Across the World
Data: Percent Households with Account at Any Financial Institution
Sources: World Bank 2014 financial inclusion database (World Bank, 2015), and IMF
2015 country classification scheme (IMF, 2015b)

Two main findings emerge from the analysis in this paper. First, optimal monetary policy smooths
the consumption of financially-excluded agents. The intuition for this result stems from the fact that
hand-to-mouth agents are not able to privately smooth consumption or insure themselves through
risk-sharing arrangements with foreign agents in the model. Their consumption is thus far more
volatile than that of financially-included agents. To mitigate the resulting macroeconomic volatility
upon shocks, optimal policy smooths the consumption of financially-excluded agents by stabilizing
their income. This can be interpreted as provision of insurance by monetary policy.
Welfare losses are minimized when the weight placed on minimizing output gap volatility, relative to domestic inflation volatility, increases with financial exclusion and openness.2 Minimizing
output gap volatility stabilizes labor demand and hence real wages, which in turn stabilizes hand-tomouth consumption upon shocks. The relative weight on stabilizing the output gap increases with
the degree of financial exclusion as there is greater need to smooth the consumption of progressively
more disposable-income driven agents. The relative weight also increases as the economy becomes
more open. To see this, note that greater openness implies that domestic agents consume more imports
relative to home goods. This increases the consequences of exchange rate volatility, which adversely
affects hand-to-mouth agents as unlike asset holders, they cannot smooth their consumption against
the increasingly volatile price of imported goods. Hence, optimal policy makes up for their inability
to privately insure themselves by stabilizing their wage income through the output gap.
2 Another way to interpret this is that as financial exclusion increases - the relative weight on stabilizing domestic inflation

decreases, since inflation erodes the value of financial assets, and there are fewer asset holders now to consider. This is
discussed also in Bilbiie (2008).

The second result is that the insurance properties of the optimal monetary plan are internalized
through the external anchor of a fixed nominal exchange rate. I find that exchange rate stability is
desirable in an economy with a large fraction of financially-excluded agents. Upon cost-push shocks,
which simultaneously decrease output and increase inflation, thus creating a trade-off for monetary
policy, targeting the exchange rate approximates the efficient dynamics through two channels. It leads
to more muted real appreciation, which prevents the consumption of financially-included agents from
falling as much. This leads to a relative output expansion, which closes the output gap, thus stabilizing
real wages and hand-to-mouth consumption. Further, lower exchange rate volatility directly stabilizes
the import component of the financially-excluded consumption basket and hence smooths their consumption. These results provide a counterpoint to Milton Friedman’s long-standing argument for
flexible exchange rates, which provides the underlying intuition for the optimality of a float in the
more recent complete financial inclusion reference model of Gali and Monacelli (2005).
Friedman advocated a float on the premise that it would allow for greater relative price adjustment between domestic and foreign goods, given that nominal rigidities constrain real adjustment in
practice. A peg would only exacerbate the lack of relative price adjustment and thus lead to greater
macroeconomic volatility. However, this does not account for high financial exclusion. My results extend Friedman’s classic arguments to an economic setting where the majority of agents cannot smooth
consumption. Even though a float continues to allow for greater relative price adjustment with nominal rigidities, this actually leads to greater loss in the presence of high financial exclusion, as it instigates a corresponding rise in hand-to-mouth consumption volatility. For EMEs, however, Friedman
advocated a peg due to the gain in credibility by anchoring domestic monetary policy to a stable, advanced country’s regime (Hanke, 2008). I corroborate these political economy reasons by providing a
new theoretical rationale for the desirability of a peg in EMEs.
Related Literature This paper contributes to three strands of research: monetary policy in emerging market economies, the dynamics of general equilibrium models with hand-to-mouth agents, and
optimal monetary policy in open economies. The former literature is burgeoning, and in a recent
study, Prasad and Zhang (2015) build a multi-sector model with traded and non-traded sectors. They
find that exchange rate targeting benefits households in the tradable sector as it fixes the domestic
price of traded goods. This paper differs in two main ways. It shows that the distribution of household asset income in EMEs has significant implications for exchange rate stabilization. Further, it
employs rigorous perturbation techniques in micro-founding the loss function, with corresponding
sharp, closed-form solutions. Other related papers, while not having a specific monetary policy focus,
have investigated business cycles in EMEs. I discuss a few of these below.
Aguiar and Gopinath (2007) estimate a frictionless RBC model to find that trend growth shocks
to output can account for a significant proportion of economic fluctuations in EMEs. These findings
are challenged and argued to be specific to a short data time series by Garcia-Cicco et al. (2010), who
pursue a similar analysis with an extended dataset. Frankel (2010) provides an extensive review of

short-run policy in EMEs, and suggests that cost-push shocks, due to food and fuel input price fluctuations, are a significant source of concern in driving business cycles. This paper complements the
existing literature on business cycles in EMEs by focusing on dynamics with cost-push shocks, and
also providing a comparison with productivity shocks. It diverges by incorporating market imperfections such as nominal rigidities and financial exclusion, and providing new theoretical results on
optimal policy in the presence of financial exclusion in the familiar New Keynesian framework.
The literature on hand-to-mouth agents in New Keynesian models started with Galí et al. (2007),
who showed that simple rules can lead to indeterminacy with a high fraction of hand-to-mouth agents,
l, in a closed economy with capital accumulation. Bilbiie (2008) further analyzes determinacy for a
version of that closed economy model without capital accumulation and derives the optimal monetary
policy. He finds that stabilizing inflation becomes less important as l increases, and like Galí et al.
(2007), that equilibrium indeterminacy with simple rules arises if l is above a particular threshold.
Eser (2009) and Ascari et al. (2011) find that hand-to-mouth agents in a currency union, and with sticky
wages, affect determinacy and also make output stabilization more important. This paper extends the
current literature in four different dimensions.
First, I analyze the implications of a fluctuating nominal exchange rate for optimal monetary policy with financial exclusion, and show the importance of paying attention to external volatility. This
is because exchange rate movements affect the heterogeneous agents in a highly asymmetric manner.
While 1

l fraction of agents can share risk internationally, so that changes to real income from ex-

change rate fluctuations are offset through the proceeds from state-contingent claims, exchange rate
volatility leads to an immediate rise in consumption volatility (in the presence of nominal rigidities)
by the other l fraction. The implied net foreign asset position in the domestic economy is non-zero,
and thus the equilibrium consequences are non-trivial.
Second, I consider the appropriate choice of an implementable nominal anchor that can approximate the optimal monetary policy. This quantitative analysis yields some new, unconventional results
including those that provide a counterpoint to Friedman’s argument for a float. Third, I develop a technically rigorous derivation of the loss function, which makes use of analytical perturbation techniques,
and does not require an ad-hoc subsidy to eliminate the linear terms - an “unappealing assumption”
(abstract, Benigno and Woodford, 2005) used for convenience by much of the optimal policy literature. Fourth, due to a non-zero net foreign asset position as l fraction of agents do not hold assets,
the resulting open economy equilibrium and optimal policy are not isomorphic to the closed economy
case, complementing other instances such as Monacelli (2005) and Farhi and Werning (2012).
A detailed review of the third strand of related research, on optimal monetary policy in open
economies, is found in Corsetti et al. (2010). This literature generally approaches optimal policy
through a linear quadratic framework, following the perturbation techniques discussed in Benigno
and Woodford (2012). The terms and weights in these papers’ quadratic micro-founded loss functions
play key roles in driving the results. This paper diverges in two ways. Technically, I do not use a convenient ad-hoc subsidy to eliminate the linear term in the loss function, and instead take second-order
5

approximations of the structural equations to replace out for it with the correct quadratic terms.
I also model an austere form of financial market incompleteness, as relevant in EMEs, where a
large proportion of households are not able to engage in financial transactions. Only a fraction of
the population is allowed to insure against aggregate uncertainty through international risk-sharing
arrangements. This fundamental asymmetry in the ability to pool risk with foreign agents is new to the
open economy optimal policy literature, and has striking implications for the exchange rate. It is worth
noting that the form of market incompleteness that has typically been considered, ie. international
trade in a single risk-free bond as opposed to state-contingent securities, is also applicable to EMEs.
This would imply that financially-included agents engage in imperfect risk-sharing. I leave open for
future research an analysis of optimal policy with financial exclusion when even financially-included
agents cannot fully insure against uncertainty.
The rest of the paper proceeds as follows. Section 2 develops an open economy model with financial exclusion. Optimal monetary policy for the model is characterized in Section 3. Section 4
compares optimal policy with simple monetary rules, and considers the choice of an implementable
nominal anchor in the presence of financial exclusion. Section 5 concludes, and discusses possible
extensions. The appendix contains additional figures.

A Small Open Economy with Financial Exclusion

I develop an open economy general equilibrium framework with nominal rigidities, aggregate uncertainty, and two types of households. The model incorporates financially-excluded agents in addition
to the standard financially-included agents considered in the open economy DSGE literature, and
builds upon the small open economy framework of Gali and Monacelli (2005). Section 2 is cast in
non-linear terms for expositional ease, and the resulting equilibrium will be linearized in Sections 3
and 4 to solve for optimal monetary policy using perturbation techniques.

2.1

Households

There exists a continuum of households indexed by l 2 [0, 1]. Fraction 1

l of households partic-

ipate in the financial markets, which are assumed to be complete both within and across countries.
Through a complete set of state-contingent securities available internationally, they are able to share
risk with foreign agents. However, a fraction l of domestic agents do not engage in financial transactions as they do not have the economic means to do so, similar to the “hand-to-mouth” consumers
in Mankiw (2000). Their sole source of income is wage income. Thus, although financially-excluded
agents can optimize labor supply, they are unable to share risk internationally or smooth consumption. Throughout the paper, financially-included households are denoted with the symbol,b, while
financially-excluded households are denoted with the symbol,ˇ.
The domestic economy, with its heterogeneous consumers, is of measure zero compared to the

world. This implies that domestic monetary policy decisions do not have any impact on the rest of
the world, which consists of a continuum of economies, j 2 [0, 1], populated by identical, financially-

included households. While different economies are subject to asymmetric and imperfectly correlated
shocks, initial net foreign asset positions are symmetrically zero across countries, and preferences and
market structures are identical. In each period t
st = (s0 , ..., st

1 , st )

0, a stochastic event, st 2 S, is realized. I denote by

the history of events until period t. The unconditional probability, as of period 0, of

observing any particular history st is µ st . The probability of history st+1 , conditional on st , is given
by µ st+1 |st . The initial realization, s0 , is taken as given so that µ (s0 ) = 1 for a particular s0 2 S.
2.1.1

Financially-Excluded Agents

Financially-excluded agents, l 2 [0, l], fully consume their income each period and cannot smooth
consumption through the financial markets. These agents gain utility from consumption, Č st , and

disutility from hours worked, Ň st . The representative household chooses its period t allocation after
the realization of the event, st , to maximize its utility, Ǔ (st ) = Âst µ(st )U Č st , Ň st

