The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
1
2022
https://doi.org/10.21033/ep-2022-1
Quantitative effects of temporary
employment contracts in Spain
Fernando Alvarez and Marcelo Veracierto
Introduction and summary
1
In many countries, employers are forced to make large severance payments to workers when their employment is terminated for reasons other than worker misconduct.1 Actually, it is not uncommon for severance
payments to exceed 20 days of pay per year worked, with a cap of one year of wages (for example, in
Argentina, Italy, and Spain). In addition, employers often face substantial legal costs when they terminate
their workers. Economic theory indicates that these firing costs have large effects on the hiring and firing
decisions of firms. Not surprisingly, in an effort to economize their immediate costs, firms respond to the
firing costs by reducing their firing rates. However, because they are afraid of the costs that they will have
to face in the future, firms also respond by reducing their hiring rates. The net effects on their employment
levels depend on whether the decrease in firing rates exceeds the decrease in hiring rates. While their effects
on average employment are ambiguous, firing costs generate a clear misallocation of labor across firms.
The reason is that firms that receive positive shocks do not expand as much as they should and firms that
receive negative shocks do not contract as much as they should. Perhaps because of this misallocation of
resources across firms, governments have introduced legislation attempting to improve the efficiency of
their countries’ labor markets. One common way that governments have done this is through the introduction of temporary employment contracts of fixed lengths. These temporary contracts effectively provide a
period of time during which workers can be fired at no costs. If a temporary worker is retained after their
temporary contract ends, they become a permanent worker subject to regular firing costs. The purpose of
this article is to provide a quantitative assessment of temporary contracts. In particular, we are interested
in determining how effectively temporary contracts of observed length bring the economy close to laissez-faire
outcomes (that is, to the economic outcomes that would be obtained under zero firing costs to firms).
In order to do this, we consider the equilibrium search model of Alvarez and Veracierto (2012), which is
an undirected search version of the Lucas and Prescott (1974) model with an out-of-the-labor-force state.
The economy comprises a continuum of islands and a home sector. Each of the islands has a unit interval
of identical firms that produce output with a decreasing returns to scale production function that uses labor
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
as its sole input. Islands are subject to idiosyncratic productivity shocks that follow a Markov process over
time. Agents value consumption and home production, and start every period of time either at home or at
one of the production islands in the economy.2 If an agent starts a period of time at home, they can choose
either to stay at home during the current period or to search. Staying at home allows them to enjoy home
production during the current period, but makes them start the following period at home again. Searching
precludes the agent from obtaining any home production during the current period, but allows them to randomly
arrive at one of the islands at the beginning of the following period (search is undirected). If an agent starts a
period of time at one of the islands, they can choose either to stay on the island (and work), to randomly
search for a new island, or to go home. Only going home and staying there provides home production to
the agent. The amount of home production obtained by staying at home is the same for all individuals.
In this framework we introduce a government policy that taxes firms for reducing their employment of
workers with J or more periods of tenure on the island.3 The firing tax on these permanent workers is equal
to τ. However, firms do not face any firing tax for reducing their employment of workers with tenure of
less than J periods. All the firing taxes collected by the government are rebated as lump-sum transfers to
the representative household. The assumption that firing taxes apply to the worker’s tenure on the island
(and not to the worker’s tenure in a firm) allows us to specify a standard competitive equilibrium.4 In
particular, we assume that there are spot labor markets for each tenure level (thus, potentially, workers of
different tenure have different wage rates). Given their previous-period employment of permanent workers,
firms maximize the present discounted value of their profits (which are given by output net of wages and
any firing taxes incurred). Because we assume that workers are fully insured, they seek to maximize the
present expected discounted values of wages and home production.
2
We use our model to explore to what extent fixed-term contracts of different lengths add flexibility to the
labor market.5 Notice that introducing fixed-term contracts of sufficiently large J is equivalent to eliminating
all the firing taxes (since workers never gain permanent status). Thus, we address the question of how much
labor market flexibility gets generated by computing how much of the gap between the firing-tax case (J = 1
and τ > 0) and the laissez-faire case (either J = ∞ or τ = 0) is closed when fixed-term contracts of empirically reasonable length are introduced. To this end, we consider the case of Spain in the mid-1980s—which
introduced long temporary contracts in a labor market characterized by large firing costs. Calibrating the
model to a stylized version of that economy, we find that temporary contracts of three years’ duration
(roughly the length of the contracts introduced in Spain) close about half of the welfare gap between the
firing-tax and the laissez-faire cases.
There is a long theoretical literature analyzing the quantitative effects of temporary contracts in structural
models. An early contribution to this literature is Cabrales and Hopenhayn (1997)—who find that the
introduction of temporary contracts has large effects on turnover rates in a partial equilibrium dynamic labor
demand model that abstracts from unemployment. Interestingly, they find that there is a large increase in
the firing rate of workers with tenure equal to the length of the temporary contracts introduced. However,
despite the large turnover effects, they find moderate effects on employment. Bentolila and Saint-Paul (1992)
and Aguirregabiria and Alonso-Borrego (2014) also analyze partial equilibrium models that abstract from
unemployment, obtaining similar results. Veracierto (2007) introduces unemployment into a small open
model economy, but in order to analyze short-run dynamics, he assumes a linear production function that
leads to equilibrium wages being independent of the aggregate state of the economy and constant across
tenure levels; in terms of steady-state employment, he finds that temporary contracts of six months’ duration
have small positive effects. Blanchard and Landier (2002) and Cahuc and Postel-Vinay (2002) also introduce
unemployment into their models, but they consider versions of the Mortensen–Pissarides matching model;
they find that introducing temporary contracts increases job turnover but can reduce aggregate employment.
Güell and Rodríguez Mora (2010) consider a Shapiro–Stiglitz model of efficiency wages and find that
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
when there is a minimum wage, introducing temporary contracts can reduce employment. With this
Economic Perspectives article, we contribute to this literature by evaluating the effects of temporary contracts
in a Lucas–Prescott islands economy with undirected search. While the theory for this framework has
already been provided in Alvarez and Veracierto (2012), the contribution of this article is to provide a
quantitative analysis.
