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Labor Market Institutions, Fiscal Multipliers, and Macroeconomic Volatility

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We study empirically how various labor market institutions - (i) union density, (ii) unemployment benefit remuneration, and (iii) employment protection - shape fiscal multipliers and output volatility. Our theoretical model highlights that more stringent labor market institutions attenuate both fiscal spending multipliers and macroeconomic volatility. This is validated empirically by an interacted panel vector autoregressive model estimated for 16 OECD countries. The strongest effects emanate from employment protection, followed by union density. While some labor market institutions mitigate the contemporaneous impact of shocks, they, however, reinforce their propagation mechanism. The main policy implication is that stringent labor market institutions render cyclical fiscal policies less relevant for macroeconomic stabilization.
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Labor Market Institutions, Fiscal Multipliers, and
Macroeconomic Volatility
Maximilian Boeck1,2
, Jesús Crespo Cuaresma2,3,4,5 and Christian Glocker4
1Vienna School of International Studies
2Vienna University of Economics and Business
3Wittgenstein Centre for Demography and Global Human Capital (IIASA, ÖAW, UniVie)
4Austrian Institute of Economic Research
5CESifo
December 2022
Abstract
We study empirically how various labor market institutions (i) union density, (ii) unem-
ployment benefit remuneration, and (iii) employment protection shape fiscal multipliers and
output volatility. Our theoretical model highlights that more stringent labor market institutions
attenuate both fiscal spending multipliers and macroeconomic volatility. This is validated em-
pirically by an interacted panel vector autoregressive model estimated for 16 OECD countries.
The strongest effects emanate from employment protection, followed by union density. While
some labor market institutions mitigate the contemporaneous impact of shocks, they, however,
reinforce their propagation mechanism. The main policy implication is that stringent labor
market institutions render cyclical fiscal policies less relevant for macroeconomic stabilization.
Keywords: fiscal policy, fiscal multipliers, labor market institutions, interacted panel VAR
JEL Codes: E62, C33, J21, J38
Corresponding Author. Maximilian Boeck: Department of International Economics, Vienna School of Interna-
tional Studies. Favoritenstrasse 15a, 1040 Vienna, Austria. E-mail: maximilian.boeck@da-vienna.ac.at. Jesús
Crespo Cuaresma: Department of Economics, Vienna University of Economics and Business. Welthandelsplatz 1,
1020 Vienna, Austria. E-mail: jesus.crespo.cuaresma@wu.ac.at. Christian Glocker: Austrian Institute of Eco-
nomic 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). We would like to thank Thomas Url 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
In this paper, we contribute to a recent literature that examines the role of labor market institutions
(henceforth LMIs) as a determinant of business cycle fluctuations. The motivation arises from the
discussion about the respective roles of structural reforms and cyclical policies for macroeconomic
stabilization. The debate is centered around the question whether an enhanced fiscal architecture
that fosters the conduct and effectiveness of cyclical policies is to be preferred over labor market
reforms (see Banerji et al., 2017; Arnold et al., 2018; Sondermann, 2018; Masuch et al., 2018;
Duval and Furceri, 2018; Aiyar et al., 2019, for instance). Several recent studies (see Zanetti,
2009; Zanetti, 2011; Abbritti and Weber, 2018; Cacciatore et al., 2016, among others) highlight the
ability of LMIs to mitigate macroeconomic volatility. Such results challenge the use of traditional
cyclical fiscal policy, whose main objective is to smooth fluctuations in economic activity. The
success of fiscal policy depends crucially on the size of fiscal multipliers, which, however, change
considerably over time (see Auerbach and Gorodnichenko, 2012; Ilzetzki, Mendoza and Végh,
2013; Leeper, Traum and Walker, 2017, among others). In turn, the ability of LMIs to mitigate
macroeconomic fluctuations underscores their important role in shaping the transmission channel
of exogenous shocks. This, however, also raises the question of the extent to which LMIs affect
cyclical fiscal policy and in particular whether they reinforce or attenuate the effects of discretionary
fiscal spending policy on the economy.
We provide an analysis of the role of LMIs as determinants of cyclical macroeconomic fluctu-
ations that centers around the following questions: How do LMIs shape fiscal spending multipliers?
How do LMIs affect macroeconomic volatility and along which channel by shaping the trans-
mission of exogenous shocks, or by affecting the contemporaneous impact of shocks? What is
the role of cyclical fiscal spending policy when stringent LMIs are in place? The answer to the
first question will allow us to assess the role of LMIs in shaping the effectiveness of fiscal policy,
while the answer to the second one helps us to judge their ability to mute cyclical fluctuations.
This eventually allows an assessment of the degree of complementarity (or substitutability) among
different LMIs and cyclical spending policies and hence provides an answer to the third question.
Likewise, this will enable a direct comparison of structural versus cyclical policies in smoothing
fluctuations in economic activity.
We start by developing a theoretical model to assess qualitatively the role of LMIs in shaping (i)
fiscal spending multipliers and (ii) macroeconomic volatility. We consider a set-up that combines
the characteristics of a Diamond-Mortensen-Pissarides model with those of a standard real business
cycle model structure. We capture union density in the theoretical model by means of workers
bargaining power within the wage negotiations, the unemployment benefit replacement rate by means
of subsidies to the unemployed which are proportional to their previous wage, and employment
2
protection by the level of firing costs per displaced worker. Then, we confront the predictions of the
theoretical model by estimating an empirical model without imposing much structure on the data.
In particular, we estimate a Bayesian interacted panel vector-autoregressive (PVAR) specification
for 16 OECD economies, where we identify the effects of LMIs on fiscal spending multipliers
and macroeconomic volatility by means of interaction terms. The structural interpretation of the
econometric model relies on two main building blocks. First, 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. Additionally, the
structure of the empirical model allows us to estimate and analyze the variation of LMIs on a lower
frequency together with time-series data on a higher frequency. Importantly to note, we only utilize
within-country variation to estimate our baseline model. In an additional exercise, we inspect the
cross-country heterogeneity. We abstain from estimating the theoretical model directly due to the
availability of LMIs only on a lower frequency within a limited time sample. This renders the panel
approach particularly useful. Nevertheless, we show the strong similarity between the outcomes of
the DSGE model and the interacted PVAR model. Both allow for an evaluation of the sensitivity
of the endogenous shock transmissions with respect to changing structural properties. Second, 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).
The results can be summarized as follows. We use our theoretical model to inspect qualitatively
the outcomes of the empirical model. The theoretical model predicts that more stringent LMIs
attenuate both fiscal spending multipliers and output volatility. However, the latter depends on
the source of the shocks under consideration. The strongest mitigation emanates from employment
protection, followed by union density and the unemployment benefit replacement rate. Our empirical
model provides evidence for this. The reduction of the size of fiscal multipliers is not limited to
output but carries over to employment and unemployment multipliers. The drop in the size of the
output multiplier is up to 40 percent and depends on the particular LMI indicator considered. These
differences highlight the loss in effectiveness of fiscal spending policy once stringent LMIs are in
place.
While our results highlight the limited ability of fiscal policy in attenuating cyclical fluctuations
once stringent LMIs are deployed, we find that LMIs by themselves mute cyclical fluctuations. The
mitigation of macroeconomic volatility (measured by the standard deviation of output) amounts to
up to 25 percent regarding employment protection. The other two LMI indicators have the same
qualitative effect, but to a lesser extent quantitatively. The distinct quantitative effects on cyclical
volatility are due to the fact that the extent of employment protection attenuates macroeconomic
volatility by mitigating both the propagation mechanism and the contemporaneous impact of shocks.
