business cycle, unemployment benefits and productivity shocks

Journal of Macroeconomics 27 (2005) 670–690

www.elsevier.com/locate/jmacro

Business cycle, unemployment benefitsand productivity shocks

Bruno Chiarini a,*, Paolo Piselli b

a University of Naples ‘‘Parthenope’’, Facolta di Economia, Via Medina 40, 83100, Napoli, Italyb Bank of Italy, Economic Research Department, Via Nazionale 91, 00184 Roma, Italy

Received 22 February 2002; accepted 19 July 2004Available online 26 July 2005

Abstract

The dimension of aggregate fluctuations is quite different between the European and USeconomies. Such a result fully justifies attention to non-Walrasian features for improving theempirical performance of the RBC model. In this paper, we introduce two features, present inEuropean economies, into the standard general setting of the infinite-horizon stochastic growthparadigm: trade union behavior and unemployment benefits. We show that this non-Walrasianeconomy (i) improves the ability to account for the stylized facts, (ii) displays realistic featuresin explaining the employment and productivity puzzles, (iii) may account for contractions.� 2005 Elsevier Inc. All rights reserved.

JEL classification: E32; D91; J22

Keywords: Real business cycle; Monopoly union model; Downturns; Unemployment benefits

1. Introduction

Data generated by real business cycle (RBC) models mimic quite well the secondorder moments of the US economy�s main macroeconomic time-series as well as the

0164-0704/$ - see front matter � 2005 Elsevier Inc. All rights reserved.doi:10.1016/j.jmacro.2004.07.002

* Corresponding author. Fax: +39 (0)81 5475750.E-mail address: [email protected] (B. Chiarini).

mailto:[email protected]

B. Chiarini, P. Piselli / Journal of Macroeconomics 27 (2005) 670–690 671

co-movements of these series with output. A substantial body of work focuses on thelabor market in RBC models. The research is motivated by several difficultiesencountered in these models in reproducing a number of labor market regularities.1

There are two main difficulties with this approach: the productivity puzzle and theemployment variability puzzle. If all shocks bringing about cycles are productivityshocks, which shift labor demand curve, models predict that productivity is highlypositively correlated with both employment and output, whereas the empirical evi-dence shows moderate correlations with output and roughly no correlation or evennegative correlation with employment. Moreover, these difficulties are related to oneof the criticisms of the real business cycle models: the inability of this framework toaccount for recessions. Since any relationship between recessions and technologicalinnovations is not convincing, several authors have highlighted particular setupscharacterized by ‘‘negative technological shocks’’.2

These limits of business cycle research become particularly evident whenEuropean labor markets are considered, leading many authors to introduce non-Walrasian elements into the RBC paradigm.

Relevant international data assembled in the paper of Danthine and Donald-son (1993), Fiorito and Kollintzas (1994) and several OECD reports, make clearthat labor market behavior is substantially different between countries, reflectingdistinct institutional arrangements. Such differences fully justify the attention tonon-Walrasian features for improving the empirical performance of the RBCmodel.

In this paper we examine the conditions under which an economy, driven by tech-nological innovations and reservation wage shocks capable of affecting the return towork, is able to match the low correlations of output and employment with produc-tivity and to exhibit recessions. This is accomplished introducing two features,present in real-world economies, into the standard general setting of the infinite-hori-zon stochastic growth paradigm. First, we incorporate a monopoly trade union inthe labor market, which picks a time path for the wage rate (and, therefore, employ-ment) and considers its effects on the consumption choices. The use of a simple rentseeking objective function for the union, as the second element introduced into themodel, allows us to consider the effects of an alternative wage (unemploymentbenefits).

Incorporating union behavior in the model provides a natural way of generating anew shock for the wage setting curve reconciling the existing RBC model, which isbased solely on productivity shocks leading to shifts in labor demand, with a mea-surable impulse that shifts the labor–supply function. A related implication is thatalternative values of the reservation wage affect the union wage positively. For a

1 See for a survey, Stadler (1994), Kydland (1995) and King and Rebelo (1999). See also Christiano andEichenbaum (1992) and Li (1999) among others.2 The Solow residual suggests that recessions are caused by a regress in technological innovations (see,

for instance, Summers, 1986; Mankiw, 1989; Calomiris and Hanes, 1995; Hartley et al., 1998). A possibledefense of the RBC model draws attention to the institutional framework which affects the shocks andproduces negative technological shocks (e.g. Hansen and Prescott, 1993).

672 B. Chiarini, P. Piselli / Journal of Macroeconomics 27 (2005) 670–690

monopoly or right-to-manage union model, a change in unemployment benefits willcause movements along the labor demand curve. Actually, there is a dearth of ana-lysis allowing for dynamic effects of alternative wages or benefits, both in partial aswell as general equilibrium setting. A positive shock to the unemployment benefitsshifts the labor supply curve (the bargaining wage curve) leftward, offsetting thestrong positive correlation between employment and wage predicted by the one-shock real business cycle models with stochastic shifts in the production function.Given a level of unemployment, a more generous benefit system will exert upwardpressure on wages, reducing the fear of job loss on the part of the unions.3

The improvement in government unemployment systems that many Europeancountries have experienced in recent decades, in an environment characterized bynon-competitive labor markets, may well be one explanation of the cyclical featuresof output and others aggregated real variables.

