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Labor Market Institutions, Fiscal Multipliers, and
Macroeconomic Volatility
Maximilian Boeck1∗
, Jesús Crespo Cuaresma2,3,4,5 and Christian Glocker4
1Friedrich-Alexander University Erlangen-Nuremberg
2Vienna University of Economics and Business
3Wittgenstein Centre for Demography and Global Human Capital (IIASA, ÖAW, UniVie)
4Austrian Institute of Economic Research
5CESifo
January 2025
Abstract
We empirically examine how labor market institutions (LMI) – union density (UD), unemployment
benefit replacement rates (BRR), and employment protection legislation (EPL) – shape fiscal multipliers
and macroeconomic volatility. Our theoretical model predicts that stringent labor market institutions
attenuate fiscal spending multipliers and reduce macroeconomic volatility, with UD showing the strongest
effects, followed by EPL and BRR. These predictions are validated through an interacted panel vector
autoregressive (IPVAR) model estimated for 16 OECD countries. Results underscore that stringent
LMIs render cyclical fiscal policies less effective for macroeconomic stabilization. The findings highlight
heterogeneities across LMIs, and while some LMIs mitigate the contemporaneous impact of fiscal shocks,
others amplify the propagation mechanism. Our findings offer important implications for policymakers
navigating labor market and fiscal policy trade-offs.
Keywords: Fiscal policy; Labor market institutions; Interacted panel VAR
JEL Codes: E62, C33, J21, J38
∗Corresponding Author. Maximilian Boeck: Friedrich-Alexander University Erlangen-Nuremberg, Lange Gasse 20, 90403
Nuremberg, Germany. E-mail: maximilian.boeck@fau.de. Jesús Crespo Cuaresma: Department of Economics, Vienna Univer-
sity of Economics and Business. Welthandelsplatz 1, 1020 Vienna, Austria. E-mail: jesus.crespo.cuaresma@wu.ac.at.
Christian Glocker: Austrian Institute of Economic Research, Arsenal Objekt 20, 1030 Vienna, Austria. E-mail:
christian.glocker@wifo.ac.at. We thank Astrid Czaloun for excellent research assistance. Furthermore, Maximilian Böck and
Christian Glocker gratefully acknowledge financial support by funds of the Österreichische Nationalbank (Austrian National Bank,
Anniversary Fund, project number: 18466). The authors are grateful to our editor Marco Del Negro and four anonymous reviewers
for helpful suggestions. Furthermore, we also thank Pia Heckl, Brigitte Hochmuth, Christian Merkl, Lorenzo Mori, Thomas Url,
Thomas O. Zörner, and participants of the ECON Theory and Policy Seminar at TU Vienna and the Annual International Conference
on Macroeconomic Analysis and International Finance for valuable comments and helpful discussions.
1
1. Introduction
Large economic downturns, such as the global financial crisis 2008 or the Covid-19 pandemic, trigger strong
fiscal responses to stabilize the economy. Policymakers are interested in the efficacy of fiscal expansions,
particularly whether they support the labor market.1However, the academic discussion on fiscal multipliers
mostly centers on output and less on (un)employment multipliers (Monacelli, Perotti and Trigari, 2010). The
debate strongly focuses on the state-dependency of fiscal multipliers (e.g., in recessions vs. expansions).2
The potential state-dependency cannot only arise due to cyclical fluctuations but also due to structural features
of the economy. As such, labor market frictions critically affect labor market outcomes beyond business cycle
fluctuations. While it is a well-established fact that labor market institutions (LMI) matter for business cycles
(see, for instance, Gnocchi, Lagerborg and Pappa, 2015 or Abbritti and Weber, 2018), there is less evidence
on the ability of different LMIs to affect fiscal (labor market) multipliers.
This paper contributes to this literature by examining how different labor market institutions affect the
size of fiscal multipliers on the labor market and their role as determinants of business cycle fluctuations. We
consider a range of labor market rigidities such as union density (UD), unemployment benefit replacement
rates (BRR), and employment protection legislation (EPL). This allows us to assess the role of different
LMIs in shaping the effectiveness of fiscal policy and in judging their ability to dampen cyclical fluctuations.
Eventually, we also evaluate the degree of complementarity (or substitutability) among these LMIs and
cyclical spending policies. This enables a direct comparison of structural and cyclical policies of fiscal
multipliers and the ability to smooth macroeconomic fluctuations, which has not been addressed in a joint
framework featuring multiple LMIs.
We start by developing a theoretical model to assess qualitatively the role of LMIs in shaping fiscal
spending multipliers and macroeconomic volatility. We combine a standard New Keynesian model with
search and matching frictions in the labor market (Thomas and Zanetti, 2009; Christoffel, Kuester and Linzert,
2009). We measure union density by means of workers’ bargaining power within the wage negotiations,
the unemployment benefit replacement rate by means of subsidies to the unemployed, and employment
1In the wake of the financial crisis 2007-09, the American Recovery and Reinvestment Act (ARRA) (Romer, 2009) explicitly
promoted to raise employment. The Coronavirus Aid, Relief, and Economic Security (CARES) Act, on the other hand, expanded
unemployment insurance in order to help unemployed workers (Ganong, Noel and Vavra, 2020; Ganong et al., 2024). The
European Union Recovery Instrument (or Next Generation EU) allowed member states flexibility in terms of the fiscal rules and
supported national relief programs.
2See, inter alia, the contributions by Blanchard and Perotti (2002), Ramey (2011), Corsetti, Meier and Müller (2012), Auerbach
and Gorodnichenko (2012), Ilzetzki, Mendoza and Végh (2013), Leeper, Walker and Yang (2013), Ramey and Zubairy (2018),
Born, Müller and Pfeifer (2020), Born et al. (2024) and Jo and Zubairy (forthcoming).
2
protection by the level of firing costs per displaced worker. In a search and matching framework on the
labor market, a positive change in the unemployment benefit replacement rates and union density crucially
affects real wages positively, which attenuates the expansion of employment following an expansionary fiscal
shock.3Employment protection, however, affects directly job creation and destruction in opposing directions.
Higher employment protection leads then to an attenuated response of the fiscal multiplier on employment.
Taken together, the model predicts that more stringent LMIs attenuate both fiscal spending multipliers and
macroeconomic volatility. The strongest mitigation emanates from employment protection, followedby union
density and the unemployment benefit replacement rate.4To evaluate these channels, we conduct an impulse
response matching exercise after the empirical outcomes are presented.
In a next step, we confront the predictions of the theoretical model by estimating a semi-structural
Bayesian interacted panel vector autoregressive (IPVAR) model for 16 OECD countries (Towbin and Weber,
2013; Sá, Towbin and Wieladek, 2014). Conditional on the interaction terms (the three LMIs in our case), we
identify and trace out the dynamic effects of a government spending shock and their effect on macroeconomic
volatility. The structural interpretation of the econometric model relies on two main building blocks. First, our
approach to identification relies on an implementation lag of government spending as outlined in Blanchard
and Perotti (2002) and applied in a panel setting by Ilzetzki, Mendoza and Végh (2013).5Second, we
assume the exogeneity of the LMIs with respect to the interacted current and lagged values of the endogenous
variables in the system. LMIs change slowly over time and correlations to cyclical variables are rather low,
which renders the choice of the interacted panel VAR model particularly convenient.6Due to the panel
dimension and the constrained availability of the LMIs, we do not estimate the theoretical model. However,
we do not only show the qualitative similarity between the outcomes of the DSGE model and the IPVAR but
also perform impulse response matching to look into the exact channels driving the differences in the shock
transmission.
3This is contrast to Ghassibe and Zanetti (2022), which investigate goods market tightness as a potential source of the size of the
fiscal multiplier. However, similar to their study, the fiscal multiplier decreases with higher goods market tightness.
4Recent contributions by Challe (2020), McKay and Reis (2021), or Kekre (2023) highlight the precautionary savings motive in
models with heterogeneous agents who are exposed to unemployment risk. In these models, higher unemployment benefits cause
an additional aggregate demand channel which boosts output and employment. We abstract from these developments in the model
presented here.
5In a robustness exercise, we control for fiscal foresight, which can pose problems when identifying government spending shocks
as pointed out by Ramey (2011), Auerbach and Gorodnichenko (2012), or Leeper, Walker and Yang (2013). Although this issue
has been resolved in panel settings (see, for instance, Born, Müller and Pfeifer, 2020) the necessary data is not available for our
full sample. Hence, we only provide a robustness check to a sample with less country and time coverage.
6Note that we estimate the model on a quarterly frequency while the LMI interaction terms are on a yearly frequency. The model
exploits only within-country variation by standardizing the interaction terms appropriately.
3
The results can be summarized as follows. The empirical model grossly corroborates the qualitative
theoretical predictions. In terms of fiscal multipliers, we find the strongest attenuation of output fiscal
multipliers for UD, followed by EPL. Similarly, both UD and EPL show a sizable reduction in the employment
fiscal multiplier along their stringency. The attenuation for the fiscal multiplier of the real wage is less
pronounced and without statistical significance. On the contrary, we find a slight increase in the output and
employment multipliers for the BRR with varying statistical significance. Although outside of our model,
we explain these findings through a reduction of the precautionary savings motive induced by unemployment
risk, which leads to an additional demand channel. These differences highlight the heterogeneous outcomes
of fiscal spending effectiveness once stringent LMIs are in place. For macroeconomic volatility, we find that
UD and EPL lead to a decrease in volatility for output, while BRR increases the volatility for output and
employment. The distinct quantitative effects on cyclical volatility are due to the fact that the extent of EPL
attenuates macroeconomic volatility by mitigating both the propagation mechanism and the contemporaneous
impact of shocks. The extent of union density and the size of the unemployment benefit replacement rates,
in turn, exacerbate the propagation mechanism of shocks while moderating their contemporaneous impact.
This paper contributes to two strands of the literature. First, we add to the vast literature which investigates
the effects of fiscal policy shocks.7An important and lively area of research in this field is the investigation
of the potential state-dependent effects of fiscal spending policy. This was initiated by the seminal paper by
Auerbach and Gorodnichenko (2012) which examines the state-dependency of fiscal multipliers in recessions
and expansions.8Most of these papers focus exclusively on cyclical factors affecting the state. To this end,
we extend this analysis in the direction of structural policies and investigate how labor market rigidities shape
the effectiveness of fiscal multipliers. Additionally, we relate to a number of contributions that focus more
strongly on labor market outcomes/multipliers (Monacelli, Perotti and Trigari, 2010; Brückner and Pappa,
2012).9
7Important contributions in the realm of identifying fiscal spending shocks in a US and panel-country context are, inter alia,
Blanchard and Perotti (2002), Mountford and Uhlig (2009), Ramey (2011), Corsetti, Meier and Müller (2012), Born, Juessen and
Müller (2013), Ilzetzki, Mendoza and Végh (2013), Miyamoto, Nguyen and Sheremirov (2019), Born, Müller and Pfeifer (2020),
or Ilori, Paez-Farrell and Thoenissen (2022).
8In subsequent contributions, others show state-dependency due to the accommodation of monetary policy (Christiano, Eichenbaum
and Rebelo, 2011; Coenen et al., 2012; Fernández-Villaverde et al., 2015; Rendahl, 2016), the exchange rate regime (Born, Juessen
and Müller, 2013; Born et al., 2024), the zero lower bound (Ramey and Zubairy, 2018; Di Serio, Fragetta and Gasteiger, 2020),
fiscal financing (Hagedorn, Manovskii and Mitman, 2019), household leverage (Demyanyk, Loutskina and Murphy, 2019),
financial turmoil (Bernardini, De Schryder and Peersman, 2020), and asymmetric effects due to downward nominal wage rigidity
(Shen and Yang, 2018; Jo and Zubairy, forthcoming) or due to market incompleteness (Barnichon, Debortoli and Matthes, 2022).
9In this context, Ball, Jalles and Loungani (2015) highlight that the link between GDP and the labor market strongly depends on
the idiosyncratic labor market institutions in place in a given economy.
4
Our paper also complements the literature on the macroeconomic effects of labor market regulation. An
increasing theoretical (Christoffel, Kuester and Linzert, 2009; Thomas and Zanetti, 2009; Zanetti, 2009;
Zanetti, 2011; Campolmi, Faia and Winkler, 2011) and empirical literature (Gnocchi, Lagerborg and Pappa,
2015; Abbritti and Weber, 2018; Hantzsche, Savsek and Weber, 2018; Cacciatore et al., 2021) assesses the
macroeconomic implications of market reforms, such as the removal of labor and product market frictions.
The empirical evidence points broadly to an attenuation of the unconditional business cycle volatility10,
while there is less work on the conditional effects to exogenous shocks. Notable exceptions are Abbritti and
Weber (2018), Hantzsche, Savsek and Weber (2018), and Cacciatore et al. (2021). While the first two papers
investigate the conditional effects of oil prices, world demand, and financing shocks, Cacciatore et al. (2021)
is closer to our work. They analyze the role of employment protection legislation for fiscal spending shocks.
However, in contrast to their work, we highlight significant heterogeneities across different LMIs. While we
corroborate their findings in terms of the EPL, we find even stronger effects for UD, which works through
differences in matching elasticities and not only job loss probability in the case of EPL. Furthermore, the
investigation of the BRR even suggests an additional aggregate demand effect (Challe, 2020; McKay and
Reis, 2021; Kekre, 2023).
The remainder of the paper is structured as follows. In Section 2 we provide a descriptive overview
of LMIs across selected OECD countries. Section 3 discusses the theoretical model and presents its main
predictions. Section 4 shows the connection between the theoretical and the empirical model, and presents
the results of the econometric analysis. Finally, Section 5 concludes.
2. Structural Labor Market Indicators in OECD Economies
We focus on the following labor market institutions in OECD countries11: union density (UD, 𝜂), the
unemployment benefit replacement rate (BRR, 𝜑), and employment protection legislation (EPL, 𝜍).12 For an
overview, we provide in Figure 1 and Figure 2 descriptive evidence on the time variation and cross-country
heterogeneity.
10 See, inter alia, also the contributions by Merkl and Schmitz (2011), Rumler and Scharler (2011), or Ferraro and Fiori (2023).
11 Our sample consists of 16 countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Great Britain,
Italy, Japan, Netherlands, Portugal, Spain, Sweden, and the United States. More details on the data sources in Appendix D.
12 There are, of course, many other important structural labor market characteristics which affect the transmission channel of fiscal
shocks. Prominent ones concern the degree of labor market openness to foreign workers (see, for instance Amuedo-Dorantes
and Rica, 2013; Godøy, 2017; Schiman, 2021), the declining trend in labor productivity (see, for instance Policardo, Punzo and
Sánchez Carrera, 2019; Li et al., 2021), or demographic changes (see, for instance Docquier et al., 2019). We limit our analysis
to the categories mentioned above due to data availability.
5
Figure 1: Labor Market Institutions in OECD Economies: Time Variation.
Union density (UD, η)
1960 1980 2000 2020
0%
20%
40%
60%
80%
100%
U. benefit repl. rates (BRR, ϕ)
1960 1980 2000 2020
0%
10%
20%
30%
40%
50%
60%
Employment protection (EPL, ς)
1960 1980 2000 2020
0
1
2
3
4
5
6
7
Notes: The figure shows the time variation in labor market institutions (union density, unemployment benefit replacement rate, and employment
protection legislation) across all countries. The dark-red dashed line reports the mean and the orange colored region one standard deviation of
the respective labor market institution. The y-axis refers to percent (union density, benefit replacement rate) or has no unit of scaling attached
(employment protection legislation). The x-axis refers to time.
UD is primarily derived from survey data or adjusted administrative data for non-active and self-employed
members. It represents the ratio of trade union members among wage and salary earners. Higher values
indicate greater trade union influence in wage negotiations. In the 1970s, UD distribution shifted upward
compared to the 1960s, followed by a steady decline in union membership rates. While this trend is reflected
in the mean (dashed dark red line), it conceals rising cross-country dispersion from the 1980s onward (15%
in France and 80% in Sweden).
The BRR measures the proportion of income maintained during unemployment as a ratio of net household
income during unemployment to income before job loss. Higher values indicate more generous systems.
BRR steadily increased until the 2000s but has since seen a slight median decline across countries. A narrow
distribution in the 1960s widened in the 1990s and 2000s, with recent trends showing some convergence
across countries.
The EPL index measures regulatory strictness on dismissals and temporary contracts, based on regulations
in force on January 1 each year. Higher values indicate stricter employment protection. While the median
EPL index has stayed constant, its dispersion has significantly narrowed, reflecting convergence, especially
among EU countries. In contrast, non-EU countries showed little change over time.
The LMIs affect different macroeconomic variables. While UD and BRR affect employment, vacancies,
and unemployment indirectly through their effect on the price of labor, EPL is likely to affect those variables
6
Figure 2: Labor Market Institutions in OECD Economies: Cross-Country Variation.
Union density (UD, η)
FRA
ESP
USA
JPN
DEU
NLD
CAN
AUS
GBR
ITA
PRT
AUT
BEL
FIN
DNK
SWE
0%
20%
40%
60%
80%
100%
U. benefit repl. rates (BRR, ϕ)
JPN
USA
ITA
CAN
GBR
AUS
SWE
DEU
FIN
AUT
ESP
PRT
FRA
BEL
DNK
NLD
0%
10%
20%
30%
40%
50%
60%
Employment protection (EPL, ς)
USA
CAN
AUS
GBR
DNK
JPN
BEL
FIN
DEU
AUT
SWE
FRA
ITA
NLD
ESP
PRT
0
1
2
3
4
5
6
7
Notes: The figure shows the cross-country variation in labor market institutions (union density, unemployment benefit replacement rate, and
employment protection legislation) for each country. The black dot reports the mean and the wishkers correspond to the 10th and 90th quantile of
the distribution. The blue points are observed data. The y-axis refers to percent (union density, benefit replacement rate) or has no unit of scaling
attached (employment protection legislation). The x-axis refers to each individual country.
directly. In what follows, we study in detail the implications of different LMIs as determinants of differences
in fiscal spending multipliers and macroeconomic volatility.
3. The Theoretical Model
In the theoretical model, we merge the structure of a Diamond-Mortensen-Pissarides model with a standard
real business cycle framework and rely on the setting put forward by Merz (1995), Andolfatto (1996) and
Krause and Lubik (2007), and Monacelli, Perotti and Trigari (2010). The model is intended to be parsimonious
and focus on the role played by labor market institutions. We consider various extensions of the set-up that
can accommodate more complex interactions in Appendix B.
We assume representative firms and households. Each firm employs 𝑛𝑡workers and posts 𝑣𝑡vacancies
to attract new workers. Firms incur a cost 𝜅per vacancy posted and firing costs 𝑏𝑠
𝑡per laid off worker from
endogenous job separations. The total number of unemployed workers searching for a job is 𝑢𝑡=1−𝑛𝑡.
The number of new hires 𝑚𝑡is determined according to the matching function 𝑚𝑡=¯𝑚𝑢𝛾
𝑡𝑣1−𝛾
𝑡, with ¯𝑚 > 0
and 𝛾∈ (0,1). The probability that a firm fills a vacancy is given by 𝑞𝑡=𝑚𝑡/𝑣𝑡=¯𝑚𝜃−𝛾
𝑡, where 𝜃𝑡=𝑣𝑡/𝑢𝑡
is the extent of labor market tightness. The probability that an unemployed worker finds a job is given by
𝑝𝑡=𝑚𝑡/𝑢𝑡=¯𝑚𝜃 1−𝛾
𝑡. Firms and workers take 𝑞𝑡and 𝑝𝑡as given. Finally, each firm separates from a
fraction 𝜚(˜𝑎𝑡)of existing workers each period. This quantity involves an exogenous component, ¯𝜚, and
an endogenous one. Following Krause and Lubik (2007), job destruction probabilities 𝑎𝑡are drawn every
7
period from a distribution with c.d.f 𝐹(𝑎𝑡)with positive support and density 𝑓(𝑎𝑡).˜𝑎𝑡is an endogenously
determined threshold value and a job is destroyed if 𝑎𝑡<˜𝑎𝑡. This gives rise to an endogenous job separation
rate 𝐹(˜𝑎𝑡). The total separation rate is given by: 𝜚(˜𝑎𝑡)=¯𝜚+ (1−¯𝜚)𝐹(˜𝑎𝑡).
3.1 Intermediate Goods-Producing Firms
The (representative, intermediate goods producing) firm uses labor to produce output 𝑦𝑡according to 𝑦𝑡=
¯
𝐴𝑛𝑡𝐴(˜𝑎𝑡), where ¯
𝐴 > 0is a common productivity factor and 𝐴(˜𝑎𝑡)=𝐸[𝑎|𝑎≥˜𝑎𝑡]=1
1−𝐹(˜𝑎𝑡)∫∞
˜𝑎𝑡𝑎𝑑𝐹 (𝑎)is
the conditional expectation of productivity being larger than the endogenously determined critical threshold.