In the next section, we describe our model economy. After this, we describe the model economy’s competitive
equilibrium—which is flexible enough to capture key features of the Spanish economy both before and
after its 1984 labor market reform. Then, we discuss the details of our computational experiments—including
the calibration of the model to match Spain’s economy prior to its 1984 reform—and the effects of
introducing temporary contracts to that economy. Finally, we provide our concluding remarks.
The economy
There is a single consumption good in the economy that is produced in a unit measure of islands. The
production function of each island is given by
yt zt nt ,
where zt is an idiosyncratic productivity shock, nt is employment, and 0 < α < 1. The productivity shock zt
follows a finite Markov process with transition matrix Q.
3
The economy is populated by a unit measure of agents. These agents start every period of time located
either on one of the islands or at home (see note 2). If an agent starts a period of time on one of the
islands, they can choose either to stay or to leave. If they stay, they work on the island during the current
period and start the following period located at the same island. If they leave, they have two alternatives
available to them: perform home production or search for a new island. If they perform home production,
they produce ω units of the home good during the current period and start the following period at home. If
they search during the current period, they do not produce but arrive randomly at one of the islands at the
beginning of the following period. We assume that search is undirected, so the probability of arriving at
an island of any given type is given by the fraction of islands of that type in the economy.6 The agents
who start a period of time located at home have the same alternatives available to them as those available
to the agents who leave the islands where they were initially located. We denote by Lt the total number of
agents who perform home production at time t, by Ut the total number of agents who search at time t, and
by Nt = 1 − Lt − Ut the total number of agents who are employed at time t. We refer to the sum Lt + Ut as
the total number of agents who are nonemployed (that is, unemployed or out of the labor force) and to the
ratio Ut /(1 − Lt ) as the unemployment rate.7
All agents have identical preferences given by
c1 1
E0 t t
ht ,
t 0
1
where ct is consumption, ht is home production, 0 < β < 1 is the discount factor, and γ ≥ 0 is the intertemporal
substitution parameter. We assume that there is a unit measure of households, each constituted by a unit
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
interval of agents, and that agents can obtain full consumption insurance within their households.8 The
preferences of the representative household are then given by
1
1
t ct
Lt .
t 0
1
Competitive equilibrium
In this section we describe a recursive competitive equilibrium with firing taxes and temporary contracts.
Since this competitive equilibrium has been described in detail in Alvarez and Veracierto (2012), only its
main ingredients are sketched here.
The state of an island is given by a pair (T, z), where T = (T0, T1, ..., TJ ) is a vector describing the number
of workers across tenure levels present on the island at the beginning of the period and where z is the
idiosyncratic productivity shock. While Tj for j = 0, ..., J − 1 represents the number of workers with tenure j,
we find it convenient to include in TJ all workers with tenure greater than J − 1. We refer to TJ as the total
number of permanent workers, to T0 as the new arrivals, and to j 1,..., J 1 T j as the total number of temporary
workers. The government imposes on the firms a firing tax τ per unit reduction in their employment of
permanent workers. However, reducing the employment of temporary workers entails no firing taxes. All
firing taxes collected across all the islands in the economy are rebated as lump-sum transfers to the
representative household.
In each island there are J + 1 spot labor markets, one for each tenure level j = 0, ..., J. As a consequence,
current wages wj (T, z) are indexed by the tenure level and the state of the island. In solving their individual
problems, both agents and firms not only take the equilibrium functions wj (T, z) as given, but also the
equilibrium law of motion for the endogenous state of the island Tꞌ = A (T, z). This law of motion is
needed to forecast future wages on the island.
4
Because workers are fully insured within their households, they seek to maximize their expected discounted
values of wages and home production. In particular, the problem for a worker with tenure j on an island of
state (T, z) is to decide whether to become nonemployed or to stay and work. Becoming nonemployed
entails a value given by θ (to be determined in equilibrium). By staying, the worker receives a wage rate
wj during the current period and gains tenure min {j + 1, J} for the following period. We denote the value
function for a j-tenure worker on a (T, z)-island as Wj (T, z). This value function must solve
W j T , z max , w j T , z Wmin j 1, J A T , z , z Q z , z
z
for all (T, z) and j = 0, ..., J.
The problem of the representative firm on an island of type (T, z) is simply to maximize the expected
present discounted value of its profits—that is, of output net of total wage payments and firing costs. The
problem of a firm that employed p permanent workers during the previous period and is on an island of
type (T, z) is described by the following Bellman equation:
B p; T , z maxJ
n j 0 j 0
Economic Perspectives
1 / 2022
J
J
z n j w j T , z n j max p nJ , 0 B nJ nJ 1 ; A T , z , z Q z , z ,
i 0
z
j 0
Federal Reserve Bank of Chicago
where B is the value function of the firm. Observe that nJ−1 is the employment of workers that in the previous
period were at the end of their temporary contracts. When these workers are employed during the current
period, they become permanent workers and must be added to nJ for determining the previous-period
employment of permanent workers that the firm will have at the beginning of the following period.
At a steady-state equilibrium, the following seven conditions must hold: 1) the employment levels nj (TJ ; T, z)
that the representative firm on an island of type (T, z) chooses must generate the law of motion A (T, z) that
agents and firms take as given (observe that because of the undirected search assumption, T0 is always
equal to the total number of agents who search U), 2) the employment levels nj (TJ ; T, z) must be willingly
supplied by the workers with tenure j at an island of type (T, z), 3) the invariant distribution of islands
across states (T, z) must be generated by the law of motion A (T, z) and the Markov process that the idiosyncratic
productivity shock z follows, 4) the total number of employed agents across all islands in the economy (or
total employment) plus the total number of searchers U plus the total number of agents doing home production
L must equal one (the total population in the economy), 5) the value of nonemployment θ is equal to the
expected discounted value of randomly drawing W0 (T, z) under the invariant distribution of islands (observe
that W0 (T, z) is the value that a newly arrived worker obtains at an island of type (T, z)), 6) the value of
nonemployment satisfies that θ = cγω + βθ (that is, the value of becoming nonemployed is equal to the
value of doing home production during the current period plus the discounted value of being nonemployed
during the following period), and 7) the total output obtained across all production islands in the economy
equals the consumption level c enjoyed by the representative household.
