International
Labour
Organization
European
Union
International
Institute for
Labour Studies
Active labour
market policies,
search costs and
positive fiscal
multiplier
EC-IILS JOINT DISCUSSION PAPER SERIES No. 8
ACTIVE LABOUR MARKET POLICIES, SEARCH
COSTS AND POSITIVE FISCAL MULTIPLIER
ACTIVE LABOUR MARKET POLICIES, SEARCH
COSTS AND POSITIVE FISCAL MULTIPLIER
INTERNATIONAL LABOUR ORGANIZATION
INTERNATIONAL INSTITUTE FOR LABOUR STUDIES
Abstract
This paper is part of a series of discussion papers that have been prepared by the International Institute
for Labour Studies (IILS) within the framework of the joint project “Addressing European labour market
and social challenges for a sustainable globalization”, which has been carried out by the European
Commission (EC) and the International Labour Organization (ILO). The discussion paper series provides
background information and in-depth analysis for two concluding synthesis reports that summarize the
main findings of the project. This paper relates to first part of the project “Addressing the short- and
medium-term labour market and social challenges of the current economic and financial crisis” and the
concluding synthesis report “Building a sustainable job-rich recovery”.
This paper discusses the efficiency of fiscal intervention. In particular, this paper models a new
instrument for fiscal policy, active labour market policies, and identifies a new transmission channel for
fiscal policy, the labour market. In the model below, active labour market policies play a key role in
supporting new jobs, by easing the matching process between searching workers and firms with job
vacancies. For that purpose, the traditional matching function is extended to incorporate labour market
spending. The Cobb-Douglas matching function is now made of three elements: searching workers,
vacancies and active labour market spending. There are ambivalent transmission channels. Fiscal spending
crowds out private consumption and investment in line with the Ricardian properties associated with
intertemporal optimizing private agents. The increase in the interest rate following fiscal expansion also
affects negatively the discounted value of an additional match and reduces the incentive for firms to hire
an additional worker. Labour market spending however improves the functioning of the labour market
and increases the rate of matching.
TABLE OF CONTENTS
Main findings
1
1 Introduction
2
2 The model
Unemployment, Vacancies and Matching . . . .
Households . . . . . . . . . . . . . . . . . . . . .
Firms . . . . . . . . . . . . . . . . . . . . . . . .
Nash bargaining in the labor market and surplus
Government policy and resource constraint . . .
Equilibrium conditions . . . . . . . . . . . . . . .
3 Steady states and calibration
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4
4
6
8
10
13
14
15
4 Results
19
Baseline dynamic results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Optimal level of labour market spending and crowding-in of consumption . . 21
Nominal price rigidities and aggregate demand effects . . . . . . . . . . . . 22
5 Conclusion
24
A Appendix
26
Nested matching function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Nominal price rigidities and aggregate demand effects . . . . . . . . . . . . 27
i
ACTIVE LABOUR MARKET
POLICIES, SEARCH COSTS AND
POSITIVE FISCAL MULTIPLIER
Main findings
• This paper addresses the issue of the effectiveness of fiscal policies and the
form that fiscal policy should take to be optimal. For that purpose, a macroeconomic model is developed to better understand the channel trough which
certain forms of fiscal spending affect the labour market and the level of unemployment.
• The model enables discussion of two aspects associated with fiscal policy. The
first aspect concerns the form that fiscal policy may take: public consumption
versus active labour market policies. The second aspect deals with the nature
of the transmission mechanism: negative and positive supply side effects and
aggregate demand effects.
• There are four main results. First, in the case of flexible price, the model is
supply side and higher government consumption crowds out private spending. The decrease in investment and consumption over-balances the impact
of higher public spending on aggregate demand. The output multiplier is negative and equal to -0.08 after four semesters.
1
Active labour market policies, search costs and positive fiscal multiplier
• Second, on the contrary, when public spending takes the form of active labour
market policies, the positive impact of government spending on the labour market boosts firms’ production, generating positive fiscal multipliers. Active labour
market policies in this framework improves the matching between unemployed
and vacancies. The output multiplier is 0.31 on impact and 0.43 after one year,
while the employment multiplier is 0.11 on impact and 0.18 after a year.
• Third, there is an optimal level of labour market spending. For certain values
of the labour market spending to GDP ratio, the positive supply side effect
is so strong that it crowds in private spending and leads to an increase in
consumption and investment. In such a case, the multiplier is much larger
at 0.56 on impact for output (0.83 after one year) and at 0.2 on impact for
employment (0.31 after one year).
• Fourth, in the presence of price rigidities, the interaction between the labour
market effects and the aggregate demand effects produces a fiscal multiplier
close to 2 on impact. In an extension of the model, prices set by firms are
characterized by rigidities generating quantity adjustment in the goods market.
Following an increase in public spending, firms facing higher aggregate demand are not able to charge higher prices and therefore increase production.
There are aggregate demand effects associated with fiscal policy.
1
Introduction
The recent episodes of fiscal stimulus and fiscal consolidation raise the issue
of the efficiency of fiscal policy. Empirical estimations of the fiscal multiplier vary
across a wide range, with some estimations of a fiscal multiplier close to zero, close
but lower than one or larger than one. A related question is the form that fiscal intervention should take, for instance tax cuts; infrastructure investment; social transfers;
government consumption or labour market policies. The plurality of tools for fiscal
intervention make it more difficult to understand their impact and their transmission
2
Active labour market policies, search costs and positive fiscal multiplier
channels, whereas monetary policy for instance focuses mainly on one type of instrument, the short-term interest rate.
This paper discusses the efficiency of fiscal intervention. In particular, this paper
models a new instrument for fiscal policy, active labour market policies, and identifies a new transmission channel for fiscal policy, the labour market. In the model
below, active labour market policies play a key role in supporting new jobs, by easing the matching process between searching workers and firms with job vacancies.
