An evolutionary model of industry dynamics and … papers/2012...J Econ Interact Coord (2012) 7:23–61 DOI 10.1007/s11403-011-0085-y REGULAR ARTICLE An evolutionary model of industry

J Econ Interact Coord (2012) 7:23–61DOI 10.1007/s11403-011-0085-y

REGULAR ARTICLE

An evolutionary model of industry dynamics and firms’institutional behavior with job search, bargainingand matching

Sandra Tavares Silva · Jorge M. S. Valente ·Aurora A. C. Teixeira

Received: 22 January 2011 / Accepted: 27 October 2011 / Published online: 12 November 2011© Springer-Verlag 2011

Abstract By combining features from distinct theoretical approaches, namely theevolutionary and the job search, matching and bargaining literatures, we propose amodel that captures the main dynamics of a world where heterogeneous firms andworkers interact and co-evolve. Within a micro-meso framework, the model focuseson the influence of firms’ labour choices (“institutional settings”) on industry dynam-ics, taking into account the existence of employment adjustment costs. The consider-ation of endogenous matching and bargaining processes in the labour market resultsin significant frictions, such as the simultaneous coexistence of unfilled job vacanciesand unemployment. In a setting where technological progress is not biased a stylizedfact of industrialized world economies in the last few decades emerges, the increasingwage inequality. Additionally, turbulence in the industry increases after a negativedemand shock. As expected, the negative demand shock causes a decrease in thenumber of vacancies and, consequently, unemployment rates increase considerably.Interestingly, and mimicking the recent experiences of countries such as US, Spain,Greece and Portugal, the rise in unemployment is matched by a rise in contractualwages. This outcome is explained by the lower ability of the firms to fill their postedvacancies, which results from friction in the interactions among agents.

S. T. SilvaCEF.UP, Faculdade de Economia, Universidade do Porto, Porto, Portugal

J. M. S. ValenteLIAAD—INESC Porto LA, Faculdade de Economia, Universidade do Porto, Porto, Portugal

A. A. C. Teixeira (B)CEF.UP, Faculdade de Economia, Universidade do Porto, INESC Porto, OBEGEF,Rua Dr Roberto Frias, 4200-464 Porto, Portugale-mail: [email protected]

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24 S. T. Silva et al.

Keywords Evolutionary · Firm behaviour · Job search · Bargaining and matching ·Micro foundations · Industrial dynamics

JEL Classification B52 · D21 · L2 · J2 · J3 · O12

1 Introduction

Understanding economic growth and business cycles involves analyzing employmentfluctuations as a response to shocks in an uncertain environment (e.g., Andersen 1999).Firms go through processes of reorganization associated with several factors, such astechnological constraints, market fluctuations and manpower mobility. Within this ana-lytical frame, the economy’s adjustment costs, as well as their structure at the microlevel, are of relevance. The timing and pattern of employment adjustment, includinghiring and firing decisions adopted by employers, are mediated by adjustment costs(e.g., Hamermesh 1993; Hamermesh and Pfann 1996; Abowd and Kramarz 2003).Wage inequality over the last two decades in several advanced and developing countriesis a stylized fact explored in several studies (for example, Freeman 1995; Richardson1995; Gottschalk 1997; Wood 1998; Katz and Autor 1999; Jolivet et al. 2006; Weissand Garloff 2011). In general, modelling efforts associated with wage inequality over-look both industrial dynamics and labour market frictions. Wage inequality is, in thesesettings, essentially explained by skill biased technological change (SBTC). How-ever, as Oesch and Menés (2011) emphasizes SBTC is not the unique explanation forincreasing wage inequality. Other explanations include the routinization hypothesis(Autor et al. 2003) and the institutional framework (Levy and Temin 2007). Addition-ally, recent empirical literature suggests that technology may not have an universalskill biased effect (Baccini and Cioni 2010), with Antonioli et al. (2011) underlying therole of specific aspects of industrial relations system. Hence, our model deals explicitlywith industrial dynamics and labour market frictions, assuming neutral technologicalprogress. The aim is to underline the relevance of microfoundations in the emergenceof wage inequality, namely those related with the choices of firms concerning labourorganization and employment adjustment costs.

Neoclassical economics has offered important insights into labour dynamics.Nevertheless, such contributions seem very stylized, in the sense that they usuallydo not focus on the firms’ diversity nor do they deal with industry dynamics. Evenreference models of labour mobility and job matching (for a survey, see for example,Mortensen and Pissarides 1999) usually ignore the interdependencies between indus-try dynamics and labour market forces. Moreover, most neoclassical labour literatureassumes a standard approach based on the idea of hyper-rational firms and work-ers. The most common perspective considers the representative agent hypothesis as atool to deal with the aggregation of heterogeneous behaviours,1 generally interpretingmacroeconomic dynamics under equilibrium conditions.

1 Some mainstream contributions, in line with Klette and Kortum (2004), take into account heteroge-neous firms. However, these studies operate with the dynamic general equilibrium models in a neoclassicalframework of optimization and stationary equilibrium.

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An evolutionary model of industry dynamics and firms 25

Evolutionary economics offers a much more realistic setting as it conceives theobserved co-evolution between aggregate variables, such as employment and output,as resulting from far-from-equilibrium interactions between heterogeneous agents.Therefore, even when some equilibrium relationship take place among aggregate vari-ables, for example, inflows and outflows from unemployment, the economy mightsystematically depart from it and follow a disequilibrium trajectory (Fagiolo et al.2004). Moreover, a methodological approach that does not forcibly require equilib-rium, assuming rather that it may emerge from interactions among all the players inthe model, allows for a broader analysis of labour markets (Richiardi 2006).

In an evolutionary world, workers and firms interact directly, and their behav-iours are influenced by the choices made in the past by both themselves and otheragents. Such interaction networks, materialized in matching rules in the labour mar-ket, are endogenous and may change over time (Fagiolo et al. 2004). Interactionoccurs both in the labour and product markets, and the firms’ survival dependson their labour choices, such as hiring and firing policies and wage-setting deci-sions. In fact, changes in the industry structure and worker mobility influence eachother. For example, Dunne et al. (1989) show that industry dynamics are associ-ated with the creation and elimination of jobs. Moreover, Haveman (1995) stressesthat industry turbulence influences the labour market not only directly, through themovement of individuals employed in established firms to new ones, and of indi-viduals allocated to exiting organizations to surviving ones, but also indirectly,through the vacancy chains associated with the founding and exiting processes offirms.

However, evolutionary economics does not usually focus on these topics, with mostmodels of evolutionary industrial dynamics emphasizing the technological and/orfinancial determinants of the evolution of industries (see e.g., Dosi et al. 1997;Sutton 1997). Therefore, mainstream contributions, particularly with regard to jobsearch, matching and bargaining processes (e.g., Mortensen 1970, 1982, 1986, 1999;Mortensen and Pissarides 1994, 1999), are important to comply with our main motiva-tion: bring labour market dynamics into the evolutionist framework. In this framework,the economy is a complex and evolving system, agents are bounded rational and heter-ogeneous in almost all their attributes, there are open-ended search spaces and noveltyis endogenous (for example, Nelson and Winter 1982, 2002; Dosi 1988; Andersen1994; Nelson 1995).

