The Long-Run Effects of Monetary Policy

NBER WORKING PAPER SERIES

THE LONG-RUN EFFECTS OF MONETARY POLICY

Òscar Jordà

Sanjay R. Singh

Alan M. Taylor

Working Paper 26666

http://www.nber.org/papers/w26666

NATIONAL BUREAU OF ECONOMIC RESEARCH

1050 Massachusetts Avenue

Cambridge, MA 02138

January 2020, Revised in September 2020

We are thankful to Gadi Barlevy, Susanto Basu, James Cloyne, Stéphane Dupraz, Gauti

Eggertsson, John Fernald, Jordi Galí, Yuriy Gorodnichenko, Pierre-Olivier Gourinchas, Juan

Pablo Nicolini, Valerie Ramey, Ina Simonovska, Andrea Tambalotti, and many seminar and

conference participants at the Barcelona Summer Forum, the NBER Summer Institute IFM

Program Meeting, the Econometric Society World Congress, the SED Annual Meeting, the

Federal Reserve Banks of Richmond, San Francisco, St. Louis, and Board of Governors, the

Midwest Macro Conference, Claremont McKenna College, the Swiss National Bank, the Norges

Bank, UC Davis, University of Wisconsin-Madison, Universität Zürich, and Vanderbilt

University, who provided very helpful comments and suggestions. Antonin Bergeaud graciously

shared detailed data from the long-term productivity database created with Gilbert Cette and

Rémy Lecat at the Banque de France. All errors are ours. The views expressed herein are solely

those of the authors and do not necessarily represent the views of the Federal Reserve Bank of

San Francisco, the Federal Reserve System, or the National Bureau of Economic Research.

At least one co-author has disclosed a financial relationship of potential relevance for this

research. Further information is available online at http://www.nber.org/papers/w26666.ack

NBER working papers are circulated for discussion and comment purposes. They have not been

peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies

official NBER publications.

of text, not to exceed two paragraphs, may be quoted without explicit permission provided that

full credit, including © notice, is given to the source.

The Long-Run Effects of Monetary Policy

Òscar Jordà, Sanjay R. Singh, and Alan M. Taylor

NBER Working Paper No. 26666

January 2020, Revised in September 2020

JEL No. E01,E30,E32,E44,E47,E51,F33,F42,F44

ABSTRACT

Does monetary policy have persistent effects on the productive capacity of the economy? Yes, we

find that such effects are economically and statistically significant and last for over a decade

based on: (1) identification of exogenous monetary policy fluctuations using the trilemma of

international finance; (2) merged data from two new international historical cross-country

databases reaching back to the nineteenth century; and (3) econometric methods robust to long-

horizon inconsistent estimates. Notably, the capital stock and total factor productivity (TFP)

exhibit strong hysteresis, whereas labor does not; and money is non-neutral for a much longer

period of time than is customarily assumed. We show that a New Keynesian model with

endogenous TFP growth can reconcile these empirical findings.

Òscar Jordà

Economic Research, MS 1130

Federal Reserve Bank of San Francisco

San Francisco, CA 94105

and University of California, Davis

[email protected]

Sanjay R. Singh

Department of Economics

University of California at Davis

1122, SSH

1 Shields Avenue

Davis, CA 95616

[email protected]

Alan M. Taylor

Department of Economics and

Graduate School of Management

University of California

One Shields Ave

Davis, CA 95616-8578

and CEPR

and also NBER

[email protected]

Are there circumstances in which changes in aggregate demand can have an

appreciable, persistent effect on aggregate supply?

— Yellen (2016)

1. Introduction

What is the effect of monetary policy on the long-run productive capacity of the economy?

Since at least Hume (1752), macroeconomics has largely operated under the assumption

that money is neutral in the long-run, and a vast literature spanning centuries has gradually

built the case (see, e.g., King and Watson, 1997, for a review). Contrary to this monetary

canon, we ﬁnd evidence rejecting long-run neutrality.

Our investigation of monetary neutrality rests on three pillars. First, it is essential to

identify exogenous movements in interest rates to obtain a reliable measure of monetary

effects and avoid confounding. Second, we focus on long-run outcomes, so we need a large

sample based on large-sample time series data and, if possible, a wide panel of countries to

obtain statistical power. Third, as we show below, the empirical method used can make

a big difference: common approaches are designed to maximize short-horizon ﬁt, but we

need methods that are consistent over longer spans of time. We discuss how we build on

each of these three pillars next.

On identiﬁcation, the ﬁrst pillar, we exploit the trilemma of international ﬁnance (see,

e.g., Obstfeld, Shambaugh, and Taylor, 2004, 2005; Shambaugh, 2004). The key idea is

that when a country pegs its currency to some base currency, but allows free movement

of capital across borders, it effectively loses control over its own domestic interest rate: a

correlation in home and base interest rates is induced, which is exact when the peg is hard

and arbitrage frictionless, but is generally less than one otherwise. Insofar as base rates are

determined by base country conditions alone, they provide a potential source of exogenous

variation in home rates. We theoretically ground this identiﬁcation strategy in a canonical

New Keynesian small open economy model (Schmitt-Groh

e and Uribe, 2016; Fornaro and

Romei, 2019). Speciﬁcally, we derive analytical results to show formally, for the ﬁrst time,

how a trilemma-based identiﬁcation approach recovers the exact monetary policy impulse

response function of interest, with or without the presence of spillover effects.

Second, moving on to the data pillar, we rely on two new macro-history databases

spanning 125 years and 17 advanced economies. First, we use the data in Jord

a, Schularick,

and Taylor (2017), available at

www.macrohistory.net/data

. This “JST Database” contains

key macroeconomic series, such as output, interest rates, as well as inﬂation, credit, and

many other potentially useful control variables for our analysis. Second, to allow a Solow

decomposition of output into its components, we incorporate data from Bergeaud, Cette,

and Lecat (2016), available at

http://www.longtermproductivity.com

Their data series

include observations on investment in machines and buildings, number of employees, and

hours worked. With these variables, we can construct measures of total factor productivity

(TFP), as we show later, and decompose impulse responses for output into TFP, capital

input, and labor input, to pinpoint the important channels of the hysteresis mechanism that

we have uncovered.

The third and ﬁnal pillar of our analysis has to do with the econometric approach. We

use local projections (Jord

a, 2005) in order to get more accurate estimates of the impulse

response function (IRF) at longer horizons. As we show formally, as long as the truncation

lag in local projections is chosen to grow with the sample size (at a particular rate that we

make speciﬁc below), local projections estimate the impulse response consistently at any

horizon. Other procedures commonly used to estimate impulse responses do not have this

property (see, e.g., Lewis and Reinsel, 1985; Kuersteiner, 2005), and this—among several

other reasons—may explain the failure of the prior literature to discern the highly persistent

effects we document here.

Supported by these three pillars we show that, surprisingly, monetary policy affects

TFP, capital accumulation, and the productive capacity of the economy for a very long

time. In response to an exogenous monetary shock, output declines and does not return

to its pre-shock trend even twelve years thereafter. Next, we investigate the source of

this hysteresis and ﬁnd that capital and TFP experience similar trajectories to output. In

contrast, total hours worked (both hours per worker and number of workers) return more

quickly to the original trend. Hence, our new ﬁndings are distinct from the usual labor

hysteresis mechanism previously emphasized in the literature (see, e.g., Blanchard and

Summers, 1986; Gal

ı, 2015a; Blanchard, 2018). These results have important implications

for how we think about standard models of monetary economies.

How do our ﬁndings stack up against the state of knowledge? A voluminous literature

based on post-WW2 U.S. data has examined the causal effects of monetary policy (see, e.g.,

Ramey, 2016; Nakamura and Steinsson, 2018, for a detailed review), but the evidence on

long-run neutrality is, at best, mixed (King and Watson, 1997). An important exception

is the work of Bernanke and Mihov (1998), which fails to reject long-run neutrality, but

ﬁnds that the point estimates of GDP response to monetary innovations do not revert to

zero even after ten years. Mankiw (2001) interprets this non-reversal as potential evidence

of long-run non-neutrality.

Recently, Moran and Queralto (2018) use three-equation VAR

We are particularly thankful to Antonin Bergeaud for sharing some of the disaggregated series from

their database that we use to construct our own series of adjusted TFP.

Mankiw notes (emphasis added): “Bernanke and Mihov estimate a structural vector autoregression and

present the impulse response functions for real GDP in response to a monetary policy shock. (See their Figure

models that ﬁnd a similar a link between monetary policy and TFP growth, which we also

see as a key factor in understanding non-neutrality.

To reconcile our empirical results with traditional economic models, we develop a

theoretical model using the formulation in Stadler (1990) to characterize endogenous TFP

growth in a parametrically convenient way in an extension of our small open economy

New Keynesian model. In particular, we estimate the hysteresis elasticity directly from

our estimated responses of TFP and output using a two-step, classical minimum distance

procedure. Our estimated elasticity is similar, for example, to that assumed in DeLong

and Summers (2012). In our model, a contractionary monetary policy shock lowers output,

which temporarily slows down TFP growth. In turn, this slowdown in TFP growth results in

permanently lower levels of output and capital, even though labor returns to the stationary

equilibrium quickly, as we ﬁnd in the data.

Our results and our model also connect to a more recent literature on productivity

research. Barro (2013), for example, provides evidence that high levels of inﬂation result in

a loss in the rate of economic growth. Work by Gopinath, Kalemli-

Ozcan, Karabarbounis,

and Villegas-Sanchez (2017) links the level of interest rates to the level of productivity.

Baqaee and Farhi (2019) construct a general framework where monetary shocks may affect

allocative efﬁciency. Work by Benigno and Fornaro (2018) links low interest rates to the

rate of growth of productivity. Moreover, although in this paper we do not need to take

a stand on the precise details of the hysteresis mechanism, many are consistent with our

setup and several recent papers have examined different potential micro-foundations of

endogenous hysteresis effects via TFP growth (Fat

as, 2000; Barlevy, 2004; Anzoategui,

Comin, Gertler, and Martinez, 2019; Bianchi, Kung, and Morales, 2019).

Going beyond

our paper, hysteresis matters for how we build models of monetary economies and what

optimal monetary policy is in those models: the welfare implications could be substantial.

2. Identification

The trilemma of international ﬁnance gives a theoretically justiﬁed source of exogenous

variation in interest rates (Jord

a, Schularick, and Taylor, 2020). The logic is straightforward

III.) Their estimated impulse response function does not die out toward zero, as is required by long-run

neutrality. Instead, the point estimates imply a large impact of monetary policy on GDP even after ten years.

Bernanke and Mihov don’t emphasize this fact because the standard errors rise with the time horizon. Thus,

if we look out far enough, the estimated impact becomes statistically insigniﬁcant. But if one does not approach

the data with a prior view favoring long- run neutrality, one would not leave the data with that posterior. The data’s best

guess is that monetary shocks leave permanent scars on the economy.”

See Cerra, Fat

as, and Saxena (2020) for a detailed review of literature on hysteresis and business cycles. In

a recent work, Meier and Reinelt (2020) provide evidence of increased misallocation following contractionary

monetary policy shocks.

under a hard peg with free capital mobility short-term rates in two countries, home and

base, will be arbitraged. With strict interest parity, rates are exactly correlated.

But even under soft pegs or dirty ﬂoats, with frictions or imperfect arbitrage, a non-

zero interest rate correlation between home and base is enough for identiﬁcation using

instrumental variables, as is well-known. In this section we present an open economy

model to make formal the conditions for identiﬁcation, even in the presence of spillovers

via non–interest rate channels. This level of detail allows us to construct the econometric

estimation procedures around the propositions derived from the model.

2.1. Baseline Model

We build on a standard open economy setup widely used today as in Schmitt-Groh

and Uribe (2016), and Fornaro and Romei (2019).

Various elements of this framework

appear also in Benigno, Fornaro, and Wolf (2020), Farhi and Werning (2017), Fornaro (2015),

Gourinchas (2018) among others. Our aim is not a new model, but how theory maps

rigorously into our trilemma identiﬁcation scheme and guides our econometric approach.

As the model is standard, many details are relegated to the Appendix. In Appendix H

we also show how the same results hold in a Mundell-Fleming-Dornbusch model with

additional ﬁnancial channels, as in Gourinchas (2018).

We assume there is perfect foresight. The environment features incomplete international

markets with nominal rigidities. We focus on two countries: a large economy that we label

the base and a small open economy, the home country. If home pegs its currency to the

base, then we label it as a peg; if it ﬂoats with respect to the base, then we label it as a ﬂoat.

We begin by describing the small economies ﬁrst.

Consumers.

The household consists of a continuum of consumers, normalized to measure

one, each of which supplies labor while taking as given the market wage. There is perfect

consumption insurance within the household. The household has CRRA preferences over a

composite good and derives disutility from supplying labor. The household problem is

max

t+1

}

∞

∑

t=0

log(C

) − ϕ

1+ν

1 + ν

The composite

is a Cobb-Douglas aggregate







1−ω



1−ω

of a tradable good

and a non-tradable good

, where

ω ∈ (0, 1)

is the tradable share,

is (inverse)

Relative to Fornaro and Romei (2019), we do not model a continuum of small open economies and

instead focus on individual small open economies.

Frisch elasticity of labor supply, and

is a scaling parameter to normalize

h = 1

in the

steady state.

Households can trade in one-period riskless real and nominal bonds. Real bonds are

denominated in units of the tradable consumption good and pay gross interest rate

taken as given (i.e., a world real interest rate). Nominal bonds issued by the domestic

central bank are denominated in units of domestic currency, and pay gross nominal interest

rate R

. That is, R

is the policy rate of interest.

The households’ budget constraint in units of domestic currency is as follows

+ P

+ B

= W

+ P

t+1

+ T

+ Z

where

and

are the prices of tradable and non-tradable goods in local currency;

is the level of real debt in units of tradable good assumed in period

t − 1

and due in

period

;

is the level of nominal debt in units of local currency assumed in period

t − 1

and due in period

;

is the nominal wage;

are nominal lump-sum transfers from the

government;

are nominal proﬁts from domestic ﬁrms owned by households; and

> 0

is the endowment of tradable goods received by the households.

The household chooses a sequence of

, C

, h

, d

t+1

, B

t+1

}

to maximize lifetime

utility subject to the budget constraint, taking initial bond holdings as given. Labor is

immobile across countries, so the wage level is local to each small open economy. The

world real interest rate is taken as given, so there can be dependence on initial conditions.

The ﬁrst-order conditions for the household’s optimization problem are

Tt+1

, (1)

Tt+1

, (2)

(1 − ω)C

ωC

, (3)

ϕ h

. (4)

We assume that law of one price on the tradable good holds. Let

be the nominal

exchange rate for home relative to the base, and let

∗

be the base price of the tradable

good denominated in base currency.

Then, we have that

= E

∗

. From Equation 1 and

It is common in the small open economy literature to treat price level in the base economy

∗

synonymous for price level of tradable goods in the base economy P

∗

Equation 2 we can then derive the interest rate parity condition,

= R

Tt+1

= R

t+1

∗

t+1

∗

. (5)

To ensure stationarity under incomplete markets, we follow Schmitt-Groh

e and Uribe (2003);

Uribe and Schmitt-Groh

e (2017) and assume that the home real interest rate is related to

foreign real interest rate through a debt-elastic interest rate premium,

= R

∗

+ ψ(e

t+1

−

− 1) . (6)

We emphasizes that this is a standard technical requirement for solving these types of

models, but we will henceforth work in the limit case

ψ → 0

, so the ﬁnancial constraint is

vanishingly small.

Production and nominal rigidities.

The non-tradable consumption good is a Dixit-Stiglitz

aggregate over a continuum of products

(i)

produced by monopolistically competitive

producers indexed by

, with

≡ (

(i)

− 1)

di)

/(e

− 1)

. Each ﬁrm

in home

produces a homogenous good with technology given by

(i) = L

(i)

, taking the

demand for its product as given by

(i) =

(

(i)

)

−e

, where we use the price

index of the non-tradable good composite,

= (

(i)

1−e

di)

/(1 − e

)

. Individual ﬁrms

reset prices at random intervals with Calvo (1983) price setting. Full details are found in

the appendix.

Fiscal policy and the bond markets.

The portfolio allocation between the real and nom-

inal bond is not determinate in this type of model. To ensure determinacy, and since all

agents at home are identical, we now assume that home domestic nominal bonds are in

net zero supply, i.e.,

t+1

= 0

. We also assume that the home ﬁscal authority follows a

balanced budget every period.

Market clearing.

We impose that the non-tradable goods market has to clear at home,

implying that production of non-tradable goods (net of misallocation costs due to price

dispersion) must equal the consumption demand for non-tradable goods. However, since

we will focus on a ﬁrst-order approximation around a deterministic steady state, this price

Equivalently, we could introduce a borrowing constraint on the household’s end-of-period debt position.

The vanishingly small ψ is not necessary for our results, and is assumed for transparent analysis.

We assume appropriate government subsidies ﬁnanced by lumpsum taxes to eliminate monopoly rents

in the intermediate goods sector.

dispersion term will be treated as zero, so

= Y

= C

(7)

Finally, the external budget constraint of the economy must be satisﬁed every period:

+ d

= Y

t+1

. (8)

Construction of small open economy GDP.