We study the ability of a monopoly union model along with supply side fiscal pol-icies to account for the business cycle behavior of the Italian labor market whenembedded in a stochastic growth model. A union model has been proposed by Maf-fezzoli (2001).4 However, Maffezzoli�s extension of the standard RBC model fails tosubstantively improve the labor market results of the canonical model. We show thatthe failure can be overcame once wage shocks are included in the model. Precisely,we show that including union behavior into the model and randomizing unemploy-ment benefits in the union preferences, (i) improves the ability to account for thestylized facts, (ii) displays realistic features in explaining the employment andproductivity puzzles, (iii) may account for contractions.

The structure of the paper is as follows. Section 2, reports on the relevance oftrade unions and benefit entitlements in the European labor markets. Sections 3–5describe the model�s behaviors and the equilibrium of the artificial economy. Sec-tions 6 and 7 report data and simulation results. Section 8 concludes.

2. Trade union influence and benefit entitlements

Recent statistics on union membership and on union coverage in European coun-tries and the United States are presented in Table 1. Although the union membershiptrend has undergone a sharp decline since 1985, a significant fraction of Europeanworkers currently belong to unions. Moreover, more than 70% of the work forcehave their wages and working conditions set through collective bargaining agree-ment. The figures also show that US union coverage and membership are muchlower than those presented in European labor markets. Furthermore, unionized

3 Evidence is documented by Nickell (1997) and Nickell and van Ours (2000) and the works quotedtherein.4 Zanetti (2003) provides a further interesting non-Walrasian labor market in a real business cycle

framework. This author extends the model to an imperfect competitive goods market in a monetaryeconomy.

Table 1Union membership, coverage and replacement rates

Union membership Coverage Replacement rates

% non-agricultural % wage-salary % of employed OECD (1994/1995)a

Labor force Earner

Belgium 38.1 51.9 90 65Denmark 68.2 80.1 90 81France 6.1 9.1 92 68Germany 29.6 28.9 90 68Italy 30.6 44.1 90 19b

Netherlands 21.8 25.6 71 82Spain 11.4 18.6 68 53United Kingdom 26.2 32.9 47 69United States 12.7 14.2 18 19

Sources: ILO, World Labor Report, Geneva, 1998; OECD, Economic Studies, No. 26, Paris, 1996.a Replacement rates: Entitlements calculated over five years of unemployment in % of previous earnings.

The average excludes the replacement rate of couples with one employed partner.b The estimates of RR for Italy do not include the CIG (wage supplementary fund) benefits that are paid

to workers affected by collective lay-offs in firms with 16 or more employees as a result of a temporarydecline in economic activity. Benefits are equal to 80% of gross earnings up to a monthly maximum, whichis about 65% of average earnings.


sectors in the US economy do not offer much scope for monopolistic wage-setting,since bargaining is conducted on an enterprise-by-enterprise basis. There is no doubtthat trade union influence and power cannot be measured merely in terms of thenumber of active members. Union membership is not the only factor for assessingunion power. In Spain and France, for instance, the union confederations have aremarkable capacity to call for action, despite the very low unionization rate. Inthese countries there exists a clear political conception of industrial relations, andunions are directly related to the parties: usually, government-sanctioned extensionsof union contracts to non-union members, a set-up confirmed by the striking gapbetween coverage and membership in those countries.

The last column of Table 1 reports another characteristic that influences the labormarket, the OECD measure of benefits entitlements: the entitlements calculated overfive years of unemployment as a percentage of previous earnings. Unemploymentbenefits are multidimensional and, therefore, difficult to define in a single indicator.5

Here, simply on the basis of replacement rates summary estimates, we emphasizethat in most European countries insurance benefits have a role in the labor market.Union behavior may be influenced by unemployment benefits because a generoussystem implies that those at risk of losing their jobs may take greater risks in collec-tive bargaining over wages. Unemployment benefits tend to reduce the cost ofbecoming unemployed. Given these extreme features of the European labor markets,setting out a real business cycle model presents an interesting challenge.

5 See Atkinson and Micklewright (1991) and OECD (1994), for criticism.


3. The economy

3.1. The environment

The model is a stochastic growth economy defined in the line of the decentraliza-tion scheme proposed by Prescott and Mehra (1980).6 Infinitely lived householdspossess the physical capital and add to the stock of capital by investing some amountof real output each period. The households work and invest. Furthermore, they rentthe capital to one-period-lived firms. Thus, households supply capital and labor tofirms which use a technology described by the aggregate production functionF(Kt,Nt) : R+ ! R, where F is continuously differentiable, monotonic and concave(separately) in K (capital stock) and N (labor input), with F(0,0) = 0. In this decen-tralization scheme, we introduce two interesting innovations. First, the model allowsfor the existence of trade unions in the labor market, postulating a preference orderover non-negative real valued sequences of wages and employment. Second, a repre-sentative union maximizes a concave and twice continuously differentiable utilityfunction, which is strictly increasing in the wage, and decreasing in reservation wageargument. This latter is an exogenous, uncontrollable AR(1) stochastic process. Fi-nally, the households� expected lifetime utility for each period reflects the preferenceorder over non-negative real-valued sequences of consumption and labor supply.However, the quantities representing the labor supplies are N(Æ), that is, the labor in-put restricted by the quantity of aggregate labor input determined by the firm-unionrelationship, where N(Æ) is the sequence of Arrow–Debreu event-contingent union�slabor demand.