3
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.
The remainder of the paper is structured as follows. The next session discusses the related
literature. In Section 3 we provide a descriptive overview of LMIs across selected OECD countries.
Section 4 introduces the theoretical model and presents its main predictions. Section 5 discusses
the connection between the theoretical and the empirical model, and presents the results of the
econometric analysis. Finally, Section 6 concludes.
2. Related Literature
Our contribution relates to various strands of the literature. First, we add to the literature on the
effects of fiscal spending policy (e.g., Blanchard and Perotti, 2002; Čapek and Crespo Cuaresma,
2020; Corsetti, Meier and Müller, 2012; Ilzetzki, Mendoza and Végh, 2013) and specifically to
the strand that evaluates their variation over time (Auerbach and Gorodnichenko, 2012; Cos and
Moral-Benito, 2016). Existing results indicate that the fiscal multiplier is higher during periods
of financial turmoil (Bernardini, De Schryder and Peersman, 2020), when household leverage is
higher (Demyanyk, Loutskina and Murphy, 2019), when the interest rates are at the zero lower
bound (Ramey and Zubairy, 2018) or, in general, when the fiscal expansion is accommodated by
monetary policy easing. Giambattista and Pennings (2017) argue that the multiplier is larger for
direct transfers to financially constrained households than for government purchases and multipliers
also depend on the way spending is financed (Hagedorn, Manovskii and Mitman, 2019). Hence,
there are both cyclical and structural factors that shape the size of spending multipliers and hence
the effectiveness of fiscal policy. The few contributions that assess the effects of fiscal policy on the
labor market tend to ignore country-specific labor market characteristics (see for instance Monacelli,
Perotti and Trigari, 2010; Brückner and Pappa, 2012; Turrini, 2013). In 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.
Second, our contribution is also related to the literature on the macroeconomic effects of labor
market regulation. While this literature has traditionally centered on the long-run implications of
market deregulation, our study is related to a more recent research program that examines their
short-run effects. For instance, Zanetti (2009) and Zanetti (2011) or Cacciatore et al. (2016)
assess theoretically the macroeconomic effects of market reforms featuring the removal of labor and
product market frictions. An increasing number of empirical studies estimate the aggregate impact
of changes in regulation (Pérez and Yao, 2015; Ordine and Rose, 2016; Duval, Furceri and Jalles,
2019). The main difference between these studies and our contribution is that the former address the
short-run macroeconomic effects of market reforms, while our focus rests upon the impact of labor
4
market regulation on the fiscal multiplier. Cacciatore et al. (2021), Abbritti and Weber (2018) and
Hantzsche, Savsek and Weber (2018) count among the few contributions that explicitly acknowledge
the role played by labor market institutions in the macroeconomic responses to exogenous shocks.
Our contribution is most closely related to the studies of Cacciatore et al. (2016) and Abbritti
and Weber (2018). Cacciatore et al. (2021) analyze the role of employment protection for fiscal
spending shocks. To this end, our contribution corroborates the findings of Cacciatore et al. (2016)
by considering a larger set of LMIs. Furthermore, our approach allows to examine the effects of
LMIs in a joint framework. Abbritti and Weber (2018), however, study the LMIs’ ability to mitigate
business cycle shocks (oil price shock and global demand shock) without paying attention to fiscal
multipliers and the extent to which they are shaped by the LMIs. Moreover, our analysis of the
LMIs role for shaping macroeconomic volatility comprises an extension to both studies. Lastly,
the present study highlights the link between fiscal multipliers and macroeconomic volatility and
the associated trade-off between structural and cyclical oriented policies. Hantzsche, Savsek and
Weber (2018), on the other hand, analyze the interaction between labor market institutions and
contractionary financing shocks.
3. Structural Labor Market Indicators in OECD Economies
The measurement of labor market institutions is limited by data availability, especially in the cross-
country dimension. In order to balance cross-country coverage and the availability of relatively long
time series information, we use OECD labor market statistics for the following three categories:
(i) union density (UD), (ii) unemployment benefit replacement rates (BRR), and (iii) employment
protection legislation (EPL). These three categories capture structural characteristics of the labor
market across distinct dimensions. We collect these data for a total of 16 OECD countries (see
Appendix C).1
The measure of union density (UD) is based on survey data wherever possible, and administrative
data adjusted for non-active and self-employed members otherwise. It is computed as the ratio of
wage and salary earners that are trade union members to the total number of wage and salary
earners. Higher values imply a higher extent of trade union membership and consequently a
higher weight of trade unions in the context of wage negotiations. The unemployment benefit
replacement rates (BRR) measure the proportion of income that is maintained after a given number
of months of unemployment. The indicator is the ratio of net household income during a selected
month of the unemployment spell to the net household income before the job loss. Higher values
1There 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.
0
10
20
30
40
50
60
70
80
90
100
110
0
10
20
30
40
50
60
0
1
2
3
4
5
6
Note: The figure shows the distribution of three labor market indicators across the sample of 16 OECD countries and their variation across countries
and over time. The Greek letters attached to each LMI indicator refer to their parametric counterpart in the theoretical model. The blue line shows
the weighted mean across countries for each decade.
imply more generous unemployment benefit systems. These two measures, UD and BRR, affect
employment, vacancies and unemployment through their effect on the price of labor. In contrast
to this, employment protection legislation (EPL) is likely to affect the quantity of labor directly,
changing wages only in the wake of second-round effects. The EPL index is a synthetic indicator
and captures the extent of regulatory strictness on dismissals and on the use of temporary contracts.
For each year, the employment protection indicator refers to the regulation in force on the 1st of
January, and higher values of the indicator imply a higher extent of employment protection.
Figure 1 shows the distributions of the three LMI indicators across countries and their variation
over time. We compute 10-year averages of the three indicators for each country. The extent of
time-variation in the distribution is displayed by means of boxplots for each decade starting in
the 1960s. The boxplots are extended by a weighted mean (blue dotted line) where the weights
correspond to the GDP share of each country (in PPP terms) relative to the aggregate of the country
group as a whole.
For UD, an upward shift of the distribution within the 1970s relative to the 1960s was followed
by subsequent downward movements driven by a steady drop in union membership rates. This
development is visible in both the median (thick black line) and the country-weighted mean (blue
dotted line). The dispersion of UD also exhibits a pronounced variation over time. It was the largest
in the 1980s and 1990s, and noticeably smaller before and after. The BRR experienced a steady
increase up to the 2000s. Since then, the median across countries has dropped. The significant
6
Figure 2: Labor Market Institutions in OECD Economies: Cross-Country Variation.
Notes: Each sub-plot shows the mean of each LMI variable for each country, together with two standard deviations in each direction (black). The
blue points are observed data points for the respective country.
time variation in the median is accompanied by a change in the shape of the distribution as a
whole. A fairly narrow distribution in the 1960s contrasts with a wide distribution in the 1990s and
2000s. The last decade was characterized by a tendency towards convergence of the unemployment
benefit replacement rates across countries. The distribution of the EPL index displays an interesting
pattern. While its median has remained rather constant over time, the dispersion of the distribution
has narrowed significantly over time. As in the case of the BRR, the EPL index has also experienced
a strong convergence across countries. This is primarily attributable to the convergent dynamics
of those countries in our sample that are part of the European Union. In many other countries, the
extent of employment protection has changed little over the period under scrutiny.
