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Hindawi Publishing CorporationISRN EconomicsVolume 2013, Article ID 138182, 13 pageshttp://dx.doi.org/10.1155/2013/138182
Research ArticleThe Effect of Labour Turnover Costs on Average LabourDemand When Recessions Are More Persistent than Booms
Pilar DΓaz-VΓ‘zquez and Luis E. Arjona-BΓ©jar
Departamento de Fundamentos del Analisis Economico, Facultad de Ciencias Economicas y Empresariales, Universidad de Santiagode Compostela, Avenida do Burgo S/N, A Coruna, 15784 Santiago de Compostela, Spain
Correspondence should be addressed to Pilar DΔ±az-Vazquez; [email protected]
Received 10 December 2012; Accepted 26 December 2012
Academic Editors: T. Kuosmanen, J. M. Labeaga, and A. Watts
Copyright Β© 2013 P. DΔ±az-Vazquez and L. E. Arjona-Bejar. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.
This paper examines how labour turnover costs affect average labour demand when troughs are more persistent than booms. Weshow that the effect of firing costs on average labour demand is more expansionary (or less contractionary): the greater is thedifference between the persistence of troughs and the persistence of booms, and themore prolonged are themacroeconomic shocks.This analysis may shed some light on the expected effect of a reduction of firing costs when an economy is sufferingmore prolongedrecessions (relative to booms): average labour demand will be lower.
1. Introduction
Politicians and journalists often attribute the high unem-ployment in many European countries to their stringent jobsecurity legislation, and particularly to their state-mandatedfiring costs. However, the theoretical literature on the long-run effects of firing costs on employment has generatedmixedresults (There is also no agreement in the empirical literature.See OECD [1], Layard et al. [2], Lazear [3], Bertola [4],Hopenhayn and Rogerson [5], Nickell [6], Heckman andPages [7].). Bentolila and Bertola [8] and Bertola [9] haveargued that firing costs tend to raise (rather than reduce) theaverage level of employment since they discourage firingmore than hiring in any given firm.Other contributions showfactors that pull in the opposite direction: Bentolila and Saint-Paul [10] indicate that when firms face heterogeneous pro-ductivity shocks, a rise in firing costs reduces the number offirms engaged in firing. Hopenhayn and Rogerson [5] con-sider that the increase in firing costs reduces the entry of firms(in an industry equilibriumwith firm entry and exit) and thuslabour demand falls. DΔ±az-Vazquez et al. [11] show that whenthere is on-the-job learning, an increase in firing costs mayreduce average employment over the cycle. This paper andDΔ±az-Vazquez and Snower [12β14] also show that the wageeffects of firing costs may reduce average employment (as
shown in the literature, firing costs give power to insidersin the wage negotiation (see Lindbeck and Snower, [15])).Ljungqvist and Sargent [16] argue that the existence of firingcosts can help explain the high European unemployment ofrecent decades.
However, this literature has not investigated how the aver-age employment effect of firing costs depends on the asym-metry in the persistence of macroeconomic booms andtroughs (in Bentolila and Bertola [8], the shocks are per-manent (namely, they are assumed to follow a random walkprocess), whereas in Bentolila and Saint-Paul [10] they aretemporary (namely, they are white noise). Bertola [4] andDΔ±az-Vazquez and Snower [12] analyze shocks whose degreeof persistence lies between these two extremes (with thedegree of persistence determined by the transition probabil-ities in a Markov process). In all of these models, macroe-conomic upturns and downturns are assumed to be equallylikely. Nunziata [17] analyzes the effect of firing costs on thedynamics of employment over the cycle, but he does not studythe average effect.).This asymmetry is important since boomsand troughs have very different implications for the influenceof firing costs on employment. Chen et al. [18] indicate thatwhen the level of macroeconomic activity is expected todrop (or growth is low), a rise in firing costs affects mainly(and adversely) the hiring decision, whereas firing costs can
2 ISRN Economics
raise employment during periods of high growth and positiveshocks. However, they do not analyse the effect of firing costson long-run employment neither they consider the effect offiring costs via the negotiated wage.
The contribution of this paper is to present a model inwhich troughs are more persistent than booms and turnovercosts also affect employment via the negotiated wage. In thiscontext, we examine how the effect of turnover costs onlabour demand depends on the persistence of macroeco-nomic fluctuations (our approach is different from the liter-ature that studies the effect of firing costs on business cyclefluctuations (see Veracierto [19] and Zanetti [20]). We focuson how average labour demand responds to turnover costswhen the macroeconomic conditions change). Turnovercosts have an ambiguous effect on average employment: onthe one hand, (i) turnover costs increase employment becausethey discourage the firing of workers in recessions. Whenthe firm encounters a recession, it faces the possibility offiring workers and paying the firing cost in the currentperiod.This current payment discourages firing and increasesemployment. Additionally, if economic conditions improve,firms will have to pay the hiring cost. On the other hand, (ii)turnover costs diminish employment because they discour-age hiring and augment the wage in booms. When economicconditions improve and the firm considers the possibility ofhiring new workers, not only the hiring cost but also theexpectation of paying the firing cost in the future discourageshiring. Additionally, in booms workers may obtain higherwages if they are protected by job security provisions.The rea-son is that firing costs worsen the firmβs fall-back position inthe negotiations, which increases the wage.The cost of hiringalso increases the wage in booms. The influence of turnovercosts on the wage depends on the bargaining power of theworkers. For this reason, the greater the strength of employeesin the wage bargaining process, the more contractionary isthe effect of turnover costs on average employment. Note thatfiring costs only increase the wage in booms, since in troughsthe rise in the firing cost worsens the firmβs fall-back positionby just as much as it reduces the marginal product of labour.
It is clear that when the persistence of troughs is greaterthan the persistence of booms, the economy will be morefrequently in recessions than in booms. In this case, the aspect(i) becomes more important than (ii), and it is more likelythat firing costs increase average employment. Any factor thatincreases the frequency of troughswill have this consequence.Thus, the more persistent are troughs relative to booms, themore expansionary or the less contractionary is the effect offiring cost on average employment.
In this context, we also demonstrate that when troughsare more persistent than booms, a proportional increase inthe persistence of both booms and troughs gives turnovercosts a more expansionary or a less contractionary influenceon average employment. We can show that the frequency oftroughs relative to booms may increase due to a proportionalincrease in the persistence of both booms and troughs: itis clear that if the economy is in troughs a greater numberof periods, a proportional increase in the duration of bothbooms and recessions will increase the frequency of reces-sions and reduce the frequency of booms.
In this context of asymmetric fluctuations, we also exam-ine how the effect of turnover costs on average employmentdepends on the characteristics of the firmsβ productionfunctions (in this respect, we extend the results of Bertola [9]to a stochastic framework). In this context we show that theresults above may hold for different production functions.
The paper is organized as follows. Section 2 presents themodel. Section 3 analyzes the influence of firing costs onemployment in the short run whereas Section 4 analyzes theinfluence of firing costs on employment in the long run.Section 5 presents the conclusions.