For that purpose, the traditional matching function is extended to incorporate labour
market spending. The Cobb-Douglas matching function is now made of three elements: searching workers, vacancies and active labour market spending. There are
ambivalent transmission channels. Fiscal spending crowds out private consumption
and investment in line with the Ricardian properties associated with intertemporal
optimizing private agents. The increase in the interest rate following fiscal expansion also affects negatively the discounted value of an additional match and reduces
the incentive for firms to hire an additional worker. Labour market spending however
improves the functioning of the labour market and increases the rate of matching.
Various forms of matching functions are discussed. The benchmark matching
function has constant return to scale on the three inputs. Alternatives specifications consider the case where the matching function has constant return to scale
on searching workers and vacancies with government spending being nested with
one of the two other inputs. We also discuss the impact of the steady state value
of public spending on the size of the multiplier and on the outcome of the main
macroeconomic variables. Public spending crowds out private consumption through
the resource constraint. On the other hand, the positive supply-side effect associated with higher matching counter-balances the tendency of private consumption to
fall. Another extension discusses the size of the multiplier when active labour market
policies are combined with nominal price rigidities. Sticky prices produce a quantity
effect associated with increases in aggregate demand and a hiring effect through
the search and matching framework.
There is growing related literature. Monacelli et al. (2010) also focus on the transmission of fiscal spending through the labour market. They use a utility function à
la Shimer (2005) where the negative wealth effect associated with higher public
3
Active labour market policies, search costs and positive fiscal multiplier
spending enters negatively the surplus from an additional match. Workers lower
their reservation wage, which increases the incentive for firms to hire. We use instead the search and matching framework developed by Ravenna and Walsh (2008),
which does not generate similar mechanisms. We are therefore able to control for
the contribution of active labour market spending in improving employment.
Ganelli (2003) introduces non-separability between private and public consumption to discuss the size of the fiscal multiplier in an open economy framework. Baxter
and King (1993) consider the case of private firms using public investment as an input for production. Galí et al. (2007) use non-optimizing households to break the
Ricardian equivalence. Monacelli and Perotti (2008) combine a GHH utility function
with sticky prices to produce positive fiscal multipliers, while Ravn et al. (2006) make
use of deep habit formation and sticky price for a similar purpose. Lastly, FernándezVillaverde (2010) shows that fiscal multipliers are positive when public consumption
takes place in the presence of financial frictions.
The paper is organized as follow. Section 3 presents the model and the main assumptions. Section 4 discusses the steady states and the calibration, while section
5 details the properties of the model by use of numerical simulations.
2
The model
Unemployment, Vacancies and Matching
At the beginning of each period, the workforce L, which is normalized to 1, is divided
between employed workers nt and unemployed workers ut .
ut = 1 − nt
The number of workers currently employed at time t is equal to the existing stock
of employment at the beginning of the period ρnt−1 plus new matches mt . The rate
of job survival is a constant ρ:
4
Active labour market policies, search costs and positive fiscal multiplier
nt = ρnt−1 + mt
New matches mt depend positively on the number of searching workers st =
1 − ρnt−1 and the number of vacancies vt . The innovative feature of this model is to
introduce labour market spending gt into the matching function. The main motivation
is that active labour market policies aim at improving the matching between searching workers and vacancies. The matching function is similar to a Cobb-Douglas
production function, with σi (i = s, v, g) the elasticities of substitution between the different inputs. The parameter σm reflects the efficiency of the matching process. The
value of the different elasticities of substitution matters for the dynamic of the economy, as they influence the return to scale of the matching function. It is assumed
through out the paper that the matching function has constant return to scale. The
sum of the elasticities of substitution is equal to one σv = 1 − σs − σg .
σ
mt = σm stσs vtσv gt g
Two alternative specifications of the matching function will be considered against
this benchmark case further below.
σvFirst, labour market spending may be associated
σg
σs
with vacancies: mt = σm st gt vt
with σv = 1 − σs . Second, labour market spend
σs
σ
ing may be associated with unemployment: mt = σm gt g st
vtσv with σv = 1 − σs .
For convenience, we use the ratio θs,t = vstt to measure labour market tightness.
The ratio θg,t = gvtt measures labour market spending per vacancy. The probability of
firms to fill up a vacancies is denoted q (θs,t ; θg,t ) and is equal to the ratio of matches
over the number of vacancies:
qt =
mt
σ
−σs σg
= σm stσs vtσv −1 gt g = σm θs,t
θg,t
vt
(1)
Similarly, the probability of an unemployed workers to find a job is given by the
ratio of new matches over the number of searching workers.
5
Active labour market policies, search costs and positive fiscal multiplier
pt =
mt
σ
1−σs σg
= σm stσs −1 vtσv gt g = σm θs,t
θg,t
st
Both probabilities of firms to fill up a vacancies and of searching workers to find
a job are increasing with public spending. Given the above definitions, new matches
in the equation for nt can be expressed as the probability of filling a vacancy times
the existing number of vacancies:
(2)
nt = ρnt−1 + qt vt
Households
1−σ
t
Households maximize their expected intertemporal utility function U (ct ) = c1−σ
by
choosing the optimal level of consumption as well as the level of investment of firms
xt and the quantity of public bonds held bt . Employed workers receive real wage wt
and unemployed households receive a replacement income wu , which is a fraction of
the steady state value of wages. A large representative household with a continuum
of members of mass one inhabits the artificial economy. All household’s members
pool their incomes to be fully insured against unemployment. The intertemporal
budget constraint of a household member is given by:
ct + xt + bt ≤ wt nt + wu (1 − nt ) + rk,t kt−1 + rt−1 bt−1 − τt + Πt
(3)
where rk,t denotes the real rental rate of capital kt , rt the interest on public bonds, τt is
a lump-sum tax, Πt is the profits received from firms. The representative household
faces an employment constraint in the labor market, with mt being expressed as a
function of the probability of unemployed members to find a job and the fraction of
searching members.