In Figure 2, we examine the cross-country variation of the three indicators of LMIs. The LMI
indicators exhibit strong country heterogeneity, most notably for UD and BRR and less so for EPL.
In particular, Scandinavian and continental European countries present the highest levels of UD
and BRR. In countries with a liberal tradition of social systems, such as the United States or Great
Britain, all indicators for LMIs tend to show relatively low values.
Finally, we inspect the distribution and variation of key labor market outcome variables over
time in Figure 3. The growth rates of employment and real wages2were buoyant in the 1960s,
followed by a subsequent moderation. The moderation in employment growth aligns with a steady
rise in the unemployment rate. While the median increases continuously, the distribution of
unemployment rates across countries experiences both periods of widening (1970s and 1980s)
2The real wage rate is measured in terms of the number of employed persons, rather than in terms of hours worked.
7
Figure 3: Labor Market Outcomes in OECD Economies
0
5
10
15
20
-1
0
1
2
3
4
5
-2
0
2
4
6
0
20
40
60
80
100
Note: The figure shows the distribution of four key labor market variables based on 16 OECD countries and the variation over time.
and periods of narrowing (from the 1990s onwards), highlighting significant variation over time
and across countries. The fourth sub-panel shows the ratio of vacancies relative to the number
of unemployed persons, that is, the slope of the Beveridge curve, which is a standard measure of
tightness in the labor market. The variable presents a close co-movement with the growth rate of
real wages. The number of vacancies was large in relation to the number of unemployed persons in
the 1960s and partly in the 1970s, when in some countries (for instance in Germany), the number
of vacancies even exceeded the number of unemployed persons. The scarcity of labor triggered a
strong upward pressure on real wages. The subsequent drop in the labor market tightness (caused
by both a decline in the number of vacancies and an increase in the number of unemployed persons)
aligns with a significant moderation in the growth rate of real wages starting in the 1980s.
8
The descriptive analysis highlights that increases in the BRR and the EPL align with lower
employment growth and less variation across decades. The reductions in UD, in turn, align with
moderation phases in real wage growth. In what follows, we study in detail the implications
of differences in these LMIs as determinants of differences in fiscal spending multipliers and
macroeconomic volatility. The theoretical model built in the next section centers on the interaction
between labor market institutions and outcomes when assessing the size of fiscal spending multipliers
and macroeconomic volatility.
4. 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
subsection A.4 of the Appendix.
We assume representative firms and households. Each firm employs 𝑛𝑡workers and posts 𝑣𝑡
vacancies 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=1𝑛𝑡. The number of new hires 𝑚𝑡is determined according to the matching function
𝑚𝑡=¯𝑚𝑢𝛾
𝑡𝑣1𝛾
𝑡, with ¯𝑚 > 0and 𝛾 (0,1). The probability that a firm fills a vacancy is given by
𝑞𝑡=𝑚𝑡/𝑣𝑡=¯𝑚𝜃𝛾
𝑡, where 𝜃𝑡=𝑣𝑡/𝑢𝑡is the extent of labor market tightness. The probability that
an unemployed worker finds a job is given by 𝑝𝑡=𝑚𝑡/𝑢𝑡=¯𝑚𝜃1𝛾
𝑡. Firms and workers take 𝑞𝑡
and 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 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).
4.1 Firms
The representative firm produces output 𝑦𝑡, for which it uses labor as the only input factor of
production according to 𝑦𝑡=¯
𝐴𝑛𝑡𝐴(˜𝑎𝑡), where ¯
𝐴 > 0is a common productivity factor and 𝐴(˜𝑎𝑡)=
˜𝑎𝑡
𝑎
1𝐹(˜𝑎𝑡)𝑑𝐹 (𝑎), where the conditional expectation is given by 𝐸[𝑎|𝑎˜𝑎𝑡]=
˜𝑎𝑡𝑎 𝑓 (𝑎)𝑑𝑎 and
1/(1𝐹(˜𝑎𝑡)) is a constant term shaping the level of 𝐴(˜𝑎𝑡). To raise the workforce in turn, firms
need to post vacancies. Hence, the firm can influence employment along two dimensions: the
9
number of vacancies posted and the number of endogenously destroyed jobs. This gives rise to the
following employment dynamics
𝑛𝑡=(1𝜚(˜𝑎𝑡)) (𝑛𝑡1+𝑚𝑡1).(4.1)
Current period profits are given by 𝜋𝐹
𝑡=𝑦𝑡𝑤𝑡𝑛𝑡𝜅𝑣𝑡𝐹(˜𝑎𝑡) (1¯𝜚) (𝑛𝑡1+𝑞𝑡1𝑣𝑡1)𝑏𝑠
𝑡where
the output price is normalized to unity, 𝑤𝑡=
˜𝑎𝑡
˜𝑤𝑡(𝑎)
1𝐹(˜𝑎𝑡)𝑑𝐹 (𝑎)is the (average) real wage weighted
according to the idiosyncratic job productivity, and the last term captures firing costs (Cacciatore
et al., 2021). In detail, (𝑛𝑡1+𝑚𝑡1) (1¯𝜚)𝐹(˜𝑎𝑡)represents the number of existing (𝑛𝑡1) and
new (𝑚𝑡1) 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 costs3. The firm maximizes the present discounted value of
expected profits: max𝑛𝑡,𝑣𝑡,˜𝑎𝑡𝐸𝑡Í𝑘0Λ𝑡,𝑡+𝑘𝜋𝐹
𝑡+𝑘, subject to the production function and Equation 4.1.
𝐸𝑡is the expectation conditional on the information up to and including time 𝑡;Λ𝑡,𝑡+𝑘denotes the
firm’s stochastic discount factor, defined below. The first order conditions give rise to4
𝐹𝑛
𝑡=𝑚 𝑝𝑙 𝑡𝑤𝑡+𝐸𝑡Λ𝑡,𝑡+1(1𝜚(˜𝑎𝑡+1))𝐹𝑛
𝑡+1𝑏𝑠
𝑡+1(1¯𝜚)𝐹(˜𝑎𝑡+1)(4.2)
𝜅
𝑞𝑡
=𝐸𝑡Λ𝑡,𝑡 +1(1𝜚(˜𝑎𝑡+1))𝐹𝑛
𝑡+1𝑏𝑠
𝑡+1(1¯𝜚)𝐹(˜𝑎𝑡+1)(4.3)
𝐴(˜𝑎𝑡)=1
¯
𝐴𝑤𝑡𝑏𝑠
𝑡𝜅
𝑞𝑡(4.4)
where 𝑚 𝑝𝑙 𝑡is the marginal product of labor and 𝐹𝑛
𝑡is the Lagrange multiplier associated with
Equation 4.1. In Equation 4.2, 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.
Equation 4.3 is the free entry condition. It relates the value of employing an additional worker
((1𝜚(˜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, Equation 4.4 sets the conditions for the idiosyncratic job productiveness ( ˜𝑎𝑡) and hence for
endogenous job destruction. Firms accept a lower idiosyncratic job productivity fromworkers 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.
3We consider the case where firing costs accrue to the government in Appendix A.4.