2. The Model
Consider a firm that produces a homogeneous output bymeans of a homogeneous labour input. In time period π
its revenue function is π (ππ, πΏπ), where π
πis a random
variable representing business conditions, and πΏπis the firmβs
employment (we assume perfect competition in the productmarket, so that the firm is a price taker.). The evolution ofbusiness conditions π
πis given by a two-state Markov chain:
there is a βgood stateβ when ππ= ππΊ and a βbad stateβ when
ππ= ππ΅, where ππΊ > π
π΅. The probability of remaining inthe good state is ππΊ and the probability of remaining in thebad state is ππ΅, so that the matrix of stationary transitionprobabilities is
(
ππΊ
1 β ππΊ
1 β ππ΅
ππ΅
) . (1)
In this context, the persistence of a good state (i.e., thepersistence of a boom) and the persistence of a bad state (i.e.the persistence of a trough) are measured by the probabilitiesππΊ and ππ΅. When the firmmakes its employment decision, it
has complete information about current business conditions,ππ. Regarding the future, the firm has rational expectations
ofππ, knowing the above Markov matrix but not the realized
value of ππ.
When a new member of the workforce is hired, the firmpays a hiring costπ», and, when an incumbent worker is fired,the firm bears a firing cost πΉ, where π» and πΉ are positiveconstants. For simplicity, we assume that the positions ofemployees in the firm are protected by the firing cost πΉ andthat all workers have the same productivity, that is, the samemarginal product for any given level of employment.
Each worker receives a real wage ππper period π. The
wage ππis the outcome of an individualistic Nash bargain
between the firm and each worker, where the employment ofall other workers is taken as given (assuming a sufficientlylarge workforce, the firmβs total employment may be takenas given in the wage setting process). Thus each employee isperceived as the marginal worker in the bargaining process,implying that the firmβs expected profit under agreement isthe workerβs marginal profit (ππ
πβ ππ
πβ βπ), where π
π
π
is the present value of the marginal employeeβs expectedprofits, excluding the current labour cost (to be definedformally below);ππ
πis the employeeβs current wage; and β
π=
π» when the firm is hiring and βπ= 0 when it is not hiring.
ISRN Economics 3
(The firing cost is not relevant here since themarginal worker,by definition, is not fired.)
Under disagreement, employees are assumed to produceno output and undertake industrial action in order to imposea cost on the firm. We assume that workers can manipulatethe level of industrial action without any cost to themselves,and thus they set it as high as possible. However, if the cost ofthe industrial action is higher than the cost of dismissing theworker, it will be optimal for the firm to dismiss the worker.Accordingly, since workers wish to retain their positions inthe firm, they will set the level of the industrial action so thatthe firm is made indifferent between retaining or dismissingthe workers. The firmβs cost of dismissing a worker is πΉ + π +
βπ, where πΉ is the firing cost and π(π > 0) is a further loss
that does not depend on themagnitude of the labour turnovercosts (such as the loss of customer good will). Consequently,the worker will set the level of the industrial action such thatthe firmβs marginal profit under disagreement is β(πΉ+π+β
π).
The workerβs income surplus in the wage bargain isπππ‘β
π0, where π
π
πis the wage under agreement in period π
and π0 is the workerβs fall-back position. Observe that the
workerβs future expected wages do not enter the workerβsincome surplus. The reason is that since the worker is notdismissed, the breakdown in the negotiations has no effecton the workerβs future expected wages. (Since the expectedfuture stream of wages is identical under agreement andunder disagreement, it does not change the workerβs strategicposition in the wage negotiation.)
Thus the Nash bargaining problem is
Maximizeππ
π
Ξ© = (ππ
πβπ0
)
π
(ππ
πβππ
πβ βπ)
1βπ
, (2)
and the solution is the negotiated wage:
ππ
π= (1 β π)π
0
+ π (ππ
π+ πΉ + π) . (3)
In other words, the negotiated wage is a weighted averageof the employeeβs fall-back position and the firmβs surplus(excluding the wage).
The firmβs employment decision is given by the followingprofit maximization problem:
MaximizeπΏπ‘
πΈ
β
β
π=π‘
πΏπβ1
{π (ππ, πΏπ) β π
ππΏπ
βπΆπ(πΏπβ πΏπβ1
)} ,
(4)
where πΏ is the discount factor. The first term is the firmβs realrevenue.The second term is its wage cost, where the wageπ
π
is given by (3). (Observe that πππdepends on the marginal
workerβs expected profit (minus the current labor cost) πππ,
which, in turn, depends on employment.Thus, when the firmmakes its decision on employment, it can predict the wagebargaining response.) The third term is its labour turnovercost, where πΆ
π= π» when πΏ
πβ πΏπβ1
> 0 and πΆπ= βπΉ when
πΏπβ πΏπβ1
< 0.For given values of the parameters, business conditions
(represented by ππΊ and π
π΅) determine the firmβs decision
on whether to hire or fire. To focus on nontrivial results, weassume that the values of ππΊ and π
π΅ are such that there arethree scenarios.
(A1) The firing scenario: when economic conditions dete-riorate, the firm finds it optimal to fire some of itsinsiders.
(A2) The hiring scenario: when economic conditionsimprove, it is optimal to hire new workers.
(A3) The retention scenario: when economic conditions donot change, any previous workforce is retained by thefirm.
The firmβs employment decision is the solution of thedynamic optimization problem (4). It can be shown that theassociated marginal condition for employment is
ππ
π‘βππ
π‘β πΆπ‘= 0. (5)
In words, the optimal level of employment is set so thatthe discounted stream of the marginal employeeβs expectedcurrent and future profits is zero. Note that this equationis equivalent to the condition that the marginal workerβsexpected stream of revenue and wage cost is equal to theturnover cost (hiring cost π» in a good state and firing costβπΉ in a bad state).
Let us now examine the form this marginal conditiontakes in the good and bad states. By the wage equationin (3) and the marginal employment condition in (5), theequilibrium wage in a good state is
ππΊ
π‘= π0
+
π
1 β π
(π» + πΉ + π) (6)
whereas in a bad state it is (this wage is unaffected by turnovercosts, since πΉ reduces both the firmβs fall-back position (βπΉ βπ) and the marginal profitability of the worker (βπΉ) so thatthe firmβs profit surplus is not changed)
ππ΅
π‘= π0
+
π
1 β π
π. (7)
As shown in the appendix, the expected marginal profit(excluding labour costs) in the good state is
ππΊ
π‘= ππ
πΊ
π‘(ππΊ
, πΏπΊ
π‘) β
πππΊ
π‘
ππΏπΊ
π‘
πΏπΊ
π‘+ πΏ [π
πΊ
π» β (1 β ππΊ
) πΉ]
(8)
which may be interpreted as follows.
(i) The first term is the current marginal revenue.(ii) The second term is the wage bargaining response to
the employment decision: The employment of themarginal worker reduces the marginal profit and,consequently, reduces the negotiated wage. Observethat, by (3),
πππΊ
π‘
ππΏπΊ
π‘
= π
πππΊ
π‘
ππΏπΊ
π‘
=
π
1 + π
πππ πΊ
π‘
ππΏπΊ
π‘
. (9)
4 ISRN Economics
Thus any increase in employment reduces the bar-gained wage, which further raises employment. Thisβfeedback effectβ ensures that any change in employ-ment is amplified through the bargained wage.
(iii) The third term of (8) is the workersβ future profitabil-ity: with probability π
πΊ the economy remains in agood state in period π‘ + 1, in which, as in period π‘, themarginal workerβs profitability equals the hiring costπ». With probability (1 β π
πΊ
) the economy falls intoa bad state, in which the firm dismisses the marginalworker and pays the firing cost πΉ.