3.2. The firm

In this economy there are a large number of identical firms which produce ahomogeneous output.7 Firms use the same constant returns-to scale Cobb–Douglasproduction function,

Y t ¼ AtKht N

1�ht . ð1Þ

The production function is subject to an aggregate productivity shock At, com-mon to all firms, while Kt and Nt denote, respectively, aggregate capital stock andemployment. The technology shock follows the stationary AR(1) process:

lnAtþ1 ¼ ð1� qÞ lnAþ q lnAt þ et; ð2Þ

6 See the seminal papers of Kydland and Prescott (1982) and Prescott (1986), the works included inCooley (1995) and the surveys of King and Rebelo (1999) and Prescott (1998). Alternative decentralizedschemes and implications of representative agent stochastic growth economies are discussed in Danthineand Donaldson (2001). Following these authors, we recognize that using non-optimal economies is clearlyinconsistent with a set-up with one-period-lived-firms and unions. We concentrate here on a simpledynamic model, though the issue should have wider extensions and applications.7 Since each firm is assumed not to have any market power, we can treat all firms as a unique production

unit.


where 0 6 q 6 1 and et is a i.i.d. random variable with the following distributionet � Nð0; r2

e Þ. lnðAÞ is the mean of the log technology shock process. The capitalstock Kt depreciates exponentially at the rate d (0 6 d < 1), so that the law of motionfor the aggregate capital stock is Kt+1 = (1 � d)Kt + Xt where Xt is the aggregateinvestment that households add to the stock of capital each period. The right todetermine the quantity of labor employed in period t is ceded to the union by thefirm. In fact, it is common knowledge that the firm solves the profit-maximizingproblem, with the first order conditions:

W t ¼ ð1� hÞAtKt

N t

� �h

; ð3Þ

Rt ¼ hY t

Kt

� �þ ð1� dÞ; ð4Þ

where Rt is the rental rate of capital. After the technology shock is revealed, at thebeginning of period t, firms and unions determine the wage and quantity of laboremployed in that period.

3.3. The union

We assume that trade unions� objective is that of rent maximization and that theunionmembers are identical workers who are all treated identically by the union.8 Un-der this simple model, the union selects wages (or employment) on its own, with nobargaining. The optimal static selection of the union preferences is specified as follows:

maxNt

N gt ðW t � BtÞ; W t > Bt; ð5Þ

where B is the reservation wage, received by non-unionized unemployed. The rentmaximization function (5) assumes that the union cares about the real wage surplus(the difference between the union wage claim and the reservation wage). However, gcan be interpreted as the relative weight in the trade union preference betweenemployment and wage. Clearly, the utility function is linear in wages (risk-neutral)and is subject to the labor demand curve:

W t ¼ f 0ðNtÞ. ð6ÞThroughout this, we assume that the union considers Bt as an exogenous, uncon-

trollable AR(1) stochastic process,

Btþ1 ¼ ð1� xÞBþ xBt þ nt; ð7Þwhere 0 6 x 6 1, B denotes the unconditional mean of the process, and nt is a i.i.d.random variable with the following distribution nt � Nð0; r2

nÞ. Thus, technology

8 See Dunlop (1944). Unions do much more than just set wages. For many of the European countries,collective agreements cover issues ranging from layoff rules, pension benefits, grievance procedures,overtime limits, equity, working conditions and broader political issues concerned with the labormovement as a whole (see Pencavel, 1991; OECD, 1994; Booth, 1995; Chiarini, 1999; among others).


shocks are not the only source of fluctuations. In picking a time path for, say,employment, the union considers the firm labor demand curve (3). The union prob-lem yields the following first order conditions:

Nt ¼ð1� hÞðg � hÞ

g

� �1=h At

Bt

� �1=h

Kt. ð8Þ

We adopt a monopoly union model to unilaterally set the employment (or equiv-alently the wage level), subject to the firm�s labor demand curve. Firms, therefore,read off from the labor demand curve the number of workers to hire at the unionwage. Two aspects must be stressed for characterizing a monopoly union outcomein a general equilibrium framework. First, the model assumes unemployment insur-ance by specifying a guaranteed income flow to each unemployed worker (reserva-tion wage or benefit). Below, we deal with unemployed individuals assumingidentical families with two heterogeneous members, employed vs. unemployed butwith identical preferences for consumption. Such an environment is not equivalentto one where the market for unemployment insurance provides a means to attain risksharing.9 Although family individuals consume identical amounts regardless of theiremployment status, we do not assume, as in Hansen (1985), that firms offer laborcontracts (including unemployment insurance) that are traded competitively, butrather that the labor market is imperfectly competitive and that union wages arehigher than unemployment benefits. Second, the union, seeking its highest level ofutility, subject to the constraints of the labor demand curve, may take into accountthat its behavior may reduce employment and, thus, union members and utility.10

The model predicts that the economic costs of unemployment, in a labor marketcharacterized by a monopoly union may be increased by the social costs due to theunemployment benefits. An increase in government spending for unemploymentencourages unions to raise wages, worsening the trade-off between real wage andemployment. In equilibrium, unemployment benefits lead to a lower level of employ-ment and a higher real wage.