, through the

following static optimization problem
Max
Ǔ (s ) = Â µ(s )
{Č(st ), Ň (st )}
st
t

(

Č st 1
1 s

s.t. P st Č st  W st Ň st

Ň st 1+f
1+f

)

(1)
(2)

where s is the inverse intertemporal elasticity of substitution (IES), f is the inverse Frisch elasticity
of labor supply, P st is the consumer price index (CPI), W st denotes nominal wages, Ň st represents hours of labor supplied, and Č st is consumption of domestically produced and imported
goods from a constant elasticity of substitution (CES) consumption basket. All these variables are
denominated in units of domestic currency.
Preferences are locally non-satiated, so that the budget constraint binds. This implies that the
consumption of excluded households derives directly from (2). Further, as these agents do not hold
bonds and thus cannot optimize intertemporally through an Euler Equation, real interest rate changes
are not internalized by l fraction of the economy. Relatedly, it is worth noting that empirical evidence
on the inverse IES, s, is unavailable for these agents. I will address this by assuming a standard
calibration for s in the optimal monetary policy analysis.
Financially-excluded households trade off leisure for consumption goods, through their optimal
W ( st )
labor supply condition, (3), where w st denotes the real wage rate, w st = P(st ) . While nominal
wages, W st , are the same for both consumers and producers, real wages faced by households, w st ,
W ( st )
differ from the real wages faced by domestic firms, P (st ) , where PH st is the domestic (monopolisH

tically set) price index. This is because households take into account the CPI, P st , which consists
of both domestic and imported good prices. The labor supply condition, derived by combining the
first-order conditions on consumption and labor, is
7

w st = Ň st
2.1.2

Č st

(3)

Financially-Included Agents

Financially-included agents, l 2 [l, 1], gain utility from consumption, Ĉ st and disutility from hours

worked, N̂ st . These agents own the domestic firms, and have access to a complete portfolio of
state-contingent bonds, which are traded sequentially in spot markets with foreign households in
each period, t

0, before st+1 occurs. The equilibrium that arises from this assumption of sequential

trading is equivalent to that which would arise from a time 0 trading of a complete set of historycontingent bonds. Notably, although financial trades are executed before uncertainty realizes, the
period t allocation is chosen after event st occurs.
I let B st , st+1 denote the representative financially-included agent’s holdings of a complete vector of state-contingent claims at time t, given history st , on time t + 1 domestic currency. One unit of
this vector pays off one unit of domestic currency if the particular state st+1 occurs and 0 otherwise.
B st , st+1 is denominated in units of domestic currency and each of its units is priced at Z st+1 |st ,

where st+1 = st , st+1 . Taking Z st+1 |st as given, the representative household maximizes its utility,

Û st = Âst µ(st )U Ĉ st , N̂ st

, subject to a sequence of budget constraints for t

0, by solving

the following dynamic optimization problem
•

•

Max
Â bt Û (st ) = Â Ât bt µ(st )
{Ĉ(st ), N̂ (st ),B(st ,st+1 )} t=0
t =0 s
s.t. P st Ĉ st +

(

Ĉ st 1
1 s

N̂ st 1+f
1+f

⇣
⌘
t +1 t
Z
s
|
s
B st , st+1  B st + W st N̂ st + W st
Â

s t +1

)
T st

(4)

where bt 2 [0, 1] is the subjective discount factor, N̂ st represents hours of labor supplied, Ĉ st is
consumption of domestically produced and imported goods from a CES consumption basket, W st

denotes profits received from ownership of domestic firms, and T st is a nominal lump-sum tax. All
these variables are denominated in units of domestic currency, and the initial condition, B(s0 ), is taken
as given. The budget constraint binds, and as standard in the optimal policy literature, the lump-sum
tax is used to finance a constant wage subsidy, t e , to offset the steady state monopolistic distortion
T st = t e W st N st

(5)

where N st is labor demanded by the monopolistic producers. Each period, financially-included
agents trade off leisure for consumption goods through their optimal labor supply condition, (6),
derived by combining the first-order conditions on consumption and labor
w st = N̂ st

Ĉ st

(6)

The first-order conditions on state-contingent bonds and consumption can be combined to yield the
Euler Equation
⇣

Z s
where P st+1 =

P ( s t +1 )
P(st )

t +1

⌘

⇣

= bµ s

t +1

"
#
⌘ Ĉ st+1
Ĉ (st )

1
P ( s t +1 )

(7)

is CPI inflation. A similar equilibrium condition with respect to domestic

currency state-contingent bonds, adjusted for the presence of the nominal bilateral exchange rate,
# j st , to ensure price equalization across the world in contingent claims, holds for the representative
household in country j
⇣

Z s

t +1

⌘

"
#
⌘ C j s t +1
= bµ st+1 |st
C j (st )
⇣

# j s t +1
1
j
j
t
# ( s ) P ( s t +1 )

(8)

where C j st , P j st , and # j st denote the consumption basket, CPI inflation, and bilateral nominal
exchange rate of country j.3 Combining the Euler Equation of the domestic household, (7), with that of
´1
each foreign household j 2 [0, 1], (8), and integrating across foreign households, C ⇤ st = 0 Cj st dj,
yields the Backus-Smith (Backus and Smith, 1993) international risk-sharing condition from the perspective of the domestic small open economy
1

Ĉ (st ) = uC ⇤ Q(st ) s

(9)

which assumes that agents across the world make appropriate ex-ante international insurance transfers through complete financial markets, to ensure that risk is pooled internationally, ie. u = 1, and
that world consumption is exogenous and constant. The precise value of the insurance transfers to the
domestic economy is given in equation (32) in section 2.6. International risk-sharing, (9), means that
the marginal utility of consumption, weighted by the real effective exchange rate, Q(st ) = #(st )

P⇤ (st )
,
P(st )

is equalized across countries, where P⇤ (st ) is the world price index and #(st ) is the nominal effective
exchange rate ie. an index of the prices of foreign currencies j 2 [0, 1] in terms of domestic currency.

Efficient risk-sharing thus implies that demand, by financially-included agents worldwide, is di-

rected at countries where it is cheaper to consume. Risk-sharing is possible because of the timing
of financial trades. Financial markets open before monetary policy decisions are made, implying
that financially-included agents are able to smooth consumption in the face of uncertainty implied
by choice of monetary regime. Further, this pooling of risk with foreign agents insures financiallyincluded agents in an open economy, compared to the closed economy case (without capital) where it
is not possible to insure against aggregate uncertainty.
3 The

representative household in country j faces the following budget constraint in each period t
0: P j st C j st +
t
+
1
t
j
t
j
t
j
t
j
t
j
t
j
t
j
t
j
t
T s , where B s represents the foreign
Â s t +1 Z s | s B s , s t + 1  # s B s + W s N s + W s
household’s holdings of the state-contingent bond denominated in units of domestic currency and # j st is the bilateral
nominal exchange rate with respect to the domestic economy ie. the price of domestic currency in units of foreign currency.
# j st serves to convert the domestic currency payoffs into foreign currency.
#j

I assume that financial asset market arbitrage opportunities do not exist, as these would lead to
indeterminacy in the international portfolio allocation problem. This implies that the equilibrium
prices - in domestic currency - of risk-free one-period uncontingent nominal bonds at home and in
foreign country j, are related to their gross returns as follows
⇣
⌘
t +1 t
Z
s
|
s
=
Â

s t +1

⇣
⌘ ⇣
⌘
t +1 t
t +1
Z
s
|
s
#
s
=
j
Â

1
1 + i (st )

s t +1

# st
1 + i j (st )

(10)

where the domestic currency price of a domestic bond, Âst+1 Z st+1 |st , is inversely related to the
gross domestic nominal interest rate, 1 + i st , and the domestic currency price of a foreign bond,
Âst+1 Z st+1 |st # j (st+1 ), is inversely related to the gross foreign nominal interest rate, 1 + i j st , ad-

justed by the bilateral nominal exchange rate. Domestic monetary policy has direct leverage over
i st . Combing the domestic and foreign bond pricing equations, and aggregating across countries
j 2 [0, 1], yields the uncovered interest rate parity (UIP) condition

ÂZ

s t +1

where i⇤ st =

´1
0

⇣

s t +1 | s t

⌘

(

(1 + i s t )

# s t +1
st )
# (st )

(1 + i ⇤

)

(11)

i j st dj is the world nominal interest rate, taken as given by the domestic small

open economy. UIP formalizes the lack of arbitrage opportunities in the international asset markets,
by implying that the nominal exchange rate is expected to adjust upon shocks to equalize the domestic
currency returns on domestic and foreign contingent bonds.
2.1.3

Aggregation

A perfectly competitive firm uses CES technology to produce an aggregate consumption good, C st ,
from domestic and foreign aggregates, respectively CH (st ) and CF (st ). The aggregate consumption
good is purchased by financially-excluded and financially-included agents according to C st
lČ st + (1

l)Ĉ st , and is produced as follows
C st = [(1

a) # I CH st

#I 1
#I

+ a # I CF s t

#I 1
#I

] #I

(12)

where a 2 [0, 1] is the share of imports in the CES basket and represents the degree of openness to
international trade in goods (conversely, 1

a is the degree of home bias), and # I is the elasticity of

substitution between domestic and foreign goods. The associated price index is
h
P s t = (1

a) PH# I st + aPF1

i 1 1#

(13)

where P st is the consumer price index (CPI), PH st is the price index for domestic goods, and
PF st is the import price index. Minimizing expenditure on the CES consumption basket (12) gives
10

rise to the following downward-sloping demand functions for domestic and imported aggregates
"

PH st
a)
P (st )

C H s t = (1

where CH st = lČH st + (1

C st

PF st
=a
P (st )

CF s t

l)ĈH st and CF st = lČF st + (1

C st

(14)

l)ĈF st . The imported

good, CF st comprises of goods from each foreign country, j, and # F denotes the elasticity of substitution between imported goods

CF s t =

"ˆ

Cj st

#F 1
#F

# # #F 1
F

(15)

The subcomponents of the domestic and imported good indices measure domestic consumption of
individual varieties of goods, i. These varieties are produced at home as well as in the continuum of
foreign small open economies, j 2 [0, 1], so that CH i, st is the consumption of domestic variety i and
Cj i, st is the consumption of variety i imported from country j
CH st =

"ˆ

CH i, st

#p 1
#p

# # #p 1
p

Cj st =

"ˆ

Cj i, st

#p 1
#p

# # #p 1
p

(16)

where, due to the assumption of identical market structures across countries, # p is the elasticity of
substitution between individual varieties, i, produced in any country j, including home. The price
indices associated with the demand for domestic and country j’s varieties are
PH st =

2.2

"ˆ

PH i, s

t 1 #p

# 1 1#

Pj st =

"ˆ

Pj i, s

t 1 #p

# 1 1#

(17)

Relative Prices and Exchange Rates

The model equilibrium will be defined in terms of the effective terms of trade, X st =

PF (st )
,
PH (st )

which

is an index of the bilateral terms of trade between the domestic economy and all foreign economies
⇣´
⌘ 1
•
t 1 # F dj 1 # F , where X
t = P st /P
t denotes the
j 2 [0, 1]. That is, X st =
X
s
H s
jH
jH s
j
0
price of country j’s goods in terms of domestic goods.