In this paper, we explicitly introduce labour market dynamics in a model thatexplores the implications of firms’ behaviour in their industry. The matching pro-cess that emerges from interactions between firms and workers in the labour market iscrucial to understanding wage inequality, (un)employment and output growth dynam-ics. These topics are extensively explored in the neoclassical approach, whereas fewformal contributions exist within evolutionary literature. One important exception isFagiolo et al. (2004), who offer a model close to both the “Agent-Based Computa-tional Economics” (ACE) approach (Tesfatsion 1997; Epstein and Axtell 1996) andself-organization models of labour markets (Lesourne 1992).

Despite such valuable and insightful contributions, the industrial level remainssomehow overlooked and disconnected from real world evidence. In fact, bothneoclassical (e.g., Geroski 1995; Cabral and Mata 2003) and neo-schumpeterian

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Fig. 1 Real wages and unemployment rates during recent economic downturn. Data source World Bankdatabase

(e.g., Pavitt 1984; Malerba and Orsenigo 1995) empirical strands reinforce the impor-tance of industrial dynamics and turbulence. It is interesting to note that in severalworld economies (e.g., US, Spain, Greece and Portugal) the recent economic down-turn (as reflected by the GDP growth rate) has been associated with rising wages (andwage inequality) and increasing unemployment (Fig. 1).

The model proposed in this paper adopts a setting similar to that put for-ward by Fagiolo et al. (2004), in terms of the job search, matching and bar-gaining mechanisms. However, our model besides including two distinct types oflabour, routine and non-routine workers (Egger and Grossmann 2005), whereasFagiolo et al. (2004) only consider homogeneous labour, also takes into accountthe industrial dynamics and turbulence. Furthermore, we focus on the idea offirms as heterogeneous organizations, with distinct “institutional settings”,2 whichevolve over time building the firms’ own “institutional setting”, and on howsuch choices interact with the evolving industrial process. In such a frame-work, our modelling exercise endeavours to capture the important dynamics of

2 We adopt the definition of “institution” proposed by Rutherford (1994, 182): “regularity of behavior ora rule that is generally accepted by members of a social group, that specifies behavior in specific situation,and that is either self-policed or policed by external authority. It is important to distinguish between generalsocial rules (sometimes called the institutional environment) and particular organizational forms (some-times called institutional arrangements). Although organizations can also be thought of as sets of rules, therules apply only internally. Organizations have constitutions, are collective actors and are also subject tosocial rules”.

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an evolutionary world where heterogeneous individuals, firms and workers inter-act and co-evolve.3 In our model coevolution intends to capture the original ideathat evolutionary changes in one economic variable, dimensions or agents area response to changes in other interacting variables, dimensions or agents. Forexample, the changes in labour market variables such as wages depend on thechanges in firm’s technological specifications. This model selects labour organi-zational choices as the substantial nature of firms’ “institutional settings”, andis based on the specificity of labour amongst the firms’ inputs, since it carriesimprinted relations and constitutes the core of the firms’ routines (Stinchcombe1965). We assume that workers have distinct attributes. Certain workers (the non-routine) are more able to learn, organize people and tasks, make decisions and adaptto changing environments. These qualities may be associated with the worker’s levelof general education, which develops her/his analytical skills and abstract reasoningcapabilities, and stimulates the ability to learn. However, they may also be associ-ated with unobservable features such as attitude, confidence, ability to organize andadaptability.

The remainder of the paper is structured as follows. Section 2 details the formalevolutionary model. In Sect. 3, the simulation exercise is presented and the results arediscussed. Finally, Sect. 4 presents some concluding remarks.

2 Model set-up

In our model, the players are firms and workers within a certain industry, heldtogether by two markets: an output market and a labour market. Firms differ withrespect to the choices they make concerning their “institutional settings”, which isapproximated by the composition of their labour force. These choices have impli-cations in the number of vacancies they post and the wages they offer, and aremade according to the firms’ profitability and market shares. Workers differ withrespect to their abilities/tasks they are able to perform (Autor et al. 2003; Eggerand Grossmann 2005), being categorized as routine and non-routine. They decideto search for a job, having a certain wage level in mind. Firms and workers inter-act then on the basis of matching and bargaining rules in the labour market, andthe contractual wages result from these interactions. Figure 2 presents the struc-tural scheme of the model. In the next sections, all the details of the model areexplained.

3 The concept coevolution was initially proposed in the Ecology field, meaning that evolutionary changesin one species are a response to changes in other interacting species The concept has been used to rep-resent different types of interaction such as biological and cultural; ecological and economic; productionand consumption; technology and preferences, and so on (Van den Bergh and Stagl 2003). According toVan den Bergh and Stagl (2003); Norgaard (1984) was the first to use this concept explicitly in a socio-eco-nomic context. The human invention of agriculture and all cultural and economic developments that wereemergent compose an example of coevolution in real economy (Campbell, 1996 cited by Van den Berghand Stagl 2003).

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Fig. 2 Structural diagram of the model

2.1 Micro level

2.1.1 Firms and workers

We consider that each firm in a certain industry is associated to one specific “institu-tional setting” that can be more or less close to the industry’s institutional frame.4 Thesurvival likelihood for each firm i depends on its ability to hire the suitable workersfor its “institutional setting” and on its ability to react to environmental change (whichare connected with the transparency of the institutional environment). The “fitness”of each firm must be defined as a function of these abilities.5

In our framework, firms cannot fully understand the complexity of the economicsystem. Information is incomplete, in particular with regard to future economic devel-opment (imperfect foresight). This study is based on the concept of bounded rationality(Simon 1955, 1956; March and Simon 1958), which appears in opposition to the tra-ditional neoclassical assumption of fully rational agents. The bounded rationality pro-gram incorporates all the constraints on human knowledge and human computation,which are responsible for the distinct behaviours of real actors when compared with

4 The modelling effort at the micro level developed here was inspired in the model of organizational culturepresented in Carrillo and Gromb (2007). This paper intends to show that an organization is more productiveif its agents “fit” into its culture and that organizations choose agents who are “good fits”, but do so in animperfect way and over time.5 Given a certain environment, fitness corresponds to the likelihood of an organization’s ability to survive.

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the predictions made by neoclassical economic theory.6 Furthermore, Simon (1956)introduces the idea that decision-making is influenced not only by information pro-cessing capabilities, but also by the environment. Following Simon’s contributions onhuman rationality and decision-making, we assume that firms make decisions based onadaptive expectations, with decisions being revised periodically, since their strategiesare likely to be inconsistent.

As mentioned above, in our model, the actors of the economic system are workersand firms within a certain industry. A single good is produced and there is no differencebetween the outputs of the firms in terms of quality. The good is sold and bought in theoutput market that takes place at the end of each period. Firms supply their maximumoutput, and the output price is determined so it clears the market.

