Switching-track after the Great Recession.
Date: 2021-10-21
Institutions: European Central Bank
Subjects: economic growth, economic model, economic recession, economic recovery, monetary policy

Francesca Vinci, Omar Licandro

Working Paper Series 

Switching-track 
after the Great Recession 

No 2596 / October 2021 

Disclaimer: This paper should not be reported as representing the views of the European Central Bank 
(ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. 

Abstract

We propose a theoretical framework to reconcile episodes of V-shaped and L-shaped recovery, en-

compassing the behaviour of the U.S. economy before and after the Great Recession. In a DSGE

model with endogenous growth, negative demand shocks destroy productive capacity, moving GDP

to a lower trajectory. A Taylor rule policy designed to reduce the output gap may counterbal-

ance the shocks, preventing the destruction of economic capacity and inducing a V-shaped recovery.

However, when shocks are deep and persistent enough, like during the Great Recession, they call

for a downward revision of potential output measures, the so-called switching-track, weakening the

recovering role of monetary policy and inducing an L-shaped recovery. When calibrated to the U.S.

economy, the model replicates well the L-shaped recovery and switching-track that followed the

Great Recession, as well as the V-shaped recoveries that followed the oil shock recessions.

Keywords: Economic Recovery, Endogenous Growth, Supply Destruction Prevention, Eco-

nomic Capacity, Monetary Policy

JEL Codes: E12, E22, E32, O41, E52

ECB Working Paper Series No 2596 / October 20211Non-technical summary

The Great Recession that followed the 2008 ﬁnancial crisis was a deep and prolonged downturn,

with permanent scarring eﬀects on the productive capacity of advanced economies. In this paper

we focus on the dynamics of economic recovery after the Great Recession, in comparison with

past episodes, to understand which factors aﬀect recoveries and what role monetary policy plays

in shaping them. Our framework is applicable to the majority of OECD countries, but we focus

on the United States, where the level of GDP fell in conjunction with the Great Recession and

then gradually resumed growing at a similar rate as before, resulting in a downward parallel

shift in the path. This implies a permanent gap between the actual level of GDP and what

it would have been had the recession not happened, giving rise to an L-shaped recovery.

In

contrast, past downturns were associated with a temporary acceleration of growth, allowing the

economy to go back to its original growth path, a dynamic referred to as a V-shaped recovery.

The paper aims to build a model to replicate episodes of V-shaped and L-shaped economic

recoveries in a single framework. We argue that an L-shaped recovery is not consistent with

a fundamental modelling assumption commonly used to represent the technology behind GDP

production in the literature aiming to model recessions through dynamic stochastic general

equilibrium models (DSGEs). A Neoclassical production function (Cobb-Douglas) assumes di-

minishing returns to capital (i.e. the productive capacity of the economy), so that a negative

shock aﬀecting the capital stock would increase the return to capital, sustaining investment and

bringing GDP back to its original growth trajectory. In this case, the level of potential output,

i.e.

the maximum level of production feasible, is not aﬀected by the recession. However, a

model with this production function does not explain L-shaped recoveries. Conversely, a pro-

duction function featuring endogenous growth technology (AK) is only consistent with L-shaped

recovery episodes because the return to capital is constant, so that a lower capital stock does

not generate a higher return to capital and thus stimulus to invest after a shock. In this case,

potential output switches track, permanently moving to a lower path.

The assumption chosen to model production technology has crucial implications for the

dynamics of economic recovery, but also for the role played by policy interventions. We focus

on monetary policy, due to the Fed’s Taylor rule policy, aiming at closing the gap between

ECB Working Paper Series No 2596 / October 20212GDP and potential output (J. Taylor, 1993). This implies a systematic countercyclical policy

response, providing stimulus when GDP falls below its potential level until the gap is closed. If

the technology assumed in the model generates a V-shaped recovery (Cobb-Douglas case), the

policy stimulus plays a supportive role. However, if production technology results in L-shaped

recoveries (AK case), policy interventions are not only supportive, but can even be the force

behind V-shaped recoveries, explaining past observed episodes as well as the L-shaped recovery

that followed the Great Recession. This is a fundamental contribution of this paper.

We propose a novel framework to combine endogenous growth and DSGEs, and shows that

a learning-by-doing technology (AK in aggregate) `a la Romer (1986) is consistent with both V-

shaped and L-shaped recovery episodes once the role of monetary policy is taken into account.

The paper builds on Christiano, Motto, and Rostagno (2014), and introduces a novel ampliﬁ-

cation mechanism through bankruptcy spillovers on the depreciation rate of capital, so that an

increase in risk and bankruptcy leads to the destruction of economic capacity. Moreover, the

standard model is augmented by allowing for the switching-track, i.e. the revision of potential

output estimates by the central bank. Calibration of the U.S. economy shows that a simple

Taylor rule with a positive weight on the output gap could give enough stimulus to replicate the

V-shaped recoveries that followed the oil crises. On the other hand, a large and highly persis-

tent demand shock such as the Great Recession has a permanent negative eﬀect on productive

capacity.

In order to generate this last result, allowing for the switching-track in the Taylor

rule is key. If the central bank updates its beliefs on the level of potential output based on past

observed GDP, as the latter falls due to the crisis, the estimate of potential output will follow, so

that the output gap will shrink over time, and the policy stimulus will get increasingly weaker.

The potential output switching-track in the Taylor rule replicates the timing of the potential

output revisions carried out by the Fed. Moreover, we show that monetary policy acts a cushion

in the model economy, preventing the destruction of productive capacity. This constitutes a

novel transmission mechanism of monetary policy and another fundamental contribution of this

paper.

In conclusion, this paper sheds new light on the drivers of economic recovery and the role

played by monetary policy in shaping them, and oﬀers a new tool to inform policy-makers.

ECB Working Paper Series No 2596 / October 202131 Introduction

The Great Recession had a profound impact on the economic performance of OECD countries.

Crucially, the crisis had a persistent level eﬀect on GDP, which still remains below its pre-

crisis path for the vast majority of advanced economies (Ball, 2014). Focusing on the United

States, past recessions were typically followed by a temporary acceleration of growth, with GDP

converging back to its pre-recession trajectory. This is commonly referred to as a V-shaped

recovery. Conversely, after the 2008 ﬁnancial shock we saw potential output switching-track

in conjunction with the crisis, as the deep and persistent fall in economic activity led to a

downward swerve of the GDP trend from its original path. Consequently, the output gap closed

following the switching-track of potential output, rather than faster GDP growth, giving rise to

a so-called L-shaped recovery (see Figure 1). This fact challenged the general consensus on the

distinct relationship between trend, growth and business cycles. If recessions are not followed

by recoveries, downturns will aﬀect the long run path of GDP, implying that potential output

cannot be represented by a stable trend in the productive capacity of the economy.

Figure 1: U.S. GDP per capita

This paper shows that the Great Recession can be seen as a large and persistent demand

shock deeply reducing economic activity for an unusually long period, translating into a per-

manent depletion of productive capacity (a supply-side eﬀect) casting the observed L-shaped

ECB Working Paper Series No 2596 / October 20214Figure 2: Switching-track

recovery. GDP moving down to a lower trajectory gradually induced a change in measured

potential output. The economy then converged to its new lower potential output path, ending

the recession without a full recovery. In this context, potential output is a measure of policy

makers’ beliefs about the level of GDP that can be feasibly sustained in the long run, a key

indicator aﬀecting monetary policy interventions, and ultimately the shape of the recovery.

Figure 2 shows that the output gap closed around 2016 following the switching-track process

of potential output revisions instead of faster growth, weakening the strength of the policy

intervention over time. The estimates of potential output published by the Congressional Budget

Oﬃce (CBO) each year were revised down as the recession unfolded, leading to the closure of

the output gap intrinsic to an L-shaped recovery –see the left panel of Figure 2. Consistently,

the output gap estimates published in the Fed’s Greenbook were revised over time, showing that

the output gap also closed in 2016 –right panel of Figure 2.

To replicate the dynamics of U.S. GDP after the Great Recession, this paper relies on the

combination of four key assumptions. First, we embed learning-by-doing `a la Romer (1986)

into a DSGE model with ﬁnancial frictions `a la Christiano et al. (2014). Under this assump-

tion, aggregate technology faces constant returns to capital. Consequently, a negative shock

to the capital stock would not allow the economy to return to its previous growth trajectory,

ECB Working Paper Series No 2596 / October 20215aﬀecting the level of GDP permanently. Second, in line with Christiano et al. (2014), the Great

Recession is modelled as a large negative shock to aggregate demand that induces a surge in

bankruptcy. Third, the depreciation rate is assumed to be endogenous and positively related

to the bankruptcy rate. A sudden increase in bankruptcy will then deplete the capital stock,

inducing a permanent decline in output. Finally, the monetary authority is assumed to follow

a standard Taylor rule, targeting inﬂation and the output gap, but we also assume that the

monetary authority revises potential output when recessions are deep and persistent. This way,

we introduce the switching-track in the model, consistently with the unprecedented downward

revision of potential output estimates that followed the large and long lasting decline in GDP

observed during the Great Recession.

Monetary policy plays a fundamental role in our model, by providing countercyclical stimulus

to aggregate demand but also protecting the productive capacity of the economy by prevent-

ing capital destruction. The latter constitutes a novel transmission channel with potentially

signiﬁcant implications for the conduct of monetary policy and, more generally, the consensus

concerning its role. The idea that large shocks can negatively aﬀect the productive capacity of

the economy permanently has gained traction in the aftermath of the Great Recession, and it

is becoming even more prominent in the face of the COVID-19 crisis, especially for monetary

policy-makers. During the press conference to announce measures in response the economic

shock from Covid-19, Mark Carney (BoE) remarked:

“In this situation, it’s disruption not

destruction of supply. Part of our job is to make sure that that is indeed the case, and so that

we’re bridging, and that’s very much part of the analysis.”1 We aim to contribute to this debate

and this paper is, to the best of our knowledge, the ﬁrst to model the destruction prevention

channel explicitly. Monetary policy operates as a cushion, protecting the economy from negative

shocks that destroy the productive capacity of the economy.

We also show that in periods characterised by negative shocks that are not overly persistent,

the standard Taylor rule is enough to generate a full recovery, making the economy converge

to its past trajectory despite aggregate constant returns to capital. The Taylor rule is then

1Bank of England Press Conference, 11th March 2020. For similar examples see the blog post by Chris-
tine Lagarde, President of the ECB, 9th April 2020 and Fed’s Chair Jerome Powell’s speech on 9th April 2020
“COVID-19 and the Economy”.

ECB Working Paper Series No 2596 / October 20216suﬃcient to drive a V-shaped recovery in normal times. Furthermore, when calibrated to the

recessions that followed the 1974 and 1990 oil shocks, the model replicates well the observed

V-shaped recoveries. Our model can then reconcile the dynamics of the U.S. economy before

and after the Great Recession. This represents another contribution of our work, as existing

models provide insights on the possible mechanisms through which endogenous growth can lead

to output shortfalls in line with the Great Recession, but such theories tend to remain silent

concerning the drivers of recovery in the past.

In particular, Benigno and Fornaro (2018) build a Schumpeterian framework, in the spirit

of Aghion and Howitt (1992), with nominal rigidities and a Taylor rule targeting the employ-

ment rate. Their model shows two stationary solutions, a good one and a stagnation trap, with

low growth and unemployment. We can interpret the Great Recession in this framework as

a fall in demand that moves the economy from the good stationary equilibrium to the stag-

nation trap. Pessimistic beliefs and the zero-lower bound (ZLB) are crucial to generate their

results. In particular, the existence of a stagnation trap is a consequence of the ZLB constraint

on monetary policy, which would otherwise restore full employment. When beliefs eventually

become optimistic again, the economy escapes the stagnation trap, moving back to the good

stationary equilibrium. Since the Taylor rule aims to restore the initial level of employment, but

not the initial level of output, the production capacity lost during the recession is not recovered

and the economy converges to a lower path, with the initial growth rate but a lower intercept.

Similarly, in our paper we ﬁnd that monetary policy is a key element in determining the level

of economic activity after a demand shock bringing the economy to the ZLB. Diﬀerently from

Benigno and Fornaro (2018), our model shares the standard property of the AK (endogenous

growth) framework, featuring a unique stationary growth rate, which makes it suitable for a

quantitative analysis capturing the permanent level eﬀects on GDP that followed the Great

Recession and the switching-track of potential output. Notably, the unique stationary growth

rate determines the slope of the balanced growth path GDP trajectory. The intercept of the

balanced growth path is in principle indeterminate, and set by the initial stock of capital, i.e.

the productive capacity of the economy. Shocks that destroy productive capacity reduce the in-

tercept of the balanced growth path, moving the economy to a lower trajectory. By preventing

ECB Working Paper Series No 2596 / October 20217destruction, monetary policy aﬀects the new intercept of the balanced growth path and plays a

role in shaping the recovery. When the economy hits the ZLB, the ability of monetary policy to

prevent capacity destruction is hampered and this results in a lower intercept in the new steady

sate.