In Alvarez and Veracierto (2012), we show that at a steady-state equilibrium there are three levels of
wages: one wage level w T , z common to all temporary workers with tenure j = 0, ..., J – 2; another
wage rate for the workers that are about to become permanent (that is, j = J − 1); and another wage rate
for permanent workers (that is, j = J ). Moreover,
1)
5
J
w T , z z n j TJ ; T , z
j 0
1
,
2) wJ 1 T , z min w T , z , wJ T , z ,
3) w T , z wJ T , z , if nJ TJ ; T , z TJ .
The intuition for why the wage rate of temporary workers with tenure less than J – 1 is equal to the marginal
productivity of labor (equation 1) is that these workers are still far from becoming permanent workers
subject to firing taxes and, therefore, firms treat them as being fully flexible. The intuition for why the wages
of temporary workers with tenure J − 1 are the lowest (equation 2) is that firms need to be compensated
for hiring them because doing so will make the firms subject to firing costs during the next period. The
intuition for why the wages of permanent workers are the highest when the representative firm fires some
of these workers (equation 3) is that in this case, the marginal value of not firing the last worker is given
by the marginal productivity of the worker plus the firing taxes saved.9
Observe that because islands are indexed by the vector T, the curse of dimensionality seems to preclude
any possibility of computing equilibriums for values of J significantly larger than 2. However, in Alvarez
and Veracierto (2012), we show that independent from the value of J, the endogenous state of an island
can always be summarized by only two values: the total number of temporary workers and the total number
of permanent workers. The undirected search assumption, under which every island receives U new arrivals
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
every period, is crucial for delivering this simplified representation of the state space and, therefore, for
being able to compute equilibriums under moderate values of J.
Computational experiments
In this section we evaluate to what extent the introduction of temporary contracts adds flexibility to the
labor market. To this end, we consider as a benchmark the case where J = 1 and τ > 0 and calibrate it to an
economy with high separation taxes and no temporary contracts—similar to Spain’s pre-1984 economy.10
Once the benchmark economy, which we refer to as the firing-tax case, is parameterized, we compute
competitive equilibriums under temporary employment contracts of different lengths (that is, with different
values of J) and evaluate their effects.
For the purposes of comparison, we also compute the equilibrium allocation under zero separation taxes,
which we refer to as the laissez-faire case. This is an interesting case to consider because the equilibrium
allocation with temporary employment contracts of long duration coincides with the equilibrium allocation
under laissez faire. The reason is quite simple: With a large enough J, firms can perfectly replicate their
laissez-faire employment levels by using only temporary workers. Given this property, we address the question
of how much flexibility the temporary contracts generate by computing what fraction of the gap between
the firing-tax and laissez-faire cases is closed when temporary contracts of different lengths J are introduced.
We note that in the laissez-faire case, which is obtained by setting either J = ∞ or τ = 0, the tenure levels
of the different workers become immaterial. This implies that while total employment is uniquely determined,
the hiring and firing rates across the different tenure levels are undetermined. Despite this, we choose to
focus on the employment adjustments obtained as the limit when τ → 0 (or equivalently, when τ is arbitrarily
small). This is useful because it helps emphasize the types of adjustments that temporary contracts lead to
even in the case in which they are totally unimportant.11
6
In the rest of this section, we present the empirical observations from mid-1980s Spain that motivate the
computational experiments we conduct; show how we calibrated the model to the pre-1984 Spanish
economy; and report the results of the exercises.
Some empirical background
Since the introduction of fixed-term contracts during the 1980s, the fraction of workers hired under this
modality had expanded steadily in European Union countries, reaching more than 17 percent by 2000
(Buddelmeyer, Mourre, and Ward-Warmedinger, 2004, figure 3.1, p. 21). However, there are large cross-country
differences in the scope and duration of fixed-term contracts. For instance, some countries restrict these
contracts to certain occupations and types of workers, while others give them broad applicability. In what
follows we focus on the case of Spain, because in 1984 Spain substantially liberalized the applicability of
temporary contracts at a time when the country had one of the highest employment protection levels in
Europe (see Cabrales and Hopenhayn, 1997, and Heckman and Pagés, 2000). From 1984 to 1991, the fraction
of workers with fixed-term contracts in Spain went from 11 percent to more than 30 percent, and almost
all the hiring in the economy was done under this form of contract (see García-Fontes and Hopenhayn, 1996).12
Figure 1, which is adapted from Cabrales and Hopenhayn (1997), displays estimates for the one-quarter
transition probabilities from employment to nonemployment during the five years before and after the
1984 reform as a function of the length of the employment spells. It shows that the firing rates increased
significantly after the reform and that a spike formed at an employment duration of three years, which
(not surprisingly) corresponds to the maximum fixed-term contract length allowed by the reform. Thus,
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
the introduction of fixed-term contracts appears to
have significant effects on worker reallocation. In
fact, there is considerable agreement in the empirical
literature that the main effects of introducing fixedterm contracts are a substantial increase in the flows
from unemployment to employment (that is, a
decrease in the average duration of unemployment)
and a significant increase in the flows from employment to unemployment (that is, an increase in the
firing rate) as can be seen, for example, in the literature
survey by Dolado, García-Serrano, and Jimeno (2002).
The net effect of these two opposing forces on the
unemployment rate is not clear, but the evidence
seems to indicate a small increase.
FIGURE 1
Firing rates in Spain before and after
the 1984 labor market reform
percentage fired, by tenure in firm
0.25
0.20
0.15
0.10
0.05
Calibration
0
2
4
6
8
10
12
14
quarters of tenure
16
18
20
We calibrate our model to the Spanish economy
prior to the 1984 labor market reform, which (as
Before 1984
After 1984
we mentioned earlier) was characterized by high
Note: The firing rates displayed here are transition
separation costs and essentially no temporary
rates from employment to nonemployment for workers
contracts (that is, high τ and J = 1). The value for τ
of different tenures five years (20 quarters) before and
after Spain’s 1984 labor market reform from Cabrales
is selected to reproduce the expected discounted
and Hopenhayn (1997).
dismissal cost when a worker is hired for the first
Source: Adapted from Cabrales and Hopenhayn (1997,
time—a measure proposed by Heckman and
figure 1, p. 191, and table 9, p. 221).