To raise the workforce in turn, firms need to post vacancies. Hence, the firm can influence employment along
two dimensions: the number of vacancies posted and the number of endogenously destroyed jobs. This gives
rise to the following employment dynamics
𝑛𝑡=(1−𝜚(˜𝑎𝑡)) (𝑛𝑡−1+𝑚𝑡−1).(3.1)
Current period profits are given by 𝜋𝐹
𝑡=𝑦𝑡/𝜇𝑡−𝑤𝑡𝑛𝑡−𝜅𝑣𝑡−𝐹(˜𝑎𝑡)(1−¯𝜚)(𝑛𝑡−1+𝑞𝑡−1𝑣𝑡−1)𝑏𝑠
𝑡where the
output price is normalized to unity, 𝑤𝑡=∫∞
˜𝑎𝑡
𝑤𝑡(𝑎)
1−𝐹(˜𝑎𝑡)𝑑𝐹 (𝑎)is the (average) real wage weighted according
to the idiosyncratic job productivity, 𝜇𝑡is the price markup (its inverse equals real marginal costs 𝑚𝑐𝑡), and
the last term captures firing costs (Cacciatore et al., 2021). In detail, (𝑛𝑡−1+𝑚𝑡−1) (1−¯𝜚)𝐹(˜𝑎𝑡)represents
the number of existing (𝑛𝑡−1) and new (𝑚𝑡−1) workers who survived the exogenous job separation (1−¯𝜚),
but got laid off due to the endogenous job separation (𝐹(˜𝑎𝑡)). 𝑏𝑠
𝑡captures the cost per laid off worker. Firm
expenses from firing are modeled as real resource costs13. The firm maximizes the present discounted value
of expected profits: max𝑛𝑡,𝑣𝑡,˜𝑎𝑡E𝑡Í𝑘≥0Λ𝑡 ,𝑡 +𝑘𝜋𝐹
𝑡+𝑘, subject to the production function and Eq. (3.1). E𝑡is
the expectation conditional on the information up to and including time 𝑡;Λ𝑡 ,𝑡 +𝑘denotes the firm’s stochastic
13 We consider the case where firing costs accrue to the government in Appendix B.
8
discount factor, defined below. The first order conditions give rise to14
𝐹𝑛
𝑡=𝑚𝑐𝑡𝑚 𝑝𝑙 𝑡−𝑤𝑡+E𝑡Λ𝑡,𝑡+1(1−𝜚(˜𝑎𝑡+1))𝐹𝑛
𝑡+1−𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1),(3.2)
𝜅
𝑞𝑡
=E𝑡Λ𝑡,𝑡 +1(1−𝜚(˜𝑎𝑡+1)) 𝐹𝑛
𝑡+1−𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1),(3.3)
𝑚𝑐𝑡𝐴(˜𝑎𝑡)=1
¯
𝐴𝑤𝑡−𝑏𝑠
𝑡−𝜅
𝑞𝑡,(3.4)
where 𝑚 𝑝𝑙 𝑡is the marginal product of labor and 𝐹𝑛
𝑡is the Lagrange multiplier associated with Eq. (3.1). In
Eq. (3.2), 𝐹𝑛
𝑡captures the (shadow) value accruing to the firm when employing one additional worker at time
𝑡and consists of four components: (i) the marginal product of a worker, (ii) the (marginal) cost of employing
one additional worker, (iii) the continuation value of keeping the worker employed and (iv) the cost per laid
off worker of the endogenous job separation. Eq. (3.3) is the free entry condition. It relates the value of
employing an additional worker ((1−𝜚(˜𝑎𝑡+1))𝐹𝑛
𝑡+1) to the cost per vacancy (𝜅/𝑞𝑡) and the cost per laid off
worker (𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1)). Finally, Eq. (3.4) sets the conditions for the idiosyncratic job productiveness
(˜𝑎𝑡) and hence for endogenous job destruction. Firms accept a lower idiosyncratic job productivity from
workers when (i) firing costs (𝑏𝑠
𝑡) and/or (ii) search costs (𝜅/𝑞𝑡) increase; however, (iii) higher wages induce
firms to require higher productivity from workers.
3.2 Final Goods-Producing Firms
Final goods producers buy intermediate goods and sell them to the households. We assume that there is
a continuum of final goods producers indexed by 𝑖∈ [0,1]. They are perfectly competitive in their input
markets and monopolistically competitive in their output market. Their price setting is subject to nominal
rigidities à la Calvo (1983). In line with Christiano, Eichenbaum and Evans (2005), firms that cannot re-
optimize their price in a given period partially index their price to the previous period’s CPI inflation rate 𝜋𝑡,
14 The first order condition with respect to ˜𝑎𝑡is given by: 𝑛𝑡¯
𝐴𝜕𝐴 (˜𝑎𝑡)
𝜕˜𝑎𝑡−𝜕𝑤𝑡
𝜕˜𝑎𝑡=(𝑛𝑡−1+𝑞𝑡−1𝑣𝑡−1)𝑏𝑠
𝑡(1−¯𝜚)𝑓(˜𝑎𝑡) + 𝐹𝑛
𝑡
𝜕 𝜚 (˜𝑎𝑡)
𝜕˜𝑎𝑡.
Using Eq. (3.3), (3.2), and (3.1), this equation can be further simplified to: (1−¯𝜚)(1−𝐹(˜𝑎𝑡)𝜕𝐴(˜𝑎𝑡)
𝜕˜𝑎𝑡−𝜕𝑤𝑡
𝜕˜𝑎𝑡=𝑏𝑠
𝑡(1−
¯𝜚)𝑓(˜𝑎𝑡) + 𝜇𝑡𝑚 𝑝𝑙𝑡−𝑤𝑡+𝜅
𝑞𝑡𝜕 𝜚 (˜𝑎𝑡)
𝜕˜𝑎𝑡. Using the derivatives of 𝜕𝐴(˜𝑎𝑡)
𝜕˜𝑎𝑡,𝜕𝑤𝑡
𝜕˜𝑎𝑡and 𝜕 𝜚 (˜𝑎𝑡)
𝜕˜𝑎𝑡yields the following expression:
˜𝑤𝑡(𝑎)=𝑏𝑠
𝑡+𝜅
𝑞𝑡+¯
𝐴𝑎. Finally, operating on both sides with ∫∞
˜𝑎𝑡
𝑑𝐹 (𝑎)
1−𝐹(˜𝑎𝑡)and using the definition of the production function gives
Eq. (3.4).
9
implying 𝑃𝑡(𝑗)=(1+𝜋𝑡−1)𝛾𝑝𝑃𝑡−1(𝑗), where 𝛾𝑝∈ [0,1]captures the extent to which prices are indexed to
the past inflation rate.15
The probability that a firm cannot re-optimize its price for 𝑘periods is given by 𝜉𝑘. Profit maximization
by the intermediate goods producer 𝑗, which is allowed to re-optimize its price at time 𝑡, implies that it chooses
a target price 𝑃∗
𝑡that maximizes the following stream of future profits E𝑡Í𝑘≥0𝜉𝑘Λ𝑡, 𝑡+𝑘∫𝑦𝑡+𝑘(𝑗)
0(𝑃∗
𝑡Ψ𝑡+𝑘−
𝑚𝑐𝑡+𝑘𝑃𝑡+𝑘)𝑑𝑞, subject to the demand constraint 𝑦𝑡+𝑘(𝑗)=(𝑃∗
𝑡/𝑃𝑡+𝑘)−𝜀𝑦𝑡+𝑘and Ψ𝑡+𝑘=𝑃𝑡−1+𝑘/𝑃𝑡−1
𝑃𝑡+𝑘/𝑃𝑡𝛾𝑝.
The first order condition with respect to the price 𝑃∗
𝑡implies that the following condition has to hold
E𝑡Í𝑘≥0𝜉𝑘Λ𝑡,𝑡 +𝑘𝑦𝑡+𝑘(𝑗)𝑃∗
𝑡Ψ𝑡+𝑘−𝜀
𝜀−1𝑚𝑐𝑡+𝑘𝑃𝑡+𝑘=0. This expression highlights that the price 𝑃∗
𝑡set by
firm 𝑗at time 𝑡, is a markup over expected future marginal costs. If prices can be adjusted at any point in time
(𝜉=0), the markup is equal to 𝜀
𝜀−1. With sticky prices, the markup varies over time. Finally, the definition
of the price index 𝑃𝑡for domestic goods implies that its law of motion is given by
𝑃𝑡=𝜉((1+𝜋𝑡−1)𝛾𝑝𝑃𝑡−1)1−𝜀+ (1−𝜉)(𝑃∗
𝑡)1−𝜀1
1−𝜀,(3.5)
which then results in the following expression for the New Keynesian Phillips curve
(1+𝛾𝑝𝜉 𝛽)𝜋𝑡=𝛽E𝑡𝜋𝑡+1+𝛾𝑝𝜋𝑡−1+(1−𝜉 𝛽) (1−𝜉)
𝜉ˆ𝑚𝑐𝑡.(3.6)
3.3 Households
We model households following the approach proposed by Merz (1995). We consider an infinitely lived
representative household consisting of a continuum of individuals of mass one. Household members pool
income which accrues from labor income and unemployment benefit remuneration from employed and
unemployed household members, respectively. Household members pool consumption to maximize the sum
of utilities, that is, the overall household utility.
The budget constraint is given by
𝑐𝑡+𝐵𝑡=𝑅𝑡−1𝐵𝑡−1+ (1−𝜏)𝑤𝑡𝑛𝑡+𝑏𝑢
𝑡(1−𝑛𝑡) + 𝑇𝑆
𝑡+𝜋𝐹
𝑡,(3.7)
where 𝑐𝑡is household consumption and 𝐵𝑡are period 𝑡holdings of government bonds, for which a rate
of return 𝑅𝑡accrues. 𝑏𝑢
𝑡and 𝑇𝑆
𝑡denote unemployment benefits per unemployed household member and
lump-sum subsidies. Finally, (1−𝜏)𝑤𝑡is the after-tax wage, corresponding to the tax rate 𝜏. In addition to
15 If 𝛾𝑝=1, then the firms that cannot re-optimize their price in period 𝑡instead adjust their price to the lagged inflation rate; if
𝛾𝑝=0, the firms that cannot re-optimize their price in period 𝑡leave their price unchanged. Uribe (2020) describes indexation as
rule-of-thumb for adjusting prices.
10
the budget constraint, the household takes into account the flow of employment by its members in line with
𝑛𝑡=(1−𝜚(˜𝑎𝑡))𝑛𝑡−1+𝑝𝑡(1−𝑛𝑡−1).(3.8)
In a given period, the household derives utility from consumption 𝑐𝑡and dis-utility from working 𝑛𝑡. The
instant utility function is 𝑢(𝑐𝑡, 𝑛𝑡). The household discounts instant utility with a discount factor 𝛽and
maximizes the expected lifetime utility function: max𝑐𝑡,𝑛𝑡E𝑡Í𝑘≥0𝛽𝑘𝑢(𝑐𝑡+𝑘, 𝑛𝑡+𝑘), subject to the budget
constraint, Eq. (3.7) and the employment flow Eq. (3.8). Optimization leads to the following conditions
1=𝑅𝑡E𝑡Λ𝑡,𝑡 +1,(3.9)
𝐻𝑛
𝑡=˜𝑤𝑏
𝑡−𝑚𝑟 𝑠𝑡+E𝑡[1−𝜚(˜𝑎𝑡+1) − 𝑝𝑡+1]Λ𝑡 ,𝑡 +1𝐻𝑛
𝑡+1,(3.10)
where 𝜆𝑡is the Lagrange multiplier attached to Eq. (3.7) and 𝜆𝑡𝐻𝑛
𝑡the one attached to equation Eq. (3.8).
Furthermore, ˜𝑤𝑏
𝑡=(1−𝜏)𝑤𝑡−𝑏𝑢
𝑡,𝑚𝑟 𝑠𝑡=−𝑢𝑛 ,𝑡 /𝜆𝑡and 𝑢𝑛,𝑡 <0is the marginal dis-utility of working.
Note that 𝜆𝑡is equal to the marginal utility of consumption in this case but also the marginal utility of wealth
because it is the (Lagrange) multiplier on the household’s budget constraint. Hence, 𝑚𝑟𝑠𝑡captures both the
marginal rate of substitution between consumption and work and the marginal value of non-work activities.
Assuming efficient financial markets implies that the stochastic discount factor, given by Λ𝑡, 𝑡+𝑘=𝛽𝑘𝜆𝑡+𝑘
𝜆𝑡,
applies to both households and firms.
Considering Eq. (3.10), 𝐻𝑛
𝑡captures the household’s (shadow) value of having one additional employed
member. It consists of three components: (i) the increase in utility owing to the higher income when having
an additional member employed, (ii) the decrease in utility from lower leisure captured by the marginal
dis-utility of work, and (iii) the continuation utility value, given by the contribution of a current match a
household’s employment in the next period.
3.4 Nash Wage Bargaining
Wages are set each period based on Nash-bargaining of the pre-tax (average) wage 𝑤𝑡between firms and
workers. The Nash wage satisfies: 𝑤𝑡=arg max𝑤𝑡(𝐻𝑛
𝑡)𝜂(𝐹𝑛
𝑡)1−𝜂where 0< 𝜂 ≤1captures workers’
bargaining power. Optimization yields: 𝜂𝐹𝑛
𝑡=(1−𝜂)𝐻𝑛
𝑡/(1−𝜏), which can be rearranged to
𝑤𝑡=(1−𝜂)𝑚𝑟 𝑠𝑡+𝑏𝑢
𝑡
1−𝜏+𝜂𝑚𝑐𝑡𝑚 𝑝𝑙 𝑡+E𝑡Λ𝑡,𝑡+1𝜅𝜃𝑡+1−𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1).(3.11)
11
The wage per worker is a weighted average of the unemployment benefit and the marginal rate of substitution
on the one hand; and the marginal product of labor, the expected search cost and the firing costs (per worker)
on the other. Higher unemployment benefits (𝑏𝑢
𝑡) and labor tax rates (𝜏) render non-work activities more
attractive, inducing a rise in the equilibrium wage rate from the side of households. Conversely, a higher
current marginal product of labor, higher expected search costs, and lower expected firing costs cause upward
pressure on the equilibrium wage from the side of firms.
3.5 Policies, Aggregate Resource Constraint, and Government Budget Constraint
The government budget constraint satisfies
𝜏𝑤𝑡𝑛𝑡+𝐵𝑡=𝑅𝑡−1𝐵𝑡−1+𝑏𝑢
𝑡𝑢𝑡+𝑇𝑠
𝑡+𝑔𝑡,(3.12)
where 𝑔𝑡is government consumption. Fiscal policy is governed by (i) an exogenous AR(1) process 𝑔𝑡(in
log-deviations), (ii) a specification for unemployment benefits according to 𝑏𝑢
𝑡=¯𝜑+𝜑𝑤𝑡−1where 𝜑is
the replacement rate of a worker with respect to his last wage received, (iii) a specification for firing costs
according to 𝑏𝑠
𝑡=¯𝜍+𝜍𝑤𝑡−1, and (iv) government subsidies: 𝑇𝑆
𝑡=¯
𝑇𝑆+𝜑𝑇𝑠𝐵𝑡. The parameters ¯
𝑇𝑆and
¯𝜍serve the purpose to simplify the steady state computations and 𝜑𝑇𝑠𝐵𝑡ensure that the necessary stability
conditions are satisfied.
Monetary policy is governed by a Taylor rule according to 𝑖𝑡=𝜌𝑖𝑖𝑡−1+ (1−𝜌𝑖)(𝜙𝜋𝜋𝑡+𝜙𝑦ˆ𝑦𝑡)where
𝑖𝑡=ln(𝑅𝑡)and the hat-notation refers to the log-deviation from the steady state.
Finally, using Eq. (3.12), Eq. (3.7), and the expression for firms’ profits (𝜋𝐹
𝑡), we obtain the aggregate
resource constraint
𝑦𝑡=𝑐𝑡+𝑔𝑡+𝜅𝑣𝑡+𝐹(˜𝑎𝑡)(1−¯𝜚)(𝑛𝑡−1+𝑞𝑡−1𝑣𝑡−1)𝑏𝑠
𝑡.(3.13)
This equation closes the model.
3.6 Embedding LMIs in the Model
The indicators for the LMIs are embedded in the model by the three structural parameters 𝜍,𝜂, and 𝜑. The
mapping between the empirical LMIs and their theoretical counterparts in the DSGE model can only be
qualitative.
12
We proxy the government’s ability to shape the extent of employment protection, 𝜍, with the EPL index.
While employment protection can take a variety of forms, such as strict layoff rules for individual occupational
groups, short-time work models that allow companies to forego layoffs due to (temporary) subsidies, and
also the existence of payments that may arise with a dismissal. In addition to severance payments, the latter
also includes, as is customary in many countries, one-time payments to the social security system due to the
burden on the unemployment insurance caused by the dismissal.16 The parameter 𝜂captures the bargaining
power of workers and is proxied by UD. It is thus a measure of the implicit advantage that employees benefit
from within the wage-setting process.17 In a more general interpretation, this can also be viewed as a measure
of union strength or as a measure of the degree of centralization of wage bargaining since a higher degree
of centralization of wage bargaining is typically considered beneficial for workers in the wage bargaining
process (Abbritti and Weber, 2018). Finally, the parameter 𝜑captures the amount of unemployment benefit
payments in relation to the wage received before dismissal. This value is usually set directly by governments
and is comparatively less ambiguous than the other two LMI parameters (𝜂and 𝜍).
3.7 Equilibrium, Model Solution, and Dynamic Simulations
We collect the LMI parameters of interest in the vector 𝝑=(𝜂, 𝜑, 𝜍)0and assess the implications of changes
in these for fiscal policy by assessing their effects on the impulse response functions to a shock in government
spending (𝑔𝑡). To this purpose, we consider a log-linearized solution of the rational expectations model
around its steady state,
𝚿0(𝝑)𝒛𝑡=𝚿1(𝝑)𝒛𝑡−1+𝜺𝑡,(3.14)
where the vector 𝒛𝑡contains the endogenous variables and the vector of exogenous shocks simplifies to 𝜺𝑡=ˆ𝑔𝑡
in our case. The matrix 𝚿1(𝝑)governs the dynamics among the dependent variables and the matrix 𝚿−1
0(𝝑)
determines the contemporaneous impact of the fiscal spending shock on the endogenous variables. Eq. (3.14)
explicitly depicts the dependency of the coefficient matrices on the three LMI parameters. We assess the
consequences of each of the three parameters individually by computing impulse response functions (IRFs)
based on a calibration of the model’s parameters as outlined in Appendix A.2. As the IRFs are continuous
16 However, the index remains qualitative. Quantitative data on firing costs are not readily available at the country level. Moreover,
as they cover only severance payments and the length of the notice period, they omit non-monetizable elements of employment
protection, as for instance administrative and judicial procedures.
17 An alternative indicator for wage bargaining power is coverage of collective bargaining. This measure is far more persistent than
union density and thus does not adequately reflect the underlying bargaining power of wage earners.
13
Figure 3: Fiscal Spending Multipliers and the LMIs (𝜇(𝝑)).
0.2 0.4 0.6
0.1
0.15
0.2
0.25
0.3
0.3 0.4 0.5 0.6
0.1
0.15
0.2
0.25
0.3
0.1 0.2 0.3 0.4 0.5
0.1
0.15
0.2
0.25
0.3
0.2 0.4 0.6
0.15
0.2
0.25
0.3
0.3 0.4 0.5 0.6
0.15
0.2
0.25
0.3
0.1 0.2 0.3 0.4 0.5
0.15
0.2
0.25
0.3
0.2 0.4 0.6
0
0.2
0.4
0.6
0.8
0.3 0.4 0.5 0.6
0
0.2
0.4
0.6
0.8
0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
Notes: The sub-figures illustrate the sensitivity of the fiscal spending multipliers to variations in the three LMI parameters (UD–union density,
BRR–(unemployment) benefit replacement rate and EPL–employment protection (legislation)). The multipliers are presented for different horizons,
with the contemporaneous multiplier (P=1) represented by a solid black square line, and the higher horizon multipliers ( P ≥ 2) indicated by black
dotted lines.
functions of 𝝑, we can display them over a whole range of values of 𝝑. We do so by considering the following
definition of the fiscal spending multiplier for some variable 𝑥
𝜇𝑥(𝜗𝑙)=ÍP
𝑖=1IRF𝑥
𝑖(𝜗𝑙)
ÍP
𝑗=1IRF ˆ𝑔
𝑗(𝜗𝑙)
,∀𝑙={1,2,3},(3.15)
where IRF𝑥
𝑡(𝜗𝑙)and IRF ˆ𝑔
𝑡(𝜗𝑙)denote the impulse response functions of some variable 𝑥and government
spending ˆ𝑔to the fiscal spending shock over the horizon P. The definition of 𝜇𝑥(𝜗𝑙)considers the response
of a variable relative to the size and persistence of the shock. In what follows, we will refer to 𝜇𝑥(𝜗)as
the multiplier for a specific variable 𝑥and focus on distinct horizons P. The results are shown in Figure 3
for output ( ˆ𝑦𝑡), employment (ˆ𝑛𝑡), and the real wage ( ˆ𝑤𝑡). The multipliers for each variable are displayed
distinctively for the first horizon (P=1) and higher horizons (P ≥ 2); this has the advantage to depict also
the dynamics. The columns consider the dependency of the multipliers on the respective LMI parameters
(𝝑).
14
An intuitive understanding of the working of the model can be gained by considering the negative wealth
effect caused by higher government spending. Consumption and leisure are both normal goods, hence they
both fall as a result of the negative wealth effect from higher expected taxation. The drop in consumption
raises the marginal utility of consumption, which gives rise to a drop in the marginal rate of substitution
between consumption and labor (𝑚𝑟𝑠𝑡=−𝑢𝑛, 𝑡 /𝑢𝑐,𝑡 ) or, in other words, a decrease in the current value of
non-work activities. As a consequence of the drop in leisure, the associated increase in employment raises
output and leads to a positive fiscal spending multiplier. The effect on the equilibrium wage is in principle
ambiguous: the drop in the marginal product of labor and the marginal rate of substitution (or equivalently,
the value of non-work activities) contrasts with a rise in the expected search cost. The comparably larger
reaction of the former two triggers a drop in the equilibrium wage rate. In a similar vein, the response of
the labor market tightness variable (𝜃𝑡) is ambiguous despite the decrease in unemployment. The drop in the
equilibrium wage raises the value to the firm of an additional worker (𝜕𝐹𝑛
𝑡/𝜕𝑤𝑡<0) which creates incentives
for firms to increase vacancy postings and hiring activities. This contrasts with the rise in expected search
costs. The overall effect on vacancies 𝑣𝑡and labor market tightness 𝜃𝑡is thus ambiguous.
In what follows, we focus on the role of the relative bargaining power of workers (UD, 𝜂), the extent of
employment protection (EPL, 𝜍) and the unemployment benefit replacement rate (BRR, 𝜑) in shaping the
responses of interest.
3.8 Implications of the LMIs
We start by considering the BRR (𝜑) and its role as a determinant of the shape of the employment and
output response to fiscal shocks, as depicted in Figure 3. While employment increases in response to the
fiscal spending rise, the positive response is larger when the unemployment remuneration is low. This can be
explained by considering the reservation wages for households and firms (𝑤𝐻
𝑡and 𝑤𝐹
𝑡).