Other papers focus on explaining the lack of recovery following ﬁnancial crises in particular,

and thus bring together endogenous growth and ﬁnancial shocks. Bianchi et al. (2019) also pro-

pose a Shumpeterian model, adding ﬁnancial frictions to explore the properties of diﬀerent kinds

of ﬁnancial shocks, and their long lasting eﬀects on the economy. Cozzi et al. (2017) propose an

estimated Shumpeterian DSGE model and stress how the inclusion of endogenous growth leads

to the ampliﬁcation of ﬁnancial shocks. Anzoategui et al. (2019) build on the pioneering work

of Comin and Gertler (2006), proposing an endogenous growth model `a la Romer (1990) with

endogenous diﬀusion and ﬁnancial frictions.2 Their model generates an endogenous response of

TFP to aggregate demand shocks through the R&D and diﬀusion channels. Their analysis also

shows that this response is consistent with the observed cyclicality of the speed of diﬀusion of

new technologies. Their estimation reveals that a shock equivalent to a risk shock can generate

medium to long-term eﬀects on the level of TFP, and thus output, due to a temporary slowdown

in productivity enhancing investments and, most importantly, technology diﬀusion. Ikeda and

Kurozumi (2019) choose a similar framework and, just like us, they propose a model where ﬁ-

nancial shocks can generate permanent shortfalls in GDP, resulting in a parallel downward shift

in the level of economic activity. Queralto (2020) also contributes to this literature, by focusing

on banking crises in an open economy expanding product variety framework. The paper shows

that ﬁnancing frictions can aﬀect the introduction of new varieties, and thus endogenous TFP.

Garga and Singh (2020) take a similar approach, but focus in the design of optimal monetary

policies in their framework.

None of these papers discusses the suitability of their approaches to generate V-shaped

recoveries in normal times. This paper aims to complement the literature by providing a frame-

work that reconciles episodes of V-shaped and L-shaped economic recovery. To achieve this, we

propose a novel way of incorporating endogenous growth into DSGE models with ﬁnancial fric-

2Comin and Gertler (2006) analysed the link between short and medium-term variations in economic activity,

drawing attention to medium-term business cycles and pointing out that recessions can have lasting eﬀects.

ECB Working Paper Series No 2596 / October 20218tions, employing a learning-by-doing technology `a la Romer (1986), where knowledge is crucial

for economic growth, and its accumulation is directly linked to the capital stock. We choose this

speciﬁcation to show that a relatively small departure from a standard DSGE model can gen-

erate a rich departure from its predictions on the medium to long-run scars of large recessions.

We picked the simplest growth model which allows us to explore the role of capital destruction

in shaping the dynamics of potential output. We also introduce a new mechanism for capital

depreciation and a Taylor rule that allows for the switching-track.

The rest of the paper is organised as follows: Section 2 discusses the role of capital destruc-

tion, Section 3 explains the model, Section 4 reports the calibration, Section 5 contains results

for the Great Recession simulations, Section 6 describes normal times, Section 7 discusses the

use of the Taylor rule at the Fed and Section 8 concludes.

2 Capital-Destruction: Evidence & Related Literature

In order to represent the dynamic of GDP during the the Great Recession we make the following

modelling choices. First, we model the Great Recession as a demand shock that combines higher

aggregate risk and lower consumer conﬁdence, reducing investment and consumption demand.

Like in Christiano et al. (2014), an increase in credit risk reduces credit and raises the probability

of bankruptcy in equilibrium.

Secondly, the rise in bankruptcies that follows the demand shock causes capital destruction

and thus a permanent supply eﬀect. To generate this result, we augment the framework in

Christiano et al. (2014) by positively linking the probability of bankruptcy to the depreciation

rate of capital. During the Great Recession, a surge of bankruptcies thus leads to a depletion of

the capital stock. The recession is then driven by a large shock to aggregate demand inducing

supply eﬀects. Our choice is motivated by empirical work by Hall (2015, 2016), who identiﬁes the

shortfalls in business capital and total factor productivity as the main drivers of the deviation of

GDP from its previous trend. This paper represents the idea by associating the Great Recession

with a substantial decline of the stock of capital and, through learning-by-doing, of total factor

productivity.

Identifying capital destruction in the data is notoriously diﬃcult. National Accounts esti-

ECB Working Paper Series No 2596 / October 20219Figure 3: Capital destruction. Left panel: Log-deviation from trend of the price of used compared to
new capital goods. Data made available by Lanteri (2018). Right panel: Capital quality. Constructed following

methodology suggested by Kozlowski et al. (2020), all details in the Appendix.

mates of the capital stock are constructed using the perpetual inventory method, and typically

employ geometric depreciation rates, held constant over time.3 As a consequence, measurement

of the capital stock in National Accounts reﬂects movements of investment, but cannot reﬂect

cyclical capital destruction. Nonetheless, the idea that recessions destroy capital is not new,

and we aim to provide new insights to the existing literature. For example, in a vintage cap-

ital framework, Caballero and Hammour (1994) provided a rational to the evidence stated by

Davis and Haltiwanger (1990) that job destruction is much more cyclically responsive than job

creation.4 Which bring them to see recessions as cleansing periods, when the productive system

eliminates outdated techniques and products. In their view, the associated physical capital be-

comes obsolete and is then scrapped. More recently, Gourio (2012) built a business cycle model

with disaster risk, characterizing disasters as episodes of large capital destruction. He noted

that economic downturns are associated with large reallocation of capital, leading to the loss of

ﬁrm speciﬁc specialised capital goods as well as intangible capital. Recent theoretical work by

Lanteri (2018) and Kozlowski et al. (2020) also contributes to this literature, and the authors

provide empirical grounding for the idea of capital destruction following the Great Recession.

Lanteri (2018) analyses the dynamics of the second-hand market for equipment in the United

3For the United States, see Fraumeni (1997).
4For an analysis of job creation and destruction in vintage capital models, see Boucekkine, del R´ıo, and

Licandro (1999)

ECB Working Paper Series No 2596 / October 202110States.5 He ﬁnds that quantities sold vary procyclically and that the price of second-hand

equipment is procyclical and more volatile than the price of new equipment, showing a signiﬁcant

decline at the beginning of the Great Recession. This evidence indicates that the value of existing

capital declined in real terms during the Great Recession (see left panel in Figure 3), suggesting

a fall in productive capacity.6 Additional evidence is provided by Kozlowski et al. (2020), who

construct a measure of the quality of corporate non-ﬁnancial assets. As can be observed in the

right panel of Figure 3, their measure of capital quality was unusually low in conjunction with the

Great Recession, which can be interpreted in their framework as an increase in the depreciation

rate of capital (see Appendix C). Overall, these ﬁndings suggest that the productive capacity

of capital goods fell during the Great Recession, and constitutes additional evidence indicating

that downturns can be associated with increasing capital depreciation rates. Motivated by

these measures, we introduce an endogenous countercyclical depreciation rate in the model,

which results in a decline in the relative price of the second-hand market for capital and the

destruction of its productive capacity following a negative shock.

3 The Model

We build a New Keynesian model of endogenous growth by introducing a learning-by-doing

technology `a la Romer (1986) in a Dynamic Stochastic General Equilibrium model with ﬁnancial

frictions. We build on the ﬁnancial accelerator framework introduced by Bernanke, Gertler, and

Gilchrist (1999) and draw from Christiano et al. (2014) for risk shocks. Households gain utility

from consumption, dis-utility from labour, and are subject to conﬁdence shocks, i.e. reductions

in their marginal utility of consumption. The production sector is comprised of a labour union,

ﬁnal good producers, intermediate good producers, capital producers and entrepreneurs. The

latter face ﬁnancial frictions, since they need to fund part of their capital expenditure with

external resources, exposing themselves to the possibility of bankruptcy. We model a risk shock

as an increase in the probability of bankruptcy for entrepreneurs. The ﬁnancial sector acts as an

5Lanteri (2018) collects data on quantities and prices from sales of second-hand capital, including commercial

aircrafts, ships, and construction equipment, among others.

6In a recent paper, Gavazza and Lanteri (2021) analysed the market for vehicles, and found that the fall in
the price of used cars was associated with a drop in upgrading during the Great Recession. As a consequence,
the overall age, and thus quality and value of the vehicle stock declined.

ECB Working Paper Series No 2596 / October 202111intermediary between the production side and households, by providing loans to entrepreneurs

and selling bonds to savers. The monetary authority sets the nominal interest rate according

to a Taylor rule, factoring in the deviation of inﬂation from its target and the output gap. We

also assume that potential output is measured as an average of past GDP values, so that large

negative shocks lead to downward revisions. The following sections describe the behaviour of

all agents in the model.

3.1 Labour Packer

Households, indexed by (cid:96) ∈ (0, 1), supply diﬀerentiated labour input to a labour packing ﬁrm,

i.e. a union, which then supplies an homogeneous labour input hp

t to the production sector. The

bundling technology is

hp
t =

(cid:18)(cid:90) 1

0

ht((cid:96))

(cid:19) ε

ε−1

ε−1
ε d(cid:96)

.

(1)

The parameter ε > 1 represents the elasticity of substitution across types of labour, which are

assumed to be gross substitutes, and ht((cid:96)) represents hours worked by household (cid:96). Labour

demand by the labour packer is

ht((cid:96)) =

(cid:19)−ε

(cid:18) Wt((cid:96))
Wt

hp
t ,

(2)

where Wt((cid:96)) is the wage of labour variety (cid:96). Substituting (2) into (1), we obtain the aggregate

wage index

W 1−ε

t =

(cid:90) 1

0

Wt((cid:96))1−εd(cid:96).

Thus total employment (measured in hours worked) is given by

ht ≡

(cid:90) 1

0

ht((cid:96))d(cid:96) = hp
t

(cid:90) 1

0

(cid:18) Wt((cid:96))
Wt

(cid:19)−ε

d(cid:96).

(3)

(4)

Deﬁning (cid:82) 1
0

(cid:17)−ε

(cid:16) Wt((cid:96))
Wt

d(cid:96) as a measure of wage dispersion across varieties implies that if the latter

is larger than 1, then aggregate labour used in production is smaller than total employment.

However, in this paper we will only consider symmetric equilibria, implying that the total labour

supply hp

t = ht.

ECB Working Paper Series No 2596 / October 2021123.2 Households

There is a continuum of households of measure one. The (cid:96)-type household consumes, supplies

labour, buys bonds and owns ﬁrms subject to wage frictions `a la Rotemberg (1982);7 when

changing its wage, it incurs in a cost assumed to be proportional to aggregate output. Since

households are assumed to be identical, diﬀering only on the type of labour they oﬀer, labour

market equilibrium is symmetric. We will then omit index (cid:96) to simplify notation.

A representative household, oﬀering a particular type of labour, maximises utility subject to

its budget constraints and labour demand (2),

max
ct,wt,Bt+1

ut = Et





∞
(cid:88)

j=0

(cid:32)

log (cid:0)ct+j − χct−1+j

βj(cid:15)c
t

(cid:1) − ψ

(cid:33)


h1+ν
t+j
1 + ν

s.t. Bt+1 + Ptct = Rt−1Bt + Ptwtht −

χω
2

(cid:18) wt
wt−1

(cid:19)2

− 1

PtYt + Dt − τt,

(5)

(6)

where ct is consumption and ht is labour, β ∈ (0, 1) is the time discount factor, χ > 0 regulates

the degree of habit formation, ν > 0 is the inverse of labour supply elasticity, ψ > 0 is a parameter

regulating labour hours in steady state and χw > 0 regulates price frictions. Bt+1 represent risk-

less one period nominal bonds, purchased at time t, earning the risk-less nominal interest factor

Rt.8 Variable wt represents the real wage rate, Pt is the price of the ﬁnal good, Dt are proﬁts

redistributed to households by ﬁrms and τt are taxes. (cid:15)c

t is a conﬁdence shock, aﬀecting the

marginal utility of consumption, which follows an AR(1) process: log((cid:15)c

t ) = ρc log((cid:15)c

t−1) + (cid:15)c,t,

where ρc ∈ (0, 1) and (cid:15)c,t ∼ N (0, σ2

c ) . This is a simple way of generating the fall in consumption

demand as well as the nominal interest rate observed during the Great Recession.9

The FOCs for ct and Bt+1 in real terms are:

λt = (ct − χct−1)−1(cid:15)c

t − βχEt(ct+1 − χct)−1(cid:15)c

t+1

(7)

7We choose this speciﬁcation for price and wage frictions because they are better suited in the context of large
shocks compared to the standard Calvo style. The letter imply a constant probability of resetting prices, which
does not account for size eﬀects. For a detailed discussion see Karadi and Reiﬀ (2019).

8All nominal variables in this paper are deﬁned in an arbitrary numeraire.
9Guerrieri and Lorenzoni (2017) provide insights into the underlying mechanism through the lens of a model
with heterogeneous households. They show that when the economy’s borrowing capacity is impaired, debtors
reduce their demand for loans and creditors increase precautionary savings, resulting in lower demand and a fall
in the nominal interest rate.

ECB Working Paper Series No 2596 / October 202113λt = βEtRt

λt+1
πt+1

,

where λt is the Lagrange multiplier associated to the budget constraint and πt = Pt
Pt−1

.

The FOC for wt gives the wage Phillips curve:

wt =

ε
ε − 1

ψhν
t (cid:15)c
t
λt

(cid:20)

+ Et

β

λt+1
λt

Ωt+1Yt+1

(cid:21)

1
ht

− Ωtπt

Yt
ht

Ωt =

χw
ε − 1

(πw

t − 1)πw
t

wt
wt−1

=

πw
t
πt

,

(8)

(9)

(10)

(11)

where ε is the degree of substitution across labour types. The RHS of (9) shows that wages

depend on the wage mark-up, the marginal rate of substitution and expectations. The expecta-

tion term implies that the labour supply is forward looking, and therefore will be less sensitive

to contemporaneous shocks. Equation (11) is an identity to pin down the equilibrium.