4The first order condition with respect to ˜𝑎𝑡is given by: 𝑛𝑡¯
𝐴𝜕𝐴 (˜𝑎𝑡)
𝜕˜𝑎𝑡𝜕 𝑤𝑡
𝜕˜𝑎𝑡=(𝑛𝑡1+
𝑞𝑡1𝑣𝑡1)𝑏𝑠
𝑡(1¯𝜚)𝑓(˜𝑎𝑡) + 𝐹𝑛
𝑡
𝜕 𝜚 (˜𝑎𝑡)
𝜕˜𝑎𝑡. Using Equation 4.3, Equation 4.2, and Equation 4.1, this equation can
be further simplified to: (1¯𝜚) (1𝐹(˜𝑎𝑡)𝜕 𝐴(˜𝑎𝑡)
𝜕˜𝑎𝑡𝜕 𝑤𝑡
𝜕˜𝑎𝑡=𝑏𝑠
𝑡(1¯𝜚)𝑓(˜𝑎𝑡) + 𝑚 𝑝𝑙𝑡𝑤𝑡+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)
1𝐹(˜𝑎𝑡)and using the definition of the production function gives Equation 4.4.
10
4.2 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, i.e., the overall household utility.
The budget constraint is given by
𝑐𝑡+𝐵𝑡=𝑅𝑡1𝐵𝑡1+ (1𝜏)𝑤𝑡𝑛𝑡+𝑏𝑢
𝑡(1𝑛𝑡) + 𝑇𝑆
𝑡+𝜋𝐹
𝑡,(4.5)
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, (1𝜏)𝑤𝑡is the after-tax wage, corresponding to the tax
rate 𝜏. In addition to the budget constraint, the household takes into account the flow of employment
by its members according to
𝑛𝑡=(1𝜚(˜𝑎𝑡))𝑛𝑡1+𝑝𝑡(1𝑛𝑡1).(4.6)
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,𝑛𝑡𝐸𝑡Í𝑘0𝛽𝑘𝑢(𝑐𝑡+𝑘, 𝑛𝑡+𝑘),
subject to the budget constraint, Equation 4.5 and the employment flow Equation 4.6. Optimization
leads to the following conditions
1=𝑅𝑡𝐸𝑡Λ𝑡,𝑡 +1,(4.7)
𝐻𝑛
𝑡=˜𝑤𝑏
𝑡𝑚𝑟 𝑠𝑡+𝐸𝑡[1𝜚(˜𝑎𝑡+1) 𝑝𝑡+1]Λ𝑡,𝑡+1𝐻𝑛
𝑡+1,(4.8)
where 𝜆𝑡is the Lagrange multiplier attached to Equation 4.5 and 𝜆𝑡𝐻𝑛
𝑡the one attached to equation
Equation 4.6. Furthermore, ˜𝑤𝑏
𝑡=(1𝜏)𝑤𝑡𝑏𝑢
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, 𝑚𝑟 𝑠𝑡captures 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 equation Equation 4.8, 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.
11
4.3 Nash Wage Bargaining
Wages are set each period based by Nash-bargaining of the pre-tax (average) wage 𝑤𝑡between firms
and workers. The Nash wage satisfies: 𝑤𝑡=arg max𝑤𝑡(𝐻𝑛
𝑡)𝜂(𝐹𝑛
𝑡)1𝜂where 0< 𝜂 1captures
workers bargaining power. Optimization yields: 𝜂𝐹𝑛
𝑡=(1𝜂)𝐻𝑛
𝑡/(1𝜏), which can be rearranged
to
𝑤𝑡=(1𝜂)𝑚𝑟 𝑠𝑡+𝑏𝑢
𝑡
1𝜏+𝜂𝑚 𝑝𝑙 𝑡+𝐸𝑡Λ𝑡,𝑡+1𝜅𝜃𝑡+1𝑏𝑠
𝑡+1(1¯𝜚)𝐹(˜𝑎𝑡+1).(4.9)
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.
4.4 Fiscal Policy, Aggregate Resource Constraint, and Government Budget Constraint
The government budget constraint satisfies
𝜏𝑤𝑡𝑛𝑡+𝐵𝑡=𝑅𝑡1𝐵𝑡1+𝑏𝑢
𝑡𝑢𝑡+𝑇𝑠
𝑡+𝑔𝑡,(4.10)
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=𝜑𝑤𝑡1where
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+𝜍𝑤𝑡1, and (iv) government subsidies: 𝑇𝑆
𝑡=¯
𝑇𝑆+𝜑𝑇𝑠𝐵𝑡;¯
𝑇𝑆and
¯𝜍serve the purpose to simplify the steady state computations and 𝜑𝑇𝑠𝐵𝑡ensures that the necessary
stability conditions are satisfied.
Finally, using Equation 4.10, Equation 4.5, and the expression for firms’ profits (𝜋𝐹
𝑡), we obtain
the aggregate resource constraint
𝑦𝑡=𝑐𝑡+𝑔𝑡+𝜅𝑣𝑡+𝐹(˜𝑎𝑡) (1¯𝜚) (𝑛𝑡1+𝑞𝑡1𝑣𝑡1)𝑏𝑠
𝑡(4.11)
This equation closes the model.
4.5 Embedding LMIs in the Model
The indicators for the LMIs as discussed in Section 3 are embedded in the model by the three
structural parameters 𝜍,𝜂and 𝜑. Considering 𝜍first, the government’s ability to shape the extent
of employment protection can take a variety of forms, such as strict layoff rules for individual occu-
pational groups, short-time work models that allow companies to forego layoffs due to (temporary)
12
subsidies, and also the existence of payments that may arise with a dismissal. In addition to sever-
ance 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.
The parameter 𝜂captures the bargaining power of workers. It is thus a measure of the implicit
advantage that employees benefit from within the wage-setting process. In a more general inter-
pretation, 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). The extent of variation
of this quantity across countries and across time is remarkable. Moreover, some countries also
adjust the extent of unemployment remuneration in relation to the severity of crises (Ganong, Noel
and Vavra, 2020).
The mapping between the empirical LMIs and their theoretical counterparts in the DSGE model
can only be qualitative. In particular, when considering the case of employment protection (EPL) for
instance, 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. Similar
limitations arise in case of the measure for union density (UD) and the unemployment benefit
replacement rates (BRR).
4.6 Equilibrium, Model Solution, and Dynamic Simulations
We collect the LMI parameters of interest in the vector 𝝑=[𝜂, 𝜑, 𝜍]and 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,
𝒛𝑡=𝚿1(𝝑)𝒛𝑡1+𝚿0(𝝑)𝜺𝑡(4.12)
where the vector 𝒛𝑡contains the endogenous variables and the vector of exogenous shocks simplifies
to 𝜺𝑡=ˆ𝑔𝑡in our case, denoting log-deviation of our variables from the steady state with a hat.
The matrix 𝚿1(𝝑)governs the dynamics among the dependent variables and the vector/matrix
𝚿0(𝝑)determines the contemporaneous impact of the fiscal spending shock on the endogenous
variables. Equation 4.12 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
13
Figure 4: Fiscal spending multipliers and the LMIs (𝜇(𝝑)).