To put prices in terms of X st , I first normalize all prices by the CPI, (13), to define them in
relative terms. These are the relative domestic price index, p H st = PH st /P st , and the relative
import price index, p F st = PF st /P st . As functions of the effective terms of trade, X st , these
are written as
h
p H st = 1

a + aX st

1 #I

1
1 #I

p F st = X st

a + aX st

1 #I

1
1 #I

(18)

The effective terms of trade, X st , can thus be written as a ratio of relative prices
X st =

The nominal effective exchange rate, #

⇣´

1
0 #j

p F st
p H (st )
1 #F
st

(19)

⌘ 1 1#

, is an index of the nominal bilateral

exchange rates between foreign countries, j 2 [0, 1], and the domestic economy. The nominal bilateral

exchange rate between home and any country j, # j st , is the price of foreign currency, j, in units of
´1
domestic currency. P⇤ st = 0 P j st dj is the world price index, where P j st is the CPI in country
j. The real effective CPI exchange rate

Q st =

# st P⇤ st
P (st )

is defined as the domestic currency price of a foreign basket of consumption, # st P⇤ st , relative to
⇣´
⌘ 1 1#
1 #F
1
F
the domestic currency price of a domestic basket of consumption, P st . Q st = 0 Q j st
dj
,
where Q j st is the real bilateral exchange rate between home and country j. Q st can be expressed
in terms of X st . Assuming that purchasing power parity holds in the imported goods market, so
that PF st = # st PF⇤ st , and that from the perspective of the domestic economy, which is small,
the world as a whole behaves like a closed economy, so that P⇤ st = PF⇤ st , I derive
h
Q s t = (1

a) X st

#I 1

i# 1

I 1

(20)

Note that the real exchange rate is a function of the effective terms of trade in this framework, so that
these two relative prices co-move upon shocks.

2.3

Firms

Goods are supplied to domestic and foreign consumers. Firms, i 2 [0, 1], are monopolistic and set

prices in a staggered fashion. In any given period and independent of time elapsed since last reset,
a fraction (1

q ) of (randomly selected) firms can re-optimize prices. Fraction q of firms cannot re-

optimize and instead adjust labor demand to meet changes in output demand upon shocks. Firms
that do reset prices upon shocks take into account that the probability of keeping this period’s price k
periods ahead is given by q k .
With production function Y (i, st ) = A st N i, st , each reoptimizing firm i sets its optimal reset price as a markup over current and expected marginal costs, where MC i, st = W st /A st ,
giving rise to domestic inflation. Noting that a firm that reoptimizes in period t will choose the price
PH⇤ i, st that maximizes current and future expected discounted profits until period t + k while this
price remains effective, so that PH⇤ i, st+k = PH⇤ i, st for k = 0, ..., •, the optimal reset price at time t

solves the following problem

•

Â ÂZ
(i,s )

Max
⇤
t

k =0 s t + k

⇣

⌘ n
⇣
⌘
st+k |st q k (1 + t e ) PH⇤ i, st Y i, st+k

⇣

⌘

PH⇤ i, st
PH (st )

s.t. Y i, st+k =

⇣

⌘

CH i, st+k +

⇣
⌘ ⇣
⌘o
W st+k N i, st+k
ˆ

⇣

⌘

CH i, st+k dj

(21)

where Z st+k |st is the stochastic discount factor (as households own the firms) in period t + k given

history st (recall that st+k = st , st+k ), t e is a steady state wage subsidy, Y i, st+k and W st+k N i, st+k
are respectively the output and total cost in period t + k for a firm that last reset its price in period t,
´1 j
and CH i, st+k and 0 CH i, st+k dj represent demand for good i in period t + k respectively by domestic consumers and foreign consumers in countries j. In a symmetric equilibrium, the same price is
chosen by all firms that can re-optimize so that PH⇤ i, st = PH⇤ st 8i. The first-order condition is
•

Â ÂZ

k =0

st+k

⇣

⌘

⇣

st+k |st q k Y i, st+k

⌘

1
# P W st+k
1 + t e # P 1 A ( st+k )

PH⇤ st

(22)

´1
Using (21), the labor-market clearing condition Nt = 0 N i, st di, the price index associated with
h´
i 1
1
t 1 # p di 1 # p , and the definition of price
the demand for monopolistic goods PH st =
P
i,
s
0 H
✓
◆ #p
t
´
PH (i,s )
1
dispersion, D st ⌘ 0
di, which follows law of motion
P (st )
H

D s

#P 1
#P

= qp H s

t #P 1

⇣

D s

t 1

⌘

+ (1

qP H st
1 q

#P 1

(23)

it is possible to derive (24), which resembles an aggregate production function, but takes into account
the technological restrictions and distributional inefficiencies associated with price dispersion
Y st D st = A st N st

(24)

where productivity shocks, A st , are determined relative to their steady state value A and follow the
following stationary autoregressive process
Ln 1 + A st

⇣
⇣
Ln(1 + A) = r A Ln 1 + A st

⌘⌘

Ln(1 + A) + stA

with r A 2 (0, 1) and stA ⇠ N (0, sA2 ). Using the price index and definition of price dispersion, the
PH (st )
optimal reset price relates to the domestic inflation rate, P H st = P (st 1 ) , as follows
H

PH⇤ st
=
PH (st )

qP H st
1 q

#P 1

! 1 1#

From the first-order condition, (22), the optimal reset price is related to aggregate variables as
PH⇤ st
F st
=
PH (st )
K (st )

(25)

where F st is the present discounted value of total costs in real terms
F st =

⇣
⌘
⇣
⌘# ⇣
⌘
1
# P Y st MC st
t +1 t
t +1 P
t +1
+
bqµ
s
|
s
P
s
F
s
H
a
s
1 + t e # P 1 C (st ) X (st )

(26)

and K st is the present discounted value of total revenues in real terms
K s

Y st X st
=
C (st )s

⇣
⌘ ⇣
⌘# P
+ bqµ st+1 |st P st+1

⇣
⌘
K s t +1

(27)

Equations (25) to (27) summarize the recursive representation of the non-linear Phillips Curve, as in
Benigno and Woodford (2005).4 The monopolistic sector faces exogenous cost-push shocks which directly increase domestic inflation without excess aggregate demand pressures. These disturbances
represent unanticipated food price or fuel input price shocks that arise in markets outside the authority’s control. As standard in the literature, and discussed further in Sutherland (2005), V st is the net
monopolistic markup,

#P
1
# P 1 1+ t e .

Markup shocks, sV
t , are assumed to arise from random changes in

the production subsidy or the degree of monopoly power. Cost-push/ markup shocks are determined
relative to their steady state value V and follow the following stationary autoregressive process
Ln 1 + V st

⇣
⇣
Ln(1 + V ) = rV Ln 1 + V st

⌘⌘

Ln(1 + V ) + sV
t

2
where rV 2 (0, 1) and sV
t ⇠ N (0, sV ).

2.4

Central Bank

Monetary policy is set according to either simple rules or a model-specific optimized rule. The strict
simple rules (in linearized terms) are domestic inflation targeting (DIT), p H st

= 0, CPI inflation

targeting (DIT), p st = 0, and a fixed exchange rate, De st = 0, and the flexible ones are Taylortype rules where the nominal interest rate responds to a measure of inflation and the output gap.
4 The

corresponding linearized version of the Phillips curve takes the familiar form: p H,t = bp H,t+1 + xmct + vt , where

(1 bq )(1 q )
q

and vt is a cost-push shock that is appended on, as standard in the literature.

2.5

Market-Clearing and Accounting

The demand for each monopolistic good i 2 [0, 1] is5
Yt i, s

= CH i, s +

CH i, st dj
j

where CH i, st is consumption of home good i by domestic consumers and CH i, st denotes consumption of home good i by country j. Replacing in the expressions for the consumption of individual
varieties, i, international risk-sharing, and the definitions of the bilateral and effective terms of trade,
I write the above as
Y s

PH st
P (st )

a)C s

+ aĈ s

Qj s

t #I

1
s

⇣

Xj s X s

⌘# F

(28)

where X j st and X j st denote bilateral variables for the domestic economy, and X j st denotes
the effective terms of trade for country j. For s = # I = # F = 1, as in the welfare analysis, Y st =
⇤
a⇥
X st
(1 a)C st + aĈ st . The labor market is Walrasian, with the real wage, w st , moving
instantly to clear demand and supply imbalances
l Ň st + (1
where

´1
0

l) N̂ st = N st =

N i, st di

(29)

Nt i, st )di is the demand for labor by each firm, i. Aggregate consumption is a weighted

average of consumption by financially-included and financially-excluded agents
C st = lČ st + (1

l)Ĉ st

(30)

The real trade balance, in terms of the CPI, P st , is defined as the imbalance between domestic
production and consumption, and given by
NX st = p H st Y st

lČ st + (1

l)Ĉ st

(31)

The trade balance is non-zero, unlike Gali and Monacelli (2005), which is nested when l = 0 in this
framework. This point is independent of calibration, but is seen more easily for s = # I = # F = 1, as
in the welfare analysis, so that NX st boils down to NX st = al Ĉ st
st

out for (28) in (31). The fact that NX

Č st

upon replacing

is away from zero is driven by l > 0, ie. a positive degree of

financial exclusion, and has implications for the domestic net foreign asset position.
Net foreign assets, NFA st are non-zero upon shocks (they are zero in the initial steady state),
and quantify the net present value of insurance transfers to the domestic financially-included house5C

i, st = (1

⇣

PH (i,st )
PH (st )

⌘

⇣

PH (st )
P(st )

⌘

C st and CH i, st = a

⇣

PH (i,st )
PH (st )

⌘

✓

PH (st )
j
# j (st ) PF (st )

◆

✓

PF (st )
P j (st )

◆

C st

holds when uncertainty realizes. In each period, the stock of NFA st , normalized by the CPI, P st ,
derived by iterating the financially included household’s budget constraint, is given by
NFA st

•

⇣
⌘h
⇣
⌘
t+k t
t+k
Z
s
|
s
NX
s
Â

k =0 s t + k

⇣ ⇣
⌘
+ C st+k

⇣
⌘⌘
Ĉ st+k

⇣
⌘⇣ ⇣
⌘
w st+k
N st+k

(32)
⇣
⌘⌘i
N̂ st+k

Equation (32) is a useful summary of the difference between closed economies with financially-excluded
agents, for example, Galí et al. (2007) and Bilbiie (2008), and an open economy. It arises because of (i)
international risk-sharing and the associated insurance transfers, possible only in an open economy
and (ii) the fact that the trade balance is not zero with l > 0. If l = 0, then NFA st = 0 in each
period, as in Gali and Monacelli (2005), and the open economy model is isomorphic to the closed case.
In the current framework, however, as only a fraction of domestic agents can share risk with
foreign agents, open economy elements do not affect the two types of agents in a symmetric fashion.
In particular, financially-included agents can share risk and smooth consumption upon exchange rate
fluctuations, whereas financially-excluded agents cannot. This fundamental asymmetry, connected
with international risk-sharing, is why NFA st 6= 0 and optimal policy in an open economy model
with financially-excluded agents is not isomorphic to the closed economy case.