3.3 Final Good Sector

The ﬁnal good Yt is produced under perfect competition and can be turned into consumption or

investment, as well as used to cover the costs associated with ﬁnancial, price and wage frictions.

Production uses intermediate goods as inputs according to the following CES technology

Yt =

(cid:18)(cid:90) 1

0

yt(i)

(cid:19) θ

θ−1

θ−1
θ di

(12)

with the elasticity of substitution θ > 1. The associated demand function for intermediate goods

is

yt(i) =

(cid:18) pt(i)
Pt

(cid:19)−θ

Yt

with aggregate price index

Pt =

(cid:18)(cid:90) 1

0

(cid:19) 1

1−θ

pt(i)1−θdi

(13)

(14)

.

ECB Working Paper Series No 2596 / October 2021143.4 Intermediate Good Sector

Each intermediate ﬁrm i, i ∈ (0, 1) operates under monopolistic competition. It employs capital

services and labour by the mean of the following technology

yt(i) = atKη

t kt(i)αht(i)1−α,

α ∈ (0, 1)

(15)

where Kt represents a measure of knowledge, freely available to all ﬁrms and acquired through
learning-by-doing. We assume that Kt = kt, where kt = (cid:82) 1

0 kt(i)di. This implies that K is a

pure externality that comes from the aggregate level of capital employed in the economy, and

0 ≤ η ≤ 1 − α represents the strength of the spillovers. at is an aggregate productivity shock,

following

log(at) = ρa log(at−1) + (cid:15)a,t,

ρa ∈ (0, 1) and (cid:15)a,t ∼ N(0, σ2). This is a moderate shock, typical of business cycle dynamics.

Solving the cost minimisation problem of the intermediate ﬁrm i, the FOCs for labour and

capital services are

wt = (1 − α)st

yt(i)
ht(i)

,

rk
t = αst

yt(i)
kt(i)

,

(16)

(17)

where rk

t is the real rental rate of capital and st is the real marginal cost (Lagrangian multiplier)

of producing yt(i), the same for all ﬁrms. Combining both FOCs

st = α−α(1 − α)α−1 w1−α

t

t )α
(rk
atKη
t

.

(18)

Intermediate good producers are monopolistically competitive and they face an adjustment

cost when changing prices. Following Rotemberg (1982), the adjustment cost increases with the

magnitude of the change in prices and the size of the economy. It is given by

φp
2

(cid:18) Pt(i)
Pt−1(i)

(cid:19)2

− 1

Yt,

(19)

where φp ≥ 0 is a measure of price rigidities. Using the demand function for intermediate goods

ECB Working Paper Series No 2596 / October 202115and assuming symmetry, the ﬁrst order condition of the optimization problem yields the New

Keynesian Phillips curve:

(1 − θ) + θst − πtφp(πt − 1) + βEt

(cid:20) λt+1
λt

πt+1φp(πt+1 − 1)

(cid:21)

Yt+1
Yt

= 0.

(20)

3.5 Capital Producers

There is a unit mass of identical perfectly competitive capital producers. Each period t, the

representative capital producer buys from entrepreneurs the current capital kt and uses it to

produce new capital kt+1 by combining it with investment it, and then sells kt+1 units to

entrepreneurs at nominal price qt. Since on average current capital depreciates at rate δt,

δt ∈ (0, 1), the average nominal price of second-hand capital is qt(1 − δt). Where note that 1 − δt

relates to the relative price of second-hand to new capital in Lanteri (2018). The behaviour of

the endogenous depreciation rate δt is modelled in the following subsection. The evolution law

of raw capital reads

(cid:18)

kt+1 = it

1 − S

(cid:19)(cid:19)

(cid:18) it
it−1

+ (1 − δt)kt.

As in Christiano et al. (2014), investment is subject to the adjustment cost function S

(21)

(cid:16) it
it−1

(cid:17)

.

This assumption helps reducing the volatility of investment and tames inﬂation as the reaction of

investment to shocks is smoother. As we will show at the end of Section 5, the Great Recession

generates a temporary increase in δt, destroying productive capacity permanently.

Capital producers maximise their ﬂow of proﬁts, where ˆqt = qt/Pt is the real price of capital,

subject to the evolution law of capital above. The FOC reads:

1 = ˆqt

(cid:18)

−S(cid:48)

(cid:18) it
it−1

(cid:19) (cid:18) it
it−1

(cid:19)

+ 1 − S

(cid:19)(cid:19)

(cid:18) it
it−1

+ βEt

λt+1
λt

ˆqt+1S(cid:48)

(cid:18) it+1
it

(cid:19) (cid:18) it+1
it

(cid:19)2

,

(22)

3.6 Entrepreneurs and Financial Intermediation

This section closely follows Christiano et al. (2014), with a few diﬀerences designed to generate

an endogenous depreciation rate depending on the fraction of ﬁrms going bankrupt. There is a

unit mass of perfectly competitive entrepreneurs. At the end of any period t, each entrepreneur

ECB Working Paper Series No 2596 / October 202116has a net worth N , N > 0.10 Even if the net worth of a particular entrepreneur is changing

over time, we omit index t to simplify notation. At equilibrium, net worth is distributed ft(N )

across entrepreneurs, with total net worth

¯Nt+1 =

(cid:90) ∞

0

N ft(N ) dN.

(23)

At the end of period t, entrepreneurs use their net worth N and loans BN

t+1 ≥ 0, to acquire
t+1 from capital producers.11 They pay price qt for any capital unit they buy such that

capital kN

t+1, BN

qtkN

t+1 = N + BN

t+1.

At equilibrium, all capital is allocated to entrepreneurs, s.t.,

kt+1 =

(cid:90) ∞

0

kN
t+1ft(N )dN.

(24)

(25)

As shown below, like in Christiano et al. (2014), the equilibrium debt-to-net-worth ratio does

not depend on N , implying that loans and capital are proportional to it. At t + 1, entrepreneurs

use capital kN

t+1 to produce capital services ωkN

t+1 that they sell to intermediate ﬁrms at price

rk
t+1Pt+1, where ω is an entrepreneur speciﬁc productivity shock and Pt+1 is the aggregate price

index. Entrepreneurs draw the idiosyncratic productivity ω at period t after buying capital kN

t+1.

Idiosyncratic productivity ω is assumed to be i.i.d. across time and ﬁrms, drawn at t from the

c.d.f. Ft(ω), log-normally distributed, with unit mean and standard deviation σt.

An entrepreneur with net worth N obtains a loan BN

t+1 from mutual funds at the interest

factor Zt+1. The interest factor is contingent on the state of the economy in t + 1 and, as shown

below, it is independent of N at equilibrium. For this reason, index N is omitted. On top of

aggregate risks, the debt contract has to take into account the presence of idiosyncratic risk,

since entrepreneurs facing low realizations of the shock ω may be unable to repay the loan, and

go bankrupt. Conversely, entrepreneurs with suﬃciently high returns on their capital will repay

10As for ﬁnancial frictions, the model mainly draws from Bernanke et al. (1999), so we assume that the
entrepreneur employs its own net worth N as well as loans from ﬁnancial intermediaries, i.e. mutual funds, to
ﬁnance his venture.

11As usual, for an arbitrary asset X, Xt+1 refers to the amount of this asset transferred from t to t + 1.

ECB Working Paper Series No 2596 / October 202117their loans and make positive cash ﬂow. For a given state contingent interest factor Zt+1, let

us deﬁne ¯ωt+1 as the state contingent productivity ω that zeroes the entrepreneur’s cash ﬂow at

t + 1, i.e.,

ΠN

t+1(¯ωt+1) = ¯ωt+1Rk

t+1 qtkN

t+1 − BN

t+1Zt+1 = 0,

(26)

where ΠN

t+1(ω) represents the entrepreneur’s cash ﬂow.12 If ω > ¯ωt+1, then ΠN

t+1(ω) > 0, whilst

if ω < ¯ωt+1, the entrepreneur goes bankrupt. The fraction of ﬁrm that go bankrupt at period t

is then Ft−1(¯ωt).

At t+1, after production takes place, an ω-type successful entrepreneur sells its undepreciated

capital (1 − ˆδt+1)ω back to capital producers at price qt+1. The depreciation rate of capital is
ˆδt+1 = δ

, a¯ω ≥ 0, where δ ∈ (0, 1) is a parameter representing the depreciation rate

(cid:17)a ¯ω

(cid:16) Ft−1(¯ωt)
F(¯ω)

at steady state. This speciﬁcation includes negative network spillovers from entrepreneurs that

went bankrupt in the previous period. It is a simpliﬁed way of representing the negative network

eﬀects on capital value associated with the disruptions in the production process generated

by economic downturns and bankruptcy. A larger bankruptcy rate will make the capital of

surviving ﬁrms less productive in the future due to the destroyed links. When the probability

of bankruptcy is at its steady state value F(¯ω), the impact of spillovers is normalised to 1. The

ex-post return at t + 1 to a unit of capital bought at t for an ω-type successful entrepreneur is

ωRk

t+1, with

Rk

t+1 =

t+1Pt+1 + (1 − ˆδt+1)qt+1
rk
qt

.

(27)

In case of bankruptcy, the mutual fund pays a monitoring cost µ, µ ∈ (0, 1), to appropri-

ate the payments generated by the capital services provided to intermediate ﬁrms as well as

the capital stock, which is then liquidated, subject to physical depreciation and obsolescence.

Moreover, when an entrepreneur goes bankrupt, the steady state depreciation rate of capital

is κ, κ ∈ (δ, 1) which is meant to capture both physical depreciation and obsolescence, obso-

lescence being measured by the diﬀerence κ − δ. Negative network spillovers aﬀect bankrupt
(cid:17)a ¯ω

entrepreneurs too, so that ˆκt+1 = κ

a¯ω ≥ 0. The ex-post return to capital for

(cid:16) Ft−1(¯ωt)
F(¯ω)

12Like Zt+1, ¯ωt+1 is independent of N at equilibrium. For this reason, index N is omitted.

ECB Working Paper Series No 2596 / October 202118bankrupt ω-type entrepreneur is ωRf

t+1, with

Rf

t+1 =

rk
t+1Pt+1 + (1 − ˆκt+1)qt+1
qt

(28)

which in this case is appropriated by mutual funds.

At time t mutual funds issue bonds to households at the risk-less factor Rt to raise the

resources needed to ﬁnance entrepreneurs. They also receive a transfer from the Monetary

Authority. The transfer is ﬁnanced by a tax on household’s proﬁts from entrepreneurial activity,

and is thus proportional to the return to capital of successful entrepreneurs. The parameter ξ

regulates the size of the transfer. This is a measure implemented to relax the cash constraint,

aiming to promote credit provision in bad times, and will assure steady state values in line

with U.S. data. For simplicity, let us assume that mutual funds specialise in entrepreneurs with

net worth N and operate under perfect competition. Since the interest factor Zt+1 is state

contingent, at each state of nature a zero proﬁt condition holds, i.e.:

(1 − µ)qtkN

t+1

(cid:90) ¯ωt+1

0

ωRf

t+1dFt(ω) + (cid:0)1 − Ft(¯ωt+1)(cid:1)BN

t+1Zt+1 + ξ

(cid:90) ¯ωt+1

0

ωdFt(ω)Rk

t+1qtkN

t+1 = BN

t+1Rt.

Divide both sides by Rk

t+1qtkN

t+1, use (26) and deﬁne leverage Lt =

N +BN
N

t+1

to get

(29)

(1 − µ)

Rf
Rk

t+1

t+1

(cid:90) ¯ωt+1

0

ωdFt(ω) + ¯ωt+1(1 − Ft(¯ωt+1)) + ξ

(cid:90) ¯ωt+1

0

ωdFt(ω) =

Rt
Rk

t+1

Lt − 1
Lt

.

The zero proﬁt condition above can then be used to ﬁnd an expression for leverage

(cid:18)

Lt =

1 −

(cid:16)

Rk
t+1
Rt

¯ωt+1(1 − Ft(¯ωt+1)) + (1 − µ)Ht(¯ωt+1) + ξGt(¯ωt+1)

(cid:17)(cid:19)−1

,

(30)

where

Ht(¯ωt+1) =

Rf
Rk

t+1

t+1

(cid:90) ¯ωt+1

0

ωdFt(ω)

Gt(¯ωt+1) =

(cid:90) ¯ωt+1

0

ωdFt(ω).

G(¯ω), G(¯ω) < 1, represents unsuccessful entrepreneurs’ contribution to the average ω, and H(¯ω), H(¯ω) <

G(¯ω), is corrected by the ratio of unsuccessful to successful returns.

Notice that the loan contract (Zt+1, BN

t+1) can be also written as a contract on (¯ωt+1, Lt). Any pair

(¯ωt+1, Lt) that satisﬁes (30) is a (t + 1)-state contingent contract oﬀered to entrepreneurs. As it will

ECB Working Paper Series No 2596 / October 202119become clear below, at equilibrium, the conditions of the loan contract (¯ωt+1, Lt) are the same for all

entrepreneurs irrespective of their net worth N . On one side, for a given net worth N , choosing loan BN

is equivalent to choosing leverage L. On the other side, setting the nominal interest factor Z determines

the cut-oﬀ productivity ¯ω.