nt = ρnt−1 + pt st
(4)
6
Active labour market policies, search costs and positive fiscal multiplier
Capital accumulation is subject to the following constraint:
kt = (1 − δ ) kt−1 + xt (1 − φt )
(5)
xt
− 1 denotes
where δ is a parameter for the rate of capital depreciation, φt ≡ φ xt−1
the capital adjustment costs that are proportional to the rate of change in investment,
0
with φ (0) = φ (0) = 0. The optimization problem that any member of the household
faces is given by:
+∞
max E0 ∑ β t U (ct )
ct ,nt .xt ,kt
t=0
subject to (3), (4) and (5). The agent’s optimization problems stated above focus
only on interior solutions, that is all the quantities are supposed to be strictly positive.
The representative household’s optimization problem can be restated with a bellman
equation as follows:
H (nt−1 , kt−1 , bt−1 , xt−1 ) =
max
ct ,nt ,xt ,kt ,bt
!
ct1−σ
+ β Et {H (nt , kt , bt , xt )}
1−σ
(6)
subject to(3), (4) and (5). The Lagrangian of the household’s problem can be written
as follows
Lt
h
ct1−σ
=
+ β Et {H (nt , kt , bt )} +
1−σ
+λt wt nt + wu (1 − nt ) + rk,t kt−1 + rt−1 bt−1 − τt + Πt − ct − xt − bt +
+λt ϕt ((1 − δ ) kt−1 + xt (1 − φt ) − kt ) + µt (nt − ρnt−1 − pt (1 − ρnt−1 ))
The first order condition for consumption links the marginal utility of wealth with the
marginal utility of consumption:
λt =
1
ctσ
(7)
7
Active labour market policies, search costs and positive fiscal multiplier
where λt is Lagrange multiplier associated with the budget constraint (3). The
first order conditions for investment and capital read:
(
)
2
0
xt 0
xt+1
ϕt 1 − φt +
φt
= 1 − β Et ϕt+1 Λt,t+1
φt+1
xt−1
xt
(8)
ϕt = β Et Λt,t+1 rk,t+1 + ϕt+1 (1 − δ )
(9)
0
with Λt,t+1 is defined as λλt+1
. ϕt is the shadow value of a unit of investment and φt
t
xt
the derivative of the capital cost function with respect to its argument xt−1
− 1. The
first order condition with respect to public bonds can be expressed as follow:
1
= βt Et
rt
λt+1
λt
(10)
We derive Hn,t the representative household’s marginal value of having one of
its member hired in the labor market rather than unemployed, which enters further
below the Nash wage bargaining. Hn,t increases with additional income gains expressed in utility from being employed rather than unemployed. Hn,t also increases
with the expected utility of being still employed in the next period.
Hn,t = λt (wt − wu ) + β ρEt Hn,t+1 (1 − pt+1 )
(11)
Firms
The economy is populated by a large number of identical firms of mass one, which
operate in a competitive goods market. In order to produce the final goods, yt , firms
use a constant return to scale Cobb-Douglas technology with two inputs labor nt and
capital kt−1 of the form:
yt = f (kt−1 , nt ) = (kt−1 )ζ (nt )1−ζ
(12)
The timing of events in the formal labor market is the same as in MPT. The representative firm posts vt vacancies in the beginning of the period in order to increase
its quantity of labor input, nt . We assume that it is costly for the representative firm
8
Active labour market policies, search costs and positive fiscal multiplier
to post a vacancy. Specifically, the vacancy cost function, C (vt ), is assumed to be
linear in the number of posted vacancies: C (vt ) = κvt , where κ > 0 is a vacancy cost
parameter. mt new matches come out of the searching mechanism. In the current
period, a fraction 1 − ρ of jobs disappears. Workers that have lost their jobs have
to wait until the next period to look for new jobs. Then, firms use the new matches
— as well as of the other inputs — to produce. Note that the new matches cannot
be broken until the next period. Thus, formally, from the firms side, the employment
evolves over time following equation 2: nt = ρnt−1 + qt vt . Firms maximize the expected flows of profits πt with respect to employment and capital and subject to the
production function and the law of motion of employment:
+∞
max Et
kt−1 ,nt
∑ β j Λt,t+ j Πt+ j
j=0
subject to (12) and (2). Profit,Πt is made of the value of output minus labour costs,
the cost of renting capital and the costs of vacancies:
Πt ≡ yt − wt nt − rk,t kt−1 − κvt
(13)
The representative firm’s optimization problem can be restated with a bellman
equation:
F (nt−1 , kt−1 ) =
max (kt−1 )ζ (nt )1−ζ − wt nt − rk,t kt−1 − κvt + β Et Λt,t+1 F (nt , kt )(14)
nt ,kt−1
f
subject to (2). The related Lagrangian of the firm’s optimization problem is Lt :
Lt
f
= (kt−1 )ζ (nt )1−ζ − wt nt − rk,t kt−1 − κvt + β Et Λt,t+1 F (nt , kt ) + ψt [nt − ρnt−1 − qt vt ]
The first order conditions of the firm’s optimization problem with respect to kt−1
equates the productivity marginal of capital with the rental rate of capital:
9
Active labour market policies, search costs and positive fiscal multiplier
rk,t = ζ
yt
(15)
kt−1
Firms first choose the optimal quantity of vacancies −ψt = qκt . Then maximizing
profits with respect to employment and making use of the envelope condition, we
get the equilibrium condition for employment:
κ
κ
= at − wt + β ρEt Λt,t+1
qt
qt+1
(16)
where at ≡ (1 − ζ ) nytt is the marginal productivity of labour. In equilibrium, the
marginal cost of hiring a workers is equal to its marginal benefits. The latter is the
difference between the marginal productivity of an additional jobs and its wage costs
at time t, plus savings from not having to hire an additional workers at time t + 1.