The reservation wage of a household (firm) is given by the minimum (maximum) wage acceptable. Since
𝐻𝑛
𝑡(𝐹𝑛
𝑡) describes the marginal value to the household (firm) of having one further worker employed, the
reservation wages of a household and a firm are hence determined by 𝐻𝑛
𝑡=0and 𝐹𝑛
𝑡=0. In this situation,
the household and the firm are not willing to increase or decrease labor supply and demand. Using Eq. (3.2)
15
and (3.10), and setting 𝜏equal to zero for simplicity, the reservation wages are given by
𝑤𝐹
𝑡=𝑚𝑐𝑡𝑚 𝑝𝑙 𝑡+E𝑡Λ𝑡,𝑡+1(1−𝜚(˜𝑎𝑡+1))𝐹𝑛
𝑡+1−𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1),(3.16)
𝑤𝐻
𝑡=𝑚𝑟 𝑠𝑡+𝑏𝑢
𝑡− (1−𝜚(˜𝑎𝑡+1) − 𝑝𝑡+1)E𝑡Λ𝑡 , 𝑡+1𝐻𝑛
𝑡+1,(3.17)
from which 𝑤𝑡=(1−𝜂)𝑤𝐹
𝑡+𝜂𝑤 𝐻
𝑡follows. Hence, higher unemployment benefits (𝜕𝑏𝑢
𝑡/𝜕𝜑 > 0) raise the
reservation wage for households (𝜕𝑤𝐻
𝑡/𝜕𝜑 > 0), which contracts their value of employment (𝜕𝐻𝑛
𝑡/𝜕𝜑 < 0)
giving rise to a negative impulse on household’s labor supply. Intuitively, an increase in unemployment
benefits raises workers’ outside option (i.e., the present value of being unemployed rises) which improves
their bargaining position for the wage negotiations. This in turn leads to an increase in the reservation wage
of households and, given a non-zero weight of households/workers in the wage bargaining process (𝜂 > 0), to
an increase in the equilibrium wage (𝑤𝑡). The higher wage, however, causes the value to the firm of having an
additional worker employed (𝜕𝐹 𝑛
𝑡/𝜕𝑤𝑡<0) to decrease. Hence, higher unemployment benefit remuneration
attenuates the expansion in employment in response to the expansionary fiscal spending shock.18 This result
conforms with Atkinson and Micklewright (1991), Gruber (1997), Fuller (2014) and Faig, Zhang and Zhang
(2016) who argue that aggregate output might be affected negatively by unemployment benefit remuneration
payments since resources are shifted away from their efficient use. The negative impact on employment and
output is countered by a stabilizing effect on consumer spending, which is particularly pronounced when
non-Ricardian consumer behavior is taken into account (see Appendix B for more details).
We now turn to the effects of workers’ bargaining power in the wage negotiation process, denoted by 𝜂.
As discussed earlier, the equilibrium wage 𝑤𝑡is a weighted average of the two reservation wages, with the
weights determined by 𝜂. From Eq. (3.16) and (3.17), we have
𝜕𝑤𝑡
𝜕𝜂 =𝑤𝐹
𝑡−𝑤𝐻
𝑡,(for 𝜏=0)
where 𝑤𝐹
𝑡> 𝑤𝐻
𝑡, as otherwise no worker-firm match would be feasible. Consequently, 𝜕𝑤𝑡
𝜕𝜂 >0, the
implication of which is that as long as 𝑤𝐻
𝑡< 𝑤𝐹
𝑡, increases in workers’ bargaining power push their
reservation wages closer to those of firms, i.e., 𝑤𝐻
𝑡→𝑤𝐹
𝑡. This generates upward pressure on equilibrium
wages, which, in turn, has two effects. Firstly, it reduces the value to the firm of employing an additional
worker, and secondly, it leads firms to require a higher idiosyncratic productivity from workers. The latter
18 Albertini and Poirier (2015) stress the role of the zero lower bound in this context. While increases in unemployment benefits
always raise unemployment in normal times, the opposite may occur at the zero lower bound as the inflationary pressure triggered
by higher unemployment benefits reduces the real interest rate, which in turn promotes consumption, output and employment.
16
effect raises the endogenous job separation rate ( ˜𝑎𝑡increases), resulting in a contraction of employment.
Therefore, in response to an expansionary demand shock, such as a fiscal spending shock, the increase in
both employment and output is smaller when workers’ bargaining power is high. This is illustrated in the
sub-panels in the first column of Figure 3, where the positive output effects diminish as workers’ bargaining
power increases. These findings are consistent with the results in Zanetti (2009), who shows that an increase
in workers’ bargaining power leads to a contraction in macroeconomic activity.
Finally, we turn to the effect of the extent of employment protection, denoted by 𝜍. Unlike the previous
variables—workers’ bargaining power in wage negotiations (𝜂) and unemployment benefits (𝜑)—employment
protection does not influence the equilibrium by affecting reservation wages or the wage bargaining process.
Instead, it directly impacts equilibrium outcomes by imposing constraints on firms’ ability to adjust em-
ployment levels optimally. This distinction is important because employment protection affects firms’
decision-making processes directly, rather than indirectly through changes in reservation wages, thus playing
a unique role in shaping labor market dynamics. The primary mechanism through which employment pro-
tection influences fiscal spending multipliers is related to its effect on the sensitivity of job destruction and
job creation, as described by Eq. (3.2) and (3.4). Starting with the latter, low firing costs increase the value
of an additional worker to the firm (𝜕𝐹 𝑛
𝑡/𝜕𝜍 < 0). In other words, lower firing costs promote job creation.
Therefore, in response to an expansionary fiscal spending shock, low firing costs lead to relatively higher job
creation, resulting in a stronger increase in employment relative to output. Regarding job destruction, Eq.
(3.4) suggests that low firing costs increase the job destruction rate (𝜕˜𝑎𝑡/𝜕 𝜍 > 0). While this effect works
in the opposite direction to job creation, both mechanisms render employment more sensitive to aggregate
shocks. Consequently, in response to an expansionary fiscal spending shock, employment exhibits a larger
response when firing costs are low. This discussion also highlights the possible heterogeneities arising from
the LMIs in altering the transmission of shocks.
We reassess these results by considering a more general calibration in Appendix A.3 and examine
the robustness to several extensions – (i) no inflation indexed prices, (ii) real wage rigidities, (iii) limited
asset market participation, (iv) firing costs as government revenues, (v) productivity-enhancing government
spending, and (vi) complementarity between consumption and leisure – in Appendix B. In short, we find
that inflation indexation of prices crucially shapes the qualitative response of the real wage to fiscal spending
shocks. Moreover, with the exception of extension (iv), the qualitative impact of the LMIs on the output and
employment multipliers remains unchanged.
17
4. The Empirical Evidence
We empirically validate the results of our theoretical model using an interacted panel vector-autoregressive
(IPVAR) specification as popularized by Towbin and Weber (2013) and Sá, Towbin and Wieladek (2014).
We examine the conditional response to fiscal spending shocks and the effect on macroeconomic volatility
for different levels of LMI indicators in a panel of developed countries. The IPVAR model is employed to
assess how the characteristics of the matrices 𝚿0(𝝑)and 𝚿1(𝝑)of the system given by Eq. (3.14) depend on
the LMIs in place. We consider a first-order Taylor expansion of these matrix functions around the sample
average of 𝝑, given by ¯
𝝑
𝚿𝑗(𝝑) ≈ 𝚿𝑗(¯
𝝑) +
3
Õ
𝑙=1𝜕𝚿𝑗
𝜕𝜗𝑙
(¯
𝝑)(𝜗𝑙−¯
𝜗𝑙), 𝑗 ∈ {0,1}.(4.1)
Substituting the matrices 𝚿0(𝝑)and 𝚿1(𝝑)in Eq. (3.15) by the Taylor approximation given by Eq. (4.1)
gives rise to an additive separable expression for the parameters 𝜗𝑙,𝑙={1,2,3}, multiplied in each case by
the endogenous variables. From an econometric point of view, this implies that interaction terms appear in
the specification after this substitution is carried out. In the following, we describe the econometric model
used to estimate 𝚿𝑗(𝝑), before presenting the results and providing a discussion of the insights gained from
the empirical evidence.
4.1 The Econometric Model
We estimate the following reduced-form IPVAR for the 𝑛-dimensional vector of endogenous time series, 𝒚𝑖 𝑡 ,
conditional on the 𝑑-dimensional vector of interaction variables, 𝝑𝑖𝑡 , for country 𝑖=1, . . . , 𝑁
y𝑖𝑡 =𝒄𝑖(𝝑𝑖𝑡 ) +
𝑝
Õ
𝑗=1
𝚽𝑖 𝑗 (𝝑𝑖𝑡 )y𝑖𝑡 −𝑗+u𝑖 𝑡 ,u𝑖𝑡 ∼ N𝑛0,𝚺𝑖(𝝑𝑖𝑡 ),(4.2)
where all coefficients are country-specific and dependent on the interaction term. 𝒄𝑖denotes the intercept, 𝚽𝑖 𝑗
the coefficient matrix for lag 𝑗=1, . . . , 𝑝, and 𝚺𝑖the covariance matrix. All these reduced-form coefficients
are a linear function of the interaction term and the parameters change depending on the exact value taken by
the interaction variable. The details of the model framework are presented in Appendix C.
The structural IPVAR representation is then given by
˜
𝚿𝑖0𝒚𝑖𝑡 =
𝑝
Õ
𝑗=1
˜
𝚿𝑖 𝑗 (𝝑𝑖𝑡 )𝒚𝑖𝑡−𝑗+𝒆𝑖 𝑡 ,𝒆𝑖𝑡 ∼ N𝑛(0,𝑰),(4.3)
18
where we have excluded the deterministic term for the sake of simplicity. The underlying idea of the panel
setup is to estimate a common economic model for all countries in our sample. This is done via a pooling
prior in the spirit of Jarociński (2010). The prior assumes that the structural country-specific coefficients
have a common underlying Gaussian distribution,
˜
𝚿𝑖 𝑗 (𝝑𝑖𝑡 ) ∼ N ( 𝚿𝑗(𝝑𝑡),𝑽𝑗), 𝑗 =1, . . . , 𝑝, (4.4)
where 𝑽𝑗denotes the covariance matrix. We exert regularization via this covariance matrix towards the
common-mean model through Bayesian global-local shrinkage priors (Griffin and Brown, 2010; Huber and
Feldkircher, 2019). The pooling prior and the exact specification of the shrinkage prior are described in
Appendix C.
The correspondence between the observable LMIs 𝝑𝑖𝑡 and the structural LMI parameters 𝝑of the DSGE
model can be made explicit by defining 𝚿𝑗(𝝑𝑡)=𝚿𝑗𝑡 and 𝚿𝑗(¯
𝝑𝑡)=¯
𝚿𝑗+𝜕𝚿𝑗(𝝑𝑡)/𝜕𝝑𝑡· (𝝑−¯
𝝑)for
𝑗=0,1, . . . , 𝑝. This implies that the coefficients of the 𝚿𝑗 𝑡 matrix vary as follows
𝚿𝑗(𝝑𝑡)=𝚿𝑗𝑡 =¯
𝚿𝑗+
𝑑
Õ
𝑙=1
𝜕𝚿𝑗(𝝑𝑡)
𝜕𝜗𝑙𝑡
(𝜗𝑙𝑡 −¯
𝜗𝑙), 𝑗 =0, ..., 𝑝. (4.5)
This relates the empirical set-up directly to Eq. (4.1) of the theoretical model. The full IPVAR model is
given by Eq. (4.3), and its equivalence with the solution of the DSGE model depicted in Eq. (3.14) and Eq.
(4.1) is evident when considering a lag length of one.
In the IPVAR specification, interactions between the endogenous variables and labor market indicators
are thus included in the specification and thus LMIs act as mediators of the effect of fiscal policy (and other)
shocks. As a result, impulse response functions can be evaluated for varying values of 𝜗𝑙. For the ease of
interpretation, we examine changes in the structural coefficients only by varying one interaction variable,
while keeping the remaining ones at a given level (i.e., at the median).
There are two potential limitations to the empirical approach adopted here. First of all, LMIs may
be endogenous to shocks hitting the economy. Given the path of the LMI variables depicted in Figure 1,
structural rather than cyclical factors appear to determine their dynamics.19 A second potential limitation is
the linearity assumption (in the parameters) embedded in the IPVAR model, which mimics the approximation
considered in Eq. (4.1). In principle, the assumption of linearity could be relaxed by considering various
non-linear extensions of 𝝑𝑡. However, depending on the number of observations and parameters of interest in
19 This is confirmed within a robustness check where we include each one of the LMI indicators in a standard panel VAR and
calculate the impulse response functions of the LMI variables. They do not significantly react to cyclical shocks.
19
the estimation, overfitting of the model becomes a problem in our setting, so we stick to linear specifications
with interactions in this piece instead of assessing more complex nonlinear parametrizations of the model.
4.2 Data and Specification
We use quarterly data ranging from 1960Q1 to 2020Q4 for 16 OECD countries to estimate the IPVAR
model.20 The vector of endogenous variables includes 𝒚𝑖𝑡 =(𝑔𝑖𝑡 , 𝑥𝑖 𝑡 , 𝑒𝑟𝑖 𝑡 , 𝜔𝑖𝑡 )0which denotes the growth
rate of real government consumption per capita, 𝑔𝑖 𝑡 , the growth rate of real GDP per capita, 𝑥𝑖𝑡 , first difference
of the employment rate, 𝑒𝑟𝑖𝑡 , and the growth rate of real wages, 𝜔𝑖𝑡 .21 We use year-on-year growth rates and
first differences and refer to Table D1 and Table D2 in the Appendix for further details.
As regards the interaction variables, we specify 𝝑𝑖𝑡 =(𝜂𝑖𝑡 , 𝜑𝑖𝑡 , 𝜍𝑖𝑡 )0and use data from the CEP-OECD
institutions database for union density (𝜂𝑖𝑡 ), unemployment benefit replacement rates (𝜑𝑖𝑡 ) and employment
protection legislation (𝜍𝑖𝑡 ).22 The original data set contains annual observations, which we interpolate to a
quarterly frequency by assigning the annual value of a particular year to each quarter of the same year. We
estimate the IPVAR model using all three interaction variables at once. Prior to estimation, we standardize
each interaction variable. This serves the purpose of comparability across countries as we exploit within-
country variation in the LMIs. We interpret our estimates thus as conservative due to the strong cross-country
heterogeneity in the LMIs. When simulating the IPVAR model along a particular interaction variable 𝜗𝑙, we
set the remaining ones 𝜗ℓ(ℓ≠𝑙) equal to its median.
All models are estimated with one lag (𝑝=1) as proposed by the Bayesian information criterion.23 The
estimation is based on 20,000 posterior draws, where we discard the first 10,000 as burn-ins.
4.3 Shock Identification
We identify fiscal spending shocks by imposing a recursive identification based on the Cholesky decompos-
ition of the reduced-form IPVAR shocks. We follow Blanchard and Perotti (2002) and assume that fiscal
spending does not react contemporaneously to shocks arising from GDP or labor market variables in the
20 The sample includes information on the following OECD countries: Australia, Austria, Belgium, Canada, Denmark, Finland,
France, Germany, Great Britain, Italy, Japan, the Netherlands, Portugal, Spain, Sweden, and the United States.
21 Following Brückner and Pappa (2012), we express all variables in per-capita terms. Additionally, we provide robustness by
applying the procedure suggested by Gordon and Krenn (2010). We divide each variable with its Hamilton (2018)-filtered trend.
As noted by Ramey (2016), the impulse responses from using this transformation are quite similar to those using log-levels and it
produces relatively narrow confidence bands. We report results in Appendix E.2.
22 For a descriptive description and further details of the LMIs, we refer the reader to Section 2 and Table D1 in the Appendix.
23 We provide robustness to this choice in Appendix E.2. Our results are robust to using two or four lags.
20
system. These three variables are hence assumed to respond within the same quarter to the fiscal spending
shock. This recursive structure is the most conventional strategy used to identify fiscal spending shocks in the
established structural VAR literature (see for instance the discussion in Čapek and Crespo Cuaresma, 2020).
We utilize this particular recursive identification approach for fiscal spending shocks for two reasons. First,
this approach is in line with recent studies that use panel VAR or country VAR methods to analyze the effects
of fiscal policy (Beetsma and Giuliodori, 2011; Bénétrix and Lane, 2013; Ilzetzki, Mendoza and Végh, 2013;
Huidrom et al., 2020, to mention a few). Second, alternative identification approaches are infeasible in the
context of our research question.24
One potential drawback in the context of a recursive approach to identification concerns the issue of fiscal
foresight. Economic agents constantly receive information and update their expectations regarding news on
fiscal policy issues. As econometricians, we may only observe a smaller information set. This misalignment
between the information sets of the economic agents and of the econometrician can generate equilibria with
a non-fundamental moving average representation (Ramey, 2011; Leeper, Walker and Yang, 2013; Ellahie
and Ricco, 2017). To resolve this issue, the information set in the VAR is enlarged to contain a variable
proxying for agents’ expectations. These expectations are not available for the full sample of countries and
time span considered here. Therefore, we show that our results are robust to this concern in a smaller setting
in Appendix E.3.25
4.4 The Effect on Fiscal Spending Effectiveness
In this section, we present the effects of the LMIs on fiscal spending effectiveness. In line with the theoretical
results, we compute multipliers for the initial impact (“impact multiplier”, horizon 𝑃=0) and for the effect
after four quarters (“one-year multiplier”, horizon 𝑃=4). Figure 4 depicts the multipliers for output,
employment, and the real wage. In each panel, we display the sensitivity of the multipliers with respect to
the LMIs. The black solid and the red dash-dotted lines refer to the median value of the impact and one-year
24 Alternative approaches can be summarized in three distinct groups: (i) event-study approaches based on defense spending changes
(Ramey and Shapiro, 1998; Ramey, 2011), (ii) sign-restrictions (Mountford and Uhlig, 2009), or (iii) narrative approaches (Romer
and Romer, 2010; Guajardo, Leigh and Pescatori, 2014). All these approaches are not feasible because they rely on additional
data (e.g., detailed institutional information or data on fiscal spending plans) or are not practical for a large panel of countries. An
interesting alternative is Miyamoto, Nguyen and Sheremirov (2019) who use military spending data in a large panel of countries
but only on a yearly frequency.
25 We follow the suggestions in Born, Juessen and Müller (2013), Born, Müller and Pfeifer (2020), or Ilori, Paez-Farrell and
Thoenissen (2022) and use two different sets of government spending forecasts. To control for fiscal foresight, we rely on data by
professional forecasters of Oxford Economics and the OECD. We restrict our sample to the G7 countries in the cross-section and
starting only in the mid 1980s (OECD) or late 1990s (Oxford Economics). We refer to the Appendix E.3 for further details.
21
multipliers and are complemented with the 80% confidence bounds in each case. The horizontal axis ranges
from the 10th to 90th quantile of the distribution of the respective LMIs, while the vertical axis depicts the
value of the fiscal multiplier for the respective variable.
We start by discussing the impact multiplier for output and its dependency on LMIs. Across all LMIs,
we find impact multipliers between 0.2-0.3 for low levels of the LMIs. At a low value of UD (𝜂), we find that
a one percent increase in fiscal spending raises real GDP by 0.3 percent; the value of the output multiplier
drops to zero when UD is at the upper end of the distribution. This gives rise to a strong decline in the output
multiplier, which is substantial and statistically significantly different from zero. In the case of the EPL (𝜍)
we do not find a strong decline in the output multiplier, while we even find a statistically significantly larger
output multiplier for higher levels of the BRR (𝜑).26 This finding is interesting and deserves a more thorough
discussion which we provide further below.
The impact multipliers for employment, while consistently positive, are negatively affected by two out
of three LMIs. The drop is sizeable in the case of UD and the EPL and amounts to around 10 log points
(from 0.10 down to 0.00), while being again moderately increasing for the BRR. The one-year multipliers
consistently exceed the impact multipliers, which highlights the inertia of the impact of government spending
shocks on economic activity. For UD and EPL, the decline of the employment multiplier is statistically
significant, while the increase for the BRR is estimated relatively imprecisely.27 For the real wage, we find
the least pronounced effects. The multiplier declines for UD both for the on impact and one-year multiplier,
while it only declines for the EPL for the one-year multiplier. However, these estimates face high uncertainty.
In the case of the BRR, we find constant multipliers.
Overall, the LMIs are found to play a role for the effectiveness of discretionary fiscal policy. This applies
to both the goods and the labor market. Among the three LMIs considered, the UD and EPL are found
to have the strongest effects. The output and employment multipliers of the IPVAR model are comparable
to those of the calibrated DSGE model. Similar to Figure 3, a strong decrease is visible for UD and EPL.
The comparably mild decline of the output multiplier with respect to the EPL highlights the limited role
severance payments and alike, which characterize the extent of employment protection (see Section B in the
26 These differences are statistically significant, as we show in Appendix E.1. We examine the dynamic responses and show IRFs
evaluated at the 10th and 90th quantile of the respective LMI distribution. Furthermore, we investigate the full posterior distribution
of the differences in these IRFs. The evidence suggests that differences are strongly significant at the on impact and one-year
horizon for UD (output and employment) and EPL (employment). For the BRR, the differences are not statistically significant.
Furthermore, we also find that most of the dynamic response happens within the first six months.
27 In fact, in subsection E.1 we show that differences are not statistically significant at the 68% level.
22
Figure 4: Fiscal Multipliers.
−10
−10
−10
−10
Real GDP
−10
−10
Employment Rate
−10
−10
Real Wage
−10
−10
UD (η)
P=0
P=4
Q10 Q30 Q50 Q70 Q90
−0.2
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
−0.2
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
−0.2
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
Notes: The sub-figures show the sensitivity of the fiscal spending multipliers to changes in the structural parameters (𝜂is union density, 𝜑is the
unemployment benefit replacement rate, and 𝜍is employment protection legislation). The y-axis gives the size of the multiplier while the x-axis
runs from the 10th to the 90th quantile in terms of the respective LMI. The multipliers are shown for different horizons: on impact (P=0, solid
black line) and one-year (P=4, dashed-dotted red line) multiplier. The lines denotes the median and the colored area refers to the 80% credible set.