Incorporating a model of union wage-setting behavior, in which alternativeopportunities affect union preferences, would exert some downwards pressure onemployment and output. This result holds for the monopoly union model and is sup-ported by some micro and macro evidence (see OECD, 1994; Nickell, 1997; and thepapers quoted therein). Because unemployment benefits reduce the cost of becomingunemployed, unions may take greater risk with the security of their members� jobs,disputing with firms over a higher wage rate.

In short, in this framework firms and unions are assumed to exist for any one per-iod and to be recursively reorganized over and over again. Firms and Unions� prob-lems are, therefore, static and hence, especially simple: after viewing the shock, they

9 See Li (1999) for an updated discussion.10 Among the possible extensions, a natural possibility is that of a monopoly union which solves adynamic optimization problem as, for instance, in Kidd and Oswald (1987). In this model, new employeesjoin the union (a post entry closed-shop model). This model augments the number of the equations ofmotion for the economy with a difference equation for the membership.


choose capital and labor so as to maximize profits and the utility function on a per-iod by period basis.

3.4. The representative household

To be coherent with the equilibrium of the model, however, we have to solve theheterogeneity which in this model focuses on the labor supply of employed unionmembers and unemployed individuals. The latter receive the reservation wage Bt

which is lower than the union�s wage Wt. This will influence consumption-savingdecisions. To cope with this problem, we follow Cho and Rogerson�s (1988) familylabor supply model, assuming a large number of identical families, each of whichconsists of two members, but with just one supplying labor. However, both theworker and the unemployed member of the family have the same strictly convexpreferences for consumption. The following form for the temporal preference is max-imized by the household, taking into account its budget constraints:

uðcit; ntÞ ¼ 2 logðcitÞ � / logðntÞ. ð9ÞNotice that individuals in this economy can supply only the quantity of labor in-

put nt required by the labor market. In other words, in this economy, aggregateemployment fluctuations are induced by changes in union wage curve and firm labordemand and, therefore, these fluctuations are not related to a consumer�s intertem-poral substitution.11 The optimal response of households to shocks is now reducedto select the aggregate quantity Nt. In this framework the wagesetting relationreplaces a standard labor–supply relation. Since a measure of the average hoursworked for the Italian economy does not exist, we may let households agree to thislabor input variation rather than determining different margins of the labor dimen-sion such as the change in the fraction of working days and the variation in averagehours.

The household has the flow budget constraint given by

2cit þ kitþ1 ¼ W tnt þ Btð1� ntÞ þ Rtkit � T t; ð10Þwhere Tt is the level of lump sum taxation. The problem can be expressed as a sta-tionary discounted dynamic programming problem. The household�s value functionis

Jtðkit;Kt;MtÞ ¼ maxcit ;kitþ1

uðcit; nitÞ þ bEtJtþ1ðkjtþ1;Ktþ1;Mtþ1Þ

� �; ð11Þ

where Mt+1 denotes the vector of stochastic disturbances (At+1,Bt+1)0, kit is the law

of motion for the household capital stock (kit,Kt,Mt) are the state variables for thehouseholds and (Kt,Mt) are the aggregate state variables. The value function is max-imized subject to the budget constraint (10).

11 The nominal contracts model of Fairise (1995) and the union model of Maffezzoli (2001) also allow todissociate employment decisions from the consumption choices. In these models, as in our model, thehousehold provides exactly the labor quantity requested by the firm.


After manipulating the necessary and sufficient first order conditions, taking intoaccount the firm and union behavior, we may describe this economy as follows:

E bCt

Ctþ1

� �Rtþ1

� �¼ 1; ð12:1Þ

Rt ¼ hAtKh�1t N 1�h

t þ ð1� dÞ; ð12:2Þ

Ct ¼ 12

�AtKh

t N1�ht þ ð1� dÞKt � Ktþ1 þ Btð1� NtÞ � T t

�; ð12:3Þ

Nt ¼ð1� hÞðg � hÞ

g

� �1=h At

Bt

� �1=h

Kt. ð12:4Þ

Eq. (12.1) is the Lucas asset pricing equation. Eq. (12.2) is derived from the firm�sprofit maximization. Given Wt and Rt, these conditions require the rental rate ofcapital to be equal to the marginal productivity of the capital stock, while the house-hold�s constraint determines Eq. (12.3). Employment fluctuations depend on capitalstock, a technological parameter h, the union preferences g, and two stochasticshocks: variations in the productivity term At and in the reservation wage term Bt.Given the slope of the demand and labor supply curve, the first shock causes fluctu-ations in employment by changing the marginal product of labor (the labor de-mand). The extent to which the second shock affects the wage setting curve (thelabor supply curve) determines the wage-employment combination.

It is worth noting that, though the economy is characterized by trade unionbehavior, the model is unable to generate data on unemployment. The model in-volves heterogeneity with the presence of both unemployed and employed individu-als as components of the family, and we simplify it by using a representativehousehold. This assumption is prompted by the observation that most of the familyincome is redistributed among its members. In the model, this assumption eliminateswealth-redistribution effects and makes an implementable real business cycle modelwith unemployment.

4. Government

The role of the government in this economy is simply to collect lump sum tax rev-enue and return it to the households as unemployment benefits. This implies that thegovernment budget constraint is

ð1� NtÞBt ¼ T t. ð13Þ

5. Equilibrium of the economy

In the economy, unions and firms choose the aggregate employment. Householdschoose the allocation between consumption and investment and supply the quantityof labor coherent with the labor market equilibrium.