Observe that, in (8), the firmβs production technologyaffects labour demand both through the form of the marginalrevenue function ππ
πΊ
π‘(ππΊ
, πΏπΊ
π‘) and through the feedback
effect of (9). Thus it is convenient to define the βnet marginalrevenueβ (πππ ) as the sum of the marginal revenue and thefeedback effect:
πππ πΊ
π‘(ππΊ
, πΏπΊ
π‘) = ππ
πΊ
π‘(ππΊ
, πΏπΊ
π‘) β
π
1 + π
πππ πΊ
π‘
ππΏπΊ
π‘
πΏπΊ
π‘. (10)
Substituting ππΊ
π‘(8) and π
πΊ
π‘(6) into the marginal
condition (5), we obtain themarginal condition for hiring (ina good state, i.e. a boom) (observe that this condition holdsin any good state, since the firm is facing the same economicconditions as in hiring times. Thus, in the retention scenariothis condition is satisfied although no newworkers are hired):
πππ πΊ
π‘(ππΊ
, πΏπΊ
π‘) β [π
0
+
π
1 β π
(πΉ + π» + π)]
+ πΏ [ππΊ
π» β (1 β ππΊ
) πΉ] = π».
(11)
Along the same lines it can be shown that the expectedmarginal profit (excluding the labour costs) in the bad state is
ππ΅
π‘= ππ
π΅
π‘(ππ΅
, πΏπ΅
π‘) β
πππ΅
π‘
ππΏπ΅
π‘
πΏπ΅
π‘
+ πΏ [βππ΅
πΉ + (1 β ππ΅
)π»]
(12)
and the marginal condition for firing (in the bad state, i.e.,a trough) is (as in a boom, this condition is satisfied in anytrough.Thus, in the retention scenario it is satisfied althoughthere is no firing)
πππ π΅
π‘(ππ΅
, πΏπ΅
π‘) β [π
0
+
π
1 β π
π]
+ πΏ [βππ΅
πΉ + (1 β ππ΅
)π»] = βπΉ
(13)
by (5), (7), and (12).Having derived the labour demand function in the
stochastic dynamic setting above, we nowproceed to examinethe employment effect of firing costs. We will analyze thiseffect first in the short run (i.e., the effect of firing costs oncurrent employment in a boom and a trough) and then in thelong run (i.e., the effect of firing costs on average employment,
given the probabilities of being in booms and troughs).Finally, on this basis, we will examine how the influenceof firing costs on employment depends on the degree ofpersistence of the booms and troughs. In the appendix weanalyse the influence of hiring costs on employment.
3. The Employment Effect of Firing Costs inthe Short Run
In order to assess the effect of firing costs on employmentin booms and troughs, it is not necessary to consider aspecific functional form of the revenue function: for anyrevenue function increasing and concave in πΏ, the netmarginal revenue is inversely related to the optimal level ofemployment. (Any variation in employment will produce achange of opposite sign in the marginal revenue, which isamplified through the feedback effect.)
To derive the effect of firing costs on employment inbooms, we differentiate (10) with respect to the firing cost πΉand obtain
ππππ πΊ
ππΉ
= πΏ (1 β ππΊ
) +
π
1 β π
> 0 (14)
which is positive; that is, firing costs increase the netmarginalrevenue and consequently discourage hiring and therebydecrease employment. As (14) shows, this effect may bedivided into two subsidiary effects:
(i) The direct effect πΏ(1 β ππΊ
): with probability (1 β ππΊ
)
the firm encounters a bad state in the next time periodand pays the firing cost, which discourages hiring inthe current period. Observe that the more persistentis the boom (i.e., the larger is ππΊ), the smaller theinfluence of firing costs on the marginal revenue andconsequently on current employment:
π2
πππ πΊ
ππΉπππΊ
= βπΏ < 0. (15)
(ii) The fall-back effect π/(1 β π): a rise in the firingcost increases the negotiated wage (and thus reduceshiring) since it decreases the firmβs fall-back positionin wage bargaining. The greater is the workerβs bar-gaining power (π), the larger will be the fall-backeffect.
Similarly, to derive the effect of firing costs on employ-ment in troughs, we differentiate (13) with respect to the firingcost πΉ and find
ππππ π΅
ππΉ
= β (1 β πΏππ΅
) < 0. (16)
This is the direct effect of firing costs: an increase in the cost offiring decreases the net marginal revenue, which discouragesfiring and thereby increases employment. The reason is thatthe cost of currently dismissing workers deters the firmfrom firing. (In this context, there is no fall-back effect offiring costs on the wage (πππ΅/ππΉ = 0), as shown in (7).)
ISRN Economics 5
Observe that the more persistent is the trough (the greaterthe probability of remaining in the bad state), the smallerwill be the effect of firing costs on the marginal revenue andconsequently on employment:
π2
πππ π΅
ππΉπππ΅
= πΏ > 0 (17)
by (16).Thus, both hiring and firing are discouraged by the
existence of firing costs; that is, firing costs decrease thevariability of employment. However, the more persistent isthe boom, the less is hiring discouraged, and the morepersistent is the trough, the less is firing discouraged. Thisimplies that more persistent economic conditions (eithergood or bad) weaken the effect of firing costs on employmentand increase the variability of employment.
4. The Employment Effect of Firing Costsin the Long Run and the Persistence ofEconomic Fluctuations
In the long run, the employment level is
πΈ (πΏ) = Ξ π΅
πΏπΊ
+ Ξ π΅
πΏπ΅
, (18)
where Ξ πΊ and Ξ π΅ are the long-run Markov probabilities for
a good and a bad state, respectively. (The expressions for thelong-run Markov probabilities for a good and a bad state areΞ πΊ
= (1 β ππ΅
)/[(1 β ππΊ
) + (1 β ππ΅
)] andΞ π΅ = (1 β ππΊ
)/[(1 β
ππΊ
) + (1 β ππ΅
)], resp.) Note that the proportion of troughsΞ π΅ is greater than the proportion of booms Ξ πΊ since we are
focusing on the case in which the persistence of troughs isgreater than the persistence of booms ππ΅ > π
πΊ.The effect of firing costs on long-term employment is
ππΈ(πΏ)/ππΉ = Ξ πΊ
ππΏπΊ
/ππΉ + Ξ π΅
ππΏπ΅
/ππΉ. Since ππΏπ
/ππΉ =
(ππππ π
/ππΉ)(ππΏπ
/ππππ π
), to study the effect of firing costson long-run employment we need to refer to a specificrevenue function. (The two components of ππΏπ/ππΉ are theeffect of firing costs on the πππ in each state of nature(ππππ
π
/ππΉ), in (14) and (16), and the responsiveness ofemployment to a change in theπππ in each state of nature(ππΏπ
/ππππ π
, π = πΊ, π΅). This last term (the inverse of theslope of the marginal revenue curve with respect to employ-ment) clearly depends on the form of the revenue function.)Let us consider the following revenue function:
π (πΏ, π) = ππ
πΏπ
β
1
2
π(πΏπ
)
2 (19)
for which πππ π
= ππ
β π/(1 + π)πΏπ. This is the simplest
case, since ππΏπ/ππππ π
= β(1 + π)/π, that is, the reaction ofemployment to a change in theπππ is constant for any stateof nature. (We show in the appendix that the results presentedin this section also hold for other revenue functions, inparticular for a revenue function linear-quadratic in laborwith multiplicative shocks and a Cobb-Douglas revenuefunction when turnover costs are sufficiently large.) Thus the
demand for labour is linear with additive shocks. (This labordemand function is derived from (11) and (13), and from theexpression for NMR.)