It is necessary to define the value for a firms of an additional workers Fn,t , which
enters the wage bargaining in the following section. Using the employment condition
for employment and making use of the equilibrium condition for posting vacancies,
we get that Fn,t = qκt . Plugging this definition into equation 16 yields:
Fn,t = at − wt + β ρEt Λt,t+1 Fn,t+1
(17)
Nash bargaining in the labor market and surplus
Each period, the real wage in the formal labor market is determined through a generalized Nash-bargaining process between the representative firm and the marginal
worker that was matched with the firm. Formally,
n
o
wt ≡ max (Hn,t )η (Fn,t )1−η ,
0<η <1
(18)
where η denotes the bargaining power of the workers and where the expressions of
Hn,t and Fn,t are given by (11) and (17), respectively. The first order condition of the
Nash-bargaining process is given by
10
Active labour market policies, search costs and positive fiscal multiplier
ηFn,t = (1 − η)
Hn,t
λt
(19)
H
where λn,tt represents the household’s marginal value of an additional worker expressed in units of consumption goods. The total surplus from a marginal match in
the labor market (or surplus for short), denoted by Sn,t , is defined as the sum of the
firm’s marginal value of an additional hiring a worker and the household’s marginal
H
value of an additional worker defined in units of consumption goods: Sn,t ≡ Fn,t + λn,tt .
Straightforwardly, one can show that the Nash-bargaining process leads the houseH
hold and the firm to share that surplus: Fn,t = (1 − η) Sn,t and λn,tt = ηSn,t . In addition,
the surplus Sn,t can also be measured by the size of the gap between firm’s reservation wage wt and the household’s reservation wage wt :
Sn,t = w̄t − wt
(20)
The household’s reservation wage wt defines the minimum value of the real wage for
which the household is willing to work in the labour market. In turn, firm’s reservation
wage wt defines the maximum value of the real wage that firms are willing to pay a
worker. The household’s marginal value of an additional worker expressed in units
H
of consumption goods becomes zero λn,tt = 0 if the real wage is set equal to the
household’s reservation wage wt = wt . In this case, equation (11) becomes:
u
wt = w − β ρEt
Hn,t+1
Λt,t+1
(1 − pt+1 )
λt+1
(21)
The household’s reservation wage, wt , increases with the replacement wage, wu . In
turn, wt decreases with the household’s expected future continuation value of the
H
match, β Et Λt,t+1 λn,t+1 ρ (1 − pt+1 ). Similarly, the firm’s marginal value of an additional
t+1
hiring of a worker is zero Fn,t = 0, if the real wage is set equal to the firm’s reservation
wage, wt = w̄t . In this case, equation (17) becomes:
11
Active labour market policies, search costs and positive fiscal multiplier
w̄t = at + β ρEt Λt,t+1 Fn,t+1
(22)
Firm’s reservation wage, w̄t , increases with the current marginal productivity of labor
and with the firm’s expected future continuation value of the match. This last element reflects that turn over is costly for firms. The bargained real wage, wt , is then
obtained by taking the average sum of the two reservation wages, the weights being
given by the bargaining powers of firms and households:
wt = η w̄t + (1 − η) wt
(23)
Equation 23 can be rearrange by using equations 21, 22 together with Fn,t =
and
Hn,t
λt
=
κ
qt
η κ
1−η qt :
pt+1
wt = ηat + (1 − η) w + ηβ ρκEt Λt,t+1
qt+1
u
(24)
The real wage is a weighted sum of the marginal productivity of labour and the
replacement income at time t and the the expected future state of the labour market
at time t + 1. The weights are made of the bargaining power of firms and workers.
We can also compute a recursive expression for the surplus, Sn,t , by plugging (21)
and (22) into (20) and by using the relations between the surplus, Sn,t , and the
marginal values of an additional labor, Hn,t and Fn,t :
Sn,t = (at − wu ) + β ρEt Λt,t+1 Sn,t+1 (1 − η pt+1 )
(25)
The surplus that arises from the current match is determined by two terms (appearing in the right-hand side of equation (25)). Sn,t increases with the gap between
the marginal productivity of labor and the replacement wage wu . The current surplus also increases with the expected next period surplus, if the current match is not
broken in the following period, β ρEt Λt,t+1 Sn,t+1 , net of the expected next period
household’s marginal value of an additional worker (expressed in units of consumption goods), derived from a new
occur in the following period,
o
n match that would
Hn,t+1
.
β ηρEt Λt,t+1 pt+1 Sn,t+1 = β ρEt Λt,t+1 pt+1 λ
t+1
12
Active labour market policies, search costs and positive fiscal multiplier
Recall that a fraction 1 − η of the surplus goes to firms: Fn,t = (1 − η) Sn,t . Combining the latter with equations 1 and taking into account that Fn,t = qκt , one gets:
κ
= (1 − η) Sn,t
qt
(26)
By making use of equations (25) and (26), one can get a recursive equation
reflecting the dynamic of employment:
κ
κ
u
= (1 − η) (at − w ) + β ρEt Λt,t+1
(1 − η pt+1 )
qt
qt+1
(27)
When either the vacancy posting cost parameter becomes close to zero,κ → 0, or
the matching efficiency parameter strongly improves, αm → +∞, the marginal productivity of labor is equal to the replacement wage in the equilibrium.
