The Macroeconomic Consequences of
Exchange Rate Depreciations
Masao Fukui

Emi NakamuraJón Steinsson*

Boston University

UC Berkeley

UC Berkeley

March 18, 2024

Abstract
We study the consequences of “regime-induced” exchange rate depreciations by comparing outcomes for peggers versus floaters to the US dollar in response to a dollar depreciation.
Pegger currencies depreciate relative to floater currencies and these depreciations are strongly
expansionary. The boom is not associated with an increase in net exports, or a fall in nominalinterest rates in the pegger countries. This suggests that expenditure switching and domestic monetary policy are not the main drivers of the boom. We develop a financially driven
exchange rate (FDX) model in which multiple shocks originating in the financial sector drive
exchange rates and households and firms can borrow in foreign currencies. Following a depreciation, UIP deviations lower the costs of borrowing from abroad and stimulate the economy,
as in the data. The model is consistent with (unconditional) exchange rate disconnect and theMussa facts, even though exchange rates have large effects on the economy.

JEL Classification: F31, F41* We thank Collin Jones for excellent research assistance. We thank Javier Bianchi, Louphou Coulibaly, Luca Fornaro,
Rohan Kekre, Tarek Hassan, Ethan Ilzetzki, Oleg Itskhoki, Sebnem Kalemli-Ozcan, Matteo Maggiori, Enrique Mendoza, Dmitry Mukhin, Maurice Obstfeld, Michael Waugh and seminar participants at various institutions for helpfulcomments and discussions. We thank the Clausen Center at UC Berkeley, the Alfred P. Sloan Foundation, and the Smith
Richardson Foundation for financial support.

1

Introduction

How does an exchange rate depreciation affect the economy? Is it expansionary? Is it contractionary? Or does it perhaps have little or no effect? Surprisingly, the answers to these questions
are unclear. Simple textbook models imply that a depreciation is expansionary due to expenditure switching in goods markets (Dornbusch, 1980; Obstfeld and Rogoff, 1996). But there is a long
literature discussing the theoretical possibility that exchange rate depreciations may be contractionary due to a contractionary real income effect (Diaz Alejandro, 1963; Cooper, 1969; Krugman
and Taylor, 1978; Auclert et al., 2021b) or a contractionary balance sheet effect (Krugman, 1999;
Aghion, Bacchetta, and Banerjee, 2001; Kalemli-Ozcan, Kamil, and Villegas-Sanchez, 2016).1 Finally, there is a prominent literature in international macroeconomics that argues that exchange
rates are largely disconnected from other macroeconomic aggregates (Meese and Rogoff, 1983;
Baxter and Stockman, 1989; Flood and Rose, 1995; Obstfeld and Rogoff, 2000; Devereux and Engel, 2002; Itskhoki and Mukhin, 2021a). Lacking clear guidance from empirical evidence, there is
precious little consensus.
These questions are difficult to answer because of the endogeneity of exchange rate movements. Consider a country that is hit by a negative shock. This may lead the exchange rate todepreciate and output growth to be unusually low. Using this type of variation to assess the effectof exchange rate depreciations on output will yield misleading results since the direct effect of thenegative shock on the economy is a confound (which in this case would bias results towards finding that exchange rate depreciations are contractionary). Since all exchange rate changes happen
for a reason, it is not clear that it is truly possible to measure the causal effect of an exchange rate
depreciation.
Our approach to tackling this challenge is to compare outcomes for countries that peg theircurrency to the US dollar to outcomes in countries with currencies that float versus the US dollar
when the US dollar exchange rate changes. A concrete example is useful. Since 2000, the South
African rand has floated versus the US dollar, while the Egyptian pound has been pegged or has
been on a crawling peg versus the US dollar. This has meant that when the US dollar depreciates
relative to its main trading partners, the Egyptian pound (EGP) has tended to depreciate relative
to the South African rand (ZAR). The question we ask is: How does this depreciation of EGP
1 Bianchi and Coulibaly (2023) present a third type of model that can generate a contractionary devaluation. In
their model, a devaluation reduces the value of collateral and thereby tightens borrowing constraints. A large literature
has also considered how stabilization plans – i.e., the prevention of further depreciation – can be expansionary in highinflation countries (Dornbusch, 1982; Rodriguez, 1982; Calvo, 1986; Helpman and Razin, 1987; Mendoza and Uribe,
2000).

1relative to ZAR affect macroeconomic outcomes in Egypt relative to South Africa?
Importantly, we are not using all variation in the exchange rate of the EGP and ZAR. We are
only using a component of the variation in these exchange rates that arises because they havedifferent pre-existing exchange rate regimes versus the US dollar (about 8% of the total variationin exchange rates in our sample). We refer to this variation as “regime-induced” variation in theexchange rate. Notice that this approach excludes all variation in exchange rates that arises fromidiosyncratic shocks to each country (such as the bad shock discussed above) since such shocks
do not move the US dollar exchange rate. We measure the US dollar exchange rate relative to 24
relatively advanced economies and exclude these countries from our baseline sample.
Our empirical results are easiest to interpret if the following assumption holds: pegs are notdifferentially exposed (relative to floats) to aggregate shocks that are correlated with the US dollar
exchange rate. If this is true, the direct effects of the shocks that drive the US dollar exchange
rate will affect pegs and floats symmetrically and will be absorbed by time fixed effects in ourempirical specification. What is left is the “regime-induced” effect of the exchange rate of the pegs
comoving with the US dollar.
The choice of exchange rate regime is, of course, an endogenous policy decision. So, considering deviations from the no-differential-exposure assumption is important. Perhaps the most likely
scenario is that peggers to the US dollar may tend to be countries that share more shocks with the
US than floaters (a standard assumption in the literature on optimal currency areas). A battery ofrobustness checks suggests this is unlikely to drive our results, which remain virtually unchanged
after controlling for differential exposure to changes in US GDP, US monetary policy, the global financial cycle indicators, and commodity price fluctuations. Also, if pegs are differentially exposedto the same negative shocks that depreciate the US dollar, one might expect them to do poorly inthe wake of a US dollar depreciation (but we find the opposite).2
There are relatively few “true floats” in our sample. Many of the countries that we classify
as floats versus the US dollar are pegs to other currencies such as the euro. Since the euro floats
versus the US dollar, currencies that peg to the euro float versus the US dollar. The choice of whichcurrency a country pegs to in many cases has deep historical roots relating to colonial origins (e.g.,
the French franc zone in West Africa). We show that our pegs and floats are quite similar on
observable characteristics, which lends credence to the view that they have similar exposure tomacroeconomic shocks.
2 If pegs are differentially exposed to positive shocks that depreciate the US dollar (e.g., productivity shocks) thenthe bias could go in the opposite direction. However, productivity shocks yield very little exchange rate variability instandard models. Moreover, controlling for US variables has little impact, as we discuss above.

2

Our main empirical finding is that regime-induced depreciations are strongly expansionary.
Consider a case when the US dollar depreciates. This results in both the nominal and real exchange rates of pegging countries depreciating relative to floating countries. These depreciations
are quite persistent. (They lasts roughly five years.) Output, consumption, and investment in pegging countries boom relative to floating countries. The boom builds gradually over several years
and peaks after about five years. Quantitatively, our estimates imply that a 10% regime-induced
depreciation results in a 5.5% increase in GDP over five years.
We consider the effects on a number of other macroeconomic outcomes. Two of these areparticularly important for interpreting our results. First, we find that net exports fall in response toa regime-induced depreciation. This rules out an export-led boom due to expenditure switching as
the main driver of our results. Second, our point estimates indicate that nominal interest rates risein response to a regime-induced depreciation (these estimates are noisy). This is inconsistent withthe depreciation resulting from looser monetary policy in pegging countries relative to floating
countries. Together, these results rule out a large set of standard models that might be used to
explain our results.
We present a financially driven exchange rate model (FDX model) that can match our empirical results. In this model, shocks emanating from the financial sector are important driversof exchange rate volatility and financial frictions in international financial markets result in noveltransmission mechanisms from these shocks to macroeconomic outcomes. Our model builds mostdirectly on Itskhoki and Mukhin (2021a), but indirectly on a large prior literature that has developed financially driven exchange rate models. We augment Itskhoki and Mukhin’s (2021a) modelin two important ways: we allow households and firms to borrow and invest in foreign currency
and we allow for more than one type of financial shock.
In our model, a depreciation of the US dollar driven by a financial shock (e.g., a UIP shock)
makes the currencies of peggers “cheap” in the sense that expected future returns from investingin these currencies are higher than for floater currencies. (We show that this is indeed the caseempirically in response to regime-induced exchange rate variation.) This return differential resultsin capital flows into pegging countries, which stimulates a domestic boom in these countries. For
this to occur, the model must have two features. First, limits to arbitrage must be pervasive, i.e.,there cannot be any “deep pocketed” investors that fully arbitrage away all return differentials.
Second, households and firms must – directly or indirectly – be able to invest and borrow inforeign currency assets.
Our empirical results raise the following question: if regime-induced exchange rate depre3

ciations have large stimulatory effects, why don’t we see a strong unconditional correlation between exchange rates and output? It is well-known that the correlation of exchange rates withmost macroeconomic aggregates is very low. Exchange rates are often said to be “disconnected”
from macroeconomic aggregates. Furthermore, when countries shift from a fixed to a flexible exchange rate, this can lead to a dramatic change in the volatility of their real exchange rate (Mussa,
1986) apparently without having much of an effect on the volatility on output, consumption, andother macroeconomic outcomes (Baxter and Stockman, 1989; Flood and Rose, 1995; Itskhoki and
Mukhin, 2021b). How can regime-induced depreciations have large effects, while exchanges rates
are more generally disconnected from macroeconomic outcomes?
We show that our FDX model is simultaneously consistent with large effects of regime-induced
depreciations, unconditional exchange rate disconnect, and the “Mussa facts” regarding changes
in volatility when countries move from a peg to a float. The crucial ingredient to match all thesefacts simultaneously is that exchange rates be driven by more than one different type of financial
shock. We consider two financial shocks. The first of these is a “UIP shock” where noise traders
reduce demand for the home currency. In response to this shock, other agents trade against thenoise traders and this results in a capital inflow into the home country and an associated boom.
The second shock is a “capital flight” shock where home households and firms reduce demand
for the home currency. This shock results in a capital outflow and a recession. The combination ofthese two shocks can then result in a low correlation between the exchange rate and output.
Similarly, moving from a floating exchange rate to a peg has two opposing effects on output
volatility in our model. On the one hand, pegging eliminates the UIP shocks. This reduces output
volatility. On the other hand, pegging makes the contractionary effects of capital flight shocks
larger. This arises for two reasons. First, the peggers can no longer respond to an adverse capitalflight shock by easing monetary policy. Second, peggers do not experience a UIP deviation after
a capital flight shock since their exchange rate does not depreciate. This means that borrowing
costs increase more for peggers after a capital flight shock than they would if these countries were
floating. Since there are opposing effects, the overall effect of pegging on exchange rate volatility
is ambiguous. Our model, thus, captures both the potentially destabilizing effects of flexible exchange rates articulated by Nurkse (1944, 1945) and the stabilizing role of flexible exchange rates
articulated by Friedman (1953). For our calibration, the second effect is larger than the first andoutput volatility decreases when a country floats.
While it is crucial that we have two shocks driving exchange rate fluctuations, not just any
two shocks will do. In standard models, most shocks generate a positive correlation between con4

sumption and the real exchange rate (booms associated with depreciations). Empirically, however,exchange rates and consumption are mildly negatively correlated (Backus and Smith, 1993). Second, many shocks fail to generate appreciable volatility in the exchange rate. We need a shock thatgenerates a negative correlation between consumption and the exchange rate and also generates
high exchange rate volatility. The capital flight shock has these two important implications.
The tradeoffs a country faces in adopting a fixed versus flexible exchange rate look fundamentally different when viewed from the perspective of models in which financial shocks play acentral role in driving the exchange rate. In traditional open economy models, the primary effectof pegging one’s currency is for monetary policy: pegging to the US dollar implies a country must
follow US interest rate policy. Our empirical findings suggest, however, that a first order consequence of pegging to the US dollar is that a country imports the financial shocks that drive the US
exchange rate, while potentially eliminating home-grown financial shocks. The importance of thisfinancial shock trade-off may greatly outstrip the importance the traditional monetary trilemma.
Related Literature.

Our analysis relates to a literature that has sought to estimate the effect ofchanges in exchange rates on macroeconomics outcomes. Rodrik (2008) shows that an “undervaluation” of the real exchange rate correlates with GDP growth. Obstfeld and Zhou (2022) estimate
the effect of changes in the US dollar exchange rate on a sample of 26 emerging market and developing countries from 1990-2019. They focus on the aggregate effect, but also find as we do thatpegs are affected more by movements in the US dollar than floats. Eichengreen and Sachs (1985)
and Bouscasse (2022) exploit the difference in the timing of the abandonment of the gold standard
in the 1930s and find that depreciations are strongly expansionary.
Our empirical strategy relates to a strand of literature that explores heterogenous responses ofmacroeconomic outcomes by exchange rate regime. Tenreyro (2007); Barro and Tenreyro (2002)
use regime induced volatility in exchange rate rates to study trade and the comovement of priceand GDP across countries. Di Giovanni and Shambaugh (2008) and Cloyne et al. (2022) study theeffect of anchor country monetary policy on peggers. Jordà, Schularick, and Taylor (2020) interact
the exchange rate regime, capital account openness, and anchor currency’s monetary policy toconstruct an instrumental variable for changes in a country’s monetary policy based on the classic
monetary trilemma. Broda (2004) assess the effects of terms of trade shocks on peggers versus
floaters. Carare et al. (2022) assess the effect of a country’s exchange rate regime for global demand shocks, while Cesa-Bianchi, Ferrero, and Rebucci (2018) consider global supply shocks. We
investigate arguably the most direct consequence of choosing one exchange rate regime versus the5other: differential exposure to movements in the anchor currency’s exchange rate.
Our model draws heavily on Itskhoki and Mukhin (2021a) and indirectly on the pioneering
work of Gabaix and Maggiori (2015). These papers in turn build on much earlier literature, e.g.,Branson et al. (1970) and Kouri (1976). Papers emphasizing UIP shocks include Devereux andEngel (2002), Gourinchas and Tornell (2004), Kollmann (2005), Bacchetta and Wincoop (2006), andEichenbaum, Johannsen, and Rebelo (2020). Also related is the literature on the carry trade (see,e.g., Burnside, Eichenbaum, and Rebelo, 2011). Our modeling of the capital flight shock builds on
Bianchi and Lorenzoni (2021). Alternative models that generate similar shocks are developed by
Kekre and Lenel (2021) and Engel and Wu (2023). These ideas, in turn, build on Calvo (1998). A
growing empirical literature documents a strong association between financial market variables
and exchange rates (Jiang, Krishnamurthy, and Lustig, 2018; Engel and Wu, 2023; Lilley et al.,2022; Jiang, Richmond, and Zhang, 2022). Our empirical results – when interpreted through thelens of our theoretical model – provide additional support for the view that the dominant driverof exchange rate fluctuations is financial shocks.
The paper proceeds as follows. Section 2 presents our empirical results. Section 3 lays out
the model we used to interpret these results. Section 4 discusses the calibration of the model.
Section 5 shows that the model can match our empirical results. Section 6 shows that our model
augmented with capital flight shocks is consistent with unconditional exchange rate disconnect,
the Backus-Smith correlation, and the Mussa facts.

2

New Evidence on the Effect of Exchange Rate Depreciations

The basic idea of our empirical approach is to compare outcomes in countries that peg their exchange rate to the US dollar to outcomes in countries with a currency that floats versus the US
dollar when the US dollar exchange rate moves. We start this section by discussing how we measure movements in the US dollar exchange rate. Next, we discuss how we classify countries into
pegs and floats. We then discuss our main empirical specification and the data we use, before
presenting our empirical results.

2.1

US Dollar Nominal Effective Exchange Rate

Our sample is annual data over the period 1973 to 2019. When assessing the response of pegs andfloats to movements in the US dollar exchange rate, we use a trade-weighted US exchange rate

6

1.1
1
.9
.8
.7
.6

1980

1990

2000

2010

2020

Year

Figure 1: US Dollar Trade-Weighted Exchange Rate
Note: This figure plots the BIS’s trade-weighted exchange rate of the US dollar against 24 countries. For a listof these countries, see footnote 3. Lower values indicate a more appreciated US dollar.

constructed by the Bank of International Settlements (BIS) relative to 24 countries.3 We exclude
these 24 countries from our sample of pegs and floats. We sometimes refer to this exchange rate as
the nominal effective exchange rate of the US dollar. Figure 1 plots the evolution of this exchange
rate over our sample period. We define the exchange rate as the domestic currency price of foreign
currency. This implies that an increase in the exchange rate is a depreciation. The US dollar’s
exchange rate experienced several large swings during our sample period. Its value rose sharply
in the early 1980s and fell sharply in the late 1980s. It rose in the late 1990s, and fell in the 2000s. It
then rose, again, substantially in the 2010s.

2.2

Exchange Rate Regimes

Exchange rate classification is notoriously difficult. Many countries follow a policy that is neither
a strict peg nor a free float and often de facto policy differs sharply from de jure policy. We classify
the exchange rate regime for each country-by-year observation as either a peg or a float versus the
US dollar based on Ilzetzki, Reinhart, and Rogoff’s (2019) classification of exchange rate regimes.
3 The countries are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong,

Ireland, Italy, Japan, Korea, Mexico, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, and United Kingdom.

7

They develop a “coarse” six-category classification, and a “fine” 15 category classification. These
classifications attempt to provide a detailed breakdown of the spectrum of de facto policy from astrict peg to a free float. Their coarse categories are: 1) peg, 2) narrow band, 3) broad band andmanaged float, 4) freely floating, 5) freely falling, 6) dual market with missing parallel market
data. We list the fine categories in Table A.2. Ilzetzki, Reinhart, and Rogoff also assign an anchor
currency to each country-by-year observation. The anchor currency for most observations is the
US dollar. A minority of observations have the euro, British pound, French franc, German mark,and other major currencies as anchors. (See appendix A for details.)
From our perspective, what matters is the extent to which currencies in different categories
comove with the US dollar. We can assess this with the following regression∆ei,t = αi + αr(i),t + ∑ γk Ii,t (k ) × ∆eUSD,t + ϵi,t ,(1)kwhere ∆ei,t denotes the log change in the exchange rate of country i from time t − 1 to t, αi denotes country fixed effects, αr(i),t denotes region-by-time fixed effects, Ii,t (k ) is an indicator for theexchange rate regime k of country i at time t, ∆eUSD,t denotes the log change in the US dollar effective exchange rate, and ϵi,t denotes unmodelled influences on the change in the exchange rate ofcountry i at time t. The region-by-time fixed effects are for four regions: Europe, Americas, Africa,
Asia/Oceania.
In this analysis, we define ∆ei,t for all countries relative to the same currency (say the US dollar). This simplifies the exposition, since a perfect peg to the US dollar moves exactly one-for-one
relative to a perfect USD float. The same holds (identically) if we define ∆ei,t relative to any othercurrency, so long as it is the same across countries (due to the presence of time fixed effects). The
level of the coefficients γk are determined by the omitted category (which we choose to be the free
floats (category 13)). In section 2.6, in contrast, we use the trade-weighted exchange rate (withcountry-specific trade weights). In practice, both approaches yield similar yield similar results, as
we describe below.
For country-by-year observations anchored to the US dollar, we define Ii,t (k ) using Ilzetzki,
Reinhart, and Rogoff’s fine classification. We exclude observations from categories 14 (freely
falling) and 15 (dual market/missing data). We assign country-by-year observations that Ilzetzki, Reinhart, and Rogoff assess as being anchored to a currency other than the US dollar (or to abasket) to one of three categories based on their coarse classification of these observations vis-a-vis
that anchor. In particular, categories 13.1, 13.2, and 13.3 in Figure 2 are currency-by-year observa8

tions with an anchor other than the US dollar and which are classified in coarse categories 1 (peg),
2 (narrow band), and 3 (broad band and managed float), respectively. We exclude the 24 countries
that the US dollar nominal effective exchange rate is defined relative to and restrict the sample tocountry-by-year observations for which real GDP data from the World Bank is available.
Figure 2 plots the γk coefficients from this regression along with 95% confidence intervals. The
key conclusion that we draw from this figure is that Ilzetzki, Reinhart, and Rogoff’s classification
works. Currencies in categories on the left in the figure (the “hardest” pegs) depreciate strongly
relative to currencies in category 13 (“free floats”) when the USD depreciates. A second observation is that currencies that are anchored to countries other than the US dollar (categories 13.1,
13.2, and 13.3) behave quite similarly to the free floats (category 13). The reason for this is simply
that the other anchor countries (mostly the euro and its predecessors) are for the most part free
floats versus the US dollar. Countries that peg to these other anchors therefore also float versus
the dollar.4
Interestingly, the degree to which the coefficients in Figure 2 fall as we move from left to rightis quite modest for the first 12 categories. Even currencies that Ilzetzki, Reinhart, and Rogoff
classify as managed floats comove by similar amounts with the US dollar at an annual frequency
as currencies that they classify as very hard pegs. This suggests that “fear of floating” is pervasive(Calvo and Reinhart, 2002).
Based on these results, we classify observations into pegs and floats as follows. We classify
observations in categories 1 through 8 in Figure 2 as pegs and observations in categories 13 - 13.3
as floats. We drop observations in categories 9 through 12 as well as observations in categories 14(freely falling) and 15 (dual market/missing data). Categories 9 through 12 (coarse category 3) are
intermediate categories that fit poorly in either the peg or float group. Our results are robust tohandling these categories differently.5
We classify roughly half of our sample as floats (see Figure A.3 and Figure A.4 for the fractionof pegs in each region). Most of the countries that we classify as floats versus the US dollar are
strongly linked to other currencies (categories 13.1, 13.2, and 13.3 above). For example, a numberof West African countries peg to the euro (and before that the French franc), which floats relative
to the US dollar. These currencies are classified as “floats” in our analysis. Therefore much of the
4 Figure A.1 presents results separately for observations anchored to baskets (that include the US dollar) and forobservations anchored to the South African rand, the Indian rupee, or the Singapore dollar – currencies that have notalways floated freely relative to the US dollar. Figure A.2 presents results analogous to Figure 2 for Ilzetzki, Reinhart,
and Rogoff’s coarse categories.
5 As robustness, we present results for both the case where we include these categories as pegs and the case where
we include them as floats (see Figures A.17 and A.18 in the appendix). Both of these sets of results are similar to ourbaseline results.