The effect of firing costs on employment in booms andtroughs, respectively, is
ππΏπΊ
ππΉ
= β
(1 + π)
π
[πΏ (1 β ππΊ
) +
π
1 β π
] < 0;
ππΏπ΅
ππΉ
=
(1 + π)
π
(1 β πΏππ΅
) > 0.
(20)
Therefore, the effect of firing costs on long-term employmentis
ππΈ (πΏ)
ππΉ
= β
(1 + π)
π
{ [Ξ πΊ
πΏ (1 β ππΊ
)
βΞ π΅
(1 β πΏππ΅
)] + [Ξ πΊ
π
1 β π
]} ,
(21)
where the first term in square brackets is the direct effect andthe second term in square brackets is the fall-back effect.
Observe in (21) that the direct effect of firing costs onaverage employment is positive because the firing cost is paidtoday (undiscounted) when the firm is firing whereas it maybe paid tomorrow (discounted) when the firm is hiring. Thisqualitative conclusion is not affected by the proportion oftroughs and booms. (The reason is that although we couldexpect a greater proportion of booms, which strengthens thehiring scenario, ππΊ > π
π΅ would also imply that the chancesof firing the new recruits in the future are smaller. Thus, theeffect of firing costs on the firing scenario dominates.)
Regarding the fall-back effect, observe that the negotiatedwage in a boom depends on the firing cost whereas thewage in a trough does not (by (6) and (7)). An increase inthe firing cost raises the wage in booms since it worsensthe firmβs fall-back position; but such an increase leaves thewage in troughs unaffected since the rise in the firing costworsens the firmβs fall-back position by just as much as itreduces the marginal product of labour. Thus the fall-backeffect only appears in booms and its influence on employmentis unambiguously negative: the greater are firing costs, thelarger is the bargained wage in booms, which reduces hiring,as (21) shows.
The overall effect of the firing cost on average employ-ment depends on the relative size of these two effects. Thisrelative magnitude depends critically on two parameters: (i)the bargaining power of the worker and (ii) the persistence ofeconomic conditions (ππΊ and ππ΅). Let us examine the effectof each parameter.
(i)How Employeesβ Bargaining Strength Influences theEmployment Effect of Firing Costs. For a sufficiently large π,the fall-back effect of firing costs via the wage may offset the
6 ISRN Economics
Fallproportion of
booms
Riseproportion of
troughs
Change
direct effect(Discounted)(ii)
(i)
Fall-back effect
(undiscounted)
Increase indE(L)/dF
Increase indE(L)/dF
Risein PB
Direct effect
(discounted)
Direct effect
(undiscounted)
dWG/dF > 0
dLB/dF > 0
dLG/dF < 0
Figure 1: The influence of more persistent troughs on the employment effect of firing costs.
direct effect and make negative the influence of firing costson average employment. This occurs for any π that satisfies
π > πβ
=
(1 β πΏ) (1 β ππΊ
)
(1 β πΏ) (1 β ππΊ) + (1 β π
π΅)
. (22)
Note that the boundary πβ from which the effect of firing
costs on average employment is negative is larger the smalleris ππΊ with respect to ππ΅.Thus, the greater is the proportion oftroughs relative to booms, the greater is the bargaining powerof the worker π for which the effect of firing costs on averageemployment becomes negative.
(ii)How the Persistence of Economic Conditions Influencesthe Employment Effect of Firing Costs. We focus on thescenario in which troughs are more persistent than booms.We first show that the more persistent are troughs relative tobooms, the more frequently the economy is in troughs andthe less frequently in booms, and the more expansionary (orless contractionary) is the effect of firing costs on averageemployment. Then, we show that the frequency of troughsmay also rise due to a proportional increase in the persistenceof both booms and troughs, so that the influence of πΉ on πΈ(πΏ)is more expansionary.
To prove that the more persistent are booms relativeto troughs, the more expansionary is the effect of πΉ onaverage employment, we analyse the case in which troughsare more prolonged for given booms. (To prove the effectof more persistent troughs relative to booms, we can showthat (a) the more persistent are troughs for given booms themore expansionary is the effect of firing costs on averageemployment, and (b) the less persistent are booms for giventroughs the more expansionary is the effect of firing costson average employment. In the appendix we prove (b) and
show that the qualitative intuition is the same as for (a).) Theinfluence of more persistent troughs is
π2
πΈ (πΏ)
ππΉπππ΅= β
(1 + π)
π
Γ {[
πΞ πΊ
πππ΅πΏ (1βπ
πΊ
)β
πΞ π΅
πππ΅(1βπΏπ
π΅
)]+[πΏΞ π΅
]}
β
(1 + π)
π
(
πΞ πΊ
πππ΅
π
1 β π
) .
(23)
The first term (in the first and second rows of (23)) is theinfluence of the greater ππ΅ on the direct effect of firing costs,whereas the second term (in the third row) is the influence ofthe greater ππ΅ on the fall-back effect of firing costs.
From (21) and (23), it is clear that more persistent troughs(i.e., an increase in ππ΅) will influence the direct effect via thechange in the following:
(i) the proportion of booms Ξ πΊ and the proportion oftroughs Ξ π΅(first term in curly brackets),
(ii) the employment effect of firing costs in troughsππΏπ΅
/ππΉ (second term in curly brackets),while the increase in π
π΅ will influence the fall-backeffect via the change in Ξ πΊ (third row).
We describe these terms below and use Figure 1 to illus-trate the analysis.
(i) Regarding the change in the proportions of boomsand troughs, it is clear that a greater persistence oftroughs (an increase in π
π΅) will augment the pro-portion of troughs Ξ π΅ and reduce the proportion ofbooms Ξ πΊ. This is represented by (i) in Figure 1.
ISRN Economics 7
βE(L
)βF
ΞΌ1ΞΌ2
ΞΌ3
PB
0
20
40
60
80
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
β80
β60
β40
β20
Figure 2: The influence of ππ΅ on ππΈ(L)/ππΉ.
The implication for the direct effect is the following:the increase in the proportion of troughs implies, on theone hand, a decrease in the frequency with which the firmβshiring is discouraged by firing costs (due to the possibility ofpaying πΉ in the future). Additionally, the greater proportionof troughs increases the frequencywithwhich the firm retainsworkers in order to avoid paying the firing cost (observe thatthis effect is undiscounted). As a consequence, the rise in Ξ π΅
and the fall in Ξ πΊ increase the positive direct effect.
(ii) Regarding the change in the direct effect of πΉ introughs, we showed in (17) that more persistent eco-nomic conditions will weaken ππΏπ΅/ππΉ. (Recall that, inthe firing scenario, a greater ππ΅ increases the proba-bility of retaining the marginal worker in the future,with profitabilityβπΉ.) Note that this effect depends onthe discount factor πΏ. This term is represented by thelast line of Figure 1.
Regarding the fall-back effect, it is only influenced bythe greater ππ΅ via the change in the proportions of boomsand troughs (Ξ πΊ and Ξ π΅). The greater proportion of troughsimplies that the firm is less frequently paying the wage inbooms (which is higher due to firing costs). Thus, the risein ππ΅ reduces the negative fall-back effect. The first row of
Figure 1 represents it.Solving (23), we obtain that
π2
πΈ (πΏ)
ππΉπππ΅=
(1 + π)
π
(1 β ππΊ
)
[(1 β ππΊ) + (1 β π
π΅)]2
Γ [(1 β πΏ) +
π
1 β π
] > 0.