Our key outcome variable of interest is the

real GDP in the small economy. To make the connection with our empirical counterparts,

and to keep our baseline discussion focused, for now we construct this real GDP variable

using constant aggregation weights implied by the Cobb-Douglas aggregator.

Clearly, variation in aggregation weights can cause changes in real GDP in a multiple

sector economy, and this deﬁnition abstracts from such potential index number problems.

That said, we present analytical results in an environment with time-varying aggregation

weights in Appendix D.

Monetary policy.

The policy rate is the home nominal interest rate on one-period domestic

currency bonds. For our small open economies hit with a base economy interest rate shock,

we ﬁrst consider the following two possible home policy conﬁgurations, a hard peg and a

pure ﬂoat (we will relax this and look at a dirty ﬂoat or soft peg below):

•

A hard peg ﬁxes the nominal exchange rate at a given level. Without loss of generality,

we assume the rule

= 1 . (9)

By Equation 62, and in the limit when

ψ → 0

, there is perfect passthrough from base

economy interest rate changes into home nominal interest rates, hence

−

∗

−

∗

, where

and

∗

denote the steady state levels of nominal interest rates in

the home and the base economy, respectively.

•

Instead, a pure ﬂoat economy sterilizes base interest rate movements so that

−

. In our model, this policy scenario can be implemented with a strict producer

inﬂation targeting rule. We assume that the net (gross) producer price inﬂation target

is zero (one).

= 1. (10)

In models with industry-speciﬁc labor, the price dispersion term does not appear in the aggregate

resource constraints.

This is a standard assumption in New Keynesian models. We could equivalently introduce a different

value for the producer price inﬂation target while assuming perfect indexation to this target by all producers.

As shown by Uribe and Schmitt-Groh

e (2017), strict producer price inﬂation targeting

is the optimal monetary policy rule in such an environment.

Based on these two alternatives, the question now is to determine the conditions under

which, using base interest rate shocks as instruments, one can recover exactly the same

impulse response as that generated by a standard domestic monetary policy shock. We

label this latter reference scenario as the benchmark, where policy is characterized as follows:

•

In the benchmark economy, the home nominal interest rate follows an exogenous path

subject to policy shocks ε

. (11)

Since we are simulating responses to one-time shocks, we interpret this policy rule

assumption as equivalent to that of temporary interest rate peg made in the zero lower

bound literature (Eggertsson and Woodford, 2003; Werning, 2011). Once the shock

abates, a policy rule that maintains local determinacy (Blanchard and Kahn, 1980)

is expected to hold in those environments with temporary interest rates at the zero

lower bound. We assume a similar equilibrium selection device that the economy

returns back to the same deterministic steady state.

10,11

The base economy.

The small country takes the path of prices

∗

and real interest rates

∗

in the base as given. Without loss of generality, we therefore assume rigid prices in the

base economy, with

∗

= 1

. Our focus is then the impulse response of small open economy

output—under peg or ﬂoat—following a shock in

∗

, and how it compares to the impulse

response of a benchmark economy following a domestic policy shock.

Equilibrium and solution method.

We present the equilibrium conditions in Appendix B.

We log-linearize the model around a deterministic steady state, and solve the model

backwards from the deterministic steady state, assuming perfect foresight. Variables in

hats will denote deviations from steady state. In the long-run PPP is assumed to hold,

and the economy returns to

d =

, where

is the level of debt in a deterministic steady

state. Policy shock sequences are i.i.d. changes to

{

∗

}

in the peg and ﬂoat home economy

conﬁgurations, and to {ε

} in the benchmark economy conﬁguration.

Similar solution methods to do counterfactual policy simulations have been developed for economies

away from the zero lower bound (Las

een and Svensson, 2011; Guerrieri and Iacoviello, 2015; Christiano, 2015).

Embedding an endogenous policy transmission through inﬂation targeting, while the shock is on, does not

change our theoretical results since we are identifying responses to non-systematic components of monetary

policy.

We solve the economy for the perfect foresight solution, and assuming that the economy returns back to

the initial steady state. While interest rate pegs are known to cause indeterminacy issues, we maintain this

assumption here to keep our results comparable to the hard peg and pure ﬂoat economy.

2.2. Identiﬁcation with trilemma: analytical results

We now present the core theoretical results of our paper as a series of propositions. We

focus on closed form analytical results. We begin by noting that tradable good consumption,

as well as real debt choice, is independent of the monetary policy regime.

This greatly

simpliﬁes the analysis.

Proposition 1.

The responses to a base interest rate shock of tradable consumption and the domestic

real interest rate (on bonds denominated in tradable goods) do not depend on whether the home

economy pegs or ﬂoats.

Proof.

The proof follows directly from Equation 1, Equation 62, and Equation 8, which

deﬁne the competitive equilibrium for {C

, r

, d

t+1

} a given sequence of {r

∗

The upshot of this well-known result is that we can now separate the determination

of all remaining variables from

, r

, d

t+1

}

. Crucially, we will take the path of these

variables as given across various policy regimes for the same foreign shock.

Deﬁnition 1.

Expressions 12, 13, 14 below summarize the log-linear equilibrium conditions

for

}

under perfect foresight in a small open economy. In addition to

these expressions, the policy regime is summarized by either Equation (peg), (ﬂoat), or

(benchmark). These conditions are for a given sequence of

{

t+1

∗

}

and

assuming ψ → 0, speciﬁcally:

Nt+1

− (

−

Nt+1

) , (12)

= β

Nt+1

+ κ

, (13)

t+1

−

∗

, (14)

t+1

−

= 0 , (peg)

= 0 , (ﬂoat)

= ε

. (benchmark)

This result is well noted in the literature at least since Obstfeld and Rogoff (1995a, Appendix) in the

case with ﬁxed base economy interest rates. Uribe and Schmitt-Groh

e (2017, Section 9.5) generalized the

result to settings where the inter-temporal elasticity of substitution is equal to the intra-temporal elasticity of

substitution between tradable and non-tradable goods.

The key difference between a peg and a ﬂoat comes from whether the nominal exchange rate is used

to counter the passthrough of foreign rates into domestic policy rates. There is an extant literature in open

economy macroeconomics that has emphasized this insight, most recently articulated by Farhi and Werning

(2012), Fornaro (2015), as well as Schmitt-Groh

e and Uribe (2016) upon which we build.

Based on these expressions, hence consider the log-linear equilibrium of a small open

economy under a (hard) peg and the log-linear equilibrium of the benchmark economy

with a domestic policy shock. Assume real GDP is constructed with constant and identical

aggregation weights in the two economies. Then the following proposition holds:

Proposition 2

(impulse response equivalence: hard pegs)

The response of real GDP to a base

interest rate shock in a peg is identical to the response of real GDP to a domestic policy shock of the

same magnitude and persistence in a benchmark economy.

Proof.

The policy rule under a peg prevents any adjustment in nominal exchange rates, i.e.,

t+1

−

= 0

. Hence the path of nominal interest rates in a peg economy,

∗

, is identical to

the path in the benchmark economy for

∗

. The equilibrium conditions summarized by

Equation 12 and Equation 13, with the same terminal condition, then solve for an identical

sequence of

{

}

in the two economies. We provide an exact solution in Appendix C.

Since the tradable output is an exogenous endowment, and we have assumed constant

aggregation weights, the response of real GDP is identical across the two economies.

2.3. Departures from the baseline model

We now extend the baseline model in two ways. First, we allow for imperfect interest rate

pass-through from the base rate into the home economy. This can happen either because

the home economy is in a soft peg or in dirty ﬂoat regime. Given this setting, we then

show that one can still use base country rates to construct the equivalent response to a

monetary shock in the benchmark economy. Second, we consider other channels through

which base interest rate shocks can spill over into the home economy. Hence we show how

one can adjust the response to base country rates and still obtain the equivalent benchmark

economy response to a monetary shock.

2.3.1 Soft pegs and dirty ﬂoats

Deﬁne the imperfect pass-through (whether for a soft peg, or a dirty ﬂoat) of base rates to

home rates using a coefﬁcient 0 < λ ≤ 1 such that: R

−

= λ(R

∗

−

∗

Proposition 3

(impulse response equivalence: imperfect pass-through)

Consider the log-

linear equilibrium of a small open economy with imperfect pass-through and the log-linear equilibrium

of the benchmark economy with a domestic policy shock. Assume real GDP is constructed with

constant and identical aggregation weights in the two economies. The response of real GDP with

imperfect pass-through to a base economy interest rate shock is a fraction

of the response of real

GDP in a benchmark economy to a domestic policy shock of same magnitude and persistence.

Proof. In an imperfect pass-through economy, we can write

= λ

∗

; λ ∈ (0, 1] . (15)

From the UIP conditions in Equation 14, the expected exchange rate appreciation is now

(1 − λ)

∗

. With the terminal condition of

= 0

, it follows that the response

∗

under an imperfect pass-through economy is

times the response of

∗

in the benchmark economy.

2.3.2 Spillovers

If there are other channels through which base interest rates can affect the model equi-

librium, these spillovers will affect the previous results derived for pegs and imperfect

pass-through economies. The equivalency with the impulse response of output in the

benchmark economy will break down.

To see this, consider the following postulated relationship between tradable output and

the base real interest rate,

= α

∗

. (16)

where

α < 0

Such a relationship is often embedded into open economy models through

modeling of the export demand (e.g, see Gal

ı and Monacelli, 2016).

Intuitively, the home economy’s ability to sell its export good to the base (or any

economy pegged to the base) is now demand constrained. This demand is not perfectly

elastic, but depends on the state of consumption demand in the base economy, which

in turn depends on the base real rate. Equation 16 is a reduced-form expression of this

dependence.

Proposition 4

(spillovers in a peg)

Consider the log-linear equilibrium of a small open economy

under a peg with spillovers (i.e., extended with Equation 16), and the log-linear equilibrium of the

benchmark economy with a domestic policy shock. Assume real GDP is constructed with constant

and identical aggregation weights in the two economies. Denote the response of real GDP in a peg

to a unit and i.i.d. base economy interest rate shock with

, and the response of real GDP in the

With persistent shocks,

may not be time-invariant. Here we ignore the time-subscript for analytical

clarity.

It is interesting to note that

can be positive in models with endogenous production of tradable goods.

In Appendix E, we show that this is indeed the case with endogenous production of tradable good with

labor input derived from an economy-wide labor market. In that environment, our baseline estimates have a

downward bias. We think the case of

α < 0

is more realistic in a world where contractionary policy shocks in

the US economy have contractionary spillovers into rest of the world.

benchmark economy to a unit and i.i.d. domestic policy shock with β. Then,

β = γ

−

α .

Proof.

From Deﬁnition 1, which delineates the log-linear equilibrium conditions in a small

open economy, the response of non-tradable output

in the peg economy to a base-

economy interest rate shock is identical to that in the benchmark economy to a similar

shock sequence. In the presence of the spillover, tradable output contracts with an increase

in base interest rates, while it is unaffected in the benchmark economy.

Using the construction of real GDP described in Section 2.1, we can compute the exact

difference in the impulse responses of real GDP as:

peg

−

benchmark

|{z}

tradable output

share in GDP

× (

peg

−

benchmark

) =

∗

Now we assume that the base shock equals the benchmark policy shock,

∗

= ε

, so we

have that

peg

∗

|{z}

≡γ

−

benchmark

| {z }

≡β

α .

Hence,

β = γ

−

α (17)

A corollary of Proposition 4 applies to an imperfect pass-through economy.

Corollary 1.

Consider the log-linear equilibrium of a small open imperfect pass-through economy

(extended with Equation 16 and the log-linear equilibrium of the benchmark economy with a domestic

policy shock. Assume real GDP is constructed with constant and identical aggregation weights in

the two economies. Denote the response of real GDP in the imperfect pass-through economy to a

unit, i.i.d. base economy interest rate shock with

, and the response of real GDP in the benchmark

economy to a unit, i.i.d. domestic policy shock with β. Then,

β =

−

To sum up, this last result shows that the same logic applies to the continuum of regimes

from hard peg (

λ = 1

) to pure ﬂoat (

λ = 0

), with appropriate scaling of responses by

Thus, for estimation purposes, we may draw on information from any economy within this

continuum, not just those with regimes at the extremes.

2.4. Model implications for econometric identiﬁcation

The ﬁnal model just introduced, with spillovers, explains how base country monetary policy

can affect the output of tradable goods (via export demand shifts) as well as the output of

nontradable goods (via interest arbitrage and conventional domestic demand shifts). These

spillover effects onto smaller open economies depend on the share of tradable output in

their GDP. Using the insights and notation from the model, in this section we explore its

implications for the identiﬁcation of our impulse responses.

Disciplining the spillover coefﬁcient.

As in Equation 15, we assume imperfect pass-

through of base rates into home rates. In regression form, this can be expressed as

= λ

∗

+ v

, (18)

where, as before,

, and

∗

are in deviations from steady state, and

λ ∈ [0, 1]

is the

spillover coefﬁcient, and is possibly different for country-time pairs nominally classiﬁed as

pegs

versus

f loats

. We omit the constant term without loss of generality and we assume

that

is a well-behaved, white noise error term. For now, it is convenient to leave more

complex dynamic speciﬁcations aside to convey the intuition simply.

Similarly, Equation 17 in regression form can be expressed as

β +

∗

θ + u

, (19)

where here too

, and

∗

are deviations from steady state. For now, we leave

unspeciﬁed whether

belongs to a peg or a ﬂoat. Note that under Equation 17, we have

θ =

α , (20)

that is, the share of tradable export output in GDP, which we denote

Φ =

/PY

, scaled by

the parameter α, which determined how

∗

affects tradable output.

According to the model, there are two main reasons we might expect

θ → 0

. One reason

is that home output is dominated by non-tradable output. In the JST database we ﬁnd

indeed that in our advanced economies, over 150 years of history, tradable export shares

are 30% at most, and usually lower in the 10%–20% range, so

Φ ≤ 0.3

. The second is the

parameter

, which measures the spillover effect of base country rates

∗

on tradable export

demand at home. It is fair to assume that this effect will be at most as strong as the effect of

domestic rates on tradable output, so

α ≤ β

. These observations will come in handy later

as a way to provide a bound on potential biases due to spillover effects.

IV estimator with no spillovers.

How then can we estimate

using the trilemma ap-

proach? In practice, as is well known, direct OLS estimation of Equation 19 likely delivers a

biased estimate of the desired coefﬁcient

since

will be endogenously determined by

the monetary authority, depending on the exchange rate regime of the country considered.

However, one can exploit the model (and the trilemma mechanism) as follows. Consider

premultiplying Equation 19 by

∗

. Taking expectations, and noting that

∗

) = 0

since

base country rates are assumed to be independent of small country factors, we get

∗

)

E(R

∗

)

∗

)

E(R

∗

)

β + θ . (21)

Now notice that the LHS of Equation 21 is the reduced-form coefﬁcient

(introduced in

the previous section) in the auxiliary regression

∗

γ + η

, (22)

where

is a well behaved, white noise error term uncorrelated with

and

. Similarly,

the ratio of expectations from the RHS of Equation 21 is the coefﬁcient

in Equation 18.

Of course, Equation 18 and Equation 22 are just another way of computing the familiar

traditional IV estimator for Equation 19.

Now in the absence of spillovers,

θ = 0

, and putting these elements together we obtain

γ = λβ =⇒ β =

, (23)

where estimates for

and

are easily obtained from reduced-form regressions Equation 18

and Equation 22. Hence,

is identiﬁed and the estimator based on the two reduced-form

regressions is simply the traditional IV estimator of Equation 19 using

∗

as the instrument.

Our data come from two subpopulations, pegs and ﬂoats, which principally differ in the

degree to which

λ → 1

. In practice we hesitate to impose the same parameters across both

subpopulations thus allowing for different γ and λ, so the reduced form regressions are

= D

∗

+ D

∗

+ η

, (24)

= D

∗

+ D

∗

+ v

, (25)

where D

= 1 for pegs, 0 otherwise, and similarly D

= 1 for ﬂoats, 0 otherwise.

In other words, if there are no spillovers, the IV estimator of

will be the ratio of the

weighted average of the

over the weighted average of the

: we will be estimating a

“model average”

using information from both of the two subpopulations, pegs and ﬂoats.

IV estimator with spillovers.

What happens if

θ 6= 0

? In that case, if we used the above

estimator, the exclusion restriction is violated and

introduces bias in our estimates of

The approach that we take here is to provide a bound for the possible values that

θ = Φα

can take based on our model, as we discussed earlier. Two quantities guide our choices: (1)

the share of tradables in GDP; and (2) the effect of base country rates on tradable output.

Note that (1) is directly measurable and, as we argued above, falls typically in the range

Φ ∈ [0.1, 0.3]

in the JST database. Regarding (2), we assume that effect of

∗

on tradable

output is, in any case, no larger than the effect of

; that is, we assume that domestic

interest rates are more inﬂuential on domestic output than base rates are, so we impose as

a conservative upper bound that α = β.

Based on these assumptions, we can write

θ = Φβ

and employ the calibrated range of

values of Φ. Then it is easy to see that one can transform the original Equation 19 as,

= (

∗

Φ)β + u

, (26)

and one can estimate

with this expression using instrumental variables along the lines

just discussed using the subpopulations of pegs and ﬂoats, that is, with the ﬁrst stage given

by Equation 25.