Pagés (2000). It turns out that a value of τ equal to
one year of average wages is needed to reproduce
this measure under the pre-1984 Spanish regime (see the appendix for details).
7
We use α = 0.64 for the curvature parameter in the production function, which roughly corresponds to the
labor share. This choice implicitly assumes that all other factors, such as capital, are fixed across locations.
Since we use a quarterly time period, we choose β = 0.96 to generate an annual interest rate of 4 percent.
For the idiosyncratic shocks z, we use a discrete Markov chain approximation for the following first-order
autoregressive process (AR(1)): log z ꞌ = ρ log z + σε, where ε is a standard normal. We choose the values
of ρ and σ so that the unemployment rate is just above 6.75 percent and the duration of unemployment is
just above one year. The exact values that we use are ρ = 0.955 and σ2 = 0.075, which correspond to a
discrete approximation that uses six truncated values for z, so that the absolute value of ε never exceeds
two standard deviations. Under these parameter values, the quarterly firing rate (total separations divided
by employment) in the benchmark case is 1.77 percent. Similarly, García-Fontes and Hopenhayn (1996)
estimate a pre-1984 firing rate of 1.8 percent per quarter. Observe that our choices are meant to capture
the situation in Spain before the 1984 reform. The reason why we choose a lower unemployment rate and
a lower duration of unemployment than those observed in Spain is that we are abstracting from its unemployment insurance system.13
We consider different values of the intertemporal substitution parameter γ. In each case we pick the value
of ω so that labor force participation equals 65 percent.14 The rest of the parameters are the same for each
pair (γ, ω).
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
Experiments
We compute equilibriums under different values of J—the length of the temporary contracts—and compare
them with the benchmark and laissez-faire cases. Since these two cases correspond to J = 1 and J = ∞,
respectively, these comparisons allow us to determine what fraction of the total potential gains in labor
market flexibility is realized by different temporary contract lengths.
As we vary the value of J, we set τ to the same proportion of economy-wide wages. It turns out that under
an isoelastic production function and firing taxes τ being proportional to economy-wide wages, a number
of statistics become independent of the intertemporal substitution parameter γ. In particular, the unemployment
rate, the firing rate, and the average duration of unemployment are the same in all cases. For this reason,
we start by describing the effects of temporary contracts on this set of statistics. Without loss of generality,
we set γ = 0. This is the simplest case to interpret because consumption and home production become
perfect substitutes and, as a consequence, the equilibrium value of θ must be equal to ω/(1 − β), a parameter
independent of policy.
8
In all three panels of figure 2, equilibrium values are reported as a function of the length of the temporary
contracts J and depicted under the “general equilibrium” label. Observe that the general equilibrium values
for J = 1 correspond to the benchmark case with firing taxes and no temporary contracts. Laissez-faire
values are reported under the “laissez faire” label. In addition, to illustrate the role of general equilibrium
effects in generating differences between the benchmark J = 1 and the laissez-faire cases, a third set of values is
reported under the “partial equilibrium” label. For each J > 1, these are the values associated with U and θ
being fixed at their benchmark values (and equilibrium conditions 5 and 6 being ignored). Observe that
any differences between the partial and general equilibrium schedules must be due to equilibrium effects
on U, since θ is fixed when γ = 0. Also observe that U will always be higher in the general equilibrium
case than in the partial equilibrium case. The reason for this is that with J > 1, there are fewer restrictions
to labor mobility. This increases the value of an additional worker at every island and induces a larger
fraction of the population to search.15 For similar reasons, the equilibrium value of U will always be
increasing with J. A consequence of this is that for 1 < J < ∞, the equilibrium value of U will always lie
between the benchmark and laissez-faire cases.
Panel A of figure 2 shows the effects on the unemployment rate ur = U/(U + N). While the fraction of agents
who search U is increasing with the lengthening of the temporary contracts, we see that the unemployment
rate initially increases with J but then displays a nonmonotonic behavior. We also see that the unemployment rate is almost 2.5 percentage points higher in the laissez-faire case than in the benchmark J = 1 case
and that with temporary contracts of three years’ duration (J = 12) the unemployment rate is 1.2 percentage
points higher than in the benchmark case. Thus, temporary contracts of three years’ duration, which are
similar to those introduced by the 1984 Spanish reform, are able to close about half of the gap with the
laissez-faire case.16 Figure 2, panel A also shows that the equilibrium effects on U are crucial for generating
the higher unemployment rates: The effects on the unemployment rate are nonmonotonic and small in the
partial equilibrium case.17
To better understand the effects on the unemployment rate (figure 2, panel A), it is helpful to decompose
them into firing rate effects (figure 2, panel B) and average duration of unemployment effects (figure 2,
panel C). Panel B of figure 2 shows the effects on the firing rate fr, defined as total firing divided by total
employment. Recall that for the laissez-faire and partial equilibrium cases, the values of U and θ are the
same across all J. As should be expected, the firing rates for the laissez-faire case are higher than the ones
for the partial equilibrium case for all values of J. Notice that the firing rates in these two cases are increasing
with the rise in J, including a large jump at J = 2. To understand this pattern, we concentrate on the
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
FIGURE 2
Unemployment rate, firing rate, and average duration of unemployment
as a function of the length of temporary employment contracts
A. Unemployment rate
unemployment rate, in percent
B. Firing rate
firing as a percentage of employment
10.5
7.0
6.5
10.0
6.0
9.5
5.5
9.0
5.0
4.5
8.5
4.0
8.0
3.5
3.0
7.5
2.5
7.0
6.5
2.0
*
0
2
4
6
8
10
12
1.5
*
0
2
4
6
8
10
12
length of the contract J, in quarters
length of the contract J, in quarters
C. Average duration of unemployment
average duration, in quarters
4.5
*
4.0
3.5
3.0
9
2.5
2.0
1.5
0
2
4
6
8
10
12
length of the contract J, in quarters
Partial equilibrium case (τ = 1 year of average wages)
General equilibrium case (τ = 1 year of average wages)
Laissez-faire case (τ → 0)
Notes: In each of the three panels, the asterisk corresponds to the value for the benchmark (J = 1) case, with firing taxes
and no temporary employment contracts (which is also referred to as the firing-tax case). See the text for further details.
laissez-faire case, where the employment on each island stays constant. Recall that we compute employment
by tenure in the laissez-faire case as the limit for an equilibrium with τ → 0. The increase in the firing rate
helps to avoid the (arbitrarily small) separation tax. The firing rate jumps between J = 1 and J = 2 because
when J = 2, the temporary workers with longest tenure are fired and replaced by newly arrived workers.