This expression slightly differs from the corresponding equation in MPT to the
extent that the marginal value of non-work activities is replaced by wu . This difference comes from the choice of utility function. In this model, employment does
not enter the utility function negatively, while MPT uses a utility function similar to
that of Shimer (2005). In MPT, the lower value of non-work activities following a
spending shock reduces the reservation wage of workers. The incentive for firm to
hire increases and lead to a positive fiscal multiplier. The absence of this transmission channel between fiscal policy and employment in this model enables to control
that public spending affects employment directly through the new formulation of the
matching function.
Government policy and resource constraint
The government issue bonds bt to finance the difference between tax income and
spending. Public debt increases with the last period stock of debt and the associated
interest payments rt−1 bt−1 and with the primary deficit dt . The primary deficit is the
difference between tax income and labour market spending. Taxes are lump sum in
this simple version of the model. Public spending are made of active labour market
13
Active labour market policies, search costs and positive fiscal multiplier
spending gt as well as unemployment benefits wu (1 − nt ).
bt = rt−1 bt−1 + dt
dt = gt + wu (1 − nt ) − τt
Public consumption gt follows an auto-regressive process. Taxes τt also follow
an auto-regressive process and adjust as well to the level of public debt.
gt = (1 − ρg ) g + ρg gt−1 + εI,t
τt = (1 − ρτ ) τ + ρτ τt−1 + τb (bt−1 − b)
The resource constraint states that aggregate demand equals the sum of private
consumption, investment, search costs and labour market spending. In the absence of nominal price stickiness, yt is determined by the supply side. The resource
constraint implies that labour market spending crowds out private consumption and
investment.
yt = ct + xt + κvt + gt
Equilibrium conditions
The equilibrium condition of the model are as follow:
−σs
qt = σm θs,t
θg,tg
σ
1−σs
pt = σm θs,t
θg,tg
vt
θs,t =
1 − ρnt−1
gt
θg,t =
vt
σ
14
Active labour market policies, search costs and positive fiscal multiplier
kt = (1 − δ ) kt−1 + xt
ζ
ηk
1−
2
xt
xt−1
2 !
−1
1−ζ
yt = kt−1 nt
nt = ρnt−1 + qt vt
1
λt = σ
c
"t
ϕt =
ϕt =
rk,t =
at =
yt =
wt =
κ σs −σg
θ θ
=
σm s,t g,t
bt =
!#
λt+1 xt+1 2
xt+1
−1
1 − β Et ϕt+1
ηk
λt
xt
xt
"
2
!#
ηk
xt
xt
xt
/ 1−
−1 +
ηk
−1
2 xt−1
xt−1
xt−1
λt+1 β Et
rk,t+1 + ϕt+1 (1 − δ )
λt
yt
ζ
kt−1
yt
(1 − ζ )
nt
ct + xt + κvt + gt
λt+1
u
ηat + (1 − η) w + ηβ κEt
θs,t+1
λt
λt+1 κ
−σg
σs
u
(1 − η pt+1 ) θs,t+1 θg,t+1
(1 − η) (at − w ) + β ρEt
λt σm
rt−1 bt−1 + dt
dt = gt + wu (1 − nt ) − τt
gt = (1 − ρg ) g + ρg gt−1 + εI,t
τt = (1 − ρτ ) τ + ρτ τt−1 + τb (bt−1 − b)
λt+1
1
= β Et
rt
λt
3
Steady states and calibration
The model contains 16 parameters, gathered in the set
15
Active labour market policies, search costs and positive fiscal multiplier
Θ ≡ β , δ , ζ , ηk , ρg , ρ, σg σs , η, σ , σm , κ, αu , ρτ , ρb , wu
and 20 variables, which steady state levels are gathered in the set
∆ ≡ y, c, x, n, k, w, rk , v, p, q, θs , θg , a, λ , ϕ, g, b, r, d, τt
In order to assign a value to each parameter and steady state variable of the
model, we solve a system formed by the deterministic steady-state expressions of
19 equilibrium equations (20 equations minus auto-correlation of the public spending
shock) and 17 additional restrictions. The deterministic steady state expressions of
the equilibrium equations are:
ϕ = 1
rk = 1/β − 1 − δ
r = 1/β
θs = 0.5
θg = 0.45
p = 0.45
σm =
p
θs1−σs θg g
σ
q = σm θs−σs θg g
θs (1 − ρ)
v =
1 − ρ + ρqθs
qv
n =
1−ρ
y
rk
=
k
ζ
y 1
ζ −1
k = n
k
y
y =
k
k
σ
16
Active labour market policies, search costs and positive fiscal multiplier
x = δk
a = (1 − ζ )
y
n
At this stage, we get the steady state values of wu and κ by solving the equations
24 and 27. We then have:
w = αu wu
v
g =
θg
c = y − x − κv − g
1
λ =
c
b = 0.6y
τ = g + wu (1 − n) − (1 − r) b
d = b/ (1 − r)
The 17 additional restrictions are put on a subset of steady state variable levels,
∆ ≡ p, θs , θg , on a subset of the model parameters
Θ
≡
β
,
δ
,
ζ
,
η
,
ρ
,
ρ,
σ
σ
,
η,
σ
,
α
,
ρ
,
ρ
,
g
g
s
u
τ
k
b
n o
b
and finally on a steady state ratio, Γ ≡ y . We assume that the time unit is a
semester, similarly to Ravenna and Walsh (2008). The calibration of ∆, Θ, and Γ
which is based on postwar U.S. data, is discussed below.