To sum up, in the empirical work which follows, we estimate the following IV model,

= (

∗

Φ)β + u

, (27)

= D

∗

+ D

∗

+ v

. (28)

which we have shown will recover the true impulse response for the benchmark model

based on impulse responses for pegs and ﬂoats.

3. Data and series construction

Macroeconomic time series.

The empirical features motivating our analysis rest on two

major international and historical databases.

Data on macro aggregates and ﬁnancial variables, including assumptions on exchange

rate regimes and capital controls, can be found in

www.macrohistory.net/data

. This

database covers 17 advanced economies reaching back to 1870 at annual frequency. Detailed

descriptions of the sources of the variables contained therein, their properties, and other

ancillary information are discussed in Jord

a, Schularick, and Taylor (2017) and Jord

Schularick, and Taylor (2020), as well as references therein. Importantly, we will rely on the

trilemma instrument discussed in Jord

a, Schularick, and Taylor (2016), and more recently

Jord

a, Schularick, and Taylor (2020), as the source of exogenous variation in interest rates.

The instrument construction details will become clearer in the next section.

The second important source of data relies on the work by Bergeaud, Cette, and Lecat

(2016) and available at

http://www.longtermproductivity.com

. This historical database

adds to our main database observations on capital stock (machines and buildings), hours

worked, and number of employees, and the Solow residuals (raw TFP). In addition, we

construct time-varying capital and labor utilization corrected series using the procedure

discussed in Imbs (1999) with the raw data from Bergeaud, Cette, and Lecat (2016) to

construct our own series of utilization-adjusted TFP. We went back to the original sources

so as to ﬁlter out cyclical variation in input utilization rates in the context of a richer

production function that allows for factor hoarding. We explain the details of this correction

in Appendix G.

Trilemma instruments.

Guided by our model and identiﬁcation strategy as discussed

above, we divide our sample into three subpopulations of country-year observations.

The bases will refer to those economies whose currencies serve as the anchor for the

subpopulation of pegging economies, labeled as the pegs. Other economies, the ﬂoats, allow

their exchange to be freely determined by the market.

Base and peg country codings can be found in Jord

a, Schularick, and Taylor (2020, Table

1 and Appendix A), and are based on older, established deﬁnitions (Obstfeld, Shambaugh,

and Taylor, 2004, 2005; Shambaugh, 2004; Ilzetzki, Reinhart, and Rogoff, 2019). A country

is deﬁned to be a peg at time

, denoted with the dummy variable

i,t

= 1

, if it maintained

a peg to its base at dates

t − 1

and

. This conservative deﬁnition serves to eliminate

Our construction of productivity assumes misallocation related-wedges are absent. We have not yet

found the data to take into account markups or sectoral heterogeneity in our productivity estimates. See Basu

and Fernald (2002) and Syverson (2011) for extensive discussions on what determines productivity.

opportunistic pegging, and it turns out that transitions from ﬂoating to pegging and

vice versa represent less than 5% of the sample, the average peg lasting over 20 years.

Interestingly, pegs are, on average, more open than ﬂoats.

Finally, let

i,t

= 1 − D

i,t

denote a non-peg, i.e., ﬂoat. The choice of exchange rate regime is treated as exogenous,

and indeed we ﬁnd zero predictability of the regime based on macroeconomic observables

in our advanced economy sample. Regimes are also highly persistent in this sample

which excludes emerging and developing countries, in contrast to the ﬁndings of limited

persistence for the full cross-section of countries as in Obstfeld and Rogoff (1995b).

Based on this discussion, we construct an adjusted instrument as follows. Let

∆R

i,t

denote changes in country

’s short-term nominal interest rate at date

, let

∆R

b(i,t),t

denote

the change in short term interest rate of country

’s base country

b(i, t)

, and let

∆

b(i,t),t

denote its predictable component explained by a variety of base country macroeconomic

aggregates. Loosely speaking, think of it as the rate that would be predicted by a policy

rule,

and hence, using the notation from the previous section, to a ﬁrst approximation

denote

∆

b(i,t),t

= (∆R

b(i,t),t

− ∆

b(i,t),t

)

. However, since countries in a given year may

not be perfectly open to capital ﬂows, we then scale the base shock, adjusting for capital

mobility using the capital openness index of Quinn, Schindler, and Toyoda (2011), denoted

i,t

∈ [0, 1] .

The resulting trilemma instruments adjusted for capital mobility are thus deﬁned as

i,t

≡ D

i,t

∆

b(i,t),t

; j = P, F (29)

where P refers to pegs and F refers to ﬂoats.

4. Solving inconsistency in long-horizon impulse responses

In thinking about the propagation of a shock, specially to distant horizons, it is generally

convenient to allow for generous lag structures—and in the limit, allowing for possibly

inﬁnite lags. Inﬁnite dimensional models have a long tradition in econometric theory and

form the basis for many standard results. For example, Berk (1974) considers the problem

In the full sample, the capital openness index averages 0.87 for pegs (with a standard deviation of 0.21)

and 0.70 for ﬂoats (with standard deviation 0.31). After WW2 there is essentially no difference between them.

The average is 0.76 for pegs and 0.74 for ﬂoats with a standard deviation of 0.24 and 0.30 respectively. See

Jord

a, Schularick, and Taylor (2020) for further details on the construction of the instrument.

The list of controls used to construct

∆i

b(i,t),t

include log real GDP; log real consumption per capita; log

real investment per capita; log consumer price index; short-term interest rate (usually a 3-month government

bill); long-term interest rate (usually a 5-year government bond); log real house prices; log real stock prices;

and the credit to GDP ratio. The variables enter in ﬁrst differences except interest rates. Contemporaneous

terms (except for the left-hand side variable) and two lags are included.

of estimating the spectral density of an inﬁnite order process using ﬁnite autoregression. In

multivariate settings, Lewis and Reinsel (1985) establish the consistency and asymptotic

normality of ﬁnite order approximations to an inﬁnite order multivariate system. Kilian

(1998) shows that the ﬁnite sample biases of the underlying ﬁnite order autoregressions can

induce severe bias on impulse response bootstrap inference based on vector autoregressions

(VARs).

In empirical practice, the well-known biases arising from impulse responses estimated

with ﬁnite VARs are further aggravated by having to choose relatively short lag lengths

due to the parametric loads required in their estimation as Kuersteiner (2005) shows. The

solution that we pursue in this paper to avoid these issues, however, is to calculate impulse

responses using local projections instead.

Suppose the data are generated by an invertible, reduced-form, inﬁnite moving average

process or

VMA( ∞)

—the well-known impulse response representation. Invertibility here

means that the space of the vector

spans the space of the residual vector,



, and that the

process can alternatively be expressed as a reduced-form, inﬁnite vector autoregression or

VAR(∞)

. This assumption allows for very general impulse response trajectories with poten-

tially interesting dynamics at long-horizons. We set aside any discussion on identiﬁcation

since the main issues discussed here do not depend on it. Let

∞

∑

h=0



t−h

; h = 0, 1, . . . ; B

= I , (30)

be the

VMA( ∞)

representation of the m-dimensional vector

(without loss of generality,

we omit the constant term). Under the well-known general invertibility assumptions

explicitly stated in Appendix A, the VAR(∞) is:

∞

∑

j=1

t−j

+ e

; j = 1, 2, . . . . (31)

The moving average matrices,

, and the autoregressive matrices,

, follow the well-

known recursion due to Durbin (1959):

= A

h−1

+ A

h−2

+ . . . + A

k−h

+ A

k+1

k−h−1

+ . . . + A

h−1

+ A

| {z }

remainder

. (32)

Lewis and Reinsel (1985) established that, under standard regularity assumptions, a

VAR(p)

provides consistent estimates of

, . . . , A

with

p, T → ∞

as long as

grows at

a rate

/T → 0

. There are two practical implications of this result. First, a researcher

choosing a truncation lag

k < p

fails to meet the consistency assumption and hence, based

on Equation 32, will obtain inconsistent impulse response estimates

, even when

relatively small.

The second and more subtle implication is the following. Suppose that indeed the

truncation lag is chosen so that

k = p

and hence the consistency condition is met. Then, as

is clear from Equation 32, estimates of the impulse response for horizons

h = 1, . . . , k

will be

consistently estimated, but not for horizons

h > k = p

. The reason is that

for

h > k = p

involves the terms

, . . . , B

k−h−1

, A

k+1

, . . . , A

—the remainder term in Equation 32—,

which have been truncated and hence their omission introduces inconsistency.

What about local projections? An extension of the proof in Lewis and Reinsel (1985)

provided in Appendix A shows that local projections are consistent for any horizon

even when the lag structure is truncated as long as

p, T → ∞

at rate

/T → 0

. Lusompa

(2019) derives a related result in the context of generalized least-squares inference of local

projections. Relatedly, Montiel Olea and Plagborg-Møller (2019) use similar asymptotic

arguments to show how lag-augmented local projections provide asymptotically valid

inference for both stationary and non-stationary data over a wide range of response

horizons.

Basically, local projections are direct estimates of the impulse response (moving average)

coefﬁcients. Truncating the lag structure, even when

h > k

, has asymptotically vanishing

effects on the consistency of the estimator. Truncated VARs on the other hand, have to be

inverted to construct the impulse response. Hence the impulse response depends on the

entire dynamic speciﬁcation of the VAR. The cumulation of small sample inconsistencies

over increasing horizons can pile up quickly and turn into non-negligible distortions to the

impulse response, specially at long horizons.

Of course, the solution would be to specify the VAR truncation lag,

, to be large (as

long as

/T → 0

). Setting aside the parametric burden imposed in the estimation, this may

not be enough to address the second of the practical issues highlighted earlier, namely the

truncation of the remainder term in Equation 32. To illustrate these issues, Figure 1 shows a

simple Monte Carlo exercise. We generate an MA process whose coefﬁcients are determined

by the impulse response function displayed in panel (a). The implied cumulative response

is also shown, as this is the object of interest when we estimate. This impulse response is

meant to loosely mimic the shape of the responses we ﬁnd later in the paper. In cumulative

terms, a shock has transitory, but long-lived effects on the variable.

Panel (b) of Figure 1 hence shows Monte Carlo averages from estimates of the cumulative

Further details on the setup of the Monte Carlo exercise along with the speciﬁcs of how the two panels

of Figure 1 are generated are in Appendix A.

Figure 1: Estimating cumulative responses: autoregressive versus local projection biases at long horizons.

(a) True responses

-.6 -.4 -.2 0 .2

0 5 10 15 20 25

Horizon

Impulse

Cumulative

(b) Lag truncation: 3, 6, 9, and 12 lags

-.6 -.4 -.2 0 .2

0 5 10 15 20 25

Horizon

True LP AR(3)

AR(6) AR(9) AR(12)

Notes: Sample size: 1,000. Monte Carlo replications: 1,000. The shaded error bands are 1 and 2 standard error bands based on

the local projection Monte Carlo average. LP refers to cumulative local projections using 2 lags. AR(k) refers to impulse responses

cumulated from an autoregressive model with k = 3, 6, 9, and 12 lags. See text.

response from a simple AR model with 3, 6, 9, and 12 lags versus local projections using

only 2 lags—a considerable handicap for the local projection. Again, to mimic the empirical

analysis, we assume a sample with 1,000 observations (results with 300 observations yield

nearly identical results). We repeat the experiment 1,000 times. The error bands displayed

are the one and two standard error bands of the local projection Monte Carlo averages.

As is evident from the ﬁgure, given the long-lived dynamics of our experiment, truncat-

ing the data below 12 lags would generate cumulative effects that are relatively short-lived

and far off the true response. The reason is fewer than lags would generally capture the

early stages of the impulse response, where not much action has yet taken place, and it

would miss entirely the undoing of the dynamics of the ﬁrst 12 periods that follow over

periods 13-24. In contrast, local projections provide quite a close estimate of the response

even though the truncation lag is quite severe. As we increase the AR lag length to 12 (the

point at which the original negative dynamics die-off as panel (a) illustrates), the AR model

with 12 lags picks up the shape of the response very nicely though it gets into trouble once

the horizon goes beyond 12 lags, and especially at the tail end, as the theory predicted. In

contrast, local projections continue to approximate the response well, even at those long

horizons.

Consider our application, which involves 9 variables. A 9-dimensional vector autoregres-

sion with 12 lags (as in the Monte Carlo application) involves 108 regressors per equation.

The correct lag length, which is 24 in our D.G.P. involves a whopping 216 regressors.

Compare that to the 18 regressors for the local projection. Further, note that even truncating

the AR at 12 lags is really on the boundary of the order needed to capture the main features

of the theoretical impulse response given the D.G.P. Typical information criteria, specially

commonly used Bayesian (or Schwartz) information criteria, will tend to select lag lengths

that are entirely too small (see Kuersteiner, 2005). Even if long lag lengths are selected, the

parametric loads make the task of analyzing the data across subsamples (as we do) even

more difﬁcult or often times, impossible.

5. The data show that monetary shocks have long-lived effects

The empirical approach from this point forward relies on local projections, estimated with

instrumental variables (LPIV), based on Equation 27 and Equation 34. The instruments,

adjusted for capital mobility, are

i,t

and

i,t

, as deﬁned earlier, and we estimate the following

(cumulative) impulse responses for the baseline, no spillover case (Φ = 0),

i,t+h

− y

i,t−1

= α

i,h

+ ∆R

i,t

+ x

i,t

+ u

i,t+h

, (33)

∆R

i,t

= κ

+ z

i,t

+ z

i,t

+ x

i,t

ζ + v

. (34)

for

h = 0, 1, . . . , H; i = 1, . . . , N; t = t

, . . . , T

, where

i,t+h

is the outcome variable, log real

GDP, for country

observed

periods from today,

i,h

are country ﬁxed effects at horizon

∆R

i,t

refers to the instrumented change in the short-term interest rate (usually government

bills), our stand-in for the policy rate; and

i,t

collects all additional controls including lags

of the outcome and interest rates, as well as lagged values of other macro aggregates.

Moreover, we control for global business cycle effects through a global world GDP control

variable to parsimoniously soak up common global shocks. Estimation is robust with

clustering by country.

Table 1 reports the ﬁrst-stage regression of the pegging country’s short term interest

The list of domestic macro-ﬁnancial controls used include log real GDP; log real consumption per

capita; log real investment per capita; log consumer price index; short-term interest rate (usually a 3-month

government security); long-term interest rate (usually a 5-year government security); log real house prices; log

real stock prices; and the credit to GDP ratio. The variables enter in ﬁrst differences except for interest rates.

Contemporaneous terms (except for the left-hand side variable) and two lags are included. We control for

contemporaneous values of other macro-ﬁnancial variables for two purposes a) base rate movements might

be predictable by current home macro-conditions, and b) we wanted to impose restrictions in the spirit of

Cholesky ordering whereby real GDP is ordered at the top. Results are robust to excluding contemporaneous

home-country controls.

Table 1: Trilemma instruments: First stage evidence.

(a) Pegs (D

i,t

= 1) All years PostWW2

0.58

∗∗∗

0.61

∗∗∗

t-statistic [7.56] [8.30]

Observations 766 585

(b) Floats (D

i,t

= 1) All years PostWW2

0.26

∗∗∗

0.24

∗∗∗

t-statistic [3.32] [3.14]

Observations 379 289

Notes:

∗∗∗

p < 0.01,

∗∗

p < 0.05,

∗

p < 0.1. Full sample: 1870–2015 excluding WW1: 1914–1919 and WW2: 1939–1947. Pre-WW2

sample: 1870–1938 (excluding 1914–1919). Post WW2 sample: 1948–2015. These regressions include country ﬁxed effects as well as up

to two lags of the ﬁrst difference in log real GDP, log real consumption, investment to GDP ratio, credit to GDP, short and long-term

government rates, log real house prices, log real stock prices, and CPI inﬂation. In addition we include world GDP growth to capture

global cycles. Estimation is robust with clustering by country. See text.

rate

∆R

i,t

on the instruments

i,t

, z

i,t

and controls

i,t

, country ﬁxed effects and (robust)

clustered standard errors. The interest-rate passthrough is roughly 0.6 for pegs and 0.25 for

ﬂoats. Thus, neither represents a hard peg or a pure ﬂoat corner case, further bolstering

the case for studying the more general imperfect pass-through case discussed earlier. Both

instruments are statistically signiﬁcant. The peg instrument,

i,t

, has a

-statistic close to

8 in the full and post-WW2 samples and is therefore not a weak instrument. The ﬂoat

instrument,

i,t

, has a

-statistic close to 3 in the full and post-WW2 samples, a weaker

instrument, as one would expect though still relevant. Nevertheless, we show that our

results are robust to excluding the weaker instrument.

5.1. Main results

The main ﬁndings in our paper are shown by the response of real GDP to a shock to

domestic interest rates. Before we show the main results, we highlight the value of our

instrumental variable by comparing the response calculated using selection-on-observables

identiﬁcation versus identiﬁcation with our trilemma instrument. This is shown in Table 2.

The table reports coefﬁcient estimates of the (cumulative) impulse response calculated

with each identiﬁcation approach for the full and post-WW2 samples, LP-OLS and LP-

IV using the trilemma instruments. We provide the coefﬁcient estimates by row, with a

test of the null hypothesis that LP-OLS and LP-IV estimates are equal. The differences

between identiﬁcation schemes could not be starker: LP-IV estimates are economically and

statistically signiﬁcant, and the LP-IV response is considerably larger at all horizons.