Appendix), while at the same time give rise to a re-distribution to households which in turn attenuates the
negative impact of a more stringent EPL on the output multiplier. Nevertheless, some differences arise. First
and most noteworthy, we find an increase in the multiplier when imposing higher values of the BRR. This
is clearly visible for the output multiplier. This could reflect that our model does not include unemployment
risk, giving rise to a precautionary savings channel. Unemployment insurance can mitigate this channel and
cause an additional demand channel (Challe, 2020; McKay and Reis, 2021; Kekre, 2023).28 Furthermore,
the null effect on the employment rate for BRR aligns well with micro-evidence from Boone et al. (2021)
examining unemployment insurance extensions. Second, our baseline model shows no strong change in the
multipliers with respect to real wages. Third, in the theoretical model, the one-year employment multiplier
28 In fact, this literature differentiate between changing the level of unemployment benefits and extending unemployment benefits,
where our results only speak to the former. While Challe (2020) investigates the interaction with monetary policy, McKay and
Reis (2021) examine the optimal unemployment insurance level as automatic stabilizer, and Kekre (2023) looks into duration
extensions. All, however, point to an additional demand channel arising through less precautionary savings when unemployment
risk is somehow insured.
23
consistently exceeds the impact multiplier, which highlights the role of limited asset market participation in
this context.29 The empirical findings point, however, to rather little inertia in the dynamic responses.
We provide the forecast error variance decomposition (FEVD) in Figure 5. The share of the variation in
output explained by fiscal spending shocks depends both on the horizon and the LMIs. As can be seen, fiscal
spending shocks explain a low fraction of the variance of output when the horizon considered is short and
a stringent value of UD is deployed (“high”). In contrast, it explains up to 8% at horizons of eight quarters
and beyond when UD are, however, less stringent (“low”). This share is substantially lower for the variables
characterizing the labor market, employment, and real wages. The forecast error variance of output is reduced
the most clearly, while less clear reductions are visible for the employment rate and the real wage. We find
similar effects, albeit to a less pronounced degree, for the EPL. Lastly, mirroring the findings of the IRF
analysis, for the BRR (𝜑) the picture changes. We find that a more stringent value of the BRR (“high”) leads
to a larger explained share of the forecast error variance for output. We do not find significant differences for
the other two variables. Overall, we find that when stringent LMIs are deployed, discretionary fiscal policy
only has a limited potential in affecting labor market outcomes.
These findings are in line with the literature as regards the size of fiscal spending multipliers for output
(Ramey, 2019), the extent of inertia (Ilzetzki, Mendoza and Végh, 2013), as well as the lower value of
the employment relative to the output multiplier (Monacelli, Perotti and Trigari, 2010). The positive real
wage multiplier is consistent with the findings in Brückner and Pappa (2012) who identify both negative and
positive multipliers across distinct countries. Note that our results refer to average effects across positive and
negative fiscal spending shocks, although asymmetries can arise (Barnichon, Debortoli and Matthes, 2022).
Our key contribution in this context concerns the assessment of the size and shape of fiscal multipliers with
respect to the LMIs. In this regard, we find strong evidence in favor of a dependency of fiscal multipliers and
hence of the effectiveness of discretionary fiscal policy on the LMIs.
Further results on the extent to which the LMIs shape the transmission channel of fiscal spending shocks
are provided in Appendix E. We report the dynamic responses as well as robustness checks to the baseline
model. In Figure E3 we control for fiscal foresight on a smaller sample which is not found to exert a
strong influence on the baseline findings. We also re-do the analysis with other labor market variables, the
29 We provide and discuss a number of extensions to the theoretical model in Appendix B. Limited asset market participation
generally yield a higher level of fiscal multipliers due to the presence of non-Ricardians.
24
Figure 5: Forecast Error Variance Decomposition.
UD (η)
Real GDP
0 4 8 12 16 20
0.00
0.02
0.04
0.06
0.08
0.10
BRR (ϕ)
0 4 8 12 16 20
0.00
0.02
0.04
0.06
0.08
0.10
EPL (ς)
Low
High
0 4 8 12 16 20
0.00
0.02
0.04
0.06
0.08
0.10
Employment Rate
0 4 8 12 16 20
0.00
0.01
0.02
0.03
0.04
0.05
0 4 8 12 16 20
0.00
0.01
0.02
0.03
0.04
0.05
0 4 8 12 16 20
0.00
0.01
0.02
0.03
0.04
0.05
Real Wage
0 4 8 12 16 20
0.01
0.02
0.03
0.04
0.05
0.06
0 4 8 12 16 20
0.01
0.02
0.03
0.04
0.05
0.06
0 4 8 12 16 20
0.01
0.02
0.03
0.04
0.05
0.06
Notes: The sub-figures show the sensitivity of the explained forecast error variance to changes in the structural parameters (𝜂is union density, 𝜑
is unemployment benefit replacement rate, and 𝜍is employment protection). The y-axis gives the share of explained forecast error variance while
the x-axis is the forecast horizon and runs up to 5 years (=20 months). The FEVD is shown for the respective LMI at the 10th quantile (low, black
dashed line) and 90th quantile (high, dashed red line). Confidence bounds refer to the 10/90 quantile of the posterior distribution.
unemployment rate and labor market tightness. Finally, we also investigate the issue of strong cross-country
heterogeneity in the LMIs as depicted in Figure 2.
4.5 The Effect on Macroeconomic Volatility
While the effects of discretionary fiscal policy potentially are decreased due to more stringent LMIs, the
question arises whether there is a strong need for these policies in an environment with stronger labor market
frictions.30 We are thus interested in the degree of substitutability between the LMIs and fiscal spending
policies.
Therefore, we use our econometric setting to assess macroeconomic volatility with respect to the LMIs.
We determine the variance of the endogenous variables of the IPVAR model conditional on the stringency of
30 The LMIs that we consider capture structural labor market characteristics across distinct dimensions, however, they can, at least
partly, be viewed as automatic stabilizers. Looking more closely at the individual LMIs, this is most evident with the BRR as an
automatic stabilizer. In case of an adverse shock, a higher level of the BRR smooths household income over the business cycle and
provides insurance for unemployment risk. The EPL and the UD work through similar channels. If these very elements already
contribute significantly to cyclical smoothing by which they render any discretionary spending policy obsolete.
25
Figure 6: Macroeconomic Volatilities Along LMIs.
Real GDP
UD (η)BRR (ϕ)EPL (ς)
1.8
2.1
2.4
2.7
3.0
3.3
Low
High
Employment Rate
UD (η)BRR (ϕ)EPL (ς)
0.6
0.8
1.0
1.2
1.4
Low
High
Real Wage
UD (η)BRR (ϕ)EPL (ς)
1.6
1.8
2.0
2.2
2.4
2.6
Low
High
Notes: Each sub-figure shows the standard deviation of the respective macroeconomic variable in a regime with low (10th quantile, dark gray)
and high (90th quantile, light gray) labor market institutions while the remaining LMIs are at their median. The labor market institutions under
consideration are union density (UD, 𝜂), unemployment benefit replacement rate (BRR, 𝜑), and employment protection legislation (EPL, 𝜍).
the LMIs.31 The covariance matrix of the endogenous variables y𝑖𝑡 in the IPVAR system is given by32
vec (𝛀(𝝑𝑡))=(𝑰−𝑭(𝝑𝑡) ⊗ 𝑭(𝝑𝑡))−1vec (𝑸(𝝑𝑡)),(4.6)
where 𝑰is an identity matrix of dimension 𝐾2=(𝑀 𝑝)2,𝑭(𝝑𝑡)denotes the 𝐾×𝐾companion matrix form
of 𝚿𝑗(𝝑𝑡)with 𝑗=1, . . . , 𝑝, and 𝑸(𝝑𝑡)denotes the 𝐾×𝐾companion matrix form of the common-mean
covariance matrix.33 It can directly be seen from the equation that the 𝐾×𝐾covariance matrix of the
endogenous variables, 𝛀(𝝑𝑡), depends on the interaction terms, 𝝑𝑡.
The results are depicted in Figure 6, where we report the model-implied volatility for a low (10th quantile,
dark gray) and high (90th quantile, light gray) value of the respective LMI.34 We observe that the LMIs have
a potentially volatility-reducing effect. For output, UD and EPL reduce the volatility but significantly only
for the latter. In contrast, higher levels of BRR clearly lead to higher volatility in output. While we do not
see strong differences in volatilities regarding the employment rate or the real wage for UD and EPL, higher
levels of BRR also lead to a higher volatility of the employment rate. We do not see strong differences for
31 We redo this analysis in the theoretical model as well, see Appendix A.4. There, however, we condition on either a government
spending or a technology shock.
32 The definition of the companion form can be found in standard time series text books, e.g., Hamilton (1994) or Kilian and
Lütkepohl (2017). The exact formula for the variance of the endogenous variables in the VAR system is 10.2.18 in Hamilton
(1994), which we have adapted for the case of the IPVAR.
33 We do not impose a pooling prior on the country-specific covariance matrices. Therefore, we use ex-post a common-mean
approach by averaging across the country-specific covariance matrices, i.e., 𝚺(𝝑)=𝑁−1Í𝑁
𝑖=1𝚺𝑖(𝝑𝑖𝑡 ).
34 We abstain from reporting the implied volatilities when setting the respective LMI to its median value. Due to the standardization
of the data, the median is zero and thus we only need half of the parameters for inspecting the median. The decreased number of
involved parameters is another source of variance minimization which we do not want to exploit.
26
the real wage.35 The theoretical model aligns with these results. It suggests sizable decreases for UD, and
no strong effects for EPL. For BRR, the theoretical model points to higher volatility for less stringent LMI
in contrast to the empirical findings. Most importantly, the theoretical results in this context highlight that
the ability of the LMIs in attenuating macroeconomic volatility crucially depends on the shocks’ sources, as
we discuss in more detail in Appendix A.4. To conclude, UD and EPL reduce volatility, while BRR leads to
higher levels of volatility.
4.6 How Do Labor Market Institutions Change the Effect on Macroeconomic Volatility?
In a next step, we are interested in how the LMIs dampen macroeconomic volatility. On the one hand, it is
possible that they affect the propagation mechanism (transmission channel) of exogenous shocks but leave
the size of the contemporaneous impact of exogenous shocks unaffected. On the other hand, the opposite
could apply equally well. In the following, we discuss this issue in more detail.
As is evident from Eq. (4.6), the effect of the LMIs on the volatility of variable 𝑘occurs along two
distinct dimensions. These concern the transmission channel of exogenous shocks (shock transmission effect,
henceforth STE) or the size of the contemporaneous impact of exogenous shocks (shock size effect, henceforth
SSE). More formally, we are interested in the partial effect of 𝜗𝑙𝑡 ∈𝝑𝑡on 𝜔𝑘 𝑘 , which is the 𝑘-th element on
the main diagonal of the matrix 𝛀(𝝑𝑡)denoting the volatility of the 𝑘th variable in the vector of endogenous
variables 𝒚𝑖𝑡 . Furthermore, we denote with ˜
𝑭(𝝑𝑡) ≡ (𝑰−𝑭(𝝑𝑡) ⊗ 𝑭(𝝑𝑡))−1and ˜
𝑸(𝝑𝑡) ≡ vec (𝑸(𝝑𝑡)). In
the following, small letters denote scalars and refer to an element of the corresponding vector ˜𝑞𝑗(𝝑𝑡) ∈ ˜
𝑸(𝝑𝑡)
or matrix ˜
𝑓𝑘 𝑗 (𝝑𝑡) ∈ ˜
𝑭(𝝑𝑡). Then 𝜔𝑘 𝑘 (𝝑𝑡)=Í𝑗˜
𝑓𝑘 𝑗 (𝝑𝑡) · ˜𝑞𝑗(𝝑𝑡)holds, and the partial effect is given by
𝜕𝜔𝑘 𝑘 (𝝑𝑡)
𝜕𝜗𝑙𝑡
=Õ
𝑗˜𝑞𝑗(𝝑𝑡)𝜕˜
𝑓𝑘 𝑗 (𝝑𝑡)
𝜕𝜗𝑙𝑡
| {z }
STE
+˜
𝑓𝑘 𝑗 (𝝑𝑡)𝜕˜𝑞𝑗(𝝑𝑡)
𝜕𝜗𝑙𝑡
| {z }
SSE
,(4.7)
which allows us to decompose the overall change in the volatility with respect to the LMIs along the proposed
dimensions: STE and SSE. For each of the two cases, the signs of the partial derivatives allow for an exact
identification of the partial effect.
The results are provided in Figure 7, where we show the change in the volatilities (Δ𝜔𝑘 𝑘 (𝝑𝑡)) when
moving from loose to stringent LMIs (Δ𝜗𝑙>0). The overall effect (Δ𝜔𝑘 𝑘 (𝝑𝑡)/Δ𝜗𝑙𝑡 ) is decomposed into
the STE (dark gray box-plots in each panel) and SSE (light gray box-plots in each panel). For a better
35 This results are robust to exchanging the employment rate with the unemployment rate, as discussed in Appendix E.4.
27
Figure 7: Change in Macroeconomic Volatilities Along LMIs.
∆UD(η) > 0
Real GDP Emp. Rate Real Wage
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
Change in Volatility
STE
SSE
∆BRR(ϕ) > 0
Real GDP Emp. Rate Real Wage
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
Change in Volatility
STE
SSE
∆EPL(ς) > 0
Real GDP Emp. Rate Real Wage
−1.2
−0.8
−0.4
0.0
0.4
Change in Volatility
STE
SSE
Notes: Each sub-figure shows the change in the standard deviation of the respective macroeconomic variable when going from the high (90th
quantile) to the low (10th quantile) regime of the respective labor market institution. STE (dark gray) refers to the shock transmission effect, while
SSE (light gray) refers to the shock size effect as depicted in Eq. (4.7). The labor market institutions under consideration are union density (UD, 𝜂),
unemployment benefit replacement rate (BRR, 𝜑), and employment protection legislation (EPL, 𝜍).
understanding, consider the change in the output volatility that arises from an increase in the UD, which is
displayed in the left panel. The higher UD affects output volatility both along the STE and SSE. The median
change in the output volatility is slightly above zero according to the STE. This implies that a higher UD
causes higher output volatility by reinforcing the propagation mechanism of shocks. While the STE gives rise
to an endogenous reinforcement of shocks, the opposite applies to the SSE as according to which a higher UD
attenuates the output volatility due to a smaller contemporaneous impact of shocks. The results are similar as
regards the employment rate volatility: on the one hand, a higher UD causes higher volatility by reinforcing
the propagation mechanism of shocks; on the other hand, a higher UD attenuates the employment volatility
due to a smaller contemporaneous impact of shocks. Most clearly, we see these effects again for the real
wage. The effects are sizeable, however, since they drift in opposite directions, the overall effect as depicted
in Figure 6 is hence negligibly small.
In the case of the BRR, we find that volatilities are higher due to both STE and SSE. We observe this
most clearly for output but to a lesser degree also for the employment rate volatility. Again, these results
align well with the findings depicted in Figure 6. Lastly, we investigate the change in the volatilities for the
EPL. Results suggest that the large decline in volatility for output visible in Figure 6 is mostly driven by the
STE. The SSE for output volatility is basically null. The other two variables do not show a strong mitigation
of the involved volatilities. The SSEs seem to matter with opposing signs but with small absolute effects.
28
To sum up, our results show that both the STE and the SSE matter with respect to the impact of the LMIs
for the output and employment volatility.36 The decline in the output volatility for UD and EPL is coming
from different sources. UD seems to affect less the transmission of the effects while EPL does so sizably.
On the contrary, the BRR paints a different picture. Both transmission and size play a role for the increase in
output and employment rate volatility. This exercise reveals that the direction of the effect is in some cases
opposite, which gives rise to an overall small effect.
4.7 Accounting for the Evidence
We move on to the exploration of structural differences that arise from different labor market institutions.
Possibly, these differences may not only give rise to but also reinforce structural disparities in other dimensions.
For example, a higher benefit replacement rate could strengthen the bargaining position of workers in wage
negotiations, as the outside option (i.e., not working) becomes more attractive due to higher non-work income.
This, in turn, could influence wage and price dynamics, thereby shaping the degree of nominal rigidities
within the economy. Nominal rigidities, in turn, play a crucial role in determining the fiscal multiplier in the
context of fiscal spending shocks.
In this regard, we assess the extent to which the theoretical model can explain the empirical evidence.
We estimate key structural parameters of the theoretical model by matching the impulse response functions
of the theoretical and empirical models. The purpose of this exercise is to contrast the theoretical model
predictions for the effects of government spending shocks under different values (low vs. high) of the LMIs.
We fix all structural parameters to their values as depicted in Table A1, except the parameters capturing
the persistence of the government spending shock (𝜚𝑔), the extent of price stickiness (𝜉) and the share of
prices that is adjusted in line with the previous period’s inflation rate (𝛾𝑝), the elasticity of matching with
respect to unemployed workers (𝛾), and the first and second moment of the distribution 𝐹(·) of idiosyncratic
job destruction (𝜇𝑎,𝜎𝑎), which are all collected in the vector 𝜽. The parameter selection is motivated by
their significant role in shaping fiscal spending multipliers (Galí, López-Salido and Valles, 2007; Dupaigne
and Fève, 2016).
In order to obtain estimates for these parameters, we match empirical (IPVAR) and theoretical impulse
responses (see, for instance, Rotemberg and Woodford, 1997). Let d
IRF be the empirical impulse response
36 These results are robust to exchanging the employment rate with the unemployment rate, as discussed in Appendix E.4.
29
Table 1: Estimated model parameters
UD (𝜂) BRR (𝜑) EPL (𝜍)
Low (𝜂=0.1) High (𝜂=0.7) Low (𝜑=0.3) High (𝜑=0.6) Low (𝜍=0.1) High (𝜍=0.6)
𝜚𝑔0.42 0.45 0.41 0.44 0.41 0.43
𝜉0.56 0.58 0.56 0.91 0.56 0.55
𝛾𝑝0.02 0.03 0.00 0.52 0.04 0.03
𝛾0.56 0.88 0.58 0.69 0.71 0.76
𝜇𝑎-0.97 0.66 1.78 1.83 1.30 -1.48
𝜎𝑎2.88 3.03 2.32 3.08 2.39 2.99
Notes: Structural parameters: 𝜚𝑔is the autoregressive of the AR(1)-government consumption spending shock, 𝜉captures
the degree of price stickiness, 𝛾𝑝denotes the share of inflation indexed prices, 𝜇𝑎and 𝜎𝑎are the first and second moments
of the distribution of the idiosyncratic job productivity ( ˜𝑎𝑡). The values in parentheses in the rows for the Low and High LMIs
represent the specific LMI values used in the matching process. All other parameters are fixed at their baseline calibration.
functions obtained from estimating the IPVAR37, and let IRF(𝜽)be its counterpart from the theoretical model.
We focus on the first 25 periods of the responses of government spending ( ˆ𝑔𝑡), output ( ˆ𝑦𝑡), employment (ˆ𝑛𝑡),
and the real wage ( ˆ𝑤𝑡). We estimate the parameter vector 𝜽by minimizing the distance38 between empirical
and theoretical impulse response functions under low and high values of the LMIs.
ˆ
𝜽=arg min d
IRF −IRF(𝜽),(4.8)
where d
IRF and IRF(𝜽)are column vectors39 of impulse responses. We establish estimates for ˆ
𝜽for (i) each
LMI individually, and (ii) separately for low and high values.
The parameter estimates are provided in Table 1. The estimated autocorrelation coefficient (𝜚𝑔) for the
government spending shock reflects a medium-high persistence and a value at the lower bound compared to
those commonly found in the literature (see, for instance, Born, Juessen and Müller, 2013). Most interestingly,
the estimates are the same across labor market regimes (that is, whether a high or a low value of any LMI is
considered). Moreover, we also observe that the second moment of the distribution function of idiosyncratic
job destruction (𝜎𝑎) is rather stable across labor market regimes.
We find a noteworthy variation of the remaining parameter estimates across distinct labor market regimes.
With respect to union density (UD), we observe a sizeable change in the estimates of 𝛾and 𝜇𝑎, both of
which crucially shape employment dynamics. The estimates suggest that the transition to a labor market
37 Specifically, as always done throughout the paper, we focus on the impulse response functions of the common mean in the model.
The common mean is an estimate, which encompasses all the information from the respective single-country models but still
allows for idiosyncrasies. We report the respective impulse response functions in Figure E1 in the Appendix.
38 We stick to a procedure that produces parameter estimates which give rise to equilibrium determinacy (i.e., saddle-path stability).
39 Their dimension is (25 ·4) × 1in each case: 25 periods of the impulse response functions for four variables.
30
characterized by a higher union density renders employment more volatile owing to (i) a higher elasticity of
matching unemployed workers (𝛾), and (ii) a higher idiosyncratic job loss probability (𝜇𝑎).40 As a result,
employment adjustments become more pronounced, which indirectly reflects the enhanced wage-setting
power of workers and the corresponding response of firms to this shift. This contrasts with the effect of
the benefit replacement rate (BRR), where a higher replacement rate increases nominal rigidities, while
leaving most of the other parameter estimates largely unchanged. The higher extent of nominal rigidities
is reflected on the one hand by a lower frequency of price adjustments (𝜉) and a higher share of inflation
indexed prices, both of which raise the extent of nominal rigidities and hence exert upward pressure on the
fiscal spending multiplier in the short run. Finally, the degree of employment protection (EPL) primarily
influences the mean of idiosyncratic job destruction (𝜇𝑎). Higher EPL is generally associated with a lower
average probability of job destruction, which reflects the intended purpose of EPL—to provide greater job
security. This reduction in job destruction, in turn, dampens the employment response to expansionary fiscal
spending shocks, and consequently mitigates their effect on output. As a result, higher EPL moderates the
fiscal spending multiplier.
5. Concluding Remarks
We have shown the eminent role of LMIs for fiscal policy and macroeconomic volatility alike. These results
emerge from a theoretical model which combines the characteristics of a Diamond-Mortensen-Pissarides
model with a standard New Keynesian setup; and from an interacted panel vector auto-regressive (IPVAR)
model estimated for a panel data of 16 OECD economies. The empirical findings confirm the theoretical
results and are robust to various extensions.
Our first key result highlights that the LMIs affect both thetransmission channel of fiscal spending shocks,
as well as the governments’ quantitative ability in shaping output fluctuations. While this finding applies to
all three LMIs under inspection, quantitative differences, though, emerge. These effects turn out strongest in
the case of union density (UD) while being weaker with respect to employment protection legislation (EPL);
unemployment benefit replacement rate (BRR) shows more mixed evidence. Using partial information
matching, we find that the mechanism runs through variations in price rigidity, matching elasticity, and
idiosyncratic job loss probability depending on the LMI.