The calibration follows Ravenna and Walsh (2008) for the parameters of the
labour market. The calibration of the discount factor is set so that the annual real
interest rate is approximately 4 percent on average. The capital is assumed to depreciate at the rate of 10 percent on an annual basis. Around one third of the economy’s income goes to capital owners. Specifically, the discount factor, the capital
depreciation rate and the capital share in the production function are set to β = 0.99,
δ = 0.025, and ζ = 31 . These values are standard in the business cycle literature.
The parameter for the adjustment of capital cost is set to ηk = 0 such that we ignore
the cost of capital adjustment in a first step. The survival rate in the labor market is
set to ρ = 1 − 0.1. The elasticity of matches to searching workers parameter is set
to σs = 0.6, in line with existing estimations ranging between 0.5 and 0.7 in the lit17
Active labour market policies, search costs and positive fiscal multiplier
Table 1: Parameters and main steady state values
Capital depreciation rate in the production function
δ
0.025
Discount factor
β
0.99
Capital share
ζ
1/3
Capital adjustment cost parameter
ηk
0
ρg , ρτ
0.9
Survival rate
ρ
0.9
Elasticity of matches to unemployment
σs
0.6
Elasticity of matches to public spending
σg
0.05
Bargaining power
η
0.6
Probability of finding a job
p
0.45
Labor market tightness
θs
0.5
Spending per vacancy
θg
0.45
1.2%
Consumption to GDP ratio
g
y
b
y
c
y
Unemployment rate
u
10%
Government auto regressive parameters
Government spending share in output
Debt to GDP ratio
60%
70%
erature. The bargaining power between firms and households is symmetric η = 0.6
to meet the Hosios condition for efficiency. We set p = 0.45 to meet the estimates
of the job finding rates and θs = 0.5 to meet the measures of US vacancies Shimer
(2005). We calibrate θg to 0.45 such that the spending to GDP ratio corresponds to
1.2% the average labour market spending to GDP ratio in OECD countries1 . The
debt to GDP ratio is also fixed at 60% and the auto-regressive parameter of the
government spending and taxes stochastic process are set to ρg = ρτ = 0.9. Table
1 below summarized the restrictions on the model parameters and on the model
steady states.
1 We
use the active labour market spending data from the social expenditure database published
by the OECD
18
Active labour market policies, search costs and positive fiscal multiplier
Figure 1: Labour market policies vs government consumptions
Output
Employment
Wages
0.6
0.2
0.15
0.4
0.1
0.1
0.2
0
0.05
0
-0.2
0
20
40
-0.05
Consumption
0
6
-0.1
4
-0.2
2
-0.3
0
-0.4
4
-0.1
0
0
20
40
-2
0
20
40
-3
x 10Interest rate
-0.2
0
20
40
Spendings
1.5
1
0.5
0
20
40
0
0
20
40
Results
This section rely on numerical simulations to investigate the properties of the
model. We study in particular the dynamic of the economy following a positive shock
on public spending and for different configurations of the economy.
Baseline dynamic results
Figure 1 displays the dynamic of the economy following a positive shocks on labour
market policy spending. For the sake of comparison, the case corresponding to an
increase in government spending (not in labour market spending, σg = 0) is also
represented on the figure (broken line). An increase in government consumption
produces the usual crowding out of private consumption and output in line with the
19
Active labour market policies, search costs and positive fiscal multiplier
properties of a Ricardian economy.
Contrastingly, an increase in labour market spending produces a positive output
multiplier effect and an increase in employment. The output multiplier is positive and
smaller to one. It is 0.31 on impact and 0.43 after one year, in contrast with the Ricardian case, which exhibits a negative output multiplier of -0.08 after one year. The
employment multiplier is positive too: 0.11 on impact and 0.18 after four semesters.
Positive effects on employment and output are related to the improved efficiency of
the labour markets induced by labour market spending. Labour market spending increases the number of matches and the overall level of employment. The Ricardian
effect through which higher government spending crowds out private consumption
is still at work as consumption drops on impact at -0.11. This experiment however
shows that active labour market policies over balance the crowding out of private
consumption through an increased efficiency of the labour market. This result is
similar with the baseline result of Monacelli et al. (2010) except that the rise in employment is not linked to the specificities of the wage bargaining. In Monacelli et al.
(2010), the positive multiplier effect is related to the crowding out of consumption,
which reduces the dis-utility of work activities and lead workers to accept a lower
wage.
In the appendix, it is shown that the positive effect of output on the fiscal multiplier holds true for different specification of the matching function. In particular, two
cases are taken into consideration. In the
labour market spending are
firstcase,
σs
σg
σv
associated with unemployment: mt = σm gt st
vt with σv = 1 − σs . In the second case, labour market
spending
are associated with vacancies in the matching
σv
σg
σs
function: mt = σm st gt vt
with σv = 1 − σs . These two sub-cases capture the
idea that labour market spending may target specifically either searching workers or
firms. Using the same set of parameters, the output and employment multipliers are
both positive. They are larger in the case of spending nested with unemployed workers given that σs is equal to 0.6. There are both however smaller than in the case of
constant return to scale as the elasticities of matching to spending are smaller (see
Figure 4).
20
Active labour market policies, search costs and positive fiscal multiplier
Figure 2: Crowding in of private consumption
Output
Employment
0.9
Consumption
0.35
0.8
0.07
0.06
0.3
0.05
0.7
0.25
0.6
0.04
0.5
0.2
0.03
0.4
0.15
0.02
0.3
0.01
0.1
0.2
0
0.05
0.1
0
0
20
40
0
-0.01
0
20
40
-0.02
0
20
40
Optimal level of labour market spending and crowding-in of consumption
Figure 2 displays the dynamic of the main macroeconomic variables following a positive shock on labour market spending when the steady state level of active labour
market spending to GDP is decreased from 1.2% to 0.7%, which correspond to the
value of this ratio for the USA2 .