9

1.5
1
.5
0
-.5
-1

.1

.2

.3

13

13

13

13

12

11

10

9

8

7

6

5

4

3

2

-1.5

1

Figure 2: Comovement with US Dollar by Category
Note: This figure plots our estimates of the γk ’s from equation (1). These are estimates of the comovement of
the exchange rate of currencies with different exchange rate regimes as classified by Ilzetzki, Reinhart, andRogoff’s (2019) fine classification. We normalize the γk for category 13 (freely floating and anchored to the
US dollar) to zero. The vertical lines extending from each point estimate represent 95% confidence intervals.
The two thin vertical lines denote the splits between categories we classify as pegs (1 through 8) and floats (13through 13.3).

variation we exploit comes from which currency a country pegs to, rather than whether a country
pegs or floats.
Our classification of observations into pegs and floats is likely far from perfect in that manyof our pegs are not completely “hard” pegs and many of our floats are not completely “free”
floats. However, a key insight is that while this issue may reduce the statistical power of our
methodology, it is not a source of bias. As in any instrumental variables analysis, misclassificationof pegs and floats will lead to a smaller differential response of pegs versus floats for both theexchange rate and other outcome variables. We are interested in the magnitude of the response ofvarious outcome variables relative to the exchange rate. Since misclassification of pegs and floats
leads both the numerator and the denominator in this ratio to be smaller, it is not necessary for theclassification of regimes to be perfect. This is analogous to the idea that an instrument need not
capture all the random variation, only a piece of it.

10

Table 1: How Do Pegs Differ from Floats
Variable
No Controls Time FE Region X Time FE
Log Population
-0.02
-0.09
0.74*
(0.31)(0.31)(0.39)
Log Real GDP Per Capita
0.36
0.32
-0.17
(0.22)(0.22)(0.23)
Export to GDP
-0.01
-0.01
0.00
(0.04)(0.04)(0.04)
Import to GDP
-0.03
-0.03
-0.03
(0.04)(0.04)(0.04)
Export Share to the US
0.04***
0.04***-0.00(0.01)(0.01)(0.01)
Import Share to the US
0.05***
0.05***
0.00(0.01)(0.01)(0.00)
NFA to GDP
0.05
0.06
-0.10
(0.18)(0.19)(0.26)Inflation Rate (p.p.)
-0.89
-0.65
2.21***(1.51)(1.41)(0.69)
TBill Rate (p.p.)
1.01
0.89
2.86***(0.84)(0.90)(0.96)
Commodity Exports to GDP
0.05*
0.06**
0.04(0.03)(0.03)(0.03)
Commodity Imports to GDP
0.01
0.01
-0.01
(0.02)(0.02)(0.02)
Note: The table reports regression coefficients for regressions of various country characteristics on an indicatorvariable for whether the country-by-year observation is a peg. The dependent variables are listed on the left.
For each dependent variable we report results of a regression with no additional control variables, results
when time fixed effects are included, and results when region-by-time fixed effects are included. Standard
errors clustered by country are reported in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.

2.3

How Do Pegs Differ from Floats?

Our empirical results are simplest to interpret if the following identifying assumption holds: pegs
are not differentially exposed (relative to floats) to shocks that are correlated with the US nominal
effective exchange rate. We can assess the plausibility of this assumption by comparing observable characteristics of pegs and floats. Table 1 reports the average differences in various observablecharacteristics between pegs and floats. We estimate this difference by regressing the characteristics on an indicator variable for whether the country-by-year observation is a peg. In each case,
we report unconditional differences (i.e., no other controls), differences conditional on time fixed
effects, and differences conditional on region-by-time fixed effects.
Conditional on region-time fixed effects, pegs and floats are quite well balanced on most ob11

servable dimensions. The average difference in their real GDP per capita is not statistically significantly different from zero. They are roughly equally open economies on average, their export
and import shares to the US are similar, as are their net foreign asset positions, and their exports
and imports of commodities as a share of GDP are also similar.6 The only observable differencesconditional on region-time fixed effects are that pegs have somewhat higher inflation, somewhat
higher short-term interest rates, and are larger in terms of population.7

2.4

Empirical Specification

We seek to estimate the differential response of various outcome variables in pegging countries
versus floating countries at different horizons to a change in the US dollar exchange rate. For thispurpose, we run the following regression:
yi,t+h − yi,t−1 = αi,h + αr(i),t,h + β h Pegi,t × ∆eUSD,t + Γ′h Xi,t−1 + γh Pegi,t + ϵi,t,h ,(2)where yi,t+h denotes an outcome variable in country i at time t + h, Pegi,t is an indicator forwhether country i at time t is a peg, ∆eUSD,t denotes the log change in the US dollar nominal effective exchange rate from time t − 1 to time t, αi,h is a country fixed effect, αr(i),t,h is a region-by-time
fixed effect, Xi,t−1 denotes additional control variables, and ϵi,t,h denotes unmodelled influenceson the outcome variable. This type of empirical specification is often called a local projection(Jordà, 2005). The region-by-time fixed effects are for the following four regions: Europe, Americas, Africa, Asia/Oceania. The coefficient of interest is β h . We run this regression on annual datafor different horizons h.8
We report standard errors that are two-way clustered on time and country. We drop the largest
and smallest 0.5% of observations for each outcome variable. This avoids our results being highly
sensitive to extreme events such as severe wars (Iraq in 2004). We also drop country-by-year
observations during which the country switches from being a peg to a float or vice versa and the6 This last result is based on a relatively coarse measure of commodity exports: the sum of agriculture and mining

exports.
7 This may, at first, seem to contradict the findings of Hassan, Mertens, and Zhang (2023), who document that large
countries tend to float. The difference comes from the fact that we exclude 24 relatively advanced economies and ourdefinition of floats include pegs to other currencies than the US dollar.
8 An alternative approach would be to instrument for the local exchange rate with Peg × ∆e
USD,t . However,i,tthis would pre-suppose that the only channel through which the shocks that move the US dollar exchange rate affectpeggers versus floaters is these countries’ exchange rates. This might not be the case (e.g., interest rates might drive
both exchange rates and affect the economy directly). Hence, we run direct regressions. However, if the exchange rate
is truly the only channel through which changes in the exchange rate of the US dollar affect peggers versus floaters, ourregressions with the nominal exchange rate as the outcome variable are akin to first stage regressions in an IV empiricalstrategy and our output regressions are akin to reduced from regressions. The IV estimate is then the ratio of the two.

12

following year.

2.5

Data

Our main data sources are the World Bank’s World Development Indicators (WDI) database, thedatabase of the United Nations Conference on Trade and Development (UNCTAD), and the International Financial Statistics (IFS) database of the International Monetary Fund (IMF). We use
data on GDP, consumption, investment, exports, and imports from WDI, all measured in constant2015 US dollars. We use data on export unit values, import unit values, and the terms of tradefrom UNCTAD. We use data on short term nominal interest rates and inflation from IFS. In addition to these sources, we use data on nominal and real effective exchange rates from Darvas(2012, 2021) (series NEER 65 and REER 65), data on the ratio of net foreign assets to GDP from theExternal Wealth of Nations Database (Lane and Milesi-Ferretti, 2018), the Bloomberg Commodity
Price Index, and the capital account openness measures from Chinn and Ito (2008).
For the nominal interest rate, we choose among the T-bill rate, the policy rate, and the money
market rate. For each country, we use the one of these series with the longest sample in the IFS
database. We construct a measure of net exports from data on exports and imports. We construct ameasure of the ex-post real interest rate from data on the nominal interest rate and inflation. Table
A.3 in the appendix provides an overview of our data sources.
As we note above, all our data is annual and our sample period is 1973 to 2019. However, ourpanel data set is unbalanced and differs in size from variable to variable. One of the robustness
exercises we do below is to rerun our empirical analysis on the largest sample for which we haveall our main variables of interest available.

2.6

Empirical Results

Figure 3 plots our estimates of β h for four outcome variables: the nominal effective exchange
rate, the real effective exchange rate, real GDP, and consumption. For the nominal and real effective exchange rates, the dependent variable is the h + 1-period change in the logarithm of thecountry’s trade-weighted exchange rate (nominal or real). For GDP, the dependent variable is(Yi,t+h − Yi,t−1 )/Yi,t−1 where Yi,t denotes the level of GDP in country i at time t. For consumption, the dependent variable is (Ci,t+h − Ci,t−1 )/Yi,t−1 , where Ci,t denotes the level of consumption
in country i at time t. The independent variable of interest ∆eUS,t is the change in the logarithmof the US dollar nominal effective exchange rate. We include three controls in addition to the13Nominal Effective Exchange Rate

Real Effective Exchange Rate

1.5

1.5

1

1

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.5

0

0

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4

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-1

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GDP

2

3
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Consumption

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5

6

7

8

9

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4

Figure 3: Response of Pegs vs. Floats for Exchange Rate, Output, and Consumption
Note: This figure plots the response of the nominal effective exchange rate, real effective exchange rate, realGDP, and consumption for pegs versus floats in response to a change in the US dollar exchange rate. For theexchange rates, the dependent variable is the change in the logarithm of the variable. For GDP, the dependent
variable is the percentage change, while for consumption it is (Ci,t+h − Ci,t−1 )/Yi,t−1 . These are our estimatesof β h in equation (2) for different horizons h when these four variables are the outcome variables. These results
are for the case with our baseline set of controls: one lag of the outcome variable, one lag of the treatment
variable, and one lag of GDP growth. The shaded areas are 95% confidence intervals.

fixed effects: the lagged growth rate of the outcome variable, a lag of the treatment variable (morespecifically, a lag of Pegi,t × ∆eUSD,t and Pegi,t ), and a lag of GDP growth.9 Recall that we define
the exchange rate as the domestic currency price of foreign currency, which implies that an increase in the exchange rate is a depreciation. The responses in Figure 3 should thus be interpreted
as responses of pegs relative to floats to a 1% depreciation in the US dollar.
In response to a 1% depreciation of the US dollar, the trade-weighted nominal effective exchange rate of pegs depreciates by 0.74% relative to floats. This depreciation persists for a numberof years, first rising slightly to 0.9% and then falling to about 0.6% in the 3-5 years after the US depreciation. The reason the response is not fully one-for-one is that our pegs are not perfectly hardpegs and our floats are not perfectly free floats. The real effective exchange rate of pegs depreciates by only slightly less relative to floats than the nominal effective exchange rate. The responseof the real effective exchange rate is also persistent, although somewhat less persistent than the re9 For the periods prior to the treatment period (h < 0), we include these controls at time h − 1.

14

sponse of the nominal exchange rate.10 Table A.4 in the appendix shows that the regime-induced
variation in exchange rates we use for identification represents roughly 8% of the total variationin exchange rates in our data.
The bottom two panels in Figure 3 show that the US dollar depreciation results in a gradualbut quite substantial increase in GDP and consumption in pegger countries relative to floater
countries. In response to a 1% US dollar depreciation, GDP eventually rises by about 0.4%. To
get a better sense for the quantitative magnitude of the GDP response, note that these estimates
imply that a 10% depreciation of the domestic currency results in a 5.5% increase in GDP over five
years.11 Recall that the consumption response we plot is the change in consumption as a fractionof time t − 1 GDP. The consumption response peaks at almost 0.4% of GDP a few years after the
depreciation.
Figure 4 presents results for investment, net exports, exports, and imports. All four variables
are measured as a fraction of GDP. For example, the dependent variable for investment is ( Ii,t+h −Ii,t−1 )/Yi,t−1 , where Ii,t is the level of investment in country i at time t. The depreciation results
in an increase in investment that is modest to begin with, but builds over time and reaches amaximum after five years. Exports increase one year after the depreciation but then fall backto zero for several years before increasing again. Contrary to the simple logic of expenditureswitching, the depreciation results in an increase in imports that builds gradually over time. For
several years, the increase in imports is larger than the increase in exports, which implies that net
exports fall.
The left two panels of Figure 5 present the response of the short-term nominal interest rate andthe CPI in pegger countries relative to floaters. For the CPI, the dependent variable is the change inthe logarithm of the CPI. For the nominal interest rate, the dependent variable is the change in thelevel of the interest rate. The nominal interest rate rises modestly in response to the depreciation(by less than 0.1 percentage point in response to a 1% depreciation). The price level also increases,
modestly at first, but more later on (by about 0.5% in response to a 1% depreciation).12
These results help distinguish between different possible underlying shocks that might bedriving the variation in the US dollar exchange rate in our regressions. If loose monetary pol10 Figure A.5 in the appendix compares the response of the trade-weighted nominal and real exchange rate (thebaseline in this section) to the response of the nominal exchange rate to the US dollar. These yield similar responses ofpegs versus floats to USD depreciations, although the exchange rate versus the USD is more persistent at long horizons.
11 The GDP response is gradual and peaks after five years at 0.4. The average nominal exchange rate response isroughly 0.7 over the first five years. We get 5.5 as 10 × 0.4 ÷ 0.7.
12 Figure A.7 presents results on the ex-post real interest rate that are implied by the responses of the nominal interest
rate and prices in Figure 5. The response of the real interest rate fluctuates around zero and is statistically insignificant
throughout.

15

Investment

Net Exports

.8

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2

Exports

3
Years

4

5

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8

9

4

5

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9

Imports

.8

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2

3
Years

4

5

6

7

8

9

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0

1

2

3
Years

Figure 4: Response of Pegs vs. Floats for Investment and Trade
Note: This figure plots the response of investment, net exports, exports, and imports for pegs versus floats in
response to a change in the US dollar exchange rate. All four variables are measured as a fraction of initial
GDP (e.g., ( Ii,t+h − Ii,t−1 )/Yi,t−1 for investment). T hese are our estimates of β h in equation (2) for different
horizons h when these four variables are the outcome variables. These results are for the case with our baseline
set of controls. The shaded areas are 95% confidence intervals.

icy were the reason for the US dollar depreciation, we would expect to see a negative relative
response of the nominal interest rate for pegs relative to floats (since pegs share US monetary policy more strongly). The fact that our estimated response for the nominal interest rate is positive,
therefore, provides evidence against the notion that the US depreciations in our regressions are
driven by monetary policy.13 We develop this idea more fully in Section 5 below.
Put differently, the joint responses of nominal exchange rates and nominal interest rates show
substantial ex-post deviations from uncovered interest parity (UIP). After the initial depreciationof pegs, their nominal exchange rates appreciate and their nominal interest rates are (if anything)higher than before (relative to floats). This implies that the return to holding assets denominatedin the currencies of the pegs are higher ex-post than returns of assets denominated in floating
currencies. Figure C.3 in the appendix shows this by plotting the impulse response of ex-post UIP
13 Our empirical analysis cannot rule out the possibility that exchange rate changes are due to changes in expectation
about far future nominal interest rates, ln(1 + i P,t+T ) − ln(1 + i F,t+T ) for T greater than 10 years. Such shocks are hardto distinguish from financial shocks. Chahrour et al. (2022) argue that far future fundamental shocks are the source ofa substantial fraction of volatility in exchange rates. This finding contrasts the findings of Miyamoto, Nguyen, and Oh(2022) that the dominant drivers of the real exchange rate are largely orthogonal to macro aggregates.

16

Nominal Interest Rate

CPI

Terms of Trade

1

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Years

5

6

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5

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9

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3 4
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5

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9

Figure 5: Response of Pegs vs. Floats for the Nominal Interest Rate, CPI, and Terms of Trade
Note: This figure plots the response of short term nominal interest rates, the CPI, and the terms of trade forpegs versus floats in response to a change in the US dollar exchange rate. For the nominal interest rate, thedependent variable is the level of the interest rate (i.e., 0.02 denotes 2%). For the CPI and the terms of trade,the dependent variables are the change in the logarithm of the variables. These are our estimates of β h inequation (2) for different horizons h when these two variables are the outcome variables. These results are forthe case with our baseline set of controls. The shaded areas are 95% confidence intervals.

deviations of pegs relative to floats. The presence of these UIP deviations are at the core of thetheoretical channel we propose in section 3 for why depreciations are expansionary in response to
regime-induced exchange rate variation.
The right panel of Figure 5 presents the response of the terms of trade. The dependent variable,in this case, is the change in the logarithm of the terms of trade. We define the terms of trade as
the price of exports divided by the price of imports (our data are unit values). We estimate thatthe terms of trade of peggers improves modestly relative to floaters at short horizons in responseto the US dollar depreciation. Further out, the improvement in the terms of trade is larger (thoughstatistically insignificant). In a world with sticky prices that are set in the producer’s currency,
the terms of trade would deteriorate in response to a depreciation (imports would become more
expensive in domestic currency). With local currency pricing, however, a depreciation results
in an improvement in the terms of trade. In a world with a dominant currency (e.g., importand export prices sticky in US dollars) the terms of trade would not respond to a change in theexchange rate. Figure A.6 in the appendix present our estimates of the response of export andimport unit values. Measured in US dollars, the price of exports is little changed, while the priceof imports falls modestly in pegging countries relative to floating countries in response to the US
dollar depreciation.
Figure 6 presents the response of output by sector for pegs relative to floats. The dependent
variable for these four sets of results is the change in the variable in question divided by initial
S
S
GDP. For example, for the service sector, the dependent variable is (Yi,t+h − Yi,t−1 ) /Yi,t−1 , where17Manufacturing GDP

Service GDP

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Agriculture GDP

0

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9

Mining, Construction, Energy GDP

.6

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4

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9

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1

2

3
Years

4

5

6

Figure 6: Response of Pegs vs. Floats by Sector
Note: This figure plots the response of output by sector for pegs versus floats in response to a change in the US
dollar exchange rate. In all cases, the dependent variable is the change in the variable in question as a fractionof initial GDP. These are our estimates of β h in equation (2) for different horizons h when these four variables
are the outcome variables. These results are for the case with our baseline set of controls. The shaded areas
are 95% confidence intervals.
S is service sector output in country i at time t. Strikingly, the bulk of the response comes fromYi,tthe service sector. The response of manufacturing and agriculture are very close to zero. So is the
response of the mining, construction, and energy sectors except for a boom at very long horizons.
This pattern of responses suggests that the depreciation kicks off a domestic boom, as opposed toan export-led boom.

2.7

Heterogeneity by Openness and Time Period

Our finding that a regime-induced depreciation results in a fall in net exports indicates that capital is flowing into these countries. This raises the question whether our results differ by a country’s capital account openness and openness to trade. Figure 7 re-estimates equation (2) for countries with above versus below-average capital account openness over the sample period when the
country’s data are available. Here we measure capital account openness by the Chinn-Ito index(Chinn and Ito, 2008). We find that the relative response of GDP is entirely driven by a set ofcountries with high capital account openness, despite the fact that the relative response of realexchange rates are similar. In contrast, the response of GDP is similar for countries with above
versus below median levels of trade openness, as measured by the sum of exports and imports
18

Real Effective Exchange Rate

Real GDP
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5

Capital Account Openess < Median

6

7

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> Median

-2

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2

3
4
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5

Capital Account Openess < Median

6

7

8

9

> MedianFigure 7: Heterogenous Response by Capital Account Openness
Note: This figure plots the response of the real exchange rate and output for pegs versus floats in response toa change in the US dollar exchange rate. We report this separately for countries with average capital accountopenness below versus above the median across countries. For the real exchange rates, the dependent variable
is the change in its logarithm. For GDP, the dependent variable is a percentage change. These are our estimatesof β h in equation (2) for different horizons h when the variables described above are the outcome variables.
These results are for the case with our baseline set of controls. The shaded areas are 95% confidence intervals.

over GDP (see Figure A.8). The heterogeneity in the results by capital account openness, and thelack of heterogeneity by trade openness, are both consistent with the model we develop in Section
3. This model puts international capital flows at center stage. Figure A.9 splits the sample period
into an early period (1973-1995) and a later period (1996-2019). We find similar responses in both
periods.

2.8

The Plaza Accord

It is perhaps useful to have a concrete example of the stimulatory effects of exchange rate depreciations that we have documented in general terms in the preceding sections. The Plaza Accordof 1985 – named after the hotel where it was announced in New York City – provides such an
example. The Plaza Accord was an agreement between France, Germany, Japan, the UK, and the
US (G5 countries) to depreciate the US dollar. The announcement at the Plaza Hotel was a culmination of a larger policy shift by the Reagan administration regarding the dollar, which started
when James Baker became Treasury Secretary in January 1985 (Frankel, 2015). This policy shift
helped trigger a rapid depreciation of the US dollar. Here, we use this event as a case study of aregime-induced depreciation of pegs to the US dollar versus floats.
Figure 8 plots the evolution of the real exchange rate and real GDP for pegs versus floats
against the USD in the years surrounding the Plaza Accord. The left panel shows that the real19

Log GDP

0

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Log Real Exchange Rate to USD

1982

1983

1984

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1986
Year

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1987

Plaza accord

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Plaza accord
1988

1989

1990

Peg to USD

1982

1983

1984

1985

1986
Year

Float vs. USD

1987

1988

1989

1990

Peg to USD

Figure 8: Case Study of the Plaza Accord
Note: The left figure plots the average of changes in the log real exchange rate relative to 1985 for countries thatfloat and peg against the USD. The right panel is analogous for GDP. We exclude G5 countries and country-byyear observation with Ilzetzki, Reinhart, and Rogoff classification 14 and 15 from the sample in constructing
the figure. We define countries that peg to USD in the same way as before: (Ilzetzki, Reinhart, and Rogoff
classification 1-8 with anchor currency USD), while other countries are classified as floats versus the USD.
Pegs and floats are defined in this figure based on their status in 1985.

exchange rate of floats appreciated relative to pegs following the Accord. The timing of the Accord
was arguably orthogonal to macroeconomic conditions in the pegs versus floats in our sample(none of which were parties to the agreement). The right panel shows that GDP grew less quickly
in the floats relative to the pegs in the years after the Accord. To quantify the response for this
episode, we regress changes in real GDP and the real exchange rate starting in 1985 on a peg
indicator for 1985. The differential response in the log real exchange rate in the first year is 12%(standard error of 2.7%) and difference in log GDP after five years is 7.4% (standard error 3.1%).
This implies a GDP response to a 10% exchange rate depreciation of 6.2% (≈ 7.4 × 10 ÷ 12), whichroughly lines up with the estimates from our baseline empirical analysis.14

2.9

Robustness

We have explored a number of variations on our baseline specification. Results for twelve suchvariations are presented in Figures A.10-A.21. Figure A.10 presents results analogous to our baseline results except that we add interactions of contemporaneous values of US GDP growth, US
inflation, and the change in the US T-bill rate with the peg indicator as controls. Adding these controls helps control for economic conditions in the United States (e.g., US monetary policy shocks).
14 We also consider a regression where we include all time periods in our data set and country and time fixed effects

to account for any country-specific growth differentials. According to this regression, a 10% initial depreciation isassociated with an 8% increase in GDP after five years.