This reshuffling cannot be done when J = 1. The smooth increase in the firing rate with J is due to the fact
that with higher J, firms can accumulate a larger proportion of their workforce as temporary workers.
With this larger proportion, if they need to decrease total employment, they can do so at the same time
that they hire newly arrived workers. Notice that the pattern of firing rates as a function of J for the partial
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
FIGURE 3
Share of permanent workers as a
function of the length of temporary
employment contracts
share of permanent workers in total employment
1.00
0.95
0.90
0.85
0.80
0.75
equilibrium case, with substantial separation costs
(one year of average wages), is generally the same
as in the laissez-faire case, with essentially zero
firing taxes.
As seen in figure 2, panel B, the value for the firing
rate in the general equilibrium case lies in between
the value for the partial equilibrium case and the
one for the laissez-faire case, and it gets closer to
the one for the laissez-faire case as J increases.
Since in general equilibrium firms receive a higher
flow of newly arrived workers (that is, a higher U),
they can engage more in the replacement of temporary
workers with high tenure for newly arrived workers
to save on separation costs.
0.70
The quarterly firing rate for the general equilibrium
case goes from 1.77 percent for J = 1 to 5.04 percent
0.60
for J = 12, roughly similar to the values for Spain
0
2
4
6
8
10
12
length of the contract J, in quarters
before and after 1984: García-Fontes and Hopenhayn
(1996) estimate quarterly firing rates of 1.8 percent
General equilibrium case (τ = 1 year of average wages)
Laissez-faire case (τ → 0)
prior to the extension of temporary contracts’ length
Note: See the text for further details.
and 4.8 percent after it. The model slightly overestimates this effect. However, the effect in the model
of going from J = 1 to J = 12 does not correspond exactly to Spain before and after 1984 because some
temporary contracts were allowed in Spain before 1984.
0.65
10
Panel C of figure 2 shows the average duration of unemployment d, defined as (1/fr) ur/(1 − ur). The three
cases display similar values. There is a large drop in the average duration between J = 1 (the benchmark
case) and J = 2. This is the result of the increased hiring of newly arrived workers that we mentioned in
our explanation of figure 2, panel B.18 Because d is similar for the three cases, it’s clear that the effects on
unemployment are accounted for by the behavior of the firing rates discussed previously. Notice that, as
opposed to the sharp change at J = 2 for the firing rate and average duration of unemployment (panels B
and C of figure 2, respectively), the increase in the unemployment rate for the general equilibrium is smooth
(panel A of figure 2). This is because for J = 2, the sharp decrease in the average duration of unemployment
coincides with a sharp increase in the firing rate.
Figure 3 displays the fraction of permanent workers among all workers for the general equilibrium and
laissez-faire cases. The fraction of permanent workers is higher for the general equilibrium case than for
the laissez-faire case because in the general equilibrium case, firms retain more permanent workers to avoid
the high separation costs. Nevertheless, the fraction of permanent workers is very similar in the two cases.
Notice also that as J increases, the fraction of permanent workers decreases steadily. For J = 12, which
corresponds to temporary contracts of three years, 33 percent of all workers are in temporary contracts (see
the solid red line in figure 3, which indicates that when J = 12, 67 percent of workers are permanent employees).
In Spain, the fraction of workers with temporary contracts went from about 11 percent before the 1984
reform to 16 percent in 1987, 22 percent in 1988, and 27 percent in 1989, before stabilizing to an average
of about 33 percent during the 1990s (García-Fontes and Hopenhayn, 1996, and Toharia Cortés, 2002).
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
Notice that the patterns displayed in panel C of
figure 2 and in figure 3 for the average duration of
unemployment and the share of permanent workers
Equilibrium employment as a function
among total workers are similar to the ones found
of the length of temporary employment
contracts for different values of γ
in Spain after the mid-1980s. These patterns have
typically been interpreted as evidence that the length
share of employed workers among total population
of temporary contracts can play an important role in
0.66
labor market dynamics. However, in our model,
0.65
similar patterns are obtained for τ equal to one year
of average wages, as well as for an arbitrarily small
0.64
value of τ—which shows that by itself large changes
0.63
in turnover do not necessarily entail large changes in
welfare and other relevant variables, such as employ0.62
ment, unemployment, aggregate consumption, and
0.61
productivity. We obtain this result under the extreme
assumption that workers with different tenure are
0.60
perfect substitutes. Under a different specification,
0.59
such as allowing for on-the-job learning, this result
0
2
4
6
8
10
12
will not be obtained. In particular, if the effect of
length of the contract J, in quarters
on-the-job learning is large enough, a small separaγ=8
γ=1
γ=0
γ = 0.5
tion cost may have a very small effect on turnover
Notes: Note that γ is the intertemporal substitution
rates. Nevertheless, we interpret the spike in figure 1
parameter. All plotted values are for the general
for tenure of about three years as evidence that the
equilibrium case (with τ = 1 year of average wages).
See the text for further details.
effects of separation taxes are not completely
outweighed by on-the-job learning.19 We leave the
examination of a model that incorporates both features for future work.
FIGURE 4
11
Figure 4 shows the behavior of employment for the general equilibrium case for different values of the
intertemporal substitution parameter γ. As J increases, there are both income and substitution effects. The
substitution effect is due to the fact that as J increases, firms have more flexibility and thus working in the
market is more attractive—that is, the equilibrium value of θ increases. The income effect is due to the
fact that the economy is more productive. For low values of γ, the substitution effect dominates, and thus,
aggregate employment increases with J. For high values of γ, the income effect dominates, and thus,
aggregate employment decreases with J.