0 0.2 0.4 0.6
0.5
0.55
0.6
0.65
0.7
0 0.1 0.2 0.3 0.4
0.5
0.55
0.6
0.65
0.7
0 0.1 0.2 0.3 0.4
0.5
0.55
0.6
0.65
0.7
0 0.2 0.4 0.6
0.55
0.6
0.65
0.7
0.75
0 0.1 0.2 0.3 0.4
0.55
0.6
0.65
0.7
0.75
0 0.1 0.2 0.3 0.4
0.55
0.6
0.65
0.7
0.75
0 0.2 0.4 0.6
-0.08
-0.06
-0.04
-0.02
0 0.1 0.2 0.3 0.4
-0.08
-0.06
-0.04
-0.02
0 0.1 0.2 0.3 0.4
-0.08
-0.06
-0.04
-0.02
Note: The sub-plots show the sensitivity of the fiscal spending multipliers to changes in the structural parameters. The multipliers are shown for
different horizons: contemporaneous multiplier ( P=0) and four quarters (P=4). The acronyms (UD, BRR, and EPL) refer to union density,
(unemployment) benefit replacement rates and employment protection (legislation).
outlined in Appendix A.2. As the IRFs are continuous 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=1IRFˆ𝑔
𝑗(𝜗𝑙)
𝑙={1,2,3}(4.13)
where IRF𝑥
𝑡(𝜗𝑙)and IRFˆ𝑔
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 4 for output ( ˆ𝑦𝑡), employment ( ˆ𝑛𝑡), and the real wage ( ˆ𝑤𝑡). The
multipliers for each variable are displayed for two distinct horizons (P={0,4}); the columns
consider the dependency of the multipliers on the respective LMI parameters (𝝑).
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
14
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 (𝑚𝑟 𝑠𝑡=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. Unemployment declines in response to the rise in employment. 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.
4.7 Implications of 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 4. 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 accept-
able. 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=0
and 𝐹𝑛
𝑡=0. In this situation, the household and the firm are not willing to increase or to decrease
labor supply and demand. Using Equation 4.2 and Equation 4.3, and setting 𝜏equal to zero for
simplicity, the reservation wages are given by
𝑤𝐹
𝑡=𝑚 𝑝𝑙 𝑡+𝐸𝑡Λ𝑡,𝑡+1(1𝜚(˜𝑎𝑡+1))𝐹𝑛
𝑡+1𝑏𝑠
𝑡+1(1¯𝜚)𝐹(˜𝑎𝑡+1),(4.14)
𝑤𝐻
𝑡=𝑚𝑟 𝑠𝑡+𝑏𝑢
𝑡 (1𝜚(˜𝑎𝑡+1) 𝑝𝑡+1)𝐸𝑡Λ𝑡 ,𝑡 +1𝐻𝑛
𝑡+1,(4.15)
from which 𝑤𝑡=(1𝜂)𝑤𝐹
𝑡+𝜂𝑤𝐻
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). Intuitively, an increase in unemployment benefits raises workers’ outside option (i.e.,
15
the present value of being unemployed) and improves their wage bargaining position. In addition,
the decrease in the search intensity of workers reduces the job finding rate and the bargaining
position of firms. The rise in the reservation wage of households causes the equilibrium wage (𝑤𝑡)
to increase, which in turn decreases the value to the firm of having an additional worker employed
(𝜕𝐹𝑛
𝑡/𝜕𝑤𝑡<0). Hence higher unemployment benefit remuneration attenuates the expansion in
employment5in response to the expansionary fiscal spending shock.
We move now to the effects of the weight of workers in the wage bargaining process (𝜂). As
highlighted above, the equilibrium wage 𝑤𝑡is a weighted average of the two reservations wages with
the weights being determined by 𝜂. From equation (4.9), 𝜕𝑤𝑡/𝜕𝜂 =𝑤𝐹
𝑡𝑤𝐻
𝑡(for 𝜏=0). Since
𝑤𝐹
𝑡> 𝑤𝐻
𝑡, as otherwise no worker-firm employment match would be created, then 𝜕𝑤𝑡/𝜕𝜂 > 0.
As long as 𝑤𝐻
𝑡< 𝑤𝐹
𝑡, increases in the bargaining power of workers hence bring their reservation
wages closer to those of firms: 𝑤𝐻
𝑡𝑤𝐹
𝑡. This exerts upward pressure on equilibrium wages,
which in turn (i) reduces the value to the firm of having an additional worker employed, and (ii)
induces firms to require a higher idiosyncratic productivity of workers. The latter hence raises
the endogenous job separation ( ˜𝑎𝑡rises). Consequently, both effects contract employment. Thus,
in response to an expansionary fiscal spending shock, the increase in employment and output is
smaller as the bargaining power of workers within wage negotiations increases. This is highlighted
in the sub-panels in the first column in Figure 4.
Finally, we turn to the effect of the extent of employment protection (𝜍). The key mechanism
through which employment protection affects fiscal spending multipliers is related to the fact that
the extent of firing costs affects the sensitivity of job destruction and job creation, as implied by
equations (4.4) and (4.2). Considering the latter first, low firing costs raise the value of an additional
worker to the firm (𝜕𝐹𝑛
𝑡/𝜕𝜍 < 0). In other words, low firing costs promote job creation. Hence,
in response to an expansionary fiscal spending shock, low firing costs give rise to relatively higher
job creation. As regards job destruction, equation (4.4) implies that low firing costs raise the job
destruction rate (𝜕˜𝑎𝑡/𝜕𝜍 > 0). While this effect works opposite to the job creation effect, both
render employment more sensitive to aggregate shocks. Hence, in response to an expansionary
fiscal spending shock, employment shows a larger reaction when firing costs are low, as can be seen
in the sub-panels in the third column in Figure 4.
The discussion so far centered on the role of the LMIs for fiscal multipliers. However, they
are likely to also shape macroeconomic volatility. To this purpose, we consider Equation 4.12 and
compute the variance of the endogenous variables in 𝒛𝑡and extend the vector of structural shocks
(𝜖𝑡) by a technology shock (𝜖𝐴
𝑡) so that the set of exogenous shocks involves both a demand and
5Albertini 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 unemploymentbenefits reduces the real interest rate, which in turn promotes consumption,
output and employment.
16
Table 1: Volatility of output, employment and the real wage.
LMI: UD (𝜂) BRR (𝜑) EPL (𝜍)
Output ( ˆ𝑦𝑡) 0.97 1.07 1.12
Employment (ˆ𝑛𝑡) 1.04 0.95 1.16
Real wage ( ˆ𝑤𝑡) 0.99 0.96 0.99
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 (𝑥𝑡s) when the respective LMIs take on a low value relat-
ive to the standard deviations when the LMIs are set at a high value
(Var(𝑥𝑡(LMIlow))/Var(𝑥𝑡(LMIhigh) )).
a supply shock. We carry out this simulation to provide an answer to the following: How do the
LMIs shape macroeconomic volatility? For the sake of brevity, we describe the analysis in detail
in Section A.5 of the Appendix and limit the discussion here to the most important implications.
We compute the variance of the vector of endogenous variables once when a low value of a LMI
is considered and compare it to the variance once a high value is used. The results are provided
in Table 1. For instance, in case of employment, a high value of the EPL gives rise to a lower
employment volatility; this is indicated by the value of 1.16 in the last column of the second row.
More generally, we find that a higher BRR and EPL attenuate output volatility, while the opposite
emerges from a higher UD. Employment volatility is mitigated by a higher UD and EPL while it gets
exacerbated by a higher BRR. The volatility of the real wage in turn is hardly affected by the UD and
EPL while gets attenuated by a higher BRR. Across all LMIs, the EPL tends to exert the strongest
effects on the volatilities of output and employment while the real wage is primarily affected by the
BRR. All these results, however, crucially depend on the source of the shock. We provide a deeper
analysis in the Appendix where we examine the sensitivity of the effects of changes in the LMIs
with respect to distinct exogenous shocks. The key finding of this is that the LMIs can potentially
mitigate output volatility, however, the nature and dominance of specific shocks is crucial.