In the labour market, there are L workers of two distinct types. First, “routine work-ers”, j R ∈ {

1, . . . , L R}, who are the agents without the ability to handle activities

involving innovative procedures, since they lack the minimum attributes required todeal with unexpected change. Their learning capability is of a learning-by-doing type.We will assume that these workers have attributes that make them “fit” into activitiesfeatured by routine or standard procedures. Second, we have “non-routine workers”,j N R ∈ {

1, . . . , L N R}

and L = L R + L N R . These agents have attributes that makethem “fit” into activities where the reaction to unexpected change and learning-by-thinking are crucial. Therefore, non-routine workers have a greater ability to performactivities involving problem-solving and complex tasks, and are thus well suited toorganizational forms that demand team work and job rotation.7

Our categorization of workers is different from that usually proposed in theliterature as unskilled and skilled workers. Routine workers are individuals withsevere difficulties in adapting to new situations, whereas the non-routine ones arehighly flexible.8 Typically, the division of job levels appears as low- and high-skilled

6 Simon sustains that decision-makers must simplify the decision actions, suggesting the “satisficing” con-cept as one possibility (Simon 1955). A decision-maker will maintain a search until a good enough solutionis found: “The player instead of seeking for a “best” move, needs only to look for a “good” move” (Simon1955: 108).7 A large amount of psychology literature documents and characterizes the heterogeneity present in theway people react to change in their environment (see, for example, Harrigton 1998). In general, a personreacts to her/his environment following some regular behaviour across several circumstances. This patternof behaviour reflects in part what the person is. She/he may usually change her/his strategies, being flexiblein the sense that her/his behaviour is driven by the conditions of the environment. In contrast, a personmay be rigid, showing a behaviour that is always close to some fundamental approach, being relativelyunresponsive to the current environment. For example, some businessmen adjust their business strategyto new market conditions while others maintain a commitment with the original plans (Rosenthal 1993;Harrigton 1998).8 Flexibility has been a major topic within the operations management and strategy literatures. In broadterms, we can understand flexibility as an absorber of environmental uncertainty and variability. Its value liesin offering protection against an unpredictable future, through resources that are fundamentally adaptableas well as constructing a set of routines that allow for a quick reorganization in response to unstable markets(Gerwin 1993; De Toni and Tonchia 1998; Beach et al. 2000). Whilst sheltering from external disordersmay be crucial for survival, the organism must have internal mechanisms to ensure a degree of reliabilityand coherence when facing environmental change. In reality, total flexibility makes it impossible for theorganization to keep a sense of identity and continuity (Weick 1982; Adler 1988; Loasby 1999). Therefore,organizations must deal with a trade-off concerning flexibility and stability, in order to survive but, at thesame time, avoid disruption to the continuity of organizational processes.

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(Finegold and Soskice 1988). High-skill jobs require professional or scientific skillsat the level of high vocational or university education. Low-skill jobs are associatedwith simple, routine tasks which mainly demand the use of hand-held tools and phys-ical effort. In our division, the routine worker can have a higher degree of formaleducation and even so be unable to react to change. She/he can perform tasks thatdemand school training at a higher level but do not require flexibility in responses,and are featured by monotony, repetitiveness and work constraints. Our routine versusnon routine categorization goes in line with Autor et al. (2003) and their routinizationhypothesis by recognizing that workers capabilities and tasks’ features may diverge.Certainly, there is a high correlation between the capability to deal with change andnew situations and the degree of professional and scientific skills. In the skilled versusunskilled categorization, it is possible that high-skilled workers are more efficient thanlow-skilled ones in low-level jobs. In our typology, we assume this is not the case.A non-routine worker is less efficient than a routine one if matched with a routinizedset of tasks. This occurs because her/his attributes require spending time looking forinnovative procedures, which is a non-profitable behaviour within a routinized andinert activity. The level at which firms and production processes call for these typesof workers is expected to vary across industries and occupations.

2.1.2 Baseline configuration

We consider an industry (Ind) composed by a certain number of firms Nt in eachdiscrete time period t , with t = 0, 1, 2, . . .. Firms produce the same homogeneousgood, with one production factor, labour, comprised of two distinct types of workers.In each period, a firm i produces Xit units of the homogeneous good whose price ispt > 0.

The industry is characterized at each time t by an exogenous institutional envi-ronment represented by the variable I I ndt .9 Each firm i in the industry, at time t , isfeatured by a specific “institutional setting” represented by the variable Ii t . The “insti-tutional fitness” of the firm at time t is measured by |Ii t − I I ndt |. The firm decideson the following set of variables in each time period

Firmit

(L R

it , L N Rit , wR

it , wN Rit , vR

it , vN Rit

), (1)

where:

• L Rit and L N R

it correspond to the number of workers associated with routine andnon-routine activities, respectively, employed by the firm in each time period;

• wRit and wN R

it correspond to the contractual wages that firms offer, in each timeperiod, to routine and non-routine workers, respectively, as the result of an endog-enous matching and bargaining process (described in detail in Sect. 2.1.3);

9 Our overall modeling approach is based on an evolutionary frame which is characterized by selection ina stable, exogenous environment (cf. natural selection—e.g., Witt 2003). The stability of the social systemsis in part explained by constant institutions or norms during a certain period of time (Ostrom 2000; Van denBergh and Stagl 2003).

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• vRit and vN R

it corresponds to the number of job openings defined by each firm at tfor routine and non-routine workers, respectively.

The firm’s output level Xit is a function of technological progress Ait , and of thenumber of workers L R

it and L N Rit :

Xit = f(

Ait , L Rit , L N R

it

), (2)

where Ait corresponds to the total factor productivity of the technique employed bythe firms in each period t .

We assume a Cobb-Douglas production function with constant returns to scaleassociated with routine and non-routine labour:

Xit = Ait

(L R

it

)β1(

L N Rit

)β2, (3)

where β1 +β2 = 1, β1 > 0 and β2 > 0. Dividing Xit by the total number of workersof firm i at time t, Lit , we obtain the firm’s product efficiency per unit of labour, xit :

XitLit

= Ait

(L R

it

)β1(L N R

it

)β2

Lit

xi t = Ait

(L R

itLit

)β1(

L N Rit

Lit

)β2

xit = Ait lβ1i t α

β2i t

, (4)

where li t represents the stock of routine workers per unit of total labour and αi t cor-

responds to the ratioL N R

itLit

(that is, the relative importance of non-routine workers).We consider a simple framework in which the “institutional setting” of each firm is

represented by αi t and by an ex-ante unobservable variable ψi t that sums up factorsthat determine this setting, but which are not controlled by the firm. More precisely,in each time period t , the Ii t variable results from the existent “institutional setting”given by αi t−1, from the investment made at time t by the firm to improve its own “fit-ness” in the institutional environment (the rearrangement of the proportion of workersthrough matching and bargaining processes, hiring and firing decisions), representedby �αi t , and from an unobservable random variable, ψi t . Formally, we have:

Ii t = αi t−1 +�αi t +�i t (5)

Ii t = αi t +�i t (6)

The firm may choose more rigid or more flexible “institutional settings”. In the firstcase, the firm has preference for more routine workers. In the second, the non-routineworkers are crucial. The variable αi t represents the firm’s institutional options, whichare made by boundedly rational agents in a context of uncertainty. Each firm faces atrade-off when choosing the “satisficing” share of workers: a very low αi t means lowwage costs but low possibilities to adjust, whereas a very high αi t corresponds to high

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possibilities to adapt, but also to high wage costs that may not be compensated by theadjustment benefit.