First, we compute the optimal level of employment and the relative price factors(Rt,Wt) determined by the union-firm equilibrium. Second, we impose market clear-ing conditions in good and labor markets, forcing individual agents� choices to beequivalent to their aggregate counterpart.

The capital accumulation rule, the technological processes and the reserva-tion wage (benefits) are the equations of motion for this economy, St = (Kt,At,Bt).Provided the state aggregate St, the state facing a household can be defined asst = (St,kit), where kit is the individual capital stock.

Once the labor optimal choices have been made, an equilibrium solution may bedefined.

Definition 1. A stationary competitive equilibrium for this economy consists of a setof decision rules, cit(st), xit(st), nit(st); a set of aggregate decision rules, Ct(St), Xt(S),Nt(S), a set of price function Wt(S), Rt(S) and a value function JtðstÞ satisfying

(a) the firm�s profit maximization (3) and (4),(b) the union�s problem (5)–(8),(c) the household�s utility maximization problem (9)–(11),(d) the aggregate resources constraint C(S) + X(S) = Y(S), for all S,(e) the government constraint (13).

Assuming a continuum of firms, uniformly distributed over a unit interval j 2 [0, 1],and a continuum of households, uniformly distributed over a unit interval, supplyinglabor i 2 [0,1], market clearing conditions hold for each market. Specifically,

1. for labor service (employment), �ni(Mt,kt,Kt)di = �nj(Mt,kt)dj = nt(Mt,kt,Kt) Nt,

2. for consumption �ci(Mt,kt,Kt)di = �cj(Mt,kt)dj = ct(Mt,kt,Kt) Ct,

3. for investment �xi(Mt,kt,Kt)di = �xj(Mt,kt)dj = xt(Mt,kt,Kt) Xt,

4. for capital �ki(Mt,kt,Kt)di = �kj(Mt,kt)dj = kt(Mt,kt,Kt) Kt.

6. Stylized facts

Stylized facts for a European country, Italy, are summarized in Table 2. Businesscycle properties are based upon ISTAT quarterly time-series data for the period1970:1–1998:3. Observed time-series have been detrended using the Hodrick–Pres-cott filter. The macroeconomic time-series considered are output (y), consumption(c), investment (x), aggregate employment (n) and labor productivity (p) calculatedas the ratio between output and employment. For each variable, the table reportsstandard deviations of fluctuations (the amplitude) both as percentage and comparedto GDP standard deviations, the autoregressive coefficient of each series (the persis-tence) and the degree of contemporaneous comovement (the correlation of each ser-ies with the real GDP). The last row expresses the correlation between employmentand labor productivity, which characterizes labor market behavior.

Table 2Cyclical properties of Italian data 1970:1–1998:3

Variable (v) y c x n p

s.d. % 1.46 1.24 3.70 1.39 2.78s.d./s.d. (y) 1 0.85 2.53 0.95 1.90AR(1) 0.85 0.92 0.91 0.90 0.80Corr(y,v) 1 0.80 0.78 0.63 0.36Corr(n,v) 0.19

Source: Istat, Series seasonally adjust, and H–P detrended.


From the table the following can be deduced: employment is procyclical(Corry,n = 0.63), and is at least as volatile as output (rn/ry = 0.95). Labor productiv-ity is not highly procyclical: the comovements of labor productivity with output aresomewhat moderate (Corry,p = 0.36). A small positive correlation is also reportedfor aggregate employment and productivity relationship (Corrn,p = 0.19).

Labor productivity fluctuates more than one and a half times as much as output(rp/ry = 1.90), while output and employment show a high degree of persistence, andemployment fluctuates half as much as productivity (rn/rp = 0.5). Finally, consump-tion is almost as volatile as income (rc/ry = 0.85), while investment fluctuates fromabout three to four times as much as income.

7. Calibration and simulation results

The model is calibrated for the Italian economy though the analysis can be gen-eralized to a number of European countries which present a sizeable unionized labormarket.

The system of equations we use to compute dynamic equilibria of the model de-pends on a set of eight parameters (see Table 3). Two pertains to union�s and house-hold�s preferences, (g,b), and two parameters pertain to technology (the capital shareh, and the capital depreciation rate d). Finally, q, x, re, rn denote the AR(1) coeffi-cients and the standard deviations in the law of motion for productivity and reser-vation wage shocks, respectively.

For setting numerical values for parameters, we use the artificial economy as thebasis for restricting the general framework and mapping that framework onto thedata. The capital share h is from Censolo and Onofri (1993). This value is consistentwith the the labor share calculated with the data. Some parameters (b,d) are cali-brated so that the non-stochastic steady state of the model matches a set of long-run averages computed from Italian time series. The following equations represent

Table 3Parameters calibration

g d b h q x re rn

0.50 0.025 0.988 0.42 0.88 0.65 0.36 0.046


the steady state of the economy12 which is the basis for calibrating these values. Eq.(14.1) is the basis for calibrating R:

bR ¼ 1. ð14:1ÞSetting b = 0.99, Eq. (14.1) provides a value of R = 1.01. Given R and b, (14.2)

yields the calibrated depreciation rate d. This value is coherent with the long-runY/K ratio:

R ¼ hYKþ ð1� dÞ; ð14:2Þ

where Y = AKhN1�h. With regard to the shocks, the steady-state value of A is setequal to 1, whereas B is calibrated to reproduce the average employment in the wholeeconomy over the period considered, using Eq. (14.3):

N ¼ fAB

� �1=h

K; ð14:3Þ

where f ¼ ð1�hÞðg�hÞg

� �1=h. The parameter values d and h provide a consumption func-

tion coherent with the steady-state consumption/output ratio and, therefore, invest-ment/output ratio:

C ¼ 12

�AKhN 1�h � dK

�ð14:4Þ

With regard to the union�s preference parameter, the value selected (g = 0.50)indicates that unions consider in some way the employment consequences of theirwage policies. Finally, for calibrating the parameters of the processes that generatethe shocks to technology and benefits, we use two different approaches. For the pro-ductivity shock we use the Solow residual estimates.13 The standard deviation is cal-ibrated to mimic the variance of actual GDP (see Cogley and Nason, 1995). Thebenefit shock parameters are drawn by filtering the series of the ordinary wage sup-plementary fund benefits paid to Italian workers affected by collective lay-offs infirms with 16 or more employees as a result of a temporary decline in economicactivity.14

In order to analyze the quantitative implications of the union theoretical modelwe use the above parameters to calibrate and simulate a standard real business cyclemodel often used for explaining the business cycle in Europe during the 1990s.15 Thisis done to allow an easier comparison between standard framework results and ourfindings. In particular, in order to examine how much of the empirical performance

12 Given our assumptions on functional forms, technology and parameter restrictions, the steady-statesolution exists and is unique. The solution method used in this paper is that suggested by King et al.(1988a,b). The essence of this method is to transform the economy�s equilibrium characterization into anapproximating first-order autoregressive linear system (see Appendix A).13 See Chiarini and Piselli (2000). The value is also similar to that obtained by Censolo and Onofri (1993)and Maffezzoli (2001).14 Source: INPS, National Institute for Social Security.15 See, for instance, the papers in Henin (1995) and in Henin et al. (1997).

Table 4Hansen�s model for the Italian economy


s.d. % 1.47 0.29 4.43 1.28 0.29s.d./s.d. (y) 1 0.20 3.02 0.87 0.20AR(1) 0.68 0.89 0.66 0.66 0.89Corr(y,v) 1 0.72 0.99 0.99 0.72Corr(n,v) 0.98

Source: H–P detrended data generated by the model.

Table 5Union�s model for the Italian economy nt = 0


s.d. % 1.45 0.46 3.93 1.33 0.12s.d./s.d. (y) 1 0.31 2.71 0.92 0.08AR(l) 0.76 0.84 0.75 0.75 0.76Corr(y,v) 1 0.88 0.99 0.99 0.99Corr(n,v) 0.98


Table 6Union�s model for the Italian economy nt 5 0


s.d. % 1.47 0.46 4.02 1.41 0.23s.d./s.d. (y) 1 0.31 2.72 0.96 0.16AR(l) 0.61 0.76 0.59 0.60 0.54Corr(y,v) 1 0.87 0.99 0.99 0.35Corr(n,v) 0.18



of the model can be plausibly attributed to each of the shock, we carry out a simu-lation between the non-Walrasian economies with and without the shock on unem-ployment benefits.16 The cyclical characteristics reported in Tables 4–6 are based ona set of 1000 simulations over 111 quarters horizon.

7.1. The labor indivisibility model

First of all, following Hansen (1985), we reproduce some statistics by simulating areal business cycle model with labor indivisibility. Table 4 shows the results.

16 One of the referees has suggested this experiment in order to assess the impact of the stochastic processof the unemployment benefit.


Although these model simulations can account for some drawbacks, some aspectsof the data generated by the model appear to be inconsistent with the Europeanlabor markets. The Hansen simulations show that productivity is highly positivelycorrelated with both output and aggregate labor input (0.72 and 0.98, respectively)whereas the actual data discussed in the list of stylized facts above show a smallpositive correlation (Corrn,p = 0.19). Literature on RBC indicates the shock on thetotal factor productivity as one of the major causes of this result.

Focusing on the labor market features we see that the models perform reasonablywell in producing procyclical employment movements closely correlated with output,although they do less well in explaining other characteristics:

(a) Employment is less volatile than output (rn/ry = 0.87).(b) Labor productivity generated by the model for Italy fluctuates much less than

four times as much as output (rp/ry = 0.20).(c) Employment in Italy fluctuates four times as much as productivity (rn/

rp = 4.4).(d) Simulated consumption is remarkably less volatile than income (rc/ry = 0.20),

while investment still fluctuates three times as much as income (ri/ry = 3.02).

It is interesting to note that similar results reproduce Hairault�s (1995) findings forFrance, and indicate that conventional RBC models are not a benchmark model forthe European countries.

7.2. The union model without the unemployment benefit shock

With the above parameter setting, now we attempt to sorting out the separate ef-fects of the two shocks on the non-Walrasian economy. Here a single source of ran-domness, a shock to total factor productivity, drives the model. Table 5 summarizesthe standard business cycle statistics under the H–P filter, for this experiment.