4.8 Key Messages and Extensions of the Theoretical Model
The results of the previous exercises illustrate how LMIs affect the functioning of fiscal spending
policy. On the one hand, a lack of labor market flexibility attenuates the ability of the government
to provide an economic stimulus via expansionary spending policies. The reduced effectiveness
of fiscal spending policies is due to a weakening of the fiscal spending multipliers by the LMIs.
Stringent LMIs themselves can dampen output volatility, which, however, crucially depends on the
source of the shocks.
17
While the theoretical results emanate from a specific model based on a particular calibration, we
provide various extensions of the theoretical setting in the Appendix. Appendix A.3, for instance,
reassesses the results provided in this section by considering a more general calibration of the
model parameters. Section A.4 considers various model extensions in the form of (i) monopolistic
competition and markup pricing, (ii) real wage rigidities, (iii) limited asset market participation,
(iv) the case when firing costs accrue to the government as revenues, and (v) productivity-enhancing
government spending. Across all extensions, the qualitative impact of the LMI parameters on the
multipliers of output and employment remain identical and only the size of the multipliers are
changed.
5. The Econometric Model
We empirically validate the results of our theoretical model by examining the conditional response
to fiscal spending shocks for different levels of LMI indicators and their effect on macroeconomic
volatility in a panel of developed countries using an interacted panel vector-autoregressive (IP-VAR)
specification as popularized by Towbin and Weber (2013) and Sá, Towbin and Wieladek (2014).
The IP-VAR model is employed to assess how the characteristics of the matrices 𝚿0(𝝑)and 𝚿1(𝝑)
of the system given by Equation 4.12 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}.(5.1)
Substituting the matrices 𝚿0(𝝑)and 𝚿1(𝝑)in Equation 4.13 by the Taylor approximation given
by Equation 5.1 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 estimation of the econometric model.
5.1 Econometric Model
We estimate the following reduced-form IP-VAR (see Equation B.1 in Appendix B) model
y𝑖𝑡 =𝒄𝑖(𝝑𝑖𝑡 ) +
𝑝
Õ
𝑗=1
𝚽𝑖 𝑗 (𝝑𝑖𝑡 )y𝑖𝑡𝑗+u𝑖𝑡 ,u𝑖𝑡 N𝑀(0,𝚺𝑖(𝝑𝑖𝑡 )),(5.2)
where 𝒚𝑖𝑡 denotes the 𝑀-dimensional vector of macroeconomic time series for country 𝑖and 𝝑𝑖𝑡
denotes the 𝑑-dimensional interaction term, with 𝑖=1, . . . , 𝑁 denoting the country and 𝑡=1, . . . , 𝑇
the time period. Coefficients of the model are a country-specific intercept vector 𝒄𝑖, a coefficient
18
matrix 𝚽𝑖 𝑗 for lag 𝑗, and a variance-covariance matrix of the vector error term, given by 𝚺𝑖.
Note that all these reduced-form coefficients are a linear function of the interaction term. Hence,
the reduced-form model is a panel VAR specification whose parameters change depending on the
exact value taken by the interaction variable. The details of the model framework are presented
in Appendix B. The structural identification of fiscal spending shocks is performed by imposing
a recursive identification scheme based on the Cholesky decomposition of the variance-covariance
matrix 𝚺𝑖of the reduced-form IP-VAR shocks. We discuss shock identification in more detail in
the next subsection.
The structural IP-VAR representation of the DSGE model comprised by Equation 4.12 is given
by
𝒚𝑖𝑡 =
𝑝
Õ
𝑗=1
˜
𝚿𝑖 𝑗 (𝝑𝑖𝑡 )𝒚𝑖𝑡𝑗+𝒆𝑖 𝑡 ,𝒆𝑖𝑡 N𝑀(0,𝑰),(5.3)
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) and explained in detail in Appendix B. The
prior assumes that the structural individual-level coefficients have a common underlying Gaussian
distribution,
˜
𝚿𝑖 𝑗 (𝝑𝑖𝑡 ) N (𝚿𝑗(𝝑),𝑽𝑗), 𝑗 =1, . . . , 𝑝, (5.4)
with a variance-covariance matrix 𝑽𝑗. We exert regularization via this variance-covariance matrix
towards the common mean model with the help of Bayesian global-local shrinkage priors (Griffin and
Brown, 2010; Huber and Feldkircher, 2019). The exact specification can be found in Appendix B.
The correspondence between the observable LMIs 𝝑𝑖𝑡 (depicted in Figure 1) and the structural
LMI parameters 𝝑of the DSGE model can be made explicit by defining 𝚿𝑗(𝝑)=𝚿𝑗𝑡 ,𝚿𝑗(¯
𝝑)=
¯
𝚿𝑗𝜕𝚿𝑗(𝝑)/𝜕𝝑·¯
𝝑,𝚪𝚿
𝑗=𝜕𝚿𝑗(𝝑)/𝜕𝝑for 𝑗=0,1, . . . , 𝑝. This implies that the coefficients of
the 𝚿𝑗𝑡 matrix vary as follows
𝚿𝑗(𝝑)=𝚿𝑗𝑡 =¯
𝚿𝑗+
𝑑
Õ
𝑙=1
𝚪𝚿
𝑗 𝑙 𝜗𝑙𝑡 , 𝑗 =0, ..., 𝑝. (5.5)
which relates the empirical set-up directly to Equation 5.1 of the theoretical model. The full IP-VAR
model is given by Equation 5.3, and its equivalence with the solution of the DSGE model depicted
in Equation 4.12 and Equation 5.1 is evident when considering a lag length of one.
In the IP-VAR 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
19
values of 𝜗𝑙. For the ease of interpretation, we examine changes in the structural coefficients only
for varying levels of one interactive variable, while keeping the remaining ones at a given level.
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.6A second
potential limitation is the linearity assumption (in the parameters) embedded in the IP-VAR model,
which mimics the approximation considered in Equation 5.1. In principle, the assumption of
linearity could be relaxed by considering various non-linear extensions of 𝝑. However, depending
on the number of observations and parameters of interest in 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.
5.2 Shock Identification
We identify fiscal spending shocks by imposing a recursive identification based on the Cholesky
decomposition of the reduced-form IP-VAR 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 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. In
particular, event-study approaches based on defense spending changes (Ramey and Shapiro, 1998;
Ramey, 2011) are not really suitable in our context, as defense spending is negligibly small in most
of the countries in our data set. The approach by Blanchard and Perotti (2002) would additionally
require institutional information on the elasticity of government spending and revenues to output
and inflation, which is not practical for a large panel of countries. Mountford and Uhlig (2009)
use sign-restrictions to identify fiscal policy shocks which is not practical in a dataset with a large
panel of countries either. Finally, the narrative approach (Romer and Romer, 2010; Guajardo,
Leigh and Pescatori, 2014) requires the availability of detailed legislative records in order to extract
6This 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.
20
policy shocks.7Such approaches would require collecting detailed institutional information and
data on fiscal spending plans for 16 countries for a sufficient long time horizon, thus rendering these
approaches infeasible for our purposes.