Figure 5 displays the welfare cost of temporary contracts of different lengths for different values of the
intertemporal substitution parameter γ. The welfare cost is measured in consumption equivalent units—
that is, it is the perpetual percentage increase in consumption flow needed to make the representative
household indifferent between being in the economy with temporary contracts of length J and being in the
laissez-faire economy. This calculation compares the stationary equilibriums of the two economies and
hence does not take into account the transition after a change in policy. Observe that for the same J, the
welfare cost is always higher when the value of γ is smaller because when γ decreases, there is greater
substitution between consumption and home production. However, the welfare costs are surprisingly
similar across the different values of γ. Interestingly, for J = 1 (the baseline case), figure 5 shows that the
welfare cost of firing taxes is 2.3 percent for γ = 1 (the case of logarithmic preferences). This number is
extremely similar to the one found by Hopenhayn and Rogerson (1993) and Veracierto (2001) under
identical preferences. As J increases, the welfare cost decreases: The welfare cost goes from 2.3 percent
for a contract length of one quarter and decreases smoothly with J until a value of around 1 percent for a
contract length of three years, or J = 12. Thus, even if some characteristics of the allocation (such as the
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
FIGURE 5
Welfare costs of temporary employment
contracts of different lengths for
different values of γ
consumption compensation, in percent
3.0
Conclusion
2.5
2.0
1.5
1.0
0.5
0
0
2
4
6
8
10
length of the contract J, in quarters
γ=0
γ = 0.5
γ=1
12
γ=8
Notes: The welfare cost plotted is the perpetual
percentage increase in consumption flow needed to
make the representative household indifferent between
being in the economy considered and being in the
laissez-faire economy. Note that γ is the intertemporal
substitution parameter. The benchmark case, or the
firing-tax case, is J = 1. See the text for further details.
12
unemployment rate in figure 2, panel A) do not
converge monotonically to their laissez-faire values
as J increases, the welfare cost—which in a sense
takes all the relevant features into consideration—does
converge monotonically. The same is true for all
values of the intertemporal substitution parameter γ.
In this article, we considered the equilibrium search
model described in Alvarez and Veracierto (2012),
which is a version of the Lucas–Prescott islands
model with undirected search and an out-of-the-laborforce state. Calibrating the model to Spain before
the major labor market reform that it introduced in
1984, we explored the quantitative effects of introducing temporary employment contracts of various
lengths. An important finding of the article is that
introducing temporary contracts of three years’
duration—the magnitude introduced by the 1984
Spanish reform—provides about 50 percent as much
labor market flexibility as moving to a laissez-faire
regime (with zero firing costs). We base this claim
about the effects of temporary contracts on two key
statistics—the unemployment rate, which summarizes
labor reallocation, and welfare, which summarizes
the overall effects on the economy of introducing
such contracts.
Notes
1
Typically, termination based on economic grounds does not exempt employers from paying severance payments. Severance
payments are the largest when the termination happens without cause.
2
In what follows, it may be useful to consider home as a special location (separate from the production islands) where agents can
always go in order to obtain home production.
3
We refer to the tenure of a worker as the number of periods that the worker has been present on the island. For instance, a recently
arrived worker has a tenure of zero periods.
4
If firing taxes applied at the firm level (instead of the island level), exactly the same competitive allocation would be obtained if
employment contracts were allowed to be multiperiod and state-contingent (see Alvarez and Veracierto, 2012). Thus, the assumption
that the firing taxes apply at the island level does not represent a loss in realism, but it allows for a much simpler description of
a competitive equilibrium.
5
While we evaluate the role of fixed-term contracts in adding flexibility to firms’ labor adjustments, we abstract from their potential
role in allowing employers to test the quality of their new workers at a reduced cost (in our model, workers are identical).
6
The type of an island is given by its current state (to be described in the second paragraph of the next section).
7
Observe that the behavior of the unemployment rate will generally differ from the behavior of Ut because of differences in the
behavior of Lt.
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
13
8
The assumptions that all search is undirected and that agents are fully insured, while extreme, will play an important role in
keeping the model tractable.
9
Actually, the saving from avoiding firing taxes does not equal the full amount τ saved during the current period because the
worker may be fired the following period.
10
When J = 1, the dismissal of anyone who has worked, even for one period, triggers the separation tax τ > 0. Thus, there are no
temporary workers in this case.
11
Observe that, independent of τ being large or small, a contracting island will always remove the workers with tenure J − 1 first,
then those with tenure J − 2, and so on until it removes those with tenure 1. Only after all workers with tenure 1 have been removed
will the island start removing permanent workers (those with tenure J). Thus, the hiring and firing rates across the different tenure
levels are well determined.
12
These reforms were partially undone during the 1990s, when the maximum length of fixed-term contracts was reduced from
three years to one year and the severance payments for ordinary indefinite-length contracts were substantially reduced. However,
even after this partial reversal, the fraction of workers under fixed-term contracts stabilized at about 33 percent (see Toharia
Cortés, 2002, figure 1, p. 119).
13
In Alvarez and Veracierto (2000), we analyzed the effects of introducing unemployment insurance (UI) benefits into the model
with firing taxes. Introducing UI benefits of the magnitude observed in Spain increases the unemployment rate by roughly
10 percent and more than doubles the average duration of unemployment (see subsection 4.4.1 on UI benefits, firing subsidies, firing
taxes, and severance payments, as well as table 5, of Alvarez and Veracierto, 2000, pp. 284–285, 298).
14
The different combinations of (γ, ω) are: (0, 1.3047), (1/2, 1.0739), (1, 0.883), and (8, 0.058). With γ = 0, there are no income
effects, since preferences are linear. With γ = 1, income and substitution effects of a permanent increase in wages cancel each
other out. With γ = 8, the income effect is much higher, so that the uncompensated labor supply elasticity is lower, similar to the
values estimated by Nickell (1997).
15
Because of the decreasing returns to scale at the island level, the higher value for U reduces the value of an additional worker at
every island and restores the general equilibrium at θ = ω/(1 − β).
16
In the data the relationship between unemployment and temporary contracts is not as clear. However, Dolado, García-Serrano,
and Jimeno (2002, p. F285) survey the literature and conclude that the introduction of temporary contracts in Spain had a “neutral
or slightly positive effect on unemployment.”