(24)
The first term in square brackets (1 β πΏ) is related tothe influence of ππ΅ on the direct effect and is positive; thatis, the more persistent are recessions, the more positive isthe direct effect of firing costs on average employment. Thismeans that what dominates here is effect (i) (via the changein the proportionsΞ πΊ andΞ π΅). The reason is that the greater
frequency with which the firm retains workers to avoid thefiring costs is undiscounted while, in contrast, effect (ii)(via the change in the employment level) is discounted. Thesecond term in square brackets (π/(1 β π)) is related tothe influence of ππ΅ on the fall-back effect (i.e., the morepersistent are troughs, the less negative is the fall-back effectof firing costs on average employment). Figure 2 illustratesthe result. In Figure 1 we represent in boxes the mechanismsthat determine the increase in ππΈ(πΏ)/ππΉ.
Now we show that the frequency of troughs relative toboomsmay also rise due to a proportional increase in the per-sistence of both booms and troughs. As a consequence,we show that the qualitative conclusions reached for morepersistent troughs also apply in the case of more persistenteconomic fluctuations.
Differentiating (21) with respect to ππΊ and ππ΅, the effect
of more persistent booms and troughs (i.e., the greater persis-tence of economic fluctuations) is (π2πΈ(πΏ)/ππΉππ = π
2
πΈ(πΏ)/
ππΉπππΊ
+ π2
πΈ(πΏ)/ππΉπππ΅):
π2
πΈ (πΏ)
ππΉππ
= β
(1 + π)
π
{[
πΞ πΊ
ππ
πΏ (1 β ππΊ
) β
πΞ π΅
ππ
(1 β πΏππ΅
)]
β [πΏΞ πΊ
β πΏΞ π΅
] }
β
(1 + π)
π
{
πΞ πΊ
ππ
π
1 β π
} ,
(25)
where πΞ π/ππ = πΞ π
/πππΊ
+ πΞ π
/πππ΅. The first term (in the
first and second rows of (25)) is the influence of the greater πon the direct effect of firing costs, whereas the second term (inthe third row) is the influence of the greaterπ on the fall-backeffect of firing costs.
As for the greater ππ΅, the greater π influences ππΈ(πΏ)/ππΉ(i) via the change in the proportions of booms and troughs(Ξ πΊ and Ξ
π΅), represented by the first term in curly bracketsin the first row and by the second row, and (ii) via the changein the direct effect in booms and the direct effect in troughs,
8 ISRN Economics
represented by the second term in curly brackets in the firstrow.
(i) Regarding the change in the proportions of boomsand troughs, a simultaneous increase in π
πΊ and ππ΅
changes the proportion of booms in the followingway(it is clear that a greater persistence of booms (anincrease inππΊ) will augment the proportion of boomsΞ πΊ; the magnitude depends on the probability of the
economy leaving troughs and moving into booms(1 β π
π΅
). On the other hand, a greater persistence oftroughs (an increase in π
π΅) will reduce Ξ πΊ; the mag-nitude depends on the probability of the economyleaving booms and moving into troughs (1 β π
πΊ
)):
πΞ πΊ
πππΊ=
(1 β ππ΅
)
[(1 β ππΊ) + (1 β π
π΅)]2> 0;
πΞ πΊ
πππ΅= β
(1 β ππΊ
)
[(1 β ππΊ) + (1 β π
π΅)]2< 0.
(26)
Thus, the net influence of a simultaneous increase in ππΊ and
ππ΅ on the proportion of booms is
πΞ πΊ
ππ
=
(ππΊ
β ππ΅
)
[(1 β ππΊ) + (1 β π
π΅)]2< 0 for ππ΅ > π
πΊ
. (27)
If the persistence of booms and troughs was symmetric (i.e.equalππΊ andππ΅), a proportional increase inππΊ andππ΅wouldgenerate two counteracting effects which will cancel out: Ξ πΊ
would not change. In contrast, in the case in which ππ΅ > ππΊ,
the probability of the economy moving from a trough to aboom (1βπ
π΅
) is smaller than the probability of moving froma boom to a trough (1 β ππΊ). Therefore, the economy is morelikely to be in troughs and the effect of the increase inππ΅ dominates (i.e., the proportion of booms decreases).
Similarly, in the case of the proportion of recessions Ξ π΅
(by the expressions for the long-run Markov probabilities,πΞ π΅
/πππΊ
= βπΞ πΊ
/πππΊ and πΞ π΅/πππ΅ = βπΞ
πΊ
/πππ΅):
πΞ π΅
ππ
= β
(ππΊ
β ππ΅
)
[(1 β ππΊ) + (1 β π
π΅)]2> 0 for ππΊ < π
π΅
. (28)
Thus, a simultaneous increase inππΊ andππ΅ raises the propor-tion of troughs and reduces the proportion of booms, forππ΅ >ππΊ (note that it is unimportant if the difference between π
πΊ
and ππ΅ is proportional or additive).This is represented by thesecond row of Figure 1, and has the same consequence as theincrease in π
π΅: the rise in Ξ π΅ and the fall in Ξ
πΊ increase thepositive direct effect and weaken the negative fall-back effect.This is the influence that dominates since it is undiscounted.
(ii) Regarding the change in the direct effect in boomsand the direct effect in troughs, this effect is dis-counted and does not determine the sign of the result.
(As to the change in the direct effect in booms andthe direct effect in troughs, we showed in Section 2thatmore persistent economic conditionswill weakenboth ππΏ
πΊ
/ππΉ and ππΏπ΅
/ππΉ. On the other hand, πΏπΊis higher since a more persistent boom reduces theprobability of firing in the future and bearing thefiring cost: π2πΏπΊ/ππΉπππΊ = πΏ((1+π)/π) > 0. Addition-ally, πΏπ΅ is lower since a greater ππ΅ increases the pos-sibility of retaining workers in the future with amarginal profit of βπΉ: π2πΏπ΅/ππΉπππ΅ = βπΏ((1 +π)/π) <
0. As the proportion of troughs is greater than the pro-portion of boomsΞ π΅ > Ξ
πΊ, what happens in troughsdominates. Note that these effects depend on thediscount factor πΏ. This term is represented by the lastline of Figure 1.)
Figure 1 is also useful to illustrate this result since thequalitative intuition is the same as in the case of a greaterpersistence of troughs.
Solving (25), we obtain that
π2
πΈ (πΏ)
ππΉππ
= β
(1 + π)
π
(ππΊ
β ππ΅
)
[(1 β ππΊ) + (1 β π
π΅)]2
Γ [(1 β πΏ) + (
π
1 β π
)] > 0.
(29)
The first term in square brackets (1 β πΏ) is related to theinfluence ofπ on the direct effect and the second term (π/(1β
π)) to the influence on the fall-back effect. As (29) shows, bothterms are positive; that is, the more persistent are economicfluctuations, the more expansionary is the effect of firingcosts on average employment (when π
πΊ
< ππ΅). As in the
case of more prolonged troughs, the greater proportion oftroughs, and the lower proportion of booms increases thepositive direct effect of firing costs. Additionally, the smallerproportion of boomsmakes the firm to pay less often thewageππΊ, which reduces the negative fall-back effect. Observe that
the results above are stronger the wider is the differencebetween the persistence of troughs and the persistence ofbooms.