The fiscal multiplier is now larger 0.56 on impact and 0.83 after one year. The
employment multiplier is larger too at 0.2 on impact and 0.31 after one year. Furthermore, consumption is now responding positively to public spending. Despite a
negative reaction on impact, consumption turns positive after three semesters. It
2 σ is
g
constant at 0.05 and θg is decreased to 0.25 from 0.45.
21
Active labour market policies, search costs and positive fiscal multiplier
seems that the increase in output generated by higher employment crowds in private consumption. The positive impact of public spending on employment boosts
output through a supply side effect. The positive impact on consumption that follows
over balances the negative impact of higher public spending on private consumption. There is therefore an optimal level of active labour market spending to GDP,
for which the efficiency of fiscal multiplier is the highest. This feedback channel
stands in contrast with existing models, which produce an increase in consumption
either by assuming non separability between employment (or hours worked) and
consumption or by relying on a wealth effect as in the perpetual youth model.
Nominal price rigidities and aggregate demand effects
Nominal price rigidities are central when discussing fiscal policy to the extent that
they generate quantity adjustment. Following fiscal policy, firms respond to the surge
in aggregate demand by raising prices. In the presence of price rigidities, firms
must also increase output to meet excess demand. Ravn et al. (2006) for instance
use price stickiness (together with deep habit formation) to produce a positive fiscal
multiplier. Adding price rigidities should trigger an increase in private consumption
given that firms increase labour inputs and that the real wage increases. Nominal
price rigidities also limit the crowding out of private consumption. Nominal price
rigidities also impact the incentive of firms to hire. The markup now enters the
marginal productivity of labour in the surplus equation from an additional match
(see equation 27). The fall in the markup raises the marginal productivity of labour
and contributes to the improvement of the labour market alongside labour market
policies. The resulting effect should be a larger multiplier effect.
We follow Ravenna and Walsh (2008) to model price rigidities3 . The program of
the firms described in the previous part of the model now corresponds to the intermediate goods producers. Intermediate goods producers face search costs in the
labour market but sell their goods in a competitive market. Intermediate goods are
then combined to produce a final good, which is sold on a non-competitive market.
Introducing prices requires to modify the equilibrium condition presented in section
3 See
also Trigari (2006) and Trigari (2009)
22
Active labour market policies, search costs and positive fiscal multiplier
Figure 3: Aggregate demand effects
Output
Employment
2
1.8
Consumption
0.8
0.04
0.7
0.035
0.6
0.03
0.5
0.025
0.4
0.02
0.3
0.015
0.2
0.01
0.1
0.005
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
20
40
0
0
20
40
0
0
20
40
23
Active labour market policies, search costs and positive fiscal multiplier
. The new set of equation is presented in the appendix . The probability that firms
cannot adjust their prices to the perfect competition prices is set at ω = 0.75. The
price elasticity in the demand function for retail goods is conventional and equal to
ε = 10. The model is closed by specifying monetary policy (see equation 28).
rtn
=
rn
n
rt−1
rn
ρm Et {πt+1 }
π
φπ (1−ρm ) yt
yt−1
φy (1−ρm )
(28)
The Central Bank adjusts the interest rate to the forward looking inflation at a
speed φπ = 1.1, while the sensitivity of the interest rate to the output gap is φy = 0.675.
ρm is the coefficient for interest rate rigidities and is equal to 0.9. The main result
is that the fiscal multiplier is now much larger and almost equal to 2 on impact.
Accordingly, the employment multiplier is also larger at 0.8. Consumption increases
and is hump-shaped. Consumption reaches a peak of 0.035 after period 17.
5
Conclusion
In this paper, we have shown that fiscal policy does not necessarily generate
negative fiscal multiplier. We have shown as well that fiscal multiplier can take place
in a supply side model. Although public spending crowds out private consumption
through the equation for resource constraint, active labor market policy spending
improves the functioning of the labor market. The increase in the matching rate that
follows improves total employment. The increase in labor input raises production in
return.
A shortcoming is that output increases but that private consumption is still crowded
out by public spending in the baseline case. We then show that for certain set of
parameters, the increase in output is so large that it overbalances the crowding out
of private consumption. In such a case, consumption and investment increases too
following an increase in public spending. Lastly, we show that the size of the fiscal
multiplier is very large (close to 2) when under-utilization of productive capacities is
24
Active labour market policies, search costs and positive fiscal multiplier
introduced through nominal price rigidities. It points that fiscal policy is more efficient
in period of under-employment of resources.
25
Active labour market policies, search costs and positive fiscal multiplier
A
Appendix
Nested matching function
This appendix discusses the impact on the fiscal multiplier of different types of
matching function. The baseline matching function has constant return to scale
in st , vt and gt with σs + σv + σg = 1. We here briefly discuss the impact of two alternative specification. In a first case, spending are nested with searching workers
and captures the idea that active labour market spending may be directed towards
unemployed:
σs
σ
mt = σm gt g st
vt1−σs
with σv = 1 − σs . The matching function has constant return on unemployment
and vacancies and decreasing return on active labour market policies. For convenience, we use the ratio θs,t = vstt to measure labour market tightness:
mt
σ σ
−σs σg σs
= σm gt g s stσs vt−σs = σm θs,t
gt
vt
mt
σ σ
1−σs σg σs
= σm gt g s stσs −1 vt1−σs = σm θs,t
=
gt
st
qt =
pt
In a second case, spending are nested with vacancies to capture the idea that
labour market policies also target firms:
1−σs
σ
mt = σm stσs gt g vt
with σv = 1 − σs . The matching function has constant return on unemployment
and vacancies and decreasing return on active labour market policies. For conve26
Active labour market policies, search costs and positive fiscal multiplier
nience, we use the ratio θs,t =
vt
st
to measure labour market tightness:
mt
σ (1−σs ) σs −σs
−σs σg (1−σs )
= σm gt g
st vt = σm θs,t
gt
vt
mt
σ (1−σs ) σs −1 1−σs
1−σs σg (1−σs )
= σm gt g
st
vt
= σm θs,t
gt
=
st
qt =
pt
The results are displayed in Figure4 with the solid line being associated with
active labour market spending nested with searching workers. Note that the set of
parameters used in both cases is the same. The output and employment multiplier
are both positive but they are larger in the case of spending nested with unemployed
workers. There are both however smaller than in the case of constant return to scale
as the elasticities of matching to spending are smaller.