The table shows that the augmented real business cycle model driven by a technol-ogy shock is not able to produce realistic business cycle variation in real quantities.The model fails to reproduce the volatility of both productivity and employment.Moreover, the simulated series for these variables still remain highly procyclical.These results are unsurprising and similar to those reached by Maffezzoli (2001)and show that labor market puzzles can not be solved by shifts in the labor demandcurve. The similarity with Maffezzoli�s result arises again in assessing the relative per-formance of the union model numerical simulation with the Walrasian stochasticgeneral equilibrium model simulation described above. A model with a monopolyunion does not seem to have a comparative advantage over the indivisible labormodel in the replication of Italian business cycle statistics. Under the benchmarkparametrization, a positive shock to productivity provides similar results for bothmodels. Now employment is almost perfectly correlated with output and productiv-ity correlation with employment is 0.99. These results sharply contrast with the ob-served correlation coefficients. Simulated series for output, consumption, investment,employment and productivity generated by the union model, however, exhibit more


realistic persistence to a positive productivity shock. The union model generates ahigher persistence in investment and (therefore) capital stock.17 This dynamics alongwith the total factor productivity drive the employment and, by the latter, provide astronger effect on the other variables.

We will see in the next two subsections that a condition for the union model todisplay realistic real wage (and productivity)-employment correlation is to introducea stochastic factor that will shift the labor supply function (the wage curve).

7.3. The union model with the unemployment benefit shock

Table 6 reproduces our findings for Italy using the union model described in theprevious sections.

One fact worth noting from the table is that this model yields a remarkableimprovement of the ‘‘troublesome facts’’ depicted by the prototype RBC models.In particular,

(a) The aggregate employment generated by the union model is at least as volatileas output for both countries: the value of (rn/ry) = 0.96 matches the stylizedfact. Moreover, the ratio of total employed persons/GDP is analogous to thedata, (re/ry) = 0.80.

(b) The model does well in matching labor productivity: the co-movements of pro-ductivity with output are somewhat moderate (Corry,p = 0.35 equals to thedata).

(c) According to the stylized facts, employment and productivity simulations showa small positive correlation (Corrn,p = 0.18, Italian data show 0.19).

(d) The generated employment shows a lower degree of persistence and an excessof procyclicality with respect to the stylized facts.

(e) Consumption is still remarkably less volatile than income.

As in the Hansen�s model, the most unsuccessful features of the union model inthe labor market are related to productivity fluctuations. The aggregate labor pro-ductivity fluctuates less than output (rp/ry = 0.15, the data shows 1.90) and theemployment-productivity fluctuations are overstated in the model (rn/rp = 4.3against the stylized fact value of 0.5). A consumption substantially smoother thanthe data is often obtained in these models and it is related to the separable formof the utility function where consumption is independent from leisure.

The most successful features of the model are in the implied correlation structure.Under the above conditions, the model seems to display realistic features for boththe employment variability puzzle and the productivity puzzle. Although the Italianunion RBC model predicts that employment is less variable than in reality, itsimprovement with respect to Hansen�s version is remarkable. The relative perfor-

17 Impulse responses to a shock in productivity for the union model is provided by the authors uponrequest. See Henin (1995) and King and Rebelo (1999) for an analysis of the ‘‘transitional dynamics’’(when the initial capital stock is different from its steady-state value) effects in real business cycle models.


mance of the Walrasian and non-Walrasian versions of the model shows that intro-ducing a factor suitable to shift the wage curve (labor supply function) is crucial tolessen the positive correlation between productivity (or wages) and employment orproductivity and output. In European countries, where trade union influence andpower is high, a way of causing shifts in labor supply is through reservation wageshocks. The improvements in the reservation wages (unemployment benefits, familyallowances, educational and different types of subsidies for temporary unemployed)and the corresponding unions� reaction that many European economies have expe-rienced in the last decades may well be one explanation why the canonical businesscycle models fail to replicate business data.

We simulate the model under the assumption of orthogonality18 of the stochasticshocks At and Bt. Following referee�s suggestion and because of lack of empirical evi-dence about the value of the correlation between these two shocks, we calculate theempirical correlation of disturbances At and Bt, after filtering them through an AR(1)process. A correlation coefficient close to zero19 allows us to assume that the shocksare orthogonal.

7.4. The impulse response

Figs. 1 and 2 trace out the impulse-response functions that result from the solu-tion of the model. They plot how our selected variables respond to a one-period unitshock in, respectively, At and Bt. The shock�s effects are measured as percent devia-tion from steady-state values. A noticeable feature concerns the contrasting perfor-mance of the variables under the two shocks. The responses of output, consumption,investment and employment due to the effect of the benefit shock are instantaneouslybelow their steady-state level and then increase to their lower stationary levels(Fig. 2). The picture is reversed when the economy is hit by a productivity shock(Fig. 1).

A negative unanticipated shock to reservation wage (an increase in benefits)diminishes the cost of being unemployed, affecting the employment-wage tradeoffin the union utility function. Employment will fall by more than output and, there-fore, productivity will increase. This is consistent with the RBC literature, whereaverage labor productivity is used as a measure of the return to work (see Christianoand Eichenbaum, 1992). Intuitively, this result arises because in the monopoly unionmodel an increase in the reservation wage increases union wages.

