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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 Díaz-Vázquez and Luis E. Arjona-Béjar

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 Dıaz-Vazquez; [email protected]

Received 10 December 2012; Accepted 26 December 2012

Academic Editors: T. Kuosmanen, J. M. Labeaga, and A. Watts

Copyright © 2013 P. Dıaz-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. Dıaz-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 andDıaz-Vazquez and Snower [12–14] 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] andDıaz-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 firm’s 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 firm’s 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 firms’ 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 𝜏

its revenue function is 𝑅(𝑍𝜏, 𝐿𝜏), where 𝑍

𝜏is a random

variable representing business conditions, and 𝐿𝜏is the firm’s

employment (we assume perfect competition in the productmarket, so that the firm is a price taker.). The evolution ofbusiness conditions 𝑍

𝜏is given by a two-state Markov chain:

there is a “good state” when 𝑍𝜏= 𝑍𝐺 and a “bad state” when

𝑍𝜏= 𝑍𝐵, where 𝑍𝐺 > 𝑍

𝐵. The probability of remaining inthe good state is 𝑃𝐺 and the probability of remaining in thebad state is 𝑃𝐵, so that the matrix of stationary transitionprobabilities is

(

𝑃𝐺

1 − 𝑃𝐺

1 − 𝑃𝐵

𝑃𝐵

) . (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 probabilities𝑃𝐺 and 𝑃𝐵. When the firmmakes its employment decision, it

has complete information about current business conditions,𝑍𝑖. Regarding the future, the firm has rational expectations

of𝑍𝜏, knowing the above Markov matrix but not the realized

value of 𝑍𝜏.

When a new member of the workforce is hired, the firmpays a hiring cost𝐻, and, when an incumbent worker is fired,the firm bears a firing cost 𝐹, where 𝐻 and 𝐹 are positiveconstants. For simplicity, we assume that the positions ofemployees in the firm are protected by the firing cost 𝐹 andthat all workers have the same productivity, that is, the samemarginal product for any given level of employment.

Each worker receives a real wage 𝑊𝜏per period 𝜏. The

wage 𝑊𝜏is 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 firm’s 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 firm’s expected profit under agreement isthe worker’s marginal profit (𝑀𝑖

𝜏− 𝑊𝑖

𝜏− ℎ𝜏), where 𝑀

𝑖

𝜏

is the present value of the marginal employee’s expectedprofits, excluding the current labour cost (to be definedformally below);𝑊𝑖

𝜏is the employee’s current wage; and ℎ

𝜏=

𝐻 when the firm is hiring and ℎ𝜏= 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 firm’s cost of dismissing a worker is 𝐹 + 𝑘 +

ℎ𝜏, where 𝐹 is the firing cost and 𝑘(𝑘 > 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 firm’s marginal profit under disagreement is −(𝐹+𝑘+ℎ

𝜏).

The worker’s income surplus in the wage bargain is𝑊𝑖𝑡−

𝑊0, where 𝑊

𝑖

𝜏is the wage under agreement in period 𝜏

and 𝑊0 is the worker’s fall-back position. Observe that the

worker’s future expected wages do not enter the worker’sincome surplus. The reason is that since the worker is notdismissed, the breakdown in the negotiations has no effecton the worker’s future expected wages. (Since the expectedfuture stream of wages is identical under agreement andunder disagreement, it does not change the worker’s strategicposition in the wage negotiation.)

Thus the Nash bargaining problem is

Maximize𝑊𝑖

𝜏

Ω = (𝑊𝑖

𝜏−𝑊0

)

𝜇

(𝑀𝑖

𝜏−𝑊𝑖

𝜏− ℎ𝜏)

1−𝜇

, (2)

and the solution is the negotiated wage:

𝑊𝑖

𝜏= (1 − 𝜇)𝑊

0

+ 𝜇 (𝑀𝑖

𝜏+ 𝐹 + 𝑘) . (3)

In other words, the negotiated wage is a weighted averageof the employee’s fall-back position and the firm’s surplus(excluding the wage).

The firm’s employment decision is given by the followingprofit maximization problem:

Maximize𝐿𝑡

𝐸

∞

∑

𝜏=𝑡

𝛿𝜏−1

{𝑅 (𝑍𝜏, 𝐿𝜏) − 𝑊

𝜏𝐿𝜏

−𝐶𝜏(𝐿𝜏− 𝐿𝜏−1

)} ,

(4)

where 𝛿 is the discount factor. The first term is the firm’s realrevenue.The second term is its wage cost, where the wage𝑊

𝜏

is given by (3). (Observe that 𝑊𝑖𝜏depends on the marginal

worker’s expected profit (minus the current labor cost) 𝑀𝑖𝜏,

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 𝐶

𝜏= 𝐻 when 𝐿

𝜏− 𝐿𝜏−1

> 0 and 𝐶𝜏= −𝐹 when

𝐿𝜏− 𝐿𝜏−1

< 0.For given values of the parameters, business conditions

(represented by 𝑍𝐺 and 𝑍

𝐵) determine the firm’s decision

on whether to hire or fire. To focus on nontrivial results, weassume that the values of 𝑍𝐺 and 𝑍

𝐵 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 firm’s employment decision is the solution of thedynamic optimization problem (4). It can be shown that theassociated marginal condition for employment is

𝑀𝑖

𝑡−𝑊𝑖

𝑡− 𝐶𝑡= 0. (5)

In words, the optimal level of employment is set so thatthe discounted stream of the marginal employee’s expectedcurrent and future profits is zero. Note that this equationis equivalent to the condition that the marginal worker’sexpected stream of revenue and wage cost is equal to theturnover cost (hiring cost 𝐻 in a good state and firing cost−𝐹 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