Nominal price rigidities and aggregate demand effects
Introducing nominal price rigidities modifies the system of equations of the model,
which now appears as follow:
−σs
qt = σm θs,t
θg,tg
σ
1−σs
pt = σm θs,t
θg,tg
vt
θs,t =
1 − ρnt−1
gt
θg,t =
vt
σ
kt = (1 − δ ) kt−1 + xt
ηk
1−
2
xt
xt−1
2 !
−1
1−ζ
ytw = kt−1 nt
ζ
nt = ρnt−1 + qt vt
1
λt = σ
ct
27
Active labour market policies, search costs and positive fiscal multiplier
Figure 4: Spending shocks - nested matching function
Output
Employment
0.25
0.1
0.2
0.08
0.15
0.06
0.1
0.04
0.05
0.02
0
0
-0.05
-0.1
0
10
20
30
40
-0.02
0
10
20
30
40
28
Active labour market policies, search costs and positive fiscal multiplier
!#
λt+1 xt+1 2
xt+1
1 − β Et ϕt+1
−1
ηk
λt
xt
xt
"
2
!#
ηk
xt
xt
xt
/ 1−
−1 +
ηk
−1
2 xt−1
xt−1
xt−1
λt+1 β Et
rk,t+1 + ϕt+1 (1 − δ )
λt
yw
ζ mct t
kt−1
yw
(1 − ζ ) mct t
nt
λt+1
u
ηat + (1 − η) w + ηβ κEt
θs,t+1
λt
λt+1 κ
−σg
σs
u
(1 − η pt+1 ) θs,t+1 θg,t+1
(1 − η) (at − w ) + β ρEt
λt σm
ct + xt + κvt + gt
"
ϕt =
ϕt =
rk,t =
at =
wt =
κ σs −σg
θ θ
=
σm s,t g,t
yt =
ytw = st yt
st = (1 − ω) p̃t −ε + ωπtε st−1
rt−1
bt−1 + dt
bt =
πt
dt = gt + wu (1 − nt ) − τt
gt = (1 − ρg ) g + ρg gt−1 + εI,t
τt = (1 − ρτ ) τ + ρτ τt−1 + τb (bt−1 − b)
πt+1
λt+1
= β Et
rt
λt
ε
−
1
ft1 =
ft2
ε
!
−1−ε
λ
p̃
t
t+1
1
ft1 = p̃t−1−ε yt mct + β ωEt
πε
ft+1
λt t+1 p̃t+1
!
−ε
λ
p̃
t
t+1
2
ft2 = p̃t−ε yt + β ωEt
π ε−1
ft+1
λt t+1 p̃t+1
r ρm E π φπ (1−ρm ) y φy (1−ρm )
rt
t t+1
t
t−1
=
r
r
π
yt−1
1 = ωπtε−1 + (1 − ω) p̃t1−ε
29
Active labour market policies, search costs and positive fiscal multiplier
References
Baxter, Marianne; King, Robert G. 1993. "Fiscal Policy in General Equilibrium", in
American Economic Review, Vol. 83, pp. 315–334.
Fernández-Villaverde, Jesús. 2010. "Fiscal Policy in a Model With Financial Frictions", in American Economic Review: Papers & Proceedings, Vol. 100, pp. 35–
40.
Galí, J.; López-Salido, J. D.; Vallés, J. 2007. "Understanding the effects of government spending on consumption", in Journal of the European Economic Association, Vol. 5, No. 1, pp. 227–270.
Ganelli, G. 2003. "Useful government spending, direct crowdingout and fiscal policy
interdependence", in Journal of International Money and Finance, Vol. 22, pp.
87–103.
Monacelli, T.; Perotti, R.; Trigari, A. 2010. "Unemployment fiscal multiplier", in Journal of Monetary Economics, Vol. ., pp. 1–52. mimeo.
Monacelli, Tommaso; Perotti, Roberto. 2008. "Fiscal Policy, Wealth Effects and
Markups", in NBER Working Paper, Vol. 14584, pp. 1–56.
Ravenna, F.; Walsh, C. E. 2008. "Vacancies, unemployment, and the Phillips curve",
in European Economic Review, Vol. 52, No. 8, pp. 1494–1521.
Ravn, Morten; Schmitt-Grohé, Stephanie; Uribe, Martin. 2006. "Deep Habits", in
Review of Economic Studies, Vol. 73, pp. 195–218.
Shimer, Robert. 2005. "The Cyclical Behavior of Equilibrium Unemployment and
Vacancies", in American Economic Review, Vol. 95(1), pp. 25–49.
Trigari, A. 2009. "Equilibrium unemployment, job flows and inflation dynamics", in
Journal of Money, Credit and Banking, Vol. 41, No. 1, pp. 1–.
30
Active labour market policies, search costs and positive fiscal multiplier
Trigari, Antonella. 2006. "The Role of Search Frictions and Bargaining for Inflation
Dynamics", in WP University Bocconi, Vol. 304, pp. 1–29.
31