The short-run profit function, πi t , of each firm i at time t is:

πi t = Xit pt − cit , (7)

where cit is the cost function.The costs of the firm depend on the workers’ wages (wR and wN R) and on the

“mix” of workers (αi t ). They also depend on a “transaction cost”, associated with theworkers’ competencies, which is defined as τi t = � (|Ii t − I I ndt |). If the firm has aproportion of labour competencies close to the one that features its environment, thismeans a lower “transaction cost”. Otherwise, this cost rises since the firm will have, forexample, to subcontract thinking workers able to react to unexpected situations or dealwith innovative procedures in industries featured by flexible “institutional settings”.On the other hand, a firm within an industry characterized by a rigid “institutionalsetting” also faces high transaction costs if it has a very flexible “institutional setting”.In fact, this firm has more costs, not only in the form of wages, since wN R > wR ,but also costs deriving from the constant search for new possibilities in a very inertenvironment.10 Formally, the cost function, cit , is defined as:11

cit = c(wR

it , wN Rit , αi t−1,�αi t , τi t

)(8)

Firms employ labour in one-period contracts, so wages are paid after one period ofemployment. As mentioned previously, the model considers distinct remunerations foreach type of worker. For routine workers, the wage iswR , and for non-routine workers,it is wN R , with wN R > wR . Therefore, on the one hand, we have workers that earnless, representing lower costs to firms, but that are incapable of adjusting. Therefore,firms with a high proportion of these workers are much more likely to perish whenfacing an unexpected and significant environmental change than those with a higherproportion of non-routine workers. On the other hand, non-routine workers receive ahigher wage, meaning a higher cost for the firm, but are flexible and able to quicklyadjust to changes. They are crucial for the firm to react to such changes, avoidingbankruptcy or even enabling the firm’s growth. Wages emerge from the interactionbetween firms and workers. They correspond to contractual wages offered by firms toworkers, as a result of matching and bargaining processes. Wage rates can be differentfor each worker, and we assume that each worker supplies only one unit of labour.

10 These transaction costs may also be interpreted as a time delay associated with ‘some time to build’ thatfirms must spend with their workers before they become productive. The higher the ‘institutional fitness’of the worker, the lower this time delay.11 In the simulation exercise costs are defined as an equation ‘cost’ which, if the firm has no workersand does not produce assumes a cost equal to zero; otherwise, it is an additive function of wage costs(number of non-routine workers times their wage plus the number of routine workers times their wage)and a fitness cost that depends on the comparison between the ‘institutional setting’ of the firm and theindustrial environment (I I ndt ). The higher this distance, the higher will be this cost. This transaction costalso includes an idiosyncratic noise for taking into account the uncertainty in the ability of the firm to adjustto its institutional setting.

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Similarly to Fagiolo et al. (2004), we adopt the following assumptions concerningwages and jobs:

• Each firm i has a satisficing wage it wants to offer at time t to any routine (non-routine) worker, ws R

it

(ws N R

it

);

• Each routine (non-routine) worker j R ∈ {1, . . . , L R

}( j N R ∈ {

1, . . . , L N R}) has

a satisficing wage, ws Rjt

(ws N R

jt

), which she/he wants to obtain from the firm at

time t ;• Any worker j will only accept contractual wages if they are equal or greater to

her/his reservation wage (denoted as wR Rjt and wRN R

jt for routine and non-routine

workers, respectively);12

• Jobs last only one period and therefore workers must search for a new job in eachperiod;

• Job openings for firm i at time t, vi t , correspond to labour demand and, at thesame time, to ex-ante vacancies or new job positions;

• The ex-post vacancies correspond to the number of unfilled job openings;• Workers can be unemployed;• Firms may not assure their labour demand.

2.1.3 Job openings, job search, job matching and bargaining procedures

Job openings Each firm i creates, at the beginning of period t , a queue of job open-ings for each type of worker.13 In each time period, each firm decides on how manyjob vacancies to open for routine workers vR

it and non-routine workers vN Rit . In terms

of the firms’ decisions about how many vacancies to open in each time period, weconsider a behavioural scenario featured by some path-dependency.14 We define theprocess in formal terms similarly to Fagiolo et al. (2004).

The total number of job openings (for both types of workers) in period t by firm idepends on the value of vacancies in t − 1 (path-dependency), and on the evolutionof the firm’s profit. If profits in t are higher or equal to profits in the previous periodthe firm increases the number of total vacancies. Otherwise, it decreases it:

vi t ={vi t−1 (1 + |F |) i f πi t ≥ πi t−1vi t−1 (1 − |F |) i f πi t < πi t−1

, (9)

12 Satisficing and reservation wages are distinct though related concepts (Simon 1955, 1956; Fagiolo etal. 2004). The wage asked by the worker—satisficing wage—changes from period to period according toher/his previous status (employment or unemployed). Reservation wage is the wage below which the workeris not willing to work, being a constant in the model.13 Thurow (1975) proposes the notion of job queues, where workers are ranked according to their train-ability, as measured by their background features. In our model, we also use the concept of job queue, butthe only hierarchy that exists between workers is their arrival rate at the queue.14 Path-dependency is here understood as typically evolutionary since it accounts for the importance ofhistory in economic analysis; the idea that that ‘history matters’. Since the seminal work by David (1985),economists recognize the existence of irreversible, self-reinforcing tendencies (associated for example withnetwork externalities and ‘learning-by-doing’), that generate increasing returns to the use of one solution ofseveral competing ones. Therefore, the increasing returns may generate ‘lock-in’ situations (David 1985).The phenomenon of path-dependency is a significant feature of evolution (e.g., Witt 2008).

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where F is an independent and identically distributed (i.i.d.) random variable, witha normal distribution marked by a zero mean and a σ 2

v > 0 variance. The varianceσ 2v offers a measure of the way firms react to the profits growth rate, enlarging or

shrinking their current queue size. A higher variance means a higher sensitivity tomarket signals.

While in Fagiolo et al. (2004) labour is homogeneous, in our model labour is heter-ogeneous, and so the process of job openings is associated with changes in each firm’s

relative importance of non-routine workers, i.e., αi t = L N Rit

Lit. The total number of job

openings will then be split into two queues, one for each type of worker, according tothe value of αi t :

vN Rit = αi tvi t and vN R

it = (1 − αi t ) vi t . (10)

We assume that firms always open at least one job vacancy for each type of worker ineach time period.

Job search In Fagiolo et al. (2004) two job search procedures are taken into account.The first scenario assumes no search inertia. This means that each worker j randomlyvisits one firm i in the market. If the chosen firm still has available places in the queue,the worker gets in and asks for her/his satisficing wage ws

j t . In the second scenario,the authors introduce some stickiness, conceived as loyalty, in firm visiting. If a cer-tain worker j was employed in firm i in period t − 1, she/he starts by visiting firm i .If this firm still has available places in the queue, the worker gets in and asks forws

j t−1.If not, the worker uses the random value defined in the no search scenario to selectfrom among the remaining Nt−1 firms. In both scenarios, a worker can only enter onequeue, and stays unemployed if she/he chooses a firm that has already filled all theavailable slots in its queue.