At time t + 1, for any realization of the aggregate shocks, the debt contract (¯ωt+1, Lt) for an en-

trepreneur with net worth N is expected to generate the cash ﬂow

(cid:90) ∞

¯ωt+1

ΠN

t+1(ω) dF(ω) =

(cid:16)

1 − Γt(¯ωt+1

(cid:1)(cid:17)

Rk

t+1LtN,

(31)

(cid:16)

where

1 − Γt(¯ωt+1

(cid:17)

is the expected share of total revenues retained for successful entrepreneurs, with

Γt(¯ωt+1) = Gt(¯ωt+1) + ¯ωt+1

(cid:16)

1 − Ft(¯ωt+1)

(cid:17)

(32)

being the expected share going to the mutual fund.

For any state of nature in t + 1, the entrepreneur chooses the contract that maximises expected proﬁt,

which is equivalent to13

max
¯ωt+1

1 −

(cid:16)

Rk
t+1
Rt

1 − Gt(¯ωt+1) − ¯ωt+1

(cid:0)1 − Ft(¯ωt+1)(cid:1)

¯ωt+1(1 − Ft(¯ωt+1)) + (1 − µ)Ht(¯ωt+1) + ξGt(¯ωt+1)

(cid:17) = max
¯ωt+1

Lt(¯ωt+1)(cid:0)1 − Γt(¯ωt+1)(cid:1).

Thus the FOC pinning down the equilibrium ¯ωt+1 reads:

1 − Ft(¯ωt+1)
1 − Γt(¯ωt+1)

=

1 −

Rk
t+1
Rt

Rk
t+1
Rt

[1 − Ft(¯ωt+1) − G(cid:48)
(cid:16)

t(¯ωt+1)(cid:0)1 −

RF
Rk

t+1

t+1

(1 − µ) − ξ(cid:1)]

¯ωt+1(1 − Ft(¯ωt+1)) + (1 − µ)Ht(¯ωt+1) + ξGt(¯ωt+1)

(cid:17) .

(33)

(34)

This shows that the loss of accepting a higher threshold for entrepreneurs equals the beneﬁt of higher

leverage. The LHS is the elasticity of the share the entrepreneur keeps w.r.t. ¯ωt+1, whilst the RHS is

the elasticity of leverage w.r.t. ¯ωt+1.14 Also, notice that this speciﬁcation implies that the elasticity of

leverage is aﬀected by credit subsidies.

It is easy to see that the equilibrium ¯ωt+1 does not depend on N . From (30), leverage does not

depend on it either. Consequently, from (26), mutual funds set the same (t + 1)-state contingent interest

factor Zt+1 irrespective of net worth.

13Use (30) to substitute for Lt in (31), then divide by Rk
14The FOC also shows that our framework reduces to the standard model in Christiano et al. (2014) in the

t+1N to get (33).

case Rk = RF and ξ = 0.

ECB Working Paper Series No 2596 / October 202120Let us assume the standard deviation of Ft(ω) follows

log

(cid:17)

(cid:16) σt
¯σ

= ρσ log

(cid:17)

(cid:16) σt−1
¯σ

+ (cid:15)σ,t,

with ¯σ > 0, ρσ ∈ (0, 1) and the risk shock (cid:15)σ,t being i.i.d. Notice that a higher value of σt implies a

higher probability of drawing a low value of ω. As the variance of the shock increases, the tails of the

distribution get thicker, increasing the probability of tail events and modifying the threshold for ¯ω, i.e..

increasing the probability of bankruptcy.

Let us ﬁnally assume that at the end of period t + 1 (after entrepreneurs pay back to mutual funds

their period t debt) a fraction (1 − γ) of successful entrepreneur’s cash ﬂow ΠN

households, γ ∈ (0, 1). Moreover, each entrepreneur receives a transfer we Pt+1kN

t+1(ω) gets transferred to
t+1 from households, we ∈

(0, 1), as a form of insurance, to compensate for risk taking, and assuring that bankrupt entrepreneurs

will keep a strictly positive net worth allowing them to buy some capital for the following period.

Since liquidating the capital of failed entrepreneurs generates physical capital depletion, the deprecia-

tion of capital is endogenous and depends on the fraction of entrepreneurs going bankrupt. The aggregate

depreciation rate at time t reads

1 − δt = (1 − ˆκt) Ft−1(¯ωt) + (1 − ˆδt)(cid:0)1 − Ft−1(¯ωt)(cid:1).

The intuition is that when bankruptcy happens some capital (tangible or intangible) is destroyed in

the process, reducing the overall value of capital. The externality aims to capture negative disruptive

spillovers generated by bankruptcy. These could be the result of some specialised machines not being

reallocated as eﬀectively as in normal times or knowledge embedded in intangible capital being lost.

Moreover, we think of depreciation spillovers as (small) bankruptcy shocks with aggregate eﬀects through

the production network, resulting in an increase in the depreciation rate of capital for the whole economy.

This interpretation draws inspiration from Acemoglu, Akcigit, and Kerr (2016), who document signiﬁcant

network-based propagation channels stemming from small shocks.

3.7 Aggregate Economy

The quantity of capital produced by capital producers must be equal to the capital purchased by en-

trepreneurs:

kt+1 =

(cid:90) ∞

0

kN
t+1ft(N )dN.

ECB Working Paper Series No 2596 / October 202121N +BN
N

t+1

1

From (24), (30) and the deﬁnition of leverage, Lt =

, the equation above becomes

qtkt+1 =

1 −

(cid:16)

Rk
t+1
Rt

¯ωt+1(1 − Ft(¯ωt+1)) + (1 − µ)Ht(¯ωt+1) + ξGt(¯ωt+1)

¯Nt+1.

(cid:17)

(35)

Consequently, the level of capital in the economy depends on aggregate net worth, as deﬁned in (23), and

ﬁnancial conditions.

All intermediate ﬁrms face the same wage and capital cost, therefore, by symmetry:

kt(i)
ht(i)

=

kt
ht

,

(36)

for all i ∈ (0, 1). Also, market clearing for capital and labour implies (cid:82) 1

0 ht(i)di = ht.
Notice that if ﬁrms could change their prices in every period, they will choose the same price and produce

0 kt(i)di = kt and (cid:82) 1

the same quantity. In which case, pt(i) = Pt and yt(i) = Yt, hence aggregate production would become

Yt = atkα+η

t

h1−α
t

.

(37)

Therefore, if η = 1 − α aggregate technology has an AK structure.

Aggregate proﬁts of all entrepreneurs at the end of time t are [1 − Γt−1(¯ωt)]Rk

t qt−1kt, so that aggregate

net worth at t + 1 is:

¯Nt+1 = γ[1 − Γt−1(¯ωt)]Rk

t qt−1kt + Ptwekt

Using the aggregate production function and Kt = kt:

t = αstatkα+η−1
rk

t

h1−α
t

wt = (1 − α)statkα+η

t

h−α
t

st =

1
αα(1 − α)1−α

1
atkη
t

w1−α
t

(rk

t )α

(38)

(39)

(40)

(41)

All bonds held by households must be equal to the amount of loans in aggregate, and transfers to

mutual funds must equal taxes:

qtkt+1 − ¯Nt+1 = Bt+1

(cid:90) ¯ωt+1

ξ

0

ωdFt(ω)Rk

t+1qtkN

t+1 = τt

Output is allocated to consumption and investment, but also to intermediary production aimed to

ECB Working Paper Series No 2596 / October 202122cover price and wage adjustment costs as well as monitoring costs, i.e.:

Yt = ct + it
(cid:124) (cid:123)(cid:122) (cid:125)
GDP

+µ

(cid:90) ¯ωt

0

ωdF(ω)RF
t

ˆqt−1
πt

kt +

φp
2

(πt − 1)2 Yt +

χw
2

(πw

t − 1)2 Yt.

(42)

GDP is then deﬁned as the sum of consumption and investment, measuring aggregate demand.

3.8 Monetary Authority

The monetary authority uses the Taylor rule to set the nominal interest rate, subject to the zero lower

bound constraint:

Rm

t = ¯R + ρπ(πt − ¯πm) + ρy log

(cid:33)

(cid:32) (cid:91)GDPt
yp
t

Rt = max(1, Rm

t ),

(43)

(44)

where Rt is the nominal interest factor, ¯R and ¯π are target values, ρπ > 0 and ρy > 0 are policy
parameters, and yp
t



t = yp
yp

t−1 + ρ



(cid:91)GDPt−4−j − yp

t−1

 0 < ρ < 1

(45)



1
n

n
(cid:88)

j=1

is a measure of potential output. It is computed as a moving average of past GDP values, de-trended by
the stationary growth rate of the economy gz, so that (cid:91)GDPt = GDPt

(1+gz)t .

We deﬁne this measure to take into account the revisions carried out by central banks in the context

of the Great Recession. We implicitly assume that the monetary authority does not have full information

about the functioning of the economy, and it infers the underlying path from observed values of GDP.

In particular, our measure takes into account the lag in potential output revisions, as we disregard the

most recent 4 periods. This implies that the estimate of potential output is not very sensitive to negative

shocks if they are small in size and duration. We set n equal to 10, to allow the central bank to consider

a long enough period of time in the estimation of the underlying trend, but also react relatively quickly

to shocks.

As we will show in the following sections, the

rule provides stimulus to the economy, inducing it to close the output gap after a negative shock. Despite

the fact that the aggregate technology is AK, and because of the monetary policy intervention, GDP

appears to ﬂuctuate around a stable linear trend in normal times, appearing consistent with diminishing

returns to capital. However, if the shock is large and prolonged, potential output will be revised down-

wards and the stimulus to the economy will lose strength over time. As a result, the economy will reveal

its AK structure and the recovery will fail to materialise.

ECB Working Paper Series No 2596 / October 2021234 Baseline Calibration

We calibrate the model on quarterly data for the United States, considering the period 1980-2008 as our

reference.15 In order for the model to have an aggregate AK technology, we set η = 1 − α. Returns to

capital are then constant, generating endogenous growth. We consistently de-trend all non-stationary

variables using the the stationary growth rate gz, so that ˜ct = ct

(1+gz)t , and so on. Then
we solve the stationarised system of non-linear equations, calibrating the model to match some key data

(1+gz)t , ˜yt = Yt

moments.16

To characterise the stationary equilibrium, we target a labour share of 60.8%, in line with the average

value of the share of labour compensation in GDP. This is achieved by setting α = 0.24 and assuming a

price mark-up of 25%. The latter implies a value of 5 for the elasticity of substitution across intermediate

good, θ. We also calibrate the model to have zero inﬂation in steady state and a quarterly growth rate of

0.6%. The latter depends on the return to capital and the ﬁnancial frictions. We set the scaling parameter

ψ = 16.8 to labour hours in steady state be 0.2, in line with the average of annual hours worked by persons

engaged. We set γ to 0.966 (close to Bernanke et al. (1999)). Concerning the depreciation rate, we set

δ to 0.028 and κ to 0.04. These are somewhat higher than standard values, but we make this

choice because our deﬁnition of capital is wider compared to National Accounts, including all

categories of intangible capital. Although these stocks are not fully included in GDP measures,

they do aﬀect the outcome of production, and they depreciate faster than traditional measures

of capital, so we account for their depreciation in our calibration. Monitoring costs are set to

µ = 0.21, in line with Christiano et al. (2014) and within the rage suggested by Carlstrom
(cid:1) to obtain a steady state bankruptcy rate of
and Fuerst (1997). We set ξ = (1 − µ)(cid:0)1 − RF
ss
Rk
ss

approximately 1%, similarly to Christiano et al. (2014).

For Rotemberg adjustment costs, we follow the approaches proposed by Ascari and Rossi

(2012) and Born and Pfeifer (2020), calculating them as follows:

15We choose data covering this time span to characterise the steady state of the model since we do not take a
stand on whether an endogenous growth model has always been a good representation of GDP, as it is possible that
that the U.S. economy evolved from a Neoclassical structure to an AK structure over time due to technological
change. For example, the increasing importance of intangible capital, human capital and knowledge spillovers
for production, as documented by Haskel and Westlake (2018), could have led to such a transformation in the
production technology.

16Table 5 in the Appendix shows the comparison between the steady state of the model and U.S. data. For a

description of the data, see Appendix A.

ECB Working Paper Series No 2596 / October 202124Parameter

Value

Description

Preferences
β
χ
ν
ψ

Frictions
θ
ε
φp
χw
S”
µ
γ
we
ξ

Technology
α
η
δ
κ
a¯ω

Monetary Policy
ρπ
ρy
ρ
n

0.99
0.7
1
16.8

5
21
46.6
141.7
5
0.21
0.966
0.0005
0.009

0.24
0.76
0.028
0.04
0.15

1.5
0.125
0.7
10

Discount factor
Habit formation parameter
Inverse of Frisch elasticity
Scaling parameter for labour hours

Substitution in ﬁnal good
Substitution in labour input
Rotemberg price adjustment parameter
Rotemberg wage adjustment parameter
Investment adjustment costs
Monitoring costs
Fraction of proﬁts going to entrepreneur
Transfer from household
Transfer to ﬁnancial intermediaries

Private returns to capital
Knowledge spillovers in production
Successful entrepreneurs’ depreciation rate
Bankrupt entrepreneurs’ depreciation rate
Strength of depreciation spillovers

Policy response to inﬂation
Policy response to output gap
Speed of potential output revision
Number of past periods in moving average

Table 1: Quarterly calibration parameters

ECB Working Paper Series No 2596 / October 202125φp =

(θ − 1)θp
(1 − θp)(1 − βθp)

χw =

((cid:15) − 1) θ−1
θ (1 − α)θw
(1 − θw)(1 − βθw)

(46)

(47)

where θw = θp = 0.75 represent the probabilities of not being able to reset prices and wages.