𝑊𝐺

𝑡= 𝑊0

+

𝜇

1 − 𝜇

(𝐻 + 𝐹 + 𝑘) (6)

whereas in a bad state it is (this wage is unaffected by turnovercosts, since 𝐹 reduces both the firm’s fall-back position (−𝐹 −𝑘) and the marginal profitability of the worker (−𝐹) so thatthe firm’s profit surplus is not changed)

𝑊𝐵

𝑡= 𝑊0

+

𝜇

1 − 𝜇

𝑘. (7)

As shown in the appendix, the expected marginal profit(excluding labour costs) in the good state is

𝑀𝐺

𝑡= 𝑀𝑅

𝐺

𝑡(𝑍𝐺

, 𝐿𝐺

𝑡) −

𝜕𝑊𝐺

𝑡

𝜕𝐿𝐺

𝑡

𝐿𝐺

𝑡+ 𝛿 [𝑃

𝐺

𝐻 − (1 − 𝑃𝐺

) 𝐹]

(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),

𝜕𝑊𝐺

𝑡

𝜕𝐿𝐺

𝑡

= 𝜇

𝜕𝑀𝐺

𝑡

𝜕𝐿𝐺

𝑡

=

𝜇

1 + 𝜇

𝜕𝑀𝑅𝐺

𝑡

𝜕𝐿𝐺

𝑡

. (9)

4 ISRN Economics

Thus any increase in employment reduces the bar-gained wage, which further raises employment. This“feedback effect” ensures that any change in employ-ment is amplified through the bargained wage.

(iii) The third term of (8) is the workers’ future profitabil-ity: with probability 𝑃

𝐺 the economy remains in agood state in period 𝑡 + 1, in which, as in period 𝑡, themarginal worker’s profitability equals the hiring cost𝐻. With probability (1 − 𝑃

𝐺

) the economy falls intoa bad state, in which the firm dismisses the marginalworker and pays the firing cost 𝐹.

Observe that, in (8), the firm’s production technologyaffects labour demand both through the form of the marginalrevenue function 𝑀𝑅

𝐺

𝑡(𝑍𝐺

, 𝐿𝐺

𝑡) and through the feedback

effect of (9). Thus it is convenient to define the “net marginalrevenue” (𝑁𝑀𝑅) as the sum of the marginal revenue and thefeedback effect:

𝑁𝑀𝑅𝐺

𝑡(𝑍𝐺

, 𝐿𝐺

𝑡) = 𝑀𝑅

𝐺

𝑡(𝑍𝐺

, 𝐿𝐺

𝑡) −

𝜇

1 + 𝜇

𝜕𝑀𝑅𝐺

𝑡

𝜕𝐿𝐺

𝑡

𝐿𝐺

𝑡. (10)

Substituting 𝑀𝐺

𝑡(8) and 𝑊

𝐺

𝑡(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):

𝑁𝑀𝑅𝐺

𝑡(𝑍𝐺

, 𝐿𝐺

𝑡) − [𝑊

0

+

𝜇

1 − 𝜇

(𝐹 + 𝐻 + 𝑘)]

+ 𝛿 [𝑃𝐺

𝐻 − (1 − 𝑃𝐺

) 𝐹] = 𝐻.

(11)

Along the same lines it can be shown that the expectedmarginal profit (excluding the labour costs) in the bad state is

𝑀𝐵

𝑡= 𝑀𝑅

𝐵

𝑡(𝑍𝐵

, 𝐿𝐵

𝑡) −

𝜕𝑊𝐵

𝑡

𝜕𝐿𝐵

𝑡

𝐿𝐵

𝑡

+ 𝛿 [−𝑃𝐵

𝐹 + (1 − 𝑃𝐵

)𝐻]

(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)

𝑁𝑀𝑅𝐵

𝑡(𝑍𝐵

, 𝐿𝐵

𝑡) − [𝑊

0

+

𝜇

1 − 𝜇

𝑘]

+ 𝛿 [−𝑃𝐵

𝐹 + (1 − 𝑃𝐵

)𝐻] = −𝐹

(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 𝐿, 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 𝐹and obtain

𝜕𝑁𝑀𝑅𝐺

𝜕𝐹

= 𝛿 (1 − 𝑃𝐺

) +

𝜇

1 − 𝜇

> 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 𝛿(1 − 𝑃𝐺

): with probability (1 − 𝑃𝐺

)

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 𝑃𝐺), the smaller theinfluence of firing costs on the marginal revenue andconsequently on current employment:

𝜕2

𝑁𝑀𝑅𝐺

𝜕𝐹𝜕𝑃𝐺

= −𝛿 < 0. (15)

(ii) The fall-back effect 𝜇/(1 − 𝜇): a rise in the firingcost increases the negotiated wage (and thus reduceshiring) since it decreases the firm’s fall-back positionin wage bargaining. The greater is the worker’s bar-gaining power (𝜇), 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 𝐹 and find

𝜕𝑁𝑀𝑅𝐵

𝜕𝐹

= − (1 − 𝛿𝑃𝐵

) < 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 (𝜕𝑊𝐵/𝜕𝐹 = 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:

𝜕2

𝑁𝑀𝑅𝐵

𝜕𝐹𝜕𝑃𝐵

= 𝛿 > 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

𝐸 (𝐿) = Π𝐵

𝐿𝐺

+ Π𝐵

𝐿𝐵

, (18)

where Π𝐺 and Π𝐵 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 areΠ𝐺

= (1 − 𝑃𝐵

)/[(1 − 𝑃𝐺

) + (1 − 𝑃𝐵

)] andΠ𝐵 = (1 − 𝑃𝐺

)/[(1 −

𝑃𝐺

) + (1 − 𝑃𝐵

)], resp.) Note that the proportion of troughsΠ𝐵 is greater than the proportion of booms Π𝐺 since we are

focusing on the case in which the persistence of troughs isgreater than the persistence of booms 𝑃𝐵 > 𝑃