We display these results graphically in Figure 2. This ﬁgure is organized into two

Table 2:

LP-OLS vs. LP-IV. Attenuation bias of real GDP responses to 100 bps shock. Trilemma instruments.

Responses of real GDP at years 0 to 12 (100 × log change from year 0 baseline).

(a) Full Sample OLS=IV (b) Post-WW2 OLS=IV

Year LP-OLS LP-IV p-value LP-OLS LP-IV p-value

(1) (2) (3) (4) (5) (6)

h = 0 0.09

∗∗∗

-0.01 0.29 0.05

∗∗

0.07 0.81

(0.03) (0.09) (0.03) (0.07)

h = 2 -0.36

∗∗∗

-1.56

∗∗∗

0.00 -0.29

∗∗

-1.09

∗∗∗

0.01

(0.12) (0.40) (0.11) (0.31)

h = 4 -0.45

∗∗

-2.36

∗∗∗

0.00 -0.33

∗

-1.32

∗∗∗

0.00

(0.18) (0.63) (0.17) (0.33)

h = 6 -0.54

∗∗

-3.54

∗∗∗

0.00 -0.39

∗

-2.64

∗∗∗

0.00

(0.27) (0.90) (0.24) (0.58)

h = 8 -0.62

∗∗

-4.55

∗∗∗

0.00 -0.42 -2.99

∗∗∗

0.00

(0.30) (1.13) (0.33) (0.81)

h = 10 -0.72

∗

-3.55

∗∗∗

0.00 -0.26 -2.78

∗∗∗

0.00

(0.38) (0.94) (0.42) (0.83)

h = 12 -0.64 -4.68

∗∗∗

0.00 -0.22 -2.98

∗∗∗

0.00

(0.44) (1.41) (0.51) (0.95)

KP weak IV 34.77 33.81

: LATE = 0 0.00 0.00

Observations 1145 1145 874 874

Notes:

∗∗∗

p < 0.01,

∗∗

p < 0.05,

∗

p < 0.1. Cluster robust standard errors in parentheses. LP-IV (OLS): Response to a 100 bps

shock in domestic short-term interest rate instrumented with the trilemma IVs (or using OLS, no instruments). Full sample: 1890–2015

excluding WW1: 1914–1919 and WW2: 1939–1947. Post WW2 sample: 1948–2015. KP weak IV refers to the Kleibergen-Paap test for

weak instruments. H

: LATE = 0 refers to the p-value of the test of the null hypothesis that the coefﬁcients for h = 0, ..., 10 are jointly

zero for a given subpopulation. OLS = IV shows the p-value for the test of the null that OLS estimates equal IV estimates. Estimation

is robust with clustering by country. See text.

columns, charts (a) and (c) refer to full sample results, and columns (b) and (d) to the

post-WW2 sample. In addition, the top row—charts (a) and (b)—is based on using the

peg and ﬂoat instruments, whereas the second row—charts (c) and (d)—only use the peg

instrument as a robustness check. Regardless of the sample used, a 1 percentage point

increase in domestic short-term interest rates has sizable and long-lasting effects on GDP.

In the full sample, GDP declines by 4.68 percent over 12 years. A similar, but moderated,

effect is found when we restrict the sample to post-WW2. The drop 12 years after impact is

2.98 percent. Both estimates are signiﬁcantly different from zero (p < 0.01).

Figure 2: Baseline response to 100 bps shock: Real GDP.

(a) Full sample: 1890–2015.

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

IV OLS

(b) Post-WW2 sample: 1948–2015.

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

IV OLS

using only the peg IV.

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

IV OLS

(d) Post-WW2 sample: 1948–2015,

using only the peg IV.

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

IV OLS

Notes: Response to a 100 bps shock in domestic short-term interest rate instrumented with the trilemma IVs. Full sample: 1890–2015

(World Wars excluded). LP-OLS estimates displayed as a dashed red line, LP-IV estimates displayed as a solid blue line with 1 S.E. and

2 S.E. conﬁdence bands. Top row uses both peg and ﬂoat instruments; bottom row uses only peg instrument. Estimation is robust with

clustering by country. See text.

5.2. Inspecting the mechanism

The results in Figure 2 are a far cry from traditional notions of long-run neutrality found

in the literature. What is the source of this persistent decline? We employ a Solow

decomposition of GDP (

) into its components, using a Cobb-Douglas production function,

to construct hours worked (

, employees times number of hours per employee); capital

stock (

, measured capital in machines and buildings); and the Solow residual, labeled as

total factor productivity (TFP).

Figure 3 displays the (cumulative) responses of each of these components to the same

shock to the domestic short-term interest rate using the trilemma instruments, both for

the full and the post-WW2 samples.

The chart displays each of the components with

one and two standard error conﬁdence bands. In the appendix Section I.2, we provide

corresponding ﬁgure for post-WW2 sample with similar ﬁndings.

Several features deserve mention. Figure 3a shows that there are similar declines in

capital and raw TFP. In terms of growth accounting and the negative real GDP response,

the capital response component accounts for two-thirds and the TFP response component

for about one-third. However, total hours worked exhibits a much ﬂatter response, with

no sign of labor hysteresis. Because capital enters the production function with a smaller

weight, it should be clear from the ﬁgure that most of the decline in GDP is explained by

the TFP variable, followed by capital , with total hours worked mostly ﬂat.

We may note that capital accumulation follows textbook dynamics in the short-run.

The capital response is initially muted but builds up over time. But unlike a textbook

New Keynesian model (Gal

ı, 2015b), the capital stock does not recover even after 12 years.

Similarly, TFP falls gradually rather than suddenly, and also does not recover.

But are these estimates based on the raw data accurate? One serious concern with

Solow decompositions, well known at least since the work of Basu and Kimball (1997), is

the issue of capacity utilization biases (See also Basu, Fernald, and Kimball 2006). When

measures the capital stock, as here, that is not capital input: input is only the capital

being used, possibly much lower in periods of slack when plant and equipment may be

idling. Likewise if

measures labor stock, but even if it measures total hours this may

be biased upwards in periods of slack if labor is hoarded, and not fully utilized. In such

cases, na

ıve use of the Solow approach will result in mismeasured factor inputs with too

weak cyclicality, leaving residual TFP with too strong cyclicality, a pervasive problem that

exaggerates the role of TFP shocks as a source of business cycles. Therefore, following the

literature, we revise the capital and labor raw data to account for cyclicality in utilization,

following the well-established method proposed by Imbs (1999). The results are shown in

Figure 3b, and reveal some subtle differences. Overall the responses are similar in terms of

shape and statistical signiﬁcance, so the qualitative story is the same. But quantitatively,

the TFP response is now muted in amplitude, as expected, and the factor responses are

accordingly larger, suggesting that the Imbs correction captures some utilization-driven

For comparability, we use the same controls in estimating responses of various components of the

production function as those used for the GDP response.

Figure 3:

Baseline response to 100 bps shock: Real GDP and Solow decomposition. Full sample, 1890–2015.

(a) Estimates using raw data

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Real GDP

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Labor

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Capital

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

TFP

(b) Estimates using Imbs correction for factor utilization

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Real GDP

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Labor

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Capital

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

TFP

Notes: Response to a 100 bps shock in domestic short-term interest rate instrumented with the trilemma IVs. Full sample: 1890–2015

(World Wars excluded). LP-IV estimates displayed as a thick lines and and 1 S.E. and 2 S.E. conﬁdence bands. The upper panel uses

raw data on capital stocks and total hours to construct TFP as a residual. The lower panel adjusts the raw data on capital stock and total

hours to obtain estimates of actual factor inputs by using the Imbs (1999) correction. Estimation is robust with clustering by country.

See text.

Figure 4:

Baseline short term nominal interest rate own response to 100 bps shock. Full sample, 1890–2015.

-.5 0 .5 1 1.5

Percent

0 4 8 12

Year

Notes: Response to a 100 bps shock in domestic short-term interest rate instrumented with the trilemma IVs. Full sample: 1890–2015

(World Wars excluded). LP-IV estimates displayed as a thick line and and 1 S.E. and 2 S.E. conﬁdence bands. Estimation is robust with

clustering by country. See text.

factor slack. We proceed using these Imbs-corrected responses as our baseline henceforth,

since they give a smaller (i.e., conservative) response of TFP and we wish to guard against

exaggerating our proposed hysteresis channel which runs via TFP.

Finally, we verify that the long-run responses we have found and not a simple mechanical

result of unusually persistent shock impulses. One possible explanation for the long-lasting

effects of the monetary shock could be that domestic interest rates remain elevated for a

long period of time as well. In other words, persistence is generated by a delayed response

in interest rates. A simple check shows that this is not the case. Figure 4 shows that the

short-term nominal interest rate returns to zero deviation after about 4 years. The response

of the nominal interest rate is typical of what has been reported often in the literature (see,

e.g., Christiano, Eichenbaum, and Evans, 1999; Ramey, 2016).

5.3. Robustness and discussion

Our baseline LP was quite saturated, and included lags and current values of global GDP

growth. This rich speciﬁcation served multiple purposes. Global shocks that caused bases

to change interest rates are controlled for during instrument construction, as well through

use of these controls during estimation of the local projections. Comparison with OLS

estimates, which control for contemporaneous home economy macro-variables (as in a

Cholesky ordering), further allay some concerns on systematic structural breaks in GDP or

TFP growth picked up as regime shifts over decades.

We now discuss further robustness checks to ensure that the persistent effects we

identiﬁed are not misattributed to monetary policy shocks.

Spillover correction for the trilemma instrument

A violation of the exclusion restriction

could occur if base rates affect home outcomes through channels other than movements

in home rates, as underscored in the theoretical model. Additional inﬂuences via such

channels are sometimes referred to as spillover effects. These could occur if base rates

proxy for factors common to all countries. That said, these factors would have to persist

despite having included global GDP to soak up such variation. Or they could occur for

other reasons, such as spillovers via trade. In addition to the control strategy used in our

baseline speciﬁcation, we now assess such spillover effects more formally by estimating a

spillover-corrected IV speciﬁcation developed in Section 2.4.

Equations 27 and 34 generalize our baseline IV estimator to accommodate spillovers

that vary with size of export share in the peg economies. With a range of values for

Φ ∈ [0.1, 0.3]

, we estimate the cumulative impulse responses to GDP. Figure 5 shows our

spillover-corrected estimates of response of output to a 100 bps monetary policy shock. A

light-green shaded area with dashed border shows the spillover corrections. While the

impulse response coefﬁcients at year 12 are somewhat smaller than the baseline estimates

(solid blue line), monetary policy shocks still exert a sizable persistent effect on output.

External factors and structural breaks

A cruder approach to validate the exclusion re-

striction is by directly controlling for a primary channel through which the spillover effects

may originate. A monetary tightening in the base country may reduce the demand for

goods from the pegging economy. This effect would amplify the effect of the trilemma

shock on home output. With soft peg regimes, there may be further effects through changes

in nominal exchange rates (Gourinchas, 2018). To account for these effects, we control for

global GDP growth rate, base country’s GDP growth rate, exchange rate of the pegging

economy with respect to the USD and the current account of the peg. Since we do not have

exchange rate data with respect to other countries, we indirectly control for those spillovers

using the current account of the peg country.

Figure 6a plots the IRFs to the trilemma identiﬁed shock. Directly controlling for open-

economy variables, motivated by export demand channels, does not affect our main result:

monetary shocks still have a large and very persistent effect on real GDP.

Fernald (2014) and Gordon (2016) have convincingly argued that there are structural

breaks in U.S. TFP growth. One may suspect that there are structural breaks in other

Figure 5: Response to 100 bps trilemma shock with spillover corrections: Real GDP.

(a) Full sample: 1890–2015.

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

IV OLS IV spillover corrected

(b) Post-WW2 sample: 1948–2015.

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

IV OLS IV spillover corrected

Notes: Response to a 100 bps shock in domestic short-term interest rate instrumented with the trilemma IVs. Full sample: 1890–2015

(World Wars excluded). Post-WW2 sample: 1948–2015. LP-OLS estimates displayed as a dashed red line, LP-IV estimates displayed

as a solid blue line with 1 S.E. and 2 S.E. conﬁdence bands, LP-IV spillover corrected estimates displayed as a light green shaded area

with dashed border, using Φ ∈ [0.1, 0.3]. Estimation is robust with clustering by country. See text.

Figure 6:

Response to 100 bps trilemma shock with additional controls: Real GDP. Full sample, 1890–2015.

(a) Open economy model based controls

-6 -4 -2 0 2

Percent

0 4 8 12

Year

(b) Structural breaks in TFP growth

-6 -4 -2 0 2

Percent

0 4 8 12

Year

Notes: Response to a 100 bps shock in domestic short-term interest rate instrumented with the trilemma IVs. Full sample: 1890–2015

(World Wars excluded). LP-IV estimates displayed as a solid blue line with 1 S.E. and 2 S.E. conﬁdence bands. Estimation is robust

with clustering by country. See text.

economies’ TFP growth rates as well. If such structural breaks coincide in time with

monetary shocks of the same sign, they could bias our results. To address this concern, we

ﬁrst estimate ﬁve structural breaks in TFP growth and GDP growth for each country in

our sample using the UD-max statistic of Bai and Perron (1998). We report these estimated

structural break dates in Appendix I.6. Then in our baseline speciﬁcation, we allow output

growth to lie in either of the ﬁve regimes at horizon zero.

Figure 6b plots the estimated impulse response when including structural breaks in

TFP growth. As evident, our results are robust to accounting for structural breaks.

conducted a variety of additional robustness checks reported in the Appendix, all of which

made no meaningful difference to the main results reported in this section.

6. A small-open economy model with long-run effects

Impulse responses calculated with standard methods that internally favor reversion to

the mean will tend to underestimate the value of the response at longer horizons. By

relying on local projections, we allow the data to more directly speak as to its long-run

properties. The evidence presented in the previous sections strongly indicate that these

long-run effects are important and require further investigation. In order to think through

a possible mechanism that explains our empirical ﬁndings, we augment our baseline model

with capital and endogenous productivity growth in a stylized manner.

We assume that physical capital is also used for production in the non-traded sector:

(i) = K

(i)

(

(i)

)

1−α

. As before, traded output is an endowment that grows at

rate of growth of

for stationarity along a balanced growth path. Non-traded output

is used for consumption and investment. As is standard in medium scale DSGE models

(Christiano, Eichenbaum, and Evans, 2005; Smets and Wouters, 2007; Justiniano, Primiceri,

and Tambalotti, 2013), we assume investment adjustment costs. We leave the formal model

to the appendix, and focus on the key departure that allows us to introduce long-run effects

on output and capital with a parametrically convenient process.

6.1. Long-run effects

In order to be able to capture the empirical features describe in the previous sections, we

examine a richer speciﬁcation of the low of motion for total factor productivity

than is

conventional. In particular, we assume that the law of motion for A

is:

log A

= log A

t−1

+ µ

+ η log



Nt−1

f ,t−1

Nt−1



, (35)

In the appendix I.5, we report the IRFs allowing for structural breaks in GDP growth.

where

is the exogenous component of the TFP growth rate, that may be subject to trend

shocks.

is non-traded output at time

f ,t−1

Nt−1

is the ﬂexible price level of output in

period

t − 1

conditional on

t−1

, and will be referred to as the potential output at time

t − 1

The second component denotes the endogenous component of TFP growth, where

is the

elasticity of TFP growth rate with respect to ﬂuctuations in output due to nominal rigidities.

We refer to this parameter as the hysteresis elasticity (so as to be consistent with DeLong and

Summers 2012).

The above law of motion allows business cycles to affect TFP growth rate only in the

presence of nominal rigidities or inadequate stabilization. For clarity, we employ this

parametric-convenient functional form for hysteresis. A similar setup was used by Stadler

(1990) in his seminal work. A micro-founded model of innovation and productivity growth

that yields this exact representation under monetary policy shocks can be found in the

recent literature embedding endogenous growth into DSGE models (Bianchi, Kung, and

Morales, 2019; Garga and Singh, Forthcoming). The effects of business cycles on TFP growth

rate that are unrelated to nominal rigidities can be denoted by time varying values of

which may depend on other shocks (markup shocks, stationary TFP shocks, discount factor

shocks, capital quality shocks etc.). For ease of exposition, we only focus on the hysteresis

effects induced by the presence of nominal rigidities and treat

as an exogenous process.

6.2. Government

The central bank follows a Taylor rule in setting the nominal interest rate

. It responds to

deviations in inﬂation, output and output growth rate from time-t natural allocations.

1 + i



1 + i

t−1

1 + i











f ,t





1−ρ

, (36)

where

is the steady state nominal interest rate,

is gross inﬂation rate,

is the steady

state inﬂation target,

f ,t

is the time-t natural output,

determines interest-rate smoothing

and e

∼ N(0, σ

) is the monetary policy shock.

We assume government balances budget every period, where total lump-sum taxes go

as a production subsidy to intermediate good producers, and a wage subsidy to workers.