2.6

Equilibrium

For a particular specification of monetary policy (which determines the nominal interest rate, i st ),
an equilibrium for the model is a state-contingent sequence of prices
⇣
⌘
{ X st , Z st+1 |st , P st , P H st , MC st , D st , # st }•
t =0
and quantities

{Č st , Ĉ st , Ň st , Ň st , CH st , CF st , C st , N st , Y st , F st , K st }•
t =0
such that
• Goods, (28) and labor, (29) markets clear
• International-risk sharing, (9), and no asset market arbitrage, (11), conditions hold
• Financially-excluded agents, l 2 [0, l], optimize: (2) and (3)
• Financially-included agents, l 2 [l, 1], optimize: (6) and (7)
• Aggregate consumer optimization of domestic and foreign goods yields: (12) and (14)
• Firms, j 2 [0, 1], optimize: (24), (25), (26), and (27)
16

taking as given initial conditions, B s0 , D s0 , X s0 , and exogenous processes for shocks and fort
eign quantities { A st , V st , i⇤ st , P⇤ st }•
t=0 . The effective terms of trade, X s , given by (19), is

the only relative price that matters for the characterization of equilibrium.

Optimal Monetary Policy

I proceed to characterize the optimal monetary policy for this model. I provide a generalized analysis
of the optimum, before specifically analyzing cost-push shocks and ranking simple rules. Some salient
results emerge. These include the insurance role played by optimal monetary policy in the presence
of nominal rigidities and financial exclusion, and the desirability of stabilizing the nominal exchange
rate in these circumstances. I focus on the Cole-Obstfeld parameterization (Cole and Obstfeld, 1991),
s = # I = # F = 1, to keep the analysis tractable. Two flexible price allocations are characterized, to
serve as references, before turning to the constrained efficient case where monetary policy plays a role.

3.1

Flexible Prices

I begin by describing the efficient allocation of economic resources in the absence of market imperfections. This is the allocation away from which optimal monetary policy, in the presence of real and
nominal rigidities, seeks to minimize deviations. The efficient allocation corresponds to the solution
of a Planner’s problem, who maximizes a weighted sum of household utilities and faces the flexible
price and perfectly competitive versions of the constraints in the optimal monetary policy problem.
The efficient allocation can be decentralized through a wage subsidy, funded through lump-sum taxes
on the financially-included household, (5).
I will show that the efficient allocation does not coincide with the flexible price version of the
model, sometimes called the natural allocation, implying that the flexible price business cycle and
steady state of the model are inefficient. I choose an appropriate wage subsidy, t e , to implement
the efficient allocation at the steady state. To derive the efficient allocation, the Planner maximizes a
weighted sum of household utilities, U st = lǓ st + (1
where c1 st

c8 st are Lagrange multipliers attached to the constraints.

Max U st = l
S(st )

l)Û st , with weights given by l, and

LnČ e st

Ň e st 1+f
1+f

+ (1

LnĈ e st

N̂ e st 1+f
1+f

⇥

s.t.

⇥

where S st =

c1 s t
st

c2
⇥
c3
⇥
c4
⇥
c5
⇥
c6
⇥
c7
⇥
c8

st
st
st
st
st
st

⇤

C e st

= lČ e st + (1

l)Ĉ e st

⇤

N e st

= l Ň e st + (1

l) N̂ e st

Y e st

= A st N e st

⇤

we st

= Č e st Ň e st

⇤

we st

= Ĉ e st N̂ e st

⇤

Č e st

= we st Ň e st

⇤

Ĉ e st

= X e st

⇤

Y e st

= aX e st

⇤

1 a
a

Ĉ e st + (1

a) X e st

C e st

Ĉ e st , Č e st , C e st , N̂ e st , Ň e st , N e st , w e st , Y e st , X e st

. The opti-

mum derives as a non-linear system of seventeen endogenous variables, which solve an equilibrium
with nine first-order conditions and eight constraints. Further to some manipulations, it is possible
to summarize the equilibrium in a more compact system of three equations with three unknowns:
X e st , N̂ e st , and the shadow value of the resource constraint, c8 st .

Xe
lf N̂ e st

1
(st )

c8 s t

l) N̂ e st
X e ( s t ) (1

✓

X e st
l N̂ e st

A st N̂ e

+ (1

c8 s t A s t (1
a)fl

st = 0
◆
a
l) +
= 0
1 a
l)

c8 s t

= 0

Proposition 1 gives the closed-form expressions for the efficient labor allocation, N e st , the financiallyincluded agent’s consumption, Ĉ e st , and the financially-excluded agent’s consumption, Č e st .
Proposition 1. (Efficient Allocation) In the first-best allocation for the economy when prices are flexible and
firms operate in perfect competition, employment is given by

N e st
1 l

a)fl

=
l

⇣

N e (st )
1 l

(1 l )
l
✓ e t
◆f
N (s )
l
(1 l ) 1 l
1 l
⌘f
l
+ (1 l ) + 1 a a
1 l
1

N e st
1 l

l
1

!f
(33)

and financially-included and financially-excluded consumption are functions of aggregate employment
Č e st
Ĉ

= A st

N e st
1 l

= A s

l
1

l
l

!fa
!

f (1 a )

Closed-form solutions for the other endogenous variables, as well as the Lagrange multipliers, are backed out
from the remaining constraints and optimality conditions.
The solution to the Planner’s problem with heterogeneous agents, when l = 0, nests Gali and Monacelli (2005) where N e st

= (1

a) 1+f . Furthermore, note that the consumption of financially-

included and financially-excluded agents differ as only 1

l fraction of the economy shares risk

internationally. This is in contrast to the closed-economy case of Bilbiie (2008), where consumption
of both agents are limited to be identical in both flexible price allocations. The competitive allocation
for the flexible price economy derives from the definition of equilibrium provided in the previous
section, and is given in closed-form in Proposition 2.
Proposition 2. (Natural Allocation) In the second-best allocation with flexible prices and monopolistic competition, employment is given by
N

t f

✓

#P 1
a)l
#P

◆

#P 1
(1
#P

l)f ((1

a)(1

l) + a)

(34)

Other variables are backed out in closed-form from the decentralized equilibrium conditions. The subsidy t e that
restores steady state efficiency is of size t e = 1

#P 1
# P / (1

a ).

Monetary policy does not play a stabilization role in either of the flexible price allocations since prices
can instantly jump. When prices are sticky, however, the relative price distortions that arise due to
sluggish real adjustment, justify policy intervention. Upon trade-off creating shocks, welfare with
sticky prices is strictly lower than with flexible prices, and for the purposes of comparison, it will be
useful to express the allocation in presence of nominal rigidities as log-deviations, x̃t , from the flexible
price reference allocations.

3.2

Sticky Prices

It is convenient to work with a linearized version of the model hereafter, as computing analytical solutions to the non-linear problem with nominal rigidities becomes intractable. This approach is also
followed by much of the analytical literature on optimal monetary policy, for eg. Farhi and Werning (2012). I characterize the constrained efficient allocation away from a symmetric deterministic
steady state with zero inflation. This is done by taking a linear approximation of the constraints
19

and a quadratic approximation of the welfare loss function. The optimal targeting rule that results
is internally consistent and a locally linear approximation of the non-linear optimal policy. These
perturbation techniques are described further in Benigno and Woodford (2012).
3.2.1

Constraints

The constraints in the Central Bank optimization problem are the first-order linear approximations,
in log-deviation or “gap” terms, of the equilibrium conditions defined in section 2.6. A linearized
variable, f st , is related to its true non-linear value and non-linear steady state, F st and F, apF ( st ) F 6
proximately as f st t
. A variable in log-deviation terms, f˜ st is defined as the sticky
F
e

price linearized variable, f st , in deviation from the efficient linearized variable, f st , so that
e
f˜ st = f st
f st . Note that each linearized variable is measured in deviations from its efficient version, as the first-best case is the relevant welfare benchmark. Henceforth, I refer to f˜ st as an
“efficient gap”. I also use f˜ st ⌘ f˜t , and the expectations operator, Et {.}, to save on notation.

It is possible to summarize the constraints in demand (dynamic IS Equation) and supply blocks

(New Keynesian Phillips Curve, or NKPC). Notably, in the presence of financially-excluded agents, it
is still possible to derive a condition that resembles the canonical IS Equation for the small open economy. This is done by substituting the resource constraint, (28), into the aggregate Euler Equation. The
latter combines the consumption of financially-excluded agents, (2), and the intertemporal optimality
condition of financially-included agents, (7), so thus summarizes the joint consumption evolution of
the heterogeneous households in the model
1

lf(1
1 l

ỹt

a x̃t =

lf(1
1 l

Et ỹt+1

aEt x̃t+1

(it

Et pt+1 )

The Phillips Curve is derived by combining the evolution of domestic inflation resulting from firm
˜ t , where x =
optimization, p Ht = bp Ht+1 + x mc

(1 bq )(1 q )
,
q

˜t=
and mc

f
1 l ỹt

+ x̃t , which is a version

of the marginal cost condition derived by replacing the resource constraint, (28), risk-sharing condition
(9), financially-excluded consumption, (2), and the optimal labor supply conditions, (3) and (6), into
˜ t = w̃t + a x̃t .7 In the NKPC, I also make use of the relation between
real marginal costs given by mc
the terms of trade and output, x̃t = U ỹt , which is derived by combining the resource constraint with
risk-sharing. Proposition 3 formalizes the constraints in the optimal monetary policy problem.
6 At the symmetric and efficient steady state with zero inflation, shocks { A, V, C ⇤ , i ⇤ } are normalized to 1. Quantities and
relative prices are endogenous. As financial assets and profits are zero in the steady state, the budget constraints of both
households coincide. Then due to the same functional form for preferences, C = Ĉ = Č and N = N̂ = Ň. It is possible
to derive that X = 1 by combining the resource constraint, Y = CX 1 a , risk-sharing condition, C = X 1 a , production
function, Y = N, marginal cost condition, 1 = wX a , and labor supply condition, w = CN f . The remaining variables are
directly backed out.
7 Real marginal costs, in terms of output, in an open economy differ from a closed economy due to the existence of a wedge
between output and consumption, and thus domestic prices and the CPI. So, mct = wt p̂ H,t at ! mct = wt + axt at
˜ t = w̃t + a x̃t .
using the relation between relative domestic prices and the terms of trade, p H,t = axt . And in gap terms: mc