One potential drawback in the context of a recursive identification scheme concerns the extent
of unpredictability of changes in government spending from the point of view of a statistician.
This might stand in contrast to economic agents, who might well have anticipated at least parts
of the fiscal shock. Legal processes usually create a time gap between the announcement and the
implementation of a given fiscal policy measure. A statistician, relying on the data a posteriori,
would attach the implementation as starting point of the policy, while economic agents might
have already reacted to the mere announcement of the policy change. Ignoring this aspect results
in a potential underestimation of the effects of fiscal spending shocks. The role played by such
anticipation effects is ultimately an empirical question. It relates to the extent of liquidity constrained
households and the share of consumption in GDP. Mertens and Ravn (2010) highlight that a simple
Cholesky decomposition delivers practically correct impulse responses for a large class of theoretical
models even if shocks are anticipated by the private sector.
5.3 Data and Specification
We use quarterly data ranging from 1960:Q1 to 2020:Q4 for 16 OECD countries to estimate the IP-
VAR model. The sample includes information for Australia, Austria, Belgium, Canada, Denmark,
Finland, France, Germany, Great Britain, Italy, Japan, the Netherlands, Portugal, Spain, Sweden,
and the United States. We specify 𝒚𝑖𝑡 ={govc𝑖𝑡 ,gdp𝑖𝑡 ,emp𝑖𝑡 ,rwage𝑖𝑡 }for our baseline specification,
where we follow Brückner and Pappa (2012) and express all variables in per-capita terms. The
variable govc𝑖𝑡 denotes the growth rate of real government consumption per capita, gdp𝑖𝑡 is the
growth rate of real GDP per capita, emp𝑖𝑡 is the growth rate of employment per capita, and rwage𝑖𝑡
is the growth rate of the real wage (see Table C1 and Table C2 in the Appendix for further details).
We consider various extensions to the baseline specification in which we substitute employment
(emp𝑖𝑡 ) by (i) the growth rate of unemployed per capita (unemp𝑖𝑡) and (ii) the labor market tightness
indicator given by the ratio of vacancies to unemployment (vu𝑖𝑡)8; see Appendix D.
As regards the interaction variables, we specify 𝝑𝑖𝑡 =(𝜂𝑖𝑡 , 𝜑𝑖𝑡 , 𝜍𝑖 𝑡 )and use data from the CEP-
OECD institutions database (see Table C1 in the Appendix for further details) for union density
(𝜂𝑖𝑡 ), unemployment benefit replacement rates (𝜑𝑖 𝑡 ) and employment protection legislation (𝜍𝑖𝑡 ).
The original data set contains annual observations, which we interpolate to a quarterly frequency
7Kraay (2012) describes yet another approach whose applications are essentially limited to developing countries as
it relies on two features which are unique to low-income countries: (1) borrowing from the World Bank and (2)
spending on World Bank–financed projects.
8In the IP-VAR model in which the labor market tightness indicator is used instead of employment, we have to reduce
the country coverage of our sample to 𝑁=13, as data for vacancies are unavailable for Belgium, Canada, and Italy.
21
by assigning the annual value of a particular year to each quarter of the same year. We estimate
the IP-VAR model using all three interaction variables at once. Additionally, we standardize each
interaction variable prior to estimation. This serves the purpose of comparability across countries,
otherwise the proposed common-mean prior specification runs into (numerical) troubles. We
abstain from the alternative taking differences of the interaction variables to have a more direct
interpretation with respect to the respective country levels. Either way, this estimation strategy only
utilizes the within-country variation of the LMIs. Hence, our estimates are of a more conservative
nature due to the strong cross-country heterogeneity in the LMIs (see Figure 2). We investigate cross-
country heterogeneity by splitting the sample of countries in two distinct groups in subsection 5.6.
Given the standardization of the interaction variables, the interpretation is as follows: A unit rise in
𝜗𝑙corresponds to a one standard deviation increase of the respective LMI within countries. When
simulating the IP-VAR model along a particular interaction variable 𝜗𝑙, we set the remaining ones
𝜗(𝑙) equal to zero (the mean).
The baseline model (and so too the remaining two) is estimated with one lag (𝑝=1) as proposed
by the Bayesian information criterion. The estimation is based on 20,000 posterior draws, where
we discard the first 10,000 as burn-ins.
5.4 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 use Equation 4.13 to 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 5 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 multipliers and are
complemented with the 68% confidence bound in each case. The horizontal axis ranges from -2 to
+2 standard deviations of the respective LMIs while the vertical axis depicts the value of the fiscal
multiplier for the respective variable.
Considering for instance the impact multiplier for output and its dependency on union density
(first panel), we find that at a low value of UD (𝜂) a one percent increase in fiscal spending raises
output by 0.5 percent; the value of the output multiplier, however, drops to around 0.3 when the
UD is at a high value. This gives rise to a decline in the output multiplier of up to 40% which is
substantial and statistically significantly different from zero. A drop of a similar size also applies
in case of the BRR (𝜑), while in case of the EPL (𝜍) the decline of the output multiplier is weaker
(around 20%; from 0.5 to 0.4).
The impact multipliers for employment, while consistently positive, are also negatively affected
by the LMIs. The drop is sizeable in case of the EPL and amounts to around 20 log points (from
22
Figure 5: Fiscal Multipliers.
Notes: The sub-plots show the sensitivity of the fiscal spending multipliers to changes in the structural parameters (𝜂is union density, 𝜑is
unemployment benefit replacement rate, and 𝜍is employment protection). The y-axis gives the size of the multiplier while the x-axis runs from -/+
2 standard deviations in terms of the respective LMI. The multipliers are shown for different horizons: contemporaneous multiplier (P=0, solid
line) and four quarters (P=4, dash-dotted line). Confidence bounds refer to the 16/84 quantile of the posterior distribution.
0.25 down to 0.05), while being a moderate for the remaining two LMIs. For both output and
employment, the one-year multipliers consistently exceed the impact multipliers which highlights
the inertia of the impact of government spending shocks on economic activity. Moreover, the
one-year multiplier for output displays a lower sensitivity to the BRR than the impact multiplier.
The opposite applies to the EPL the drop is now close to 30%. In case of the UD the sensitivity
does not change across impact and one-year multiplier.
The output multiplier of the IP-VAR model is comparable to those of the calibrated DSGE
model. Nevertheless, we stress the role of nominal rigidities (see Section A.4 in the Appendix).
The one-year employment multiplier consistently exceeds the impact multiplier, which highlights
the role of limited asset market participation in this context (see Section A.4 in the Appendix). 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
A.4 in the 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.
23
The most noteworthy deviations from the (baseline) theoretical predictions apply to the real
wage. The IP-VAR model gives rise to a positive real wage multiplier; moreover, the multiplier
abates with the horizon quickly. At the same time the real wage multiplier increases with the
EPL, while the opposite applies for the UD and to a lesser extent for the BRR. This highlights the
presence of nominal ridigities and productivity enhancing government spending (see Section A.4
in the Appendix) for explaining the positive value of the real wage multiplier both frictions give
rise to a theoretic real wage multiplier replicating the course of its empirical counterpart.
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).