In the presence of endogenous state variables, the timing assumptions on ﬂexible prices matter in

deﬁning appropriate natural rate. We follow Woodford (2003, Sec 5.4) in deﬁning natural rate as the level

of variables at time

such that prices are set ﬂexibly beginning at time

taking as given the evolution of

state-variables up to time t. See also Garga and Singh (Forthcoming) for a detailed discussion.

Table 3: Point estimates for hysteresis elasticity η

1890–2015 1948–2015

η 0.25 0.67

[95% conﬁdence interval] [0.21,0.30] [0.34,0.99]

Notes: The point estimates are estimated with a two-step classical minimum distance approach using the IRF of utilization-adjusted

TFP and the IRF of cyclical gaps to the monetary policy shock in the second step. See text.

6.3. Calibration and simulation

As the extended model is intentionally stylized, we take parameters from papers in the

literature (Justiniano et al., 2013; Schmitt-Groh

e and Uribe, 2016). We report these in the

appendix in Table A1. The new parameter in our model, relative to the business cycles

literature, is

: the hysteresis elasticity. Table 3 reports the point estimates for

implies by

the estimated impulse responses. We use a two-step classical minimum distance approach

to recover

. In the ﬁrst step, we estimate the IRFs of utilization-adjusted TFP and a

measure of cyclical gap to monetary policy shock. Using the estimated coefﬁcients (see

Figure 3), we then estimate

using Equation 35.

Following the persistent drop in output

after the Great Recession in the US, DeLong and Summers (2012) infer that this parameter

could be as high as

0.24

. While our estimate is on the higher side, there is considerably

large conﬁdence interval. In our calibration henceforth, we use the value of 0.25.

Figure 7 plots the model-implied impulse responses for output, capital stock, and

utilization-adjusted TFP after a monetary policy shock. Solid blue line reports the IRFs

for endogenous growth model with

η = 0.25

, and dashed blue line reports IRFs for the

comparable exogenous growth benchmark i.e.

η = 0

. The IRFs for output, capital stock

and TFP are plotted in percent deviations from an exogenous trend. Time is in quarters.

The model replicates the estimated empirical patterns. There is a persistent decline in

capital stock, output and TFP. A monetary shock reduces aggregate output and investment

in exogenous growth model, and they return back to their long-run levels. The effects of

monetary shock in an exogenous growth model do last for nearly six years, as can be seen

by slow recovery of capital stock to the pre-shock level. On the other hand, capital stock and

Formally, using the concept of time-

natural output (taking evolution of state variables up to time

as given), the cyclical output gap in the model with utilization adjustments is

log Y

− log Y

f ,t

= αu

+ ( 1 −

α)e

+ ( 1 − α) log L

, where

is capital utilization rate,

is labor-utilization rate, and

is labor input. Now,

let

be the estimated IRF of utilization-adjusted TFP (

) at horizon

, and let

be the estimated IRF of

the cyclical gap. We empirically estimate

and

h = 0, ..., 12

as in Figure 3b. Using Equation 35, we can

recover the estimating equation that delivers estimates for η as λ

= η

∑

k=0

Figure 7: Model response of output, capital stock, and TFP to a 100 bps increase in nominal interest rate

-2 -1.5 -1 -.5 0

Percent

0 10 20 30 40 50

Horizon

Exogenous growth model

Endogenous growth model

Output

-2 -1.5 -1 -.5 0

Percent

0 10 20 30 40 50

Horizon

Capital stock

-2 -1.5 -1 -.5 0

Percent

0 10 20 30 40 50

Horizon

TFP

Notes: The ﬁgure plots the model-implied IRFs for output, capital stock and utilization-adjusted TFP to a transitory shock to the

assumed Taylor rule. Solid blue line reports the IRFs for endogenous growth model with η = 0.25, and dashed red line reports IRFs for

the comparable exogenous growth benchmark i.e. η = 0. Time is in quarters. IRFs are traced following a one-time exogenous shock in

the federal funds rate of 100 basis points. The IRFs are plotted in percent deviations from an exogenous trend.

output do not return to pre-shock trend even after twelve years when TFP is endogenous.

Furthermore, the endogenous growth model exhibits considerable ampliﬁcation to the

transitory shock because of the large hysteresis elasticity.

7. Conclusion

This paper challenges the widely accepted view that money is neutral in the long-run.

We ﬁnd that monetary policy has real effects that last for a decade or more. We spent

considerable time and energy with the three pillars of our empirical strategy—identiﬁcation,

data, and methods—to ensure the reader that our results are solid. We believe they are.

The source of the main hysteresis result—that monetary policy shocks have long-lasting

effects on output—surprised us. We ﬁnd that capital and TFP growth are the main drivers

of this result, but not hours worked, in contrast to standard models of labor hysteresis. Our

ﬁndings do not negate the inﬂuence of labor frictions in shaping the business cycle. Instead,

we do not ﬁnd a strong role for such labor scarring in explaining why monetary policy has

such long-lived effects.

Our next task was to provide an economic framework to understand where our results

come from. We do this using the same open economy framework that we used to justify

our identiﬁcation of monetary policy shocks. Simple extensions to the existing paradigm

replicate the empirical ﬁndings that we document here.

There is much that is left unexplored in this paper. Determining the micro-foundations

that explain TFP growth hysteresis would require a different paper devoted to the topic

with a completely different data set. Exploring the optimality of the monetary policy rule in

more general settings, and the welfare consequences of the hysteresis results documented

here are of ﬁrst order importance for policymakers. Perhaps more importantly, our paper

challenges long-held views that require a reexamination of standard business cycle models.

References

Anzoategui, Diego, Diego Comin, Mark Gertler, and Joseba Martinez. 2019. Endogenous Technol-

ogy Adoption and R&D as Sources of Business Cycle Persistence. American Economic Journal:

Macroeconomics 11(3): 67–110.

Bai, Jushan, and Pierre Perron. 1998. Estimating and Testing Linear Models with Multiple Structural

Changes. Econometrica 66(1): 47–78.

Baqaee, David Rezza, and Emmanuel Farhi. 2019. Productivity and Misallocation in General

Equilibrium. Quarterly Journal of Economics 135(1): 105–163.

Barlevy, Gadi. 2004. The cost of business cycles under endogenous growth. American Economic

Review 94(4): 964–990.

Barro, Robert J. 2013. Inﬂation and Economic Growth. Annals of Economics and Finance 14(1): 85–109.

Basu, Susanto, and John G Fernald. 2002. Aggregate productivity and aggregate technology. European

Economic Review 46(6): 963–991.

Basu, Susanto, John G. Fernald, and Miles S. Kimball. 2006. Are Technology Improvements

Contractionary? American Economic Review 96(5): 1418–1448.

Basu, Susanto, and Miles S Kimball. 1997. Cyclical productivity with unobserved input variation.

NBER Working Paper 5915.

Benigno, Gianluca, and Luca Fornaro. 2018. Stagnation Traps. The Review of Economic Studies 85(3):

1425–1470.

Benigno, Gianluca, Luca Fornaro, and Martin Wolf. 2020. The global ﬁnancial resource curse. FRB of

New York Staff Report (915).

Bergeaud, Antonin, Gilbert Cette, and R

emy Lecat. 2016. Productivity Trends in Advanced Countries

between 1890 and 2012. Review of Income and Wealth 62(3): 420–444.

Berk, Kenneth N. 1974. Consistent autoregressive spectral estimates. Annals of Statistics 2(3): 489–502.

Bernanke, Ben S., and Ilian Mihov. 1998. The liquidity effect and long-run neutrality. Carnegie-

Rochester Conference Series on Public Policy 49(1): 149–194.

Bianchi, Francesco, Howard Kung, and Gonzalo Morales. 2019. Growth, slowdowns, and recoveries.

Journal of Monetary Economics 101(C): 47–63.

Blanchard, Olivier. 2018. Should We Reject the Natural Rate Hypothesis? Journal of Economic

Perspectives 32(1): 97–120.

Blanchard, Olivier J., and Lawrence H. Summers. 1986. Hysteresis and the European unemployment

problem. In NBER Macroeconomics Annual 1986, volume 1, 15–90. Cambridge, Mass.: MIT Press.

Blanchard, Olivier Jean, and Charles M. Kahn. 1980. The Solution of Linear Difference Models under

Rational Expectations. Econometrica 48(5): 1305–1311.

Calvo, Guillermo A. 1983. Staggered prices in a utility-maximizing framework. Journal of Monetary

Economics 12(3): 383–398.

Cerra, Valerie, Antonio Fat

as, and Sweta Saxena. 2020. Hysteresis and Business Cycles. CEPR

Discussion Paper 14531.

Christiano, Lawrence. 2015. Applications of DSGE Model: What Happens if we Switch from Fixed

to Flexible Interest Rate Regime? Unpublished. Northwestern University.

Christiano, Lawrence J., Martin Eichenbaum, and Charles L. Evans. 1999. Monetary policy shocks:

What have we learned and to what end? In Handbook of Macroeconomics, edited by Taylor, J. B., and

M. Woodford, volume 1 of Handbook of Macroeconomics, chapter 2, 65–148. Amsterdam: Elsevier.

Christiano, Lawrence J., Martin Eichenbaum, and Charles L. Evans. 2005. Nominal Rigidities and

the Dynamic Effects of a Shock to Monetary Policy. Journal of Political Economy 113(1): 1–45.

DeLong, Bradford J., and Lawrence H. Summers. 2012. Fiscal Policy in a Depressed Economy.

Brookings Papers on Economic Activity 1: 233–297.

Durbin, J. 1959. Efﬁcient Estimation of Parameters in Moving-Average Models. Biometrika 46(3/4):

306–316.

Eggertsson, Gauti B., and Michael Woodford. 2003. The Zero Bound on Interest Rates and Optimal

Monetary Policy. Brookings Papers on Economic Activity 2003(1): 139–211.

Farhi, Emmanuel, and Ivan Werning. 2012. Dealing with the Trilemma: Optimal Capital Controls

with Fixed Exchange Rates. NBER Working Paper 18199.

Farhi, Emmanuel, and Iv

an Werning. 2017. Fiscal Unions. American Economic Review 107(12):

3788–3834.

Fat

as, Antonio. 2000. Do business cycles cast long shadows? Short-run persistence and economic

growth. Journal of Economic Growth 5(2): 147–162.

Fernald, John G. 2014. A quarterly, utilization-adjusted series on total factor productivity. Federal

Reserve Bank of San Francisco Working Paper 2012-19.

Fornaro, Luca. 2015. Financial crises and exchange rate policy. Journal of International Economics

95(2): 202–215.

Fornaro, Luca, and Federica Romei. 2019. The Paradox of Global Thrift. American Economic Review

109(11): 3745–79.

Gal

ı, Jordi. 2015a. Hysteresis and the European Unemployment Problem Revisited. NBER Working

Paper 21430.

Gal

ı, Jordi. 2015b. Monetary policy, inﬂation, and the business cycle: an introduction to the new Keynesian

framework and its applications. Princeton, N.J.: Princeton University Press.

Gal

ı, Jordi, and Tommaso Monacelli. 2016. Understanding the Gains from Wage Flexibility: The

Exchange Rate Connection. American Economic Review 106(12): 3829–68.

Garga, Vaishali, and Sanjay R. Singh. Forthcoming. Output hysteresis and optimal monetary policy.

Journal of Monetary Economics .

Gopinath, Gita,

S¸

ebnem Kalemli-

Ozcan, Loukas Karabarbounis, and Carolina Villegas-Sanchez.

2017. Capital Allocation and Productivity in South Europe. Quarterly Journal of Economics 132(4):

1915–1967.

Gordon, Robert J. 2016. The Rise and Fall of American Growth: The U.S. Standard of Living since the Civil

War. Princeton, N.J.: Princeton University Press.

Gourinchas, Pierre-Olivier. 2018. Monetary Policy Transmission in Emerging Markets: An Appli-

cation to Chile. In Monetary Policy and Global Spillovers: Mechanisms, Effects and Policy Measures,

edited by Mendoza, Enrique G., Ernesto Past

en, and Diego Saravia, volume 25 of Central Banking,

Analysis, and Economic Policies Book Series, chapter 8, 279–324. Santiago: Central Bank of Chile.

Guerrieri, Luca, and Matteo Iacoviello. 2015. OccBin: A toolkit for solving dynamic models with

occasionally binding constraints easily. Journal of Monetary Economics 70(C): 22–38.

Hume, David. 1752. ‘Of Money’, ‘Of Interest’ and ‘Of the Balance of Trade’. In Essays Moral, Political,

and Literary, edited by Miller, Eugene F. Indianapolis, Ind.: Liberty Fund.

Ilzetzki, Ethan, Carmen M. Reinhart, and Kenneth S. Rogoff. 2019. Exchange Arrangements Entering

the Twenty-First Century: Which Anchor will Hold? Quarterly Journal of Economics 134(2): 599–646.

Imbs, Jean M. 1999. Technology, growth and the business cycle. Journal of Monetary Economics 44(1):

65–80.

Jord

Oscar. 2005. Estimation and Inference of Impulse Responses by Local Projections. American

Economic Review 95(1): 161–182.

Jord

Oscar, Moritz Schularick, and Alan M. Taylor. 2016. The great mortgaging: housing ﬁnance,

crises and business cycles. Economic Policy 31(85): 107–152.

Jord

Oscar, Moritz Schularick, and Alan M. Taylor. 2017. Macroﬁnancial History and the New

Business Cycle Facts. NBER Macroeconomics Annual 31(1): 213–263.

Jord

Oscar, Moritz Schularick, and Alan M. Taylor. 2020. The effects of quasi-random monetary

experiments. Journal of Monetary Economics 112: 22–40.

Justiniano, Alejandro, Giorgio E. Primiceri, and Andrea Tambalotti. 2013. Is There a Trade-Off

between Inﬂation and Output Stabilization? American Economic Journal: Macroeconomics 5(2): 1–31.

Kilian, Lutz. 1998. Small-sample Conﬁdence Intervals for Impulse Response Functions. Review of

Economics and Statistics 80(2): 218–230.

King, Robert G., and Mark W. Watson. 1997. Testing Long-Run Neutrality. Federal Reserve Bank of

Richmond Economic Quarterly 83(3): 69–101.

Kuersteiner, Guido M. 2005. Automatic Inference For Inﬁnite Order Vector Autoregressions. Econo-

metric Theory 21(1): 85–115.

Las

een, Stefan, and Lars E. O. Svensson. 2011. Anticipated Alternative Policy Rate Paths in Policy

Simulations. International Journal of Central Banking 7(3): 1–35.

Lewis, Richard, and Gregory C. Reinsel. 1985. Prediction of multivariate time series by autoregressive

model ﬁtting. Journal of Multivariate Analysis 16(3): 393–411.

Lusompa, Amaze B. 2019. Local projections, autocorrelation, and efﬁciency. Unpublished. UC Irvine.

Mankiw, N. Gregory. 2001. The inexorable and mysterious tradeoff between inﬂation and unem-

ployment. Economic Journal 111(471): 45–61.

Meier, Matthias, and Timo Reinelt. 2020. Monetary Policy, Markup Dispersion, and Aggregate TFP.

University of Mannheim. Unpublished.

Montiel Olea, Jos

e Luis, and Mikkel Plagborg-Møller. 2019. Simultaneous conﬁdence bands: Theory,

implementation, and an application to SVARs. Journal of Applied Econometrics 34(1): 1–17.

Moran, Patrick, and Albert Queralto. 2018. Innovation, productivity, and monetary policy. Journal of

Monetary Economics 93: 24–41.

Nakamura, Emi, and J

on Steinsson. 2018. Identiﬁcation in Macroeconomics. Journal of Economic

Perspectives 32(3): 59–86.

Obstfeld, Maurice, and Kenneth Rogoff. 1995a. Exchange rate dynamics redux. Journal of Political

Economy 103(3): 624–660.

Obstfeld, Maurice, and Kenneth Rogoff. 1995b. The Mirage of Fixed Exchange Rates. Journal of

Economic Perspectives 9(4): 73–96.

Obstfeld, Maurice, Jay C. Shambaugh, and Alan M. Taylor. 2004. Monetary sovereignty, exchange

rates, and capital controls: The trilemma in the interwar period. IMF Staff Papers 51(3S1): 75–108.

Obstfeld, Maurice, Jay C. Shambaugh, and Alan M. Taylor. 2005. The Trilemma in History: Tradeoffs

Among Exchange Rates, Monetary Policies, and Capital Mobility. Review of Economics and Statistics

87(3): 423–438.

Quinn, Dennis, Martin Schindler, and A. Maria Toyoda. 2011. Assessing measures of ﬁnancial

openness and integration. IMF Economic Review 59(3): 488–522.

Ramey, Valerie A. 2016. Macroeconomic Shocks and Their Propagation. In Handbook of Macroeco-

nomics, edited by Taylor, John B., and Harald Uhlig, volume 2 of Handbook of Macroeconomics,

chapter 2, 71–162. Amsterdam: Elsevier.

Schmitt-Groh

e, Stephanie, and Martın Uribe. 2003. Closing small open economy models. Journal of

international Economics 61(1): 163–185.

Schmitt-Groh

e, Stephanie, and Martin Uribe. 2016. Downward Nominal Wage Rigidity, Currency.

Pegs, and Involuntary Unemployment. Journal of Political Economy 124(5): 1466–1514.