5. Conclusions
This paper studies the influence of turnover costs on averagelabour demand when the persistence of recessions is greaterthan the persistence of booms. In doing so, we also take intoaccount the influence of turnover costs on the negotiatedwage. We show that the more persistent are troughs relativeto booms, the more frequently firms are in a situation wherefiring costs discourage firing and so the more positive is theeffect of firing costs on labour demand. In this way, when aneconomy is suffering more prolonged recessions (relative tobooms), our analysis suggests that a reduction in firing costswill also reduce average labour demand.
ISRN Economics 9
Appendices
A. Revenue Function Linear Quadratic inLabour with Additive Shocks
A.1. Firing Costs. We prove that the less persistent are boomsrelative to troughs, the more expansionary is the effect of fir-ing costs on average employment:
β
π2
πΈ (πΏ)
ππΉπππΊ=
(1 + π)
π
(1 β ππ΅
)
[(1 β ππΊ) + (1 β π
π΅)]2
Γ [(1 β πΏ) +
π
1 β π
] > 0.
(A.1)
A.2. Hiring Costs
A.2.1. Short Run. The effect of hiring costs on employment inbooms is, by (10),
ππΏπΊ
ππ»
= β
(1 + π)
π
[(1 β πΏππΊ
) +
π
1 β π
] < 0. (A.2)
This effect may be divided into two subsidiary effects.
(i) The direct effect (1βπΏππΊ): hiring costs discourage hir-ing. However, the greater is ππΊ, the less important isthe fixed cost of hiring:
π2
πΏπΊ
ππ»πππΊ= πΏ > 0. (A.3)
(ii) The profitability effect π/(1 β π): the cost of hiringincreases themarginal profit of theworker, and he canobtain a higher wage in the negotiation.The greater isπ, the larger will be the profitability effect.
The effect of hiring costs on employment in troughs is,from (13),
ππΏπ΅
ππΉ
=
(1 + π)
π
(1 β πΏππ΅
) > 0, (A.4)
that is, hiring costs discourage firing: the higher the cost ofhiring themore workers will be retained in bad times to avoidthe hiring cost if economic conditions improve.The greater isππ΅ the less important is this effect:
π2
πΏπ΅
ππ»πππ΅= βπΏ < 0 (A.5)
by (A.4).
A.2.2. Long Run. The effect of hiring costs on long-termemployment is
ππΈ (πΏ)
ππ»
= β
(1 + π)
π
{ [Ξ πΊ
(1 β πΏππΊ
) β Ξ π΅
πΏ (1 β ππ΅
)]
+ [Ξ πΊ
π
1 β π
]} ,
(A.6)
where the first term in square brackets is the direct effectand the second term in square brackets is the profitabilityeffect.The direct effect of hiring costs on average employmentmay be positive or negative, depending on πΏ. Regarding theprofitability effect, the negotiated wage in a boom dependson the hiring cost whereas the wage in a trough does not (by(6) and (7)). The overall effect of the firing cost on averageemployment depends on the relative size of these two effects,which in turn depends on π, ππΊ and ππ΅.
(i) How employeesβ bargaining strength influences theemployment effect of hiring costs: since the profitabil-ity effect is formally identical to the fall-back effect,the qualitative result in the case of firing costs holdsalso in the case of hiring costs.
(ii) How the persistence of economic conditions influ-ences the employment effect of firing costs.
These equations are very similar to the case of firing costs.The influence of less persistent booms is
β
π2
πΈ (πΏ)
ππ»πππΊ=
(1 + π)
π
(1 β ππ΅
)
[(1 β ππΊ) + (1 β π
π΅)]2
Γ [(1 β πΏ) +
π
1 β π
] > 0.
(A.7)
The influence of more persistent troughs is
π2
πΈ (πΏ)
ππ»πππ΅=
(1 + π)
π
(1 β ππΊ
)
[(1 β ππΊ) + (1 β π
π΅)]2
Γ [(1 β πΏ) +
π
1 β π
] > 0.
(A.8)
The effect of more prolonged booms and troughs is
π2
πΈ (πΏ)
ππ»ππ
= β
(1 + π)
π
(ππΊ
β ππ΅
)
[(1 β ππΊ) + (1 β π
π΅)]2
Γ [(1 β πΏ) + (
π
1 β π
)] > 0,
(A.9)
that is, the more persistent are economic fluctuations, orthe more persistent are troughs relative to booms, the moreexpansionary is the effect of hiring costs on average employ-ment (when ππ΅ > π
πΊ).
B. Revenue Function Linear-Quadratic inLabour with Multiplicative Shocks andCobb-Douglas Production Function
The effect of firing costs on long-term employment is
ππΈ (πΏ)
ππΉ
= [Ξ πΊ
πΏ (1 β ππΊ
)
ππΏπΊ
ππππ πΊ
βΞ π΅
(1 β πΏππ΅
)
ππΏπ΅
ππππ π΅] + Ξ
πΊπ
1 β π
ππΏπΊ
ππππ πΊ,
(B.1)
10 ISRN Economics
where the first term (with square brackets) is the direct effectand the second term (without brackets) is the fall-back effect.The term ππΏ
π
/ππππ π depends on the form of the revenue
function. We consider two additional revenue functions.
(a) (πΏ, π) = ππ
(πΏπ
βπ/2(πΏπ
)2
), for whichπππ π
= π(1βπ/
(1 + π)πΏπ
). In this case, ππΏπ/ππππ π
= β(1 + π)/ππ
π,that is, the reaction of employment to a change inthe πππ depends on the state of nature π
π: sinceππΊ
> ππ΅, πΏπ΅ is more responsive than πΏ
πΊ to anidentical change in theπππ (|ππΏπΊ/ππππ
πΊ
| < |ππΏπ΅
/
ππππ π΅
|).(b) π (πΏ, π) = π
π
(πΏπ(1βπ½)
/(1 β π½)) (Cobb-Douglas revenuefunction). Thus πππ
π
= ππ
πΏπ(βπ½)
[1 + π½π/(1 + π)];that is, the πππ is convex in employment. In thiscase, the responsiveness of employment to a change intheπππ is ππΏπ/ππππ
π
= βπΏπ(π½+1)
/{ππ
π½[1 + π½π/(1 +
π)]}. Observe that, for the Cobb-Douglas revenuefunction, the relative magnitude of ππΏ
πΊ
/ππππ πΊ
with respect to ππΏπ΅/ππππ π΅depends not only on the
business conditions ππ, but also on the employmentlevels πΏπΊ and πΏπ΅. We derive the levels of employmentfrom the first-order condition in (8) and (12) and theπππ :
πΏπΊ
π‘= (
ππΊ
π‘β πΏππΊ
π» + πΏ (1 β ππΊ
) πΉ + π»
ππΊ(1 + π½π/ (1 + π))
)
β1/π½
,
πΏπ΅
π‘= (
ππ΅
π‘β πΏ (1 β π
π΅
)π» + πΏππ΅
πΉ + π»
ππΊ(1 + π½π/ (1 + π))
)
β1/π½
.
(B.2)
πΏπΊ must be greater than πΏπ΅, which implies that
ππΊ
ππ΅> ( (π
0
+ π/ (1 β π) (π» + πΉ + π) β πΏππΊ
π»
+πΏ (1 β ππΊ
) πΉ + π»)
Γ (π0
+ π/ (1 β π) π β πΏ (1 β ππ΅
)π»
+πΏππ΅
πΉ β πΉ)
β1
) .