20

Figure A.11 adds an interaction of the change in the logarithm of commodity prices with the peg
indicator as a control.15 Figure A.12 adds an interaction of the change in the global factor in risky
asset prices of Miranda-Agrippino and Rey (2015, 2020).16 This addresses the concern that our
results might be driven by peggers being systematically more exposed to global financial cycles,
which are correlated with the movements in US dollar exchange rate. In all three cases, the results
are very similar to our baseline result.
The region-by-time fixed effects in our baseline specification imply that the variation we use to
identify our main results is within-region variation. Figure A.13 presents results for a case that is
identical to our baseline specification except that the region-by-time fixed effects are replaced bytime fixed effects. This allows us to exploit variation in exchange rate regimes not only within but
also between continents. For example, in the baseline version, pegs in Latin America are not being
compared with floats in Europe (this variation is absorbed by the region-by-time fixed effects).
This specification yields similar point estimates, with smaller standard errors. One difference isthat the response of net exports is less negative.
Figures A.14 and A.15 consider alternative sets of controls (no controls other than fixed effects
and two lags of the outcome variable, the treatment variable, and GDP, respectively). Figure
A.16 presents results where we drop the largest and smallest 1% of observations for each variable(instead of 0.5% in the baseline). Figures A.17 and A.18 consider alternative assumptions about
how to categorize Ilzetzki, Reinhart, and Rogoff’s coarse category 3 (included among floats or
pegs, respectively, rather than dropped). Figure A.19 presents results for the case where we replace
the BIS trade-weighted nominal effective exchange rate for the US dollar as our treatment variablewith a US dollar exchange rate that is constructed using GDP weights for the same set of countries.
Figure A.20 presents results for the case where we include the 24 countries that the US dollar
nominal effective exchange rate is defined relative to in the sample of floats. In all of these cases,
the responses are very similar to our baseline case.
Figure A.21 presents results for the largest sample where we have data on all nine of our main
variables. In this case, the response of the nominal and real effective exchange rates is estimated tobe more transient, although the standard errors are very large. The estimated response for output,
consumption, investment, and net exports is similar to our baseline. The estimated response of the
15 Since 2000, commodity prices have tended to comove negatively with the US dollar. This is less true before
2000 and is potentially spurious given the high persistence of both series— see Figure A.24 in the appendix. The
correlation between the log-changes in the trade-weighted US dollar exchange rate and the log-change in the Bloomberg
commodity price index is 0.22 before 2000 but 0.71 after 2000.
16 We use the updated version of their standardized measure for the period of 1980-2019. We downloaded these datafrom Hélène Rey’s website.

21

terms of trade is larger than in our baseline. The large standard errors arise because the sample
size in this case is only about 20% the sample size in our baseline specification. The primaryconstraint here is the availability of the interest rate data.
Finally, one might ask whether either tourism or government expenditures are driving our results. Figure A.22 shows the response of tourist inflows and outflows in our baseline specification.
Neither of them is statistically significantly different from zero. Figure A.23 shows the responseof government expenditures. The response is positive but quantitatively small in magnitude.

3

An FDX Model of Pegs and Floats

To explain our empirical findings from Section 2, we introduce a model in which exchange rates
are driven by financial shocks. We call this a financially driven exchange rate model, or FDX model
for short. The core of the model is a relatively standard open economy New Keynesian model. To
this we add financial frictions in international financial markets and shocks emanating from thefinancial sector. Our model builds most directly on Itskhoki and Mukhin (2021a), but indirectly on
a substantial prior literature that has sought to introduce financial frictions and financial shocks
to international macro models (e.g., Kouri, 1976; Gabaix and Maggiori, 2015).
Relative to the model in Itskhoki and Mukhin (2021a), we add two features. First, we allow
households and firms to trade in foreign currency assets. This is important for explaining ourempirical findings from Section 2. Our second important departure from Itskhoki and Mukhin(2021a) is to allow for a second financial shock that yields a different correlations between theexchange rate and output. This is important for jointly explaining our empirical findings from
Section 2 and unconditional moments that have been emphasized in the open economy literature:exchange rate disconnect, the Backus-Smith correlation, and the Mussa facts. For expositional
clarity, we delay introducing the second financial shock until Section 6.

3.1

Standard Open Economy New Keynesian Model Features

Consider an economy consisting of a continuum of small open economies, i ∈ [0, 1]. Each of these
economies belongs to one of three regions, i ∈ {U, P, F }, where U is the United States with the US
dollar as its currency, P is a monetary union consisting of a set of countries that peg their currency
to the US dollar, and F is a monetary union consisting of a set of countries with a currency thatfloats versus the US dollar. The economies within each of these groups are identical. (This meansthat we model the US as a continuum of identical small economies in a monetary union.) We
22

define the nominal exchange rate E jit as the price of currency j in terms of currency i at time t. An
increase of E jit then represents a depreciation of currency i against currency j. Analogously, wedefine the real exchange rate as Q jit = E jit Pjt /Pit , where Pit is the price level of the economy i.
The core features of our model are standard in the open economy New Keynesian literature.
Households consume and supply labor. We assume that they have preferences that feature habit
formation. This helps capture the hump-shaped impulse response of consumption. Household
preferences over goods produced in the economy take a standard nested CES form with home bias.
Labor unions set wages as in Erceg, Henderson, and Levin (2000). Firms produce goods using
labor, capital, and intermediate inputs. They invest in capital subject to investment adjustment
costs as in Christiano, Eichenbaum, and Evans (2005). Firms set prices as in Calvo (1983). We
allow for prices to be set in any currency, i.e., we allow for any combination of producer currency
pricing, local currency pricing, and dollar currency pricing. We relegate the detailed description ofthese standard parts of the model to Appendix B.1. When solving the model, we take a log-linear
approximation around a symmetric deterministic steady state. We characterize the steady state inAppendix B.3.

3.2

Household and Firm Portfolio ChoiceHouseholds in each region invest in domestic equity and foreign currency bonds. Firms fundthemselves by issuing domestic equity and foreign currency bonds. Since we abstract from domestic currency financial frictions, domestic equity and domestic bonds are identical assets fromthe households’ perspective. We refer to these assets as domestic equity for brevity’s sake. Likewise, the fact that we refer to foreign currency assets traded by households and firms as “bonds”
is for brevity. These are meant to include foreign direct investment, portfolio investments in foreign equity, investment in foreign real estate, and other foreign investments, in addition to foreign
borrowing and lending.
We denote the real return on domestic equity in country i between time t and t + 1 by rit+1 . We
denote the real return that households in country i earn when they invest in bonds from countryj ̸= i by rijt+1 . The gross real return on foreign currency bonds is then given by the foreign
currency real return adjusted for the change in the real exchange rate:(1 + rijt+1 ) ≡ (1 + r jt+1 )Q jit+1
.
Q jit

(3)

All agents in the model that are able to trade assets internationally – including households and23

firms – face financial frictions that limit their ability to arbitrage away expected return differentials
across currencies. In other words, no agent in the model is “deep pocketed” in the sense of being
able to fully arbitrage away uncertain expected return differentials. This implies that uncovered
interest parity (UIP) will not hold in the model and the expected return from investing domestically and abroad will not be equal (Et (1 + rit+1 ) ̸= Et (1 + rijt+1 )). The response of households andfirms to these expected return differentials yields capital flows that are crucial to the workings ofthe model.
Households Households choose each period how large a fraction of their portfolio of assets toinvest in domestic equity and foreign currency bonds. Since we solve the model only up to afirst-order approximation around its deterministic steady state, the steady-state portfolio sharesof households are indeterminate. We treat the steady state portfolio shares as primitives andcalibrate them based on their counterparts in the real-world data. When shocks hit the world
economy, the households adjust these portfolio shares with the objective of maximizing returns.
However, the households incur adjustment costs when they deviate from the steady state portfolio
shares. These adjustment costs limit the adjustment of the households’ portfolio shares and, thus,
limit the ability of households to arbitrage away expected return differentials.
Formally, the households seek to maximize:
max Eth }{sijt
j∈[0,1]


1−

Z 1
0

h
sijt
dj



(1 + rit+1 ) +

Z 1
0

h
h
sijt
(1 + rijt+1 ) − Φijh (sijt
)




dj

(4)

h is the share of their portfolio that households in country i invest in bonds in country
where sijt

j at time t per unit measure of that country’s size. Letting dj denote the measure of country j’s
h dj corresponds to the portfolio share that households in country i invests in country j. The
size, sijt
R1 hremaining share 1 − 0 sijt
dj is held in domestic equity.17 The households’ portfolio adjustmenth − s̄ )2 , where s̄ denotes steady state portfocosts per unit of asset take the form Φijh (sijt ) = 2s̄Γ ij (sijtijijhlio shares. The adjustment costs are incurred in terms of final consumption goods. An underlying
assumption here is that adjustment costs scale with household assets. With this, the portfolio
problem is separable from the rest of the household problem. We denote the maximized value ofthe return on the household’s portfolio as 1 + rith +1 .18 This is the return the household uses when
17 We solve this portfolio problem assuming perfect foresight. Since we solve the model only up to a first-order approximation, the solution to the perfect foresight problem coincides with the first order approximation of the stochastic
equilibrium (Boppart, Krusell, and Mitman, 2018).
18 These adjustment costs are incurred in terms of the deviation from the steady state portfolio, rather than fromthe previous period’s portfolio. We make this choice for tractability. This allows us to avoid keeping track of the24making its consumption-savings decision.
Solving the household’s portfolio choice problem yields the following optimality condition:hsijt− s̄ij =s̄ij 
Et (1 + rijt+1 ) − Et (1 + rit+1 ) .
h
Γ

(5)

Intuitively, this condition indicates that household “chase returns”, i.e., when the expected returnon foreign currency bonds is high relative to domestic equity they shift their portfolio towards foreign currency bonds. However, the degree to which they do this is limited by the adjustment cost.
In particular, the parameter Γh governs the (inverse) elasticity of household demand for foreign
currency bonds in response to changes in the returns on these bonds. In traditional open economy
models without financial frictions, Γh = 0. In this case, even an arbitrarily small expected return
differential between home and foreign assets generates arbitrarily large financial flows, arbitraging away any effect of financial shocks on the exchange rate. In contrast, the FDX model limits thesize of these financial flows, allowing financial shocks to generate expected return differentials.
Firms Production firms finance their operations with a mix of domestic equity and foreign currency debt. They face an analogous portfolio problem to households. For analytical simplicity,
we assume that the steady state foreign currency debt share of production firms is equal to thesteady state foreign currency asset share of households. This implies that the net foreign currency
position for each country is zero in the steady state. Lane and Shambaugh (2010) and Bénétrix,
Lane, and Shambaugh (2015) document that it is common for countries to have large gross foreign
currency asset and liability positions but small net foreign currency asset positions. For simplicity,
we set steady state net foreign currency asset positions to zero.19
Production firms choose their portfolio of liabilities to minimize the total financing costs net ofadjustment costs
min Etf{sijt } j∈[0,1]


1−

Z


Z 1n
o 
f
f
f
f
sijt dj (1 + rit+1 ) +(1 + rijt+1 )sijt + Φij (sijt ) dj
0

(6)

f

where sijt denotes the share of firm value financed via debt in currency j at time t per unit meaf

sure of that country’s size. Similarly to households, sijt dj corresponds to the share of firm value
R1 f
in country i financed via debt in currency j. The remaining share 1 − 0 sijt dj is financed with
distribution of portfolios.
19 Christiano, Dalgic, and Nurbekyan (2021) present a model where such foreign currency positions arise endogenously as an efficient risk-sharing between households and firms.

25

domestic equity. The adjustment cost they incur when they adjust their portfolio of funding away
Γfrom its steady state takes the form Φij (sijt ) = 2s̄(sijt − s̄ij )2 , where s̄ij is the steady state share
ij
f

f

f

f

of firm’s value financed via debt in currency j. We denote the firms’ minimized financing cost asf(1 + rit+1 ). This is the return firms use when they make investment decisions. Intuitively, production firms discount future earnings with a rate of return that reflects the rates of returns on the mixof financial instruments that they finance themselves with net of adjustment costs.
Solving the portfolio problem of the production firms yields the optimality conditionfsijt − s̄ij =s̄ij 
E
(
1
+
r
)
−
E
(
1
+
r
)
.
t
t
ijt
+
1
it
+
1
Γf

(7)

Intuitively, firms shift their mix of funding away from foreign bonds when the expected returnon foreign bonds from their perspective is high. As with households, the production firms arelimited in their ability to switch away from expensive funding sources by the adjustment costs. In
particular, the parameter Γ f governs the (inverse) elasticity of firm demand for foreign currency
bonds as a funding source with respect to the expected return on these bonds. See Appendix B.2.1
for a more detailed discussion of the financing decisions of production firms.

3.3International Financial Market

In addition to households and firms, there are two other types of agents who trade assets internationally: noise traders and international bond arbitrageurs. Fluctuations in asset demand by noise
traders are one source of exchange rate volatility and expected return differentials across countries. The international bond arbitrageurs trade against the noise traders, as do the households
and firms. We next describe the behavior of the noise traders and international bond arbitrageurs.
Noise Traders and UIP Shocks Noise traders sell US bonds and use the proceeds to purchasebonds from countries j ∈/ U, and vice versa. There is a unit measure of such noise traders.20 Their
position in country j bonds is ψjt , where ψjt follows an AR(1) process:ψψjt = ρψ ψjt−1 + ϵ jt , for j ∈
/ U.

(8)

ψ

We refer to the shock to this equation {ϵ jt } as the “UIP shock” following Itskhoki and Mukhin(2021a). A positive shock to ψjt implies that the demand for country j ∈ F bonds increases relative
20 We normalize the measure to one without loss of generality since it is not distinguishable from the size of eachtrader’s position.

26

to the demand for US bonds, resulting in a depreciation of the USD against currency j ∈ F.
International Bond Arbitrageurs International bond arbitrageurs engage in the currency carry
I dollars in the bonds of floater country j and a short position
trade by taking a long position of BUjt
I denotes a carry trade position in which the bond arbitrageursof equal value in US bonds. Here Bijt

borrow in currency i and invest in currency j. The unit in which this position is expressed iscurrency i. For each currency j, we assume that there is a measure one of international bondarbitrageurs specializing in the carry trade between that currency and US dollars. The nominalEI
return on the carry trade position BUjt
is R̃Ujt+1 ≡ (1 + i jt ) EjUtjUt+1 − (1 + iUt ) per dollar invested,

where i jt is the nominal interest rate in country j at time t. The international bond arbitrageurs
choose their portfolio to maximize the following CARA utility function over the real return on
their portfolio expressed in US dollars:max −Et
I
BUjt




1
1
I
exp −γ R̃Ujt+1
BUjt
γ
PUt+1

In Appendix B.2.2 we show that the solution to this problem implies that the demand of international bond arbitrageurs for bonds from currency j ∈ F is
I
BUjt
=

1
[ln(1 + i jt ) − ln(1 + iUt ) + Et ∆ ln E jUt+1 ]ΓBup to a first-order approximation, where Γ B ≡ γvar(∆ ln E jU ), and var(∆ ln EUj ) is the steady statevariance of the change in the logarithm of the nominal exchange rate.
Deviations from Uncovered Interest Parity Adding up the demand for bonds from currencyj ∈ F from international bond arbitrageurs, noise traders, households, and firms and setting thisequal to the supply of such bonds (which is zero) yields the following equilibrium condition to afirst order approximation around a symmetric steady state:(1 + iU,t ) = Et (1 + i j,t )E jU,t+1
exp(Ω({ NFAkt }k , ψjt )).
E jU,t(9)

In this equation, the deviation from uncovered interest parity (UIP) is given byΩ({ NFAkt }k , ψjt ) ≡ Γ



1−

R

R


s̄ ji di NFA jt + s̄ij NFAit di + ψjt ,

27

(10)

where NFA jt is the net foreign asset position of country j. The size of this term is determined by
the size of noise trader demand ψjt and the parameters governing the strength of financial frictions
for households, firms, and international bond arbitrageurs through the composite parameter Γ ≡
h

i R

1/ Γ1B + Γ1h + Γ1f βā i∈{ P,U } (s̄ ji + s̄ij )di , where ā is steady state asset holdings (i.e., the capitalstock). We derive this condition in Appendix B.2.3.
Equation (9) shows that the financial frictions in our model imply that uncovered interest
parity (UIP) does not hold for floater countries. The expression for Ω({ NFAkt }k , ψjt ) lists the“sources” of UIP deviations. The last term represents demand from noise traders. The first two
terms reflect the fact that the portfolio shares of households and firms are anchored at certain
steady state values (i.e., it is costly for these agents to adjust their portfolio shares). This implies
that when households and firms in a particular country build up foreign assets, this increases thedemand for assets in the countries that their steady state portfolio of assets is biased towards. This
will bid up the price of assets in these countries, and thereby reduce the expected returns on theseassets.
In the wake of a noise trader shock, that drives down the expected return on domestic bonds
relative to foreign bonds, international bond arbitrageurs, households, and firms sell domestic
bonds and buy foreign bonds to take advantage of the expected return differential. If the combined
response of these agents was strong enough, they would eliminate the return differential and UIP
would hold. In our model, however, this profit-driven demand response is limited by financial
frictions and the UIP deviation is not eliminated. The parameter, 1/Γ, measures the aggregate
strength of profit-driven trading in the international bond market. If Γ is small, international
financial frictions are small and UIP deviations are small.21
In contrast to floaters, uncovered interest parity holds for peggers versus the US:(1 + iUt ) = Et (1 + i jt )E jUt+1
E jUt

for j ∈ P

(11)

The reason is that there is no exchange rate risk between peggers and the US. Thus, even riskaverse arbitrageurs are willing to perfectly arbitrage any return differentials between bonds ofpeggers and the US.

21 Regarding UIP deviations, Itskhoki and Muhkin’s (2021a) model is a special case of our model with s̄j.

28

ij = 0 for all3.4

Monetary Regimes

The central banks in region F adjust nominal interest rates according to the following monetary
policy rule:ln(1 + i jt ) = ln R̄ + ρm ln(1 + i jt−1 ) + (1 − ρm )ϕπ π jt + ϵm
jt

for j ∈ F,

(12)

where R̄ ≡ 1/β is the steady state gross interest rate, ρm ∈ [0, 1) governs the degree of inertia inmonetary policy, ϕπ is the Taylor coefficient, and ϵm
jt is a monetary policy shock. The central bankin the US follows analogous monetary policy rule:mln(1 + iUt ) = ln R̄ + ρm ln(1 + iUt−1 ) + (1 − ρm )ϕπ πUt + ϵUt,

where πUt ≡ |U1 |

R

j ∈U

(13)

π jt dj is the average inflation rate in the US.

Central banks in region P fix the nominal exchange rate of their currency to the US dollar:

E jUt = Ē jU

for j ∈ P.

(14)

Together with equation (11), this implies that interest rates in region P track the nominal interest
rate in the US, i jt = iUt for j ∈ P.
We define the equilibrium of our model in Appendix B.1.3 and discuss our solution method in
Appendix B.1.4.

4

Calibration

We assign standard values to most parameters of our model. We relegate a detailed discussion ofthese choices to Appendix B.4 and focus here on a few key parameters. We calibrate our modelso that each period is a year, as in our empirical analysis. Our benchmark parametrization is
to assume prices are sticky in local currency. We set the trade elasticity to η = 1.5, a relatively
standard value in the international macroeconomics literature. We choose the openness parameterto match the average imports-to-GDP ratio in our sample of 40%. We set the size of the three
countries in our model to approximate the GDP share of the US, countries that peg to the US, andcountries that float versus the US in the data, averaged over our sample period. This results in|U | = 0.3, | F | = 0.5, | P| = 0.2.
In Section 5, we assume that the primary driver of the US dollar exchange rate is a US
29

UIP shock as argued by Itskhoki and Mukhin (2021a) and Eichenbaum, Johannsen, and Rebelo(2020).22 We show in Section 5.2 that monetary and productivity shocks yield counterfactual implications about the effects of regime-driven depreciations. In Section 6, we show that a different
financial shock – which we call a “capital flight shock” – can also match the effects of regimedriven depreciations, and that a two-shock model fits important unconditional moments of thedata better. For simplicity, we assume that all shocks in the model have the same persistence andset this persistence parameter to ρ = 0.89. This is the same shock persistence as is assumed in
Itskhoki and Mukhin (2021a) (0.97 at a quarterly frequency).
We set the steady state net foreign asset position of each country to zero. We assume that thesteady state gross foreign currency portfolio share is the same in all countries and denote this bys̄. The remaining portfolio share, 1 − s̄, is held in domestic equity in steady state. This assumption
implies that the steady state bilateral portfolio shares per unit measure of country j’s size ares̄ij =

s̄
|U |+| P| 0

for i ∈ F, j ∈ {U, P}

s̄ij =

for i, j ∈ F, j ̸= i.




s̄
| F|

 0

for i ∈ { P, U }, j ∈ F

.

(15)

for i, j ∈ { P, U }, j ̸= i.

The portfolio share that country i invests or borrows in currency j is given by s̄ij dj. This ensures
R1
that the steady state total foreign currency share is equal to 0 s̄ij dj = s̄ in all countries. We set s̄ =0.24 to match the average value of gross foreign currency assets in our sample. We first computetotal assets held by a country as the sum of domestic stock market capitalization and foreign
assets, where we obtain the stock market capitalization from the World Bank World Federationof Exchanges database and foreign assets from Bénétrix, Lane, and Shambaugh (2015). Then wecompute the fraction of assets held in foreign currency that a country floats against, s̄, by dividing
the foreign currency assets by the total assets. Specifically, for a country pegging to USD, we
compute the fraction of non-USD currency assets. For a country floating against USD, we computethe fraction of USD currency assets.23
UIP deviations resulting from movements in net foreign asset positions are governed by Γ inour model. We set Γ to a small value (Γ = 0.001) following Itskhoki and Mukhin (2021a). Thisimplies that UIP deviations resulting from movements in net foreign asset positions are small in
our model. Even with a small Γ, UIP shocks can have large effects if their variance is sufficiently
large.
22 Formally, we consider a shock to ϵψ for all j ∈ F, which increases noise trader demand for floater country bonds
jt

relative to US bonds (ψjt = ψFt > 0 for all j ∈ F). We refer to this as a US UIP shock.
23 Using household-level micro data, Drenik, Pereira, and Perez (2018) document that 70% of household assets in
Uruguay are denominated in foreign currencies.

30

We choose the slopes of the price and wage Phillips curves, κ p and κw (or equivalently, therigidity of prices and the wages), and the habit parameter, h, to best fit our empirical impulse
responses. This yields small values for κ p and κw (i.e., quite flat price and wage Phillips curves),
indicating that a substantial amount of price and wage rigidity is needed to match our evidence.
It yields a relatively large value for h, indicating that a substantial amount of habit formation isneed to match the hump-shaped nature of our impulse responses for consumption and output.
See Appendix B.4 for the formal description of the procedure.

5

Regime-Driven Depreciations: Model vs. Data

In Section 2 we demonstrate that regime-driven exchange rate depreciations lead to macroeconomic booms. We also highlight a number of features of these booms that make them difficult tomatch using standard models: net exports fall implying that the booms are not export led, andnominal interest rates do not seem to fall (if anything they rise) implying that the booms do notarise from easy monetary policy. Here we show that our FDX model can match these impulse
responses.

5.1

Impulse Responses

Figures 9 and 10 plot the impulse responses of key variables to a regime-induced depreciation in
the data and in the model. For the model, we plot responses of peggers relative to floaters after
a US UIP shock that leads the US dollar to depreciate.24 We see that the model matches the mainfeatures of the responses in the data. The model generates a large boom in output, consumption,and investment in response to the regime-induced depreciation. The response is hump-shaped
and very persistent, as in the data.
The boom does not arise from loose monetary policy in the pegging countries. Interest rates in
the pegger countries actually rise somewhat relative to interest rates in the floater countries in themodel as in the data. This reflects the fact that the boom is inflationary in the pegger countries,
which leads monetary policy to tighten. Net exports fall in the model as in the data. This contrasts
with traditional open economy models in which a regime-induced depreciation leads net exports
to rise due to expenditure switching in goods markets. In our model, the expenditure switching

24 This corresponds to the coefficient on the peg interacted with the US exchange rate that we emphasize in Sectionψ

2 (up to sampling error). When computing impulse response functions, we set the size of the initial US UIP shock, ϵU0 ,to match the initial response of the relative nominal exchange rates of peggers and floaters.