Shambaugh, Jay C. 2004. The Effect of Fixed Exchange Rates on Monetary Policy. Quarterly Journal

of Economics 119(1): 301–352.

Smets, Frank, and Rafael Wouters. 2007. Shocks and Frictions in US Business Cycles: A Bayesian

DSGE Approach. American Economic Review 97(3): 586–606.

Stadler, George W. 1990. Business Cycle Models with Endogenous Technology. American Economic

Review 80(4): 763–78.

Syverson, Chad. 2011. What determines productivity? Journal of Economic Literature 49(2): 326–365.

Uribe, Martin, and Stephanie Schmitt-Groh

e. 2017. Open Economy Macroeconomics. Princeton, N.J.:

Princeton University Press.

Werning, Ivan. 2011. Managing a Liquidity Trap: Monetary and Fiscal Policy. NBER Working

Papers 17344, National Bureau of Economic Research, Inc.

Woodford, Michael. 2003. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton,

N.J.: Princeton University Press.

Yellen, Janet L. 2016. Macroeconomic Research After the Crisis. Speech at the conference “The

Elusive ‘Great’ Recovery: Causes and Implications for Future Business Cycle Dynamics,” Federal

Reserve Bank of Boston, October.

Online Appendix

A. Proofs of consistency for impulse responses

This section provides the basic ideas behind the proofs of consistency for truncated VARs and

LPs when the true DGP is an invertible MA(

∞

). The reader is referred to the references cited for

additional details.

A.1. Data generating process and main assumptions

Assume the data generating process for the m–dimensional vector process y

is:

∞

∑

j=0



t−j

; B

= I;

∞

∑

j=0

||B

|| < ∞ , (37)

where

||B

= tr(B

)

and

B(z) =

∑

∞

j=0

such that

det{B(z)} 6= 0

for

|z| ≤ 1.

Under these

assumptions, this invertible MA(∞) can also be expressed as:

∞

∑

j=1

t−j

+ 

;

∞

∑

j=1

||A

|| < ∞; det{A(z)} 6= 0 for |z| ≤ 1 .

Further, we make assumptions 1–4 following Lewis and Reinsel (1985), and Lusompa (2019) (Kuer-

steiner (2005) makes somewhat stronger assumptions because he later derives testing procedures to

determine the optimal lag length). These assumptions are:

Assumption 1 {y

} is generated by Equation 37.

Assumption 2 E|e

| ≤ γ

< ∞ for 1 ≤ i, j, k, l ≤ m.

Assumption 3

The truncation lag

is chosen as a function of the sample size

such that

/T → 0 as p, T → ∞.

Assumption 4 p is chosen as a function of T such that

1/2

∞

∑

j=p+1

||A

|| → 0 as p, T → ∞.

Then, as discussed in the text, Lewis and Reinsel (1985) show:

− A

−→ 0 as p, T → ∞.

This well-known result says that even when the data are generated by an inﬁnite-order process, the

coefﬁcients of the ﬁrst

terms are consistently estimated. We show next that despite this result,

inconsistencies in the estimation of impulse responses can crop up.

A.2. Potential sources of bias in truncated VARs

In ﬁnite samples, inconsistent estimates of the impulse response function can arise from at least two

sources that we now quantify: (1) the truncation lag is too short given Assumptions 1–4; and (2) the

truncation lag is appropriate, but the impulse response is calculated for periods that extend beyond

the truncation lag. To investigate the ﬁrst source of inconsistency, rewrite the VAR(∞) as

∑

j=1

t−j

+ u

∑

j=k+1

t−j

∞

∑

j=p+1

t−j

+ 

where we assume

k < p

and

is the truncation lag that meets Assumptions 1–4 of the proof of

consistency. Hence rewrite the previous expression as

= A(k)X

k,t−1

+ u

; A(k) = (A

, . . . , A

); X

k,t−1

= (y

t−1

, . . . , y

t−k

)

The least-squares estimate of A(k) is therefore

A(k) =

T − k

∑

k,t−1

T − k

∑

k,t−1

−1

Hence

A(k) = A(k) +

T − k

∑

k,t−1

T − k

∑

k,t−1

−1

Given the three components of

, it is easy to see that the source of inconsistency in estimates of

the ﬁrst k autoregressive terms will come from the component

T − k

∑

j=k+1

t−j

k,t−1

T − k

∑

k,t−1

−1

since the proof of consistency in Lewis and Reinsel (1985) shows that the other two terms vanish

asymptotically. The source of inconsistency can be quantiﬁed by noticing that

T − k

∑

k,t−1

−1

→







Γ(0) Γ(1) · · · Γ(k)

Γ(1) Γ(0) · · · Γ(k − 1)

Γ(k) Γ(k − 1) · · · Γ( 0)







−1

→ Γ

−1

as shown in Lewis and Reinsel (1985), where

E(y

t−j

) = Γ(j)

and

Γ(−j) = Γ(j)

. Hence, asymptot-

ically, the source of inconsistency is

∑

k+1

(

Γ(j − 1), . . . , Γ(j − k)

)

−1

However, even when the lag-length

is chosen to be sufﬁciently large, another source of bias can

crop up into the estimation of the impulse response. In particular, following Durbin (1959), we know

that

= A

h−1

+ A

h−2

+ · · · + A

h−1

+ A

If the VAR is truncated at lag k, for k ≤ p, it is easy to see that the previous expression becomes

= A

h−1

+ A

h−2

+ · · · + A

k−h

+ A

k+1

k−h−1

+ · · · + A

h−1

+ A

| {z }

remainder

and, hence,

− B

|| = ||A

k+1

(

k−h−1

− B

k−h−1

) + . . . + A

h−1

(

− B

) + A

|| 6→ 0 ,

since ||

k+j

− B

k+j

|| for j ≥ 1 is not guaranteed to vanish asymptotically.

Next notice that the impulse response for horizons h > k will be estimated using the recursion

k+j

k+j−1

+ . . . +

; j = 1, . . . , H .

Even if k = p, and hence ||

|| → A

for j = 1, . . . , k, the fact remains that the remainder term

k+1

k−h−1

+ · · · + A

h−1

+ A

cumulates increasing sums of coefﬁcients that are not estimated in the model. As the Monte Carlo

exercise showed earlier, the inconsistency at longer horizons tends to accumulate.

A.3. The consistency of the local projections estimator

In this section we use the same assumptions as in the previous section to establish the consistency

of the local projections estimator at any horizon.

Using the VAR(∞) representation of the DGP and recursive substitution, it is easy to see that

t+h

= B

h+1

t−1

+ {C

h+2

t−2

+ C

h+3

t−3

+ · · · } + e

t+h

+ B



t+h−1

+ 

where

h+2

= B

+ · · · + B

+ A

h+1

h+3

= B

+ · · · + B

h+1

+ A

h+2

h+k

= B

k−1

+ · · · + B

h+k−2

+ A

h+k−1

Now, consider truncating the lag of the local projection at

k = p

, where

meets Assumptions 1–4 of

the Lewis and Reinsel (1985) consistency theorem discussed in the previous section.

Then the truncated local projection can be written as

t+h

= B

h+1

t−1

+ C

h+2

t−2

+ C

h+3

t−3

· · · + C

h+k

t−k

+ u

t+h

= 

t+h

+ {B



t+h−1

+ B



t+h−2

+ · · · + B



} + {C

h+k+1

t−k−1

+ C

h+k+2

t−k−2

+ · · · } .

Let

D = (B

, C

h+2

, . . . , C

h+k

)

and

t−1

= (y

t−1

, . . . , y

t−k

)

as deﬁned earlier but where the

subscript k is omitted here for simplicity. Then the local projection can be compactly written as

t+h

= DX

t−1

+ u

t+h

The least-squares estimate of D is simply

D =

T − h − k

T−h

∑

t+h

t−1

T − h − k

T−h

∑

t−1

−1

from where consistency can be determined from the following expression

D = D +

T − h − k

T−h

∑

t+h

t−1

T − h − k

T−h

∑

t−1

−1

Lewis and Reinsel (1985) show that

||Γ

−1

is uniformly bounded where we use the fact that

||AB||

≤ ||A||

||B||

;

as well as

||AB||

≤ ||A||

||B||

where

||C||

= sup

l6=0

Cl/l

, the largest

eigenvalue of C

C (see Wiener and Masani, 1958).

Now we turn our focus to the terms

T − h − k

T−h

∑

t+h

t−1

T − h − k

T−h

∑

(

t+h

+ B



t+h−1

+ · · · + B



t−1

T − h − k

T−h

∑

h+k

t−k−1

+ C

h+k+1

t−k−2

+ · · · )X

t−1

It is easy to see that

T − h − k

T−h

∑



t+h

t−1

→ 0 ,

T − h − k

T−h

∑



t+h−j

t−1

→ 0 ,

since ||B

|| < ∞ for j = 1, · · · , h. Hence, the only tricky part is to examine the terms

h+k+j

T − h − k

T−h

∑

t−k−(j+1)

t−1

for j = 0, 1, . . . .

Note that

h+k+j

= B

k+k

+ · · · + B

h+k+j−1

+ A

h+k+j

j = 0, 1, . . . ,

hence

∞

∑

j=0

||C

h+k+j

|| =

∞

∑

j=0

||B

k+k

+ · · · + B

h+k+j−1

+ A

h+k+j

≤

∞

∑

j=0

||B

k+j

|| + · · · +

∞

∑

j=1

||B

h+k+j−1

|| +

∞

∑

j=0

||A

h+j+j

= ||B

∞

∑

j=0

||A

k+j

|| + · · · + ||B

∞

∑

j=1

||A

h+k+j−1

|| +

∞

∑

j=0

||A

h+k+j

||.

From the assumptions we know that the ||B

are uniformly bounded, and also that

1/2

∞

∑

j=0

||A

k+j

|| → 0 =⇒ k

1/2

∞

∑

j=0

||C

h+k+j

|| → 0 ,

and this condition can now be used to show that

∑

∞

j=0

h+k+j

T − h − k

T−h

∑

t−k−(j+1)

t−1

→ 0, as k, T → ∞ .

Summarizing, these derivations show that the same conditions that ensure consistency of the

coefﬁcients estimates in a truncated VAR also ensure consistency of the local projections with

truncated lag length. However, because the coefﬁcient for

t−1

in the local projection is a direct

estimate of the impulse response coefﬁcient, then we directly get a proof of consistency for the

coefﬁcients of the impulse response at any horizon regardless of truncation.

A.4. Monte Carlo results for impulse response estimators

This section provides details of the Monte Carlo experiments reported in the main text in addition

to presenting complementary Monte Carlo experiments based on the same simulated data, but

presenting the impulse response (rather than the cumulated response itself).

The data are generated as a

MA(25)

model whose coefﬁcients are generated by the following

Gaussian Basis Function:

= a exp(−((j − b)/c)

)

for

j = 1, . . . , 25

and for

a = −0.5; b = 12;

and

c = 6

. This results in the impulse and cumulative responses shown in panel (a) of Figure 1.

The error terms are assumed to be standard Gaussian. The left hand side variable is expressed

in the differences to replicate exactly the estimation of the cumulative response in the empirical

section. We simulate samples of size 1,500, but the ﬁrst 500 observations are then discarded to avoid

initialization issues. Using these data, we then estimate

AR(k)

models for

k = 3, 6, 9, 12

and local

projections using 2 lags.

As a complement to Figure 1, Figure A1 presents the experiments based on the impulse response

itself to illustrate the consistency of the

AR(k)

estimators up to horizon

h ≤ k

but not beyond. The

solid blue line is the true response based on our parameter choices for the D.G.P. The dashed blue

line with Monte Carlo one and two standard error bands are the local projections using two lags

only. The dotted maroon lines are the impulse responses from AR models with 3, 6, 9, and 12 lags as

in the Monte Carlo in the main text. As the ﬁgure clearly shows, impulse response coefﬁcients are

estimated well using the

AR(k)

models up to horizon

h = k

, as the asymptotic theory just presented

showed. In contrast, the local projection estimator does well across all horizons. The cumulative

versions of these responses are the experiments reported in Figure 1 in the main text.

Figure A1:

Estimating non-cumulative responses: autoregressive versus local projection biases at long

horizons.

-.15 -.1 -.05 0 .05 .1

0 5 10 15 20 25

Horizon

True LP AR(3)

AR(6) AR(9) AR(12)

Notes: sample size = 1,000. Monte Carlo replications: 1,000. Error bands in light blue are 1 and 2 standard error bands based on the

local projection Monte Carlo average. AR(k) for k = 3, 6, 9, 12 refers to impulse responses from an autoregressive model with k lags.

See text.

B. Equilibrium conditions in the baseline model

A perfect foresight equilibrium in the baseline model (subsection 2.1) is given by a sequence of

16 processes

, C

, d

t+1

, p

, Π

, R

, w

, L

, ∆

pNt

, E

, Π

, K

Npt

, Z

Npt

}

that satisfy the

following equilibrium conditions for a given sequence of exogenous processes

, R

∗

, Π

∗

}

and

initial values {d

, E

−1

, p

−1

, ∆

pN−1

+ d

= Y

t+1

, (38)







1 − ω



1−ω

, (39)

(1 − ω) C

ωC

, (40)

−1

= βE

(

−1

Tt+1

)

, (41)

−1

= βE

−1

Tt+1

, (42)

= R

∗

+ ψ(e

t+1

−

− 1) , (43)

Npt

, (44)

Npt

− 1

(1 − τ

) w

+ θ

Tt+1

Nt+1

Npt+1

, (45)

Npt

= p

+ θ

Tt+1

−1

Nt+1

Npt+1

, (46)

1 = θ

−1

+ (1 − θ

)

1−e

, (47)

ϕL

= w

, (48)

∆

= C

, (49)

∆

= (1 − θ

)

−e

+ θ

∆

Nt−1

, (50)

t−1

, (51)

t−1

∗

. (52)

and one of the following three equations for the respective policy regime:

= 1 (peg)

= 1 (ﬂoat)

(benchmark)

C. Solution for the baseline model

The following system of equations solves for equilibrium in ﬁve endogenous variables under the

peg and benchmark economy respectively:

Tt+1

−

∗

, (53)

Nt+1

− (

−

Nt+1

) , (54)

= β

Nt+1

+ κ

, (55)

t+1

−

∗

, (56)

t+1

−

= 0 , (peg)

= ε

. (benchmark)

Furthermore, let the shocks to R

∗

or ε

follow AR(1) process with persistence ρ.

We solve the model backwards. Denote the time at which the economy returns back to initial

steady state with

t + 1

such that

t+1

∗

t+1

= 0

. Tradable

goods consumption, under a peg, is given by

t−s

= −

∑

j=0

∗

t−j

; ∀ 0 ≤ s ≤

, whereas tradable goods’ consumption does not change in response to shock to

in the benchmark

economy. The solution of non-tradable output and non-tradable goods inﬂation is given by

t−s

= −α

t−s

;

t−s

= −α

t−s

where for

s < 0

t−s

= α

t−s

= 0

;

= 1

= κ

; and

∀ 0 < s ≤

t−s



t−s+1

+ α

t−s+1



ρ + 1 > 0; and α

t−s



κα

t−s

+ ρβα

t−s+1



> 0.

For a similar shock process, the drop in non-tradable output is identical across the peg and

benchmark economies.

D. Extension: time-varying aggregation weights

We consider the more general extension of the baseline model (subsection 2.1) allowing for time-

variation in aggregation weights in the construction of total output. The consumption aggregator is :

= ΨC

1−ω

, where

Ψ ≡ ω

−ω

(1 − ω)

1−ω

is a scaling factor. This implies that domestic CPI is

given by

= P

1−ω

. Total nominal output is

+ P

. Let total output be denoted with

, and is given by:

+ P

= p

ω−1

+ p

where p

≡

. From the optimality conditions, we have that

(1 − ω) C

ωC

In terms of log-deviations from steady state, total output is given by

( ω − 1)p

ω−1

+ ωp



−



When ω → 0 (tradable goods share is inﬁnitesimally small),

= p

−1



−



In the baseline model, with exogenous endowment of tradable goods,

= p

−1



−



Recall that

is identical across the peg and the benchmark economy as proved in Proposition

2. From results in Appendix C, sequence of

< 0

under a peg and equal to 0 under benchmark

economy. Hence the response of total output under a peg is downward biased relative to that under

the benchmark economy, where the bias is given by:

−1

∑

j=0

∗

t−s

; ∀ 0 ≤ s ≤

. The converse

result applies when ω → 1.

E. Extension: endogenous tradable output in the baseline model

We extend the baseline model (subsection 2.1) by allowing tradable output to be produced with a

constant returns to scale production function in labor. Labor is fully mobile across the tradable and

non-tradable sector. Thus, economy-wide real wages (in units of tradable goods) are constant. The

Furthermore, it follows from the above solution, the drop in non-tradable goods output is larger than the

drop in tradable goods consumption due to a deﬂationary effect of the shock on non-tradable goods prices.

intra-temporal labor supply condition is



+ (1 −

)



= 0 ,

where

is fraction of total labor force allocated to the tradable goods sector in the steady state.

The non-tradable goods price-Phillips curve is

= β

Nt+1

+ κ

− κ

The rest of the equations are same as described in Appendix C. We show the solution under two

assumptions on persistence of the shock process.