40 As outlined in the Appendix, the idiosyncratic productivity ˜𝑎is assumed to be i.i.d. log-normally distributed with c.d.f. 𝐹of
which we estimate the first and second moments (𝜇𝑎=𝐸[ln(˜𝑎)] and 𝜎𝑎=p𝑉𝑎 𝑟 [ln(˜𝑎)], where 𝜇𝑎∈Rand 𝜎𝑎∈R+).
31
The second key result is that LMIs by themselves mute output volatility for UD and EPL. Our approach
enables an assessment of distinct explanations in this respect. It permits to consider distinct observable
structural elements for explaining volatility changes in macroeconomic time series and to assess whether
distinct structural elements reduce macroeconomic volatility either by mitigating the propagation mechanism
of shocks (STE) or by changing their contemporaneous impact characteristics (SSE). Results suggest that in
several instances the STE is responsible for the reduction in volatility.
A key policy implication of our findings is that stringent labor market institutions render expansionary
spending policies less effective while at the same time reduce the pain of fiscal consolidations. Moreover,
while more stringent labor market institutions attenuate macroeconomic volatility, the fact that in some
cases this occurs by attenuating the contemporaneous impact of shocks while concurrently exacerbating their
propagation mechanism allows for the build up of risks and imbalances underneath a seemingly tranquil
macroeconomic surface. This suggests a cautionary tale of stringent labor market institutions.
Declaration of Interest
The authors declare to have no conflict of interest.
32
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39
Online Appendix: Labor Market Institutions, Fiscal
Multipliers, and Macroeconomic Volatility∗
Maximilian Boeck1, Jesus Crespo Cuaresma2,3,4,5, and Christian Glocker4
1Friedrich-Alexander University Erlangen-Nuremberg
2Vienna University of Economics and Business
3Wittgenstein Centre for Demography and Global Human Capital (IIASA, ÖAW, UniVie)
4Austrian Institute of Economic Research
5CESifo
Appendix Material
This appendix contains additional material not reported in the main text. Appendix A provides
further details on the theoretical model, while we present extensions to the theoretical model in
Appendix B. Appendix C provides further details on the econometrical model. Data sources,
availability, and transformations are listed in Appendix D. We present a number of further
empirical results in Appendix E.
∗Corresponding Author. Maximilian Boeck: Friedrich-Alexander University Erlangen-Nuremberg, Lange Gasse 20, 90403 Nurem-
berg, Germany. E-mail: maximilian.boeck@fau.de. Jesús Crespo Cuaresma: Department of Economics, Vienna Univer-
sity of Economics and Business. Welthandelsplatz 1, 1020 Vienna, Austria. E-mail: jesus.crespo.cuaresma@wu.ac.at.
Christian Glocker: Austrian Institute of Economic Research, Arsenal Objekt 20, 1030 Vienna, Austria. E-mail:
christian.glocker@wifo.ac.at
1
A. Further Details on the Theoretical Model
This section provides further details on the solution of the baseline model. The model extensions considered
also rest upon the solution procedure outlined here.
A.1 Equilibrium Equations
The following provides an overview as regards the equations that characterize the equilibrium. The particular
functional form of the instantaneous utility function is given by: 𝑢(𝑐, 𝑛)=𝑐1−𝜎(1+ ( 𝜎−1)𝜙𝑛)𝜎−1
1−𝜎.
Production
•𝑦𝑡=¯
𝐴𝑛𝑡𝐴(˜𝑎𝑡), with 𝐴(˜𝑎𝑡)=∫∞
˜𝑎𝑡
𝑎
1−𝐹(˜𝑎𝑡)𝑑𝐹 (𝑎)
•𝜅
𝑞𝑡
=E𝑡Λ𝑡,𝑡 +1(1−𝜚(˜𝑎𝑡+1)) 𝐹𝑛
𝑡+1−𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1)
•𝐹𝑛
𝑡=𝑚𝑐𝑡𝑚 𝑝𝑙 𝑡−𝑤𝑡+E𝑡Λ𝑡,𝑡+1(1−𝜚(˜𝑎𝑡+1))𝐹𝑛
𝑡+1−𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1)
•𝑚𝑐𝑡𝑚 𝑝𝑙 𝑡=𝑤𝑡−𝑏𝑠
𝑡−𝜅
𝑞𝑡
•(1+𝛾𝑝𝜉 𝛽)𝜋𝑡=𝛽E𝑡𝜋𝑡+1+𝛾𝑝𝜋𝑡−1+(1−𝜉 𝛽) ( 1−𝜉)
𝜉ˆ𝑚𝑐𝑡
Households
•1=E𝑡Λ𝑡,𝑡 +1𝑅𝑡with Λ𝑡,𝑡+1=𝛽𝜆𝑡+1/𝜆𝑡and 𝜆=𝑢𝑐, 𝑡
•𝑚𝑟 𝑠𝑡=−𝑢𝑛 ,𝑡 /𝜆𝑡
Labor market and Nash wage
•𝑛𝑡=(1−𝜚(˜𝑎𝑡)) (𝑛𝑡−1+𝑞𝑡−1𝑣𝑡−1)with 𝜚(˜𝑎𝑡)=¯𝜚+ (1−¯𝜚)𝐹(˜𝑎𝑡)
•𝑞𝑡=𝑚𝑡/𝑣𝑡,𝑝𝑡=𝑚𝑡/𝑢𝑡with 𝑢𝑡=1−𝑛𝑡and 𝜃𝑡=𝑣𝑡/𝑢𝑡
•𝑚𝑡=¯𝑚𝑢𝛾
𝑡𝑣1−𝛾
𝑡
•𝑤𝑡=(1−𝜂)𝑚𝑟 𝑠𝑡+𝑏𝑢
𝑡
1−𝜏+𝜂𝑚𝑐𝑡𝑚 𝑝𝑙 𝑡+E𝑡Λ𝑡,𝑡+1𝜅𝜃𝑡+1−𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1)
Constraints and Policies
•𝜏𝑤𝑡𝑛𝑡+𝐵𝑡=𝑅𝑡−1𝐵𝑡−1+𝑏𝑢
𝑡𝑢𝑡+¯
𝑇𝑠
𝑡+𝑔𝑡
2
•𝑦𝑡=𝑐𝑡+𝑔𝑡+𝜅𝑣𝑡+𝐹(˜𝑎𝑡)(1−¯𝜚)(𝑛𝑡−1+𝑞𝑡−1𝑣𝑡−1)𝑏𝑠
𝑡
•Monetary policy: 𝑖𝑡=𝜌𝑖𝑖𝑡−1+ (1−𝜌𝑖) (𝜙𝜋𝜋𝑡+𝜙𝑦ˆ𝑦𝑡)
•Fiscal policy: ˆ𝑔𝑡∼AR(1), 𝑏𝑠
𝑡=¯𝜍+𝜍𝑤𝑡−1,𝑏𝑢
𝑡=¯𝜑+𝜑𝑤𝑡−1and 𝑇𝑠
𝑡=¯
𝑇𝑠+𝜑𝑇𝑠𝐵𝑡
where 𝑚 𝑝𝑙 𝑡=𝑦𝑡/𝑛𝑡,ˆ𝑚𝑐𝑡indicates the relative deviation of (real) marginal costs from the steady state level
¯𝑚𝑐 =𝜀
𝜀−1, and 𝑎is log-normally distributed of which 𝐹is the c.d.f. The expression for the total surplus is
finally given by: 𝑆𝑡=𝐹𝑛
𝑡+𝐻𝑛
𝑡where 𝐻𝑛
𝑡=(1−𝜏)𝑤𝑡−𝑏𝑢
𝑡−𝑚𝑟 𝑠𝑡+ (1−𝜚(˜𝑎𝑡+1) − 𝑝𝑡+1)E𝑡Λ𝑡 ,𝑡 +1𝐻𝑛
𝑡+1.
A.2 Calibration and the Steady State
We compute the steady state for the purpose of simulating the model. Variables without a time subscript
denote steady state values. We start by considering an ex-ante calibration of the probability of an unemployed
person finding a job (𝑝𝑡), the labor market tightness (𝜃𝑡), and the ratio between the marginal rate of substitution
between consumption and labor on the side of the households and the marginal product of labor on the side
of the firms (𝜁𝑡=𝑚𝑟𝑠𝑡/𝑚 𝑝 𝑙𝑡). Additionally, we calibrate the steady-state separation rate 𝜚(˜𝑎)and following
the argument in den Haan, Ramey and Watson (2000), we also calibrate the exogenous job destruction rate ¯𝜚.
The idiosyncratic productivity ˜𝑎is assumed to be i.i.d. log-normally distributed with c.d.f. 𝐹of which we
calibrate the first and second moments (𝜇𝑎=𝐸[ln(˜𝑎)] and 𝜎𝑎=p𝑉 𝑎𝑟 [ln(˜𝑎)] , where 𝜇𝑎∈Rand 𝜎𝑎∈R+).
Given steady state values for 𝑝𝑡,𝜃𝑡,𝜁𝑡and values for the structural parameters outlined in Table A1 in Section
A.2, we then compute values for 𝜅and ¯𝑚and the remaining variables of the model.
In particular, from ¯𝑚=𝑝/𝜃1−𝛾we get the probability of a vacancy being filled 𝑞=¯𝑚𝜃 −𝛾, the number
of employed and unemployed persons 𝑛=(1−𝜚(˜𝑎)) 𝑝/( (1−𝜚(˜𝑎)) 𝑝+𝜚(˜𝑎)) and 𝑢=1−𝑛, the number of
vacancies posted 𝑣=𝜃·𝑢, and the number of matches 𝑚=¯𝑚𝑢𝛾𝑣1−𝛾in the steady state. Given the assumptions
on the steady-state separation rate 𝜚(˜𝑎)and the exogenous job destruction rate ¯𝜚, the endogenous separation
rate is then given by 𝐹(˜𝑎)=𝜚𝑛=(𝜚(˜𝑎) − ¯𝜚)/(1−¯𝜚). From this we can obtain the steady-state threshold
for the idiosyncratic productivity: ˜𝑎=𝐹−1(𝜚𝑛), which allows us to compute the conditional expectation
𝐴(˜𝑎)=∫∞
˜𝑎
𝑎
1−𝐹(˜𝑎)𝑑𝐹 (𝑎). Given employment 𝑛, we can then compute the level of output in the steady state
𝑦=¯
𝐴·𝑛·𝐴(˜𝑎), the marginal product of labor 𝑚 𝑝𝑙 =𝑦/𝑛and the level of government spending 𝑔=𝑔𝑦𝑦.
Using equations Eq. (3.2), Eq. (3.3) and Eq. (3.11) and the marginal product of labor, the vacancy posting
cost parameter 𝜅can be computed by 𝜅=𝑏1·𝑚 𝑝𝑙 where 𝑏1is a parameter composed of the various structural
model parameters (𝜑,𝜂,𝛽,𝜏,¯𝜚,𝜁, ...). Given 𝜅and the marginal rate of substitution (𝑚𝑟𝑠 =𝜁·𝑚 𝑝𝑙 ), the
3
steady state real wage rate is then given by 𝑤=𝑏1·𝑚𝑝 𝑙 +𝑏2𝜅. Finally, using equation Eq. (3.4), we calibrate
¯𝜍such that 𝐴(˜𝑎)=(𝑤−𝑏𝑠−𝜅/𝑞)/ ¯
𝐴.
Household consumption is given by 𝑐=𝑦−𝑔−𝜅𝑣. Using the steady state values for consumption and
labor, the marginal utilities of consumption and labor and the parameter 𝜙=𝑚𝑟𝑠/(𝜎𝑐 −𝑚𝑟 𝑠 · (𝜎−1)𝑛)can
then be computed. Finally, assuming net-government debt to be zero in the steady state (𝐵=0), the amount
of lump-sum transfers ¯
𝑇𝑠is then given by ¯
𝑇𝑠=𝜏𝑤𝑛 −𝜑𝑤 (1−𝑛) − 𝑔. If ¯
𝑇𝑠<0, it can be interpreted as
lump-sum taxes and as lump-sum subsidies if ¯
𝑇𝑠>0.
Our benchmark calibration is summarized in Table A1. Given that our focus is on the role of the LMIs in
the transmission of fiscal spending shocks, we do not calibrate our model to a particular economy. We closely
follow Christoffel, Kuester and Linzert (2009) for the choice of the values of the structural parameters.1
The complementarity coefficient 𝜎in the households’ instantaneous utility function 𝑢(𝑐, 𝑛)is set to 1,
which corresponds to the separable utility case. We also need to calibrate the shock process, for which we
assume that the logarithm of fiscal spending ˆ𝑔𝑡follows an AR(1) process with auto-correlation equal to 0.85.
We calibrate the standard deviations of the two shocks (std(𝜖𝐺
𝑡)=0.48 and std(𝜖𝐴
𝑡)=0.39) in line with
Christoffel, Kuester and Linzert (2009).
A.3 A Quantitative Evaluation Based on a More General Calibration
While the purpose of this exercise is to highlight the general effects of the LMIs on fiscal spending multipliers,
the results presented in Section 3 might, however, be due to the specific calibration chosen. In order to assess
the validity of the model’s implications in a more general setting, we now extend the analysis.
We consider a continuum of values for all parameters other than 𝜂,𝜑and 𝜍for which Table A1 provides
the details. We simulate the model over a wide range of different values for the parameters. To this purpose,
we attach a uniform distribution to each parameter and define upper and lower bounds as indicated in the
fourth column (Range) in Table A1. We simulate the model 2000 times and compute the difference of the
impulse response functions for the following two scenarios: low value of 𝜗𝑖versus high value of 𝜗𝑖where 𝜗𝑖
refers to one of the three parameters of interest (𝜂,𝜑and 𝜍). We focus on the impact responses. The three
scenarios (UD, 𝜂; BRR, 𝜑; and EPL, 𝜍) are depicted in the sub-panels in Figure A1.2The box-plots show the
1Christoffel, Kuester and Linzert (2009) estimate a DSGE model with an extended labor market structure in their model based on
the data for the euro zone. Since most of the countries in our sample are part of the euro zone, we hence rely on the estimates in
Christoffel, Kuester and Linzert (2009).
2We draw values for the structural parameters shown in Table A1. For instance, in the case for 𝜂: for a particular draw, we solve the
model for 𝜂=0.5and compute impulse response functions. For the same draw we also solve the model using 𝜂=0.6– in both
4
Table A1: Calibration of the Model.
Parameter Description Value Range
𝛽Discount factor 0.992 [0.95 – 0.999]
𝛾Elasticity of matching of unemployed persons 0.45 [0.05 – 0.95]
𝑔𝑦Government consumption share in total output 0.3 [0.1 – 0.5]
𝜁Ratio of 𝑚𝑟 𝑠 to 𝑚 𝑝 𝑙 0.7 [0.55 – 0.95]
𝜃Labor market tightness 0.43 [0.05 – 0.95]
𝑝Probability of an unemployed person finding a job 0.30 [0.05 – 0.95]
𝜏Labor tax rate 0 [0 – 0.5]
𝜇𝑎Steady state mean of idiosyncratic productivity 0.0 [-2 – 2]
𝜎𝑎Steady state standard-deviation of idiosyncratic productivity 0.15 [0.01 – 5]
¯𝜚Exogenous job separation rate 0.03 [0.01 – 0.15]
𝜚(˜𝑎)(Overall) Job separation rate 0.05 [0.03 – 0.2]
𝜎Complementarity coefficient 0.2 [0.05 – 1]
𝜙𝜋Inflation sensitivity in the Taylor rule 1.5 [1.0 – 2.5]
𝜙𝑦Output sensitivity in the Taylor rule 0.5 [0.0 – 0.9]
𝜌𝑖Nominal interest rate smoothing 0.3 [0.0 – 0.7]
𝜌𝐺Government consumption smoothing 0.95 [0.85 – 0.99]
𝜉Calvo price stickiness 0.7 [0.45 – 0.95]
𝛾𝑝Share of inflation indexed prices 0.3 [0.0 – 0.5]
𝜂Bargaining power of workers (UD) 0.4 —
𝜑Unemployment benefit replacement rate (BRR) 0.0 —
𝜍Firing costs in relation to last wage (EPL) 0.0 —
difference in the impact response for each of the three cases for the following variables: output, employment,
unemployment, the labor market tightness (𝑣𝑡/𝑢𝑡) and real wage. The difference is computed by considering
the impulse response functions with a low value of the parameter of interest relative to a high value.
Considering the output response ( ˆ𝑦𝑡) in the left sub-panel as an example, we notice that it is positive
throughout due to the fact that the impact response of output when workers have a low power within the wage
negotiations (𝜂=0.3), is systematically higher than that when they have a high power (𝜂=0.7). The positive
range of values in this particular plot replicates the path of the fiscal spending multipliers shown in Figure 3.
The employment response replicates that of output, unemployment shows instead a negative reaction, that
is, in response to an expansionary fiscal spending shock, unemployment declines by more if workers’ power
within the wage negotiations is low. The figure highlights also that the impact response of the real wage is
hardly affected by the 𝜂, and the reaction in the labor market tightness (𝜃𝑡) is ambiguous due to the different
effects of 𝜂on the job creation and job destruction activities by firms on the one hand, and labor supply
decisions of households on the other hand.
cases holding the remaining parameters fixed. The difference in the impact values of the impulse response functions is depicted
in Figure A1. By this procedure we can uniquely attach the difference in the impulse response functions to changes in 𝜂, while at
the same time allowing for flexibility in the model calibration. We carry out the same exercise for 𝜍and 𝜑.
5
Figure A1: Fiscal Spending Shocks and the LMIs.
-0.06
-0.04
-0.02
0
0.02
0.04
-0.06
-0.04
-0.02
0
0.02
0.04
-0.2
-0.1
0
0.1
The remaining two sub-panels show the results for the unemployment benefits replacement rate (𝜑) and
the extent of employment protection (𝜍). In both cases, the box-plots for output and employment are positive
throughout, highlighting the extent to which values of 𝜑and/or 𝜍attenuate fiscal spending multipliers.
We conclude that the general results provided here confirm those put forward in Section 3. The assessment
carried out in this section only concerns the calibration of the model’s parameters; however, it ignored the
extent to which the structure of the model might shape the overall results. Against this background, the
following Sections will address specific extensions of the model.
A.4 The LMIs and Macroeconomic Volatility
The current section serves to assess the consequences of the LMIs on the overall macroeconomic volatility.
To this purpose, we consider a government spending shock next to a technology shock so that the model
comprises a demand and supply shock. We decompose the effect of LMIs on the volatility of the endogenous
variables to the two shocks. That is, we examine the extent to which LMIs affect macroeconomic volatility in
the wake of demand and supply shocks and analyze each shock separately. This is motivated by the fact that
distinct shocks give rise to distinct cross-correlations (sign and values). While such a setting is admittedly
unrealistic, it allows us to assess whether our results are driven by a specific shock and if the heterogeneity
in the volatility of the endogenous variables conditional on the LMIs is important. Considering equation Eq.
(3.14) and following Hamilton (1994, Chapter 10.2), the variance covariance matrix 𝚺𝒛(𝝑)of the vector of
6
Table A2: Volatility of output, employment and the real wage.
LMI: UD (𝜂) BRR (𝜑) EPL (𝜍)
Government spending shock (𝜖𝐺
𝑡)
Output ( ˆ𝑦𝑡) 2.00 2.40 1.00
Employment (ˆ𝑛𝑡) 2.00 2.40 0.99
Real wage ( ˆ𝑤𝑡) 3.27 2.93 0.75
Consumption ( ˆ𝑐𝑡) 0.68 0.63 1.34
Technology shock (𝜖𝐴
𝑡)
Output ( ˆ𝑦𝑡) 1.02 1.52 0.90
Employment (ˆ𝑛𝑡) 1.15 3.08 0.46
Real wage ( ˆ𝑤𝑡) 2.25 2.83 0.73
Consumption ( ˆ𝑐𝑡) 1.01 1.54 0.79
Notes: The table shows the sensitivity of the output, employment and the real
wage volatilities to changes in the LMIs. The shocks considered are a government
spending and a technology shock. The values indicate the standard deviation of
output, employment and the real wage (𝑥𝑡’s) when the respective LMIs take on a
low value relative to the standard deviations when the LMIs are set at a high value
(Var(𝑥𝑡(LMIlow))/Var(𝑥𝑡(LMIhigh))). The shocks considered are a technology
shock (𝜖𝐴
𝑡) and the government spending shock (𝜖𝐺
𝑡).
endogenous variables 𝒛𝑡of the solved DSGE model, is given by
vec(𝚺𝒛(𝝑)) =𝐼−𝚿−1
0𝚿1⊗𝚿−1
0𝚿1−1vec 𝚿−1
0Σ𝝐𝚿0
0−1(A.1)
where the dependency of 𝚿0and 𝚿1on 𝝑has been omitted to preserve notational simplicity. This expression
explicitly accounts for the fact that the volatility depends on the structural parameters of interest, UD (𝜂),
BRR (𝜑) and EPL (𝜍), in 𝝑=(𝜂, 𝜑, 𝜍)0. In what follows we again confine the analysis to the volatility of
output ( ˆ𝑦𝑡), employment (ˆ𝑛𝑡) and the real wage ( ˆ𝑤𝑡). We use the estimated values put forth in Christoffel,
Kuester and Linzert (2009) to calibrate the parameters for the auto-correlation coefficients (𝜌𝑖) of the AR(1)
shocks. The calibration of the idiosyncratic variances (𝜎2
𝑖) is described in Section A.2 and we consider two
values (high and low) for each LMI in this respect.
The results are depicted in Table A2. The table only shows the values of the variance of the endogenous
variables (output, employment, and the real wage) for a low value of the LMIs relative to their variances
when a high value is used. A few results emerge from the analysis. First, in the case of a technology
shock, the ability of UD to influence fluctuations in output and consumption is limited, whereas its impact
is sizable in the case of a government spending shock. In contrast, employment protection legislation (EPL)
exhibits the opposite pattern, having a greater effect on output and consumption fluctuations in the case
of a technology shock. Second, in the case of government spending shocks, high values of UD and BRR
7
tend to decrease output volatility while exacerbating consumption volatility. In the case of a technology
shock, both output and consumption volatility drop with higher values of UD and BRR. Again, the opposite
pattern is observed with EPL, where the volatility dynamics are reversed. Third, the quantitative impact of
LMIs on macroeconomic volatility in response to technology shocks exceeds the corresponding impact of a
government spending shock only when EPL is considered, whereas this is not the case for UD and BRR. In
summary, these findings suggest that LMIs can potentially mitigate macroeconomic volatility. However, this
effect is highly dependent on the type of shock that prevails and the specific LMI in question.