𝐺.The effect of firing costs on long-term employment is

𝜕𝐸(𝐿)/𝜕𝐹 = Π𝐺

𝜕𝐿𝐺

/𝜕𝐹 + Π𝐵

𝜕𝐿𝐵

/𝜕𝐹. Since 𝜕𝐿𝑖

/𝜕𝐹 =

(𝜕𝑁𝑀𝑅𝑖

/𝜕𝐹)(𝜕𝐿𝑖

/𝜕𝑁𝑀𝑅𝑖

), to study the effect of firing costson long-run employment we need to refer to a specificrevenue function. (The two components of 𝜕𝐿𝑖/𝜕𝐹 are theeffect of firing costs on the 𝑁𝑀𝑅 in each state of nature(𝜕𝑁𝑀𝑅

𝑖

/𝜕𝐹), in (14) and (16), and the responsiveness ofemployment to a change in the𝑁𝑀𝑅 in each state of nature(𝜕𝐿𝑖

/𝜕𝑁𝑀𝑅𝑖

, 𝑖 = 𝐺, 𝐵). 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:

𝑅 (𝐿, 𝑍) = 𝑍𝑖

𝐿𝑖

−

1

2

𝑏(𝐿𝑖

)

2 (19)

for which 𝑁𝑀𝑅𝑖

= 𝑍𝑖

− 𝑏/(1 + 𝜇)𝐿𝑖. This is the simplest

case, since 𝜕𝐿𝑖/𝜕𝑁𝑀𝑅𝑖

= −(1 + 𝜇)/𝑏, that is, the reaction ofemployment to a change in the𝑁𝑀𝑅 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

𝜕𝐿𝐺

𝜕𝐹

= −

(1 + 𝜇)

𝑏

[𝛿 (1 − 𝑃𝐺

) +

𝜇

1 − 𝜇

] < 0;

𝜕𝐿𝐵

𝜕𝐹

=

(1 + 𝜇)

𝑏

(1 − 𝛿𝑃𝐵

) > 0.

(20)

Therefore, the effect of firing costs on long-term employmentis

𝜕𝐸 (𝐿)

𝜕𝐹

= −

(1 + 𝜇)

𝑏

{ [Π𝐺

𝛿 (1 − 𝑃𝐺

)

−Π𝐵

(1 − 𝛿𝑃𝐵

)] + [Π𝐺

𝜇

1 − 𝜇

]} ,

(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, 𝑃𝐺 > 𝑃

𝐵 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 firm’s fall-back position; but such an increase leaves thewage in troughs unaffected since the rise in the firing costworsens the firm’s 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 (𝑃𝐺 and 𝑃𝐵). Let us examine the effectof each parameter.

(i)How Employees’ Bargaining Strength Influences theEmployment Effect of Firing Costs. For a sufficiently large 𝜇,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 𝜇 that satisfies

𝜇 > 𝜇∗

=

(1 − 𝛿) (1 − 𝑃𝐺

)

(1 − 𝛿) (1 − 𝑃𝐺) + (1 − 𝑃

𝐵)

. (22)

Note that the boundary 𝜇∗ from which the effect of firing

costs on average employment is negative is larger the smalleris 𝑃𝐺 with respect to 𝑃𝐵.Thus, the greater is the proportion oftroughs relative to booms, the greater is the bargaining powerof the worker 𝜇 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 𝐹 on 𝐸(𝐿)is more expansionary.

To prove that the more persistent are booms relativeto troughs, the more expansionary is the effect of 𝐹 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

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃𝐵= −

(1 + 𝜇)

𝑏

× {[

𝜕Π𝐺

𝜕𝑃𝐵𝛿 (1−𝑃

𝐺

)−

𝜕Π𝐵

𝜕𝑃𝐵(1−𝛿𝑃

𝐵

)]+[𝛿Π𝐵

]}

−

(1 + 𝜇)

𝑏

(

𝜕Π𝐺

𝜕𝑃𝐵

𝜇

1 − 𝜇

) .

(23)

The first term (in the first and second rows of (23)) is theinfluence of the greater 𝑃𝐵 on the direct effect of firing costs,whereas the second term (in the third row) is the influence ofthe greater 𝑃𝐵 on the fall-back effect of firing costs.

From (21) and (23), it is clear that more persistent troughs(i.e., an increase in 𝑃𝐵) will influence the direct effect via thechange in the following:

(i) the proportion of booms Π𝐺 and the proportion oftroughs Π𝐵(first term in curly brackets),

(ii) the employment effect of firing costs in troughs𝜕𝐿𝐵

/𝜕𝐹 (second term in curly brackets),while the increase in 𝑃

𝐵 will influence the fall-backeffect via the change in Π𝐺 (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 𝑃

𝐵) will augment the pro-portion of troughs Π𝐵 and reduce the proportion ofbooms Π𝐺. This is represented by (i) in Figure 1.

ISRN Economics 7

∂E(L

)∂F

μ1μ2

μ3

PB

0

20

40

60

80

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

−80

−60

−40

−20

Figure 2: The influence of 𝑃𝐵 on 𝜕𝐸(L)/𝜕𝐹.

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 firm’shiring is discouraged by firing costs (due to the possibility ofpaying 𝐹 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 Π𝐵

and the fall in Π𝐺 increase the positive direct effect.