E.1. One period unanticipated shock

When the shock is one-period lived at time

, then the solution of non-tradable output at time

(when the shock hits) is given by

= −

The tradable goods output at time t

is given by

= −

−1

−



− 1



The tradable goods output production goes up in response to a one-time increase in

in the

benchmark economy and

∗

in the peg economy. This arises due to an increase in labor supply in

the tradable goods sector following a contraction in demand for labor in the non-tradable sector.

While the impulse response of non-tradable output is identical across the peg and the benchmark

economy, total output response is biased downwards in the peg economy relative the benchmark

economy. The downward bias is given by

−ν

−1

, where

= −

∗

for the peg economy.

The tradable goods consumption does not change in response to shock to

in the benchmark

economy.

E.2. Unanticipated AR(1) shock

Let the shocks to R

∗

or ε

follow AR(1) process with persistence ρ.

We solve the model backwards. Denote the time at which the economy returns back to initial

steady state with

t + 1 such that

t+1

∗

t+1

= 0.

Benchmark Economy

Tradable goods consumption does not change in response to shock to

in the benchmark econ-

omy. The response of non-tradable output and non-tradable goods’ inﬂation is same as solved in

Appendix C. That is, the solution of non-tradable output and non-tradable goods inﬂation is given

t−s

= −α

t−s

;

t−s

= −α

t−s

where for

s < 0

t−s

= α

t−s

= 0

;

= 1

= κ

; and

∀ 0 < s ≤

t−s



t−s+1

+ α

t−s+1



ρ + 1 > 0; and α

t−s



κα

t−s

+ ρβα

t−s+1



> 0.

The tradable goods output is given by

= −



− 1



∀t .

Peg Economy

Tradable goods consumption, under a peg, is given by

t−s

= −

∑

j=0

∗

t−j

; ∀ 0 ≤ s ≤

t .

Under a peg, the solution of non-tradable output and non-tradable goods inﬂation is given by

t−s

= −

∑

j=0

∗

t−j

;

t−s

= 0 .

The tradable goods output is given by

= −

−1

−



− 1



∀t .

E.3. Downward bias in estimates from peg

The response of total output is downward biased under a peg relative to that under the benchmark

economy. With a persistent shock, there are two sources of bias: 1) increase in tradable goods

production is higher under a peg relative to the benchmark economy, and (2) reduction in non-

tradable goods output is lower under a peg relative to the benchmark economy. The second source

of bias is absent in the case of a one-period shock.

F. A medium scale small-open economy DSGE model with hysteresis

Relative to the baseline model, production of non-tradable goods uses capital as well as labor.

Investment is done in the form of non-tradable goods. Capital accumulation is subject to investment

adjustment costs. And there are frictions to adjusting capital utilization.

F.1. Household

Consumers

Each household supplies differentiated labor indexed by

. Household

chooses consumption

aggregate

, risk-free nominal bonds

, real foreign bonds

t+1

, investment

and capital utilization

to maximize the utility function, with external habits over consumption,

∞

s=t

s−t



log(C

j,s

) −

1 + ν

1+ν

j,s



The composite good

is a Cobb-Douglas aggregate of a tradable good

and a non-tradable

good

such that

= Ψ (C

)

− hC

Nt−1

)

1−ω

where

Ψ = ω

−ω

(1 − ω)

1−ω

is a scaling factor,

A10

0 < ω < 1

is the weight on tradable goods,

is the degree of (external) habit formation in

non-tradable good consumption,

ν > 0

is the inverse Frisch elasticity of labor supply,

ϕ > 0

a parameter that pins down the steady-state level of hours, and the discount factor

satisﬁes

0 < β < 1.

We assume perfect consumption risk sharing across the households.

As a result, household’s budget constraint in period t is given by

+ B

+ P

(1 + τ

j,t

+ P

+ E

t+1

1 + r

t+1

1 + i

+ T

+ Z

+ R

− P

a(u

, (57)

where

and

denote the prices of a unit of tradable and non-tradable good, respectively, in

units of local currency;

is the level of real debt denominated in units of tradable good assumed

in period

t − 1

and due in period

;

is the level of nominal debt denominated in units of local

currency assumed in period

t − 1

and due in period

;

is investment in physical capital,

the nominal wage; Labor income

j,t

is subsidized at a ﬁxed rate

are nominal lump-sum

transfers from the government; and

are nominal proﬁts from domestic ﬁrms owned by the

households; and

> 0

is the endowment of tradable goods received by the households. Since

households own the capital and choose the utilization rate, the amount of effective capital that the

households rent to the ﬁrms at nominal rate R

= u

The (nominal) cost of capital utilization is

a(u

)

per unit of physical capital. As in the literature

(Smets and Wouters 2007) we assume

a(1) = 0

in the steady state and

> 0

. Following Christiano,

Eichenbaum, and Evans (2005), we assume investment adjustment costs in the production of capital.

Law of motion for capital is as follows:

t+1



1 − S



(1 + g

t−1



+ (1 − δ

where g

≡

µ is the steady state growth rate of aggregate productivity A

Utility maximization delivers the ﬁrst order condition linking the inter-temporal consumption

smoothing to the marginal utility of nominal and real bonds

1 = β E



t+1

(

1 + i

)

Tt+1



, (58)

1 = β E



t+1

(

1 + r

)



, (59)

where Λ

is the marginal utility of tradable goods consumption given by

Marginal rate of substitution between tradable and non-tradable goods is equal to relative price

(1 − ω) C

ω(C

− hC

Nt−1

)

. (60)

A11

Deﬁne relative price of non-tradables as

≡

. We assume that law of one price on the

tradable good holds. Let

be the nominal exchange rate for home relative to the base, and let

∗

the base price of the tradable good denominated in base currency.

Then, we have that

= E

∗

From consumption euler equations, we can then derive the interest rate parity condition,

(1 + i

) = (1 + r

)

Tt+1

= (1 + r

)

t+1

∗

t+1

∗

. (61)

Henceforth, we normalize P

∗

= 1.

To ensure stationarity under incomplete markets, we follow Schmitt-Groh

e and Uribe (2003);

Uribe and Schmitt-Groh

e (2017) and assume that the home real interest rate is related to foreign real

interest rate through a debt-elastic interest rate premium,

1 + r

1 + g

t+1

1 + r

∗

1 +

∗

+ ψ(e

t+1

−

− 1) . (62)

where g

is productivity growth at home and g

∗

is productivity growth rate in the base economy.

The stochastic discount factor in period t + 1 is given by

t,t+1

= β

t+1

Tt+1

The household does not choose hours directly. Rather each type of worker is represented by a

wage union who sets wages on a staggered basis. Consequently the household supplies labor at the

posted wages as demanded by ﬁrms.

We introduce capital accumulation through households. Solving household problem for invest-

ment and capital yields the Euler condition for capital

= βE



t+1



t+1

− a(u

t+1

) + q

t+1

(1 − δ

)





where r

t+1

= R

t+1

Nt+1

, and the (relative) price of installed capital q

is given by



1 − S



(1 + g

t−1



− S



(1 + g

t−1



(1 + g

t−1



+ β

t+1

(1 + g

)



t+1





t+1

(1 + g



= 1 .

Choice of capital utilization rate yields

= a

( u

) .

It is common in the small open economy literature to treat price level in the base economy

∗

synonymous for price level of tradable goods in the base economy P

∗

Due to the presence of endogenous growth in the tradable good sector, the relevant real interest rate

parity adjusts for productivity growth rate differentials between home and the base economy. Further note

that for stationarity, we assume that D

t+1

= d

t+1

≡

where Φ

is the Lagrange multipler on the capital accumulation equation.

A12

Wage setting

Wage Setting follows Erceg, Henderson, and Levin (2000) and is relatively standard.

Perfectly competitive labor agencies combine

type labor services into a homogeneous labor

composite L

according to a Dixit-Stiglitz aggregation



−1

j,t



−1

where e

> 1 is elasticity of substitution across labor varieties.

Labor unions representing workers of type

set wages on a staggered basis following Calvo

(1983), taking given the demand for their speciﬁc labor input

j,t



j,t



−e

, where W



1−e

j,t



1−e

In particular, with probability

1 − θ

, the type-

union is allowed to re-optimize its wage contract

and it chooses

to minimize the disutility of working for laborer of type

, taking into account

the probability that it will not get to reset wage in the future.

By the law of large numbers, the

probability of changing the wage corresponds to the fraction of types who actually change their

wage.

Consequently, the nominal wage evolves according to

1−e

= (1 − θ

)

1−e

+ θ

−1

t−1

where the nominal wage inﬂation and non-tradable goods price inﬂation are related to each other

t−1

1 + g

and where

≡

Nt−1

is the inﬂation rate in non-tradable goods sector,

≡

is the produc-

tivity adjusted real wage and g

is the growth rate of A

F.2. Production

The non-tradable consumption good is a Dixit-Stiglitz aggregate over a continuum of products

(i) produced by monopolistically competitive producers indexed by i, with

≡ (

(i)

−1)

di)

−1)

Each ﬁrm

in home produces a homogenous good with technology given by

(i) = (A

(i))

1−α

(i)

taking the demand for its product as given by

(i) =



(i)



−e

We assume imperfect wage indexation in our nominal wage rigidity assumption. We ignore specifying it

here for ease of exposition, but specify those in the equilibrium conditions later on.

A13

where we use the price index of the non-tradable good composite,

= (

(i)

1−e

di)

(1−e

)

Each ﬁrm

is assumed to set prices on a staggered basis following Calvo (1983). With probability

(1 − θ

), a ﬁrm adjusts its price independent of previous history.

Firms may not be able to adjust their price in a given period, but they will always choose inputs

to minimize total cost each period. The cost minimization yields the input demand functions.

= (1 − α) mc

(i)A

1−α



(i)



, R

= α mc

(i)A

1−α



(i)



α−1

The ﬁrst order condition implies that the capital labor ratio at the ﬁrm level is independent on

ﬁrm-speciﬁc variables:

(i)

1 − α

Thus, (nominal) marginal cost is independent of ﬁrm speciﬁc variables:

(i) = P

1−α







1 − α



1−α

For stationarity along the balanced growth path, we assume that the tradable good endowment

grows at the rate of A

F.3. Government

The central bank follows a Taylor rule in setting the nominal interest rate

. It responds to deviations

in inﬂation, output and output growth rate from time-t natural allocations.

1 + i



1 + i

t−1

1 + i











f ,t





1−ρ

, (63)

where

is the steady state nominal interest rate,

is gross producer-price inﬂation rate,

is the corresponding steady state inﬂation target,

f ,t

is the time-t natural output,

determines

interest-rate smoothing and e

∼ N(0, σ

) is the monetary policy shock.

We assume net zero supply of nominal bonds at home and that the government balances budget

every period. There is no government spending.

F.4. Market clearing

Nontradable goods are consumed, invested and spent in utilization adjustment with

= C

+ I

+ a(u

The external borrowing constraint must be satisﬁed with

+ D

= Y

t+1

1 + r

A14

F.5. Aggregate GDP

We construct aggregate GDP using constant aggregation weights implied by the utility function

along the balanced growth path.

F.6. Stationary allocation

We normalize the following variables:

= Y

; y

= Y

= C

; c

= C

= K

; k

= K

t−1

; I

= I

(capital investment)

= W

/(A

); r

= R

= Λ

Table A1: Parameters

(a) Medium-scale DSGE parameters

β δ

α µ

Discount

factor

Capital

depreciation rate

Capital

Trend

growth rate

0.999 0.025 0.28 2%

Wage Calvo

probability

Elasticity of substitution

across labor types

Price Calvo

probability

Elasticity of substitution

across non-tradables

0.75 8 0.75 8

ν h η

(1)

Inverse

Frisch elasticity

(external)

habit

Hysteresis

elasticity

Capital

utilization cost

1.00 0.50 0.25 4

S”(1) φ

Investment

adjustment cost

Taylor rule

inﬂation response

Taylor rule (normalized)

output response

Persistence

coefﬁcient

2 1.50 0.125 0.5

(b) Small-open economy parameters

d ψ ω

Parameter of

debt-elastic interest rate

Parameter of

debt-elastic interest rate

Tradable share

in expenditure

2.9 0.0000335 0.30

Notes: The table shows the parameter values of the model for the baseline calibration. See text.

A15

F.7. Calibration

To provide an illustration in the main text, we choose parameters from medium-scale DSGE literature

(Justiniano et al., 2013) and small-open economy literature (Schmitt-Groh

e and Uribe, 2016). We list

the calibrated parameters in Table A1.

G. Imbs correction

We follow Imbs (1999) and adjust TFP for utilization of capital and labor inputs. See Paul (2020)

for a related construction of utilization-adjusted TFP in the historical data. We assume perfectly

competitive factor markets and a technology which is constant returns to scale in effective capital

and labor. In aggregate, and for the representative ﬁrm, the production function is

= A

(

)

(

)

1−α

where

is output,

is capital stock,

is total hours worked, and

and

denote the respective

factor utilizations.

is the utilization adjusted TFP. We assume perfect competition in the input

and the output markets. Higher capital utilization increases the depreciation of capital

= δu

where

φ > 1

. As a result, ﬁrms choose capital utilization rate optimally. Labor hoarding is calculated

assuming instantaneous adjustment of effort

against a payment of a higher wage

w(e

)

, while

keeping ﬁxed employment (determined one period in advance). The ﬁrm’s optimization problem is

given by:

max

(

)

(

)

1−α

− w(e

− (r

+ δu

))K

Households choose consumption, labor supply and effort to maximize their lifetime utility subject

to their budget constraint (with complete asset markets)

max

∞

∑

t=0

ln C

−

(

)

1+ν

1 + ν

−

(

)

1+ν

1 + ν

Normalizing the long-run capital-utilization and labor-utilization rates to one, the utilization rates

can be derived from



Y/K



r+δ

; e





1+ν

;

where Y, C, L and K are the steady-state values of output, consumption, labor, and capital.

The Solow residual then can be decomposed into utilization-adjusted TFP and utilization

corrections, with

TFP

≡

1−α

= A

× u

1−α

To construct country-speciﬁc steady state values of

Y/K

, we extract a HP-ﬁlter trend from the data

series.

In the utilization adjusted series used in the main text, we set

α = 0.33

, and

ν = 1

. Results

are robust to constructing country speciﬁc values of these parameters.

Our empirical results are robust to computing moving averages over a 10 year window, using time-

varying values of

constructed from labor-income data, and reasonable parameters of the aggregate capital

depreciation rate. Bergeaud, Cette, and Lecat (2016) constructed capital stock for machines and buildings

separately using the perpetual inventory method with data on investment in machines and buildings and

different depreciation rates. Our results are robust to choosing different depreciation parameters.

A16

H. Mundell-Fleming-Dornbusch model

Although the arbitrage mechanism behind the trilemma is easily grasped, in this section we

investigate the economic underpinnings of our identiﬁcation strategy more formally with a variant

of the well known Mundell-Fleming-Dornbusch model. In particular, we incorporate the extensions

to the model discussed in Blanchard (2016) and Gourinchas (2018), which embed various ﬁnancial

spillover mechanisms.

Speciﬁcally, consider a framework made of two countries: a small domestic economy and a large

foreign economy, which we can call the United States, for now. Foreign (U.S.) variables are denoted

with an asterisk. Assume prices are ﬁxed.

Given interest rates, the following equations describe the setup:

Y = A + NX ,

A = ξ − ci − f E ,

NX = a( Y

∗

− Y) + bE ,

∗

= A

∗

= ξ

∗

− c

∗

E = d(i

∗

− i) + gi

∗

+ χ ,

where

a, b, c, c

∗

, d, f , g, χ ≥ 0

. Domestic output

is equal to the sum of domestic absorption

and

net exports

. Domestic absorption depends on an aggregate demand shifter

, and negatively on

the domestic (policy) nominal interest rate

denotes ﬁnancial spillovers through the exchange

rate (e.g., balance sheet exposure of domestic producers in a dollarized world).

f ≥ 0

, then a

depreciation of the exchange rate E hurts absorption.

Net exports depends positively on U.S. output

∗

, negatively on domestic output

, and

positively on the exchange rate. U.S. output is determined in similar fashion except that the U.S. is

considered a large country, so it is treated as a closed economy. Finally, the exchange rate depends

on the difference between domestic and U.S. interest rates and on a risk-premium shock. The term

g is intended to capture risk-premium effects associated with U.S. monetary policy.

In order to make the connection between the instrument as we deﬁned it earlier and this stylized

model, we now think of

∆i

∗

as the instrument

j,t

≡ k

j,t

( ∆i

b(j,t) ,t

−

∆i

b(j,t) ,t

)

described earlier. The

proposition below explores the benchmark setting of the trilemma to derive the basic intuition.

The textbook speciﬁcation with hard pegs

Under the assumption that

f = g = χ = 0

, many interesting channels are switched off and the

model just introduced reduces to the textbook Mundell-Fleming-Dornbusch version. Consider what

happens when the U.S. changes its interest rate,

∆R

∗

. Since

g = 0

, to maintain the peg it must

be that

∆i = ∆i

∗

. The one-to-one change in the home interest rate has a direct effect on domestic

absorption given by −c∆i.

However, notice that changes in the U.S. rate affect U.S. absorption and in turn net exports.