Proposition 3. (Canonical Equilibrium) For a particular specification of monetary policy, the equilibrium
with inflexible prices is
1
(it Et p Ht+1
U
=
U (1 r a ) a t
x
= bp H,t+1 + y˜t + vt
L

ỹt = Et ỹt+1
rte
p H,t
where U =
NKPC, and

1 l lf(1 a)
(1 q )(1 bq )
1 l
,x =
, L = 1 l lf
,
1 l
q
(1 a)+f
e
rt is the equilibrium efficient rate of interest.

rte )

(35)
(36)
(37)

vt is an exogenous cost-push shock in the

These constraints nest Gali and Monacelli (2005) when l = 0. Note, however, that a enters the canonical equilibrium when l > 0. In the presence of financial exclusion, openness, a (or conversely home
bias, 1

a), plays an explicit role in linking inflation and output. As financially-excluded agents can-

not smooth consumption, they are adversely affected by the increased consequences of exchange rate
volatility as the economy opens up.
Notably, Divine Coincidence (Blanchard and Galí, 2007) is present, implying that the central planner can simultaneously stabilize domestic inflation and the efficient output gap. In the absence of
cost-push shocks, setting p H,t = 0 closes the natural output gap, yt yn , when f˜t = f t f n in Propot

sition 3. But natural and efficient output are scalar functions of each other, so that strict domestic
yet = 0 in

inflation targeting (DIT), p H,t = 0, is able to achieve the first-best allocation of p H,t = yt

the absence of cost-push shocks. This has implications for the optimal monetary policy response to
productivity shocks, as discussed further in Section 4.2.
Equilibrium Determinacy The equilibrium is determinate for all degrees of financial exclusion, l,
regardless of the values of the other parameters, as long as the optimal targeting rule is implemented,
which corroborates the analogous closed economy optimal policy result in Bilbiie (2008). This point
will be discussed further after giving the optimal targeting rule, (42), in Proposition 5. With standard
active simple rules, the equilibrium is indeterminate for extreme values of l, and determinacy requires
that financial exclusion is below a certain threshold, l⇤ , as in other DSGE models with hand-to-mouth
agents, for instance Galí et al. (2007) and Bilbiie (2008). This threshold depends on other structural
parameters, ie. l < l⇤ =

1
,
1+ f (1 a )

as shown in the appendix. Indeed, it is possible to have l⇤ as

high as 0.8 with a standard range of calibrations for f and a, so that the threshold value does not
restrict my analysis or affect any of the results or conclusions. It is worth noting that the percentage of
financially excluded agents, l, in the vast majority of emerging market economies, is much less than
80%. Intuition for why the equilibrium is determinate when l < l⇤ is as follows.
When l < l⇤ , the elasticity of output with respect to the nominal interest rate,

1
U,

from the

IS Equation, (35), is negative so that ceteris paribus, contractionary monetary policy would lead to a
real contraction as one would expect. Of course, this point ignores the simultaneous effect on output
21

of movements in expected output, inflation, and the exchange rate, so that in general equilibrium,
output and the nominal interest rate may may not end up being negatively correlated. However,
when l

l⇤ , the interest elasticity of output is positive, ie.

1
U

> 0, a point that was originally

discussed in Bilbiie (2008), and continues to hold in an open economy. Implied by this, when l

l⇤ ,

simple active rules lead to indeterminacy (discussed in the appendix). Although optimal monetary
policy leads to equilibrium determinacy with all l, I prefer to keep l < l⇤ in this paper (so that l is
always less than around 80%), making it possible to compare optimal policy with active simple rules
in a unique, rational expectations equilibrium.
3.2.2

Micro-founded Objective

The objective of optimal monetary policy is to maximize the expected utility of households. Motivated
by this, Benigno and Woodford (2005) show that it is possible to derive a quadratic approximation to
household welfare that takes the form of a discounted quadratic loss function with terms including
those in inflation and the output gap, in the case where exogenous disturbances are sufficiently small
in amplitude. The loss function is minimized to yield a local approximation to optimal policy. The
advantage of using this method to “micro-found” the monetary policy objective is that is affords a
precise characterization of which terms appear in the loss function, with relative weights that depend
on the specific monetary transmission mechanism in the model considered.
In this framework, the Central Bank is required to maximize the expected utilities of two types of
households. It is still possible, however, to derive a purely quadratic approximation of a weighted
average of household utilities, by replacing for linear terms with second-order approximations of the
structural equations. This means that I can cast the Central Bank’s optimization problem in the familiar
linear-quadratic form: here, the quadratic welfare loss function is minimized with respect to the linear
aggregate demand and supply constraints. The solution to this problem is a flexible inflation targeting
rule, (42), that maximizes a weighted sum of household utilities.
To derive the quadratic Central Bank loss function, I begin by taking a second-order approximation of the weighted sum of household utility functions: U st

= lǓ st + (1

l)Û st . As an

initial step, this yields some non-zero linear terms, where t.i.p. stand for “terms independent of policy” (constants and functions of disturbances), and o (3) contains terms of third-order and higher (to
place a bound on the amplitude of the perturbations)

Lt =

•

s =0

⇢

1# 2
U N
p
+ N ỹt+s + c̃t+s
2 x H,t+s UC C

+ t.i.p. + o (3)

To be able to correctly evaluate optimal policy upto second-order, the linear terms in ỹt+s and c̃t+s
need to be eliminated. I follow the method of Benigno and Woodford (2005) to eliminate ỹt+s and c̃t+s
through the analytical approach of replacing for these terms through second-order approximations

of the following non-linear equilibrium conditions: the consumption of financially-excluded agents,
(2), labor supply by both agents, (3) and (6), risk-sharing, (9), evolution of price dispersion, (23), the
aggregate “production function”, (24), equations from the recursive representation of the NKPC, (25),
(26), and (27), the resource constraint, (28), and finally aggregate labor and consumption, (29) and (30).
The resulting loss function is an expression with purely quadratic terms, described in Proposition 4.
Proposition 4. (Micro-founded Quadratic Loss Function) Central Bank preferences in a small open econxte and ỹt = yt

omy with financially-excluded agents, with x̃t = xt
Lt =

yet , are represented as

•
1
Et Â bs Yp p 2H,t+s + Yy ỹ2t+s + Ys x̃t2+s
2 s =0

(38)

with weights on domestic inflation, output gap, and terms of trade gap written as
Yp =

#P
(XL (1 + n)
x

a)F) nl)

# P UN N
x UC C

(1 a) l(1 l)n2 XLl(1
⇣
⌘ 1+fU N
N
+X L 1 + L
1 l UC C
= (1 a) (1 2a) + 2(1 a)wU XL (1 2a)

Y y = l (1

(1 + (1

a )2 n2

a ) n2

2XLwU

and composite parameters written as
U =
L =
w =
n =

lf(1 a)
1 l
1 l
l lf(1 a) + f
l

lf(1

a )2 + a (1
1 l

f
1

X = (1

l
a)U + ln +

F = XL

UN N
UC C

where the efficient variables xte and yet are functions of structural parameters and shocks, as in Proposition 1.
The loss function in an open economy model with financial exclusion features a quadratic term in
the terms of trade beyond what is usually found in models where all households are financiallyincluded. When l = 0, the criterion collapses to that in Gali and Monacelli (2005) where x̃t2 = ỹ2t :
Yp |l=0 = YpGM =

# P UN N
x UC C

N
and Yy |l=0 + Y x |l=0 = YyGM = (1 + f) U
UC

N
C.

I give the loss function below

with l = 0, ie. the nested Gali and Monacelli (2005) case, as this serves as a useful point of comparison
for some of the results. (39) requires that

UN N
UC C

(1
23

a), ie. the steady state is rendered efficient.

L t | l =0 =

L tGM

a
2

•

Âb

s =0

⇢

# 2
p
+ (1 + f)ỹ2t+s
x H,t+s

(39)

The key driver for the differences in Central Bank preferences in the presence of financial exclusion
is the asymmetry in the ability of domestic households to share risk. Recall that financially-included
households can pool risk with foreign agents, (9), by receiving (or making) appropriate international
insurance transfers, (32). This smooths their consumption upon fluctuations in their income. In sharp
contrast, financially-excluded agents must fully consume their income, (2). This implies that, unlike
the l = 0 case, (39), that the stabilization of the terms of trade gap, x̃t2 , is required in (38) to minimize
welfare loss.
Result 1. Terms of trade fluctuations have first-order distortionary effects in the presence of financial exclusion.
In an economy where all agents can smooth consumption, changes to purchasing power from exchange rate fluctuations are offset through the proceeds from state-contingent claims. For instance, import price volatility, caused by exchange rate movements, does not affect financially-included agents
by much as they adjust their financial asset holdings in a manner that consumption is smoothed.
However, changes to the purchasing power of financially-excluded agents when import prices fluctuate cause an equivalent rise in consumption volatility, and hence greater aggregate welfare loss. This
gives the Central Bank an incentive to stabilize the terms of trade.
Policy Trade-offs Result 1 is one dimension of the loss-minimizing objective, but what do Central Bank
preferences look like overall? It is useful to provide more intuition on the micro-founded objective,
(38), as this drives most of the results in the optimal policy analysis. However, the weights in (38) are
fairly complicated functions of structural parameters, so that their implications are not transparent.
This can be addressed by re-writing the loss function in terms of only domestic inflation, p H,t , and the
output gap, ỹt , as (40), by using the proportionality between the terms of trade gap and the output
gap, x̃t = U ỹt . The optimal policy trade-offs that arise are then captured by the relative weight, (41).8
Lt =

n
o
•
1
Et Â bs p 2H,t+s + Fl ỹ2t+s
2 s =0

(40)

where the relative weight on ỹt , Fl , is given by
l

F =

X L

2a) FU2
#
x

((1

l ) + (1

a)F) ln2

2FwU

(XL (1 + n)

(1 + (1

a)F) nl)

# P UN N
x UC C

1+ f U N N
1 l UC C

(41)

8 A numerical check yields that the relative weight, Fl , is strictly positive when the structural parameters in the loss
function, a, l, f, #, b, q, jointly satisfy the following system of inequalities: 0 < a < 0.95, 0 < l < 0.9, 0 < q < 1, 0 < b < 1,
# P > 0, f > 0. The positive weight implies that the quadratic loss function is convex so that the second-order sufficient
conditions are satisfied. Note that convexity ensues for a wide range of parameter values in this model due to the logarithm
and isoelastic functional forms in utility, as also in Benigno and Woodford (2005).