(ii) Regarding the change in the direct effect of 𝐹 introughs, we showed in (17) that more persistent eco-nomic conditions will weaken 𝜕𝐿𝐵/𝜕𝐹. (Recall that, inthe firing scenario, a greater 𝑃𝐵 increases the proba-bility of retaining the marginal worker in the future,with profitability−𝐹.) Note that this effect depends onthe discount factor 𝛿. This term is represented by thelast line of Figure 1.

Regarding the fall-back effect, it is only influenced bythe greater 𝑃𝐵 via the change in the proportions of boomsand troughs (Π𝐺 and Π𝐵). 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 𝑃𝐵 reduces the negative fall-back effect. The first row of

Figure 1 represents it.Solving (23), we obtain that

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃𝐵=

(1 + 𝜇)

𝑏

(1 − 𝑃𝐺

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2

× [(1 − 𝛿) +

𝜇

1 − 𝜇

] > 0.

(24)

The first term in square brackets (1 − 𝛿) is related tothe influence of 𝑃𝐵 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 proportionsΠ𝐺 andΠ𝐵). 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 (𝜇/(1 − 𝜇)) is related tothe influence of 𝑃𝐵 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 𝜕𝐸(𝐿)/𝜕𝐹.

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 𝑃𝐺 and 𝑃𝐵, the effect

of more persistent booms and troughs (i.e., the greater persis-tence of economic fluctuations) is (𝜕2𝐸(𝐿)/𝜕𝐹𝜕𝑃 = 𝜕

2

𝐸(𝐿)/

𝜕𝐹𝜕𝑃𝐺

+ 𝜕2

𝐸(𝐿)/𝜕𝐹𝜕𝑃𝐵):

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃

= −

(1 + 𝜇)

𝑏

{[

𝜕Π𝐺

𝜕𝑃

𝛿 (1 − 𝑃𝐺

) −

𝜕Π𝐵

𝜕𝑃

(1 − 𝛿𝑃𝐵

)]

− [𝛿Π𝐺

− 𝛿Π𝐵

] }

−

(1 + 𝜇)

𝑏

{

𝜕Π𝐺

𝜕𝑃

𝜇

1 − 𝜇

} ,

(25)

where 𝜕Π𝑖/𝜕𝑃 = 𝜕Π𝑖

/𝜕𝑃𝐺

+ 𝜕Π𝑖

/𝜕𝑃𝐵. The first term (in the

first and second rows of (25)) is the influence of the greater 𝑃on the direct effect of firing costs, whereas the second term (inthe third row) is the influence of the greater𝑃 on the fall-backeffect of firing costs.

As for the greater 𝑃𝐵, the greater 𝑃 influences 𝜕𝐸(𝐿)/𝜕𝐹(i) via the change in the proportions of booms and troughs(Π𝐺 and Π

𝐵), 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 𝑃

𝐺 and 𝑃𝐵

changes the proportion of booms in the followingway(it is clear that a greater persistence of booms (anincrease in𝑃𝐺) will augment the proportion of boomsΠ𝐺; the magnitude depends on the probability of the

economy leaving troughs and moving into booms(1 − 𝑃

𝐵

). On the other hand, a greater persistence oftroughs (an increase in 𝑃

𝐵) will reduce Π𝐺; the mag-nitude depends on the probability of the economyleaving booms and moving into troughs (1 − 𝑃

𝐺

)):

𝜕Π𝐺

𝜕𝑃𝐺=

(1 − 𝑃𝐵

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2> 0;

𝜕Π𝐺

𝜕𝑃𝐵= −

(1 − 𝑃𝐺

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2< 0.

(26)

Thus, the net influence of a simultaneous increase in 𝑃𝐺 and

𝑃𝐵 on the proportion of booms is

𝜕Π𝐺

𝜕𝑃

=

(𝑃𝐺

− 𝑃𝐵

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2< 0 for 𝑃𝐵 > 𝑃

𝐺

. (27)

If the persistence of booms and troughs was symmetric (i.e.equal𝑃𝐺 and𝑃𝐵), a proportional increase in𝑃𝐺 and𝑃𝐵wouldgenerate two counteracting effects which will cancel out: Π𝐺

would not change. In contrast, in the case in which 𝑃𝐵 > 𝑃𝐺,

the probability of the economy moving from a trough to aboom (1−𝑃

𝐵

) is smaller than the probability of moving froma boom to a trough (1 − 𝑃𝐺). Therefore, the economy is morelikely to be in troughs and the effect of the increase in𝑃𝐵 dominates (i.e., the proportion of booms decreases).

Similarly, in the case of the proportion of recessions Π𝐵

(by the expressions for the long-run Markov probabilities,𝜕Π𝐵

/𝜕𝑃𝐺

= −𝜕Π𝐺

/𝜕𝑃𝐺 and 𝜕Π𝐵/𝜕𝑃𝐵 = −𝜕Π

𝐺

/𝜕𝑃𝐵):

𝜕Π𝐵

𝜕𝑃

= −

(𝑃𝐺

− 𝑃𝐵

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2> 0 for 𝑃𝐺 < 𝑃

𝐵

. (28)

Thus, a simultaneous increase in𝑃𝐺 and𝑃𝐵 raises the propor-tion of troughs and reduces the proportion of booms, for𝑃𝐵 >𝑃𝐺 (note that it is unimportant if the difference between 𝑃

𝐺

and 𝑃𝐵 is proportional or additive).This is represented by thesecond row of Figure 1, and has the same consequence as theincrease in 𝑃