17
These partial equilibrium effects are consistent with previous findings in the literature: We know at least since Bentolila and
Bertola (1990) that the effects of firing costs on average employment are ambiguous in that setting.
18
To better understand what is happening in our model, it may be useful to consider the case of an island that would like to have the
same total employment level that it had during the previous period. When J = 1, the island will not hire any of the new arrivals U
(since replacing permanent workers with new arrivals would involve paying firing taxes). However, when J = 2 the island will
want to replace all the workers with tenure j = 1 with new arrivals in order to avoid the j = 1 workers from becoming permanent
workers. For this reason, it is harder to transit out of unemployment under J = 1 than under J = 2. This is also the reason why
the firing rate jumps up from when J = 1 to when J = 2 in figure 2, panel B. Even when the firing taxes are arbitrarily small, the
temporary contracts induce the islands to churn their workers quite significantly.
19
With on-the-job learning and firing costs, if the effect of learning is strong enough, it will not be optimal for the firm to fire first
the temporary workers with higher tenure. In this case, the spike at the end of the fixed-term contracts shown for Spain in figure 1
would not be obtained.
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
APPENDIX: CALIBRATION OF τ
Heckman and Pagés (2000) propose to summarize employment protection policies into a single statistic.
The measure they use is the expected discounted cost, at the time that a worker is hired, of dismissing the
worker in the future. Their index I is given by
T
I t t 1 1 bt aSt j 1 a Stu ,
t 1
where T is the maximum tenure considered in the index, β is a time discount factor, δ is the survival rate
(probability of remaining employed next period if employed during the current period), bt is the wage
earned during the advance-notice period for a worker of tenure t, a is the probability that a dismissal is
considered “justified” (that is, “fair” or “objective”), St j is the severance payment to a worker of tenure t
if the dismissal is classified as “justified,” and Stu is the severance payment to a worker of tenure t if the
dismissal is “not justified.”
Heckman and Pagés (2000) use a year as the time period, along with the following values: β = 0.92 (an
8 percent interest rate), δ = 0.88 (a turnover rate of 12 percent, based on data for the United States), and a
value of T of 20 years; in addition, for Spain they advocate for using a = 0.2 for the period before 1997,
based instead on the information from Bertola, Boeri, and Cazes (2000). Heckman and Pagés (2000) compute
their job security index for Spain in the late 1990s. Since we calibrate our model to the period before the
broadening in the applicability of temporary contracts, we recompute their index for the policies in place
before the 1984 labor market reform. We use the following values:
• bt: one month of wages for tenure 1 and two and three months for higher tenure (Organisation for
Economic Co-operation and Development, 1999, table 2.2, p. 57);
14
• a: 0.2 (since their argument applies prior to 1984);
• St j::two-thirds months per year, up to a maximum of 12 months (Organisation for Economic Co-operation
and Development, 1999, table 2.A.2, p. 96); and
• Stu ::one and a half months per year, up to a maximum of 42 months (Organisation for Economic
Co-operation and Development, 1999, table 2.A.5, p. 101).
We consider two cases. The first case is as follows: With these choices for bt , a, St j, and Stu, along with the
values for β and δ used by Heckman and Pagés (2000), we obtain a value of I prior to 1984 of 0.42 as a
fraction of annual average wages. And the second case is the following: If instead we use β = 0.96, which
is the same value we use in our main text discussion, and δ = 0.93, which is closer to the one for Spain
prior to 1984 according to Cabrales and Hopenhayn (1997), we obtain a value of I prior to 1984 of 0.56 as
a fraction of annual average wages.
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
Finally, since in our benchmark case the firing taxes do not depend on the tenure of the workers, we select
the value of τ so that the value of the index I will yield the value we calibrate for Spain prior to the 1984
reform. This value solves the equation:
T
I
t 1
t
t 1
1 1
1
T
1
or
I
1
1 1
T
.
The value of τ that corresponds to the first case is 0.74 of annual average wages, and the value of τ that
corresponds to the second case is 0.98 of annual average wages. We think that for our purposes the
choices of the second case better reflect the situation prior to 1984 in Spain, and hence, we calibrate the
model to τ equivalent to one year of average wages.
References
Aguirregabiria, Victor, and Cesar Alonso-Borrego, 2014, “Labor contracts and flexibility: Evidence
from a labor market reform in Spain,” Economic Inquiry, Vol. 52, No. 2, April, pp. 930–957. Crossref,
https://doi.org/10.1111/ecin.12077
Alvarez, Fernando, and Marcelo Veracierto, 2012, “Fixed-term employment contracts in an equilibrium
search model,” Journal of Economic Theory, Vol. 147, No. 5, September, pp. 1725–1753. Crossref,
https://doi.org/10.1016/j.jet.2012.05.015
15
Alvarez, Fernando, and Marcelo Veracierto, 2000, “Labor-market policies in an equilibrium search
model,” in NBER Macroeconomics Annual 1999, Ben S. Bernanke and Julio J. Rotemberg (eds.), Vol. 14,
Cambridge, MA: MIT Press, pp. 265–304. Crossref, https://doi.org/10.1086/654391
Bentolila, Samuel, and Giuseppe Bertola, 1990, “Firing costs and labour demand: How bad is
Eurosclerosis?,” Review of Economic Studies, Vol. 57, No. 3, July, pp. 381–402. Crossref,
https://doi.org/10.2307/2298020
Bentolila, Samuel, and Gilles Saint-Paul, 1992, “The macroeconomic impact of flexible labor contracts,
with an application to Spain,” European Economic Review, Vol. 36, No. 5, June, pp. 1013–1047. Crossref,
https://doi.org/10.1016/0014-2921(92)90043-V
Bertola, Giuseppe, Tito Boeri, and Sandrine Cazes, 2000, “Employment protection in industrialized
countries: The case for new indicators,” International Labour Review, Vol. 139, No. 1, March, pp. 57–72.