In our model, a similar approach is used but always with search inertia, since werecognize the existence of important transaction costs associated with the process ofjob search, not only for firms, but also for workers (although they are not explicitlydefined in our model), which are certainly more significant than just loyalty consid-erations. Beyond contractual reasons, firms prefer workers who are already familiarwith their structures, technologies and methods. A similar preference is experienced byworkers. These preferences reveal the need to reduce transaction costs and uncertainty(e.g., Nickell 1986; Teixeira 2004).

Moreover, we consider two types of workers. Each of these workers searches for ajob opening for their particular type. For the sake of simplicity, we assume that work-ers may not apply to job openings that do not correspond to their particular type. Forexample, a non-routine worker cannot search for a routine job opening, and a routineworker cannot search for a non-routine vacancy.

Job matching and bargaining After workers queue up, the process of job matchingand bargaining takes place. As in Fagiolo et al. (2004), we assume that firms startexploring the workers’ wage demands to match them with their offers. At each timeperiod t , firm i observes the workers in its two queues. Let 0 < m N R

it ≤ vN Rit and

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0 < m Rit ≤ vR

it denote the number of workers in the non-routine and routine queues,respectively. The firm then computes the average wage wi t demanded by workers inboth queues. Formally:

wN Rit = 1

m N Rit

m N Rit∑

j=1

ws N Rjt−1nd (11)

and

wRit = 1

m Rit

m Rit∑

j=1

ws Rjt−1 (12)

The firm then sets the contractual wages for period t as a linear combination of theaverage wages, wN R

it and wRit , and the satisficing wages, ws N R

it−1 and ws Rit−1. Thus:

wN Rit = βs N R

it−1 + (1 − β)wN Rit (13)

and

wRit = γ s R

it−1 + (1 − γ )wRit (14)

where β, γ ∈ [0, 1] and β < γ . In line with Fagiolo et al. (2004), we define theinstitutional parameters β and γ to govern the firm’s strength in wage bargaining. Thepower of the firms in the wage setting process increases with the value of β and γ .Assuming β < γ means that firms have more power in the setting of the wages forthe routine workers than for the non-routine ones.15

Following this procedure, each firm sets the contractual wage that it is willing tooffer to workers in the queues. However, any given worker will only accept the jobposition if the contractual wage is equal or larger than her/his reservation wage.

After this matching and bargaining process, updating of the satisficing wage values,for both firms and workers, takes place, within a bounded rationality frame. We con-sider that when a routine (non-routine) worker j accepts a job position, she/he changesthe satisficing wage to the new earned wage, i.e., ws R

jt−1 = wRit (w

s N Rjt−1 = wN R

it ). Inaddition, each firm i which has filled at least one job vacancy in each queue will alsoreplace its satisficing wages, ws R

it−1 = wRit and ws N R

it−1 = wN Rit .

15 This assumption is based on empirical evidence. As Howell and Wolff (1991) and Gregg and Wadsworth(1995) show for the US and the UK workplaces, respectively, occupations requiring high cognitive andinteractive skills have grown faster than those demanding low skills. At the same time, there has been anincreasing inequality in what concerns the earnings of low- and high-skilled workers. This evolution mayreflect the declining role played by unions and centralized negotiating processes (e.g., Acemoglu et al.2001). Another possible explanation for this increasing inequality may be the higher importance of tacitlyacquired firm-specific skills. Workers that have specific attributes are in a better position to negotiate forrelatively higher wages than those who do not have them (Howell and Wolff 1991).

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Fagiolo et al. (2004) additionally consider the possibility that surviving firms andworkers may wish to revise their satisficing wages according to their perceptions aboutthe result of the economy’s dynamic. In this vein, we assume that each firm has a fixeddesired ratio of filled to opened job positions for each type of work: ρR

i ∈ [0, 1] andρN R

i ∈ [0, 1].16

The above ratios are then compared to the current effective ratios: r Rit = L R

it

vRit

and

r N Rit = L N R

it

vN Rit

.

Indeed, if the firm has not hired enough workers, as compared with the number ofjob positions it had decided to open, it will be willing to increase the wages offered toworkers. Otherwise, it may want to decrease them. A simple rule is adopted to give aformal meaning to this behaviour. For routine workers, we have:

ws Rit

={ws R

it−1(1 + |Y |) if r R

it< ρR

iws R

it−1(1 − |Y |) if r R

it≥ ρR

i, (15)

where Y is an i.i.d. random variable with a standard normal distribution and ws Rit−1 =

wRit if the firm has hired at least one routine worker. Similarly, for non-routine workers:

ws N Rit

={ws N R

it−1(1 + |Y |) if r N R

it< ρN R

iws N R

it−1(1 − |Y |) if r N R

it≥ ρN R

i, (16)

where ws N Rit−1 = wN R

it if the firm has hired at least one non-routine worker.Given the number of both types of workers hired by each firm, the model then

computes each firm’s production, the price and profits. Each firm’s ex-post vacancies,vR

it and vN Rit , are defined as:

vRit = vR

it − L Rit (17)

and

vN Rit = vN R

it − L N Rit . (18)

In what concerns the updating of the workers’ satisficing wages, we assume that anyworker who remains unemployed after the matching and bargaining process mightwant to reduce her/his satisficing wage, without violating the threshold imposed bythe reservation wage. Otherwise, she/he may want to ask for a higher wage in the nextbargaining round. In formal terms, we have:

16 We could adopt a simpler rule by which if all vacancies were fulfilled the contractual wage would bereduced, otherwise it would increase. Our choice took into account the fact that the labour market is rigid.Thus, we adopt a satisficing behaviour for the firms. That is, since firms hardly filled all vacancies theyoffer, they choose to be satisfied if they fulfill a certain percentage of these vacancies.

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ws Rjt

={

max{wR R

j , ws Rjt−1 (1 − |Y |)

}if j R unemployed

ws Rjt−1 (1 + |Y |) if j R employed

(19)

and

ws N Rjt

={

max{wRN R

j , ws N Rjt−1 (1 − |Y |)

}if j N R unemployed

ws N Rjt−1 (1 + |Y |) if j N R employed

(20)

where Y is an i.i.d. random variable with a standard normal distribution, ws Rit−1 = wR

it

and ws N Rit−1 = wN R

it if j R and j N R have just been hired.