𝐵: the rise in Π𝐵 and the fall in Π

𝐺 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 𝜕𝐿

𝐺

/𝜕𝐹 and 𝜕𝐿𝐵

/𝜕𝐹. On the other hand, 𝐿𝐺is higher since a more persistent boom reduces theprobability of firing in the future and bearing thefiring cost: 𝜕2𝐿𝐺/𝜕𝐹𝜕𝑃𝐺 = 𝛿((1+𝜇)/𝑏) > 0. Addition-ally, 𝐿𝐵 is lower since a greater 𝑃𝐵 increases the pos-sibility of retaining workers in the future with amarginal profit of −𝐹: 𝜕2𝐿𝐵/𝜕𝐹𝜕𝑃𝐵 = −𝛿((1 +𝜇)/𝑏) <

0. As the proportion of troughs is greater than the pro-portion of boomsΠ𝐵 > Π

𝐺, what happens in troughsdominates. Note that these effects depend on thediscount factor 𝛿. 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

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃

= −

(1 + 𝜇)

𝑏

(𝑃𝐺

− 𝑃𝐵

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2

× [(1 − 𝛿) + (

𝜇

1 − 𝜇

)] > 0.

(29)

The first term in square brackets (1 − 𝛿) is related to theinfluence of𝑃 on the direct effect and the second term (𝜇/(1−

𝜇)) 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 𝑃

𝐺

< 𝑃𝐵). 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 thewage𝑊𝐺, 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:

−

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃𝐺=

(1 + 𝜇)

𝑏

(1 − 𝑃𝐵

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2

× [(1 − 𝛿) +

𝜇

1 − 𝜇

] > 0.

(A.1)

A.2. Hiring Costs

A.2.1. Short Run. The effect of hiring costs on employment inbooms is, by (10),

𝜕𝐿𝐺

𝜕𝐻

= −

(1 + 𝜇)

𝑏

[(1 − 𝛿𝑃𝐺

) +

𝜇

1 − 𝜇

] < 0. (A.2)

This effect may be divided into two subsidiary effects.

(i) The direct effect (1−𝛿𝑃𝐺): hiring costs discourage hir-ing. However, the greater is 𝑃𝐺, the less important isthe fixed cost of hiring:

𝜕2

𝐿𝐺

𝜕𝐻𝜕𝑃𝐺= 𝛿 > 0. (A.3)

(ii) The profitability effect 𝜇/(1 − 𝜇): the cost of hiringincreases themarginal profit of theworker, and he canobtain a higher wage in the negotiation.The greater is𝜇, the larger will be the profitability effect.

The effect of hiring costs on employment in troughs is,from (13),

𝜕𝐿𝐵

𝜕𝐹

=

(1 + 𝜇)

𝑏

(1 − 𝛿𝑃𝐵

) > 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 is𝑃𝐵 the less important is this effect:

𝜕2

𝐿𝐵

𝜕𝐻𝜕𝑃𝐵= −𝛿 < 0 (A.5)

by (A.4).

A.2.2. Long Run. The effect of hiring costs on long-termemployment is

𝜕𝐸 (𝐿)

𝜕𝐻

= −

(1 + 𝜇)

𝑏

{ [Π𝐺

(1 − 𝛿𝑃𝐺

) − Π𝐵

𝛿 (1 − 𝑃𝐵

)]

+ [Π𝐺

𝜇

1 − 𝜇

]} ,

(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 𝛿. 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 𝜇, 𝑃𝐺 and 𝑃𝐵.

(i) How employees’ 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

−

𝜕2

𝐸 (𝐿)

𝜕𝐻𝜕𝑃𝐺=

(1 + 𝜇)

𝑏

(1 − 𝑃𝐵

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2

× [(1 − 𝛿) +

𝜇

1 − 𝜇

] > 0.

(A.7)

The influence of more persistent troughs is

𝜕2

𝐸 (𝐿)

𝜕𝐻𝜕𝑃𝐵=

(1 + 𝜇)

𝑏

(1 − 𝑃𝐺

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2

× [(1 − 𝛿) +

𝜇

1 − 𝜇

] > 0.

(A.8)

The effect of more prolonged booms and troughs is

𝜕2

𝐸 (𝐿)

𝜕𝐻𝜕𝑃

= −

(1 + 𝜇)

𝑏

(𝑃𝐺

− 𝑃𝐵

)

[(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)]2

× [(1 − 𝛿) + (

𝜇

1 − 𝜇

)] > 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 𝑃𝐵 > 𝑃

𝐺).

B. Revenue Function Linear-Quadratic inLabour with Multiplicative Shocks andCobb-Douglas Production Function

The effect of firing costs on long-term employment is

𝜕𝐸 (𝐿)

𝜕𝐹

= [Π𝐺

𝛿 (1 − 𝑃𝐺

)

𝜕𝐿𝐺


−Π𝐵

(1 − 𝛿𝑃𝐵

)

𝜕𝐿𝐵

𝜕𝑁𝑀𝑅𝐵] + Π

𝐺𝜇

1 − 𝜇

𝜕𝐿𝐺

𝜕𝑁𝑀𝑅𝐺,

(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 𝜕𝐿

𝑖

/𝜕𝑁𝑀𝑅𝑖 depends on the form of the revenue

function. We consider two additional revenue functions.