31

Real Exchange Rate

Data
Model

GDP
% of s.s. GDP% deviation from s.s.

Years

Years

Net Exports

Nominal Interest Rate

% of s.s. GDP% of s.s. GDP

Years

Consumption

p.p. deviation from s.s.

% deviation from s.s.

Nominal Exchange Rate

Years

Years

Years

Figure 9: Model Fit: Main Variables
Note: This figure plots the response of peggers relative to floaters to a US UIP shock in the model and in thedata. The dashed lines represent the 95% confidence interval in the data.

channel is operational, but it is dominated by a foreign credit channel pushing in the opposite
direction.
International capital flows are the key channel through which a regime-induced exchange rate
depreciation stimulates the economies of peggers in our model. A depreciation of the peggers’ currency driven by a US UIP shock makes it cheap for households and firms in the pegging countries
to borrow in foreign currency. It also increases the expected returns of foreigners from investingin the pegging countries. Households and firms in both the pegging countries and elsewhere thus
have an incentive to bring money into the pegging countries. This stimulates consumption andinvestment (and thus imports).
To see why a US UIP shock makes foreign borrowing cheap in pegger countries, it is useful toconsider the response of the rate firms in pegging countries can finance themselves with to such ashock. To a first order, this can be written asfd ln(1 + rit+1 ) = d ln(1 + rit+1 ) − s̄dΩ({ NFAkt }k , ψFt ),(16)which we obtain as a first-order approximation of equation (6) after substituting in equations (3),(9), and (15). The same equation can be derived for d ln(1 + rith ). The change in the cost of borrowing in domestic currency is d ln(1 + rit+1 ). For peggers, this turns out to be positive in equilibrium32

Imports% of s.s. GDP

Exports% of s.s. GDP% of s.s. GDP

Investment

Years

Real Interest Rate

% deviation from s.s.

Yearsp.p. deviation from s.s.

Years

Inflation
p.p. deviation from s.s.

Years

Terms of Trade

Years

Years

Figure 10: Model Fit: Additional Variables
Note: This figure plots the response of peggers relative to floaters to a US UIP shock in the model and in thedata. The dashed lines represent the 95% confidence interval in the data.

because inflation increases and monetary policy responds to the higher inflation. The change in thecost of borrowing in foreign currency, however, differs from d ln(1 + rit+1 ) by dΩ({ NFAkt }k , ψFt )(the change in the UIP deviation): d ln(1 + rijt ) = d ln(1 + rit ) − dΩ({ NFAkt }k , ψFt ). After a depreciation caused by a US UIP shock (higher ψFt and hence higher dΩ), this UIP deviation is negative
for peggers, which means that for them the cost of borrowing abroad falls. Figure C.3 plots theimpulse response of the ex-post UIP deviation for peggers in the model and compares it to thedata. In the data there is a substantial ex-post UIP deviation after regime-induced changes in theexchange rate. Our model generates a similar but smaller UIP deviation.
Intuitively, the domestic currency of peggers is cheap due to a shift in noise trader demandaway from US dollar assets. In real terms, the domestic currency is expected to appreciate morethan UIP implies. Conversely, the currency of floaters is expected to depreciate in real terms
more than UIP implies. This means that borrowing abroad is cheap for households and firms
in the pegger countries. As long as households and firms finance themselves partly in foreign
currency (i.e., s̄ > 0), they will respond to this shift by borrowing from abroad (relative to theirprior positions). Likewise, foreign agents will perceive a high expected return from investing in
the pegging countries and will shift their portfolios accordingly. This capital inflow will financeincreased consumption and investment in pegger countries and result in these economies running33

Household and Firm Financial Discounts% deviation from s.s.

p.p. deviation from s.s.

Real Exchange RateGDP

Net Exports% of s.s. GDP

Years% of s.s. GDP

Years

Years

Years

Figure 11: Comparison with a Model without Foreign Credit Channel
Note: The figure plots the response of peggers relative to floaters to a US UIP shock for the baseline modeland version of the model with s̄ = 0. For the model with s̄ = 0, we plot results for two cases: 1) a case with{κ p , κw , h} unchanged, 2) a case where {κ p , κw , h} is re-estimated. Household and firm financial discountsfrefer to rith and rit .

a trade deficit (i.e., net exports will fall).25
Figure 11 demonstrates the importance of the foreign currency portfolio share s̄ in our model,
by comparing the impulse responses in our baseline case of s̄ > 0 with a case of s̄ = 0 (no foreign currency investing by households and firms). The boom in output is an order of magnitude
smaller with s̄ = 0 than it is in our baseline case (bottom-left panel). The reason for this is thathouseholds and firms do not experience a decline in borrowing costs associated with the regimeinduced depreciation when s̄ = 0 (top-right panel).26 The small boom that remains in the s̄ = 0
case is driven by an increase in net exports that occurs for standard expenditure switching reasons(bottom-right panel).27
25 In thinking about equation (16), it is important to keep in mind that we assume that firms (and households) faceadjustment costs to their portfolio shares (not their positions). Since their portfolio shares are set optimally in the steadystate, the change in their cost of funds that results from the change in their portfolio share after the shock is a second
order term.
26 Borrowing costs actually increase slightly due to tighter domestic monetary policy when s̄ = 0.
27 We keep Γ unchanged when we set s̄ = 0. This can be thought of as a slight recalibration of the other components
of Γ.

34

The foreign credit channel (s̄ > 0) is what distinguishes our analysis from the analysis in
Itskhoki and Mukhin (2021a). In Itskhoki and Mukhin (2021a), households and firms do not haveaccess to foreign currency borrowing (or investing). Their model is thus similar to our model
when we set s̄ = 0. In this case, the exchange rate is largely disconnected from real outcomesin response to UIP shocks. This is much less true when s̄ > 0. Empirically, large gross foreign
currency positions are a prominent feature of the data, suggesting that the s̄ > 0 case is more
realistic.

5.2

Robustness and Extensions

Shocks Driving US Dollar We have so far assumed in this section that US UIP shocks drive
movements in the US exchange rate. Table 2 considers other potential drivers of US dollar exchange rate fluctuations. In particular, Table 2 considers US productivity shocks and US monetary
policy shocks in addition to our baseline results with US UIP shocks. In the data, the response ofinterest rates to a regime-induced depreciation is small. Our model matches this when US dollar
exchange rate movements are driven by US UIP shocks.28 This is also consistent with the fact that
US dollar depreciations are only mildly correlated with US interest rates.29
In sharp contrast, when US dollar exchange rate movements are driven by either US monetaryor productivity shocks the nominal interest rate in pegging countries falls substantially relative tothe nominal interest rate in floating countries when the US dollar depreciates. In the monetaryshock case, this arises because interest rates in the pegging countries must track US interest rates
to maintain the peg. They thus fall relative to interest rates in floating countries. In the productivity shock case, the direct effect of the shock on peggers and floaters is identical and is therefore
differenced out when we consider relative responses. The asymmetric effect arises from the US
monetary policy response to the productivity shock. Interest rates in the pegging countries will
track the US interest rate response to the productivity shock, while interest rates in the floating
country will not. This same logic applies to many other potential sources of variation in the US
dollar exchange rate.
An important point to emphasize is that, conditional on matching the joint behavior of nominalinterest rate and nominal exchange rate, the choice of which shock drives the US dollar exchange
28 Jiang, Richmond, and Zhang (2022) argue movements in asset demand, which UIP shocks are meant to capture,explain a large fraction of USD exchange rates behavior over the period of 2011-2019.
29 The correlation between changes in the nominal interest rate and the changes in log USD effective exchange rate is
0.12. On average the US dollar appreciates when interest rates fall: the opposite direction from what you might expect
if uncovered interest rate parity were driving exchange rates.

35

Data

Table 2: Alternative Shocks Driving USD
Impact Response
5Y Average Response
e
i
e
i
0.74
0.07
0.70
0.03

Model
US UIP ShockUS Monetary Policy ShockUS Technology Shock

0.74
0.74
0.74

0.01
-0.41
-0.72

0.59
0.26
-0.97

0.01
-0.14
-0.87

Note: This table shows the impulse response of the log of the nominal effective exchange rate (e) and thenominal interest rate (i) of peggers relative to floaters. Impact response indicates the response at h = 0, while
the 5Y average response is the average of the response at horizons h = 0 through h = 4. The top row of thetable shows our empirical estimates for these responses. The remaining rows show the simulated impulse
response in our model in response to the shock listed to the left in that row. We choose the size of each shocksuch that the impact response of the nominal effective exchange rate matches the impact response in the data.

rate is not important. The reason for this is that the peggers and floaters are identical except for
their monetary regime. This means that the differential effect of regime-induced exchange ratechanges must come through a combination of the exchange rate and the nominal interest rate (i.e.,
monetary policy). As a consequence, any combination of shocks will induce the same impulse
responses for peggers versus floaters as long as they match the path of the relative response of
the nominal exchange rate and the nominal interest rate that we have estimated. This implies
that our conclusions should carry over to richer models where UIP deviations are endogenous toeconomic fundamentals, for example, due to currency risk premia (Hassan and Zhang, 2021, andthe references therein), term premia (Gourinchas, Ray, and Vayanos, 2022), or liquidity premium(Bianchi, Bigio, and Engel, 2021; Devereux, Engel, and Wu, 2022).
Alternative Models without a Foreign Credit Channel Table 3 presents results for a wide rangeof calibrations without a foreign credit channel (i.e., with s̄ = 0). Here we focus on the response of
output and net exports. We see from this table that none of these models is able to fit our impulse
responses (even qualitatively). We consider a model with producer currency pricing, a modelwith dominant currency pricing, a model with a low trade elasticity, and a model with hand-tomouth households. None of these models absent a foreign credit channel can jointly explain alarge positive GDP response and a fall in net exports in response to regime-induced depreciation.
Without an off-setting foreign credit channel, expenditure switching in the goods market yields
positive comovement between output and net exports in all of these models.

36

Table 3: Models without Foreign Credit Channel
Fixed Parameters
Re-estimated
5Y Average Response of:
GDP
NX
GDP
NX
Data
0.22
-0.16
0.22
-0.16
Baseline Model
0.26
-0.13
0.26
-0.13
Models with s̄ = 0(a) Benchmark(b) PCP(c) DCP(d) Low η(e) Hand-to-Mouth

0.06
0.33
0.19
0.05
0.07

0.02
0.68
0.31
0.00
0.01

0.04
0.35
0.21
0.05
0.07

0.02
0.58
0.28
0.00
0.01

Note: The table shows the response of the log GDP and the ratio of net exports to GDP averaged over horizons
h = 0 through h = 4. The response is for peggers relative to floaters to a US UIP shock. Columns “FixedParameters” use the parameter estimates in the Panel B of table B.1. Columns “Re-estimated” re-estimate Θ.
Row “Benchmark” uses our baseline parameter values from table B.1. Appendix B.6 describes the “PCP” and“DCP” calibration. “Low η” sets η = 1.0 instead of η = 1.5. Appendix B.8 describes the model with hand-tomouth agents.

Price and Wage Rigidity In addition to a foreign credit channel, our model needs strong Keynesian features to fit the data. We estimate fairly flat slopes of both the price and the wage Phillips
curves, reflecting a combination of nominal rigidity and unmodeled strategic complementarity
in price setting. We show in Appendix B.5 that without a large degree of nominal rigidity, ourmodel is not able to generate the magnitude of the booms we observe in the data, because of alarge endogenous real interest rate response.30 Habit formation in consumption plays the conventional role of explaining the delays we observe in the consumption response to regime-driven
depreciations.31
Alternative Pricing Regimes In our baseline calibration, we assume that firms price in local
currency (LCP). In Appendix B.6, we present results under producer currency pricing (PCP) anddominant currency pricing (DCP). In these alternative cases, the fit of the model to the data fornet exports and the terms of trade deteriorates substantially. In both of these alternative cases, net
exports increase. This is because the expenditure switching force is stronger under these pricing
regimes. Moreover, the model with DCP predicts almost no response in the terms of trade, while

30 Itskhoki and Mukhin (2021a) argue that price rigidity is not important to fit a certain set of unconditional momentsof exchange rate and real variables. We are trying to fit a wider range of facts – particularly the effects we estimate ofregime-driven depreciations.
31 There are various other potential microfoundations for such delayed responses, including household’s inattention
to movements in financial markets or doubts about attention and responsiveness of others, as formalized by Angeletosand Huo (2021).

37

the model with PCP predicts a substantial deterioration in the terms of trade.32 In the data, theterms of trade actually improve somewhat.
Non-Tradables and Tradables Recall that Figure 6 shows that most of the increase in GDP comesfrom the service sector, which is largely non-tradable, as opposed to the manufacturing or agricultural sectors, which are tradable. In Appendix B.7, we extend our baseline model to a two sector
model featuring tradable and non-tradable sectors. We find that, consistent with our results, theincrease in GDP is almost entirely driven by the non-tradable sector. The response of GDP in the
tradable sector is small. The intuition for this is simply that a domestic boom drives an increase in
consumption and investment, but much of the needed increase in production of tradeables comesfrom abroad.
Heterogenous agents In our baseline model, all households have access to financial markets.
Since the boom resulting from a regime-induced depreciation in our model is driven by foreign
credit, one might conjecture that the boom would be weaker if some households did not haveaccess to financial markets. In Appendix B.8, we extend our baseline model to allow for the presence of hand-to-mouth households who do not have access to financial markets. We find thatthe response of consumption and GDP are virtually unchanged in the presence of hand-to-mouthhouseholds. The reason for this is closely related to the argument in Werning (2015). While handto-mouth households do not directly respond to the movements in financial market variables, they
instead react more to the indirect effect of an increase in labor income. The net effect is ambiguous.33

6

Exchange Rate Disconnect, Backus-Smith and the Mussa Facts

Our evidence on the large real effects of regime-induced depreciations might, at first blush, seemto contradict well known unconditional facts about the exchange rate, including exchange rate
disconnect, the Backus-Smith correlation, and the Mussa facts. If depreciations cause booms andexchange rate are so volatile, why isn’t there a strong unconditional correlation between exchange
rate depreciations and booms? In this section, we show that this apparent contradiction is a mirage
arising from the distinction between conditional and unconditional moments. If exchange rates
32 As shown by Auclert et al. (2021b), the model with DCP is isomorphic to, and therefore can alternatively beinterpreted as, the commodity exporter model of Schmitt-Grohé and Uribe (2016).
33 Since our benchmark parametrization assumes local currency pricing, the real income channel emphasized in
Auclert et al. (2021b) is muted.

38

respond to several different shocks that each results in a different conditional correlation between
the exchange rate and output, the unconditional correlation between the exchange rate and output
can be small.
To demonstrate this, we introduce a second shock, which we refer to as a “capital flight” shock(Bianchi and Lorenzoni, 2021). This shock might alternatively be termed a “flight to safety” shock.
It is similar to the “safety” shock in Kekre and Lenel (2021) and also similar to the “sudden stop”
shocks of Calvo (1998). The capital flight shock has two characteristics that are crucial to matching
the unconditional moments: it generates large exchange rate volatility and it generates the opposite correlation between output and the exchange rate from our UIP shock. Intuitively, a negative
UIP shock is a time when noise traders get “spooked” and reduce demand for a currency. In thiscase households and firms trade against the noise traders and capital flows into the country. In
contrast, a negative capital flight shock is a time when all investors in a region get spooked andreduce demand for a currency. In this case, capital flows out of the country.

6.1

An FDX Model with Capital Flight Shocks

We model the capital flight shocks as arising from financial intermediation: households and firms
have access to foreign currency bonds only through banks. This introduces a stochastic wedge
between the return agents in country i earn when they invest in country j bonds and the return
agents in country j earn from investing in these bonds. We denote this intermediation wedge asζ it . The intermediation wedge implies that equation (3) in our earlier model becomes(1 + rijt+1 ) ≡ (1 + r jt+1 )Q jit+1
exp(ζ it )
Q jit

(17)

When ζ it = 0, households and firms face the foreign real interest rate adjusted for the real exchange rate as in our earlier model. Here, we assume that the intermediation wedge follows an
AR(1) process:ζζ it = ρζ ζ it−1 + ϵit .

(18)

ζ

We refer to {ϵit } as capital flight shocks. We provide a microfoundation for the intermediation
wedge in Appendix B.9 based on Bianchi and Lorenzoni (2021). The micro-foundation introduces
financial constraints to banks. Stochastic shocks to the tightness of these financial constraints yield
the shock ζ it .
39

Capital flight shocks lead to UIP deviations as we show in Appendix B.2.3. With capital flightshocks, UIP deviations are given by
h
R
R


Ω { NFAkt }k , ψjt , {ζ kt }k ≡ Γ 1 − s̄ ji di NFA jt + s̄ij NFAit diRRi+ ψjt + mζ − s̄ ji diζ jt + s̄ij ζ it di ,where mζ ≡

h

1
+ Γ1f
Γh

i

ā
β.

(19)

It is the last term on the right hand side that arises because of thecapital flight shocks: when it becomes more costly to borrow in foreign currency due to the capitalflight shock (a high ζ jt ), agents borrow more in domestic currency, which decreases demand fordomestic currency and depreciates the domestic exchange rate. Equation (19) replaces equation(10), and equation (17) replaces equation (3). The rest of the model is unchanged.
The capital flight shock affects the economy differently from the UIP shock. This can be illustrated by considering a first order approximation of the rate at which firms finance themselves in a
floating country i ∈ F. (A similar condition holds for the rate of return households in this country
have access to when saving.) We can use equation (17) to derivefd ln(1 + rit+1 ) = d ln(1 + rit+1 ) + s̄ζ it + s̄dΩ({ NFAkt }k , ψit , {ζ kt }k ),(20)

which is the counterpart of equation (16) in our earlier model.34
Notice that the capital flight shock affects firm borrowing costs through two channels – i.e.,shows up in two places on the right hand side of equation (20) – while the UIP shock only affects
firm borrowing costs through one of these two channels. First, the capital flight shock affects firmborrowing costs directly (second term on the right hand side of equation (20)). This captures thefact that a bad capital flight shock (positive ζ it ) increases firm borrowing costs (when s̄ > 0) byincreasing the intermediation wedge firms must pay on foreign borrowing. The second channel
operates in the same way as a UIP shock: it depreciates the exchange rate in a way that results in
a UIP deviation going forward. This lowers the cost of firm borrowing.
Intuitively, UIP shocks only affect the relative demand for home versus foreign bonds, not the
total demand for bonds: noise traders buy foreign bonds in exchange for the same amount ofhome bonds. Such a shift in the relative demand for home versus foreign bonds by noise tradersresults in a change in the relative price of home and foreign bonds (i.e., a change in the exchangerate). In contrast, capital flight shocks increase the demand for foreign bonds without decreasing
34 Equation (16) is for a pegging country, while this equation is for a floating country.

40the demand for home bonds, since households and firms have access to a higher rate of return on
foreign bonds. Therefore capital flight shocks not only increase the relative demand for foreign
bonds (and hence depreciate the home exchange rate), but also increase overall saving and thus
reduce aggregate demand. In this sense, one can think of the capital flight shock as a combinationof a UIP shock and an aggregate demand (discount factor) shock in the home country.
We choose the parameter mζ – which governs the degree to which the capital flight shock
induces fluctuations in the exchange rate – to match the unconditional correlation between output
and the real exchange rate. We set the persistence of capital flight shocks equal to the persistenceof other shocks, ρζ = 0.89.
Impulse Responses Figure 12 contrasts the response of the economy to a UIP shock and a capitalflight shock. Panel (a) plots responses to a UIP shock, while panel (b) plots responses to a capitalflight shock. In both panels, the shock hits the floater region. The solid and dashed lines in the
figure plot responses for two cases: a case where the currency of the floater region floats versus
the US dollar (solid lines), and a case where the currency of the floater region pegs versus the US
dollar (dashed lines). In the second case, all countries are pegged to the US dollar. We calibratethese two shocks such that the initial response of the nominal exchange rate is a depreciation of
the same size in the case where the floater currencies float (solid lines / left panels).
Consider first the solid lines. The responses of the nominal interest rate (middle panels) andoutput (right panels) are sharply different for the two shocks. In the case of the UIP shock, output
and the nominal interest rate increase. The UIP shock to the floater currency is isomorphic to theregime-induced depreciation we consider earlier in the paper. This causes a boom, which leads
to an endogenous increase in the nominal interest rate. In sharp contrast, the capital flight shock
results in output and the nominal interest rate falling. In this case, the depreciation arises froman increase in the intermediation wedge that the floating countries face (i.e., capital flight). This
leads households and firms to consume and invest less, which causes output to fall. Interest rates
fall endogenously as a consequence.
Next consider the dashed lines. If the floater region pegs, the UIP shock has no effect on either
the exchange rate or the real economy. International arbitrageurs (and the central banks) fully
arbitrage away the shock. This is not the case for the capital flight shock. In fact, the capital flightshock generates a larger recession when the countries that are hit by it are pegged than when theyfloat. This occurs for two reasons. First, floaters that are hit by a capital flight shock can respond to
the shock by easing monetary policy (this is what the monetary policy rule we specify implies they41

YearsGDP% deviation from s.s.

Floaters float
Floaters peg

Nominal interest ratep.p. deviation from s.s.

% deviation from s.s.

Nominal Exchange Rate

Years

Years

(a) Impulse Response to a UIP Shock

Years

GDP
% deviation from s.s.

Floaters float
Floaters peg

Nominal interest ratep.p. deviation from s.s.

% deviation from s.s.

Nominal Exchange Rate

Years

Years

(b) Impulse Response to a Capital Flight Shock

Figure 12: Impulse Responses to a UIP and a Capital Flight Shock
Note: Panels (a) and (b) plot the impulse response to a UIP shock and a capital flight shock, respectively. The
darker solid line shows the response of the floater countries when the shock hits these countries. The lighted
dashed line shows a case where these countries peg their exchange rate to the US dollar and they are hit by UIP
and capital flight shocks. In this case, all countries are pegged to the US dollar. The shock size is normalized
so that the nominal exchange rate depreciates by 1% upon impact in the floating case.

will do). When they peg, they cannot respond in this way.35 Second, if they peg, their exchange
rate does not depreciate in response to an adverse capital flight shock. This means that they do
not experience a UIP deviation. Their borrowing costs therefore increase even more than if they
were floating. This also contributes to a more severe recession. These differences demonstrate therole of the exchange rate as an endogenous stabilizer (Friedman, 1953).
Regime-Induced Depreciations with Capital Flight Shocks

In our analysis of regime-induced

depreciations in Section 5, we assume for simplicity that the US dollar exchange rate is driven by
US UIP shocks. In Appendix B.10, we show that the facts we document about regime-induced
depreciations in Section 2 can just as well be matched assuming that the US dollar exchange rate
35 The nominal interest rate falls even when the countries hit by the shock peg because the US reacts to the capitalflight shock due to negative spillovers from the shock on US economy. Recall that in this experiment we are shocking
the entire floater region. So, the shock is not “small.”42

is driven by US capital flight shocks (which in this case may more naturally be thought of as flightto safety shocks). The response of the economy to UIP shocks and capital flight shocks differs as
we emphasize above. But this difference is “differenced out” when we consider regime-induced
depreciations since in that case we are comparing the response of pegs and floats to a US shock.