Some insight behind these labor market predictions can be obtained recalling theclassical labor market diagram. As productivity shocks increase product, the labordemand curve shifts rightwards, affecting employment. However, when consideringthe impact of the productivity cycle on the union model with the alternative oppor-tunities Bt which affect union preferences, the wage-supply curve shifts leftwards andemployment and wages move in opposite directions. Consequently, the correlation

18 Orthogonality is often assumed in multi-shock models (Christiano and Eichenbaum, 1992; Bencivenga,1992).19 These results can be provided by the authors upon request.

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

Years after shock

Per

cent

dev

iatio

n fr

om s

tead

y st

ate

consumption

output

employment

investment

productivity

Fig. 1. Impulse response to a shock in technology.

0 1 2 3 4 5 6 7 8-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

Years after shock

Perc

ent d

evia

tion

from

ste

ady

stat

e

consumption

output

employment

investment

productivity

Fig. 2. Impulse response to a shock in reservation wage.


between productivity and employment falls matching the data while output andemployment may continue to fall dampening the productivity shock effect.

The union model provides a low correlation between output and both labor pro-ductivity and employment. A productivity shock produces a shift in labor demandalong a flat wage (labor supply) curve. Labor input will be very responsive and real


wages (marginal and average labor productivity) will change little, if any. A benefitshock can be viewed as upward shifts in the wage curve along a somewhat flat down-ward sloping labor demand curve. This is the case with a Cobb–Douglas productionfunction. In such a setup, there is not a prior reason to expect a positive correlationbetween wages (or productivity) and employment or output. In contrast with thestandard RBC models, if real wage changes by more than employment, the modelpredicts a counter-cyclical relationship between the variables.20 Thus, as the impulseresponse function reported in Fig. 2 shows, under these circumstances, there may bea recession if technological innovations are not large enough to offset wage increasesthat depress profits.

The contribution of these simulations is twofold. First, they show that includingunion behavior and randomizing unemployment benefits in the union preferencesimproves the RBC model performance. Second, they show how a series of exogenoustechnological shocks may imply the occurrence of a recession if unemploymentbenefits are driven by political institutions in a unionized labor market.

8. Conclusions

One frequently quoted shortcoming of the standard RBC model is that productiv-ity is highly positively correlated with employment and output and, therefore, itsinability to account for recessions. In the previous sections we have seen that oneway to solve this puzzle is allowing both labor demand and labor supply to shift.We reach this result specifying the unemployment benefits as a further stochasticshock in a unionized labor market. This framework is important because empiricalobservations and econometric studies suggest that for the European countries wagerigidity, union density and union coverage and unemployment provisions are ele-ments that cannot be neglected in the model.21 Thus, it is crucial for these economiesto construct models with non-Walrasian elements in the labor market. Moreover, themodel is now able to account for recessions. The improvements in the benefit systemand job protection, along with union wage claims that many European economieshave experienced in recent decades, may well be one explanation why these econo-mies have had growth problems and employment persistence. Thus, they may alsocreate the conditions under which an economy driven by technological shocksmay exhibit recessions. In the monopoly union framework, fiscal shocks, which im-pinge on the union utility function, may depress the economy when there are no largetechnological shocks to offset union behavior. Changes in the benefit system haveeffects that are similar to productivity shocks and, therefore, they may producerealistic patterns of co-movement among variables. Although the benefit system

20 A way of causing shift in labor supply is adding a further shocks such as monetary policy shocks(Cooley and Hansen, 1989), taste shocks (Bencivenga, 1992), shock to home production (Benhabib et al.,1991) or underground production (Busato and Chiarini, 2004), and government spending shocks(Christiano and Eichenbaum, 1992).21 See OECD (1994), Nickell (1997) and Chiarini (1999), among others.


changes infrequently, its positive relationships with the union wage claim makes it aproxy of the latter and a potential explanation for European business cycle fluctua-tions. Our basic RBC model, enriched by a simple union behavior hyphothesis, ac-counts for the business cycle pattern of the Italian labor market. The model is able toreplicate many labor market correlations and co-movements and to account forcontractions.

Acknowledgments

We are indebted to John Donaldson, Roger Farmer, Francesco Busato, AndreaBrandolini and Luca Dedola for their helpful comments. Edward Prescott�s adviseon the first version of this paper has proved very useful. Two referees have contrib-uted most valuable critical comments. Some of the work on this paper was donewhile Chiarini was visiting the School of Business at Columbia University (NY).The usual caveats apply. The views contained here are those of the authors onlyand do not necessarily reflect those of the institutions for which they work.

Appendix A

The following equations are the transformation of the economy�s equilibriumcharacterization into an approximating first-order autoregressive linear system (seeCampbell, 1994; Uhlig, 1999; among others):

ct ¼YCat þ

YC

h þ ð1� dÞKC

� �kt þ

YCð1� hÞnt �

KCktþ1; ðA:1Þ

rt ¼ hYKR

at þ ðh � 1Þkt þ ð1� hÞntð Þ; ðA:2Þ

yt ¼ at þ hkt þ ð1� hÞntð Þ; ðA:3Þ0 ¼ Et ðct � ctþ1Þ þ rtþ1½ �; ðA:4Þ

nt ¼ fKN

1

hat �

1

hbt þ kt

� �; ðA:5Þ

btþ1 ¼ pbt þ nt; ðA:6Þatþ1 ¼ qat þ et. ðA:7Þ

Notice, here the endogenous variables are deviation around the non-stochasticsteady state.

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