(B.3)
Recall from Section 1 that the higher πΉ and π», the moreemployment is stabilized over the cycle, and the closer areπΏπΊ and πΏ
π΅. Thus, when πΏπΊ and πΏ
π΅ are sufficiently close (i.e.,turnover costs sufficiently high relative to (ππΊ β π
π΅)), it mayhappen that |ππΏπΊ/ππππ
πΊ
| < |ππΏπ΅
/ππππ π΅
|. This inequalityis satisfied when
ππΊ
ππ΅< ( (π
0
+ π/ (1 β π) (π» + πΉ + π) β πΏππΊ
π»
+πΏ (1 β ππΊ
) πΉ + π»)
Γ(π0
+π/(1βπ)πβπΏ(1βππ΅
)π»+πΏππ΅
πΉβπΉ)
β1
)
(π½+1)
.
(B.4)
In contrast, when πΏπΊ and πΏ
π΅ are sufficiently different(turnover costs sufficiently low), it may happen that |ππΏπΊ/ππππ
πΊ
| > |ππΏπ΅
/ππππ π΅
| (the inequality in (B.4) must holdin the opposite direction).Thus, for sufficiently large turnovercosts, the Cobb- Douglas revenue function satisfies the fol-lowing condition: |ππΏπΊ/ππππ
πΊ
| β€ |ππΏπ΅
/ππππ π΅
|. (Thiscondition also depends on the persistence of macroeconomicfluctuations since the more prolonged is the boom the higheris employment in a good state, and the more prolonged is thetrough, the lower is employment in the bad state. Observein the expressions for πΏ
πΊ and πΏπ΅ that, in the absence of
turnover costs, the persistence of the shock has no influenceon employment.)
Regarding the direct effect in (B.1), when |ππΏπΊ
/
ππππ πΊ
| β€ |ππΏπ΅
/ππππ π΅
|, the direct effect of firing costson average employment is positive. When |ππΏ
πΊ
/ππππ πΊ
| >
|ππΏπ΅
/ππππ π΅
| (the case of the Cobb-Douglas revenuefunction with low turnover costs), the direct effect maybecome negative since the hiring scenario becomes moreimportant. The fall-back effect is negative. The overall effectof the firing cost on average employment depends on therelative size of these two effects, which depends on π and ππΊ
and ππ΅. Let us examine the results above for each productionfunction.
We show that the effect ofπΉ onπΈ(πΏ) ismore expansionary,when |ππΏ
πΊ
/ππππ πΊ
| β€ |ππΏπ΅
/ππππ π΅
| and ππ΅
> ππΊ, the
greater is the persistence of economic fluctuations and themore prolonged are troughs.
B.1. Revenue Function Linear-Quadratic in Labour withMulti-plicative Shocks. The effect of firing costs on average employ-ment equals, by (B.1),
ππΈ (πΏ)
ππΉ
= [βΞ πΊ
πΏ (1βππΊ
)
(1 + π)
ππΊπ
+ Ξ π΅
(1βπΏππ΅
)
(1 + π)
ππ΅π
]
β Ξ πΊ
π
1 β π
(1 + π)
ππΊπ
,
(B.5)
ππΈ(πΏ)/ππΉ is smaller than 0 when
π > πβ
= ((1 β ππΊ
) [ππΊ
(1 β πΏππ΅
) β ππ΅
πΏ (1 β ππ΅
)])
Γ ( (1 β ππΊ
) [ππΊ
(1 β πΏππ΅
) β ππ΅
πΏ (1 β ππ΅
)]
+ππ΅
(1 β ππ΅
))
β1
.
(B.6)
ISRN Economics 11
The effect of a greater persistence of economic conditions is
π2
πΈ (πΏ)
ππΉππ
= β
(1 + π)
ππΊππ΅π
[
πΞ πΊ
ππ
ππ΅
πΏ (1 β ππΊ
)
+
πΞ π΅
ππ
ππΊ
(1 β πΏππ΅
)]
β
(1 + π)
ππΊππ΅π
[
πΞ πΊ
ππ
ππ΅
π
1 β π
βπΏ(ππ΅
Ξ πΊ
β ππΊ
Ξ π΅
)]
(B.7)
which rearranging is
π2
πΈ (πΏ)
ππΉππ
=
ππ΅
πΏ [(1 β ππΊ
)
2
+ (1 β ππ΅
)
2
]
(π [(1 β ππΊ) + (1 β π
π΅)] ππΊππ΅) / (1 + π)
β (ππΊ
[πΏ(1 β ππΊ
)
2
+ (1 β ππ΅
) (1 β πΏππ΅
)
β (1 β ππΊ
) (1 β πΏ)] )
Γ (π [(1βππΊ
)+(1βππ΅
)]ππΊ
ππ΅
/ (1 + π))
β1
> 0.
(B.8)
This expression is positive. Recall from the text that for therevenue function for which |ππΏπΊ/ππππ
πΊ
| = |ππΏπ΅
/ππππ π΅
|,the more persistent the fluctuations the more expansionary isthe effect of πΉ on πΈ(πΏ) (when π
π΅
> ππΊ) because the greater
persistence increases the proportion of troughs and thereforeincreases the importance of the positive direct effect of πΉ onemployment in troughs (which is undiscounted). As shownabove, for the revenue function linear-quadratic in labourwith multiplicative shocks |ππΏπΊ/ππππ
πΊ
| < |ππΏπ΅
/ππππ π΅
|.Given that the bad state is more important in relative terms,the increase in the proportion of troughs is also the effect thatdominates.The intuition is the same as in the case of a revenuefunction liner-quadratic in labour with additive shocks.
This explanation also applies for the case of more persis-tent troughs:
π2
πΈ (πΏ)
ππΉπππ΅=
(1 + π)
ππΊππ΅π
Γ ((1 β ππΊ
) [ππ΅
πΏ (1 β ππΊ
) + ππ΅
(π/ (1 β π))
+ππΊ
(1 β πΏππ΅
)])
Γ ([(1 β ππΊ
) + (1 β ππ΅
)]
β2
)
β
(1 + π)
ππΊππ΅π
πΏππΊ
Ξ π΅
=
(1 + π)
ππΊππ΅π
Γ ( (1 β ππΊ
) [ππ΅
πΏ (1 β ππΊ
) + ππ΅
(π/ (1 β π))
+ππΊ
(1 β πΏ (2 β ππΊ
))] )
Γ ([(1 β ππΊ
) + (1 β ππ΅
)]
β2
).
(B.9)
This equation is positive whenππΊ/(ππΊβππ΅) < πΏ(1βππΊ
)/(1β
πΏ). As to less persistent booms:
β
π2
πΈ (πΏ)
ππΉπππΊ=
(1 + π)
ππΊππ΅π
Γ ((1 β ππ΅
) [ππ΅
πΏ (1 β ππΊ
) + ππ΅
(π/1 β π)
βππΊ
(1 β πΏππ΅
)])
Γ ([(1 β ππΊ
) + (1 β ππ΅
)]
β2
)
β
(1 + π)
ππΊππ΅π
πΏππ΅
Ξ πΊ
= ( (1 β ππ΅
) [ππ΅
πΏ (1 β ππ΅
) + ππ΅
(π/1 β π)
+ππΊ
(1 β πΏππ΅
)] )
Γ (ππΊ
ππ΅
π[(1 β ππΊ
)+(1βππ΅
)]
2
/ (1 + π))
β1
> 0.