Finally, we set a¯ω to 0.15, which implies that a 1% deviation of the probability of bankruptcy

from its normal value leads to an increase in the depreciation rate of approximately 0.1%. This is

considerably smaller compared to the values in Lanteri (2018)’s data and capital quality shocks

in Kozlowski et al. (2020), but our choice is conservative as the model is not expected to represent

all dimensions of the data. Our view is that there is suﬃcient evidence to support the capital

destruction channel as quantitatively relevant, but a precise estimate to base the calibration on

is not available. We therefore choose the parameter a¯ω to bring our model simulations close to

the fall in GDP observed in the data. The persistence of the conﬁdence and risk shocks during

the Great Recession, ρc = 0.9 and ρσ = 0.97 respectively, are taken from Christiano et al. (2014).

5 The Great Recession

Great Recession Shock. We model the Great Recession as the reaction of the economy

to a large and persistent demand shock that combines a risk shock and a conﬁdence shock,

both hitting at the same time.17 The magnitude of the risk shock is set to 15.7% increasing the

bankruptcy probability from a baseline value of 1% to 4%, in line with the smoothed bankruptcy

rate estimated by Christiano et al. (2014). We set the size of the conﬁdence shock to 12.56%,

in line with the decline of the HP-ﬁltered University of Michigan’s consumer sentiment for the

U.S. at the start of the Great Recession.

The conﬁdence shock brings the economy to the ZLB region. However, since our model does

not capture the unconventional monetary policies implemented by the Fed, nor forward guidance,

the model economy remains in the ZLB region only for a few quarters after the occurrence of

the Great Recession shock. We use U.S. data to build an alternative measure of the nominal

17In order to appropriately account for the sizeable deviation of endogenous variables from the original steady
state and the ZLB constraint, we solve the model non-linearly, employing a Newton-type method (Adjemian et
al., 2011) (Juillard et al., 1996).

ECB Working Paper Series No 2596 / October 202126Figure 4: Taylor rule vs FFR

interest rate consistent with the standard Taylor rule, i.e.,18

(cid:26)

TRt = max

0, T R + 1.5 (πt − ¯π) + 0.5 log

(cid:18) GDPt
yp
t

(cid:19)(cid:27)

,

setting the target nominal interest rate T R to 3.64%, the 2004-2007 average of the Federal Funds

Rate (FFR), and the inﬂation target ¯π to its oﬃcial value of 2%. Quarterly GDP is measured

in real terms and potential output yp
t

is real-time CBO data (in 2012 dollars).19 Inﬂation is

measured as the GDP deﬂator.20 In line with our simulations, as displayed in Figure 4, the

nominal interest rate TRt predicted by the Taylor rule shows a much shorter ZLB episode

compared to the Federal Funds Rate.

Summing up: The Great Recession shock combines a 15.7% risk shock and a 12.56% con-

ﬁdence shock. As a result, the bankruptcy rate increases in line with data, and the simulated

nominal interest follows the hypothetical FFR predicted by the Taylor rule when applied to

observed inﬂation and output gaps.

18A similar exercise was also conducted by the Board of Governors of the Federal Reserve System, among

others, with comparable results. See link here.

19Real-time CBO data are constructed employing the estimates published by the CBO at the beginning of

each year. It thus captures the unfolding of all revisions.

20Additional Details on data series used can be found in the Appendix.

ECB Working Paper Series No 2596 / October 202127Data Comparison.

In order to compare the simulations with key data dynamics in the U.S.,

we follow the approach of Christiano, Eichenbaum, and Trabandt (2015) to estimate targets

gap ranges from the data. We measure the deviation of variables from the path they would

have followed, had the recession not happened, by calculating the percentage diﬀerence from

a linear trend, ﬁtted on past data.

In order to select time intervals, we aim to follow the

CBO’s methodology for projections of potential output as closely as possible. “Typically, a

trend is considered to extend from at least one previous business cycle through the most recent

quarter of data (because the peak of the current cycle is not known at the time of a forecast).”21

They consider full peak-to-peak business cycles, so we build our estimates by including data

from the business cycles peaks preceding the Great Recession, up to the period before the

downturn. We construct min-max targets by considering the intervals [x : 2008Q2], with x =

(1990Q3, 2001Q1). We consider aggregate series retrieved from the FRED database for GDP,

consumption, investment, credit and the Federal Funds Rate. Finally, in order to compare the

switching-track of potential output in our model and in the data, we employ the measure of

potential output we built to calculate the Taylor rule in Figure 4. More details on data sources

can be found in the Appendix.

The Great Recession. Figure 5 shows impulse responses for some key variables in our model

to the Great Recession shock. The fall in conﬁdence slows down consumption demand, and

the sharp rise in risk depresses investment demand and raises bankruptcy. As bankruptcy

rates increase, capital depreciates faster resulting in capital destruction. Even when the shock

subsides and ﬁnancial variables converge back to the previous steady state values, due to capital

destruction the negative eﬀects on GDP, consumption and investment do not dissipate and

the economy displays an L-shaped recovery. Our model ﬁts the data quite well, especially for

GDP and consumption, which both fall by almost 10% at the new steady state, converging

monotonically in the same way as the data. As for investment, the simulation does not capture

the full depth of the total shortfall, which was partially driven by the the real estate market.

Nonetheless, results are more in line with private non-residential investment data. The model

ﬁts the data for credit well at the beginning of the sample, set aside the collapse of the credit

21From the report: ‘Revisions of CBO’s potential output since 2007’, (Shackleton, 2014).

ECB Working Paper Series No 2596 / October 202128Figure 5: Model impulse responses to Great Recession shock vs U.S. data

boom that we do not model, and performs worse for later periods. This is likely because we are

not modelling unconventional monetary policies providing credit easing. The behaviour of the

nominal interest rate is in line with the Taylor rule estimated in Figure 4, and thus does not

replicate the Federal Funds Rate after 2010, which remains for a long while at the ZLB, likely

due to unconventional monetary policies.

Switching-Track. Figure 6 clearly shows that the model economy replicates quite well the

switching-track of potential output in the data.22 The simulated output gap shrinks with time,

thus reducing its impact on the Taylor rule. Our simulations are in line with the U.S. experience,

and our speciﬁcation approximates well the timing of output gap dynamics observed in the data.

22The ﬁgure shows a slight increase in potential output in 2013, which is the result of the comprehensive
revision of the national income and product accounts (NIPAs) to include new investment categories. This led
to an increase in GDP value. We adjusted the potential output measures published, following the methodology
indicated by the CBO in their 2014 report, but a small margin of error remains.

ECB Working Paper Series No 2596 / October 202129Figure 6: GDP and potential output

Model’s Mechanics.

In order to better understand the mechanics of the two shocks, Figure

19 in the Appendix includes the impulse response of other variables to the Great Recession

shock. As it is common in ﬁnancial crises, credit declines and net worth contracts, mirroring a

stock market crash. Monetary policy is in place to mitigate the shock, but the ZLB constraint

limits its eﬀectiveness and, most importantly, the severity and the length of the recession put

downward pressure on potential output estimates, giving rise to a switching-track. Without

a strong policy intervention, the economy switches track moving to a lower GDP trejectory,

revealing its AK nature. In Figure 20 in the Appendix, we compare the results of our baseline

calibration with the case in which the Fed’s measure of potential output is much less sensitive to

past observed data. In this case, the policy remains much stronger, and the negative level eﬀects

on the trajectory of GDP are considerably reduced, showing the policy’s potential to partially

prevent the destruction of productive capacity and in shaping the the recovery. A slower revision

of potential output (inducing a weaker switching-track ) results in lower depreciation, directly

preventing the destruction of productive capacity and sustaining consumption and investment

ECB Working Paper Series No 2596 / October 202130demand. As a result, inﬂation gets stronger and the real interest rate rises faster, promoting

savings and a stronger recovery compared to the baseline simulation. The policy then induces

households to consume and save more, and entrepreneurs to invest more, with the economy

settling on a higher level.

Zero-Lower-Bound. Figure 21 in the Appendix highlights the role of the ZLB constraint in

our results, showing that the level eﬀect on GDP would have been less severe had the constraint

not been binding

Risk Shock. The risk shock is the main driver of our results. Figure 22 represents the impulse

response functions to the risk shock, once the conﬁdence shock is removed. The economy does

not reach the ZLB in this scenario, as the severe supply eﬀect of the shock drives inﬂation up.

Capital Destruction Channels.

In our model, bankruptcy destroys capital through two

diﬀerent channels: A liquidation channel operates directly through the partial destruction of

the capital stock of entrepreneurs going bankrupt, and a disruption spillovers channel through

the negative externality that bankruptcy has on the the productive capacity of capital for all

entrepreneurs. The ﬁrst captures the direct destruction of capital that follows bankruptcy, as

we assume that bankrupt ﬁrms face a liquidation cost in terms of capital equal to κ − δ > 0.

These ﬁrms are hit by the risk shock the hardest, but their aggregate eﬀect is not strong enough

to generate a downturn as large as the Great Recession. Figure 7 shows that the same demand

shock generates a permanent level eﬀect on GDP even with no disruption spillovers, but the

magnitude of the impact is considerably smaller. The second channel is the result of disruption

spillovers, capturing the idea that in downturns most ﬁrms are worse oﬀ, not just the ones that

exit.23 This modelling choice is indirectly supported by Lanteri (2018) data, which shows that

the price of used capital goods relative to new ones fell in the whole secondary market, and not

just for bankrupt ﬁrms. This second channel is key to replicate the magnitude of the Great

Recession in the model, as it is clear from Figure 7.

23In a similar spirit, Guerrieri et al. (2020) provide a theoretical argument in favour of a business exit multiplier
in the context of the COVID-19 crisis, showing that the exit of some ﬁrms may lead to negative ampliﬁcation
eﬀects in the economy.

ECB Working Paper Series No 2596 / October 202131Figure 7: Baseline simulation vs case without disruption spillovers

Revision intensity Faster than baseline Baseline Slower than baseline

ρ
Welfare losses

0.9
-7.3%

0.7
-6.8%

0.04
-6.4%

Table 2: Welfare losses for diﬀerent intensity of potential output revision

ECB Working Paper Series No 2596 / October 202132Welfare Losses.

In order to evaluate the impact of the policy, we calculate consumption

equivalent welfare losses, by comparing the path of utility following the Great Recession shock

to the path of utility at the initial steady state (where the economy would have stayed had

the Great Recession not happened). We conduct the analysis for 500 periods. Moreover, we

calculate welfare for diﬀerent intensities of potential output revision (switching-track ). The

Baseline column in Table 2 gives the welfare losses produced by the Great Recession demand

shock when output gap is revised following the baseline revision rule. The other two columns

do the same for alternative revision rules. Comparing columns, we conclude that faster revision

rules generate larger losses, which implies that a weaker policy intervention in the model wouldn’t

have been optimal.

In an AK world, when capital is destroyed output moves to a lower path. The optimal

reaction to such a shock is to remain in the new lower balanced growth path. Any policy

forcing households to save more than optimal in order to make capital return to its previous

trajectory is suboptimal. Why is it then the case that a Taylor rule forcing output to go back

to its previous track generates welfare gains? The fundamental reason lies in the destruction

prevention channel of monetary policy. In an economy with a negative externality stemming from

disruption spillovers, the cushioning eﬀect of the policy intervention tames bankruptcy down and

lowers depreciation, counteracting the shocks and allowing higher levels of consumption in the

new steady state, without forcing excessive savings along the transition.

What if We Relax the AK Assumption? In the previous sections we assumed η = 1 − α,

which implies an aggregate AK technology. Is such a strong assumption necessary to generate

our results? To test this, we simulate the model for lower values of η.24 We pick η = 0.06 to

get a quasi standard Cobb-Douglas technology. Figure 23 in the Appendix shows that when we

subject this version of the model to comparable shocks to simulate the Great Recession, and

we keep potential output constant to reproduce a more standard DSGE, the model generates a

quick and full recovery.25 This shows that the AK technology, and not the nature of the shocks,

24Note that in this case the model does not grow endogenously any more, implying that the growth rate of the

economy converges to zero.

25The model would also generate a similar recovery if we reduced the weight of the output gap in the Taylor

rule, as the recovery is a consequence of diminishing returns to capital.

ECB Working Paper Series No 2596 / October 202133Figure 8: Great Recession shock for η = 0.6

is the source of the parallel downward shift of GDP in this model.

We then try an intermediate case, setting η = 0.6 to get closer to an AK model, and allowing

potential output revisions. Figure 8 shows that the shocks result in a persistent recession

of reduced depth. Although this version of the model could be a good representation of GDP

dynamics in the presence of additional shocks, we prefer our baseline speciﬁcation, as it captures

key aspects of the Great Recession in a parsimonious way.

6 Normal Times and V-Shaped Recoveries

In this section, we begin by studying the mechanics of our model, and show that it can generate

policy-driven V-shaped recoveries when shocks are not overly severe or particularly persistent.

Moreover, we show that these mechanics can help our model replicate the dynamics of pre-Great

Recession recoveries.26 Throughout this section, we hold the value of potential output constant,

26Since in normal times the ZLB is never binding, we solve the model with perturbation methods.