8
B. Extensions to the Theoretical Model
This section considers various extensions to the baseline model outlined in Section 3. These include shutting
down the inflation indexation of prices, real wage rigidity, limited asset market participation of one group
of households, the case when firing costs accrue to the government as revenues, productivity enhancing
government spending, and a deeper look into the consumption and leisure complementarity. We always
consider one extension at a time, as otherwise the precise role of the additional frictions considered becomes
difficult to assess.
B.1 Inflation indexation of prices
Our baseline model incorporates nominal frictions along two dimensions. The first dimension pertains to
the infrequent adjustment of prices towards their optimal levels. The second involves a rule-of-thumb price
adjustment mechanism for prices that cannot be optimally adjusted within a given period. The latter represents
a commonly observed price-setting behavior. This extension increases the degree of inflation inertia and
amplifies the real costs associated with prices being set sub-optimally.
This section examines the immediate consequences of this rule-of-thumb price adjustment mechanism
on fiscal spending multipliers. The results are presented in Figure B1. The figure contrasts the baseline
results (depicted in black), which assume (𝛾𝑝=0.3) (indicating that 30% of prices are adjusted based on
the previous period’s inflation rate), with those in which inflation indexation is absent (𝛾𝑝=0.0), shown by
the red lines. As observed, the fiscal spending multiplier for output is smaller when inflation indexation is
absent, underscoring the significance of delayed price adjustments in determining the overall impact of an
expansionary demand shock on output.
B.2 Real Wage Rigidity
The existence of real wage rigidities has been pointed to by many authors as a feature needed to account for a
number of labor market facts (see Hall, 2005, among others). Krause and Lubik (2007) stress the role of real
wage rigidity in the sort of models considered in Section 3 to improve the predictions of the labor market.
Real wage rigidity might comprise a particularly important aspect for our case: A rigid real wage strongly
increases the incentive to create jobs in the wake of an expansionary fiscal spending shock (or expansionary
demand shock in more general terms), since firms share less of the benefit with their workers. However, at
9
Figure B1: Fiscal spending multipliers and the LMIs (𝜇(𝝑)) – No inflation indexation of prices
0.2 0.4 0.6
0.1
0.15
0.2
0.25
0.3
0.3 0.4 0.5 0.6
0.1
0.15
0.2
0.25
0.3
0.1 0.2 0.3 0.4 0.5
0.1
0.15
0.2
0.25
0.3
0.2 0.4 0.6
0.15
0.2
0.25
0.3
0.3 0.4 0.5 0.6
0.15
0.2
0.25
0.3
0.1 0.2 0.3 0.4 0.5
0.15
0.2
0.25
0.3
0.2 0.4 0.6
-0.2
0
0.2
0.4
0.6
0.3 0.4 0.5 0.6
-0.2
0
0.2
0.4
0.6
0.1 0.2 0.3 0.4 0.5
-0.2
0
0.2
0.4
0.6
Notes: The sub-figures illustrate the sensitivity of the fiscal spending multipliers to variations in the three LMI parameters (UD–union density,
BRR–(unemployment) benefit replacement rate and EPL–employment protection (legislation)). The multipliers are presented for different horizons,
with the contemporaneous multiplier (P=1) represented by a solid black square line for the baseline model (𝛾𝑝=0.3) and by a red dashed line for
the model without inflation indexation of prices (𝛾𝑝=0.0). The higher-horizon multipliers (P ≥ 2) are indicated by black dotted lines (baseline
model) and red dotted lines (model without inflation indexation).
the same time, as vacancies rise and unemployment falls, there is a substantial increase in the cost of hiring
workers (𝜅/𝑞𝑡rises since 𝑞𝑡falls on the back of an increase in vacancies 𝑣𝑡) which are a component of
firms’ real marginal costs. Hence the role of rigid real wages can be confined to two elements, of which one
becomes more rigid while the other more volatile.
We assume that real wages (𝑤𝑡) respond sluggishly to changes in labor market conditions. To simplify
the exposition, we proceed by considering real wage inertia as a result of some imperfection or friction in
labor markets which are modeled in a reduced form. Specifically, we assume the partial adjustment model
which extends equation Eq. (3.11) to the following
𝑤𝑡=𝜚𝑤𝑤𝑡−1+ (1−𝜚𝑤)ˇ𝑤𝑡(B.1)
where ˇ𝑤𝑡=(1−𝜂)𝑚𝑟 𝑠𝑡+𝑏𝑢
𝑡
1−𝜏+𝜂𝑚 𝑝𝑙 𝑡+E𝑡Λ𝑡,𝑡+1𝜅𝜃𝑡+1−𝑏𝑠
𝑡+1(1−¯𝜚)𝐹(˜𝑎𝑡+1). The parameter 𝜚𝑤captures
the extent of real wage rigidity and we choose a value equal to 0.4. Equation Eq. (B.1) can be considered as
10
Figure B2: Fiscal spending multipliers and the LMIs (𝜇(𝝑)) – The role of real wage rigidity
0.2 0.4 0.6
0.1
0.15
0.2
0.25
0.3
0.3 0.4 0.5 0.6
0.1
0.15
0.2
0.25
0.3
0.1 0.2 0.3 0.4 0.5
0.1
0.15
0.2
0.25
0.3
0.2 0.4 0.6
0.15
0.2
0.25
0.3
0.3 0.4 0.5 0.6
0.15
0.2
0.25
0.3
0.1 0.2 0.3 0.4 0.5
0.15
0.2
0.25
0.3
0.2 0.4 0.6
0
0.2
0.4
0.6
0.8
0.3 0.4 0.5 0.6
0
0.2
0.4
0.6
0.8
0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
Notes: The sub-figures illustrate the sensitivity of the fiscal spending multipliers to variations in the three LMI parameters (UD–union density,
BRR–(unemployment) benefit replacement rate and EPL–employment protection (legislation)). The multipliers are presented for different horizons,
with the contemporaneous multiplier (P=1) represented by a solid black square line for the baseline model (𝜚𝑤=0.0) and by a red dashed line
for the model with real wage rigidity (𝜚𝑤=0.4). The higher-horizon multipliers (P ≥ 2) are indicated by black dotted lines (baseline model) and
red dotted lines (model with real wage rigidity).
a parsimonious but ad hoc way of modeling the sluggish adjustment of real wages to changes in labor market
conditions, as found in a variety of models of real wage rigidities, without taking a stand on what the right
model is. Alternative formalizations, explicitly derived from staggering of real wage decisions and alike, are
presented in Blanchard and Galí (2007), Zanetti (2007), and Gertler, Huckfeldt and Trigari (2020) and the
papers cited therein. The results of the model extended for real wage rigidities are shown and compared to
the baseline model in Figure B2. Considering first the dependency of the output multiplier on 𝜑and 𝜍shown
in in the sub-panels in the second and third columns, it can be seen that the shape of the output multiplier
with respect to the two LMIs does not change, instead, the extent of real wage rigidity causes a, more or
less, proportional drop in the size of the multiplier. This highlights that the rise in hiring costs in the wake
of the expansionary demand shock dominates the drop in the benefit firms have to share with workers. This
11
attenuates firms incentives to create jobs. The output and employment multipliers are hence smaller when
real wage rigidities are present.
In case of 𝜂, the multipliers for output and employment are affected more profoundly when real wage
rigidities are present. Both multipliers now show a concave pattern with respect to 𝜂: when 𝜂is low, increases
therein raise fiscal spending multipliers, while the opposite occurs when 𝜂is already high. The intuition is
that when 𝜂is low the drop in the benefits firms have to share with workers now dominate to increase in
hiring costs giving rise to a positive dependency between 𝜂and the output and employment multipliers. For
higher values of 𝜂, the dominance structure changes and the baseline results (higher 𝜂causes a smaller output
multiplier) applies again. Nevertheless, a concave pattern shows up only modestly and is confined to small
values of 𝜂.
B.3 Limited Asset Market Participation
Galí, López-Salido and Valles (2007) show how the interaction of rule-of-thumb consumers with sticky
prices and deficit financing can account for the existing evidence on the effects of government spending.
In this context, rule-of-thumb consumers are characterized by limited asset market participation which
implies that they lack any ability of smoothing their consumption profile; as a consequence, they spend
(consume) each period all of their income. This rule-of-thumb gives rise to a consumption pattern that
strongly aligns with wage income. This gives rise to a positive consumption response in the wake of an
expansionary fiscal spending shock. We follow Galí, López-Salido and Valles (2007) and add the second
consumer type into the baseline model. The consumers outlined in the baseline model are now referred to
as Ricardian consumers and their consumption is henceforth referred to as 𝑐𝑟
𝑡(same for their labor supply
𝑛𝑡). Rule-of-thumb households are assumed to behave in a “hand-to-mouth” fashion, fully consuming
their current labor income. Their period utility is given by 𝑢(𝑐𝑛𝑟
𝑡, 𝑛𝑛𝑟
𝑡)and they are subject to the budget
constraint 𝑐𝑛𝑟
𝑡=(1−𝜏)𝑤𝑡𝑛𝑛𝑟
𝑡+𝑏𝑢
𝑡(1−𝑛𝑛𝑟
𝑡) + 𝑇𝑠,𝑛𝑟
𝑡. Aggregate consumption and employment are given by
a weighted average of the corresponding variables for each consumer type. Formally, 𝑐𝑡=𝜆𝑐𝑛𝑟
𝑡+ (1−𝜆)𝑐𝑟
𝑡,
𝑛𝑡=𝜆𝑛𝑛𝑟
𝑡+ (1−𝜆)𝑛𝑟
𝑡. It is further assumed that the labor market is characterized by a structure which gives
rise to wages being negotiated in a centralized manner by an economy-wide union with firms.
Figure B3 shows the results of the LMIs on the multipliers for output, employment, etc. in the extended
model (labeled “non-Ricardian”) and compares them to the baseline model. The simulations are based on a
share of one-quarter of non-Ricardian households (𝜆=0.25). As can be seen, the multipliers are throughout
12
Figure B3: Fiscal Spending Multipliers and the LMIs (𝜇(𝝑)) – The Role of Limited Asset Market Participation
0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.1 0.2 0.3 0.4 0.5
0.1
0.2
0.3
0.4
0.2 0.4 0.6
0.15
0.2
0.25
0.3
0.35
0.3 0.4 0.5 0.6
0.15
0.2
0.25
0.3
0.35
0.1 0.2 0.3 0.4 0.5
0.15
0.2
0.25
0.3
0.35
0.2 0.4 0.6
0
0.5
1
0.3 0.4 0.5 0.6
0
0.5
1
0.1 0.2 0.3 0.4 0.5
0
0.5
1
Notes: The sub-figures illustrate the sensitivity of the fiscal spending multipliers to variations in the three LMI parameters (UD–union density,
BRR–(unemployment) benefit replacement rate and EPL–employment protection (legislation)). The multipliers are presented for different horizons,
with the contemporaneous multiplier (P=1) represented by a solid black square line for the baseline model (𝜆𝑝=0.0) and by a red dashed line for
the model with limited asset market participation (𝜆𝑝=0.25). The higher-horizon multipliers (P ≥ 2) are indicated by black dotted lines (baseline
model) and red dotted lines (model without inflation indexation).
higher; this applies to both the output and employment multipliers, but also for the real wage. The reason
for the higher multiplier throughout is due to the different reaction of consumption. In the baseline model,
consumption declines owing to the negative wealth effect that comes along with the (deficit financed) increase
in fiscal spending. The (absolute) size of the decline is, however, decreasing in 𝜆, reflecting the offsetting
role of rule-of-thumb behavior on the conventional negative wealth and intertemporal substitution effects
triggered by the fiscal expansion. The figure hence illustrates the amplifying effects of the introduction of
rule-of-thumb consumers. Most important, though is the fact that the introduction of limited asset market
participation does not change the dependency of the multipliers on the LMIs. With a view on the output
multiplier, the negative relation with the LMIs still applies. Even more, the negative relation now turns out
stronger than in the baseline model.
13
Figure B4: Fiscal Spending Multipliers and the LMIs (𝜇(𝝑)) – When Firing Costs Accrue to the Government
0.1 0.2 0.3 0.4 0.5
0.15
0.2
0.25
0.3
0.1 0.2 0.3 0.4 0.5
0.2
0.22
0.24
0.26
0.28
0.3
0.1 0.2 0.3 0.4 0.5
0.2
0.4
0.6
0.8
1
Notes: The sub-figures illustrate the sensitivity of the fiscal spending multipliers to variations in the three LMI parameters (UD–union density,
BRR–(unemployment) benefit replacement rate and EPL–employment protection (legislation)). The multipliers are presented for different horizons,
with the contemporaneous multiplier (P=1) represented by a solid black square line for the baseline model and by a red dashed line for the model
with in which firms’ firing costs accrue to the government as revenue. The higher-horizon multipliers (P ≥ 2) are indicated by black dotted lines
(baseline model) and red dotted lines (model in which firms’ firing costs accrue to the government as revenue).
B.4 Firing Costs as Government Revenues
The baseline model specifies firing costs as real resource costs. This is a quite strong assumption, as in many
countries firing costs arise in the context of severance payments, etc. which will eventually be re-distributed
back to households. Against this background, we now assess the implications of 𝜍, once firms’ expenses
on firing accrue to the government as revenues. These additional revenues will eventually be re-distributed
back to households in the form of lump-sum subsidies or alike. Hence in this case, the government budget
constraint (Eq. (3.12)) and the real resource constraint (Eq. (3.13)) are then given by:
𝐹(˜𝑎𝑡)(1−¯𝜚)(𝑛𝑡−1+𝑞𝑡−1𝑣𝑡−1)𝑏𝑠
𝑡+𝜏𝑤𝑡𝑛𝑡+𝐵𝑡=𝑅𝑡−1𝐵𝑡−1+𝑏𝑢
𝑡𝑢𝑡+𝑇𝑠
𝑡+𝑔𝑡(B.2)
𝑦𝑡=𝑐𝑡+𝑔𝑡+𝜅𝑣𝑡(B.3)
We extend the baseline model in this respect. Since the simulations for 𝜂and 𝜑are based on zero firing costs
(𝜍=0), this extension hence has no effect on the shape of the multipliers with respect to 𝜂and 𝜑.
The results are shown in Figure B4 for output, employment and the real wage. As can be seen, when firing
costs accrue to the government, fiscal spending multipliers are notably higher. In particular, the reaction in
employment and output is more positive (for values of 𝜍 > 0) while at the same time the contraction in the
real wage is augmented too. The key element behind this pertains to the re-distributional element which
operates in the background. When firing costs accrue to the government, they are re-distributed back to
households giving rise to a smaller drop in consumption in response to the fiscal spending shock which in
14
turn raises the output multiplier. In contrast to this, when firing costs enter the aggregate resource constraint,
then this implies that they are real resource costs which cannot be uncovered. This loss attenuates the
output multiplier; the attenuation effect increases with 𝜍which captures the firing costs per laid off worker.
While this attenuation effect is also present when firing costs get re-distributed back to households via the
government, the re-distribution channel raises the output multiplier. This effect is absent in the other case.
B.5 Productivity Enhancing Government Spending
The standard assumption in macroeconomics is that government spending is unproductive. An even more
extreme but common assumption is that government spending is entirely purposeless with purchases com-
prising real resource costs. These assumptions contrast with the observation that various public goods indeed
enhance the productivity of the economy. Examples include the extensive rail system in Europe, public edu-
cation, government-funded research, among other projects (Daniel and Gao, 2015). Against this background,
we extend the baseline model to allow for productivity enhancing public spending. The literature considers
distinct approaches in this respect. Daniel and Gao (2015) for instance model productive government spend-
ing as subsidies to education, which build up the human capital stock. Kumhof et al. (2010) consider a set-up
in which government spending accumulates a productive capital stock which enters the production function.
We proceed by assuming that government spending 𝑔𝑡builds up the public capital stock which then enters
the production function. The public capital stock evolves according to
𝑘𝐺
𝑡=(1−𝛿)𝑘𝐺
𝑡−1+𝑔𝑡(B.4)
where 𝛿is the depreciation rate of the public capital stock which we set equal to 0.01 (quarterly data
frequency). Importantly, the public capital stock is identical for all firms and provided free of charge to the
end user (but not of course to the taxpayer). This approach conforms with the set-up in Kumhof et al. (2010).
We modify the production function as follows
𝑦𝑡(𝑔𝑡)=¯
𝐴𝑛𝑡𝐴(˜𝑎𝑡) · 𝑘𝐺
𝑡
¯
𝑘𝐺𝛼𝑔
(B.5)
The parameter 𝛼𝑔∈ [0,1]captures the sensitivity (elasticity) of the aggregate production with respect
to changes in the public capital stock and ¯
𝑘𝐺is the steady state value for 𝑘𝑔
𝑡. Note that this production
function exhibits constant returns to scale in private inputs (𝑛𝑡) while the public spending enters externally,
in an analogous manner to exogenous technology. Hence government spending augments labor productivity
15
Figure B5: Fiscal Spending Multipliers and the LMIs (𝜇(𝝑)) – Productivity Enhancing Government Spending.
0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.1 0.2 0.3 0.4 0.5
0.1
0.2
0.3
0.4
0.2 0.4 0.6
0.15
0.2
0.25
0.3
0.35
0.3 0.4 0.5 0.6
0.15
0.2
0.25
0.3
0.35
0.1 0.2 0.3 0.4 0.5
0.15
0.2
0.25
0.3
0.35
0.2 0.4 0.6
0
0.5
1
0.3 0.4 0.5 0.6
0
0.5
1
0.1 0.2 0.3 0.4 0.5
0
0.5
1
Notes: The sub-figures illustrate the sensitivity of the fiscal spending multipliers to variations in the three LMI parameters (UD–union density,
BRR–(unemployment) benefit replacement rate and EPL–employment protection (legislation)). The multipliers are presented for different horizons,
with the contemporaneous multiplier (P=1) represented by a solid black square line for the baseline model (𝛼𝑔=0.0) and by a red dashed line for
the model with a productive public capital stock (𝛼𝑔=0.1). The higher-horizon multipliers ( P ≥ 2) are indicated by black dotted lines (baseline
model) and red dotted lines (model with a productive public capital stock).
directly: 𝑚𝑝 𝑙𝑡(𝑘𝑔
𝑡)=𝑦𝑡(𝑘𝑔
𝑡)/𝑛𝑡. We chose a conservative value for the elasticity 𝛼𝑔=0.1which implies
that a one percent increase in the public capital stock (relative to the steady state) raises labor productivity by
0.1 percent.
We carry out the same simulations as in Section 3. The results thereof are shown in Figure B5. As can
be seen, productive government spending leads to a significantly higher output multiplier. At the same time,
the employment multiplier is attenuated owing to the rise in labor productivity and the higher real wage. The
latter comprises the most noteworthy change compared to the baseline results. The higher labor productivity
causes a rise in the real wage already at impact. For us, the most important, though, is the impact of the
LMIs on the output multiplier. With a view to Figure B5, while the output response increases with the extent
of productive government spending, the dependency of the output multiplier with respect to the three LMIs
16
Figure B6: Fiscal Spending Multipliers and the LMIs (𝜇(𝝑)) – Consumption/leisure complementarity.
0.2 0.4 0.6
0
0.2
0.4
0.6
0.8
0.3 0.4 0.5 0.6
0
0.2
0.4
0.6
0.8
0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
0.2 0.4 0.6
0
0.2
0.4
0.6
0.8
0.3 0.4 0.5 0.6
0
0.2
0.4
0.6
0.8
0.1 0.2 0.3 0.4 0.5
0
0.2
0.4
0.6
0.8
0.2 0.4 0.6
0
0.5
1
1.5
0.3 0.4 0.5 0.6
0
0.5
1
1.5
0.1 0.2 0.3 0.4 0.5
0
0.5
1
1.5
Notes: The sub-figures illustrate the sensitivity of the fiscal spending multipliers to variations in the three LMI parameters (UD–union density,
BRR–(unemployment) benefit replacement rate and EPL–employment protection (legislation)). The multipliers are presented for different horizons,
with the contemporaneous multiplier (P=1) represented by a solid black square line for the baseline model (𝑠𝑖𝑔𝑚𝑎 =0.2) and by a red dashed
line for the model with additively separable consumption and leisure (𝜎=1). The higher-horizon multipliers ( P ≥ 2) are indicated by black dotted
lines (baseline model) and red dotted lines (model with a productive public capital stock).
remains, however, unchanged compared to the baseline results. In each of the three cases (UD, BRR, and
EPL), a higher value attenuates the output reaction in response to a government spending increase.
B.6 Consumption and leisure complementarity
The utility function specification allows for both complementarity and separability between consumption and
leisure (or, equivalently, the negative of labor supply), with the relationship determined by the parameter 𝜎.
When 𝜎=1, consumption and leisure are additively separable, while for 0< 𝜎 < 1, they exhibit varying
degrees of complementarity. The degree of complementarity is particularly relevant in the context of fiscal
spending shocks. In addition to price rigidities, a deficit-financed increase in government spending generates
a negative wealth effect. The magnitude of this wealth effect depends on whether consumption and leisure
are separable.
17
The negative wealth effect arises because, in response to a future anticipated tax burden, forward-looking
households adjust their behavior by reducing current consumption and increasing labor supply (i.e., reducing
leisure). The relative strength of the response in consumption and leisure is determined by the degree of
complementarity between the two, as captured by the parameter 𝜎. In what follows we consider the case of
𝜎=1as an alternative scenario to the baseline result which relies on 𝜎=0.2. Figure B6 provides the results.
The decline in consumption and leisure is attenuated when complementarity between the two prevails,
thereby moderating the overall negative wealth effect. Specifically, when 𝜎 < 1, the negative wealth effect
is relatively weak. As a result, the reduction in leisure and the corresponding increase in labor supply are
modest. This leads to a relatively small increase in output, implying a smaller fiscal spending multiplier
compared to the case where 𝜎=1, which corresponds to the separability between consumption and leisure
and generates a more pronounced negative wealth effect.
Intuitively, when 𝜎 < 1, agents substitute leisure for consumption, which mitigates the negative wealth
effect on consumption. The extent of this mitigation depends on the degree of complementarity between labor
and consumption, with stronger complementarity leading to a more pronounced response in consumption.