Not least the positive real wage multiplier aligns with the findings in Brückner and Pappa (2012)
who identify both negative and positive multipliers across distinct countries. 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 D. There, we also show the impulse response functions and
additionally provide results for the alternative two models featuring unemployment and the vacancy-
to-unemployment ratio (labor market tightness, 𝑣𝑡/𝑢𝑡) instead of employment. These alternative
models confirm the size of the output multipliers and their dependency on the LMIs of the baseline
model. The same applies to the real wage multipliers. Moreover, the additional models highlight
the negative (positive), though, sluggish effects on unemployment (labor market tightness), both of
which are in line with the theoretical model.
We extend the previous analysis for the forecast error variance decomposition (FEVD). The
results are provided in Figure 6. 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 stringent LMIs are
deployed (“high”). In contrast, they explain up to 28% at horizons of eight quarters and beyond when
the LIMs are, however, less stringent (“low”). This share is substantially lower for the variables
characterizing the labor market, employment and real wages. In particular, while a higher level
of the LMIs reduce the explained forecast error variance of output only slightly, the attenuation is
sizable for employment in case of the BRR (𝜑) and the EPL (𝜍), and for the real wage in case of
the UD (𝜂). From an economic point of view, more stringent LMIs abate the amount of variation
explained in labor market variables by fiscal spending shocks. Put differently, when stringent
LMIs are deployed, discretionary fiscal policy only has a limited potential in affecting labor market
outcomes.
24
Figure 6: Forecast Error Variance Decomposition.
Notes: The sub-plots show the sensitivity of the explained forecast error variance to changes in the structural parameters (𝜂is union density, 𝜑is
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 6 years (=24 months). The FEVD is shown for a regime with low (2sd) and high (+2sd) LMIs.
As a robustness check, we re-do the analysis with other labor market variables: unemployment
and our measure for the labor market tightness (𝑣𝑡/𝑢𝑡). The results are provided in Figure D5 in the
Appendix. In both models, we observe no stark differences to the baseline results. Furthermore,
the reduction in the explained forecast error variance is even stronger to some extent.
Overall, the LMIs are found to play a role for the effectiveness of discretionary fiscal policy,
though most of the results are borderline significant only. This applies to both the goods and the
labor market. Among the three LMIs considered, the UD is found to have the strongest effect on
real wages, while the EPL on employment. As the BRR is targeting both, quantity and prices, it
hence shapes both employment and real wages as our results highlight. Most importantly, more
stringent LMIs limit the fiscal authority’s ability in affecting cyclical swings in economic activity.
This, however, does not indicate anything as to whether discretionary policy measures attenuate or
reinforce cyclical fluctuations. In the end, this crucially depends on the timing of fiscal interventions
(if timed adequately, a counter-cyclical policy stance emerges which smooths cyclical fluctuations)
and the size of the interventions (if sized too big, an overshooting might occur which by itself
25
exacerbates cyclical fluctuations). While these factors shape the success of fiscal policy, the LMIs
counteract its effectiveness. This raises the question of whether the LMIs themselves contribute to
mitigating cyclical fluctuations which is what we focus on in the following section.
5.5 The Effect on Macroeconomic Volatility
The analysis so far has shown that the effects of discretionary fiscal policy potentially decrease
the more stringent the LMIs are. However, this raises a fundamental question: Is there a need
for discretionary fiscal policy in an environment of stringent LMIs? After all, the main objective
of discretionary (spending) policies is to stimulate aggregate demand in the event of a negative
demand shock or to tighten in the opposite case. In other words, aggregate demand is smoothed
over the business cycle. However, it may well be that in an environment with already stringent
LMIs, these very elements already contribute significantly to cyclical smoothing by which they
render any discretionary spending policy obsolete. Hence, we want to assess whether there is a
degree of substitutability between the LMIs and cyclical spending policies.
The LMIs that we consider capture structural labor market characteristics across distinct dimen-
sions, 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
hence over households’ employment/unemployment states which in turn stabilizes consumption at
the individual and aggregate level. The EPL and the UD work through similar channels. Hence, we
expect output volatility to be lower in an economy with a more rigid labor market. Our econometric
setting allows for an assessment of macroeconomic volatilities with respect to the LMIs. With
this in mind, we analyze the impact of the LMIs on macroeconomic volatility. To this end, we
determine the variance of the endogenous variables of the IP-VAR model9and examine the impact
of the LMIs. The variance covariance matrix of the endogenous variables y𝑖𝑡 in the IP-VAR system
is given by
vec (𝛀(𝝑))=(𝑰𝑭(𝝑) 𝑭(𝝑))1vec (𝑸(𝝑))(5.6)
where 𝑰is an identity matrix of dimension 𝐾2=(𝑀 𝑝)2,𝑭(𝝑)denotes the 𝐾×𝐾companion
matrix form of 𝚿𝑗(𝝑)with 𝑗=1, . . . , 𝑝, and 𝑸(𝝑)denotes the 𝐾×𝐾companion matrix form
of the common-mean variance-covariance matrix 𝚺(𝝑)=𝑁1Í𝑁
𝑖=1𝚺𝑖(𝝑).10 As can be seen from
Equation 5.6, the variance covariance matrix of the endogenous variables thus depends on the
interaction term 𝝑, which are the LMIs in our setting. It follows that 𝛀(𝝑)is the 𝐾×𝐾variance
9The results of the DSGE model of this exercise are presented in Section A.5 in the Appendix.
10 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 IP-VAR.
26
Figure 7: Macroeconomic Volatilities Along LMIs.
Notes: Each sub-plot shows the standard deviations of the respective macroeconomic variable in a regime with low (2sd) and high (+2sd) LMIs. The
LMIs under consideration are union density (UD(𝜂)), unemployment benefit replacement rate (BRR(𝜑)), and employment protection (EPL(𝜍)).
covariance matrix of the VAR system in stacked form. The results are depicted in Figure 7. We
focus on output and employment only and provide further details in the Appendix. In Figure 7, we
measure volatility with the model-implied standard deviations of output and employment from the
baseline model and compare the volatilities for high (+2sd) and low (-2sd) values of the respective
LMIs.11 We observe that the LMIs have a potentially volatility-reducing effect. For instance, a
high UD attenuates output volatility by around 10% with a probability of 67%, while the effect
on employment is smaller in size (reduction of around 3% with a probability of 56%). In case of
the BRR, the effects are rather muted for both variables. While the output volatility tends to be
negatively affected by a higher BRR (the probability that the volatility declines is 56%), the opposite
applies to the employment volatility the probability that the employment volatility declines with
a higher BRR is only 35%. The largest effects emanate from the EPL. A more stringent EPL gives
rise to a drop in the volatilities of output and employment of around 25% (with a probability of
85%) and 30% (with a probability of 93%), respectively. Again, these results align well with the
theoretical predictions as shown in Table 1. Our theoretical model also suggests that EPL can
mitigate macroeconomic volatility to the largest extent in terms of output and employment. Most
importantly, the theoretical results in this context highlight that while the ability of the LMIs in
abating macroeconomic volatility crucially depends on the shocks sources, as we discuss in more
detail in A.5. To conclude, EPL reduces volatility more pronounced compared to the UD and BRR.
11 We abstain from reporting the implied variances when setting the respective LMI to its mean. Due to the standardiza-
tion of the data, the mean is zero and thus we only need half of the parameters for inspecting the mean. The decreased
number of involved parameters is another source of variance minimization which we do not want to exploit.
27
How do the LMIs shape the effects of shocks? The ability of the LMIs to dampen macroeco-
nomic volatility thus classifies them as important elements for the purpose of smoothing cyclical
fluctuations. At the same time, however, this raises a crucial question: How do the LMIs da