ECB Working Paper Series No 2596 / October 202134Figure 9: Potential output revisions in past recessions (CBO data)

so that the output gap measures the deviation of GDP from the initial steady state.27 We do

not update the potential output measure because the revision procedure adopted after the Great

Recession started was the ﬁrst of its kind in the U.S. monetary policy history, as documented

by Coibion, Gorodnichenko, and Ulate (2017). Figure 9 illustrates this point for the two most

recent recessions before 2008 using CBO historical data. These are the the 1990 recession and

the 2000 dot.com recession. In both cases, the CBO revisions of potential output projections are

minor. Older vintages are unfortunately not available, so we rely on the statement in Shackleton

(2014) concerning the CBO’s methodology: “Recessions typically have little eﬀect on historical

estimates of potential output because the methodology aims to exclude cyclical eﬀects”. The

Great Recession was the only exception to this rule.

27An alternative practice in the literature is to model potential output as the level of output that would prevail
without nominal rigidities. We do not adopt this measure because the level of output at the balanced growth
path in an AK economy is fundamentally indeterminate, and as such depending on the policy intervention itself.
Moreover, central banks commonly use measures of potential output as deviations of output from trend. For
example, see Edge et al. (2008) for a discussion of the Fed’s FRB/US model or Vetlov et al. (2011), for the ECB’s
NAWM.

ECB Working Paper Series No 2596 / October 2021356.1 TFP Shocks

Let us ﬁrst show that small negative TFP shocks are followed by fast V-shaped recoveries by

implementing a textbook minus 1% TFP shock with persistence ρa = 0.79. The persistence of

the shock is in line with the literature, and was selected to illustrate a case where the economy

quickly recovers to the previous steady state.28 In Figure 10, we plot simulation results for our

baseline calibration as well as for a pure inﬂation targeting, i.e. following a Taylor rule with no

weight on the output gap. This ﬁgure shows that small shocks have permanent eﬀects on GDP

when ρy = 0, whilst the economy recovers when ρy = 0.125. A positive weight on the output

gap implies that the monetary authority will respond with stimulus to aggregate demand when

the output gap is negative, by oﬀering a lower nominal interest rate for each level of inﬂation.

A negative TFP shock reduces the supply of output, which puts pressure on prices to increase,

raising inﬂation. The presence of the output gap in the Taylor rule, compared to a scenario

where the weight of the output gap is zero, puts additional pressure on prices by leading to

higher consumption and investment.

More importantly, the presence of the output gap in the Taylor rule enables the prevention

destruction channel of monetary policy to operate. The stimulus aﬀects demand by lowering

the wedge between the return to capital for successful entrepreneurs and the risk-less rate, thus

eﬀectively reducing the inﬂuence of ﬁnancial frictions on the economy (see Figure 25 in the

Appendix). The condition for leverage (30), clearly shows that a fall in the wedge implies that

ﬁnancial intermediaries will oﬀer contracts with lower leverage for each feasible value of ¯ω. In

equilibrium, the entrepreneur will then ﬁnd it optimal to pick a contract with lower leverage

and lower ¯ω, keeping a larger share of her returns. Bankruptcy is thus reduced, leading to less

capital destruction. The spread between the interest rate on loans and the risk-less rate is also

reduced as a consequence of the policy intervention, so we conclude that a positive weight on the

output gap tames risk in the economy overall, sustains aggregate demand and prevents capital

destruction, keeping output and savings higher until the output gap closes. By preventing capital

destruction monetary policy leads to a V-shaped recovery.

28The Taylor rule systematically generates a full recovery after a TFP shock, but Figure 24 in the Appendix

shows that the recovery is fast as long as the persistence of the shock is not too high.

ECB Working Paper Series No 2596 / October 202136Figure 10: Eﬀects of a 1% negative TFP shock

Weight on the output gap
150 periods

ρy = 0
-0.22%

ρy = 0.125
-0.08%

Table 3: Welfare losses of TFP shock for diﬀerent weights on the output gap

Table 3 shows the welfare gains associated to monetary policy in this framework.29 For a

pure inﬂation targeting Taylor rule, with ρy = 0, a minus 1% transitory TFP shock generates

sizeable 0.22% (consumption equivalent) welfare losses. When the output gap is added to the

Taylor rule, with standard (quarterly measured) ρy = 0.125, we ﬁnd that following the mandate

of economic stability in monetary policy interventions unequivocally improves welfare, halving

welfare losses of a recessions from 0.22% to 0.08%–see Table 3.

6.2 Small Demand Shocks

In this section, we aim to represent demand shocks in normal times, which we characterise as

periods subject to shocks that are not as severe and persistent as during the Great Recession.

29In order to compute welfare gain and losses, we run the simulation with second-order perturbation methods.

ECB Working Paper Series No 2596 / October 202137We target an increase in the bankruptcy probability of approximately 0.5 percentage points, to

mirror Christiano’s estimation for the recessions preceding the ﬁnancial crisis. Thus, we opt for

a 5% increase in risk combined with a 4.5% conﬁdence shock and we reduce the persistence of

shocks to 0.7. This is close to pre-Great Recession estimates on conﬁdence shocks documented

by Angeletos, Collard, and Dellas (2018) and with the analysis of Christiano et al. (2015), who

illustrate the increased persistence of ﬁnancial shocks during the Great Recession compared to

previous downturns. Figure 11 shows that monetary policy drives a V-shaped type of recovery

in this case as well, although the economy will not converge back to the previous steady state

within the 50 quarters period. Since we assume that potential output is never revised, the

economy will eventually converge to the previous trajectory. In any case, the remaining output

gap is small enough not to be perceived as a change of trajectory resulting from the demand

shock.

Figure 11: Eﬀects of a small demand shock

In order to understand the mechanics behind the recovery role of monetary policy, it is useful

to think about the policy in place as a force counteracting the negative shocks. As the demand

ECB Working Paper Series No 2596 / October 202138Figure 12: Oil and conﬁdence shocks measure

shock hits and GDP falls, a larger output gap gives the policy strength, but as the recovery

starts to materialise and inﬂation recovers, the monetary authority faces a trade-oﬀ between

above target inﬂation and a negative output gap. The higher weight on inﬂation in the Taylor

rule results in a slowdown in the recovery, although GDP will eventually go back to the initial

steady state.

6.3 Historical V-Shaped Recoveries

This section exempliﬁes the ability of our model to generate V-shaped recoveries in line with

the recovery episodes that followed the 1974 and 1990 oil shock recessions.30

Shocks. Both recessions followed large oil price increases, concomitantly associated with strong

declines on consumers conﬁdence. The left panel of Figure 12 represents the HP ﬁlter cyclical

component of the ratio between the GDP deﬂator and the U.S. Crude Oil Composite Acquisi-

tion Cost by Reﬁners, both expressed as indexes with 2012 set equal to one. The conﬁdence

shocks are represented in the right panel of Figure 12 by the HP ﬁlter cyclical component of

the Michigan Consumer Sentiment index. Both ﬁgures show large negative oil and conﬁdence

shocks in 1974 and 1990, larger in 1974 and more persistent in 1990.

30We don’t aim to replicate the 1980 oil shock because the recession was driven by the disinﬂation eﬀort
initiated by Paul Volker. Similarly, we do not attempt to replicate the the dot.com recession as it was primarily
driven by the collapse of the equity market.

ECB Working Paper Series No 2596 / October 202139The 1974 Oil Shock Recession.

In October 1973, the Organization of Arab Petroleum

Exporting Countries (OAPEC, the Arab majority of the OPEC) announced large cuts in oil

production and an oil embargo aﬀecting the U.S., among other countries. By March 1974, when

the embargo ended, oil prices had tripled. Such a disruption in oil supply and increase in oil

prices led to a deep recession, cumulating a large decline in U.S. GDP between the last quarter

of 1973 and the ﬁrst quarter of 1975, the size of the U.S. output gap reaching 5% according to

Fed and CBO data.

In order to characterise the recovery that followed the First Oil shock, we construct a measure

of output gap by de-trending real GDP consistently with the methodology we followed for the

Great Recession.31 Figure 13 shows that de-trended GDP follows closely the CBO output gap

despite expected diﬀerences in methodology as well as diﬀerences driven by data revisions, as

documented by Orphanides (2003). More importantly, Figure 13 shows for both measures of

the output gap that the First Oil shock recession was followed by a V-shaped recovery, bringing

GDP back to its previous track by the end of 1978 .

Let us here use our baseline model to replicate the reaction of the U.S. economy to the 1979

oil shock.32 In line with Rotemberg and Woodford (1996) and Herrera, Karaki, and Rangaraju

(2019), we include oil in the model as an input of production.

In our framework oil shocks

are equivalent to TFP shocks, resulting in rising production costs and a reduction in GDP. We

thus represent oil price shocks as TFP shocks,33 and set the size of the shock to generate a fall

in GDP in line with data. Conversely, for the conﬁdence shock we follow closely the result in

Figure 12. We then model the First Oil Shock as a negative 18% TFP shock and a negative

16% conﬁdence shock, setting the persistence of the shocks to 0.82 and 0.7, respectively, in line

with the persistence of the shocks in the data (approx 3 years for the oil shock and 2 years for

the conﬁdence shock).

The left panel in Figure 13 compares the dynamics of the model with the CBO output Gap

31GDP is linearly de-trended including data from two previous business cycle peaks, in line with CBO method-

ology.

32Note that we did not modify our baseline calibration for this exercise to ease comparison with previous
results, but also because some key steady state moments remained in line with the data even considering previous
time periods (see Table 6 and Table 7 in the Appendix).

33See Appendix E for a formal argument in favour of using TFP shocks to represent oil price shocks in our

framework.

ECB Working Paper Series No 2596 / October 202140Figure 13: 1974 and 1990 Oil Shock Recessions - Model vs data

and our measure of de-trended GDP, and shows that the model replicates well the V-shaped

recovery observed in the data.

The 1990 Recession.

The 1990 recession was triggered by the Iraqi invasion of Kuwait

in August 1990, lasting less than one year and leading to an increase in oil prices that was

smaller and shorter than after the First Oil shock. However, the recovery was slow, as can be

seen by comparing both panes in Figures 13, and jobless –see Schreft, Singh, et al. (2003). The

fundamental reason is widely attributed to the persistent drop in conﬁdence that followed the

spike in oil prices. The Michigan consumer sentiment index shows longer persistence after the

starting of the 1990 that after the start of the 1974 oil shock recession. Similarly to the 1974

excise, the right panel in Figure 13 compares to the CBO output gap and detrended GDP to

the response of the model to a combined negative 15% TFP and 6% conﬁdence shocks. The

persistence of the shocks is 0.82 and 0.84, respectively, also in line with the persistence of the

shock in the data (approx 3 years for the oil shock and 4 years for the conﬁdence shock). The

resulting dynamics follow closely the slow-V-shaped recovery in the data.

Overall, these ﬁndings show that our model can generate V-shaped recoveries in line with

historical episodes.

ECB Working Paper Series No 2596 / October 2021417 The Taylor Rule and the Fed

The joint promotion of price stability and strong economic activity has been the main objective

of the Federal Reserve System since its inception. Following the DSGE literature, this paper

represents the decision process followed by the Fed, which ultimately aims at fulﬁlling its dual

mandate of price and macroeconomic stability, by the J. Taylor (1993) rule.34 In our model, the

Taylor rule plays a critical role in shaping economic recoveries.35 On one side, the existence of a

V-shaped recovery relies on the assumption that the weight given to the output gap in the Taylor

rule is positive and strong enough to bring the economy back to its original potential output track

after a negative supply or demand shock. On the other side, the existence of an L-shaped recovery

relies on the revision of potential output estimates during deep and persistent downturns, i.e.

the switching-track. As a result, in our model the shape of economic recoveries critically depends

on the speciﬁcation of the Taylor rule and on the monetary authority’s information set when

measuring the output gap.

In this section, we provide a consistency check to substantiate the notion that the Taylor

rule represents the Fed’s policy choices, supporting our modelling strategy and validating our

conclusions. We also discuss whether there are alternative rules consistent with the behaviour

of the Fed that would call into question our conclusions on the dynamics of economic recovery.

Moreover, we conduct deeper analysis to deﬁne the Fed’s information set and asses the

validity of the indicators we use in the paper. The research staﬀ at the Federal Reserve Board

of Governors regularly prepares projections about how the U.S. economy will fare in the future.

These projections are published in the Greenbook of the Federal Reserve Board before each

meeting of the Federal Open Market Committee, and are part of the information set setting the

ground for monetary policy decisions. Unfortunately, output gap protections in the Greenbook

are made available with a six year lag and the corresponding time series are not as long as

the Congressional Budget Oﬃce (CBO) data. For this reason, throughout this paper, we use

34For a detailed historical account of monetary policy objectives in the United States see Orphanides (2003).
35In an AK growth model, the intercept of the balanced growth path for GDP is indeterminate, and pinned
down by the initial value of capital and capital accumulation in the transition to the stationary growth rate (the
slope of the GDP balanced growth path). A monetary policy set to stabilise the output gap when facing negative
supply or demand shocks, increases the intercept of the new balanced growth path by accelerating growth in the
transition.

ECB Working Paper Series No 2596 / October 202142data from the CBO to proxy the changes in the Fed’ beliefs about potential output. In this

section, we use available data from the Greenbook to check for discrepancies between the two

data sources, and test whether they matter in estimating the Taylor rule.