18
C. Bayesian Interacted Panel Vector Autoregressions
In this section, we provide estimation details on the Bayesian Interacted Panel Vector Autoregression (IPVAR).
The model is similar to the model proposed by Towbin and Weber (2013) and Sá, Towbin and Wieladek
(2014). The model is estimated in its recursive form to allow for contemporaneous interactions. Structural
analysis (e.g., IRFs or FEVDs) is then carried out given a particular value of the interaction term.
Let {𝒚𝑖𝑡 }𝑇𝑖
𝑡=1and {𝝑𝑖𝑡 }𝑇𝑖
𝑡=1denote an 𝑛- and 𝑑-dimensional time series process for country 𝑖=1, . . . , 𝑁,
respectively. Note that we allow for differing sample lengths for country 𝑖, specified with sample length 𝑇𝑖.
We write the IPVAR as follows
𝑱𝑖𝑡 𝒚𝑖𝑡 =𝒂𝑖+
𝑝
Õ
𝑗=1 𝑨𝑖 𝑗 𝒚𝑖𝑡 −𝑗+
𝑑
Õ
𝑙=1
𝑩𝑖 𝑗𝑙 𝒚𝑖 𝑡−𝑗×𝜗𝑖 𝑙𝑡 !+˜𝒖𝑖𝑡 ,˜𝒖𝑖𝑡 ∼ N𝑀(0,𝛀𝑖).(C.1)
We denote with 𝒂𝑖the 𝑛×1country-specific intercept vector, while 𝑨𝑖 𝑗 denotes the 𝑛×𝑛country-specific
autoregressive coefficient matrix for lag 𝑗=1, . . . , 𝑝. The 𝑛×1vector of residuals 𝒖𝑖𝑡 is assumed to be
uncorrelated across countries and normally distributed with mean zero and a 𝑛×𝑛covariance matrix 𝛀𝑖.
Due to the recursive structure of the VAR, the covariance matrix is diagonal, i.e., 𝛀𝑖=diag(𝜔𝑖1, . . . , 𝜔𝑖 𝑛).
The interaction term 𝝑𝑖𝑡 is allowed to influence the dynamic relationship between the endogenous variables
of the system via the 𝑛×𝑛coefficient matrices 𝑩𝑖 𝑗 𝑙 for lag 𝑗=1, . . . , 𝑝 and interaction variable 𝑙=1, . . . , 𝑑.
Last, we have to discuss the nature of the 𝑛×𝑛matrix 𝑱𝑖𝑡 , which is a lower unitriangular matrix. This matrix
exhibits a time index 𝑡because we allow the interaction term to affect the contemporaneous relationships
between equations. The contemporaneous effect of the 𝑞-th ordered variable on the 𝑤-th ordered variable is
given by −[𝑱𝑖𝑡 ]𝑤 𝑞 , where we denote the scalar element in the 𝑤-th row and 𝑞-th column of the matrix 𝑱𝑖 𝑡 as
[𝑱𝑖𝑡 ]𝑤 𝑞 . The elements are modeled as follows
[𝑱𝑖𝑡 ]𝑤 𝑞 =
[˜
𝑱𝑖0]𝑤𝑞 +Í𝑑
𝑙=1[˜
𝑱𝑖𝑙 ]𝑤 𝑞 𝜗𝑖𝑙𝑡 ,if 𝑞 < 𝑤,
1,if 𝑞=𝑤,
0,if 𝑞 > 𝑤.
(C.2)
The model parameters can be re-written as a function of 𝝑𝑖𝑡 . Hence, this results into
𝒚𝑖𝑡 =𝒄𝑖(𝝑𝑖𝑡 ) +
𝑝
Õ
𝑗=1
𝚽𝑖 𝑗 (𝝑𝑖𝑡 )𝒚𝑖𝑡−𝑗+𝒖𝑖 𝑡 ,𝒖𝑖𝑡 ∼ N𝑛(0,𝚺𝑖(𝝑𝑖𝑡 )),(C.3)
19
where 𝒄𝑖(𝝑𝑖𝑡 )=𝑱−1
𝑖𝑡 𝒂𝑖,𝚽𝑖 𝑗 (𝝑𝑖 𝑡 )=𝑱−1
𝑖𝑡 𝑨𝑖 𝑗 +Í𝑑
𝑙=1𝑩𝑖 𝑗 𝑙 𝜗𝑖𝑙𝑡 , and 𝚺𝑖(𝝑𝑖𝑡 )=(𝑱−1
𝑖𝑡 )𝛀𝑖(𝑱−1
𝑖𝑡 )0. From this
representation it is straightforward to derive impulse response functions (IRFs) or compute the forecast error
variance decomposition (FEVD) given a particular value of the interaction term 𝝑𝑖𝑡 .
We pursue a Bayesian approach to estimation of the model. Therefore, we discuss our prior setup
next. The prior setup is similar in spirit to the one presented in Jarociński (2010) but we additionally
impose regularization with global-local shrinkage priors (Griffin and Brown, 2010). This has been shown
to be beneficial when applied to VARs (Huber and Feldkircher, 2019). We use a variant of the Normal-
Gamma (NG) shrinkage prior for each level of the model. In particular, we use the lagwise version of
the Normal-Gamma prior such that we are inducing more shrinkage to higher-order lags. Furthermore, we
shrink coefficients in the estimation equation to its common mean and the common mean towards zero.
For the specification of the prior distribution, we start with stacking to a 𝑘=(1+𝑑)𝑛2-dimensional vector
𝜷𝑖 𝑗 =vec(𝑨𝑖 𝑗 ,𝑩𝑖 𝑗1, . . . , 𝑩𝑖 𝑗 𝑑 )for lag 𝑗and country 𝑖and specify the prior distribution as follows
[𝜷𝑖 𝑗 ]𝑠|𝜆2
𝑖 𝑗 ,[𝜽𝑖 𝑗 ]𝑠∼ N [𝒃𝑗]𝑠,2/𝜆2
𝑖 𝑗 [𝜽𝑖 𝑗 ]𝑠,[𝜽𝑖 𝑗 ]𝑠∼ G (𝜗𝜃, 𝜗𝜃), 𝑠 =1, . . . , 𝑘 . (C.4)
Here [𝜷𝑖 𝑗 ]𝑠,[𝒃𝑗]𝑠, and [𝜽𝑖 𝑗 ]𝑠denotes the 𝑠-th element of the respective vector. The latter one is the
local-shrinkage component on which we specify a Gamma-distribution with hyperparameter 𝜗𝜃. This
hyperparameter is governing the strength of the regularization towards the specified mean. For instance,
centering the hyperparameter on unity translates into the Bayesian LASSO (Park and Casella, 2008). Instead,
we allow for additionally flexibility and put a hyperprior on 𝜗𝜃∼𝐸 𝑥 𝑝 (1), centered a priori on unity.
𝜆2
𝑖 𝑗 denotes the global-shrinkage component. The lagwise NG prior setup features one global-shrinkage
component per lag to impose more shrinkage for higher order lags (similar in spirit to the Minnesota prior
setup of Doan, Litterman and Sims, 1984). Hence, the prior distribution on 𝜆2
𝑖 𝑗 is a multiplicative Gamma
prior
𝜆2
𝑖 𝑗 =
𝑗
Ö
𝑔=1
𝜁𝜆
𝑖𝑔 , 𝜁𝜆
𝑖𝑔 ∼ G (𝑐0, 𝑑0),(C.5)
with 𝑐0=𝑑0=0.01. As long as the global-shrinkage parameter 𝜆2
𝑖 𝑗 exceeds unity, this prior shrinks
coefficients associated with higher lags more towards zero. This implies that the coefficient vector 𝜷𝑖 𝑗
becomes increasingly sparse for higher lags. Next, we impose an NG prior on the free off-diagonal elements
20
of ˜
𝑱𝑖𝑡
[˜
𝑱𝑖𝑙 ]𝑠𝑡 |𝛿2
𝑖𝑙 ,[𝜽˜
𝐽
𝑖𝑙 ]𝑠𝑡 ∼ N [𝒈𝑙]𝑠 𝑡 ,2/𝛿2
𝑖𝑙 [𝜽˜
𝑱
𝑖𝑙 ]𝑠𝑡 ,[𝜽˜
𝑱
𝑖𝑙 ]𝑠𝑡 ∼ G 𝜗˜
𝑱
𝜃, 𝜗 ˜
𝑱
𝜃,(C.6)
with 𝑠=2, . . . , 𝑛 and 𝑡=1, . . . , 𝑠 −1, denoting the respective row or column index. Again, we specify a
hyperprior on 𝜗˜
𝑱
𝜃∼𝐸 𝑥 𝑝(1)allowing for additional flexibility. Similar to before, we assume a Gamma prior
on 𝛿2
𝑖𝑙 ∼ G (𝑐0, 𝑑0). For the intercept vector, 𝒂𝑖, we specify for each element a simple Gaussian N (0,100)
to be uninformative. We have not yet discussed the prior distributions of the common means, 𝒃𝑗and 𝒈𝑙.
They do not feature a country-indicator 𝑖anymore, establishing linkages between the country models. This
constitutes the second layer of the prior setup in which we shrink coefficients towards zero. The prior setup
looks thus as follows
[𝒃𝑗]𝑠|𝜅2
𝑗,[𝝓𝑗]𝑠∼ N 0,2/𝜅2
𝑗[𝝓𝑗]𝑠,[𝝓𝑗]𝑠∼ G 𝜗𝜙, 𝜗𝜙, 𝑠 =1, . . . , 𝑘 . (C.7)
As before, [𝒃𝑗]𝑠, and [𝝓𝑗]𝑠denotes the 𝑠-th element of the respective vector. We put a hyperprior on
𝜗𝜙∼𝐸 𝑥 𝑝(1). Also, similar to before, we use the lagwise NG prior setup for the global component.
Therefore, the prior distribution on 𝜅2
𝑗looks as follows
𝜅2
𝑗=
𝑗
Ö
𝑔=1
𝜁𝜅
𝑔, 𝜁 𝜅
𝑔∼ G (𝑐0, 𝑑0).(C.8)
We conclude the second-layer by specifying the NG prior as well for the off-diagonal elements of 𝒈𝑙, which
is given by
[𝒈𝑙]𝑠𝑡 |𝜏2
𝑙,[𝝓𝒈
𝑙]𝑠𝑡 ∼ N 0,2/𝜏2
𝑙[𝝓𝒈
𝑙]𝑠𝑡 ,[𝝓𝒈
𝑙]𝑠𝑡 ∼ G 𝜗𝒈
𝜙, 𝜗𝒈
𝜙,(C.9)
with 𝑠=2, . . . , 𝑛 and 𝑡=1, . . . , 𝑠 −1. Again, 𝝑𝒈
𝜙∼𝐸 𝑥 𝑝(1)and 𝜏2
𝑙∼ G(𝑐0, 𝑑0). We conclude the prior
setup by specifying a prior on the diagonal elements of 𝛀𝑖,
𝜔𝑖𝑠 ∼ I G (𝑐0, 𝑑0), 𝑠 =1, . . . , 𝑛, 𝑖 =1, . . . , 𝑁 . (C.10)
21
D. Data Sources
All series were gathered from the sources listed below, including OECD Main Economic Indicators, OECD
National Accounts Quarterly, Eurostat, Annual Macroeconomic (AMECO) database, FRED database, or a
national source. All time series cover the period 1960Q1 to 2020Q4. All series are seasonally adjusted. The
gathered data consists of 𝑁=16 countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France,
Germany, Great Britain, Italy, Japan, Netherlands, Portugal, Spain, Sweden, United States.
In Table D1, we define the exact transformations of the variables used in the estimation. Note that we use
year-on-year growth rates. In Table D2, we show the exact sample coverage for each of the estimated models.
In particular, we use for the model featuring employment / unemployment 𝑁=16 countries while we only
use 𝑁=13 countries for the model with the labor market tightness indicator. Sample sizes also reduces for
this indicator, compared to the other two labor market variables.
Table D1: Variable Definitions.
Variable Transformation Details
𝑔𝑖𝑡 100 ×hln RGOVC𝑖𝑡
POP𝑖𝑡 −ln RGOVC𝑖𝑡 −4
POP𝑖𝑡−4i RGOVC𝑖 𝑡 is General Government Final Consump-
tion Expenditure, Constant Prices, seasonally ad-
justed
𝑥𝑖𝑡 100 ×hln RGDP𝑖𝑡
POP𝑖𝑡 −ln RGDP𝑖𝑡 −4
POP𝑖𝑡−4i RGDP𝑖 𝑡 is Gross Domestic Product, Constant
Prices, seasonally adjusted
𝑒𝑟𝑖 𝑡 100 ×hln EMP𝑖𝑡
EMP𝑖𝑡 +UE𝑖𝑡 −ln EMP𝑖𝑡 −4
EMP𝑖𝑡−4+UE𝑖 𝑡−4i EMP𝑖𝑡 is Total Employment, Persons, seasonally
adjusted
𝑢𝑟𝑖 𝑡 100 ×hln UE𝑖𝑡
EMP𝑖𝑡 +UE𝑖𝑡 −ln UE𝑖 𝑡−4
EMP𝑖𝑡−4+UE𝑖 𝑡−4i UE𝑖𝑡 is Harmonised Unemployment, Persons, sea-
sonally adjusted
𝑣𝑖𝑡 /𝑢𝑖𝑡 ln VAC𝑖 𝑡
UE𝑖𝑡 VAC𝑖𝑡 is Vacancies, Persons, seasonally adjusted
𝜔𝑖𝑡 100 ×[ln (RWAGE𝑖𝑡 )−ln (RWAGE𝑖 𝑡−4) ] RWAGE𝑖𝑡 is Wages & Salaries, Constant Prices,
seasonally adjusted
𝜂𝑖𝑡 UD𝑖𝑡 −UD𝑖
𝜎2
UD,𝑖
UD𝑖𝑡 is Trade Union Density
𝜑𝑖𝑡 BRR𝑖𝑡 −BRR𝑖
𝜎2
BRR,𝑖
BRR𝑖𝑡 is Average Gross Unemployment Benefit Re-
placement Rates
𝜍𝑖𝑡 EPL𝑖𝑡 −EPL𝑖
𝜎2
EPL,𝑖
EPL𝑖𝑡 is Employment Protection
Notes: POP𝑖𝑡 refers to Total Population (Persons),PRICE𝑖𝑡 refers to Gross Domestic Product Deflator.
22
Table D2: Sample Coverage in Different Models.
Countries / Model with... Employment Rate Unemployment Rate Tightness
Australia 1966Q3-2020Q2 1964Q1-2020Q4 1978Q2-2020Q4
Austria 1970Q1-2020Q4 1970Q1-2020Q4 1970Q1-2020Q4
Belgium 1980Q4-2020Q4 1980Q4-2020Q4 no data
Canada 1961Q1-2020Q4 1961Q1-2020Q4 no data
Denmark 1980Q1-2020Q4 1980Q1-2020Q4 2009Q1-2020Q4
Finland 1965Q1-2020Q4 1960Q1-2020Q4 1960Q1-2020Q4
France 1960Q1-2020Q4 1960Q1-2020Q4 1995Q1-2020Q4
Germany 1991Q1-2020Q4 1991Q1-2020Q4 1991Q1-2020Q4
Great Britain 1971Q1-2020Q4 1971Q1-2020Q4 1970Q1-2020Q4
Italy 1960Q1-2020Q4 1960Q1-2020Q4 no data
Japan 1960Q1-2020Q4 1960Q1-2020Q4 1960Q1-2020Q4
Netherlands 1975Q1-2020Q4 1975Q1-2020Q4 1996Q1-2020Q4
Portugal 1995Q1-2020Q4 1995Q1-2020Q4 1995Q1-2020Q4
Spain 1961Q1-2020Q4 1976Q3-2020Q4 196Q1-2020Q4
Sweden 1960Q1-2020Q4 1960Q1-2020Q4 1960Q3-2020Q4
United States 1960Q1-2020Q4 1960Q1-2020Q4 2000Q1-2020Q4
Notes: The sample refer to data availability. In the estimation we loose four observations due
to the applied transformation.
23
E. Further Empirical Results
This subsection presents further empirical results. First, we report the dynamic effects of government
spending shocks conditional on the LMIs. Second, we provide robustness to various choices for the baseline
model specification. Third, we investigate the issue of controlling for fiscal foresight. Fourth, we inspect
other labor market indicators such as the unemployment rate and labor market tightness given by the vacancy-
unemployment ratio. Fifth, we examine cross-country heterogeneity and cluster countries in two groups
according to their overall level of the LMIs or their consumption share in total GDP.
E.1 Dynamic Effects
In this subsection, we report the dynamic effects of government spending shocks conditional on the labor
market institutions. In Figure E1 we show the impulse response functions of all the variables in the system
by varying one LMI and keeping the others constant. They correspond to the first and last point in Figure 4
where we focus on the evolution of the marginal effects. Here, we focus more on the dynamic evolution of
the IRFs themselves.
We report three panels, one for each LMI: union density (UD), unemployment benefit replacement rate
(BRR), and employment protection legislation (EPL). We vary the value of the LMI as follows: Either we
set it to the 10th (upper row) or the 90th (middle row) of its respective empirical distribution. The remaining
LMIs we set to their median value. In the lower row, we also report the full posterior distribution of the
differences to look into statistical significance.
While confirming the overall picture and findings presented in the main text, a few remarks are in order.
First, note that the difference in the impulse response of government spending is not affected at all by varying
the intensity of the LMIs. This is reassuring that the government spending shock and its transmission is
not driving the results. Second, the dynamic propagation of the impulse responses confirms conventional
wisdom. Output, employment, and real wages increase to a government spending shock. In some instances,
the effect of the employment rate is not statistically significantly different from zero. This holds particularly
true for the models using high levels of the LMIs. Third, we can examine whether differences are statistically
significant. From Figure 1a and Figure 1c we conclude that the differences are strongly statistically significant.
For BRR, we only find that the difference for output is statistically significant.
24
Figure E1: Dynamic Effects of Government Spending Shocks.
Government Spending (UD: Q10)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (UD: Q10)
0 6 12 18
−0.4
−0.2
0.0
0.2
Employment Rate (UD: Q10)
0 6 12 18
−0.2
−0.1
0.0
0.1
Real Wage (UD: Q10)
0 6 12 18
−0.1
0.0
0.1
0.2
Government Spending (UD: Q90)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (UD: Q90)
0 6 12 18
−0.4
−0.2
0.0
0.2
Employment Rate (UD: Q90)
0 6 12 18
−0.2
−0.1
0.0
0.1
Real Wage (UD: Q90)
0 6 12 18
−0.1
0.0
0.1
0.2
Government Spending (UD: Q90−Q10)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (UD: Q90−Q10)
0 6 12 18
−0.4
−0.2
0.0
0.2
Employment Rate (UD: Q90−Q10)
0 6 12 18
−0.2
−0.1
0.0
0.1
Real Wage (UD: Q90−Q10)
0 6 12 18
−0.1
0.0
0.1
0.2
(a) Impulse Responses: Union Density.
Government Spending (BRR: Q10)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (BRR: Q10)
0 6 12 18
−0.1
0.0
0.1
0.2
0.3
Employment Rate (BRR: Q10)
0 6 12 18
−0.05
0.00
0.05
0.10
0.15
Real Wage (BRR: Q10)
0 6 12 18
−0.1
0.0
0.1
0.2
Government Spending (BRR: Q90)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (BRR: Q90)
0 6 12 18
−0.1
0.0
0.1
0.2
0.3
Employment Rate (BRR: Q90)
0 6 12 18
−0.05
0.00
0.05
0.10
0.15
Real Wage (BRR: Q90)
0 6 12 18
−0.1
0.0
0.1
0.2
Government Spending (BRR: Q90−Q10)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (BRR: Q90−Q10)
0 6 12 18
−0.1
0.0
0.1
0.2
0.3
Employment Rate (BRR: Q90−Q10)
0 6 12 18
−0.05
0.00
0.05
0.10
0.15
Real Wage (BRR: Q90−Q10)
0 6 12 18
−0.1
0.0
0.1
0.2
(b) Impulse Responses: Unemployment Benefit Replacement Rate.
Government Spending (EPL: Q10)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (EPL: Q10)
0 6 12 18
−0.1
0.0
0.1
0.2
Employment Rate (EPL: Q10)
0 6 12 18
−0.15
−0.10
−0.05
0.00
0.05
0.10
Real Wage (EPL: Q10)
0 6 12 18
−0.2
−0.1
0.0
0.1
0.2
Government Spending (EPL: Q90)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (EPL: Q90)
0 6 12 18
−0.1
0.0
0.1
0.2
Employment Rate (EPL: Q90)
0 6 12 18
−0.15
−0.10
−0.05
0.00
0.05
0.10
Real Wage (EPL: Q90)
0 6 12 18
−0.2
−0.1
0.0
0.1
0.2
Government Spending (EPL: Q90−Q10)
0 6 12 18
0.0
0.2
0.4
0.6
0.8
1.0
Real GDP (EPL: Q90−Q10)
0 6 12 18
−0.1
0.0
0.1
0.2
Employment Rate (EPL: Q90−Q10)
0 6 12 18
−0.15
−0.10
−0.05
0.00
0.05
0.10
Real Wage (EPL: Q90−Q10)
0 6 12 18
−0.2
−0.1
0.0
0.1
0.2
(c) Impulse Responses: Employment Protection Legislation.
Notes: This figure reports impulse response functions to a government spending shock. The black solid line refers to the median estimate while the
gray areas refer to 68/80/90% credible sets. In each panel, we report the value of the LMI between its 10th (upper row) and 90th quantile (middle
row) while setting the other LMI values to its median. We also report the difference (lower row). Panel (a) reports the conditional effects of union
density, panel (b) the conditional effects of the unemployment benefit replacment rate, and panel (c) the conditional effects of employment protection
legislation.
25
E.2 Robustness of Model Specification
In this subsection, we explore the robustness of the baseline specification in more detail. We conduct a
number of robustness checks to the baseline model specification to check the stability of the results. The
results are presented in Figure E2, where we report the on impact (panel (a)) and one-year (panel (b)) fiscal
multipliers. The baseline results (black solid line) with 80% credible sets (gray area) are the ones from the
baseline model reported in Figure 4. Additionally, we add colored lines with distinct points to the figure for
the alternative models.