6.2

Exchange Rate Disconnect and the Backus-Smith Correlation

A large empirical literature demonstrates that – at least unconditionally – exchange rates arelargely disconnected from other macroeconomic aggregates (Meese and Rogoff, 1983; Baxter andStockman, 1989; Flood and Rose, 1995; Obstfeld and Rogoff, 2000; Devereux and Engel, 2002; Itskhoki and Mukhin, 2021a). Related to this, exchange rates are mildly negatively correlated with
consumption in the data, as opposed to strongly positively correlated as in traditional open economy macroeconomic models (Backus and Smith, 1993). Table 4 demonstrates these facts in our
sample. Nominal and real exchange rates of floating countries are three to four times more volatile
than GDP and consumption (i.e., they are largely “disconnected”).36 Moreover, real exchange rates
are mildly negatively correlated with both GDP and consumption.
Model vs. Data

Table 5 assesses the ability of our FDX model to match these facts. The data

column reproduces the results for floaters from Table 4. Column (1) presents results for the floater
countries in our FDX model when economic fluctuations are caused by a combination of UIP
and capital flight shocks. Column (2) presents results when economic fluctuations are caused
by UIP and productivity shocks. Columns (3)-(6) present results when economic fluctuations arecaused by a single shock: UIP shocks, capital flight shocks, productivity shocks, and monetaryshocks, respectively. In columns (1) and (2), we choose the volatility of the two shocks to target
the volatility of the nominal exchange rate and GDP in the data. In columns (3)-(6), we choose thevolatility of the shock to match the volatility of GDP in the data. Column (7) presents the same
set of results when economic fluctuations are cause by UIP and productivity shocks but s̄ is set tozero. Recall that our model with s̄ = 0 is similar to the model in Itskhoki and Mukhin (2021a).
Only the model with both UIP and capital flight shocks fits the small negative correlation

36 We include a larger set of countries than earlier work, which has largely focused on OECD countries. The sample

used in Table 4 includes both the countries that we estimate our impulse responses for in Section 2 and the UnitedStates and the 24 relatively advanced countries that we exclude from the analysis in Section 2. In this analysis, we
divide countries into pegs and floats in a somewhat different way than in Section 2 since the focus is not on pegging
versus the US but rather pegging in general. We define country-year observations in Ilzetzki, Reinhart, and Rogoff’scoarse categories 1 and 2 (fine categories 1 through 8) as pegs and those in coarse categories 3 and 4 (fine categories 9through 13) as floats. As before, we exclude fine categories 14 (freely falling) and 15 (dual market / missing data).

43

Table 4: Exchange Rate and Macroeconomic Volatility in the Data
Peg vs. Float (Post-1973)
Pre- and Post-1973
Peg
Float
Pre-1973 Post-1973
A. Volatility
std(∆NER)
0.082
0.114
0.070
0.090
std(∆RER)
0.069
0.091
0.058
0.075
std(∆GDP)
0.044
0.037
0.046
0.042
std(∆C)
0.048
0.042
0.044
0.047
std(∆NX)
0.039
0.032
0.034
0.038
std(∆(1 + i ))
0.030
0.031
0.012
0.030
B. Correlationcorr(∆RER, ∆NER)
corr(∆RER, ∆GDP)
corr(∆RER, ∆C)corr(∆RER, ∆NX)
corr(∆RER, ∆(1 + i ))0.553
-0.045-0.069
0.040
0.171

0.712
-0.068-0.137
0.213
0.130

0.592
-0.042-0.0170.146-0.1340.601-0.051-0.0880.093
0.150

Note: The table reports the standard deviation and correlations of real and nominal effective exchange rates,
GDP, consumption, net exports to GDP ratio, and nominal interest rate for each subsample. All variables arein logs except for net exports, which are relative to GDP. The sample contains all countries in our dataset(including the US and the 24 relatively advanced economies we use to define the US exchange rate earlier inthe paper). See footnote 36 for more detail on the sample and the definition of pegs and floats. The third andforth columns split the sample by year as opposed to by exchange rate regime. For each variable (e.g., ∆NER),
we drop outlying observations (the top and bottom 0.5%) when computing these moments.

between the real exchange rate and both GDP and consumption.37 The model with a combinationof UIP and productivity shocks fails to do so, and the model with any single shock also fails
to do so. The intuition for this is simple. As we demonstrate in Figure 12, the UIP and capitalflight shocks generate opposite correlations between the exchange rate and GDP. A model with
only UIP shocks generates a strong positive correlation between the real exchange rate and GDP,
while a model with only capital flight shocks generates a strong negative correlation (columns (3)and (4)). The combination of these two shock can thus generate a small negative unconditionalcorrelation. Productivity and monetary shocks also yield strong positive correlations (columns (5)and (6)).38
Productivity shocks alone generate very little volatility in the real exchange rate when theirvolatility is chosen to match the volatility of real GDP. Combining capital flight shocks and either

37 Table C.1 presents a variance decomposition for the model with UIP and capital flight shock.
38 This analysis shares a similar perspective to recent work by Mullen and Woo (2022).

Like us, Mullen and Woo(2022) introduce multiple shocks as drivers of exchange rate and show that a combination of trade cost shocks, UIP
shocks, and a model with a dynamic trade elasticity can successfully replicate the unconditional moments of the US
data. Our work differs in that we place emphasis on the financial channel and on matching conditional moments.

44

Table 5: Exchange Rate Disconnect
Data
Model
(1)
(2)
(3)
(4)
(ψ, ζ )
(ψ, A)
ψζBaseline

(5)
A

(6)
m

(7)
(ψ, A)s̄ = 0A. Volatility
std(∆NER)
std(∆RER)
std(∆GDP)
std(∆C)std(∆NX)
std(∆(1 + i ))

0.114
0.091
0.037
0.042
0.032
0.031

0.114
0.113
0.037
0.045
0.016
0.001

0.114
0.113
0.037
0.030
0.022
0.002

0.141
0.140
0.037
0.036
0.022
0.001

0.093
0.093
0.037
0.049
0.009
0.001

0.006
0.005
0.037
0.017
0.021
0.004

0.075
0.075
0.037
0.035
0.010
0.085

0.114
0.114
0.037
0.018
0.022
0.004

B. Correlationcorr(∆RER, ∆NER)
corr(∆RER, ∆GDP)
corr(∆RER, ∆C)corr(∆RER, ∆NX)
corr(∆RER, ∆(1 + i ))0.712
-0.068-0.137
0.213
0.130

1.000
-0.068-0.121-0.297
0.206

1.000
0.504
0.665
-0.501
0.355

1.000
0.607
0.699
-0.6290.849

1.000-0.710-0.6930.421-0.739

0.781
0.878
0.674
0.910
-0.930

1.000
0.720
0.759
-0.718-1.0000.999
0.123-0.0930.003
0.166

Note: The table shows the volatility and correlation of macro variables in the data, and in the model in response
to various shocks. The data column reproduces the second column of Table 4. All series except for net exports(NX) are in logs. Net exports (NX) are expressed as a fraction of GDP. Column (1) considers UIP (ψ) andcapital flight (ζ) shocks. Column (2) considers UIP (ψ) and TFP (A) shocks. Column (3) considers UIP (ψ)
shocks only. Column (4) considers capital flight (ζ) shocks only. Column (5) considers TFP (A) shocks only.
Column (6) considers monetary policy shocks (m) only. Column (7) considers UIP (ψ) and TFP (A) shocks in amodel where households and firms do not have direct access to foreign bonds (s̄ = 0). In columns (1), (2), and(7), we choose the volatility of shocks to match the volatility of GDP and the volatility of the nominal exchange
rate. In columns (3)-(6), we match the volatility of GDP.

productivity shocks or monetary policy shocks can match the small negative correlation of theexchange rate with output and consumption (Backus-Smith correlation). However, since productivity shocks generate little exchange rate volatility, the combination of productivity shocks andcapital flight shocks that matches the Backus-Smith correlation and the volatility of the exchange
rate yields a volatility of GDP that is much too high. A combination of monetary shocks and capital flight shocks that matches the Backus-Smith correlation generates a counterfactually negative
correlation between the exchange rate and the nominal interest rate.
Itskhoki and Mukhin (2021a) fit some of the facts in Table 5 using a model with productivity
and UIP shocks but where exchange rates have very modest effects on the real economy. Column(7) of Table 5 reproduces similar results for our model with s̄ = 0. This calibration is, however,inconsistent with our empirical findings regarding the substantial real effects of regime-induced
depreciations as we discuss in Section 5.1. In Itskhoki and Mukhin’s model, the key mechanism
45

behind the model’s ability to match the Backus-Smith correlation is that an exchange rate depreciation causes real interest rates to increase because monetary policy responds to inflation associatedwith imported intermediates. This increase in real interest rates causes consumption to decline,
despite output increasing (due to expenditure switching). In our model, both output and consumption have the same (small negative) correlation with the real exchange rate, whereas in theirmodel, these correlations have opposite signs. In the data, the real exchange rate has a small
negative correlation with both output and consumption.

6.3

Mussa Facts

Mussa (1986) drew attention to the fact that the volatility of the real exchange rate rose substantially when the Bretton Woods system of fixed exchange rates broke down in 1973. Table 4 demonstrates this fact in our sample. Comparing columns 3 and 4 of this table reveals a large increase in
the volatility of both the nominal and real exchange rates after 1973.39 Comparing columns 1 and
2 of Table 4 shows, furthermore, that the volatility of both the nominal and real exchange rate aresubstantially larger for floats than pegs after 1973.
Earlier work has pointed out that the large change in the volatility of the real exchange rate in1973 was not accompanied by substantial changes in the volatility of other real outcomes such as
GDP and consumption (Baxter and Stockman, 1989; Flood and Rose, 1995; Itskhoki and Mukhin,2021b). This can be seen in Table 4 for our sample. Table 4 also shows that the volatility of output
and consumption is not lower for pegs than for floats after 1973 despite pegs having substantiallylower volatility of the real exchange rate. In fact, the volatility of output is somewhat higher forpegs than for floats after 1973 and somewhat higher before 1973 than after 1973.
These facts might be seen to constitute a conundrum. Why does higher exchange rate volatility
not translate into higher volatility of output and consumption in these cases? One answer is thatpegs and floats may differ in other ways and the period after 1973 may differ from the period
before 1973 in other ways. Ignoring this omitted variables explanation, one might be tempted toconclude that these facts imply that exchange rates are disconnected from other macro aggregates.
But our result on large responses to regime-induced depreciations is hard to square with exchange
rates not mattering for macro aggregates.
Our model with UIP shocks and capital flight shocks provides a different explanation. In thismodel, pegging the exchange rate has two effects on output volatility. On the one hand, pegging
39 It is important to note that the discontinuity in the volatility of the real exchange rate is starker for G7 countries

than for the countries we focus on in our analysis. Also, it is less stark when one focuses on trade-weighted exchange
rates, a point emphasized by Petracchi (2022).

46

std(∆NER)
std(∆RER)
std(∆GDP)
std(∆C)std(∆NX)
std(∆(1 + i ))Table 6: Mussa Facts(ψ, ζ )
ψ onlyFloat Peg
Float Peg
0.114 0.000
0.088 0.000
0.113 0.001
0.087 0.000
0.037 0.049
0.023 0.000
0.045 0.057
0.022 0.000
0.016 0.016
0.014 0.000
0.001 0.001
0.001 0.000

ζ onlyFloat Peg
0.073 0.000
0.073 0.001
0.029 0.049
0.039 0.057
0.007 0.016
0.001 0.001(ψ, A)
Float Peg
0.114 0.000
0.113 0.002
0.037 0.016
0.030 0.008
0.022 0.014
0.002 0.001

Note: The table shows the volatility of macro variables of countries in region F in the model under a floatingexchange rate regime and under a fixed exchange rate regime. All variables except for net exports (NX) arein logs. The net export is expressed as a fraction of steady state GDP. The first two columns consider UIP (ψ)
and capital flight (ζ) shocks. The third and forth columns consider UIP (ψ) shocks only. The fifth and sixth
columns consider capital flight (ζ) shocks only. The seventh and eighth columns consider UIP (ψ) and TFP (A)shocks.

reduces output volatility by eliminating UIP shocks. One the other hand, pegging increases output
volatility by tying the hands of policy makers in the face of capital flight shocks. As we demonstrated in Figure 12, capital flight shocks cause larger output fluctuations when countries peg thanwhen they float. This is because pegging prevents them from engaging in stabilizing monetary
policy in the face of capital flight shocks and also prevents the capital flight itself from generatinga stabilizing depreciation. Whether output volatility increases or decreases in our model whena country exogenously shifts from floating to pegging depends on the relative size of these two
opposing forces.
Table 6 compares these forces quantitatively in our model, by comparing the volatility of theexchange rate and real macroeconomic variables for floats versus pegs.40 In the first two columnsof Table 6, we do this for the same calibration as we use in column (1) of Table 5. In this case,pegging reduces the volatility of the real exchange rate by a factor of 20. In contrast, the volatilityof GDP and consumption increase slightly. This prediction lines up well with the data. In contrast,
the model with only UIP shocks or with a combination of UIP and productivity shocks cannot
match these facts.

6.4

Cross-Country Heterogeneity

The model we develop in this section matches unconditional statistics averaged across the many
countries in our sample. Countries differ, however. Figure 13 plots one interesting dimensionof this heterogeneity: the country-wise correlation between real exchange rates and net exports
40 Specifically, we compare the cases where the F countries float vs. peg.

47

-.2

0

Corr(ΔRER, ΔNX)
.2
.4

.6

Country Size and Corr(ΔRER, ΔNX)

20

22

24
Mean Log Real GDP

26

28

Figure 13: The Correlation between Real Exchange Rates and Net Exports by Country Size
Note: The figure plots the country-wise correlation between log changes in real exchange rates and changes in
net exports over GDP as a function of mean log real GDP over the sample period. The figure is a binned-scatterplot with 20 bins. The red line denotes a linear fit. The slope is 0.044 with standard error of 0.010.

against mean log real GDP over the sample period. The figure shows that while the correlation
is close to zero for small countries (the bulk of our sample) it is non-zero for large countries. The
high correlation for large countries has been emphasized by Alessandria and Choi (2021).41
Our FDX model with both UIP shocks and capital flight shocks provides a straightforward
way of fitting this pattern if we allow capital flight shocks to play a larger role in bigger countries. Figure C.2 demonstrates that varying the relative importance of the capital flight shocks
results in the correlation between the real exchange rate and net exports varying.42 Of course, thisleaves open the question of why capital flight shocks might be relatively more important in larger
countries, a question we leave for future research.

7

Conclusion

We estimate the effects of “regime-induced depreciations” on macroeconomic outcomes. Our
main conclusion is that regime-induced depreciations cause large booms. Interestingly, net exports fall and nominal interest rates rise in response to such depreciations. These conditional
41 The coefficient in an OLS regression of correlation between real exchange rates and net exports on mean log real
GDP is 0.044 with standard error 0.010.
42 Additionally, the Backus-Smith correlation is more negative for larger countries in the data (see Figure C.1 inthe appendix). This is again consistent with the idea that capital flight shocks are relatively more important in larger
countries.

48

statistics provide valuable discipline on models of how exchange rate depreciations affect theeconomy. Traditional open economy models, which emphasize expenditure switching effects andmonetary policy cannot explain our empirical results. We develop a ”financially driven exchange
rate” model (FDX model) to explain these facts. In this model, regime-induced depreciations cause
an inflow of foreign credit that results in a boom with net exports falling and nominal interest
rates rising. Despite regime-induced depreciations having a large causal effect on macroeconomy,
a two-shock version of our model with both UIP shocks and capital flight shocks can explain
exchange rate disconnect, the Backus-Smith correlation, and the Mussa facts.

49

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54

Appendix
A

Empirical Appendix

A.1

Details on Exchange Rate Regime Classification

Table A.1 lists of anchor currencies for the country-year observations that we classify as floats. A
large majority of our sample of floats have European currencies as their anchor currencies. Other
anchor currencies include the South African rand (ZAR), Australian dollar (AUD), Indian rupee(INR), and Singapore dollar (SGD). Ilzetzki et al. (2019) classify a few countries as anchoring to abasket of currencies (USD-EUR, USD-AUD) or the SDR.
One may be concerned that countries anchoring to a basket of currencies that include the US
dollar, or to a currency that may be weakly pegged to the US dollar (e.g., ZAR, INR, SGD) should
be classified as pegs to the US dollar rather than floats against the US dollar. Our choice is based on
the empirical observation that the comovement of these currencies with the US dollar is similar tothat of other categories that we classify as floats. Figure A.1 presents results analogous to Figure 2
but with separate categories for (i) observations anchored to ZAR, INR, SGD and (ii) observations
anchored to a basket of USD and EUR or USD and AUD. The figure shows that the currencies ofthese two groups of countries behave extremely similar to freely floating countries (category 13)
in terms of comovement with the U.S. dollar.
Additionally, an important point to note in this context is that the choice of how to categorize
these observations affects the strength of the “first stage” in our analysis (the strength of the differential effect of the change in the USD on the exchange rate of pegs versus floats). Misclassificationof exchange rate regimes will weaken the statistical power of the “first stage” of our analysis but
does bias our results. To be concrete, if our exchange rate regimes contain substantial noise, achange in the USD will lead to little effect on the relative trade-weighted exchange rate of peggers
versus floaters (classified according to our measure). But Figure 3 shows that this is not the case.

55

Table A.1: Anchor Currencies of Floats Sample
Anchor currency
AUD
BEF
BRL
DEM
EUR
FRF
GBP
INR
ITL
PTE
RUB
SDR
SGD
TRL
USD
USD-AUD
USD-EUR
ZAR
n.a.

Observations
117
1
5
124
771
430
54
71
2
24
65
72
46
5
36
68
107
204
32

Note: The table lists the anchor currencies of our floats
sample based on Ilzetzki, Reinhart, and Rogoff (2019).
We only include samples with GDP data.

56

1.5
1
.5
0
-.5
-1

Z
.2
SD AR
-E , IN 13.
3U
R R, S
,U
G
SD D
-A
U
D

.1

U

13

13

13

12

11

10

9

8

7

6

5

4

3

2

1

-1.5

Figure A.1: Comovement with US Dollar by Category with Extra Categories
Note: This figure plots our estimates of the γk ’s from Equation (1) that is analogous to Figure 2 but we include
dummies for two separate categories: pegs to ZAR, INR, or SGD and pegs to USD-EUR or USD-AUD.

57

A.2

Additional Figures and Tables
Table A.2: Ilzetzki, Reinhart, and Rogoff’s (2019) Exchange Rate Regime Classification
Fine
Code
1
2
3
4
5

Coarse
Code
1
1
1
1
2

6

2

7
8
9
10
11
12
13
13.1
13.2
13.3

2
2
3
3
3
3
4
4.1
4.2
4.3

Description
No separate legal tender or currency union
Pre announced peg or currency board
Pre announced horizontal band that is narrower than or equal to ±2%
De facto Peg
Pre announced crawling peg;de facto moving band narrower than or equal to ±1%
Pre announced crawling band that is narrower than or equal to ±2%
or de facto horizontal band that is narrower than or equal to ±2%
De facto crawling peg
De facto crawling band that is narrower than or equal to ±2%
Pre announced crawling band that is wider than or equal to ±2%
De facto crawling band that is narrower than or equal to ±5%
Moving band that is narrower than or equal to ±2%
De facto moving band ±5% / Managed floating
Freely floating
Other anchor and course classification 1 to that anchor
Other anchor and course classification 2 to that anchor
Other anchor and course classification 3 to that anchor

Note: The table lists the exchange rate regime classification of Ilzetzki, Reinhart, and Rogoff (2019). The table
excludes two categories: “freely falling” and “dual market with missing parallel market data.” The bottom
three rows are three categories we create in our analysis.

58

Table A.3: Data Series and Sources
Variable
Nominal effective exchange rate
Real effective exchange rate
Exchange rate to USD
GDPConsumption
Investment
ExportImportNet Exports
Nominal Interest Rate
CPI
Ex-post Real Interest Rate
Export Unit Value
Import Unit Value
Terms of Trade
Manufacturing GDP
Service GDP
Agriculture GDP
Mining, Construction, Energy GDP

SourceDarvas (2021)
Darvas (2021)
IFS
WDI
WDI
WDI
WDI
WDI
Constructed
IFS
IFS
Constructed
UNCTADUNCTAD
Constructed
WDI
WDI
WDI
WDI

Observations
5012
4905
4997
4975
3244
3220
3319
3319
3319
2409
4462
2139
3831
3697
3697
3773
3899
4184
3643

Countries
149
149
150
158
137
136
142
142
142
98
153
92
158
158
158
146
148
151
144

Note: This table lists the variables and data sources we use. Column 3 presents the number of observations inour baseline sample. Column 4 presents the number of countries in our baseline sample.

Table A.4: Share of Variation that is Regime Induced
Horizon, hAdjusted R2
Including
Dropping
Peg Variables Peg Variables
0
0.38
0.30
1
0.33
0.28
2
0.32
0.29
3
0.35
0.30
4
0.38
0.32
5
0.41
0.35
6
0.43
0.37
7
0.46
0.39
8
0.49
0.40
9
0.52
0.39
Note: The table reports adjusted R2 from regression (2) for each horizon h, where the outcome variable isthe log nominal effective exchange rate. The columns “Including Peg Variables” correspond to our baseline
specification where Pegi,t and its interaction with ∆eUS,t as well as their lags are included. The columns“Dropping Peg Variables’ correspond to the one where they are removed from the explanatory variables.

59

1.5
1
.5
0
-.5

2

3

4.

4.

1
4.

4

3

2

-1

1

Figure A.2: Comovement with US Dollar by Category
Note: This figure plots our estimates of the γk ’s from Equation (1). These are estimates of the comovementof the exchange rate of currencies with different exchange rate regimes as classified by Ilzetzki, Reinhart, andRogoff’s (2019) coarse classification. We normalize the γk for category 4 (freely floating and anchored to the
US dollar) to be zero. Categories 4.1 through 4.3 are currencies anchored to other currencies than the US dollar
and classified in coarse categories 1 through 3, respectively, relative to their anchor currency. The vertical lines
denotes the splits between categories we classify as pegs (1 and 2) and floats (4 through 4.3).

1

.8

.6

.4

.2

0
1980

1990

2000

2010

2020

Year
Floats vs. USD

Pegs to USD

Figure A.3: Pegs and Floats over Time
Note: This figure plots the faction of countries that we classify as pegs and floats over time among observations
where GDP data is available.

60

Africa

Americas

40

40

30

30

20

20

10

10

0

0
1970

1980

1990

2000

Floats vs. USD

2010

2020

1970

1980

Pegs to USD

1990

2000

Floats vs. USD

Asia/Oceania

2010

2020

Pegs to USD

Europe

40

40

30

30

20

20

10

10

0

0
1970

1980

1990
Floats vs. USD

2000

2010

2020

Pegs to USD

1970

1980

1990
Floats vs. USD

2000

2010

2020

Pegs to USD

Figure A.4: Exchange Rate Regimes over Time by Region
Note: This figure plots the number of countries that we classify as pegs and floats over time by region. We
only include samples where GDP data is available. The number of countries in Europe is small before 1990
because we exclude the 24 countries that we define the US dollar exchange rate against most of which are inEurope.