Crossref, https://doi.org/10.1111/j.1564-913X.2000.tb00402.x
Blanchard, Olivier, and Augustin Landier, 2002, “The perverse effects of partial labour market reform:
Fixed-term contracts in France,” Economic Journal, Vol. 112, No. 480, June, pp. F214–F244. Crossref,
https://doi.org/10.1111/1468-0297.00047
Buddelmeyer, Hielke, Gilles Mourre, and Melanie E. Ward-Warmedinger, 2004, “Recent developments
in part-time work in EU-15 countries: Trends and policy,” IZA (Institute of Labor Economics), discussion
paper, No. 1415, November, available online, https://www.iza.org/en/publications/dp/1415/
recent-developments-in-part-time-work-in-eu-15-countries-trends-and-policy.
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
Cabrales, Antonio, and Hugo A. Hopenhayn, 1997, “Labor-market flexibility and aggregate employment
volatility,” Carnegie-Rochester Conference Series on Public Policy, Vol. 46, June, pp. 189–228. Crossref,
https://doi.org/10.1016/S0167-2231(97)00008-0
Cahuc, Pierre, and Fabien Postel-Vinay, 2002, “Temporary jobs, employment protection and labor
market performance,” Labour Economics, Vol. 9, No. 1, February, pp. 63–91. Crossref,
https://doi.org/10.1016/S0927-5371(01)00051-3
Dolado, Juan J., Carlos García-Serrano, and Juan F. Jimeno, 2002, “Drawing lessons from the boom
of temporary jobs in Spain,” Economic Journal, Vol. 112, No. 480, June, pp. F270–F295. Crossref,
https://doi.org/10.1111/1468-0297.00048
García-Fontes, Walter, and Hugo Hopenhayn, 1996, “Flexibilización y volatilidad del empleo,”
Moneda y Crédito, No. 202, pp. 205–227, available online, http://www.cervantesvirtual.com/obra-visor/
moneda-y-credito--3/html/02822e00-82b2-11df-acc7-002185ce6064_21.html#I_26_.
Güell, Maia, and José Vicente Rodríguez Mora, 2010, “Temporary contracts, incentives and unemployment,” Centre for Economic Policy Research, discussion paper, No. DP8116, November, available online,
https://cepr.org/active/publications/discussion_papers/dp.php?dpno=8116.
Heckman, James J., and Carmen Pagés, 2000, “The cost of job security regulation: Evidence from Latin
American labor markets,” National Bureau of Economic Research, working paper, No. 7773, June.
Crossref, https://doi.org/10.3386/w7773
Hopenhayn, Hugo, and Richard Rogerson, 1993, “Job turnover and policy evaluation: A general
equilibrium analysis,” Journal of Political Economy, Vol. 101, No. 5, October, pp. 915–938. Crossref,
https://doi.org/10.1086/261909
16
Lucas, Robert E., Jr., and Edward C. Prescott, 1974, “Equilibrium search and unemployment,”
Journal of Economic Theory, Vol. 7, No. 2, February, pp. 188–209. Crossref,
https://doi.org/10.1016/0022-0531(74)90106-9
Nickell, Stephen, 1997, “Unemployment and labor market rigidities: Europe versus North America,”
Journal of Economic Perspectives, Vol. 11, No. 3, Summer, pp. 55–74. Crossref, https://doi.org/10.1257/
jep.11.3.55
Organisation for Economic Co-operation and Development, 1999, OECD Employment Outlook:
June 1999, report, Paris, June, available online, https://read.oecd-ilibrary.org/employment/
oecd-employment-outlook-1999_empl_outlook-1999-en#page1.
Toharia Cortés, Luis, 2002, “El modelo español de contratación temporal,” Temas Laborales, No. 64,
pp. 117–139, available online, https://dialnet.unirioja.es/descarga/articulo/255200.pdf.
Veracierto, Marcelo, 2007, “On the short-run effects of labor market reforms,” Journal of Monetary
Economics, Vol. 54, No. 4, May, pp. 1213–1229. Crossref, https://doi.org/10.1016/j.jmoneco.2006.02.007
Veracierto, Marcelo, 2001, “Employment flows, capital mobility, and policy analysis,” International
Economic Review, Vol. 42, No. 3, August, pp. 571–596. Crossref, https://doi.org/10.1111/1468-2354.00125
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
Fernando Alvarez is the Saieh Family Professor of the
Kenneth C. Griffin Economics Department of the University
of Chicago, an Econometric Society Fellow, an Economic
Theory Fellow of the Society for the Advancement of
Economic Theory, a research associate of the National
Bureau of Economic Research, and a member of the
American Academy of Arts and Sciences. Marcelo Veracierto
is a senior economist and research advisor in the Economic
Research Department at the Federal Reserve Bank of
Chicago. The authors are grateful to Gadi Barlevy for his
valuable comments.
Krane, Senior Vice President and Senior Research Advisor;
Sam Schulhofer-Wohl, Senior Vice President and Director
of Financial Policy and Outreach; Gene Amromin, Vice
President, Finance; Alessandro Cocco, Vice President,
Markets; Jane Dokko, Vice President, Community
Development and Policy Studies; Jonas D. M. Fisher, Vice
President, Macroeconomics; Leslie McGranahan, Vice
President, Regional Analysis; Marcelo Veracierto, Senior
Economist and Economics Editor; Helen Koshy and
Han Y. Choi, Editors; Julia Baker, Senior Production
Editor ; Sheila A. Mangler, Editorial Assistant.
© 2022 Federal Reserve Bank of Chicago
Economic Perspectives articles may be reproduced in
whole or in part, provided the articles are not reproduced
or distributed for commercial gain and provided the
source is appropriately credited. Prior written permission
must be obtained for any other reproduction, distribution,
republication, or creation of derivative works of Economic
Perspectives articles. To request permission, please
contact Helen Koshy, managing editor, at 312-322-5830
or email Helen.Koshy@chi.frb.org.
Economic Perspectives is published by the Economic
Research Department of the Federal Reserve Bank of
Chicago. The views expressed are the authors’ and do not
necessarily reflect the views of the Federal Reserve Bank
of Chicago or the Federal Reserve System.
Charles L. Evans, President; Anna L. Paulson, Executive
Vice President and Director of Research; Daniel G. Sullivan,
Executive Vice President and Director, Economic Mobility
Project; Daniel Aaronson, Senior Vice President, Associate
Director of Research, and Director, Microeconomics; Spencer
ISSN 0164-0682
17
Economic Perspectives
1 / 2022
Federal Reserve Bank of Chicago
@FedFRASER