(B.10)
B.2. Cobb-Douglas Revenue Function. The effect of πΉ on πΈ(πΏ)is
ππΈ (πΏ)
ππΉ
= β
Ξ πΊ
πΏπΊ(π½+1)
[πΏ (1 β ππΊ
) + π/ (1 β π)]
ππΊπ½ [1 + π½π/ (1 + π)]
+
Ξ π΅
πΏπ΅(π½+1)
(1 β πΏππ΅
)
ππ΅π½ [1 + π½π/ (1 + π)]
.
(B.11)
12 ISRN Economics
Regarding the persistence of the fluctuations, the generalexpression is
π2
πΈ (πΏ)
ππΉππ
= {βπΏΞ πΊ
+
πΞ πΊ
ππ
[πΏ (1 β ππΊ
) +
π
1 β π
]}
Γ
ππΏπΊ
ππππ πΊβ [βπΏΞ
π΅
+
πΞ π΅
ππ
(1 β πΏππ΅
)]
Γ
ππΏπ΅
ππππ π΅
+ {Ξ πΊ
[πΏ (1 β ππΊ
) + π/ (1 β π)]}
ππΏπΊ
ππππ πΊπππΊ
β Ξ π΅
(1 β πΏππ΅
)
ππΏπ΅
ππππ π΅πππ΅
.
(B.12)
The first three rows of (B.12) are the same for any of theproduction functions. The last two lines appear only for theCobb-Douglas revenue function since ππΏπ/ππππ
π dependson the persistence of the fluctuations. These are relativelysmall effects and do not determine the result. We concentratein the first two lines.
For the Cobb-Douglas revenue function there are twoscenarios (described above): (i) for sufficiently large turnovercosts the condition |ππΏ
πΊ
/ππππ πΊ
| < |ππΏπ΅
/ππππ π΅
| is sat-isfied, while (ii) for sufficiently small turnover costs thecondition |ππΏπΊ/ππππ
πΊ
| > |ππΏπ΅
/ππππ π΅
| is satisfied.
(i) This case is qualitatively the same as the case ofthe revenue function linear quadratic in labour withmultiplicative shocks.
(ii) In this case employment in booms is more responsiveto a given change in the NMR. Regarding the directeffect, for the increase in the proportion of troughs(and the increase in the importance of the undis-counted positive effect of πΉ on employment in firingtimes) to dominate, it is necessary that the discountfactor πΏ is sufficiently large.
The influence of less persistent booms is
β
π2
πΈ (πΏ)
ππΉπππΊ= β {βπΏΞ
πΊ
+
πΞ πΊ
πππΊ[πΏ (1 β π
πΊ
) +
π
1 β π
]}
Γ
ππΏπΊ
ππππ πΊ+ [
πΞ π΅
πππΊ(1 β πΏπ
π΅
)]
ππΏπ΅
ππππ π΅
β {Ξ πΊ
[πΏ (1 β ππΊ
) + π/ (1 β π)]}
Γ
ππΏπΊ
ππππ πΊπππΊ
.
(B.13)
The explanation of the sign of (B.13) is identical to the expla-nation of the sign of (B.12).
The influence of more persistent troughs is
π2
πΈ (πΏ)
ππΉπππ΅= {
πΞ πΊ
πππ΅[πΏ (1 β π
πΊ
) +
π
1 β π
]}
ππΏπΊ
πNMRπΊ
β [βπΏΞ π΅
+
πΞ π΅
πππ΅(1 β πΏπ
π΅
)]
ππΏπ΅
πNMRπ΅
β Ξ π΅
(1 β πΏππ΅
)
ππΏπ΅
πNMRπ΅πππ΅.
(B.14)
Regarding (B.14), we need to differentiate between two sce-narios:
(i) Sufficiently large turnover costs: this case is qualita-tively the same as the case of the revenue functionlinear quadratic in labour with multiplicative shocks.
(ii) Sufficiently small turnover costs: given that employ-ment in booms is more responsive, the reduction inthe proportion of booms is the effect that dominates.Thus the qualitative result is the same as for the rev-enue function linear quadratic in labour with additiveshocks.
References
[1] OECD, Employment Outlook 2004, Organisation for EconomicCo-operation and Development, 2004.
[2] R. Layard, S. Nickell, and R. Jackman, Unemployment: Macroe-conomic Performance and the Labor Market, Oxford UniversityPress, Oxford, UK, 1991.
[3] E. P. Lazear, βJob security provisions and employment,β Quar-terly Journal of Economics, vol. 105, no. 3, pp. 699β726, 1990.
[4] G. Bertola, βJob security, employment and wages,β EuropeanEconomic Review, vol. 34, no. 4, pp. 851β886, 1990.
[5] H. A. Hopenhayn and R. Rogerson, βJob turnover and policyevaluation: a general equilibrium approach,β Journal of PoliticalEconomy, vol. 101, no. 5, pp. 915β938, 1993.
[6] S. Nickell, βUnemployment and labor market rigidities: Europeversus North America,β Journal of Economic Perspectives, vol. 11,no. 3, pp. 55β74, 1997.
[7] J. Heckman and C. Pages, βThe cost of job security regulation:evidence from Latin American labor markets,β NBERWorkingPaper 7773, 2000.
[8] S. Bentolila andG. Bertola, βFiring costs and labor demand: howbad is eurosclerosis?β Review of Economic Studies, vol. 57, no. 3,pp. 381β402, 1990.
[9] G. Bertola, βLabor turnover costs and average labor demand,βJournal of Labor Economics, vol. 10, pp. 389β411, 1992.
[10] S. Bentolila and G. Saint-Paul, βA model of labor demand withlinear adjustment costs,β Labour Economics, vol. 1, no. 3-4, pp.303β326, 1994.
[11] P. DΔ±az-Vazquez, D. J. Snower, and L. E. Arjona-Bejar, βOn-the-job learning, firing costs and employment,β Contributionsto Economic Analysis and Policy, vol. 4, no. 1, article 2, 2005.
[12] P. DΔ±az-Vazquez and D. J. Snower, βEmployment, macroeco-nomic fluctuations and job security,β CEPR Discussion Paper1430, CEPR, London, UK, 1996.
ISRN Economics 13
[13] P. DΔ±az-Vazquez and D. J. Snower, βCan insider power affectemployment?β German Economic Review, vol. 4, no. 2, pp. 139β150, 2003.
[14] P. DΔ±az-Vazquez and D. J. Snower, βOn-the-job learning and theeffects of insider power,β Labour Economics, vol. 13, no. 3, pp.317β341, 2006.
[15] A. Lindbeck and D. J. Snower, The Insider-Outsider Theory ofEmployment and Unemployment, MIT Press, Cambridge, Mass,USA, 1989.
[16] L. Ljungqvist and T. J. Sargent, βTwo questions about Europeanunemployment,β Econometrica, vol. 76, no. 1, pp. 1β29, 2008.
[17] L. Nunziata, βLabour market institutions and the cyclical dy-namics of employment,β Labour Economics, vol. 10, no. 1, pp. 31β53, 2003.
[18] Y. F. Chen, D. Snower, and G. Zoega, βLabour-market institu-tions and macroeconomic shocks,β Labour, vol. 17, no. 2, pp.247β270, 2003.
[19] M. Veracierto, βFiring costs and business cycle fluctuations,βInternational Economic Review, vol. 49, no. 1, pp. 1β39, 2008.
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