We have done the following robustness checks. First, we have varied the number of lags, using 𝑝=2and
𝑝=4lags. Results are robust to this choice, where the median estimates are within the 80% posterior credible
sets. In almost all cases, both median estimates are within the credible sets of the baseline model. As a next
check, we follow Ramey (2016) and transform variables with trend using the procedure proposed by Gordon
and Krenn (2010). The original Gordon and Krenn (2010) procedure involves estimating a polynomial trend
and dividing the respective series by this trend. However, due to the end-point problem in both the polynomial
trend estimation and in using the Hodrick-Prescott filter, we use the Hamilton (2018) filter. By using this
transformation instead of differentiation to remove the unit root, we retrieve similar fiscal multipliers. Some
smaller differences arise, such as a stronger reduction in the fiscal multiplier for UD or a less pronounced
multiplier for BRR in the case of real GDP. Furthermore, one-year multiplier for real wages is, in all cases,
relatively constant and zero. Overall, however, the dynamics are similar to the baseline model, particularly
for the contemporaneous multipliers. We also estimate the model in (log-)levels instead of growth rates.
Results are robust to this choice as well, besides minor differences. The strongest differences arise again with
respect to the one-year fiscal multiplier of real wages, which is quite subdued.
As a last check, we restrict our sample to a smaller set of countries. We only estimate the model for the G7
countries: Canada, France, Germany, Italy, Japan, United Kingdom, and the United States. This comparison
is interesting for two reasons. The first reason is to investigate the strong cross-country heterogeneity, while
the second reason is that this comparison will be important when we control for fiscal foresight in the next
subsection. Generally, the overall qualitative pattern is similar for the G7 countries. Particularly, it is not
only similar, but fiscal multipliers are even more pronounced. We do not only find higher fiscal multipliers
(e.g., up to 0.6 for real GDP) but also more negatively sloped marginal effects.
26
Figure E2: Robustness: Model Specification and Sample.
−10
−10
−10
−10
Real GDP
−10
−10
Employment Rate
−10
−10
Real Wage
−10
−10
−10
−10
UD (η)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
Q10 Q30 Q50 Q70 Q90
−0.10
−0.05
0.00
0.05
0.10
Q10 Q30 Q50 Q70 Q90
0.1
0.2
0.3
0.4
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
Q10 Q30 Q50 Q70 Q90
−0.10
−0.05
0.00
0.05
0.10
Q10 Q30 Q50 Q70 Q90
0.1
0.2
0.3
0.4
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
Q10 Q30 Q50 Q70 Q90
−0.10
−0.05
0.00
0.05
0.10
Q10 Q30 Q50 Q70 Q90
0.1
0.2
0.3
0.4
−10
−10
Baseline p=2 p=4 Gordon−Krenn (Log−)Level G7
(a) Fiscal Multipliers: On Impact.
−10
−10
−10
−10
Real GDP
−10
−10
Employment Rate
−10
−10
Real Wage
−10
−10
−10
−10
UD (η)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
−10
−10
Baseline p=2 p=4 Gordon−Krenn (Log−)Level G7
(b) Fiscal Multipliers: One Year.
Notes: The sub-figures show the sensitivity of the fiscal spending multipliers to changes in the structural parameters (𝜂is union density, 𝜑is the
unemployment benefit replacement rate, and 𝜍is employment protection legislation). The y-axis gives the size of the multiplier while the x-axis
runs from the 10th to the 90th quantile in terms of the respective LMI. The multipliers are shown for different horizons: on impact (upper panel) and
one-year (lower panel) multiplier. The black solid line denotes the median and the gray area refers to the 80% credible set of the baseline model. The
colored lines with different points refer to alternative models.
27
To summarize, the baseline model is robust to a number of choices in a qualitative sense. Quantitatively,
results are in some cases different. When using different transformations, effects are somewhat subdued,
but when looking at a smaller country set, then effects are even magnified. The overall pattern, however, is
remarkably robust.
E.3 Controlling for Fiscal Foresight
In this subsection, we explore the issue of fiscal foresight in more detail. As pointed out by Ramey (2011) or
Leeper, Walker and Yang (2013), econometric models can suffer from informational insufficiency due to a
misalignment between the information sets of the economic agents and the econometrician. The identification
of government spending shocks can be clouded by potential anticipation effects of fiscal policy changes due
to their lagged implementation. This is particularly the case for structural vector autoregressions (SVARs)
identifying fiscal shocks because they rely mostly on a small number of endogenous variables, as in our
case of four variables. In order to add this missing information to the model, the literature has suggested
two strategies to circumvent this issue. Either one controls directly for anticipation effects by including
expectations data to the model or by enlarging the information set to mirror the one of the economic agents,
which they use to predict fiscal policy changes.
Both approaches are problematic in our setup. A large information set and data on expectations for a
broad panel of countries over a long time period (1960Q1 to 2020Q4 in this case) are hardly possible to
gather. However, by reducing the sample of countries and the time frame, it allows us to control for fiscal
foresight. To fix ideas, we include government spending forecasts, Δ𝑔𝑒
𝑖𝑡 , to the vector of endogenous variables
which yields 𝒚𝑖𝑡 =(𝑔𝑖𝑡 ,Δ𝑔𝑒
𝑖𝑡 , 𝑥𝑖 𝑡 , 𝑒𝑟𝑖 𝑡 , 𝜔𝑖𝑡 )0.3We rely on two different data sources for the measurement of
government spending forecasts, following suggestions in the literature on cross-country analyses (Auerbach
and Gorodnichenko, 2013; Born, Juessen and Müller, 2013; Born, Müller and Pfeifer, 2020; Ilori, Paez-Farrell
and Thoenissen, 2022). First, we rely on government spending forecasts provided by Oxford Economics, a
large forecasting firm that serves 1,500 clients, among them international corporations, financial institutions,
government organizations, and universities. These forecasts are available starting in the late 1990s. Second,
we also use semi-annual professional forecasts by the OECD disseminated in its Economic Outlook. These
forecasts are consistently available for all G7 countries since the mid 1980s4and tend to perform comparably
3Results are robust when exchanging the order of the variables, ordering the government spending forecast first.
4For the remaining countries in our sample, we have forecasts available starting in the mid 1990s.
28
Figure E3: Controlling for Fiscal Foresight.
−10
−10
−10
−10
Real GDP
−10
−10
Employment Rate
−10
−10
Real Wage
−10
−10
−10
−10
UD (η)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
0.8
Q10 Q30 Q50 Q70 Q90
−0.3
−0.2
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.2
0.4
0.6
0.8
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
0.8
Q10 Q30 Q50 Q70 Q90
−0.3
−0.2
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.2
0.4
0.6
0.8
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
0.8
Q10 Q30 Q50 Q70 Q90
−0.3
−0.2
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.2
0.4
0.6
0.8
−10
−10
G7 G7 (OECD EO) G7 (Oxf Econ) OECD EO Oxf Econ OECD EO (UD−BRR) Oxf Econ (UD−BRR)
(a) Fiscal Multipliers: On Impact.
−10
−10
−10
−10
Real GDP
−10
−10
Employment Rate
−10
−10
Real Wage
−10
−10
−10
−10
UD (η)
Q10 Q30 Q50 Q70 Q90
0.0
0.5
1.0
Q10 Q30 Q50 Q70 Q90
−0.2
0.0
0.2
0.4
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
0.8
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
0.0
0.5
1.0
Q10 Q30 Q50 Q70 Q90
−0.2
0.0
0.2
0.4
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
0.8
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
0.0
0.5
1.0
Q10 Q30 Q50 Q70 Q90
−0.2
0.0
0.2
0.4
Q10 Q30 Q50 Q70 Q90
0.0
0.2
0.4
0.6
0.8
−10
−10
G7 G7 (OECD EO) G7 (Oxf Econ) OECD EO Oxf Econ OECD EO (UD−BRR) Oxf Econ (UD−BRR)
(b) Fiscal Multipliers: One Year.
Notes: The sub-figures show the sensitivity of the fiscal spending multipliers to changes in the structural parameters (𝜂is union density, 𝜑is the
unemployment benefit replacement rate, and 𝜍is employment protection legislation). The y-axis gives the size of the multiplier while the x-axis
runs from the 10th to the 90th quantile in terms of the respective LMI. The multipliers are shown for different horizons: on impact (upper panel) and
one-year (lower panel) multiplier. The black solid line denotes the median and the gray area refers to the 80% credible set of the baseline model. The
colored lines with different points refer to alternative models.
29
well compared to other professional forecasts (Auerbach and Gorodnichenko, 2012). These forecasts are
prepared twice a year, in June and December. We follow the suggestion in Ilori, Paez-Farrell and Thoenissen
(2022) and interpolate the semi-annual series to a quarterly series using linear interpolation. Both series are
used in growth rates rather than levels due to irregular base-year changes for the countries in our sample.
We have to restrict our sample in terms of country coverage and time frame. We reduce the set of
countries to the G7 countries: Canada, France, Germany, Italy, Japan, United Kingdom, and United States.
For a comparison, we re-estimate the model over the full sample using the G7 countries. The results are
presented in Figure E3, where we report the on impact (panel (a)) and one-year (panel (b)) fiscal multipliers.
The model outcome of the G7 countries is reported by the median (black solid lines) together with 80% credible
set (gray area). We have discussed the comparison to the baseline model in the previous subsection. As a
first test, we cut the sample to the availability of government spending forecasts from the OECD Economic
Outlook (labeled G7 (OECD EO) and Oxford Economics (labeled G7 (Oxf Econ) without including the
forecasts themselves in the model. Shortening the sample to start in the mid 1980s (OECD) or late 1990s
(Oxf Econmics) also affects the cross-sectional dimension. In the OECD model, we have five countries left
(Germany, France, Italy, Japan, and the United Kingdom)5, while in the Oxford Economics model we only
have four countries left (France, Italy, Japan, and the United Kingdom).6The reason is that for the other
countries no time variation is left in one of the LMIs, and thus we have excluded these countries from the
model. This is driven by the relatively weak time variation in the EPL, a point to which we return later.
On the same country coverage and sample size, we have then added the government spending forecasts to
the model (labeled as OECD EO and Oxf Econ in the figure). A few interesting observations arise. First,
overall the findings are quite robust to the comparison model. For output and real wages, the marginal effects
are even more pronounced, while for employment more subdued. Qualitatively, the shape of the marginal
effects is robust with some exceptions (mostly for the employment rate). Second, the marginal effects for
the models including and excluding the government spending forecasts (e.g., G7 (OECD EO) and OECD
EO) are extremely similar. Hence, differences across models seem not to be driven by anticipation effects
but rather due to subsample stability and heterogeneity issues. This point is also highlighted by Ellahie and
Ricco (2017).
5In more detail, the estimation sample spans 1986Q3 to 2020Q4 except for Germany which only starts in 1992Q1. Due to the
unavailability of data on wages, Germany also starts in the baseline model only at this point, as detailed in Table D2.
6In more detail, the estimation sample spans 2000Q1 to 2020Q4.
30
As a last check, we exclude the EPL from the set of LMIs and re-estimate the model. This leaves us with
all seven G7 countries in the sample (labeled OECD EO (UD-BRR) and Oxf Econ (UD-BRR)). The results are
qualitatively stable. Interestingly, we even find that the subdued response of the employment rate for the G7
(OECD EO) and OECD EO model vanishes when we extend the sample. This is a clear indication that not
anticipation effects are an issue but rather sub-sample (in-)stability. In some instances, the marginal effects of
fiscal multipliers are more subdued when using the Oxford Economics government spending forecasts (e.g.,
output for the one-year multiplier). However, we do note that the sample is relatively short and we lose a lot
of information in the LMIs, which could drive the results as well.
E.4 Different Labor Market Indicators
In this subsection, we explore other labor market indicators. We exchange the employment rate in the baseline
model with either the unemployment rate or the labor market tightness (𝑣𝑖𝑡 /𝑢𝑖𝑡 locus). Similar to Figure 4,
we report the contemporaneous and one-year fiscal multipliers.
Results are provided in Figure E4. We report the results for the unemployment rate in panel (a) and for
the labor market tightness in panel (b). The results for the unemployment rate confirm our main findings. We
find a strong downward-shaped curve for the marginal effects for UD and now an upward-shaped curve for
the unemployment rate. The effects on the EPL are dampened, while the output multiplier for BRR is upward
sloping. Similar to the baseline model, there are no statistically significant differences for the unemployment
rate for BRR. The real wage is not strongly reacting along the stringency of the LMIs.
The model including labor market tightness is characterized by relatively large volatility around the
estimates, pointing to instability. We have also added the employment rate to the model, as in the baseline.
While the multipliers on impact are strongly centered around zero, we see an attenuation of marginal effects
for the one-year multiplier. However, none of these outcomes is statistically significant and we are thus not
too confident about the outcomes of the model.
In Figure E5 we report the implied volatilities and the change in the volatilities for the model featuring
unemployment. In comparison to the baseline model, we do not find stark differences. The only difference
is that the volatility for the unemployment rate increases when moving from the low to the high regime
when looking at UD. Similarly, there is a sign change for the change in the volatilities when looking at the
unemployment rate.
31
Figure E4: Fiscal Multipliers Using Other Labor Market Indicators.
−10
−10
−10
−10
Real GDP
−10
−10
Unemployment Rate
−10
−10
Real Wage
−10
−10
UD (η)
P=0
P=4
Q10 Q30 Q50 Q70 Q90
−0.2
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.3
−0.2
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
−0.2
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.3
−0.2
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
−0.2
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.3
−0.2
−0.1
0.0
0.1
0.2
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
(a) Unemployment Rate.
−10
−10
−10
−10
Real GDP
−10
−10
Labor Market Tightness
−10
−10
Real Wage
−10
−10
UD (η)
P=0
P=4
Q10 Q30 Q50 Q70 Q90
−1
0
1
2
3
4
5
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−2
0
2
4
6
8
10
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
−1
0
1
2
3
4
5
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−2
0
2
4
6
8
10
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
−1
0
1
2
3
4
5
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−2
0
2
4
6
8
10
(b) Labor Market Tightness (𝑣𝑖𝑡 /𝑢𝑖𝑡 ).
Notes: The sub-figures show the sensitivity of the fiscal spending multipliers to changes in the structural parameters (𝜂is union density, 𝜑is the
unemployment benefit replacement rate, and 𝜍is employment protection legislation). The y-axis gives the size of the multiplier while the x-axis
runs from the 10th to the 90th quantile in terms of the respective LMI. The multipliers are shown for different horizons: on impact (P=0, solid
black line) and one-year (P=4, dashed-dotted red line) multiplier. The lines denotes the median and the colored area refers to the 80% credible set.
32
Figure E5: Volatilities.
Real GDP
UD (η)BRR (ϕ)EPL (ς)
1.8
2.1
2.4
2.7
3.0
3.3
Low
High
Unemployment Rate
UD (η)BRR (ϕ)EPL (ς)
0.6
0.8
1.0
1.2
1.4
Low
High
Real Wage
UD (η)BRR (ϕ)EPL (ς)
1.6
1.8
2.0
2.2
2.4
2.6
Low
High
(a) Volatilities.
∆UD(η) > 0
Real GDP Unemp. Rate Real Wage
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
Change in Volatility
STE
SSE
∆BRR(ϕ) > 0
Real GDP Unemp. Rate Real Wage
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
0.8
1.0
Change in Volatility
STE
SSE
∆EPL(ς) > 0
Real GDP Unemp Rate Real Wage
−1.2
−0.8
−0.4
0.0
0.4
Change in Volatility
STE
SSE
(b) Change in Volatilities.
Notes: The upper panel shows the standard deviation of the respective macroeconomic variable in a regime with low (10th quantile) and high (90th
quantile) labor market institution (LMIs) while the remaining LMIs are at their median. The lower panel shows the change in the standard deviation
of the respective macroeconomic variable when going from the high (90th quantile) to the low (10th quantile) regime. STE refers to the shock
transmission effect, while SSE refers to the shock size effect as depicted in Eq. (4.7). The LMIs under consideration are union density (UD, 𝜂),
unemployment benefit replacement rate (BRR, 𝜑), and employment protection legislation (EPL, 𝜍).
E.5 Cross-Country Heterogeneity
In this subsection, we explore heterogeneous effects utilizing between-country variation since the analysis in
the main text is based on within-country variation of the LMIs. When discussing Figure 2 we have already
noticed that there is considerable cross-country heterogeneity in the LMIs. We conduct two robustness
exercises: First, we investigate whether effects differ in countries with more stringent deployed (e.g., in
Scandinavia) to countries with more flexible labor markets (e.g., Anglo-Saxon countries). Second, we
examine whether there are cross-country differences with respect to the consumption share in GDP. For both
33
Figure E6: Classification of Countries.
Union density (UD, η)
FRA
ESP
USA
JPN
DEU
NLD
CAN
AUS
GBR
ITA
PRT
AUT
BEL
FIN
DNK
SWE
0%
20%
40%
60%
80%
100%
U. benefit repl. rates (BRR, ϕ)
JPN
USA
ITA
CAN
GBR
AUS
SWE
DEU
FIN
AUT
ESP
PRT
FRA
BEL
DNK
NLD
0%
10%
20%
30%
40%
50%
60%
Employment protection (EPL, ς)
USA
CAN
AUS
GBR
DNK
JPN
BEL
FIN
DEU
AUT
SWE
FRA
ITA
NLD
ESP
PRT
0
1
2
3
4
5
6
7
Notes: Each sub-figure shows the mean of each labor market institution (union density, unemployment benefit replacement rate, and employment
protection legislation) for each country, together with the 10th and 90th quantile of its distribution. The points are observed data for the respective
country. Color shadings differentiate countries belonging to the Upper Group (blue) and Lower Group (orange).
approaches we cluster the countries in two groups. Then, we re-estimate the model in Eq. (4.2) for both
groups. We only allow for two groups to have enough variation in both country groups to estimate the IPVAR.
The clustering for the first approach is done via k-means clustering of the LMIs.7We standardize the
data (over all countries) before using the algorithm such that no variable has a stronger influence due to its
scaling. In case a country is not classified entirely to one group, we apply a 50% rule: If more than 50% of
the observations of one country are classified to one group, the country is classified to the same group. From
the clustering algorithm, we get two groups which we label as follows. Upper group: Austria, Belgium,
Denmark, Finland, the Netherlands, Portugal, and Sweden. Lower group: Australia, Canada, Germany, Great
Britain, Italy, Japan, Spain, and the United States. The groups align well with various definitions of welfare
regimes and are depicted in Figure E6. The second classification is done via average household consumption
shares (as percent of GDP). Those range from 43.55% to 68.06% and yield the following groups: Upper
group: Canada, France, Great Britain, Italy, Japan, Portugal, Spain, and the United States. Lower group:
Australia, Austria, Belgium, Denmark, Finland, Germany, Netherlands, and Sweden.
In Figure E7, we examine the fiscal multipliers both on a within- and between-country variation basis,
where we report the on impact (panel (a)) and one-year (panel (b)) fiscal multipliers. The baseline results
(black solid line) with 80% credible sets (gray area) are the ones from the baseline model reported in Figure 4.
There is quite some cross-country heterogeneity although the overall picture is qualitatively similar. This
exercise reveals some interesting insights. First, the upper consumption share group and the lower LMI group
7This is a frequently employed clustering algorithm based on the idea that each observation belongs to the cluster with the nearest
mean (or cluster centroid).
34
Figure E7: Cross-Country Heterogeneity.
−10
−10
−10
−10
Real GDP
−10
−10
Employment Rate
−10
−10
Real Wage
−10
−10
−10
−10
UD (η)
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
Q10 Q30 Q50 Q70 Q90
−0.05
0.00
0.05
0.10
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
Q10 Q30 Q50 Q70 Q90
−0.05
0.00
0.05
0.10
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
Q10 Q30 Q50 Q70 Q90
−0.05
0.00
0.05
0.10
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
−10
−10
Baseline Cons Lower Cons Upper LMI Lower LMI Upper
(a) Fiscal Multipliers: On Impact.
−10
−10
−10
−10
Real GDP
−10
−10
Employment Rate
−10
−10
Real Wage
−10
−10
−10
−10
UD (η)
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
−10
−10
BRR (ϕ)
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
−10
−10
EPL (ς)
Q10 Q30 Q50 Q70 Q90
−0.1
0.0
0.1
0.2
0.3
0.4
Q10 Q30 Q50 Q70 Q90
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
Q10 Q30 Q50 Q70 Q90
0.0
0.1
0.2
0.3
0.4
0.5
−10
−10
Baseline Cons Lower Cons Upper LMI Lower LMI Upper
(b) Fiscal Multipliers: One Year.
Notes: The sub-figures show the sensitivity of the fiscal spending multipliers to changes in the structural parameters (𝜂is union density, 𝜑is the
unemployment benefit replacement rate, and 𝜍is employment protection legislation). The y-axis gives the size of the multiplier while the x-axis
runs from the 10th to the 90th quantile in terms of the respective LMI. The multipliers are shown for different horizons: on impact (upper panel) and
one-year (lower panel) multiplier. The black solid line denotes the median and the gray area refers to the 80% credible set of the baseline model. The
colored lines with different points refer to alternative models.
35
yield generally larger fiscal multipliers than the baseline model. The marginal effects along the stringency
of the LMIs shows also more time variation, i.e., a stronger attenuation effect of fiscal multipliers for UD or
EPL. The effect on the shape of the fiscal multipliers is particularly pronounced for the upper consumption
group whereas we find less strong evidence on the shape of the marginal effects in the lower LMI group.
On the contrary, the lower consumption share group and the upper LMI group yield less pronounced fiscal
multipliers. Similarly, the marginal effects are dampened for this group. This holds not only for the on impact
multipliers but also for the one-year multipliers.
These results are in line with conventional predictions. Countries with a higher consumption share are
stronger dependent upon output fluctuations by demand-side shocks, such as a government spending shock.
Similarly, in countries with a generally lower level of LMIs, the findings are more pronounced. This provides
an indication that also the level of the LMIs matter and not only their change over time. These results have
to be interpreted with a grain of salt since we use the same identifying restrictions across all models.
Overall, the results outlined here strengthen the implications of our baseline results as of Section 4. In the
“upper” group of countries, cyclical policies do not have a strong effect on labor market variables. Cyclical
policies still affect the fiscal multipliers in the “lower” group of countries – with a clear downward-sloping
effect along the within-country variation.
36
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