2.1.4 Technological progress

In terms of labour productivity dynamics, two technological scenarios are analyzed.The first considers an equal technological level for all firms, that is Ait = At ∀i ,

where At = At−1eg and g is the exogenous rate of technological progress. Thesecond scenario assumes the presence of firm-specific technological progress. Weconsider that the industry has an exogenous technological trajectory Aht , defined asAht = Aht−1eg , which corresponds to the maximum value that the firms within theindustry can achieve. We associate with each firm a measure of technological effi-ciency, μi t , 0 < μi t ≤ 1, such that the technological progress for each is representedas:

Ait = Ahtμi t (21)

and

μi t = function (|Ii t − I I ndt | , αi t ) . (22)

Each firm’s efficiency measure increases with the firm’s fitness and with the relativeimportance of each firm’s innovative non-routine workers.17

2.2 Industry level

The aggregate output of the industry is computed at each time period as the sum ofthe output of all the firms in the industry at that time:

Xt =Nt∑

i=1

Xit . (23)

17 In our simulation exercise we first consider that technological progress (A) for a firm is equal to theindustry’s technological progress (Ah). Then, the A value is double reduced comparing to the possiblemaximum (Ah): (1) according to the firm fitness—the highest this fitness, the smallest the A reduction; (2)according to the comparison between the number of non routine workers of the firm and a chosen thresholdvalue—if the firm hires more non routine workers than this threshold, it will be in disadvantage.

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We assume that the short-term equilibrium price results from the confrontation of thetotal supply with a constant price-elasticity demand function:

pt = Dt

(Xt )1/η , (24)

where η is the demand price elasticity and Dt > 0 is the exogenous demand.The number of firms operating in the industry in each time period t, Nt , is constant,

since we assume that the firms that leave the market are automatically replaced by anequal number of firms with characteristics close to the average of the attributes of thesurviving firms in that period.

2.3 Labour market

As mentioned earlier, workers may be unemployed. In aggregate terms, the numberof unemployed workers of each type is equal to:

U Rt = L R −

Nt∑

i=1

L Rit (25)

and

U N Rt = L N R −

Nt∑

i=1

L N Rit (26)

The aggregate values of routine vacancies and non-routine vacancies are:

V Rt =

Nt∑

i=1

vRit (27)

and

V N Rt =

Nt∑

i=1

vN Rit . (28)

3 Simulation exercise

3.1 Details on the computational model, simulation trials and robustness

The computational model was built in Lsd (the “Laboratory for Simulation Develop-ment”), a free-use language for simulation models written by Marco Valente (see, forexample, Valente 1998; Valente and Andersen 2002).

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The simulation model executes the following steps:

1. Given the initial position of the institutional set of firms and the institutional envi-ronment in the industry at t = 0, we solve for the output and profits of firms, andthe market price.

2. Firms decide to maintain or to change their institutional setting in the next period,according to the evolution of their profits and their market shares. This decisionis materialized in the mix of their workers. If the profits in t + 1 are higher thanin t and the market share in t + 1 is higher than in t , firms do not change their mixof workers. They only do so, if this is not the case.

3. After the decision to maintain or change the mix of workers, job search, matchingand bargaining takes place:(a) The firms decide how many vacancies for each type of worker they want to

open in period t + 1. Each firm opens at least one posting of each type.(b) Routine (non-routine) workers search for a firm posting at least one job

opening of the routine (non-routine) type and queue up.(c) The process of job matching and bargaining takes place: firms look in their

queues and start bargaining with workers who have queued up (if any) forboth types of jobs to decide whether to hire or not.

4. After hiring, production takes place. Aggregate demand is exogenous and theaggregate supply is obtained by simply aggregating the individual supplies.

5. After a certain number of runs, firms undergo a selection process. We establishedthat firms that accumulate negative or nil profits during the last five time stepsleave the market. Each exiting firm is replaced by a new firm with initial fea-tures close to the average characteristics of the surviving firms at that time period.This procedure allows us to keep an invariant number of firms in the economy ateach t .

6. Firms and workers update their satisficing wages.7. Technological progress takes place. As mentioned previously, we consider equal

technological progress and firm-specific technological progress scenarios.

The simulation requires us to set initial values for several variables and for all theparameters. Our calibration work was guided by some available empirical literatureon labour markets and on internal firm organization, for example, Davis et al. (1996),Lorenz and Valeyre (2004) and Bartelsman and Doms (2000). In the Appendix, wepresent a synthesis of the chosen initial values and the possible combinations definedfor some relevant parameters.

The simulation model consists of an industry composed by 10 firms. The industryis characterized by its “institutional setting”, αt , which is an exogenous variable, onlypartially observable by the firms. For simulation purposes, we consider that α, whileapproximated by the relative importance of routine and non-routine workers in theemployment structure behind the industry, is equal to 0.5.18 Since we do not introducethe determinants of the labour supply in our model,α is kept constant, as it corresponds

18 Lorenz and Valeyre (2004), in a study based on the 3rd European Survey on Working Conditions inthe 15 member states of the EU in 2000, offer one of the first systematic comparisons of the adoptionof new organizational forms across Europe. The paper stresses the idea that phenomena of globalizationand intensified international competition are leading to a restructuring of management practices in most

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to structural, institutional characteristics that are remarkably stable over time. In fact,the characteristics associated with skills and education employment structures arelikely to present a high degree of inertia (see Baron et al. 1996). Therefore, the modelconsiders that firms are able to change their “institutional settings”, but maintain theglobal, exogenous “institutional setting” stable.

In period t = 0 we have each firm’s mix of workers, αi0 and profits, πi0. We con-struct the initial configuration according to the chosen parameters and scenarios. Inaddition, the initial values of each firm’s institutional setting, αi0, were drawn froma uniform distribution in the ]0, 1[ interval. We also set initial values for the distincttypes of workers and the technology of each firm (see the “Appendix”) to implementthe model.

The simulation exercise has two main sets: one that considers equal technologicalprogress for all firms (EqualTP), and another that assumes idiosyncratic technologicalbehaviours (FirmSpecificTP).19 Moreover, the study considers two stages: one thatassumes a completely stable exogenous environment, and another that considers twodistinct exogenous demand shocks after a certain number of time runs (a reductionand an increase of around 30%).

In each simulation exercise, a total of 250 time periods (T = 250) is considered.Several experiments were performed in order to validate the model and ascertain its

robustness. For considerations on the processes and techniques associated to the val-idation and verification of simulation models, see for example Sargent (1999). Morespecifically, the following experiments were conducted.

On the one hand, we ran the model using 10 different seeds for the random numbergenerator. Also, we considered alternative values (both lower and higher) for six ofthe key elements in the model, namely the initial workers’ satisficing wages ws R

j0and

ws N Rj0

, the bargaining powers β and γ , the desired filled vacancies ratios ρRi and ρN R

i ,the exogenous rate of technological progress g, the number of periods with accumu-lated negative or nil profits until firms exit the market and the production functionelasticities β1 and β2. Finally, alternative sizes (both lower and higher) for the twotypes of demand shock were also considered.

A thorough analysis of the results provided by these experiments showed that themodel is indeed rather robust. On the one hand, the results obtained with each of the 10different seeds were quite similar (and therefore all the variables behaved in the sameway).