Does the Taylor Rule Summarise the Fed’s Policy? In order to answer this question, we

ﬁrst build measures of the nominal interest rate consistent with the Taylor rule, and compare

them with the Federal Funds Rate. We do that by measuring the nominal interest rate (in

annual terms) emerging from the original J. Taylor (1993) rule36

TRt = r∗
(cid:124)(cid:123)(cid:122)(cid:125)
TR−π

+πt + φπ (πt − π) + φy xt,

(48)

with ππ = φy = 0.5. The real interest rate r∗ is set to 2%. Inﬂation πt is measured as year on

year percentage changes in the quarterly GDP deﬂator, and ¯π is set to 2%. The output gap

xt is one of the three following measures: the CBO’s output gap (as reported in the February

2021 revision), the Greenbook output gap (as reported in February 2021), as well as a real time

measure of the latter, i.e. using for each quarter the last historical estimate of the output gap

published in the corresponding quarter. As it can be observed in Figure 14, the nominal interest

rate series that emerge from the above Taylor rule, for the three diﬀerent measures of the output

gap, closely follow the Federal Funds Rate.37 38

As an additional check, we estimate the policy parameters φπ and φy of the standard Taylor

rule, following the approach suggested by Kahn (2012), and considering the Federal Funds Rate

as the policy instrument. To allow the target FFR, measured by TR to change, we estimate

(48) between 1960 and 2019 for the following sub-periods:

(cid:136) 1960Q1-1979Q3: Great Relaxation (GRel)

(cid:136) 1979Q4-1986Q4: Great Disinﬂation (GD, Volcker era)

(cid:136) 1987Q1-2001Q1: Great Moderation (GM)

36Which is in line with the Board of Governors of the Federal Reserve System. See FRED Blog (St Luis Fed)

link here.

37The discrepancies observed after 2010 are discussed in Section 5.
38Note that here CBO data corresponds to the time series published in 2021, whilst in Figure 4 we constructed
a real-time estimate. As we could not build the same measure for the whole time period due to data limitations,
we relied on the latest revision in this section.

ECB Working Paper Series No 2596 / October 202143Figure 14: Taylor rule with alternative output gap measures

(cid:136) 2001Q2-2019Q4: Great Deviation and Great Recession (GDe-GR).39

The results of the estimations in Table 4 show that the output gap is generally a strong

predictor of the FFR, and coeﬃcients are in line with the original J. Taylor (1993) rule. The

only exception is the Volcker era, which comes at no surprise as the eﬀort associated with

reducing inﬂation levels likely generated a deviation from the standard Taylor rule during this

period.40 These ﬁndings support our modelling choices on the speciﬁcation of the policy rule as

well as our calibration.41

Did the Fed’s Beliefs about Potential Output Switch-Track after the Great Reces-

sion? The left panel in Figure 2 clearly shows the switching-track in the CBO estimations of

potential output during the Great Recession. However, did the Fed’s beliefs about potential

output, implicit in the output gap measures reported in the right panel of Figure 2, change

39Here we refer to J. B. Taylor (2011), who points out that policy makers started deviating form the TR

already at the beginning of the century, giving rise to a Great Deviation ahead of the Great Recession.

40Similarly, the historical account of Orphanides (2003) found that the largest deviations from the Taylor rule

occurred before the Great Relaxation and during the Volcker disinﬂation period.

41As a robustness check, we also estimated the policy parameters for the whole period, accounting for changes

in the policy target through period dummies, and found comparable results.

ECB Working Paper Series No 2596 / October 202144(GRel)
FFR
b/se
0.823∗∗∗
(0.062)
0.391∗∗∗
(0.057)

(GD)
FFR
b/se
1.088∗∗∗
(0.111)
0.078
(0.104)

(GD)
FFR
b/se
1.090∗∗∗
(0.111)

0.024
(0.089)

(GM)
FFR
b/se
1.731∗∗∗
(0.102)
0.682∗∗∗
(0.081)

(GM)
FFR
b/se
1.422∗∗∗
(0.094)

0.522∗∗∗
(0.067)

(GDe-GR)
FFR
b/se
0.921∗∗∗
(0.185)
0.425∗∗∗
(0.061)

Inﬂation Gap

CBO

GB

GB RT

TR

3.402∗∗∗
(0.118)
79
0.762
Note: Robust standard errors in parentheses.

7.453∗∗∗
(0.428)
29
0.812

Number obs.
R2

7.274∗∗∗
(0.346)
29
0.810

5.462∗∗∗
(0.121)
57
0.763

5.297∗∗∗
(0.133)
57
0.753

2.217∗∗∗
(0.161)
75
0.621

(GDe-GR)
FFR
b/se
1.138∗∗∗
(0.195)

(GDe-GR)
FFR
b/se
1.062∗∗∗
(0.236)

0.266∗∗∗
(0.047)

1.860∗∗∗
(0.152)
71
0.588

0.333∗∗∗
(0.068)
2.391∗∗∗
(0.240)
59
0.612

Table 4: Taylor rule estimation - Output Gap

consistently? Figure 14 shows that the output gap measures emerging from the CBO and the

Greenbook data yield similar results when using the Taylor rule to estimate the nominal interest

rate.42 We then conclude that the implicit potential output measure in the Greenbook is consis-

tent with the CBO potential output estimates, which is in strong support of the hypothesis that

Fed’s beliefs concerning potential output switched track after the Great Recession. Estimations

of the output gap policy parameter in Table 4 conﬁrm that CBO data can be considered a good

proxy of the Fed’ beliefs on potential output, and we can thus conclude that the Switching-track

mattered for the Fed’s policy choices during the Great Recession.

Alternative Rules. We showed that the classic Taylor rule can adequately summarize the

Fed’s policy making, supporting our claim that monetary policy interventions play a critical role

in shaping economic recoveries. Nonetheless, the impact of economic activity on monetary policy,

as represented by the Taylor rule, could be modelled in diﬀerent ways. Two other measures of

economic activity are widely considered as alternatives to the output gap in the Taylor rule: the

unemployment gap and the growth gap. The former is measured as the diﬀerence between the

unemployment rate and the non-accelerating inﬂation rate of unemployment (NAIRU), while

the latter is measured as the gap between the actual and the long term growth rate. Could these

diﬀerent alternative speciﬁcations alter the key result of this paper, i.e. that the Taylor rule

shapes economic recoveries? Is there an alternative rule, consistent with the historical behaviour

42In fact, Figure 26 in the Appendix shows that both output gap measures tend to be extremely close.

ECB Working Paper Series No 2596 / October 202145Figure 15: Alternative output gap measures

of the Fed that would not generate a V-shaped recovery in our model?

Firstly, it is important to stress that the NAIRU is estimated similarly to potential output, so

that the unemployment gap in the data looks like the mirror image of the output gap, as shown

by the left panel of Figure 15.43 As a consequence, when accurately modelling unemployment,

a Taylor rule targeting the unemployment gap will likely yield similar results as a Taylor rule

targeting the output gap.44

As for the growth gap, we measure it as the distance between quarterly GDP growth, year

on year, and the long term growth rate of 2.2%. The resulting growth gap is depicted in the

right panel of Figure 15, and although it clearly moved in line with the output gap, it tends

to shrink faster.

Incorporating the growth gap in the Taylor rule in our model would then

provide less stimulus after negative shocks, which might not be enough to generate V-shaped

recoveries before the Great Recession. To check for this, we take two steps, detailed in Appendix

D. Firstly, we check whether the growth gap can be considered as a good predictor of the FFR

by estimating the relative policy parameters, and ﬁnd that this was the case during the Great

Disinﬂation and the Great Moderation. We then incorporate the growth rule in our model,

and check how the model would react to the oil shocks considered in the previous section. As

expected, the recovery in the model weakens compared to our baseline as a result of the policy

change. GDP does not return to the original steady state, but the recovery remains V-shaped

43Unemployment data was retrieved from the U.S. Bureau of Labor Statistics, while the NAIRU estimate is

taken from CBO data.

44We do not run this type of exercise using our framework since there is no unemployment in our model.

ECB Working Paper Series No 2596 / October 202146in both cases. To sum up, the growth gap is more likely to yield incomplete V-shaped recoveries

compared to the output gap, but the diﬀerences are likely to be small in a context of moderate

shocks.

Overall, the results presented in this section support our modelling choices and the idea that

monetary policy interventions played a critical role in shaping recoveries in the United States.

8 Conclusion

Our paper contributes to the literature by showing that an endogenous growth model can repro-

duce the dynamics of U.S. GDP well, once the role of monetary policy is taken into account. In

our framework, the diﬀerentiating factors between the Great Recession and previous recessions

were the size and persistence of the shocks, the subsequent capital destruction, the binding of

the zero lower bound and the introduction of the switching-track.

This paper opens several avenues for future research. Firstly, it would be interesting to

explore whether the economy has in fact evolved from a Neoclassical technology to an AK

model because of the rise of intangible capital. “Because intangible investments, on average,

behave diﬀerently from tangible investments, we might reasonably expect an economy dominated

by intangibles to behave diﬀerently too.”45 Secondly, we are keen to further investigate the

destruction prevention channel of monetary policy and its implications for optimal monetary

interventions. Lastly, this paper does not fully address the role of unconventional monetary

policies implemented following the ﬁnancial crisis. It would be interesting to explore this aspect,

by evaluating further the impact of central bank credit policies on the recovery process in our

model, following the example of Gertler and Karadi (2011).

45(Haskel & Westlake, 2018) page 10.

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ECB Working Paper Series No 2596 / October 202150Appendix

A Model-data Comparison and Data Sources

Taylor Rule: GDP is Real Gross Domestic Product, Billions of Chained 2012 Dollars,

Seasonally Adjusted Annual Rate, inﬂation is Gross Domestic Product: Implicit Price

Deﬂator, Index 2012=100, Seasonally Adjusted (percentage change from a year ago), FFR

is the Eﬀective Federal Funds Rate, Percent, Not Seasonally Adjusted. Potential output

historical estimates were retrieved from the Congressional Budget Oﬃce website.

Data for Model Simulation Comparison: all data was retrieved from the FRED

database. GDP is Real Gross Domestic Product, consumption is Real Personal Consump-

tion Expenditures, investment is Real Gross Private Domestic Investment and private

non-residential investment is Private Nonresidential Fixed Investment, divided by its de-

ﬂator (retrieved from BEA). All variables are expressed in billions of chained 2012 dollars,

quarterly, seasonally adjusted annual rates and in per capita terms. The bankruptcy prob-

ability is the estimated risk shock in Christiano et al. (2014). Credit is Total Credit to the

Non-Financial Corporations, adjusted for breaks, in billions of U.S. Dollars, divided by the

GDP deﬂator. The nominal interest rate is the Eﬀective Federal Funds Rate (quarterly

averages).

Data for Model Steady State Comparison: All values are averages over the period

1980-2008Q2 or 2008 when data was available annually. The labour share is the average of

the share of labour Compensation in GDP, and labour hours are the average of the time

series average annual hours worked by persons engaged for United States, calculated as a

percentage of total hours in the year. GDP growth per capita was retrieved from FRED

(BEA data) and the investment to GDP ratio is calculated in real terms from BEA data.

The real interest rate data was retrieved from the World Bank database. The interest

spread is the corporate bond credit spread constructed by Gilchrist and Zakrajˇsek (2012),

i.e., the average diﬀerence between the interest rate on ﬁrm speciﬁc loans in COMPUSTAT

and the rate the U.S. government would have paid for a comparable maturity. Leverage is

ECB Working Paper Series No 2596 / October 202151proxied by the average of real debt over real assets for the Non-ﬁnancial private sector in

COMPUSTAT, where total assets were deﬂated using the BEA investment deﬂator, whilst

total debt was deﬂated using the GDP deﬂator.

Moment

Model

U.S. Data

Labour share (1980-2008)

60.8%

61%

Labour hours (1980-2008)

20%

20.5%

Quarterly GDP growth pc (1980-2008Q2)

0.6%

0.5%

Investment share(1980-2008)

12%

15%

Real interest rate (1980-2008)

1.6%

0.6 %

Interest spread(1980-2008Q2)

1.2 pp

1.6 pp

Leverage(1980-2008)

0.5

0.5

Table 5: Aggregate data and model steady state values

Moment

Model U.S. Data

Labour share (1950-1973)

60.8%

63.4%

Labour hours (1950-1973)

20%

22%

Quarterly GDP growth pc (1947-1973Q3)

0.6%

0.6%

Investment share(1947-1973Q3)

12%

11%

Real interest rate (1961-1973)

1.6%

0.6%

Table 6: Aggregate data and model steady state values - 1947-1973

ECB Working Paper Series No 2596 / October 202152Moment

Model U.S. Data

Labour share (1980-1990)

60.8%

61.2%

Labour hours (1980-1990)

20%

20%

Quarterly GDP growth pc (1990-1990Q3)

0.6%

0.5%

Investment share(1980-1990Q3)

12%

14%

Real interest rate (1980-1990)

1.6%

1.68%

Table 7: Aggregate data and model steady state values - 1980-1990Q3

ECB Working Paper Series No 2596 / October 202153B Taylor Rule Mechanics

With a positive weight in the output gap, the Taylor rule implies that a negative output gap

will put pressure on the nominal interest rate to fall. However, in our simulations we ﬁnd that

adding to the Taylor rule a positive weight on the output gap generates higher nominal interest

rates and inﬂation in equilibrium, compared to pure inﬂation targeting (see Figures 10 and 11).

More importantly, the real interest rate is also higher, depressing economic activity instead of

promoting it. This appears to be puzzling. In order to understand how a positive weight on the

output gap can generate an increase in both the nominal interest rate and inﬂation, we propose

a simple exercise of comparative statics. In our model, as in the standard New Keynesian model,

the nominal interest rate and inﬂation are determined by the intersection of the Euler equation

and the Taylor rule. These can be represented by the following linear relationships between

inﬂation and the nominal interest rate, ignoring the ZLB constraint,

Taylor rule : R =

1 + gz
β

+ 1.5 (π − ¯π) + 0.125 log

(cid:33)

(cid:32) ˆGDPt
¯ˆGDP

Euler equation : R =

1 + gz
β

ˆλt
ˆλt+1

πt+1
πt

π.