61

Nominal Effective Exchange Rate

Real Effective Exchange Rate

1.5

1.5

1

1

.5

.5

0

0

-.5

-.5

-1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

Nominal Exchange Rate to USD
1.5

1

.5

0

-.5

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

Figure A.5: Response of US Dollar Exchange Rate for Pegs vs. Floats
Note: This figure plots the response of the nominal effective exchange rate, real effective exchange rate, andcountry i’s US dollar exchange rate for pegs versus floats in response to a change in the US dollar nominal
effective exchange rate. In all three cases the dependent variable is the change in the logarithm of the variable. These are our estimates of β h in Equation (2) for different horizons h when these three variables are theoutcome variables. These results are for the case with our baseline set of controls. The shaded areas are 95%
confidence intervals.

Exports Unit Value (in USD)

Imports Unit Value (in USD)

1

1

.5

.5

0

0

-.5

-.5

-1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

Figure A.6: Response of Pegs vs. Floats for Export and Import Prices
Note: This figure plots the response of export and import unit values in US dollars for pegs versus floats in
response to a change in the US dollar exchange rate. For both variables, the dependent variable is the change
in the logarithm of the variable. These are our estimates of β h in Equation (2) for different horizons h whenthese two variables are the outcome variables. These results are for the case with our baseline set of controls.
The shaded areas are 95% confidence intervals.

62

CPI

-.1

0

0

.1

.5

.2

.3

1

Nominal Interest Rate

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-.5

0

.5

Real Interest Rate

-3

-2

-1

0

1

2

3
Years

4

Figure A.7: Response of Interest Rates and Prices for Pegs vs. Floats
Note: This figure plots the response of the short term nominal interest rate, the CPI, and the ex-post real interest
rate for pegs versus floats in response to a change in the US dollar nominal effective exchange rate. For the
CPI, the dependent variable is the change in the logarithm of the CPI. For the nominal and real interest rates,
the dependent variable is the variable in levels (i.e., 0.02 denotes 2%). These are our estimates of β h in Equation(2) for different horizons h when these three variables are the outcome variables. These results are for the casewith our baseline set of controls. The shaded areas are 95% confidence intervals.
Real Effective Exchange Rate

Real GDP
1.5

1
.5

1

0
.5
-.5
0
-1
-1.5

-.5
-3

-2

-1

0

1

2

3
4
Years

Trade Openess < Median

5

6

7

8

9

-3

> Median

-2

-1

0

1

2

3
4
Years

5

Trade Openess < Median

6

7

8

9

> MedianFigure A.8: Response of Pegs vs. Floats by Trade Openness
Note: This figure plots the response of real exchange rate and GDP for pegs versus floats in response to achange in the US dollar exchange rate. We estimate these responses separately for the sample of countries
with an average trade openness below median and above median. We measure the average trade openness ofa country as the sum of exports and imports divided by GDP, averaged over our sample period. For the realexchange rates, the dependent variable is the change in the logarithm of the variable. For GDP, the dependent
variable is the percentage change. These are our estimates of β h in Equation (2) for different horizons h. These
results are for the case with our baseline set of controls. The shaded areas are 95% confidence intervals.

63

Real Effective Exchange Rate

Real GDP

2

1

1

.5

0

0

-1

-.5

-2

-1
-3

-2

-1

0

1

2

3
4
Years

1973-1995

5

6

7

8

9

-3

1996-2019

-2

-1

0

1

2

3
4
Years

1973-1995

5

6

7

8

9

1996-2019

Figure A.9: Response of Pegs vs. Floats by Sample Period
Note: This figure plots the response of real exchange rate and GDP for pegs versus floats in response to achange in the US dollar exchange rate. We estimate these responses separately for the first and the second halfof our sample period. For the real exchange rates, the dependent variable is the change in the logarithm of thevariable. For GDP, the dependent variable is the percentage change. These are our estimates of β h in Equation(2) for different horizons h. These results are for the case with our baseline set of controls. The shaded areas
are 95% confidence intervals.

64Change from Baseline: Control for Interaction btwn. US GDP, US T Bill, US inflation.
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1.5

GDP

1.5
.8

1

1

.5

.5

% of initial GDP

%

%

.6

0

0

-.5

-.5

.4
.2
0
-.2

-1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-.4
-3

-2

-1

0

1

3
Years

4

5

6

7

8

9

-3

.6

.6

.6

.4

.4

.4

.2
0

% of initial GDP

.8

.2
0

-.2
-.2

0

1

2

3
Years

4

1

5

6

7

8

9

2

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.2
0

-.4

-.4
-1

0

-.2

-.4

-2

-1

Net Exports

.8

-3

-2

Investment.8% of initial GDP% of initial GDP

Consumption

2

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

CPI

2

3
Years

4

Terms of Trade

1.5

.3

1

.1

0

1

.5
%

% of initial GDP% of initial GDP

.2

0
.5

-.5

-.1
0
-.2

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.10: Responses with Added US Controls
Note: This figure plots responses for a specification analogous to our baseline specification except that we add
the interaction of contemporaneous US GDP growth, US inflation, and the US T-bill rate with the peg indicatorvariable as controls (red diamonds). We also plot the baseline responses for comparison (blue circles). The
shaded areas and broken lines are 95% confidence intervals.

65

Change from Baseline: Control Peg X Commodit Price Change
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1.5

GDP

1.5
.8

1

1

.5

.5

% of initial GDP

%

%

.6

0

0

-.5

-.5

.4
.2
0
-.2

-1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-.4
-3

-2

-1

0

1

Consumption

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment
.8

.8

.6

.6

.6

0

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4

.4

% of initial GDP% of initial GDP.22

Net Exports.8.4% of initial GDP

2

.2

0

-.2

.2
0
-.2

-.2

-.4

-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

CPI

2

3
Years

4

Terms of Trade

1.5
1

.3

1

.1

0

.5

%

% of initial GDP% of initial GDP

.2

.5

0

0

-.5

-.1

-.2

-.5
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.11: Responses with Added Commodity Price Controls
Note: This figure plots responses for a specification analogous to our baseline specification except that we add
the following control: log changes in commodity price index interacted with the peg indicator variable (reddiamonds). We also plot the baseline responses for comparison (blue circles). The shaded areas and brokenlines are 95% confidence intervals.

66

Change from Baseline: Control for Interaction btwn. Global Financial Cycle.
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1.5

GDP

1.5
.8

.5

% of initial GDP

.5

.6

%

1

%

1

0

0

-.5

-.5

.4
.2
0

-1

-.2

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-.4
-3

-2

-1

0

1

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment

.8

.8

.6

.6

.4

.4

2

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

Net Exports
.8
.6

.2
0

% of initial GDP.4% of initial GDP% of initial GDP

Consumption

2

.2

0

-.2

.2
0
-.2
-.4

-.2
-.4
-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-1

0

1

CPI

2

3
Years

4

Terms of Trade

1

.3

1

.2

.5

.1

0

.5
%

% of initial GDP% of initial GDP

-2

0

0
-.5

-.1
-.5
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.12: Responses with Added Global Financial Cycles Controls
Note: This figure plots responses for a specification analogous to our baseline specification except that we add
the following control: changes in Global Financial Cycle measure by Miranda-Agrippino and Rey (2015, 2020)
interacted with the peg indicator variable (red diamonds). We also plot the baseline responses for comparison(blue circles). The shaded areas and broken lines are 95% confidence intervals.

67

Change from Baseline: Time FE instead of Time X Region FE
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1

.5

.5

.6

% of initial GDP

1

0

0

-.5

-.5

-1
-2

-1

0

1

2

3
Years

4

5

6

7

8

9

.4

.2

0

-.2

-1
-3

-.4
-3

-2

-1

0

1

Consumption

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment
.8

.8

.6

.6

.6

.4

.4

0

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4
% of initial GDP.22

Net Exports.8% of initial GDP% of initial GDP

GDP
.8

%

1.5

%

1.5

.2

0

.2
0
-.2

-.2

-.2
-.4

-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-1

0

1

CPI

2

3
Years

4

Terms of Trade

1

.3

1

.1

0

.5

.5
%

% of initial GDP.2% of initial GDP

-2

0

0
-.5

-.1
-.5
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.13: Responses with Time Fixed Effects
Note: This figure plots responses for a specification analogous to our baseline specification except that regionby-time fixed effects have been replaced by time fixed effects (red diamonds). We also plot the baseline responses for comparison (blue circles). The shaded areas and broken lines are 95% confidence intervals.

68Change from Baseline: No Controls (but still FEs).
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1.5

1.5

1

1

.5

.5

GDP
.8

% of initial GDP

%

%

.6

0

0

-.5

-.5

.4
.2
0
-.2

-1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-.4
-3

-2

-1

0

1

Consumption

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment
.8

.8

.6

.6

.6

0

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4

.4

% of initial GDP% of initial GDP.22

Net Exports.8.4% of initial GDP

2

.2

0

.2
0
-.2

-.2
-.2

-.4

-.4
-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

4

5

6

7

8

9

-3

-2

-1

0

1

CPI

.4

2

3
Years

4

Terms of Trade

1.5

1

.5

0

1
%

.2

% of initial GDP% of initial GDP

3
Years

0

.5
-.5

0
-.2

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.14: Responses with No Controls Other than Fixed Effects
Note: This figure plots responses for a specification analogous to our baseline specification except that no controls are included other than fixed effects (red diamonds). We also plot the baseline responses for comparison(blue circles). The shaded areas and broken lines are 95% confidence intervals.

69

Change from Baseline: Two lags of controls, instead of one.
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1.5

GDP

1.5
.8

.5

% of initial GDP

.5

.6

%

1

%

1

0

0

-.5

-.5

.4
.2
0

-1

-.2

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-.4
-3

-2

-1

0

1

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment
.8

.8

.6

.6

.6

.4

.4

0

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4
% of initial GDP.22

Net Exports.8% of initial GDP% of initial GDP

Consumption

2

.2

0

.2
0
-.2

-.2

-.2
-.4

-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

CPI

.4

1.5

.2

1

2

3
Years

4

Terms of Trade

0

.5
%

% of initial GDP% of initial GDP

1

0

.5

-.5
0
-.2

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.15: Responses with Two Lags of Controls
Note: This figure plots responses for a specification analogous to our baseline specification except that two lagsof controls are included (red diamonds). We also plot the baseline responses for comparison (blue circles). The
shaded areas and broken lines are 95% confidence intervals.

70

Change from Baseline: Drop top and bottom 1% of outcome.
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1

.5

.5

.6

% of initial GDP

1

0

0

-.5

-.5

-1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

.4

.2

0

-.2

-.4
-3

-2

-1

0

1

Consumption

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment
.8

.8

.6

.6

.6

.4

.4

0

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4
% of initial GDP.22

Net Exports.8% of initial GDP% of initial GDP

GDP
.8

%

1.5

%

1.5

.2

0

.2
0
-.2

-.2

-.2
-.4

-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-1

0

1

CPI

2

3
Years

4

Terms of Trade

1

.3

1

.2

.5

.1

.5
%

% of initial GDP% of initial GDP

-2

0

0
-.5
0

-.1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.16: Responses when Top and Bottom 1% of Observations are Dropped
Note: This figure plots responses for a specification analogous to our baseline specification except that we drop
the top and bottom 1% of observations (red diamonds). We also plot the baseline responses for comparison(blue circles). The shaded areas and broken lines are 95% confidence intervals.

71

Change from Baseline: Classify 3 as Floats.
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1

.5

.5

.6

% of initial GDP

1

0

0

-.5

-.5

-1
-2

-1

0

1

2

3
Years

4

5

6

7

8

9

.4

.2

0

-.2

-1
-3

-.4
-3

-2

-1

0

1

Consumption

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment
.8

.8

.6

.6

.6

.4

.4

0

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4
% of initial GDP.22

Net Exports.8% of initial GDP% of initial GDP

GDP
.8

%

1.5

%

1.5

.2

0

.2
0
-.2

-.2

-.2

-.4

-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-1

0

1

CPI

2

3
Years

4

Terms of Trade

2

.3

1

.1

0

.5

1

%

% of initial GDP.2% of initial GDP

-2

0

0
-.5

-.1
-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.17: Responses with Coarse Category 3 Included as Floats
Note: This figure plots responses for a specification analogous to our baseline specification except that we include observations in Ilzetzki, Reinhart, and Rogoff’s coarse category 3 as Floats (red diamonds). We also plot
the baseline responses for comparison (blue circles). The shaded areas and broken lines are 95% confidence
intervals.

72

Change from Baseline: Classify 3 as Pegs.
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1

.5

.5

.6

% of initial GDP

1

0

0

-.5

-.5

-1
-2

-1

0

1

2

3
Years

4

5

6

7

8

9

.4

.2

0

-.2

-1
-3

-.4
-3

-2

-1

0

1

Consumption

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment
.8

.8

.6

.6

.6

.4

.4

0

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4
% of initial GDP.22

Net Exports.8% of initial GDP% of initial GDP

GDP
.8

%

1.5

%

1.5

.2

0

.2
0
-.2

-.2

-.2
-.4

-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-1

0

1

CPI

2

3
Years

4

Terms of Trade

1

.3

1

.2

.5

.1

.5

%

% of initial GDP% of initial GDP

-2

0

0
-.5
0

-.1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.18: Responses with Coarse Category 3 Included as Pegs
Note: This figure plots responses for a specification analogous to our baseline specification except that we
include observations in Ilzetzki, Reinhart, and Rogoff’s coarse category 3 as pegs (red diamonds). We also plot
the baseline responses for comparison (blue circles). The shaded areas and broken lines are 95% confidence
intervals.

73

Change from Baseline: GDP weighted U.S. Dollar Exchange Rate
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1

.5

.5

.6

% of initial GDP

1

0

0

-.5

-.5

-1
-2

-1

0

1

2

3
Years

4

5

6

7

8

9

.4

.2

0

-.2

-1
-3

-.4
-3

-2

-1

0

1

Consumption

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Investment
.8

.8

.6

.6

.6

.4

.4

0

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4
% of initial GDP

.2

3
Years

Net Exports.8% of initial GDP% of initial GDP

GDP
.8

%

1.5

%

1.5

.2

0

.2
0
-.2

-.2

-.2
-.4

-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-1

0

1

CPI

.3

2

3
Years

4

Terms of Trade

1

1

.2

.5

.1

.5

%

% of initial GDP% of initial GDP

-2

0

0
-.5
0

-.1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.19: Responses with a GDP-Weighted US Dollar Exchange Rate
Note: This figure plots responses for a specification analogous to our baseline specification except that the US
dollar exchange rate is constructed using GDP weights rather than trade weights (red diamonds). We also plot
the baseline responses for comparison (blue circles). The shaded areas and broken lines are 95% confidence
intervals.

74

Change from Baseline: Include 24 Advanced Countries
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1

.5

.5

.6
% of initial GDP

1

0

0

-.5

-.5

-1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

.4
.2
0
-.2
-.4

-3

-2

-1

0

1

Consumption

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment
.8

.8

.6

.6

.6

.4

.4

0

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

.4
% of initial GDP.22

Net Exports.8% of initial GDP% of initial GDP

GDP
.8

%

1.5

%

1.5

.2

0

.2
0
-.2

-.2

-.2
-.4

-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

CPI

.4

2

3
Years

4

Terms of Trade

1
1

.3

.1

.5

%

% of initial GDP% of initial GDP

.5
.2

0

0

-.5
0

-.1

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.20: Responses Including 24 “Advanced” Countries
Note: This figure plots responses for a specification analogous to our baseline specification except that we
include the 24 countries that the BIS US trade-weighted exchange rate is defined relative to (red diamonds).
We also plot the baseline responses for comparison (blue circles). The shaded areas and broken lines are 95%
confidence intervals.

75

Change from Baseline: Non-missing for all variables
Nominal Effective Exchange Rate

Real Effective Exchange Rate

1

.5

.5

.6

% of initial GDP

1

GDP
.8

%

1.5

%

1.5

0

0

-.5

-.5

-1
-2

-1

0

1

2

3
Years

4

5

6

7

8

9

0

-.4
-3

-2

-1

0

1

Consumption

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

Investment

2

3
Years

4

5

6

7

8

9

5

6

7

8

9

5

6

7

8

9

Net Exports

.8

.8
.6

.8

.6
.4

.4
.2
0

.4

% of initial GDP% of initial GDP.6% of initial GDP

.2

-.2

-1
-3

.4

.2

0

.2
0
-.2
-.4

-.2

-.2
-.4

-.4
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

Nominal Interest Rate

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

CPI

.6

2

3
Years

4

Terms of Trade

1

.2

0

.5
1
%

% of initial GDP% of initial GDP

.4

.5
0

0
-.5

-.2

-.5
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

Figure A.21: Responses with Same Sample for All Variables
Note: This figure plots responses for a specification analogous to our baseline specification except that we
estimate it on the largest sample where we have all nine variables (red diamonds). We also plot the baseline
responses for comparison (blue circles). The shaded areas and broken lines are 95% confidence intervals.

76

Tourist Inflows

Tourist Outflows

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

Figure A.22: Responses of Tourist Inflows and Outflows
Note: This figure plots the response of tourist inflows and outflows for pegs versus floats in response to achange in the US dollar exchange rate. The dependent variables are the change in the logarithm of the variable.
These are our estimates of β h in Equation (2) for different horizons h. These results are for the case with ourbaseline set of controls. The shaded areas are 95% confidence intervals. We obtain data for tourists flow fromWorld Bank’s World Tourism Organization, Yearbook of Tourism Statistics, Compendium of Tourism Statistics
and data files.

Government Expenditure
.15

.1

.05

0

-.05

-.1
-3

-2

-1

0

1

2

3
Years

4

5

6

7

8

9

Figure A.23: Responses of Government Expenditure
Note: This figure plots the response of government purchases for pegs versus floats in response to a regimedriven change in the US dollar exchange rate. The dependent variable is ( Gi,t+h − Gi,t−1 )/Yi,t−1 , where Y
denotes GDP and G denotes government purchases, both of which are expressed in constant 2015 US Dollars.
The data is from World Bank World World Development Indicators. These are our estimates of β h in Equation(2) for different horizons h when the variable described above is the outcome variables. These results are forthe case with our baseline set of controls. The shaded areas are 95% confidence intervals.

77

9

160

180

1.1

140

1

120

.9

100

.8

80

.7
.6

1980

1990

2000

2010

2020

Year
US Dollar Trade-Weighted Exchange Rate (left axis)
Bloomberg Commodity Price Index (right axis)

Figure A.24: US Dollar Trade-Weighted Exchange Rate and Commodity Price Index
Note: This figure plots the BIS’s trade-weighted exchange rate of the US dollar against 24 countries and theBloomberg Commodity Index. Lower values indicate a more appreciated US dollar.

78

B

Theory Appendix

B.1

Standard Open-Economy New Keynesian Model Features

Here, we describe the features that our model shares with standard open economy New Keynesianmodels without financial frictions. If we set the adjustment costs in the portfolio problem of thehouseholds and the firms in our model to zero (see the description of these portfolio problems in
Section 3 of the main text), our model becomes a standard open economy New Keynesian models
without financial frictions in which UIP holds for all currency pairs.
B.1.1

Households

There is a unit measure of identical households in each economy. These households derive utility
from consumption and disutility from labor. They maximize∞

E0 ∑ βt [u(Cit − hCit−1 ) − χ(nit )] ,

(B.1)

t =0

where Cit denotes consumption of households from country i at time t of a composite of homeand foreign goods discussed below, nit denotes labor supplied by households in country i at timet, β is the households’ subjective discount factor, h is a parameter governing the strength of theirhabit formation in consumption,u(Cit − hCit−1 ) =(Cit − hCit−1 )1−σ,1−σχ(nit ) =n1it+ν
,1+ν

where σ is inversely related to the household’s intertemporal elastiticy of substitution, and ν is theinverse of the Frisch elasticity of labor supply.
The composite consumption good Cit is a constant elasticity of substitution (CES) basket ofgoods produced in different countriesCit =(1 − α )1/η(ciit )

η −1
η

+α

1/η

Z 1
0

(c jit )η −1η η −η 1
dj,

where c jit denotes the consumption by household in country i of a basket of goods produced incountry j, α ∈ [0, 1] determines the weight on foreign goods in Cit , and η > 0 is the elasticity of
substitution between goods from different countries. The index c jit is a CES basket of a continuum79

of varieties c jit (υ) produced in country j:c jit =

Z 1
0(c jit (υ))ϵ p −1ϵp

 ϵ ϵ−p 1dυp,where the elasticity of substitution across goods produced by country j is ϵ p > 1.
Households in country i maximize utility subject to the following budget constraint:
Cit + ait = ait−1 (1 + rith ) + (1 − τin )Wit Nit /Pit + Tit ,(B.2)

where ait denotes the value of the portfolio of assets that households purchase in period t, rith is thereal return on the portfolio that households purchased in period t − 1, Wit is an index of the wages
the households earn for supplying labor at time t, Nit is the composite index of labor services thehouseholds supply to firms (described below), Pit is the price level in country i at time t, τin is atime-invariant labor income tax imposed by the government, and Tit denotes transfers received
from the government. We introduce the labor income tax to offset steady state markup distortions
due to union power in the labor market.
Households in country i optimally trade off consumption today versus consumption in the
future. This gives rise to the following consumption Euler equation
MUit = Et [(1 + rith +1 ) MUit+1 ],(B.3)

MUit = u′ (Cit − hCit−1 ) − βhu′ (Cit+1 − hCit )

(B.4)

where

is the marginal utility from increasing consumption by one unit today.
Households optimally choose how much to consume of goods from each country. This choicegives rise to a demand function given by
  
−η

 α p jit
Cit
for j ̸= iPit
c jit = −η (1 − α) p jit
Cit for j = i
Pitwhere p jit is the price index of goods consumed in country i that were produced in country j.
The households furthermore optimally choose how much of each variety to consume among the80

varieties produced in each country. This choice gives rise to a demand function given byc jit (υ) =p jit (ν)
p jit

−ϵ p
c jit .

Cost minimization by households implies thatp jit ≡

Z 1
0

p jit (υ)

1− ϵ p1/(1−ϵ p )
dυ

(B.5)

and

Pit =
Labor Unions(1 − α)( piit )1−η + α

Z 1
0( p jit )1−η dj1/(1−η ).