Footnote 18 continuedEuropean countries, as a way to achieve greater flexibility and cooperation at the workplace. They concludethat two types of organizational forms, the “Learning Model” and the “Lean Model”, which correspond toorganizational forms where variables measuring autonomy, task complexity, learning and problem-solvingare over-represented, account for respectively 39 and 28% of the employees. At the same time, the twoother classes of the proposed typology, the “Taylorist Model” and the “Traditional Model”, both associatedwith minimal learning dynamics, low complexity and low autonomy, account for, respectively, 14 and 19%of the employees. Since the study is applied to the economy as a whole, and our model only concernsmanufacturing, the value of 50% associated to non-routine sets of tasks seems a reasonable feature for theexogenous industrial environment.19 The consideration of these two sets is supported by the literature on firms’ dynamic capabilities Teeceet al. 1997 and industry technological trajectories (Pavitt 1984).

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On the other hand, changing the values of the six key elements, as well as the sizeof the demand shocks, did not change the behaviour of the various variables or theirrelative positions, with only one exception noted below, though their specific valuescan necessarily change in some cases. This essentially means that the effects andconclusions described in the next sections would remain unchanged had other config-urations been used. As an example, the values of several variables can be somewhatlower or higher when the demand shock is more or less intense. However, regardlessof the size of the demand shock, the variables exhibit the same behaviour (i.e. increaseor decrease) and the same relative position (i.e. one wage higher or lower than anotherwage). The same is valid for the six key elements.

The only exception concerns one experiment with the initial workers’ satisficingwages, in which the original evolution for one variable, the contractual wage for thenon-routine workers, was not achieved, though all the remaining variables evolved asin the original scenario. Thus, the model is indeed quite robust, since its conclusionsremain valid when different values are used for the random number generator seed,the key elements and the size of the demand shocks.

Statistical tests were not performed, since the thorough analysis of the sensitivitytests deemed them unnecessary. Indeed, the statistical tests would not be testing forcloseness or equality of the values of the various variables since, as previously men-tioned, those values can or must be higher or lower as the key element/demand shockvaries. Rather, the tests would have to check whether the behaviour of the variables,and their relative positions, was the same. A thorough analysis of tables and charts withthe values of the various variables showed us that this always happened, with the singleexception noted above, so any statistical test could only lead to the same conclusion.

We remark that a 30% increase or reduction in demand might seem excessive. How-ever, this is not a change in a country’s aggregate demand, but only in the demandof a certain industry. As such, this percentage is not unreasonable. Indeed, highervalues can occur in various conditions. Some examples are: the appearance of a moresophisticated substitute product or a price cut/increase in an existing substitute prod-uct; particularly good or adverse season conditions in the case of seasonal products;cancellation or postponement of public investment in infrastructures due to restrictivefiscal policies such as those recently adopted in the Euro Zone due to the need forpublic financial consolidation. Nonetheless, and as mentioned above, our results arerobust in the size of the demand shock, and remain valid for smaller or larger shocks.

3.2 Results

3.2.1 Stable exogenous environment

In the stable environment configuration, in both the EqualTP and the FirmSpecificTPsets, the industry observes an initial strong shake-out period, with most firms leavingafter 10 time steps (see Table 1). As a consequence, there is a clear improvement inthe average fitness of the population of incumbent firms. Afterwards, the entry andexit of firms leads to a slow but regular improvement of that variable in the EqualTPset, and to a more irregular path in the FirmSpecificTP set. The first set has two initial

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Table 1 EqualTP model versus FirmSpecificTP model

Time steps Number of initialfirms in the market

Final average ‘institu-tional gap’ in industry(0.305at T = 0)

Inverse of theHerfindal index

Firms turnover

Equal Firm Equal Firm Equal Firm Equal FirmTP Specific TP TP Specific TP TP Specific TP TP Specific TP

T = 10 2 2 0.058 0.086 9.719 9.677 0.800 0.800

T = 50 2 1 0.104 0.088 9.279 8.766 0.300 0.420

T = 100 0 0 0.067 0.115 9.560 8.636 0.270 0.410

T = 250 0 0 0.070 0.101 9.143 9.308 0.280 0.400

T = 500 0 0 0.060 0.125 9.122 8.662 0.390 0.380

surviving firms at T = 50, firm 1 (αi0 = 0.404) and firm 5 (αi0 = 0.512), whereas thesecond set has only one, firm 7 (αi0 = 0.659). This result is not surprising, since in theFirmSpecificTP set the technological progress rate depends not only on each firm’s“institutional fitness”, but also on each firm’s relative weight of non-routine workers.When compared with firms 1 and 5, firm 7 has a lower initial fit, but benefits from ahigher relative number of non-routine workers.

The EqualTP scenario shows less turbulence, and has a less concentrated marketstructure, with the inverse Herfindhal index showing an almost minimal concentration(see Table 1). In addition, the turnover of firms,20 after the initial shake out, is higherfor the FirmSpecificTP set. This is also not surprising, since in the EqualTP set thefirms have the same technological path, whereas in the FirmSpecificTP set the firmshave distinct technological efficiencies.

Figures 3 and 4, which give the number of entries in each period, clearly show thatthe FirmSpecificTP set is more unstable. The peak in period 5 provides additionalevidence of the initial shake-out.

In terms of the co-evolution of the population of firms and the population of workers,both sets show that the introduction of matching and bargaining processes in the labourmarket results in important frictions, as shown by the existence of ex-post vacanciesand unemployment. The EqualTP set is featured by a higher creation of job vacanciesand by a lower ability of the firms to fill them (in Fig. 5, we present the evolution of thetotal vacancies in both sets). As a result, since in our model [cf. Eqs. (15) and (16)]the wages offered by the firms depend on the ability to fill the ex-ante vacancies (thefirm only increases the wage in the next period if it did not attain the desired ratioof vacancies in the last period), the wages for both types of workers increase morein the EqualTP set than in the FirmSpecificTP set. This is clearly shown in Figs. 6and 7, which give the evolution of the wages for non-routine and routine workers,respectively.

In both sets, the average wage of non-routine workers increases over time, whereasthe average wage of the routine workers decreases in the FirmSpecific set and, after

20 The turnover of firms is the ratio between the total number of firm exits (equal to the number of entries)and the number of time periods.

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Fig. 3 Entry of firms EqualTP model

Fig. 4 Entry of firms FirmSpecificTP model

the initial shake out in the industry, slightly increases in the EqualTP configuration.We have not tried to match our typology of workers with empirical data. If we roughlymatch non-routine workers with skilled labour and routine workers with unskilledlabour, the similarity between our computational results and empirical data is interest-ing to note, despite the assumption of neutral/non-occupationally biased technologicalchange. Indeed, several studies have found evidence of an increase in wage-incomeinequality over the last two decades in several advanced and developing countries (forexample, Borjas and Ramey 1994; Freeman 1995; Richardson 1995; Gottschalk 1997;Jensen and Troske 1997; Johnson 1997; Wood 1998; Katz and Autor 1999; Jolivet etal. 2006; Antonioli et al. 2011; Oesch and Menés 2011; Weiss and Garloff 2011).