Jiang, Krishnamurthy, and Lustig (2019) provide a micro-foundation to generate these spillovers associ-

ated with the global ﬁnancial cycle (Rey, 2015).

Itskhoki and Mukhin (2019) argue that such risk-premia violations of UIP are smaller under exchange

rate pegs, i.e., g is smaller.

A17

Piecing things together:

∆Y = ∆A + ∆NX ,

∆Y = −

1 + a

∆i −

∗

1 + a

∆i

∗

As is clear from the expression,

∆i

∗

affects domestic output directly (and not just through

∆i

resulting in a violation of the exclusion restriction central to instrumental variable estimation.

However, note that this violation is easily resolved by including net exports as a control, or even just

base country output, something we do later in the estimation. Moreover, in this simple static model,

all effects are contemporaneous. However, in practice the feedback loop of higher U.S. interest rates

to lower net exports to lower output will take place gradually, in large part alleviating the exclusion

restriction violation.

Financial spillovers with soft pegs

Consider now a more general setting with ﬁnancial spillovers, that is,

g > 0

and

f > 0

and a soft

peg. That is, the central bank may adjust using interest rates and allow some movement of the

exchange rate.

This will affect the pass through of U.S. interest rates to domestic rates since now:

∆i =

∆e +

d + g

∆i

∗

where ∆E ∈ ±∆e refers to some band within which the exchange rate is allowed to ﬂuctuate.

The effect on output from changes in U.S. interest rates is very similar, but with an added term:

∆Y =

1 + a

∆i −

∗

1 + a

∆i

∗

+ (b − f )∆e .

Under a hard peg policy, with

∆e = 0

, an increase in U.S. interest rates boosts home interest rates

but it no longer does so one-to-one, as explained earlier. Partial ﬂexibility in exchange rates under a

soft peg, with

|∆e| > 0

, gives some further monetary autonomy to the home economy, and reduces

the pass-through to home interest rates, all else equal. This additional ﬂexibility in exchange rates,

however, results in other ﬁnancial and trade spillovers due to dependence of domestic absorption

and net exports on the exchange rate as shown by the term (b − f )∆e.

Summarizing our discussion, it is important to recognize that exogenous variation in interest

rates (induced either through the trilemma mechanism as just discussed, or through alternative

channels) has effects through domestic absorption and through net exports. This secondary channel,

if not properly controlled for, generates violations of the exclusion restriction.

A18

I. Additional figures

I.1. LPIV responses for GDP per capita

Figure A2: Baseline response to 100 bps trilemma shock: Real GDP per capita

(a) Full sample: 1890–2015

-10 -8 -6 -4 -2 0

Percent

0 4 8 12

Year

Full Sample: 1890-2015

Real GDP

(b) Post-WW2 sample: 1948–2015

-6 -4 -2 0

Percent

0 4 8 12

Year

Post-WW2 Sample: 1948-2015

Real GDP

Notes: Response to a 100 bps shock in domestic interest rate instrumented with the trilemma. Responses for pegging economies. Full

sample: 1890–2015 (World Wars excluded). Post-WW2 sample: 1948–2015.LP-IV estimates displayed as a solid blue line and and 1 S.E.

and 2 S.E. conﬁdence bands constructed using cluster-robust standard errors. See text.

I.2. LPIV responses for components in Post WW2 sample

Figure A3 plots the response of components of a Cobb-Douglas production function for the post-

WW2 sample.

A19

Figure A3:

Baseline response to 100 bps shock: Real GDP and Solow decomposition. Post ww2 sample,

1948–2015.

(a) Estimates using raw data

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Real GDP

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Labor

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Capital

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

TFP

(b) Estimates using Imbs correction for factor utilization

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Real GDP

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Labor

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Capital

-10 -8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

TFP

Notes: Response to a 100 bps shock in domestic short-term interest rate instrumented with the trilemma IVs. Post-WW2 sample: 1948–

2015. LP-IV estimates displayed as a thick lines and and 1 S.E. and 2 S.E. conﬁdence bands. The upper panel uses raw data on capital

stocks and total hours to construct TFP as a residual. The lower panel adjusts the raw data on capital stock and total hours to obtain

estimates of actual factor inputs by using the Imbs (1999) correction. See text.

A20

I.3. LPIV responses: controls in levels, differences, and number of lags

We report the robustness of IRFs estimated in the baseline to adding the control variables

j,t

levels instead of ﬁrst differences in the left panel of Figure A4, as well as to including up to 5 lags of

the control variables in the right panel.

Figure A4: Response to 100 bps trilemma shock with controls in levels: Real GDP

-8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Real GDP: controls in levels

-10 -8 -6 -4 -2 0

Percent

0 4 8 12

Year

Real GDP: controls in differences

Notes: Response to a 100 bps shock in domestic interest rate instrumented with the trilemma. Responses for pegging economies. Full

sample: 1890–2015 (World Wars excluded). LP-IV estimates displayed as a solid blue line and 1 S.E. and 2 S.E. conﬁdence bands. See

text.

A21

I.4. LPIV responses for various macro-ﬁnancial variables

Figure A5: Baseline response to 100 bps trilemma shock: Full Sample (1890-2015)

-10 -8 -6 -4 -2 0

Percent

0 4 8 12

Year

Real GDP per capita

-10 -8 -6 -4 -2 0

Percent

0 4 8 12

Year

Real consumption per capita

-10 -5 0

Percent

0 4 8 12

Year

Real investment per capita

-8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Price level

-.5 0 .5 1 1.5

Percentage pts

0 4 8 12

Year

Short-term interest rate

-.5 0 .5 1

Percentage pts

0 4 8 12

Year

Long-term interest rate

-15 -10 -5 0 5

Percent

0 4 8 12

Year

Real house prices

-20 -10 0 10 20

Percent

0 4 8 12

Year

Real stock prices

-4 -2 0 2

Percent

0 4 8 12

Year

Private credit/GDP

Notes: Response to a 100 bps shock in domestic interest rate instrumented with the trilemma. Responses for pegging economies. Full

sample: 1890–2015 (World Wars excluded). Conﬁdence bands are one and two standard errors using cluster-robust standard errors.

See text.

A22

Figure A6: Baseline response to 100 bps trilemma shock: Post-WW2 Sample (1948-2015)

-6 -4 -2 0

Percent

0 4 8 12

Year

Real GDP per capita

-6 -4 -2 0 2

Percent

0 4 8 12

Year

Real consumption per capita

-6 -4 -2 0 2

Percent

0 4 8 12

Year

Real investment per capita

-10 -8 -6 -4 -2 0

Percent

0 4 8 12

Year

Price level

-1 -.5 0 .5 1 1.5

Percentage pts

0 4 8 12

Year

Short-term interest rate

-1 -.5 0 .5 1

Percentage pts

0 4 8 12

Year

Long-term interest rate

-8 -6 -4 -2 0 2

Percent

0 4 8 12

Year

Real house prices

-10 0 10 20

Percent

0 4 8 12

Year

Real stock prices

-2 0 2 4

Percent

0 4 8 12

Year

Private credit/GDP

Notes: Response to a 100 bps shock in domestic interest rate instrumented with the trilemma. Responses for pegging economies.

PostWW2 sample: 1948–2015 (World Wars excluded). Conﬁdence bands are one and two standard errors using cluster-robust standard

errors. See text.

A23

I.5. LPIV responses with structural breaks

Figure A7: Response to 100 bps trilemma shock with structural breaks: Real GDP

(a)

-8 -6 -4 -2 0

Percent

0 4 8 12

Year

Real GDP

5 breaks in TFP

(b)

-8 -6 -4 -2 0

Percent

0 4 8 12

Year

Real GDP

5 breaks in GDP

Notes: Response to a 100 bps shock in domestic interest rate instrumented with the trilemma. Responses for pegging economies. Full

sample: 1890–2015 (World Wars excluded). LP-IV estimates displayed as a solid blue line and 1 S.E. and 2 S.E. conﬁdence bands. See

text.

A24

I.6. Structural break dates in TFP growth and GDP growth

-20 -10 0 10

1890 1915 1940 1965 1990 2015

Year

TFP growth for AUS

-40 -20 0 20 40

1890 1915 1940 1965 1990 2015

Year

TFP growth for BEL

-20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

TFP growth for CAN

-10 0 10 20 30

1890 1915 1940 1965 1990 2015

Year

TFP growth for CHE

-100 -50 0 50

1890 1915 1940 1965 1990 2015

Year

TFP growth for DEU

-20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

TFP growth for DNK

-30 -20 -10 0 10

1890 1915 1940 1965 1990 2015

Year

TFP growth for ESP

-20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

TFP growth for FIN

A25

-40 -20 0 20 40

1890 1915 1940 1965 1990 2015

Year

TFP growth for FRA

-10 -5 0 5

1890 1915 1940 1965 1990 2015

Year

TFP growth for GBR

-20 -10 0 10 20 30

1890 1915 1940 1965 1990 2015

Year

TFP growth for ITA

-80 -60 -40 -20 0 20

1890 1915 1940 1965 1990 2015

Year

TFP growth for JPN

-40 -20 0 20 40 60

1890 1915 1940 1965 1990 2015

Year

TFP growth for NLD

-10 -5 0 5 10 15

1890 1915 1940 1965 1990 2015

Year

TFP growth for NOR

-10 -5 0 5 10 15

1890 1915 1940 1965 1990 2015

Year

TFP growth for PRT

-10 -5 0 5 10 15

1890 1915 1940 1965 1990 2015

Year

TFP growth for SWE

A26

-10 -5 0 5 10 15

1890 1915 1940 1965 1990 2015

Year

TFP growth for USA

-20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

GDP growth for USA

A27

-20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

GDP growth for AUS

-40 -20 0 20 40

1890 1915 1940 1965 1990 2015

Year

GDP growth for BEL

-20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

GDP growth for CAN

-10 -5 0 5 10 15

1890 1915 1940 1965 1990 2015

Year

GDP growth for CHE

-100 -50 0 50

1890 1915 1940 1965 1990 2015

Year

GDP growth for DEU

-20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

GDP growth for DNK

-30 -20 -10 0 10

1890 1915 1940 1965 1990 2015

Year

GDP growth for ESP

-20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

GDP growth for FIN

A28

-40 -20 0 20 40

1890 1915 1940 1965 1990 2015

Year

GDP growth for FRA

-10 -5 0 5 10

1890 1915 1940 1965 1990 2015

Year

GDP growth for GBR

-30 -20 -10 0 10 20

1890 1915 1940 1965 1990 2015

Year

GDP growth for ITA

-40 -20 0 20

1890 1915 1940 1965 1990 2015

Year

GDP growth for JPN

-40 -20 0 20 40 60

1890 1915 1940 1965 1990 2015

Year

GDP growth for NLD

-10 -5 0 5 10 15

1890 1915 1940 1965 1990 2015

Year

GDP growth for NOR

-10 -5 0 5 10 15

1890 1915 1940 1965 1990 2015

Year

GDP growth for PRT

-15 -10 -5 0 5 10

1890 1915 1940 1965 1990 2015

Year

GDP growth for SWE

A29

J. Additional tables

Table A2:

LP-OLS vs. LP-IV. Attenuation bias of real GDP per capita responses to interest rates.

Trilemma instrument.

Responses of real GDP per capita at years 0 to 10 (100 × log change from year 0 baseline).

(a) Full Sample OLS-IV (b) Post-WW2 OLS-IV

Year LP-OLS LP-IV p-value LP-OLS LP-IV p-value

(1) (2) (3) (4) (5) (6)

h = 0 0.05 -0.02 0.52 0.02 0.04 0.76

(0.03) (0.11) (0.02) (0.07)

h = 2 -0.35

∗∗

-1.88

∗∗∗

0.00 -0.37

∗∗

-1.41

∗∗∗

0.00

(0.14) (0.36) (0.14) (0.25)

h = 4 -0.32 -2.73

∗∗∗

0.00 -0.35

∗

-2.00

∗∗∗

0.00

(0.22) (0.53) (0.21) (0.39)

h = 6 -0.45 -3.36

∗∗∗

0.00 -0.28 -3.00

∗∗∗

0.00

(0.37) (0.70) (0.31) (0.51)

h = 8 -0.63

∗

-4.90

∗∗∗

0.00 -0.27 -3.36

∗∗∗

0.00

(0.35) (1.10) (0.31) (0.70)

h = 10 -0.62

∗

-4.40

∗∗∗

0.00 0.06 -3.20

∗∗∗

0.00

(0.35) (1.02) (0.31) (0.73)

h = 12 -0.62 -6.50

∗∗∗

0.00 0.04 -4.02

∗∗∗

0.00

(0.40) (1.68) (0.36) (0.87)

KP weak IV 47.54 62.43

H 0: LATE = 0 0.00 0.00 0.00 0.00

Observations 963 774 710 585

Notes:

∗∗∗

p < 0.01,

∗∗

p < 0.05,

∗

p < 0.1. Cluster robust standard errors in parentheses.Full sample: 1890 − 2015 excluding

WW1: 1914 − 1919 and WW2: 1939 − 1947. Post WW2 sample: 1948 − 2015. Matched sample indicates LP-OLS sample

matches the sample used to obtain LP-IV estimates. KP weak IV refers to the Kleibergen-Paap test for weak instruments.

: LATE = 0 refers to the p-value of the test of the null hypothesis that the coefﬁcients for h = 0, ..., 10 are jointly zero for a

given subpopulation. OLS = IV shows the p-value for the Hausmann test of the null that OLS estimates equal IV estimates.

See text.

A30

Appendix references

Bergeaud, Antonin, Gilbert Cette, and R

emy Lecat. 2016. Productivity Trends in Advanced Countries

between 1890 and 2012. Review of Income and Wealth 62(3): 420–444.

Blanchard, Olivier. 2016. Currency Wars, Coordination, and Capital Controls. Working Paper 22388,

National Bureau of Economic Research.

Calvo, Guillermo A. 1983. Staggered prices in a utility-maximizing framework. Journal of Monetary

Economics 12(3): 383–398.

Christiano, Lawrence J., Martin Eichenbaum, and Charles L. Evans. 2005. Nominal Rigidities and

the Dynamic Effects of a Shock to Monetary Policy. Journal of Political Economy 113(1): 1–45.

Durbin, J. 1959. Efﬁcient Estimation of Parameters in Moving-Average Models. Biometrika 46(3/4):

306–316.

Erceg, Christopher J., Dale W. Henderson, and Andrew T. Levin. 2000. Optimal monetary policy

with staggered wage and price contracts. Journal of Monetary Economics 46(2): 281–313.

Gourinchas, Pierre-Olivier. 2018. Monetary Policy Transmission in Emerging Markets: An Appli-

cation to Chile. In Monetary Policy and Global Spillovers: Mechanisms, Effects and Policy Measures,

edited by Mendoza, Enrique G., Ernesto Past

en, and Diego Saravia, volume 25 of Central Banking,

Analysis, and Economic Policies Book Series, chapter 8, 279–324. Santiago: Central Bank of Chile.

Imbs, Jean M. 1999. Technology, growth and the business cycle. Journal of Monetary Economics 44(1):

65–80.

Itskhoki, Oleg, and Dmitry Mukhin. 2019. Mussa puzzle redux. Princeton University. Unpublished.

Jiang, Zhengyang, Arvind Krishnamurthy, and Hanno Lustig. 2019. Dollar Safety and the Global

Financial Cycle. Research Paper 19-16, Stanford University Graduate School of Business.

Justiniano, Alejandro, Giorgio E. Primiceri, and Andrea Tambalotti. 2013. Is There a Trade-Off

between Inﬂation and Output Stabilization? American Economic Journal: Macroeconomics 5(2): 1–31.

Kuersteiner, Guido M. 2005. Automatic Inference For Inﬁnite Order Vector Autoregressions. Econo-

metric Theory 21(1): 85–115.

Lewis, Richard, and Gregory C. Reinsel. 1985. Prediction of multivariate time series by autoregressive

model ﬁtting. Journal of Multivariate Analysis 16(3): 393–411.

Lusompa, Amaze B. 2019. Local projections, autocorrelation, and efﬁciency. Unpublished. UC Irvine.

Paul, Pascal. 2020. Historical patterns of inequality and productivity around ﬁnancial crises. Federal

Reserve Bank of San Francisco Working Paper 2017-23.

Rey, H

ene. 2015. Dilemma not Trilemma: The Global Financial Cycle and Monetary Policy

Independence. NBER Working Papers 21162, National Bureau of Economic Research, Inc.

Schmitt-Groh

e, Stephanie, and Martın Uribe. 2003. Closing small open economy models. Journal of

International Economics 61(1): 163–185.

A31

Schmitt-Groh

e, Stephanie, and Martin Uribe. 2016. Downward Nominal Wage Rigidity, Currency.

Pegs, and Involuntary Unemployment. Journal of Political Economy 124(5): 1466–1514.

Smets, Frank, and Rafael Wouters. 2007. Shocks and Frictions in US Business Cycles: A Bayesian

DSGE Approach. American Economic Review 97(3): 586–606.

Uribe, Martin, and Stephanie Schmitt-Groh

e. 2017. Open Economy Macroeconomics. Princeton, N.J.:

Princeton University Press.

Wiener, Norbert, and Pesi Masani. 1958. The prediction theory of multivariate stochastic processes,

II: The linear predictor. Acta Mathematica 99(1): 93–137.

A32