(B.6)

Households supply labor through a continuum of labor unions, ℓ ∈ [0, 1]. Each

union converts household labor nit into labor services of a specialized type Nit (ℓ). (Total household labor supply nit is the simple integral of Nit (ℓ) over ℓ.) The labor types Nit (ℓ) enter the
production function of firms through the CES basket

Nit =

Z 1
0

( Nit (ℓ))

ϵw −1
ϵw

 ϵ ϵw−1dℓw,where ϵw > 1 is the elasticity of substitution between the labor types in production. Cost minimization by firms results in each union facing a downward sloping demand curve for its labor
servicesNit (ℓ) =Wit (ℓ)Wit

 − ϵwNit ,where Wit =Z 1
0

Wit (ℓ)1− ϵw

1/(1−ϵw )dℓ,Wit (ℓ) denotes the nominal wage for labor of type ℓ, and Wit denotes the nominal wage index for
economy i.
Each labor union chooses the wage Wit (ℓ) to maximize household utility. Each period there isa constant probability 1 − δw that union ℓ can reoptimize its wage, as in Erceg, Henderson, andLevin (2000). The union then supplies all labor that is demanded at this wage. This implies thatin periods when it is able to reoptimize the wage, union ℓ chooses {Wit (ℓ), Nit (ℓ)} to maximize∞∑ ( βδw )s−t [(u(Cis − hCis−1 ) − χ(nis ))]

s =0

81

where

nis =

Z 1
0

Nis (ℓ)dℓ

subject to
Nis (ℓ) =Wit (ℓ)Wis

Cit + ait+1 = ait (1 + ritr ) + (1 − τin ) − ϵw
Nis ,

Z 1
0

Wit (ℓ) Nit (ℓ)dℓ/Pit + Tit ,where the wage index is given by

Wit =

Z 1
0

Wit (ℓ)1− ϵw

1/(1−ϵw )
dℓ

.

Nis
Nis (ℓ) − Wit (ℓ)ϵw
Wis



(B.7)

Optimal wage setting then implies that∞∑ ( βδw )

s =0

s−t

Nis
χ (nis )ϵw
Wis
′



Wit (ℓ)Wis

λis (1 − τin )+Pis

 − ϵw −1

Wit (ℓ)Wis

−ϵw −1 !!

= 0,where λis is the Lagrange multiplier on the budget constraint. Household optimization implies
λis = MUis . We can rewrite the above expression as
χ′ (n )

isw
∑s=t ( βδw )s−t Nis (ℓ) MUis (1 − τin ) ϵw −1 MUis.
Wit (ℓ) =∑s=t ( βδw )s−t Nis (ℓ) MUis (1 − τin ) P1s

ϵ

(B.8)

Log-linearizing this last equation around a steady state with no inflation yields
d is + ν N̂is ,Ŵit (ℓ) = (1 − βδw ) ∑ ( βδw )s−t P̂s − MU

(B.9)

s=t

where the hatted variables denote log-deviations from steady state of the corresponding hatless
R1
variables. Notice that n̂it = 0 N̂it (ℓ)dℓ = N̂it .
Log-linearization of the wage index in equation (B.7) yields
Ŵit = δw Ŵit−1 + (1 − δw )Ŵit (ℓ).

(B.10)

Combining equations (B.9) and (B.10), we obtain the New Keynesian Wage Phillips Curve:
πitw = κw ln



( Nit )νMUit Wit /Pit



+ βEt πitw+1 ,(B.11)

where πitw ≡ Wit /Wit−1 − 1 is wage inflation in country i at time t and κw ≡ (1 − δw )(1 − βδw )/δw .
82

B.1.2

Firms

There are two types of firms in the economy: production firms and price-setting firms. We describe
these in turn.
Production Firms In each country, there are a continuum of ex-ante identical production firms.
These firms produce a homogeneous country-specific good and sell this good to local pricesetting firms in a competitive country-specific wholesale market at a price pitmc that is equal totheir marginal cost of production. The production firms in country i operate the following CobbDouglas technology:
Yit = Ait (Kitκ Nit1−κ )1−ω Xitω ,(B.12)

where Ait denotes aggregate productivity, Kit denotes capital, Xit denotes intermediate inputs,and κ and ω are parameters. The intermediate inputs consist of the same CES basket of goods as
the households in country i consume. Aggregate productivity is stochastic and follows an AR(1)process in logarithms:
ln Ait = ρ A ln Ait−1 + ϵitA .

(B.13)

Production firms own the capital they use. Their capital stock evolves as follows:
Kit+1 = Kit (1 − δk ) + Iit ,(B.14)

where Iit denotes investment and δk is the fraction of the existing capital stock that depreciates
each period. The investment good Iit consists of the same CES basket of goods as Cit and Xit .
Investment is subject to investment adjustment costs, S( Iit /Iit−1 ) = 2I ( Iit /Iit−1 − 1)2 . We assumeϕthat the production firms own a diversified portfolio of price-setting firms.
The real earnings of production firms are given by





Iit
1
p
mc
Dit =
p Yit − Pit Iit 1 + S− Wit Nit − Pit Xit + Πit ,Pit itIit−1(B.15)

pwhere Πit denotes the profits the production firms earn from their ownership of the portfolio of
price-setting firms – which is equal to the average profit of price-setting firms in each period. The
production firms choose a sequence for { Iit , Xit , Nit , Kit+1 } as well as individual types of labor and83

varieties of investment and intermediate inputs to maximize their value∞

1

Vit = Dit + Et ∑ft
s=t ∏k =0 (1 + rik+1 )Dis+1 ,

(B.16)fwhere rit+1 is their discount rate between period t and period t + 1.
The firms’ problem can be written recursively as1
Vit (Kit , Iit−1 ) =max
Ii,t ,Kit+1 ,Nit ,Xit Pits.t.

pitmc Ait (Kitκ Nit1−κ )1−ω ( Xit )ω − Wit Nit − Pit Xit



1
Iit
+ Et
Vitk+1 (Kit+1 , Iit )− Pit Iit 1 + S
f
Iit−1
1 + rit+1

Kit+1 = (1 − δk )Kit + Iit .

The first order conditions with respect to Ii,t is



1+S



Iit

+S

Iit−1

′





Iit

Iit

Iit−1

Iit−1


∂Vit+1 (Kit+1 , Iit ) ∂Vit+1 (Kit+1 , Iit )
1
= Et
+
.
f
∂Iit
∂Kit+1(1 + r )it+1

The envelope conditions for Iit−1 and Kit are( Iit )2
Iit−1 ( Iit−1 )2(1 − ω )κ pitmc Ait (Kitκ Nit1−κ )1−ω ( Xit )ω /Kit+1∂Vit (Kit , Iit−1 )
=
∂Kit
Pit
1 − δk ∂Vit+1 (Kit+1 , Iit )+ Et
f∂Kit+1(1 + r )∂Vit (Kit , Iit−1 )= S′∂Iit−1



Iit



it+1

Defining “marginal Q” as Jit ≡ ∂Vit (Kit , Iit−1 )/∂Kit , the above conditions simplify to

1+S

Iit
Iit−1



+ S′



Iit
Iit−1



Iit
Iit−1

"

= Et



1
f

1 + rit+1

S′



Iit+1
Iit



( Iit+1 )2+ Jit+1( Iit )2"#
(1 − ω )κ pitmc Yit /Kit
1 − δkJit =+ Et
Jit+1 .
fPit
1 + rit+1

84

#(B.17)(B.18)

Optimal choice of Nit and Xit satisfies the following first-order conditions:
Wit Nit = (1 − ω )(1 − κ) pitmc Yit ,Pit Xit = ωpitmc Yit .

and(B.19)

Price-setting Firms. Price-setting firms in country i purchase local goods from production firms
and differentiate them. Each price-setting firm is then a monopoly supplier of their brand orppvariety. They purchase goods at a price pitmc (1 − τi ), where τi is a time-invariant tax imposed by
the government to offset the steady state markup distortion of the price-setting firms.
The price-setting firms sell their varieties both domestically and abroad. They must decide
at which price to sell. They face pricing frictions which imply that they can only reoptimize theprice of their varieties with a probability 1 − δp each period, as in Calvo (1983). When selling domestically, they set prices in the domestic currency. When selling abroad, a fraction θijk ∈ [0, 1] ofprice-setting firms in country i selling to country j set prices in currency k. The fractions θijk determine how prevalent producer currency pricing (PCP), local currency pricing (LCP), and dominantcurrency pricing (DCP) are in the economy.
Consider the problem of a price-setting firm selling variety υ from country i to country j with
its price for these sales set in currency k. The optimal reset price solves∞kkk(υ)yijs(υ) − (1 − τir ) pismc yijs
(υ))
∑ Mis (δp )s−t (Ekis pijtmaxk ( υ ),{ yk ( υ )}∞pijt
s=t s = t
ijs

s.t.

k
yijs
(υ) =

k (υ)
pijt

(B.20)!−ϵ p
Zijs ,

pijs(B.21)

where Zijs ≡ Cijs + Xijs + Iijs is the total demand for goods from country i in country j and Mi,sis the nominal discount factor in country i between period t and period s. The nominal discountfactor Mi,s is defined as Mi,s ≡ ∏sς=t 1/(1 + iiς ), where iiς is the nominal interest rate in country i
at time ς.
Differentiation with respect to pijt (υ) yields the optimality condition∞∑ Mi,s (δp )

s−t



k
k
Ekis pijt(υ)yijs
(υ) −

s=t

ϵp
k
(1 − τir ) pismc yijs(υ)
( ϵ p − 1)



= 0.

(B.22)

Linearizing this equation and combining it with a log-linear approximation of equation (B.5) – i.e.,p̂ij,t = (1 − δp ) p̂ij,t (υ) + δp p̂ij,t−1 – yields a Phillips curve for prices of goods produced in country85

i and sold in country j that are denominated in currency k:kπ̂ijt= (1 − βδp )δp  mckkp̂it − p̂ijt− Êkit + βπ̂ijt+1 ,1 − δp(B.23)k ≡ pk /pk
where πijt
ijt−1 − 1.
ijt

We next derive a Phillips curve for the prices of all goods produced in country i and sold tocountry j. This is a weighted average of equation (B.23) across currencies of denomination k using
the weights θijk . When we take this weighted average, we denominate all prices in the currency ofthe destination country. This yields
πijt − ∑ θijk ∆ ln Ekjt = κ p ln
k



pitmc
Eijt
pijt



"

#

+ βEt πijt+1 − ∑ θijk ∆ ln Ekjt+1 ,(B.24)kwhere πijt ≡ pijt /pijt−1 − 1 and κ p ≡ (1 − βδp )(1 − δp )/δp . Aggregate inflation in country j isgiven byπ jt = απ jjt + (1 − α)Z 10πijt di.

The average nominal profits of price-setting firms are, to a first-order approximation,pΠit = [ln( piit yiit ) − ln ( pitmc yiit )] p̄ii ȳii +Z 1
0ln(Eijt pijt yijt ) − ln pitmc yijtp̄ij ȳij dj,(B.25)

where p̄ij ȳij is the steady state revenue of country i selling to country j, and

 −η

 (1 − α) piit
(Cit + Iit + Xit ) for i = jPyijt = −η it
 α pijt(Cjt + Ijt + X jt )for i ̸= j
Pjt

(B.26)As described above, we assume that production firms own a diversified portfolio of price-setting
firms and that the profits of price-setting firms therefore accrue as dividends to the production
firms. We make this assumption for convenience, since it avoids us having to keep track of multiple asset prices in each economy.

86B.1.3Equilibrium Definition

In each country, the government sets the steady state labor and product market taxes to offset thesteady state markup distortions,p(1 − τin ) = µw ,p

(1 − τi ) = 1/µ p ,Tit = τin Wit Nit /Pit + τi pitmc Yit /Pit ,(B.27)

ϵpwwhere µw ≡ ϵwϵ−1 and µ p ≡ ϵ p −1 are wage and price markups, respectively.

The goods market clearing condition is, to a first-order,Yit = (1 − α)

piit
Pit

−η

(Cit + Iit + Xit ) + α

Z 1
0

pijt
Pjt

We define the equilibrium of this economy as follows.
technology, UIP shocks,

ψ{ϵitm , ϵitA , ϵit },−η(Cjt + Ijt + X jt )dj.

(B.28)

Given a sequence of monetary,

initial prices, { pij,−1 , Wi,−1 , Ei,−1 }, and the initial cap-

ital stock and investment, {Ki,0 , Ii,−1 }, the equilibrium consists of the path of allocationsfph , s , N , K , a , D , Π }, the path of shock processes, { A , ψ }, the{Cit , MUit Yit , Iit , Xit , yijt , sijt
it
it it
it
it
it
it
it
f

path of prices { pijt , Eijt , Qijt , Pit , Wit , iit , rit+1 , rijt+1 , rith +1 , rit+1 , Jit , pitmc , πijt , πit , πitw , Vit }, the path ofptaxes {τi , τin , Tit } such that equations (4)-(12), (B.2), (B.3), (B.4), (B.6), (B.11), (B.12), (B.13), (B.14),(B.15), (B.17), (B.18), (B.19), (B.24), (B.25), (B.26), (B.27), and (B.28) as well as the following accounting equations hold: πitw = Wit /Wit−1 − 1, πijt = pijt /pijt−1 − 1, πit = Pit /Pit−1 − 1.
B.1.4

Solution Method

We compute the impulse response of the economy to a shock as follows. Starting from the deterministic and symmetric steady state, we solve for the first-order approximation of the perfectforesight equilibrium in response to the shock in sequence space (Boppart et al., 2018). This isequivalent to the first-order approximation of the stochastic equilibrium. We truncate the transition path at 100 years and assume that the economy returns to the steady state. Given the impulse
responses to the various shocks in the model, we compute the second moments of the model using
analytical second moments, as in, for example, Auclert, Bardóczy, Rognlie, and Straub (2021a).

87

B.2

Model Derivations

B.2.1

Capital Structure of Goods-Producing Firms

Consider a firm in country i with a sequence of corporate earnings { Dit } that issues a sequence{bijt } of debt in currency j ̸= i. Apart from issuing foreign debt, the firm is financed with domestic
equity. The share of firm’s ex-dividend value financed via debt from currency j per unit measureof country j’s size is denoted sijt . The firm’s leverage is then given by
dividend value can be written as1
and total firm exR f
1− sij dj

1
R f vit , where vit is the ex-dividend value of the firm’s equity.
1− sij djfUsing this notation, the debt the firm issues in currency j is bijt =sijt
R f vit .
1− sijt dj

We assume thatthe firm’s debt structure is sticky in the sense that the firm incurs adjustment costs when its debt
structure deviates from a steady state. For mathematical simplicity, we assume that the adjustment
cost is incurred in the following period and is proportional to total firm value:ff
1
R f vit Φij ( sijt ),1− sij djΓwhere Φij (sijt ) = 2s̄(sijt − s̄ij )2 .
ij
f

f

f

f

f

The firm chooses its debt structure {sijt } to maximize the sum of ex-dividend equity value andthe current dividend at t = 0:
Vi0 ≡ Di0 += Di0 +

ZZ

bij0 dj + vi0(B.29)f

sij0
R f vi0 dj
1 − sij0 dj
∞1+ E0 ∑

t
t=0 ∏k =0 (1 + rik +1 )

 Dit+1 −ff
f
Z (1 + r
ijt+1 ) sijt + Φij ( sijt )

1−

R

f

sijt dj

vit dj +Zfsijt+1
vit dj ,R f
1 − sijt+1 dj(B.30)

where the last two terms in the square bracket represent the repayment of last period’s foreign
debt with interest and the payment of last period’s adjustment costs (second-to-last term) and thefunds received from issuing new debt (last term).
The solution to the above problem is equivalent to that of the following period-by-period portfolio choice problem that is analogous to the households’ problem:
min 1 −
f

sijt

Z

f
sijt dj(1 + rit+1 ) +

Z 

88


f
f
f
sijt (1 + rijt+1 ) − Φij (sijt ) dj

(B.31)

f

The first-order optimality condition for sijt is then given byfsijt = s̄ij − s̄ij

1
Et [(1 + rijt+1 ) − (1 + rit+1 )].
Γf(B.32)

Let’s next simplify (B.30). The definition of vi0 implies thatZ
Z (1 + r ) s f + Φ f ( s f )ij1 ij0
1 
ij ij0vi0 dj + bij1 dj + vi1  .
vi0 = E0
Di1 −R f
1 + ri1
1 − s dj
ij0This equation says that the firm’s ex-dividend equity value at t = 0 is equal to the discounted sumof dividends at t = 1 (the sum of the first three terms) and the ex-dividend equity value at t = 1(the last term). Solving for vi0 gives

R f


Z
1 − sij0 djo  Di1 + bij1 dj + vi1 .
vi0 = E0 
R f
Rn
f
f
f
(1 + rij1 )sij0 + Φij (sij0 ) dj
(1 + ri1 )(1 − sij0 dj) +Notice also thatZRf

sij0 dj
bij0 dj =R f vi0 .
1 − sij0 dj

Substituting these last two equations back into (B.29), we obtain
Vi0 = Di0 +1
R f vi01 − sij0 djZ1o  Di1 + bij1 dj + vi1 .
= Di0 + 
R f
Rn
f
f
f
(1 + ri1 )(1 − sij0 dj) +(1 + rij1 )sij0 + Φij (sij0 ) dj
Following the same steps as above to solve for vi1 and substituting the resulting expression into
the above equation eliminates {bij1 }. This process can then be repeated for for t = 2, 3, . . .. This
allows us to express the firm’s value as∞

1

Vi0 = Di0 + ∑ft
t=0 ∏k=0 (1 + rik+1 )Dit+1 ,

wheref
(1 + rit+1 ) ≡ (1 + rit+1 )


1−

Z

f
sijt dj



89

+

Z n

o
f
f
f
(1 + rijt+1 )sijt + Φij (sijt ) dj

(B.33)

is the firm’s discount rates.
B.2.2

International Bond Arbitrageurs

The model we adopt for international bond arbitrageurs builds on Itskhoki and Mukhin (2021a).
For each currency j, we assume that there is a unit measure of international bond arbitrageurs
engaging in the carry trade between currency j and USD. These bond traders take a long position
Iof BUjt
dollars in bonds from country j and a short position of equal value in US bonds. The

E

nominal return from such a carry trade is R̃Ujt+1 ≡ (1 + i jt ) EjUtjUt+1 − (1 + iUt ) per dollar invested.
We assume that the international bond arbitrageurs seek to maximize the CARA utility functionof the real return on this carry trade expressed in US dollars:
max −
I
BUjt




1
1
I
exp −γ R̃Ujt+1
BUjt.
γ
PU,t+1

We can rewrite the above problem as
"
#!
I
BUjt
1
max − exp −γ (1 − exp(r̃Ujt+1 )) exp(πUt+1 )
,
I
γ
PUt
BUjt

(B.34)

where r̃Ujt+1 ≡ ln(1 + i jt ) − ln(1 + iUt ) − ∆ ln E jUt+1 and πUt+1 = PUt+1 /PUt − 1. As in Campbell
and Viceira (2002) and Itskhoki and Mukhin (2021a), we approximate the portfolio problem of theinternational bond arbitrageurs as the time interval gets short so that (r̃Ujt+1 , πUt+1 ) corresponds
to the increment of the following diffusion processdRUjt+1
dPUt+1





=


µR



 dt + 

µπ



σe2

σeπ

′
σeπ

σπ2

 dZt ,

where µ R ≡ Er̃Ujt+1 is mean return from carry trade, µπ ≡ E[πUt+1 ] is the mean US inflation rate,
σe2 ≡ var(r̃Ujt+1 ) = var(∆ ln E jUt+1 ), σeπ ≡ [cov(r̃Uj,t+1 , πt+1 )] j , and σπ2 = var(πUt+1 ) are the set of
second moments.

90

Applying Ito’s lemma, we can rewrite the objective function in (B.34) as follows

i
1
1 h
I
− exp −γ
(1 − exp(dRUjt+1 )) exp(dPU,t+1 ) BjUt
γ
PUt



1
1
1
2
I
= − exp −γ(−dRUjt+1 + (dRUjt+1 ) + dRUjt+1 dPUt+1 ) BUjt
γ
PUt
2

 
1 I
1
1
γ2 1
2
I
2
σ
γ
BUjt (µ R + σe2 + σeπ ) −(B)= − exp
dt .
γ
PU,t
2
2 ( PUt )2 e Ujt
Therefore, the optimal portfolio problem collapses to a standard mean variance portfolio problem.
The optimal carry trade position is then given byI
BUjt/PUt =

1
1(µ R + σe2 + σeπ ).
2γσe2We log-linearize the above condition around our steady state equilibrium where shocks are small
and PUT = 1. But we also proportionally increase risk aversion, γ, so that γσe2 remains the same, as
in Hansen and Sargent (2011). The terms σe2 and σeπ go to zero as shocks become small. Therefore
the log-linearized condition around a steady state with PUt = 1 is
I
BUjt
=

1
[ln(1 + i jt ) − ln(1 + iUt ) + Et ∆ ln E jUt+1 ],ΓBwhere Γ B ≡ γσe2 .
B.2.3

Equilibrium in the International Bond Market

Here, we provide a general derivation that applies to both the model in Section 3 and the modelin Section 6. To recover the results for the model in Section 3, simply set ζ it = 0 for all i, t. The
demand for currency j bonds from households and firms is



R f 
R h
R f
R
Bjt = 1 − shjit di a jt − 1 − s jit di Ṽjt + sijt
ait di − sijt Ṽit di.
where Ṽjt denotes the value of the firm in country j excluding their current-period dividend. The
first term is the portion of the asset position of households in country j that is invested in domestic
assets. Some of the household’s domestic assets are equity in domestic firms as opposed to domestic bonds. The second term subtracts this amount – which is equal to the portion of firm value
financed domestically. The third and fourth terms represent demand for bonds in country j fromforeign households and firms, respectively.
91

A first-order approximation of the last equation yields (x ≈ x̄ + ∇ x)
Z

Z

R

f
∇s jit ādi + 1 − s̄ ji di ∇Ṽjt
Z
Z
R
R

f
h
+ ∇sijt
di ā + 1 − s̄ij di ∇ a jt − ∇sijt ādi + s̄ij ∇Ṽit di,∇ Bjt = −∇shjit di ā +

1−

R



s̄ ji di ∇ a jt +(B.35)

where ā denotes steady state households’ wealth (which also corresponds to steady state firm
value excluding current dividend, Ṽjt ). First-order approximations of equations (5) and (7) give1 ∇ ln(1 + rijt+1 ) − ∇ ln(1 + rit )
h
βΓ

1 
= s̄ij h ∇ ln(1 + i jt ) − ∇ ln(1 + iit ) + Et ∆∇ ln E jit+1 − ∇ζ jt
βΓ

1 
f
∇sijt = −s̄ij f ∇ ln(1 + rijt+1 ) − ∇ ln(1 + rit )βΓ1 = −s̄ij f ∇ ln(1 + i jt ) − ∇ ln(1 + iit ) + Et ∆∇ ln E jit+1 − ∇ζ jt ,
βΓ
h
∇sijt
= s̄ij(B.36)(B.37)

where we have used equation (17) in the second line of each equation.
Substituting equations (B.36) and (B.37) into equation (B.35), we can approximately write Bjt ≈∇ Bjt asRs̄ ji di NFA jt + s̄ij NFAit di
1
1 ā Rs̄ ji (ln(1 + i j,t ) − ln(1 + ii,t ) + Et ∆ ln E ji,t+1 − ζ jt )di+ h+ fΓΓ β1 ā R1+ h+ fs̄ij (ln(1 + i j,t ) − ln(1 + ii,t ) + Et ∆ ln E ji,t+1 + ζ it )di
Γ
Γ β
R
R

= 1 − s̄ ji di NFA jt + s̄ij NFAit di
1 ā R1(s̄ ji + s̄ij )(ln(1 + i j,t ) − ln(1 + iU,t ) + Et ∆ ln E jU,t+1 )di+ h+ fΓΓ β i∈{ P,U }


R
R

1
1 ā
− s̄ ji diζ jt + s̄ij ζ it di+ h+ fΓΓ β

Bjt = 1 −R

where NFA jt ≡ a jt − Ṽjt , and we have used the fact that all floaters are identical and the economies
in P peg their exchange rates to U.
Since the noise traders’ position in currency j bonds is ψjt , total bond demand for country
I + B + nψ . These bonds are in zero net supply. This implies that the market clearingj ∈ F is BUjt
jt
jt

92

condition for these bonds is given byRR
0 = 1 − s̄ ji di NFA jt + s̄ij NFAit di




1
1 ā R1(s̄ ji + s̄ij )di (ln(1 + i j,t ) − ln(1 + iU,t ) + Et ∆ ln E jU,t+1 )+ h+ f+ΓBΓΓ β i∈{ P,U }


R
R

1
1 ā
+ h+ f− s̄ ji diζ jt + s̄ij ζ it di + ψjt .
ΓΓ βThis is the same equation as equations (9) and (10) in Section 3 (when ζ jt = 0) and equation (19)in Section 6 of the main text.