(a) (𝐿, 𝑍) = 𝑍𝑖

(𝐿𝑖

−𝑏/2(𝐿𝑖

)2

), for which𝑁𝑀𝑅𝑖

= 𝑍(1−𝑏/

(1 + 𝜇)𝐿𝑖

). In this case, 𝜕𝐿𝑖/𝜕𝑁𝑀𝑅𝑖

= −(1 + 𝜇)/𝑍𝑖

𝑏,that is, the reaction of employment to a change inthe 𝑁𝑀𝑅 depends on the state of nature 𝑍

𝑖: since𝑍𝐺

> 𝑍𝐵, 𝐿𝐵 is more responsive than 𝐿

𝐺 to anidentical change in the𝑁𝑀𝑅 (|𝜕𝐿𝐺/𝜕𝑁𝑀𝑅

𝐺

| < |𝜕𝐿𝐵

/


|).(b) 𝑅(𝐿, 𝑍) = 𝑍

𝑖

(𝐿𝑖(1−𝛽)

/(1 − 𝛽)) (Cobb-Douglas revenuefunction). Thus 𝑁𝑀𝑅

𝑖

= 𝑍𝑖

𝐿𝑖(−𝛽)

[1 + 𝛽𝜇/(1 + 𝜇)];that is, the 𝑁𝑀𝑅 is convex in employment. In thiscase, the responsiveness of employment to a change inthe𝑁𝑀𝑅 is 𝜕𝐿𝑖/𝜕𝑁𝑀𝑅

𝑖

= −𝐿𝑖(𝛽+1)

/{𝑍𝑖

𝛽[1 + 𝛽𝜇/(1 +

𝜇)]}. Observe that, for the Cobb-Douglas revenuefunction, the relative magnitude of 𝜕𝐿

𝐺

/𝜕𝑁𝑀𝑅𝐺

with respect to 𝜕𝐿𝐵/𝜕𝑁𝑀𝑅𝐵depends not only on the

business conditions 𝑍𝑖, but also on the employmentlevels 𝐿𝐺 and 𝐿𝐵. We derive the levels of employmentfrom the first-order condition in (8) and (12) and the𝑁𝑀𝑅:

𝐿𝐺

𝑡= (

𝑊𝐺

𝑡− 𝛿𝑃𝐺

𝐻 + 𝛿 (1 − 𝑃𝐺

) 𝐹 + 𝐻

𝑍𝐺(1 + 𝛽𝜇/ (1 + 𝜇))

)

−1/𝛽

,

𝐿𝐵

𝑡= (

𝑊𝐵

𝑡− 𝛿 (1 − 𝑃

𝐵

)𝐻 + 𝛿𝑃𝐵

𝐹 + 𝐻

𝑍𝐺(1 + 𝛽𝜇/ (1 + 𝜇))

)

−1/𝛽

.

(B.2)

𝐿𝐺 must be greater than 𝐿𝐵, which implies that

𝑍𝐺

𝑍𝐵> ( (𝑊

0

+ 𝜇/ (1 − 𝜇) (𝐻 + 𝐹 + 𝑘) − 𝛿𝑃𝐺

𝐻

+𝛿 (1 − 𝑃𝐺

) 𝐹 + 𝐻)

× (𝑊0

+ 𝜇/ (1 − 𝜇) 𝑘 − 𝛿 (1 − 𝑃𝐵

)𝐻

+𝛿𝑃𝐵

𝐹 − 𝐹)

−1

) .

(B.3)

Recall from Section 1 that the higher 𝐹 and 𝐻, the moreemployment is stabilized over the cycle, and the closer are𝐿𝐺 and 𝐿

𝐵. Thus, when 𝐿𝐺 and 𝐿

𝐵 are sufficiently close (i.e.,turnover costs sufficiently high relative to (𝑍𝐺 − 𝑍

𝐵)), it mayhappen that |𝜕𝐿𝐺/𝜕𝑁𝑀𝑅

𝐺

| < |𝜕𝐿𝐵

/𝜕𝑁𝑀𝑅𝐵

|. This inequalityis satisfied when

𝑍𝐺

𝑍𝐵< ( (𝑊

0

+ 𝜇/ (1 − 𝜇) (𝐻 + 𝐹 + 𝑘) − 𝛿𝑃𝐺

𝐻

+𝛿 (1 − 𝑃𝐺

) 𝐹 + 𝐻)

×(𝑊0

+𝜇/(1−𝜇)𝑘−𝛿(1−𝑃𝐵

)𝐻+𝛿𝑃𝐵

𝐹−𝐹)

−1

)

(𝛽+1)

.

(B.4)

In contrast, when 𝐿𝐺 and 𝐿

𝐵 are sufficiently different(turnover costs sufficiently low), it may happen that |𝜕𝐿𝐺/𝜕𝑁𝑀𝑅

𝐺

| > |𝜕𝐿𝐵


| (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: |𝜕𝐿𝐺/𝜕𝑁𝑀𝑅

𝐺

| ≤ |𝜕𝐿𝐵


|. (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 𝐿

𝐺 and 𝐿𝐵 that, in the absence of

turnover costs, the persistence of the shock has no influenceon employment.)

Regarding the direct effect in (B.1), when |𝜕𝐿𝐺

/


| ≤ |𝜕𝐿𝐵


|, the direct effect of firing costson average employment is positive. When |𝜕𝐿

𝐺


| >

|𝜕𝐿𝐵


| (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 𝜇 and 𝑃𝐺

and 𝑃𝐵. Let us examine the results above for each productionfunction.

We show that the effect of𝐹 on𝐸(𝐿) ismore expansionary,when |𝜕𝐿

𝐺


| ≤ |𝜕𝐿𝐵


| and 𝑃𝐵

> 𝑃𝐺, 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),

𝜕𝐸 (𝐿)

𝜕𝐹

= [−Π𝐺

𝛿 (1−𝑃𝐺

)

(1 + 𝜇)

𝑍𝐺𝑏

+ Π𝐵

(1−𝛿𝑃𝐵

)

(1 + 𝜇)

𝑍𝐵𝑏

]

− Π𝐺

𝜇

1 − 𝜇

(1 + 𝜇)

𝑍𝐺𝑏

,

(B.5)

𝜕𝐸(𝐿)/𝜕𝐹 is smaller than 0 when

𝜇 > 𝜇∗

= ((1 − 𝑃𝐺

) [𝑍𝐺

(1 − 𝛿𝑃𝐵

) − 𝑍𝐵

𝛿 (1 − 𝑃𝐵

)])

× ( (1 − 𝑃𝐺

) [𝑍𝐺

(1 − 𝛿𝑃𝐵

) − 𝑍𝐵

𝛿 (1 − 𝑃𝐵

)]

+𝑍𝐵

(1 − 𝑃𝐵

))

−1

.