(49)

(50)

At any period t, equilibrium inﬂation πt and nominal interest rates Rt are the pair {π, R} that

solves (49) and (50). The straight-lines crossing point SS in both plots in Figure 16 represent

(49) and (50) at the non-stochastic steady state.

How would equilibrium change if we considered the response of the economy to a TFP shock?

To answer this question, we use values of

ˆλt
ˆλt+1

, πt+1
πt

and

ˆGDPt
¯ˆGDP

from our baseline TFP shock

simulation at times 1 and 5 to plot (49) and (50). The left panel in Figure 16 represents both

equations in a pure inﬂation targeting economy –when zeroing the coeﬃcient of the output gap

in (49). As the shock hits, the Taylor rule does not move but the Euler equation moves upwards,

and then gradually comes back to the initial value. The transition is consistent with the IRFs

in FGDe-GRigure 10, as the TFP shock results in a temporary increase in the nominal interest

rate and inﬂation. The real interest rate goes up during the transition, since the slope of the

Taylor rule is larger than one.

ECB Working Paper Series No 2596 / October 202154Figure 16: TFP shock mechanics with no weight on the output gap

We repeat the exercise for the scenario in which the weight on the output gap is positive.

The right panel in Figure 16 shows that in this case the Taylor rule shifts to the right as the

output gap pushes the intercept down, so that Rt and πt are higher in equilibrium at time 1,

compared to the pure inﬂation targeting case, consistently with our results in Figure 10. More

importantly, the eﬀect on the real interest rate relative to the pure inﬂation targeting scenario

depends on the slope of the Euler equation, in turn eﬀected by aggregate shocks and the policy

intervention. This simple exercise shows that a positive weight on the output makes the the

monetary authority oﬀer a lower nominal interest rate for each level of inﬂation, stimulating

substitution from savings to consumption through the Euler equation. The resulting dynamic

can entail a larger interest rate compared to inﬂation targeting, but this equilibrium result does

not imply a contractionary policy impact.

C Capital Quality

In this section we compare the depreciation rate in our model for the Great Recession to a

measure of capital quality constructed by Kozlowski et al. (2020). They employ the Fed’s Flow

of Funds data for non-ﬁnancial assets held by corporations, at market value (MV) and historical

cost (HC). We replicate their methodology with quarterly series, assuming the depreciation rate

to be at our steady state value. They deﬁne a capital quality shock as a decline in the productive

ECB Working Paper Series No 2596 / October 202155value of installed capital, which is equivalent to a rise in depreciation in our model. Assuming:

kt = φtˆkt, the capital used in production kt depends on the installed capital ˆkt and the shock

φt, equal to 1 in normal times.

Let us denote by kt the stock of capital at the end of period t, and by xt and pt real investment

and the price of capital at time t, respectively. Past capital (net of depreciation) and current

investment cumulate in ˆkt that suﬀers a quality shock φt before becoming the end of period

capital kt, i.e.:

ˆkt = xt + (1 − δ)kt−1

and

kt = φtˆkt.

Kozlowski et al. (2020) assume that historical capital is measured following

HCt = pt−1xt + (1 − δ)HCt−1

Then, assuming ptkt = MVt, from (51) and (52) we can recover

(51)

(52)

pt−1ˆkt = (1 − δ)pt−1kt−1 + pt−1xt = (1 − δ)MVt−1 + HCt − (1 − δ)HCt−1.

(53)

then using the non-residential investment deﬂator from BEA:

φt =

kt
ˆkt

=

ptkt
pt−1ˆkt

P riceIndext−1
P riceIndext

(54)

The resulting measure has an average value of 1.01 in the interval we consider, and displays

a large negative realization in conjunction with the Great Recession. This mostly captures

variations in the market value of structures, as the methodology behind the data adjusts the

market value of commercial real estate. In this sense, this series complements Lanteri (2018)’s

data, which was informative as to the value of equipment.

Mapping into our model, φt = 1−δt

1−δ . We normalise the data to average 1 to ease comparison,

and Figure 17 shows that our model is consistent with the dynamics of the data. The magnitude

of the model’s fall in capital value is considerably smaller compared to the constructed measure,

conﬁrming our conservative approach.

ECB Working Paper Series No 2596 / October 202156Figure 17: Capital quality measure from Kozlowski et al. (2020) in the data and the model

D The Growth Gap and the Taylor Rule

In order to evaluate the role of the growth gap for monetary policy in the United States, we

repeat the steps followed in Section 7, quantifying the growth gap as the distance between

quarterly GDP growth, year on year, and the 2.2% trend. Table 8 shows the estimation of the

Taylor rule using the growth gap instead of the output gap. The growth gap performs similarly

to the output gap during the Great Moderation, but much worse after the year 2000, as the

coeﬃcient turns negative.

We then check how the growth gap would aﬀect the behaviour of our model. If we assume

that policy makers were following the growth gap before the Great Recession, can we still

generate V-shaped recoveries in line with data? To do this, we substitute the Taylor rule (43)

in the model by46

Rt = ¯R + ρπ(πt − ¯πm) + ρy log

(cid:32) (cid:91)GDPt
(cid:92)GDPt−4

(cid:33)

.

(55)

We then run the model to replicate the 1974 and the 1990 oil driven recessions. Figure 18

shows that the model still generates a V-shaped recovery, but this is incomplete, as GDP fails

46Output is de-trended in steady state in our model, hence growth is null. Consequentially, the year on year

growth gap is equivalent to the deviation of the log of de-trended GDP from its fourth lag.

ECB Working Paper Series No 2596 / October 202157(GRel)
FFR
b/se
0.782∗∗∗
(0.074)
0.118
(0.076)
3.632∗∗∗
(0.134)
79
0.634

(GD)
FFR
b/se
1.266∗∗∗
(0.075)
0.283∗∗
(0.115)
6.712∗∗∗
(0.284)
29
0.855

(GM)
FFR
b/se
1.615∗∗∗
(0.149)
0.441∗∗∗
(0.083)
5.063∗∗∗
(0.187)
57
0.550

(GDe-GR)
FFR
b/se
1.724∗∗∗
(0.212)
-0.167∗
(0.096)
1.453∗∗∗
(0.135)
75
0.492

InﬂationGap

GrowthGap

TR

Number of obs.
R2

Legend: GRel= Great Relaxation: 1960Q1-1979Q3; GD=Great Disinﬂation: 1979Q4-1986Q4; GM= Great
Moderation: 1987Q1-2001Q1; GDe-GR= Great Deviation-Great Recession: 2001Q2-2019Q4. Note: Robust
standard errors in parentheses.

Table 8: Taylor rule estimation - Growth Gap

Figure 18: 1974 and 1990 Oil Shock Recessions - Model vs data

to reach its previous steady state. Nevertheless, the distance is small. If we were to increase the

persistence of the shocks then model results would start to diverge more signiﬁcantly. Overall,

these ﬁndings suggest that a growth Taylor rule and an output gap Taylor rule are almost

equivalent with moderate shocks consistent with historical data, validating the thesis that V-

shaped recoveries were policy driven.

E Energy

In order to account for oil price shocks in our model, we draw inspiration from papers in the

literature who explicitly model energy as a production input (see for example Rotemberg and

ECB Working Paper Series No 2596 / October 202158Woodford (1996) and Herrera et al. (2019)).

Let energy be a production input for intermediate producers, with e(i) representing the

consumption of energy by ﬁrm i –let us omit the time index t to simplify notation. The supply

of energy is inﬁnitely elastic at price pe. Let us then add energy e(i) to (15), so that production

technology becomes

y(i) = AaKηe(i)β(cid:16)

(cid:17)1−β

,

k(i)αh(i)1−α
(cid:124)
(cid:123)(cid:122)
(cid:125)
x(i)

(56)

where β ∈ (0, 1) represents the energy share in production and A > 0 is an arbitrary constant.

We will solve the problem in two stages. In the ﬁrst stage, and following the same logic as in

the main text, there exist a marginal cost px = α−α(1 − α)1−α(rk)αw1−α that minimizes the

cost of producing one unit of x(i). Notice that x(i) represents the value added generated by i

and px represents its shadow price. Since capital and labour services are homogeneous, px is the

deﬂator of value added.

In the second stage, and following a similar logic, ﬁrm i chooses e(i) and x(i) in order to

minimize the cost of producing output y(i). From the ﬁrst order conditions of the minimization

problem

e(i)
x(i)

= aKη

(cid:19)β

(cid:18) px
pe

x(i),

under the normalisation assumption that A =

(cid:17)−β

(cid:16) β
1−β

. After substitution of this equation in

(56), production of good i becomes

y(i) = a

(cid:124)

(cid:19)β

(cid:18) px
pe

(cid:123)(cid:122)
TFP

(cid:16)

Kη

(cid:125)

k(i)αh(i)1−α
(cid:123)(cid:122)
(cid:125)
(cid:124)
x(i)

(cid:17)

.

We can then interprete shocks to the energy price (relative to the GDP deﬂator) as TFP shocks.

Consequentially, an oil price shock will reﬂect in a TFP shock, bringing about a fall in GDP

and a rise in production costs. To replicate the reaction of the model to the oil shock recessions,

we then impose a TFP shock, combined with and conﬁdence shock to capture the observed

ﬂuctuations in consumer sentiment.

ECB Working Paper Series No 2596 / October 202159Figure 19: The Great Recession (baseline): Quarterly model simulations

ECB Working Paper Series No 2596 / October 202160Figure 20: The Great Recession for diﬀerent values of potential output revision intensity

Note that GDP, consumption and investment fall more as the shock hits when the revision of potential
output is slower than baseline, i.e. the policy intervention is stronger. This is a consequence of the ZLB binding,
as stronger demand stimulus generates higher inﬂation compared to the baseline, resulting in a sharp fall in the
real interest rate with a binding ZLB. The latter provides stimulus to the marginal utility of consumption, but
results in a sharper contraction in the labour supply, negatively aﬀecting the level of economic activity. As soon
as the nominal interest rate leaves the ZLB, the real interest rate re-bounces and monetary policy generates a
partial recovery.

ECB Working Paper Series No 2596 / October 202161Figure 21: The Great Recession: Quarterly model simulations, without the ZLB constraint

ECB Working Paper Series No 2596 / October 202162Figure 22: The risk shock: Quarterly model simulations

ECB Working Paper Series No 2596 / October 202163Figure 23: The Great Recession shock with a quasi standard Cobb-Douglas technology and no
potential output revisions

ECB Working Paper Series No 2596 / October 202164Figure 24: TFP shock for diﬀerent values of persistence: Baseline calibration

ECB Working Paper Series No 2596 / October 202165Figure 25: TFP shock: Additional variables

ECB Working Paper Series No 2596 / October 202166Figure 26: Alternative output gap measures

ECB Working Paper Series No 2596 / October 202167Figure 27: TFP shock: Baseline vs No-wage-no-price frictions

ECB Working Paper Series No 2596 / October 202168Figure 28: Relaxing the AK assumption: small demand shock for diﬀerent intensities of knowl-
edge spillovers

ECB Working Paper Series No 2596 / October 202169Figure 29: Relaxing the AK assumption: TFP shock for diﬀerent intensities of knowledge
spillovers

ECB Working Paper Series No 2596 / October 202170Acknowledgements 

We thank Ufuk Akcigit, Guido Ascari, Francesco Bianchi, Lorenzo Caliendo, Fabrice Collard, Diego Comin, Guido Cozzi, Wouter Den 
Haan, Luca Fornaro, Jordi Galí, Manuel Garcia-Santana, William Gatt, Veronica Guerrieri, Giammario Impullitti, Derrick Kanngiesser, 
Julian Kozlowski, Andrea Lanteri, Joseba Martinez, Michael McMahon, Andrea Modena, Morten Ravn, Pontus Rendahl, Petr Sedlacek, 
Mathieu Taschereau-Dumouchel, Patrizio Tirelli, Mathias Trabandt, Iván Werning, all participants to the International Economic 
Association World Congress 2021, the Bank of Canada Monetary Policy Workshop 2021, the 37th GdRE International Symposium on 
Money, Banking and Finance, the 19th Workshop on Macroeconomic Dynamics: Theory and Applications (Bank of Italy), the Secular 
Stagnation, Low Interest Rates and Low Inflation Conference (EC-CEPR-JEDC), the 1st NuCamp virtual PhD workshop (Oxford), the 
RIDGE 2019 December forum on Growth and Development in Macroeconomics/International Trade, the 7th Workshop in Macro 
Banking and Finance, the Nottingham macro working group as well as CFCM seminars for their helpful comments. This study is a 
continuation of work presented in the PhD Thesis “Essays on Growth and Business Cycles”, submitted by Francesca R. Vinci and 
examined at the University of Nottingham in 2020. The first version of this paper was circulated in 2019. 

Francesca Vinci 
European Central Bank, Frankfurt am Main, Germany; email: francesca_romana.vinci@ecb.europa.eu 

Omar Licandro 
University of Nottingham, Nottingham, United Kingdom; 
Institute of Economic Analysis - Consejo Superior de Investigaciones Científicas, Barcelona, Spain; 
Graduate School of Economics, Barcelona, Spain; email: omar.licandro@nottingham.ac.uk 

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