B.3

Steady State Characterization

In the symmetric steady state, the net foreign asset position in all countries is zero, NFAi = 0.
We normalize price index and exchange rates in all countries to one: Pi = Eij = 1. The aggregate
variables {Yi , Xi , Ci , Ii , Ki , Ni , ri } then solve
Yi = Ci + Ii + Xi ,Y = Ai (Ki )κ ( Xi )ω ( Ni )1−κ−ω ,Xi = ωYi ,(ri + δ)Ki = κ Yi ,( Ni )ν (Ci − hCi )σ = (1 − ω − κ)Yi ,Ii = δKi ,ri = 1/β − 1,
where we have imposed the fact that government subsidies offset the steady state product andlabor markups.

B.4

Calibration Details

Panel A of Table B.1 lists the parameters that we calibrate externally. We set the discount factor toβ = 0.96, which implies a steady state annual real interest rate of 4%. We set the curvature of theconsumption utility function σ to 0.5.43 We set the Frisch elasticity of labor supply 1/ν to 0.5. The
43 With habit formation, the elasticity of intertemporal substitution (EIS) around the steady state in our model isgiven by 1+1h−+hh2 σ1 . At our estimate value of habit, the EIS is 0.57, a relatively standard value in the macroeconomics
literature.

93

Parameter

Description

Table B.1: Calibration of Parameters
Value
Note/Source

A. Externally Assigned Parameters
βDiscount factorσCurvature in consumption utility
1/ν
Frisch elasticity
ωIntermediate inputs shareαOpennessκCapital share in value-added
δkCapital depreciation rate
ϕI
Investment adjustment costϕπTaylor coefficientρmMonetary policy inertiaη
Trade elasticitys̄Foreign currency assets & liabilities
ρ
Shock persistence{θijk }
Pricing regimeΓBond demand inverse elasticity

0.96
0.5
0.5
0.5
0.2
0.43
0.04
2.0
1.5
0.43
1.5
0.24
0.89
See text
0.001

Annual interest rate 4%
Standard
Standard
Itskhoki and Mukhin (2021a)
Imports-to-GDP ratio 40%
Investment-to-GDP ratio 22%
Penn World Table 10.0
Christiano et al. (2005)
Standard
Smets and Wouters (2007)
StandardBénétrix et al. (2015)
Itskhoki and Mukhin (2021a)
LCP
Itskhoki and Mukhin (2021a)

B. Estimated Parameters
κpPrice Phillips curve slope
κw
Wage Phillips curve slope
h
Habit

0.005
0.003
0.719

(0.003)(0.002)(0.048)

Note: Panel A of the table lists the parameters are externally assigned along with the values we assign for them.
Panel B of the table lists the parameters we estimate along with our estimates. Standard errors are reported inparentheses.

annual capital depreciation rate is set to δk = 0.04, based on the average value in the Penn World
Table version 10.0 (Feenstra, Inklaar, and Timmer, 2015). We set the share of intermediate inputs
in gross output to 50%, ω = 0.5, following Itskhoki and Mukhin (2021a). The share of capital invalue added is set to 43% to match a steady state investment-to-GDP ratio of 22%, which is theaverage value in our sample. We set the investment adjustment cost parameter to ϕ I = 2.0, whichis in the middle of estimates provided by Christiano, Eichenbaum, and Evans (2005).
We set the coefficient on inflation in the monetary policy rule to ϕπ = 1.5 as suggested by
Taylor (1993). Monetary policy inertia is set to ρm = 0.43, to match the estimate of 0.81 at thequarterly frequency obtained by Smets and Wouters (2007). The elasticity of substitution between
goods produced in different countries is set to η = 1.5, following a large literature in international
macro (e.g., Chari, Kehoe, and McGrattan, 2002). This value is also consistent with the mediumrun (5-10 year) estimates in Boehm, Levchenko, and Pandalai-Nayar (2023). As described in the94main texts, we set the size of each region as follows: |U | = 0.3, | F | = 0.5, | P| = 0.2. We choose theopenness parameter, α, to match the average imports-to-GDP ratio in our sample of 40%. Since theimports-to-GDP ratio in the steady state of our model is α/(1 − ω ), this implies α = 0.4 × 0.5 = 0.2.
As mentioned in the main text, our benchmark parametrization is to assume that all prices are set
in local currency: for all i, θijk = 1 for k = j and θijk = 0 for k ̸= j.
We choose the remaining parameters – the price and wage Phillips curves, κ p and κw , (orequivalently, the rigidity of prices and the wages, δp and δw ), and the habit parameter, h – to best
fit our estimated impulse responses. More specifically, we set these parameters Θ ≡ (κ p , κw , h) at
the solution to the following problem:Θ̂ = arg min ( IRF (Θ) − IRF )′ Σ−1 ( IRF (Θ) − IRF ),Θ(B.38)

where IRF denotes a vector of the estimated relative impulse response functions of the tradeweighted nominal and real exchange rates, GDP, consumption, investment, exports, imports, inflation, nominal interest rates, and the terms of trade. For each of these variables, we include ten
elements of the impulse response (h = 0 to h = 9). IRF (Θ) is the simulated model counterpart of
IRF in response to a US UIP shock, which is as function of Θ. We set the weighting matrix Σ to be
an identity matrix. When computing the IRF, we always set the size of the initial US UIP shock,ψ

ϵU0 , to match the initial response of the relative nominal exchange rates. We report standard errors of our estimates of Θ using the asymptotic covariance matrix of Θ̂: V̂ =where′
∂IRF (Θ̂) −1 ∂IRF (Θ̂)
Σ
∂Θ
∂Θ ,

∂IRF (Θ̂)
is the Jacobian of the list of impulse responses evaluated at Θ = Θ̂. Our parameter∂Θestimates are listed in Panel B of Table B.1.

B.5

Varying Price and Wage StickinessOur baseline estimate of the price and wage rigidity parameters in our model are δp = 0.87 andδw = 0.95 (see Table B.1). This is a considerable degree of rigidity. Figure B.1 presents results forthe case where we halve both δp and δw and contrast these results with our benchmark case. We seethat the response of GDP is substantially smaller with less nominal rigidity. The reason for this isthat with less nominal rigidity, the depreciation leads inflation to increase sharply, which triggers
a large monetary policy response. As a consequence, real rates increase sharply, which dampens
the booms in GDP. Additionally, the real exchange rate is less volatile and less persistent with lessnominal rigidity. This result can be avoided by assuming sufficiently responsive monetary policythat stabilizes inflation, as shown by Itskhoki and Mukhin (2021a). However, with even more95

% of s.s. GDP

GDP

Years

Real Interest Ratep.p. deviation from s.s.

Years

Nominal Interest Ratep.p. deviation from s.s.

Years

Inflation

p.p. deviation from s.s.

% deviation from s.s.

Half Wage/Price StickinessBaseline

Real Exchange Rate

% deviation from s.s.

Nominal Exchange Rate

Years

Years

Years

Figure B.1: Varying Price/Wage StickinessNote: This figure plots the impulse response of peggers relative to floaters in response to a US UIP shock for
different price and wage stickiness parameters. The dark blue solid line is the case where we halved the sizeof δ p and δw from our baseline estimates, while the light-blue dashed line uses our baseline parameters.

responsive monetary policy, the boom in GDP will be even weaker.

B.6

Alternative Pricing Regimes

In the benchmark parameterization, we have assumed that firms price in local currency (LCP).
Here, we explore two other commonly assumed pricing regimes: producer currency pricing (PCP)
and dominant currency pricing (DCP). PCP corresponds to the following case: 1 if k = iθijk =
 0 otherwise.
The DCP corresponds to the following case:
1 if k = USD and i ̸= jθijk =
1 if k = j and i = j 0 otherwise.
Figure B.2 shows results on net exports and the terms of trade for these two cases in addition to
our baseline case. We plot the response of these variable in pegging countries relative to floating
96

Net Exports

Terms of Trade% of s.s. GDP% deviation from s.s.

LCP
DCP
PCP

Years

Years

Figure B.2: Alternative Pricing Regimes
Note: This figure plots the response of net exports and the terms of trade for peggers relative to floaters in
response to a US UIP shock for different pricing regimes.

countries after a US UIP shock. In the left panel, we see that with PCP and DCP net exports
increase in pegging countries. This contrasts with our empirical results and our baseline LCP casein the model. The reason for the difference is that there is more expenditure switching underthese alternative pricing regimes. In the right panel, the terms of trade response little with DCP,
while the model generates a substantial deterioration in the terms of trade with PCP. In the data,
we observe a mild improvement in terms of trade, which the model with LCP fits. For both net
exports and the terms of trade, the model fits best when we assume LCP.

B.7

Tradable and Non-tradable Sectors

Consider an extension of our baseline model to a case with a tradable sector and a non-tradable
sector. Both tradable and non-tradable goods are produced with the same technology as in equation (B.12), and factors are freely mobile across sectors. The aggregate consumption basket is given
by


ι −1
ι −1
Cit = (1 − ς)1/ι (CitNT ) ι + ς1/ι (CitT ) ι ,(B.39)

where ι > 0 is the elasticity of substitution between tradable and nontradable sectors, and ς ∈ [0, 1]
governs the share of tradable goods in the consumption basket. Tradable consumption is in turna CES basket of goods from different countries
CitT =

(1 − α )1/η(ciit )

η −1
η

+α

97

1/η

Z 1
0

(c jit )η −1η η −η 1
dj.

(B.40)

As in the baseline model, {c Tjit } and CitNT are all CES baskets of a continuum of varieties υ ∈ [0, 1]
with elasticity of substitution ϵ p > 1:

c jit =

Z 1
0(c jit (υ))ϵ p −1ϵp

 ϵ ϵ−p 1dυpCitNT =,

Z 10

 ϵ ϵ−p 1

ϵ p −1(CitNT (υ)) ϵ p

dυp

The price index for aggregate consumption is given by1/(1−ι)
Pit = (1 − ς)( PitNT )1−ι + ς( PitT )1−ι,
1/(1−η )
Z
1− η
1− η
T
+ α ( p jit ) dj,
Pi = (1 − α)( piit )(B.42)

PitNT = piit ,(B.43)(B.41)

where the last equation follows from the fact that factors are freely mobile across sectors, andtherefore, the price index of non-tradable goods are equal to the price index of tradable goods
produced domestically. Note that we assume that both the non-tradable goods and tradable goods
sold domestically are priced in domestic currency.
We assume that both the intermediate inputs and the investment goods have the same nested
CES structure as consumption. Therefore, the bilateral goods trade flows are given by  −η  T −ι −ι 
Pit
p

iit

+ (1 − ς) pPiitit(Cit + Xit + Iit ) for i = j (1 − α ) ς P T
Pit
it




yijt =
−η
−ι
PjtT

p

 ας PijtT(Cjt + Ijt + X jt )for i ̸= j
Pjt

(B.44)

jt

The market clearing condition for each country i’s goods is"
Yi = (1 − α)ς

+

Z 1
0

ας

piit
PitT
pijt
PjtT

!−η

!−η

PitT
Pit

!−ι

PjtT

!−ι

Pjt



+ (1 − ς )

piit
Pit

−ι #

(Cit + Xit + Iit )(B.45)(Cjt + X jt + Ijt )dj.

The equilibrium definition of this economy modifies the definition in Section B.1.3 by replacing
equations (B.6) with (B.41)-(B.43), (B.26) with (B.44), and (B.28) with (B.45).
We calibrate this economy as follows. We first set the elasticity of substitution between tradable
and non-tradable goods to ι = 1. We then set ς = 0.5 to match the average share of the service
sector in GDP in our sample, which is 50%. Since the imports-to-GDP ratio in this model is ςα/(1 −98Two Sectors
Baseline

Real Exchange RateGDP

% of s.s. GDP% deviation from s.s.

% deviation from s.s.

Nominal Exchange Rate

Years

% of s.s. GDP

Years

Non-tradable GDP% of s.s. GDP

Years

Tradable GDP% of s.s. GDP

Years

Net Exports

Years

Years

Figure B.3: Tradable and Non-tradable Sectors
Note: This figure plots impulse responses of peggers relative to floaters in response to a US UIP shock for thebaseline model (dashed line) and the two-sectors model (solid line).

ω ), we re-calibrate the value of openness to α = 0.4 to match the same imports-to-GDP ratio of
40%. Other parameters are unchanged.
Figure B.3 plots the impulse response of peggers relative to floaters in response to a US UIPshock in this model. We find that extending the model to two sectors barely changes the behaviorof aggregate variables. Looking at the response of sectoral output, we find that the increase in
GDP is almost entirely driven by the non-tradable sector.

B.8

Hand-to-Mouth Households

Consider an extension of our baseline model in which some households live hand-to-mouth, i.e.,
consume their labor income period-by-period. More specifically, assume that a fraction φ HtM ofhouseholds in each country do not have access to financial markets. Their budget constraint istherefore,
CitHtM = (1 − τin )Wit Nit /Pit + Tit .

(B.46)The remaining fraction of households – which we refer to as permanent income households –solve the same problem as in the baseline model. We denote their consumption as Citr . Their99

consumption Euler equation isp

MUitr = Et (1 + rit+1 ) MUitr +1 ,(B.47)

where the marginal utility from a unit increase in consumption is
MUitr = u′ (Citr − hCitr −1 ) − βhu′ (Citr +1 − hCitr ).
Analogously, the marginal utility of hand-to-mouth households is
′
HtM
HtM
MUitHtM = u′ (CitHtM − hCitHtM).
−1 ) − βhu (Cit+1 − hCit

The labor union now maximizes a weighted average of the two types of households’ utility
function:
∞

h
i
s−t
HtM
HtM
HtM
HtM
r
r
(
u
(
C
−
hC
)
−
χ
(
n
))
+
(
1
−
φ
)(
u
(
C
(
βδ
)
φ
−
hC
)
−
χ
(
n
))
,
is
is
∑ w
is
is−1
is
is−1

s =0

subject to
nis =

Z 1

Nis (ℓ) =Nis (ℓ)dℓ
 − ϵw
Wit (ℓ)
Nis
Wis

0



Citr + ait = ait−1 (1 + rith ) + (1 − τin )CitHtM = (1 − τin )

Z 1
0

Z 1
0

Wit (ℓ) Nit (ℓ)dℓ/Pit + Tit

Wit (ℓ) Nit (ℓ)dℓ/Pit + Tit .

Solving the above and taking a first-order approximation around the steady state yields the following New Keynesian wage Phillips Curve:w
d it + νn̂it − Ŵit + βπ̂i,t
π̂itw = κw P̂it − MU
+1 ,(B.48)

whered is = Λ HtM MU
d isHtM + (1 − Λ HtM ) MU
d ris
MU
i
i
is the weighted average of the log-changes in marginal utility from a unit increase in consumption
100Real Exchange RateGDP

Hand to Mouth
Baseline% of s.s. GDP% deviation from s.s.

% deviation from s.s.

Nominal Exchange Rate

% of s.s. GDP

Years

Net Exports% of s.s. GDP

Years

Investment% of s.s. GDP

Years

Consumption

Years

Years

Years

Figure B.4: Hand-to-Mouth Agents
Note: This figure plots impulse responses of peggers relative to floaters in response to a US UIP shock for thebaseline model (dashed line) and the model with hand-to-mouth agents (solid line).

between the two types of households, and the weight is given by the steady state share of marginal
φ HtM MU HtM

utility: ΛiHtM = φ HtM MU HtM +(1−i φ HtM ) MU r .
iiAggregate consumption is given by
Cit = φ HtM CitHtM + (1 − φ HtM )Citr .

(B.49)The equilibrium definition for this economy modifies the definition in Section B.1.3 by replacing equations (B.3) with (B.47), (B.46), and (B.49), and (B.11) with (B.48).
We set the share of hand-to-mouth agents to be 30%, φ HtM = 0.3. The rest of parameters areunchanged. Figure B.4 shows the response to a US UIP shock for this economy. We find that,
if anything, the presence of hand-to-mouth agents amplifies the response of consumption, butdampens the response of investment. The response of GDP is nearly unchanged.

B.9

Microfoundations of the Capital Flight ShockAs explained in the main text, banks intermediate foreign currency bonds between households
and firms and the international financial market. We assume that these banks face a constraint on
the amount of intermediation they can engage in: bijt ≤ b̄it , where bijt is the net issuance of foreign
bonds of currency j in country i, and b̄it is the intermediation constraint of the bank. The bank101

solves,max(1 + rijt+1 )bijt − (1 + r jt )
bijt

s.t.

Q jit+1
bijt
Q jit
bijt ≤ b̄it .

A Lagrangian for this problem ismax(1 + rijt+1 )bijt − (1 + r jt )bijt

Q jit+1
bijt + ζ̃ it (b̄it − bijt ),Q jitwhere ζ̃ it is the Lagrangian multiplier on the borrowing constraint. The bank’s optimality condition is then given by(1 + rijt+1 ) = (1 + r jt )Q jit+1+ ζ̃ it
Q jit(B.50)

Defining ζ it = β1 ζ̃ it , equation (B.50) is equivalent to equation (17) to a first-order approximation
around the symmetric steady state.

B.10

Regime-Induced Depreciations with Capital Flight Shocks

Table B.2 and Figure B.5 present results that are directly analogous to Table 2 and Figure 9, respectively, for the case where variation in the US exchange rate results from US capital flight shocks
rather than US UIP shocks. These responses use the same calibration as we used in Section 5. The
results with US capital flight shocks are very similar to the results with US UIP shocks. In otherwords, we can match our empirical responses to regime-induced exchange rate variation witheither US UIP shocks or US capital flight shocks, or any combination of these shocks.
Responses of the world economy to a US capital flight shock do differ from the response to a
US UIP shock. But these differences are due to the direct effects of the shock. These direct effects(i.e., effects that do not run through the exchange rate) are “differenced out” in our analysis ofregime-induced depreciations, which compare outcomes between pegs and floats. These conditional moments are, in this sense, not sensitive to the choice of shocks driving the exchange rate
in our model.

102Real Exchange RateGDP
% of s.s. GDP% deviation from s.s.

Data
Model

Years

Years

Net Exports

Nominal Interest Rate

% of s.s. GDP

p.p. deviation from s.s.

Years

Consumption% of s.s. GDP% of s.s. GDP

Years

Imports% of s.s. GDP

Years

Exports% of s.s. GDP

Years

Investment

Years

Years

Inflation

Real Interest Rate

% deviation from s.s.

p.p. deviation from s.s.

Years

Terms of Trade

Yearsp.p. deviation from s.s.

% deviation from s.s.

Nominal Exchange Rate

Years

Years

Figure B.5: Model Fit: US Capital Flight Shock
Note: This figure plots the response of peggers relative to floaters to a US capital flight shock in the model andin the data. The dashed lines represent the 95% confidence interval in the data.

103

Data

Table B.2: Regime-Induced Depreciation
Impact Response
5Y Average Response
e
i
e
i
0.74
0.07
0.70
0.03

Model
US UIP ShockUS Capital Flight ShockUS Monetary Policy ShockUS Technology Shock

0.74
0.74
0.74
0.74

0.01
0.00
-0.41
-0.72

0.59
0.57
0.26
-0.97

0.01
0.00
-0.14
-0.87

Note: This table reports the impulse response of the log of the nominal effective exchange rate (e) and thenominal interest rate (i) of peggers relative to floaters. Impact response indicates the response at h = 0, while
the 5Y average response is the average of the response at horizons h = 0 through h = 4. The top row of thetable shows our empirical estimates for these responses. The remaining rows show the simulated impulse
response in our model in response to the shock listed to the left in that row. We choose the size of each shocksuch that the impact response of the nominal effective exchange rate matches the impact response in the data.

104

C

Additional Figures and Tables-.4

Corr(ΔRER, ΔC)
-.2
0

.2

Country Size and Corr(ΔRER, ΔC)

20

22

24
Mean Log Real GDP

26

28

Figure C.1: The Correlation between Real Exchange Rates and Consumption by Country Size
Note: The figure plots the country-wise correlation between the log change in consumption and the log change
in the real exchange rate as a function of mean log real GDP over the sample period. The figure is a binnedscatter plot with 20 bins. The red line denotes the linear fit. The slope is -0.028 with standard error of 0.010.

105

Figure C.2: Corr(∆RER, ∆NX) versus Relative Volatility of capital flight Shocks
Note: This figure plots Corr(∆RER, ∆NX) – the correlation of log changes in real exchange rates and changes
in the ratio of net exports to GDP – as a function of the relative variance of capital flight shocks to UIP shocks
in our FDX model. The relative variance of these two shocks is reported relative to its value in our baseline
calibration.

Figure C.3: Ex-Post UIP Deviations
Note: The figure plots the response of ex-post UIP deviations for pegs versus floats in response to a change inthe US dollar nominal effective exchange rate. The dependent variable is ∆eUSD+ ln(1 + ii,t ) − ln(1 + iU,t ),i,twhere ∆eUSD
denotes log-changes in the exchange rate of country i to the USD from time t − 1 to t, ii,t is thei,tnominal interest rate of country i from time t − 1 to t, and iU,t is the US nominal interest rate. The results in blue
plot estimates of β h from equation (2) for different horizons h when UIP deviations are the outcome variable.
These results are for the case with our baseline set of controls. The broken lines indicate 95% confidence
intervals. The results in orange plot the response of this variable in our model in response to a US UIP shock.

106

Table C.1: Variance Decomposition
ψ

ζ

∆NER

59.05%

40.95%∆RER

58.85%

41.15%∆C

24.54%

75.46%∆GDP

38.50%

61.50%∆NX

77.62%

22.38%∆ (1 + i )60.22%

39.78%

Note: The table reports a variance decomposition of our baseline model in Column (1) of
Table 5. Each row decomposes the variance of the variable listed in that row into the partcaused by UIP shocks ψ and the part caused by capital flight shocks ζ. All variables except
for NX are in logs. NX is expressed as a fraction of steady state GDP.

107