Result 2. The relative weight on output gap stabilization, Fl , is increasing in a and l.
It is instructive to compare Fl with the Gali and Monacelli (2005) model, where the relative weight,
FGM =

1+ f
#
x

, is invariant with respect to openness, a. In contrast, Fl in this model increases with a. To

see this, note that as the economy becomes more open, domestic agents consume more imports relative
to home goods. This increases the consequences of exchange rate volatility, which in an economy with
financial exclusion, results in an equivalent rise in hand-to-mouth consumption volatility. To mitigate
the ensuing macroeconomic volatility and hence greater loss, it is optimal to stabilize the output gap by
more as a increases. Doing so stabilizes labor demand and hence real wages, which in turn stabilizes
the consumption of financially-excluded agents.

∂Fl
∂a

6= 0 is thus completely dependent on l > 0, ie. a

fraction of agents not being able to insure against uncertainty.

Similarly, Fl increases with l to minimize the greater loss as progressively more agents cannot
smooth consumption. This analysis is depicted in Figure 2 which plots Fl as a function of l and a for
l, a 2 [0, 0.6] (Fl increases disproportionately for higher calibrations). The steady state is rendered

efficient ie.

UN N
UC C

N 1+ f =

a), to better permit comparison with the baseline case of Gali

and Monacelli (2005) (the analogous relative weight there does not change with either a or l).

Figure 2: Optimal Relative Weight on Output Gap

Result 3. The closed economy case is not isomorphic for l > 0.
This point is of independent interest to the question at hand, but deserves a mention. Optimal policy in the open economy model with financially-excluded agents does not necessarily converge to the
closed economy case when a ! 0. Usually considered desirable from a modeling perspective, other

instances can be found in Monacelli (2005) and Farhi and Werning (2012). There is an irreversible open
economy asymmetry in this model compared to the closed economy version of Bilbiie (2008), as only
a fraction of domestic consumers share risk with foreign agents. Exchange rate movements affect the
heterogeneous agents in completely different ways, implying that consumption patterns fundamen25

tally diverge over the business cycle, and overriding the type of closed economy isomorphism that
characterizes Gali and Monacelli (2005).
This can be seen as follows. In the closed economy limit ie. as a ! 0, a fixed nominal exchange

rate, et
it⇤ )

= 0 amounts to a fixed nominal interest rate (equal to the exogenous foreign interest rate,

through the UIP condition, it = it⇤ + Et et+1

et . However, it is known that a fixed nominal interest

rate implies equilibrium indeterminacy in a closed economy (Galí, 2009). I correspondingly find that
a fixed nominal interest rate, it = 0, results in indeterminacy in my model when a = 0, and indeed
for all a. When a > 0, however, an exchange rate peg, et

= 0, ensures a unique equilibrium

and moreover approximates the optimal policy, as will be discussed in Section 4. Technically, the
equilibrium correspondence with a fixed exchange rate is not lower hemi-continuous in the parameter,
a. This argument is similar to that in Farhi and Werning (2012), and corroborates their conclusion on
being cautious in using closed economy models to approximate the open.
Targeting Rule I now derive the flexible inflation targeting rule for the model under dynamically
consistent timeless commitment, where the optimal plan set in later periods is the same as the one that
would have been set initially (Woodford, 2011). This requires minimizing the quadratic loss function
(38) with respect to the linear aggregate supply relation, (37). The IS Equation does not bind since the
nominal interest rate is unconstrained. I attach the Lagrange multiplier, cp,t , on the NKPC and take
first-order conditions with respect to domestic inflation, p H,t , and the output gap, y˜t
2Yp p H,t + cp,t
2Yy y˜t

cp,t
1

= 0

cp,t = 0

These can be combined to yield the optimal plan.
Proposition 5. (Optimal Policy) The optimal plan under timeless commitment is implemented as follows
p H,t =

L l
F (y˜t
x

ỹt

(42)

where yet is efficient output as defined in Proposition 1.
The optimal plan, (42), implies the classic “leaning against the wind” analogy of contracting the output
gap to bring down domestic inflation, whenever the latter is inefficiently high. The targeting rule holds
only if prices are slow to adjust, x 6= •, as it would be redundant in a flexible price environment where
inflation creates no real distortions.

Determinacy It is useful to note that determinacy with the optimal plan, (42), ensues for all l 2 [0, 1),

which corroborates the closed economy analog in Bilbiie (2008). This can be seen by combining (42)

with the NKPC (37) to get the following second-order difference equation
Et yt˜+1



1
= 1+
b

✓

x2 1
1+ 2 l
L F

◆

1
ỹt
b

y˜t

1x 1
vt
b L Fl

whose roots are on the opposite sides of the unit circle, for all l 2 [0, 1), as required for a unique,
rational expectations equilibrium. Thus, following through with the optimal plan prevents the indeterminacy issues associated with very high l for standard, active simple rules.
Closed-form solutions for relative domestic prices, p̂ H,t , and the output gap, y˜t , are derived by
combining the targeting rule (42) and the Phillips Curve (37). The corresponding choice ofpnominal
1
1 4a2 b
interest rate, it , is derived by replacing (43) and (44) in the IS Equation (35). Defining d =
2
2ab
⇣
⌘
⇣
⌘
⇣
⌘ 1
2
Ux
Ux
(0, 1), g1 = LF
1 (1 d), g2 = LF
1 d, and a = 1 + b + L2xFl
, it follows that
l
l
p̂ H,t = d p̂ H,t

•

+ dEt

Â ( bd)k vt+k

(43)

k =0

y˜t =

x
p̂ H,t
LFl

it = rte + g1 p̂ H,t

(44)
g2 Et

•

Â ( bd)k vt+k

(45)

k =0

Closed-form solutions for the remaining endogenous variables can be backed out as follows: the employment gap from the production function (46), the financially-included agent consumption and labor supply gaps from the risk-sharing condition (47) and intratemporal optimality condition (48), the
financially-excluded agent consumption and labor supply gaps from the budget constraint (49) and
intratemporal optimality condition (50), the real wage gap from the firm’s marginal cost condition
(51), the terms of trade gap from the resource constraint (52), and finally CPI inflation from its linkage
with domestic inflation and the terms of trade (53)
(46)

ỹt = ñt
ĉ˜t = (1

ỹt = a x̃t + (1

a) x̃t

(47)

w̃t = ĉ˜t + fn̂˜ t

(48)

č˜t = w̃t

(49)

w̃t = č˜t + fň˜ t

(50)

0 = w̃t + a x̃t

(51)

a) lč˜t + (1

pt = p Ht + aD x̃t

l)ĉ˜t + aĉ˜t

(52)
(53)

3.2.3

Optimal Dynamics

I now seek to analyze how the optimal plan, (42), which governs the optimal evolution of the endogenous variables in equations (43) to (53), responds to unexpected disturbances. The focus is primarily
on cost-push shocks as these have been predominant in emerging market economies, and arise in
practice due to domestic food price volatility and fuel input price volatility (Frankel, 2010). I also
analyze productivity shocks. Dynamics are analyzed based on a calibrated version of the framework.
Calibration is a challenging task, as the required micro-level data is scarce for EMEs. I thus select parameters from the existing open economy literature, and pair this with extensive sensitivity analysis.
The fraction of randomly chosen monopolistic producers that can reset prices, q, is set at 0.75, which
implies an average period of one year between price adjustments, as in Gali and Monacelli (2005).
The household discount factor b equals 0.99, which implies a steady state real interest rate of
around four percent. The elasticity of substitution between differentiated monopolistic goods is set
at # P = 6, which implies a steady state markup of around 20%. The degree of openness, a, is set
at 0.5 and the inverse Frisch elasticity of labor supply, f, at 1. These values implies a simple rule
1
, of around 0.7, which my analysis does not go beyond. With
1+ f (1 a )
a = 0.7, as in the sensitivity analysis, l⇤ is around 0.8. The persistence of shocks, ie. r j in the stationary
(linearized) autoregressive process jt = r j jt 1 + s j,t , where jt = {vt , at , it⇤ }•
t=0 , is set at 0.9, consistent

indeterminacy threshold, l⇤ =

with the evidence for emerging market economies provided in Aguiar and Gopinath (2007). In most
cases, optimal policy with complete financial market participation, l = 0, is contrasted with l = 0.6,
which is around the EME financial exclusion average (World Bank, 2015).

Figure 3: Optimal Monetary Policy and Financial Exclusion

Figure 3 provides dynamics for varying degrees of financial exclusion upon a unit positive cost-push
shock. There is an immediate rise in domestic inflation that arises independently from variations
28

in domestic demand. The corresponding jump up in domestic prices leads to a real exchange rate
appreciation, and the Central Bank contracts output to control inflation. A recession ensues. Domestic
inflation is allowed to rise by more as the fraction of financially-excluded agents increase, as per by the
optimal trade-off, (41), embodied in the flexible inflation targeting rule, (42). This erodes the value of
domestic currency, putting pressure on the nominal exchange rate to depreciate by more as l increases.
The nominal interest rate, unconstrained in this model, moves in a direction that supports the optimal
trade-off. To mitigate the recession, it decreases with low l. It increases, however, when l is high as
this allows the nominal exchange rate to be expected to depreciate by more through the UIP condition,
which stabilizes the output gap as the expense of higher domestic inflation.
Note that, overall there is pressure on the nominal exchange rate to depreciate upon the cost-push
shock (apart from very low l where it falls, so that domestic asset returns decrease to the extent that,
as per UIP, expected nominal appreciation is required to equalize asset returns internationally and
hence prevent arbitrage). The higher domestic inflation and greater nominal depreciation as financial
exclusion increases account for the lower real exchange rate appreciation. The lower real appreciation
prevents the consumption of financially-included agents from falling as much, so that producers do
not decrease their demand for working hours as much, implying that real wages remain more stable.
The lower real appreciation also stabilizes the consumption of financially-excluded agents due to the
relatively cheaper imports and relatively higher wages. The real interest rate, rt = it

Et p H,t+1 ,

supports these dynamics, and CPI inflation in the economy rises by more as l increases, due to the
higher domestic inflation and lower real exchange rate appreciation.
Result 4. Monetary policy plays an additional insurance role in the presence of financial exclusion.
For l > 0, optimal monetary policy takes into account the inability to share risk and hence the more
volatile consumption of financially-excluded agents. Implementation of the optimal plan, (42), results
in disposable income (real wages) being stabilized by more as financial exclusion increases. This can be
interpreted as provision of insurance by monetary policy to agents who cannot smooth consumption
by themselves, and is a required transmission channel in the efficient plan. Thus, besides macroeconomic stabilization, monetary policy plays an additional insurance role when l > 0. The amount of
insurance varies depending on the degrees of openness and price stickiness, as shown next.
3.2.4

Sensitivity Analysis

I analyze the implications of the optimal targeting rule (42) for a = {0.1, 0.4, 0.7} and q = {0.7, 0.75, 0.8}.
The limited (l = 0.6) financial inclusion case with varied a is depicted below in Figure 4 (correspond-

ing l = 0 case is in Figure 6 in the appendix). The analysis suggests that the amount of insurance
provided by monetary policy is increasing in openness and price flexibility.