(B.6)

ISRN Economics 11

The effect of a greater persistence of economic conditions is

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃

= −

(1 + 𝜇)

𝑍𝐺𝑍𝐵𝑏

[

𝜕Π𝐺

𝜕𝑃

𝑍𝐵

𝛿 (1 − 𝑃𝐺

)

+

𝜕Π𝐵

𝜕𝑃

𝑍𝐺

(1 − 𝛿𝑃𝐵

)]

−

(1 + 𝜇)


[

𝜕Π𝐺

𝜕𝑃

𝑍𝐵

𝜇

1 − 𝜇

−𝛿(𝑍𝐵

Π𝐺

− 𝑍𝐺

Π𝐵

)]

(B.7)

which rearranging is

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃

=

𝑍𝐵

𝛿 [(1 − 𝑃𝐺

)

2

+ (1 − 𝑃𝐵

)

2

]

(𝑏 [(1 − 𝑃𝐺) + (1 − 𝑃

𝐵)] 𝑍𝐺𝑍𝐵) / (1 + 𝜇)

− (𝑍𝐺

[𝛿(1 − 𝑃𝐺

)

2

+ (1 − 𝑃𝐵

) (1 − 𝛿𝑃𝐵

)

− (1 − 𝑃𝐺

) (1 − 𝛿)] )

× (𝑏 [(1−𝑃𝐺

)+(1−𝑃𝐵

)]𝑍𝐺

𝑍𝐵

/ (1 + 𝜇))

−1

> 0.

(B.8)

This expression is positive. Recall from the text that for therevenue function for which |𝜕𝐿𝐺/𝜕𝑁𝑀𝑅

𝐺

| = |𝜕𝐿𝐵


|,the more persistent the fluctuations the more expansionary isthe effect of 𝐹 on 𝐸(𝐿) (when 𝑃

𝐵

> 𝑃𝐺) because the greater

persistence increases the proportion of troughs and thereforeincreases the importance of the positive direct effect of 𝐹 onemployment in troughs (which is undiscounted). As shownabove, for the revenue function linear-quadratic in labourwith multiplicative shocks |𝜕𝐿𝐺/𝜕𝑁𝑀𝑅

𝐺

| < |𝜕𝐿𝐵


|.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:

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃𝐵=

(1 + 𝜇)


× ((1 − 𝑃𝐺

) [𝑍𝐵

𝛿 (1 − 𝑃𝐺

) + 𝑍𝐵

(𝜇/ (1 − 𝜇))

+𝑍𝐺

(1 − 𝛿𝑃𝐵

)])

× ([(1 − 𝑃𝐺

) + (1 − 𝑃𝐵

)]

−2

)

−

(1 + 𝜇)


𝛿𝑍𝐺

Π𝐵

=

(1 + 𝜇)


× ( (1 − 𝑃𝐺

) [𝑍𝐵

𝛿 (1 − 𝑃𝐺

) + 𝑍𝐵

(𝜇/ (1 − 𝜇))

+𝑍𝐺

(1 − 𝛿 (2 − 𝑃𝐺

))] )

× ([(1 − 𝑃𝐺

) + (1 − 𝑃𝐵

)]

−2

).

(B.9)

This equation is positive when𝑍𝐺/(𝑍𝐺−𝑍𝐵) < 𝛿(1−𝑃𝐺

)/(1−

𝛿). As to less persistent booms:

−

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃𝐺=

(1 + 𝜇)


× ((1 − 𝑃𝐵

) [𝑍𝐵

𝛿 (1 − 𝑃𝐺

) + 𝑍𝐵

(𝜇/1 − 𝜇)

−𝑍𝐺

(1 − 𝛿𝑃𝐵

)])

× ([(1 − 𝑃𝐺

) + (1 − 𝑃𝐵

)]

−2

)

−

(1 + 𝜇)


𝛿𝑍𝐵

Π𝐺

= ( (1 − 𝑃𝐵

) [𝑍𝐵

𝛿 (1 − 𝑃𝐵

) + 𝑍𝐵

(𝜇/1 − 𝜇)

+𝑍𝐺

(1 − 𝛿𝑃𝐵

)] )

× (𝑍𝐺

𝑍𝐵

𝑏[(1 − 𝑃𝐺

)+(1−𝑃𝐵

)]

2

/ (1 + 𝜇))

−1

> 0.

(B.10)

B.2. Cobb-Douglas Revenue Function. The effect of 𝐹 on 𝐸(𝐿)is

𝜕𝐸 (𝐿)

𝜕𝐹

= −

Π𝐺

𝐿𝐺(𝛽+1)

[𝛿 (1 − 𝑃𝐺

) + 𝜇/ (1 − 𝜇)]

𝑍𝐺𝛽 [1 + 𝛽𝜇/ (1 + 𝜇)]

+

Π𝐵

𝐿𝐵(𝛽+1)

(1 − 𝛿𝑃𝐵

)

𝑍𝐵𝛽 [1 + 𝛽𝜇/ (1 + 𝜇)]

.