Openness
When financial inclusion is complete, l = 0, the trade-off is independent of openness as changes
to real income from exchange rate fluctuations are offset through the proceeds from state-contingent
claims. This independence is broken in the presence of financial exclusion, l > 0. Here, exchange
rate volatility causes equivalent volatility in the consumption of financially-excluded agents (and by
a greater amount as a ! 1 due to the increased consumption of imports), unlike that of financial

asset holders. To mitigate the resulting greater macroeconomic volatility, optimal monetary policy
is required to smooth the consumption of hand-to-mouth agents by more. It does so by contracting
the output gap by less upon a cost-push shock as l increases. The supporting nominal interest rate
increases by more to induce the greater expected nominal depreciation required for a relative output
expansion and higher domestic inflation as per the optimal trade-off, (41). This leads to more muted
real appreciation, which stabilizes the consumption of both type of agents as imports are relatively
cheaper, and that of financially-excluded agents in particular because real wages fall by less.

Figure 4: Optimal Monetary Policy with Financial Exclusion, Varying Openness

Nominal Rigidities
Stickier prices, q ! 1, imply that fewer randomly chosen price-setters re-optimize each period. Thus,

upon a cost-push shock, the required downward re-optimization of prices (in anticipation of future
high domestic inflation) is hindered. This leads to more domestic inflation volatility, requiring a grater
contraction of the output gap as per the optimal plan. The resulting steeper recession dampens labor
demand by more. Consequently, lower real wages clear the market, implying that hand-to-mouth consumption decreases by more. Nominal rigidities thus hamper the provision of insurance by optimal
monetary policy. These dynamics are found in Figure 7 in the appendix.
30

Nominal Anchor: Peg or Float?

I proceed to analyze the appropriate choice of nominal anchor in an economy with financial exclusion.
To do so, simple and implementable monetary rules are ranked in terms of lowest welfare losses
away from the optimum. Simple rules as approximations of optimal monetary policy are in particular
useful, since the optimum can sometimes be cast as a complicated and unintuitive function of model
parameters. Optimal policy is thus often not as transparent and implementable in practice as a simple
rule. I will show that targeting the exchange rate is an implementable way to internalize the insurance
properties of the optimal plan characterized in the previous section.
Table 1 reports the welfare losses associated with standard active simple rules compared to the
benchmark optimal policy, upon trade-off creating cost-push shocks. There are two columns: the first
reports welfare losses in the case of complete financial inclusion, l = 0, whereas the second does
likewise with high financial exclusion, l = 0.6. All entries in Table 1 are, as in Gali and Monacelli
(2005), percentage units of steady-state consumption and in deviation from the first-best case of optimal monetary policy. It can be seen that while strict CPI Inflation Targeting, pt = 0, best approximates
the optimal policy when all agents can smooth consumption, a fixed exchange rate, Det = 0, is least
suboptimal when financial exclusion is high.
Simple Rule

Financial Inclusion

Financial Exclusion

7.8

9.9

12.6

57.1

56.0

0.2

21.7

18.2

1312.4

292.5

Strict CPI IT (CIT)
pt = 0
Strict domestic IT (DIT)
p H,t = 0
Fixed exchange rate (PEG)
Det = 0
Flexible CPI IT
i = 1.5pt
i = 1.5pt + 0.5y˜t
Flexible domestic IT
i = 1.5p H,t
i = 1.5p H,t + 0.5y˜t

83.5

45.0

1312.4

324.0

Table 1: Welfare Loss Relative to Optimal Policy

Result 5. A nominal exchange rate peg is least suboptimal with high financial exclusion.
Table 1 indicates that fixed exchange rates are preferred to flexible exchange rates (all the inflation
targeting rules) in the presence of high financial exclusion. The intuition for this result stems from
first recalling from section 3.2.3 that with high l, welfare losses are minimized when optimal policy
prevents high real appreciation, which smooths the consumption of financially-excluded agents due to
greater real wage and imported good price stabilization. Now, note that a nominal exchange rate peg
is the most effective out of all the monetary policy rules in containing real appreciation in the presence
31

of nominal rigidities. Indeed, dynamics under a fixed exchange rate almost completely mirror those
under optimal policy, as shown in Figure 5 below, which compares PEG with the optimal targeting
rule, (42), CIT (least suboptimal policy when l = 0 upon cost-push shocks), and DIT (optimal policy
in this model upon productivity shocks). Corresponding volatility numbers are found in Table 2.

Figure 5: Optimal Policy Versus Simple Rules, Financial Exclusion

Output

Optimal

DIT

CIT

PEG

227.0

466.3

306.5

236.1
6.2

Domestic inflation

7.1

2.0

CPI inflation

2.9

10.9

2.2

Real wages

189.5

389.2

255.9

197.0

Real exchange rate

59.9

123.0

80.8

62.3

Nominal depr. rate

0.1

68.3

4.5

Table 2: Cyclical Properties of Alternative Policy Regimes, Financial Exclusion

Result 6. CPI Inflation Targeting is appropriate when all agents are insured through asset markets.
When financial inclusion is complete, compared to the financial exclusion case, domestic inflation
volatility gives rise to greater welfare loss. Thus, optimal policy places greater weight on stabilizing
domestic inflation. Now, under a peg, the muted real appreciation implies that marginal costs, and
hence domestic inflation, increase by too much. Thus, PEG is highly suboptimal. DIT, on the other
hand, leads to extreme output gap volatility (which is still penalized, albeit by less) in fully stabilizing
domestic inflation. CIT strikes the appropriate in-between as it results in less output gap volatility than
DIT (it stabilizes both domestic and imported good inflation, and the output gap responds to domestic
inflation only as per the targeting rule, (42)), and less domestic inflation volatility than PEG due to
32

greater real appreciation. These dynamics are found in Figure 8 in the appendix, with corresponding
volatility numbers in Table 3 below.

Output

Optimal

DIT

CIT

PEG

149.8

183.9

129.4

102.8

Domestic inflation

0.4

1.3

4.3

CPI inflation

0.8

5.9

1.5

Real wages

383.4

470.8

331.2

263.3

Real exchange rate

53.9

66.2

46.6

37.0

Nominal depr. rate

9.6

36.8

3.0

Table 3: Cyclical Properties of Alternative Policy Regimes, Complete Financial
Inclusion

4.1

Role of Openness

I vary the degrees of openness and nominal rigidities, to analyze whether CIT and PEG remain robust.
I find that they do. Price stickiness matters to the extent that the simple rules approximate optimal
policy better as nominal rigidities lessen ie. q ! 0 (because the role of optimal policy diminishes with
increased price flexibility); however, varying a yields an interesting result.

Result 7. When a > 0, CIT and PEG work better with low degrees of openness. When a = 0, this does not
hold due to an open economy discontinuity.
CIT, pt = 0, approximates the l = 0 optimal monetary policy better, and PEG, Det = 0, does likewise
for the l = 0.6 optimal policy, as a ! 0. Note, however, that this does not imply that p H,t = 0 and
it = 0 (the closed economy analogs of CIT and PEG) perform well when a = 0. In the former case,

p H,t = 0 is achieved at the expense of high output gap volatility, which is suboptimal - CIT does not
require this. Furthermore, it = 0 results in an indeterminate equilibrium for a = 0 - there is an open
economy discontinuity in this model as was discussed in Result 3 in Section 3.2.2. Intuition for the
better CIT and PEG approximations with low a > 0 is as follows.
Consider first the l = 0 case. It is useful to note first the following facts: (i) lower a implies
that more domestic goods are consumed relative to imported goods, (ii) CIT targets both domestic
and import price inflation, and (iii) upon a cost-push shock, while relative domestic prices increase,
relative import prices decrease due to an expenditure-switching effect. Now, as a ! 0, CIT implies

the stabilization of progressively more domestic inflation (which has increased), which requires higher
real appreciation (preventing import deflation would, in contrast, require real depreciation). This higher
real appreciation as a decreases matches that under optimal policy for the complete financial inclusion
case. PEG does not provide the required high real appreciation for l = 0.
Now, consider the l = 0.6 case, where the weight on output gap stabilization increases with
a to smooth the consumption of financially-excluded agents. This requires progressively less real
appreciation, as discussed in section 3.2.4. With very high a, the optimal real appreciation is required
33

to be so low that although a nominal peg comes closest to engendering this, even it cannot completely
mirror the optimal policy (a different simple rule, perhaps targeting the real exchange rate itself, might
be appropriate here). However, for low (a = 0.1) and moderate (a = 0.4) degrees of openness, the
real appreciation under the peg is appropriate. In contrast, CIT is inefficient for all a with financial
exclusion, since it requires suboptimally high real appreciation. The corresponding dynamics for l =
0 and l = 0.6 are found in Figures 9 and 10 in the appendix.

4.2

Productivity Shocks

Result 8. A fixed nominal exchange rate in a high financial exclusion economy is appropriate only if cost-push
shocks predominate.
It is useful to understand the circumstances under which a fixed exchange rate provides the most efficient stabilization. As a robustness check, I analyze optimal monetary policy with domestic productivity shocks. I discuss the case with l = 0.6, with the analogous l = 0 exercise in Gali and Monacelli
(2005). In an economy with financial exclusion, I find that the type of shock matters for choice of domestic versus external nominal anchor. As shown in Proposition 3, optimal policy with productivity
shocks leads to perfect stabilization and is strict domestic inflation targeting (DIT). This can be seen
by setting p H,t = 0 in the system of equations, (35), (36), and (37), in the absence of cost-push shocks,
vt , so that the output gap is also perfectly stabilized, ỹt = 0. This policy requires considerable nominal
exchange rate volatility, implying that a peg is no longer appropriate.9 In the presence of financial
exclusion, exchange rate stability is appropriate only if cost-push shocks predominate.

Conclusion

This study analyzed optimal monetary policy and the choice of nominal anchor in a small emerging
market economy with high financial exclusion. The main findings were that, upon cost-push shocks,
optimal policy smooths the consumption of financially-excluded agents who cannot do so themselves,
and that a fixed nominal exchange rate internalizes the insurance provision properties of the optimal
plan. The desirability of exchange rate stability provides a counterpoint to Milton Friedman’s longstanding argument for a float. This paper sought to establish benchmark analytical results, and lends
itself to some extensions. It would be useful to incorporate another form of nominal rigidity, sticky
wages, as well as incomplete financial markets. The latter would imply that international risk-sharing
is imperfect, as relevant in practice, and which would be interesting to interact with the form of financial market incompleteness considered in this paper. I leave these extensions to future research.
9 A productivity shock puts downward pressure on prices and upward pressure on output (but in the absence of optimal
policy, sticky price output, yt , does not increase by as much as efficient output, yet , so that there is downward pressure on the
output gap, ỹt = yt yet , too). Unrestricted depreciation of the nominal exchange rate is required to support the transitory
increase in domestic inflation and expansion in output required to set p H,t = 0 and close the output gap.