(B.11)

12 ISRN Economics

Regarding the persistence of the fluctuations, the generalexpression is

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃

= {−𝛿Π𝐺

+

𝜕Π𝐺

𝜕𝑃

[𝛿 (1 − 𝑃𝐺

) +

𝜇

1 − 𝜇

]}

×

𝜕𝐿𝐺

𝜕𝑁𝑀𝑅𝐺− [−𝛿Π

𝐵

+

𝜕Π𝐵

𝜕𝑃

(1 − 𝛿𝑃𝐵

)]

×

𝜕𝐿𝐵


+ {Π𝐺

[𝛿 (1 − 𝑃𝐺

) + 𝜇/ (1 − 𝜇)]}

𝜕𝐿𝐺

𝜕𝑁𝑀𝑅𝐺𝜕𝑃𝐺

− Π𝐵

(1 − 𝛿𝑃𝐵

)

𝜕𝐿𝐵

𝜕𝑁𝑀𝑅𝐵𝜕𝑃𝐵

.

(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 𝜕𝐿𝑖/𝜕𝑁𝑀𝑅

𝑖 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 |𝜕𝐿

𝐺


| < |𝜕𝐿𝐵


| is sat-isfied, while (ii) for sufficiently small turnover costs thecondition |𝜕𝐿𝐺/𝜕𝑁𝑀𝑅

𝐺

| > |𝜕𝐿𝐵


| 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 𝐹 on employment in firingtimes) to dominate, it is necessary that the discountfactor 𝛿 is sufficiently large.

The influence of less persistent booms is

−

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃𝐺= − {−𝛿Π

𝐺

+

𝜕Π𝐺

𝜕𝑃𝐺[𝛿 (1 − 𝑃

𝐺

) +

𝜇

1 − 𝜇

]}

×

𝜕𝐿𝐺

𝜕𝑁𝑀𝑅𝐺+ [

𝜕Π𝐵

𝜕𝑃𝐺(1 − 𝛿𝑃

𝐵

)]

𝜕𝐿𝐵


− {Π𝐺

[𝛿 (1 − 𝑃𝐺

) + 𝜇/ (1 − 𝜇)]}

×

𝜕𝐿𝐺

𝜕𝑁𝑀𝑅𝐺𝜕𝑃𝐺

.

(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

𝜕2

𝐸 (𝐿)

𝜕𝐹𝜕𝑃𝐵= {

𝜕Π𝐺

𝜕𝑃𝐵[𝛿 (1 − 𝑃

𝐺

) +

𝜇

1 − 𝜇

]}

𝜕𝐿𝐺

𝜕NMR𝐺

− [−𝛿Π𝐵

+

𝜕Π𝐵

𝜕𝑃𝐵(1 − 𝛿𝑃

𝐵

)]

𝜕𝐿𝐵

𝜕NMR𝐵

− Π𝐵

(1 − 𝛿𝑃𝐵

)

𝜕𝐿𝐵

𝜕NMR𝐵𝜕𝑃𝐵.

(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, “Job security provisions and employment,” Quar-terly Journal of Economics, vol. 105, no. 3, pp. 699–726, 1990.

[4] G. Bertola, “Job security, employment and wages,” EuropeanEconomic Review, vol. 34, no. 4, pp. 851–886, 1990.

[5] H. A. Hopenhayn and R. Rogerson, “Job turnover and policyevaluation: a general equilibrium approach,” Journal of PoliticalEconomy, vol. 101, no. 5, pp. 915–938, 1993.

[6] S. Nickell, “Unemployment and labor market rigidities: Europeversus North America,” Journal of Economic Perspectives, vol. 11,no. 3, pp. 55–74, 1997.

[7] J. Heckman and C. Pages, “The cost of job security regulation:evidence from Latin American labor markets,” NBERWorkingPaper 7773, 2000.

[8] S. Bentolila andG. Bertola, “Firing costs and labor demand: howbad is eurosclerosis?” Review of Economic Studies, vol. 57, no. 3,pp. 381–402, 1990.

[9] G. Bertola, “Labor turnover costs and average labor demand,”Journal of Labor Economics, vol. 10, pp. 389–411, 1992.

[10] S. Bentolila and G. Saint-Paul, “A model of labor demand withlinear adjustment costs,” Labour Economics, vol. 1, no. 3-4, pp.303–326, 1994.

[11] P. Dıaz-Vazquez, D. J. Snower, and L. E. Arjona-Bejar, “On-the-job learning, firing costs and employment,” Contributionsto Economic Analysis and Policy, vol. 4, no. 1, article 2, 2005.

[12] P. Dıaz-Vazquez and D. J. Snower, “Employment, macroeco-nomic fluctuations and job security,” CEPR Discussion Paper1430, CEPR, London, UK, 1996.

ISRN Economics 13

[13] P. Dıaz-Vazquez and D. J. Snower, “Can insider power affectemployment?” German Economic Review, vol. 4, no. 2, pp. 139–150, 2003.

[14] P. Dıaz-Vazquez and D. J. Snower, “On-the-job learning and theeffects of insider power,” Labour Economics, vol. 13, no. 3, pp.317–341, 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, “Two questions about Europeanunemployment,” Econometrica, vol. 76, no. 1, pp. 1–29, 2008.

[17] L. Nunziata, “Labour market institutions and the cyclical dy-namics of employment,” Labour Economics, vol. 10, no. 1, pp. 31–53, 2003.

[18] Y. F. Chen, D. Snower, and G. Zoega, “Labour-market institu-tions and macroeconomic shocks,” Labour, vol. 17, no. 2, pp.247–270, 2003.

[19] M. Veracierto, “Firing costs and business cycle fluctuations,”International Economic Review, vol. 49, no. 1, pp. 1–39, 2008.

[20] F. Zanetti, “Labormarket institutions and aggregate fluctuationsin a search and matching model,” European Economic Review,vol. 55, no. 5, pp. 644–658, 2011.

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