References
Aguiar, M. and Gopinath, G. (2007). Emerging market business cycles: The cycle is the trend. Journal
of Political Economy, 115(1):69–102.
Ascari, G., Colciago, A., and Rossi, L. (2011). Limited Asset Market Participation: Does It Really
Matter For Monetary Policy? Bank of Finland Research Discussion Paper 15.
Backus, D. K. and Smith, G. W. (1993). Consumption and Real Exchange Rates in Dynamic Economies
with Non-Traded Goods. Journal of International Economics, 35(3):297–316.
Benigno, P. and Woodford, M. (2005). Inflation Stabilization and Welfare: The Case of a Distorted
Steady State. Journal of the European Economic Association, 3(6):1185–1236.
Benigno, P. and Woodford, M. (2012). Linear-Quadratic Approximation of Optimal Policy Problems.
Journal of Economic Theory, 147(1):1–42.
Bilbiie, F. O. (2008). Limited Asset Markets Participation, Monetary Policy and (Inverted) Aggregate
Demand Logic. Journal of Economic Theory, 140(1):162–196.
Blanchard, O. and Galí, J. (2007). Real Wage Rigidities and the New Keynesian Model. Journal of
Money, Credit and Banking, 39(1):35–65.
Blanchard, O. J. and Kahn, C. M. (1980). The solution of linear difference models under rational
expectations. Econometrica: Journal of the Econometric Society, pages 1305–1311.
Cole, H. L. and Obstfeld, M. (1991). Commodity Trade and International Risk Sharing: How Much Do
Financial Markets Matter? Journal of Monetary Economics, 28(1):3—24.
Corsetti, G., Dedola, L., and Leduc, S. (2010). Optimal Monetary Policy in Open Economies. Handbook
of Macroeconomics, 3.
Eser, F. (2009). Monetary Policy in a Currency Union with Heterogeneous Limited Asset Markets
Participation. Department of Economics, University of Oxford, Working Paper 464.
Farhi, E. and Werning, I. (2012). Dealing With the Trilemma: Optimal Capital Controls With Fixed
Exchange Rates. NBER Working Paper 18199.
Frankel, J. A. (2010). Monetary Policy in Emerging Markets: A Survey. NBER Working Paper 16125.
Galí, J. (2009). Constant Interest Rate Projections Without The Curse Of Indeterminacy: A Note. International Journal of Economic Theory, 5(1):61–68.
Galí, J., López-Salido, J. D., and Vallés, J. (2007). Understanding the Effects of Government Spending
on Consumption. Journal of the European Economic Association, 5(1):227–270.
35

Gali, J. and Monacelli, T. (2005). Monetary Policy and Exchange Rate Volatility in a Small Open Economy. The Review of Economic Studies, 72(3):707–734.
Garcia-Cicco, J., Pancrazi, R., and Uribe, M. (2010). Real Business Cycles in Emerging Countries?
American Economic Review, 100(5):2510–31.
GES (2014). Background Note: Global Economic Symposium, Kuala Lampur, Malaysia, September 6-8, 2014. In http://www.global-economic-symposium.org/knowledgebase/monetary-policy-and-incomeinequality.
Hanke, S. H. (2008). Friedman: Float or Fix? Cato Journal, 28(2).
IMF (2015a). Causes and Consequences of Income Inequality: A Global Perspective. International
Monetary Fund, Staff Discussion Note 15/13.
IMF (2015b). Uneven growth: Short- and long-term factors. International Monetary Fund, World Economic Outlook (WEO).
Mankiw, N. G. (2000). The Savers-Spenders Theory of Fiscal Policy. American Economic Review,
90(2):120–125.
Monacelli, T. (2005). Monetary policy in a Low Pass-Through Environment. Journal of Money, Credit
and Banking, 37(6):1047–1066.
Prasad, E. (2013).

Distributional Effects of Macroeconomic Policy Choices in Emerging Market

Economies. Bank of Korea-IMF Conference on Asia: Challenges of Stability and Growth.
Prasad, E. and Zhang, B. (2015). Distributional Effects of Monetary Policy in Emerging Markets. NBER
Working Paper 21471.
Sutherland, A. (2005). Cost-push shocks and monetary policy in open economies. Oxford Economic
Papers, 57(1):1–33.
Woodford, M. (2011). Interest and Prices: foundations of a theory of monetary policy. Princeton University
Press.
World Bank (2009). Employment, Poverty and Distributional Impacts of the Global Financial Crisis:
An Overview of Recent Evidence. World Bank Poverty Reduction and Economic Management (PREM)
Note.
World Bank (2015). The Global Findex Database 2015: Measuring Financial Inclusion Around the
World. Policy Research Working Paper S7255.

Appendix
1
U

(it Et p Ht+1 rte ), note that the interest
elasticity of output is U1 , where U =
We have that U1 < 0 if l < 1+f(11 a) , but U1 > 0 if l
1
. In the region implied by the latter inequality, active rules give rise to indeterminacy, a phenomenon
1+ f (1 a )
called the inverted aggregate demand logic (IADL) by Bilbiie (2008). What is the IADL? It is useful to note first
that dynamics become more volatile as l increases, since hand-to-mouth agents have a marginal propensity
to consume of 1. These agents spend on output, which thus also becomes more volatile as l increases, which
in turn creates volatility in labor demand, and real wages. Upon a contractionary interest rate surprise that
decreases aggregate demand, wages thus fall more as l increases. This dampens hand-to-mouth consumption,
which further dampens real wages and output, and hence asset holder consumption. This effect might initially
seem monotonic, so that a monetary contraction would actually have a greater impact as l increases.
However, due to the specific interaction, with very high l, of sticky prices with countercyclical profits in
the New Keynesian model, there is a critical high l⇤ where wages fall by so much (output does not fall as
much as wages due to sticky prices), that the corresponding big rise in profits implies a big wealth effect for
financially-included agents. Then, despite their initial fall in demand, financially-included agents now demand
more output, which leads to an increase in wages and financially-excluded agent demand as well. Thus, an
initial monetary contraction leads to an ultimate real expansion with l
l⇤ due to sticky prices and countercyclical profits. The empirical relevancy of the IADL channel and associated implications for equilibrium
determinacy with passive rules have been subject to critique (see for eg. Ascari et al. (2011)), and I avoid the
IADL region by always setting l < l⇤ in this paper. Indeed, as l⇤ goes as high as 0.8 with a standard range
of calibrations, and as the vast majority of EMEs have less than 80% of households excluded from the financial
markets, the threshold value for indeterminacy does not impact any of my results or conclusions.
I now discuss how the IADL region implies equilibrium indeterminacy with standard active Taylor Rules.
As in the literature, “active” refers specifically to the Taylor Principle being satisfied ie. c > 1 in any of the
following rules: it = cp H,t , it = cpt , it = cDet . Note that the strict targeting rules, p H,t = 0, pt = 0, and
Det = 0, are special cases of the above with a high enough value for c (and certainly the Taylor Principle
being satisfied). I provide an analytical proof for the first case, it = cp H,t , that being in the IADL region, ie.
1
l
, implies that c > 1 gives rise to indeterminacy. A numerical check reveals that this holds true for
1+ f (1 a )
the other similar rules considered. The method of proof is similar to that provided in Bilbiie (2008). I substitute
the rule, it = cp H,t , in the IS Equation, (35) so that the equilibrium in Proposition 3, (35), (36), and (37), is now
0
a dynamic system in two jump variables, p H,t and ỹt , which can be written, for the zt ⌘ (ỹt , p H,t ) vector of
0
endogenous variables and the ut ⌘ (rte , vt ) vector of disturbances, as
Equilibrium Determinacy From the IS Equation, ỹt = Et ỹt+1
1 l lf(1 a)
.
1 l

Et zt+1 = Azt + But

where

A=4

x
bUL
1 x
bL

1
U

⇣

c
1
b

1
b

⌘ 3
5

1
U

1
bU
1
b

As per the Blanchard-Kahn conditions (Blanchard and Kahn, 1980), determinacy requires that both eigenvalues
of A are greater than 1, as p H,t and ỹt are jump variables. This in turn requires that (i) det
⇣ ( A) >⌘1, (ii) det ( A)
x
1
tr ( A) > 1, and (iii) det ( A) + tr ( A) < 1 (Woodford, 2011), where det ( A) = b 1 + UcL
and tr ( A) =

x
bUL

+ b1 . The following conditions satisfy these restrictions for a unique, rational expectations equilibrium.

l < l⇤ :
l

l⇤ :

where l⇤ =

c 2 (1, •) ie. the Taylor Principle

⇢
◆ ✓
⇢
LU ( b 1)
2LU ( b + 1)
c 2 0, min 1,
, 1
[ max 1,
x
x

1
1+ f (1 a )

2LU ( b + 1)
x

,•

◆

is the threshold value above which the interest elasticity of output becomes positive ie.

the IADL region occurs. In the first case above, when l < l⇤ , a standard active rule gives rise to determinacy.
In the second case, ie. the IADL region l

l⇤ , determinacy only ensues with either a passive rule (c < 1) or

an extremely active rule (c > 30). To (i) be able to rank standard rules such as it = 1.5p H,t as well as the stricter
rules such as p H,t = 0 and (ii) avoid the inverted dynamics in the IADL region above l⇤ - I always have l < l⇤
in this paper, so that the equilibrium is determinate under simple rules. This allows for a welfare ranking of
standard active simple rules against optimal policy, a primary focus of this paper.
It is worth noting that the simple rule indeterminacy region in an open economy is actually smaller than that
in a closed economy (where l⇤ |a=0 =

1
1+ f

as in Bilbiie (2008)). This is because contractionary monetary policy

in an open economy is generally re-inforced by exchange rate appreciation, which is additionally contractionary.
Thus, it takes a higher l⇤ to reverse the initial contraction into an expansion. The higher threshold value for
indeterminacy is useful as it makes it possible to calibrate l at a very high number and still ensure a unique,
rational expectations equilibrium.

Figures

Figure 6: Optimal Monetary Policy with Complete Financial Inclusion: Varying
Openness

Figure 7: Optimal Monetary Policy with Financial Exclusion: Varying Stickiness

Figure 8: Optimal Policy Versus Simple Rules: Complete Financial Inclusion

Figure 9: Optimal Policy Versus Simple Rules: Complete Financial Inclusion,
Low Openness

Figure 10: Optimal Policy Versus Simple Rules: Financial Exclusion, Low Openness

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Full text of Working Papers (Federal Reserve Bank of Chicago) : Optimal Monetary Policy in an Open Emerging Market Economy, Working Paper 2016-06

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