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Fig. 5 Total vacancies EqualTP model versus FirmSpecificTP model

Fig. 6 Average wages NR EqualTP model versus FirmSpecificTP model (T = 250)

In Fig. 8, we can see that our artificial economy does indeed lead to increasinginequality between both types of workers. This evolution must be understood withinan industry where the non-routine workers are more productive per unit of output thanroutine workers, and where the firms have less negotiable power when bargaining withnon-routine workers.21

21 Our economy has the same number of the two types of workers and there are no training investments.Also, we assume that a worker cannot join a queue that does not correspond to its type. In addition, we donot endogenize the labour supply in the model, so there are no actions that might contribute to alter therelative number of workers, such as education/training opportunities. Moreover, technological change isnot “occupational”-biased in our model. This aspect could be an interesting research avenue to explore inthe future.

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Fig. 7 Average wages R EqualTP model versus FirmSpecificTP model

Fig. 8 Relative wage EqualTP model versus FirmSpecificTP model

Since the FirmSpecificTP set is more turbulent and firms create fewer vacanciesfor both types of workers, the unemployment rates are higher in this set (Fig. 9). Inboth configurations, the initial shake-out leads to a peak in the unemployment rates.As expected, unemployment has a similar influence on both types of workers, sincethe respective population is exogenous and constant, technological change is neutraland wages are higher for the more productive workers.

Table 2 presents the average final period results for each configuration. The num-bers in parentheses correspond to the variances. Note that the average wages paid toboth types of workers, as well as the relative wage, are higher in the EqualTP con-figuration. This occurs because the average rates of filling the vacancies (denoted asAvg_r_NR and Avg_r_R for non-routine and routine workers, respectively) are higherin the FirmSpecificTP set and, thus, according to our formal model, firms do not need

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Fig. 9 Total unemployment rate EqualTP model versus FirmSpecificTP model

Table 2 Average final periodsimulation results (T = 25)

Variables EqualTP Firm specific

Average fitness 0.076 (0.001) 0.085 (0.001)

Inverse Herfindhal 9.318 (0.832) 9.395 (0.622)

Avg_r_NR 0.781 (0.004) 0.814 (0.004)

Avg_r_R 0.783 (0.004) 0.820 (0.005)

TotalUnemploymentRate_NR 1.570 (3.490) 3.520 (6.650)

UnemploymentRate_NR 1.520 (4.560) 3.300 (9.350)

UnemploymentRate_R 1.610 (5.250) 3.730 (11.570)

AverageWages_NR 0.363 (0.000) 0.314 (0.000)

AverageWages_R 0.115 (0.000) 0.111 (0.000)

RelativeWage 3.142 (0.012) 3.069 (0.005)

to increase wages as often in this configuration. The higher instability of the FirmSpe-cificTP set is associated with higher unemployment rates for both workers. In termsof the firms’ “institutional gap”, in both sets the average fitness of the incumbent firmsis substantially improved with the industry initial shake out. The average fitness thenevolves around a long-run equilibrium threshold that may be called an evolutionarystationary state. By evolutionary we mean that history matters, as the path trajectory ofthe variable shows, since it reveals reversions and path dependency. Figure 10 presentsthe time trajectories of the average fitness in each configuration set. In addition, Table 2shows that, for T = 250, the average fitness is quite good (0.076 for the EqualTP setand 0.085 for the FirmSpecificTP Model, with low variances).

3.2.2 Demand shocks

Using the configuration that seems closer to economic reality, the FirmSpecif-icTP Model, we induce exogenous demand shocks and study their impact on the

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Fig. 10 Average fitness EqualTP model versus FirmSpecificTP model

Fig. 11 Average fitness FirmSpecificTP model with and without a reduction in demand

coevolution of the industry and the labour market. Two types of shocks are consid-ered: a reduction and an increase in demand of around 30% that occurs at T = 125.

The impact is rather surprising in terms of job posts and wage evolution whencompared with a standard neoclassical labour demand model. In fact, the existence ofmatching and bargaining processes means that the response of firms to a variation indemand is not automatically absorbed in terms of job places and wages, as is the casein standard neoclassical models. Important differences associated with these shocksare also visible in the market structure, since they lead to an important process of exitsand entries in the industry, and to a change in the concentration index. The adjustmentin terms of “institutional gap” is similar before and after the shock. To understand this

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Fig. 12 Entry of firms FirmSpecificTP model. Negative demand shock

Fig. 13 Total vacancies FirmSpecificTP model with and without a reduction in demand

result, it is important to recall that the number of firms in the population is assumedas constant and that, although some randomness does exist, the entrant firms havefeatures close to the average characteristics of the surviving firms.

Reduction in the demand An exogenous reduction in demand leads to a smallimprovement in the “institutional fitness” of the incumbent firms in comparison withthe behaviour of the economy without shocks (see Fig. 11).

This improvement in the institutional fit may be associated with a strong selectionprocess that eliminates the less fit firms in a more restrictive environment. The tur-bulence in the industry increases strongly after the demand shock, as Fig. 12 shows.

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Fig. 14 Total unemployment rate FirmSpecificTP model. Negative demand shock

Fig. 15 Average effective filled vacancies ratio (r) for NR workers (r_NR) and for R workers (r_R),FirmSpecificTP model. Negative demand shock

Without the shock, the industry registers a turnover of firms around 0.4 for T = 250.For the overall 250 time period, with the shock, this value increases to 0.96, whereaswhen restricting the analysis only to the post-shock period (after T = 125) the turnoveris 1.55. For a constant population of 10 firms, these values mean a significant increasein the industry’s turbulence. As the literature mentions (for example, Christensen andRosenbloom 1995), changes in demand represent a major variation in the environmentin which firms operate, and may favour the entry of new firms rather than the successof established ones.

As expected, the reduction in demand induces a decrease in the number of vacancies(Fig. 13). Consequently, the unemployment rates substantially increase (Fig. 14).

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Fig. 16 Average wages for the NR and R workers FirmSpecificTP model with and without a reduction indemand

Table 3 Average final periodsimulation results: negativedemand shock

Variables Firm specific Firm specificz no shocks demand reduction

Average fitness 0.085 (0.001) 0.069 (0.001)


Avg_r_NR 0.814 (0.004) 0.749 (0.016)

Avg_r_R 0.820 (0.005) 0.749 (0.017)




AverageWages_NR 0.314 (0.000) 0.345 (0.000)

AverageWages_R 0.111 (0.000) 0.112 (0.000)

RelativeWage 3.069 (0.005) 3.090 (0.009)

This increase in unemployment is accompanied by an increase in wages for bothtypes of workers. This happens because the ability of the firms to fill their vacanciesdecreases after the shock. Therefore, since the range of firms that do not satisfy thedesired ratio of filled vacancies increases (see Fig. 15), the firms increase their wages.Consequently, we observe a small increase in wages, although the economy suffers anegative shock, as Fig. 16 shows. This an emergent result, associated with the presenceof frictions in the labour market, such as higher unemployment, ex-post vacancies andrising wages.

Table 3 presents an overview of the results obtained with the average of the mostrelevant variables. The numbers in parentheses represent the variances. Note that theaverages for the set with the demand shock correspond to the entire period, and notonly to the post-shock period. Therefore, the results appear smoother. For example,the average total unemployment rate for the period after the shock is 6.8%, whereas

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Fig. 17 Average fitness FirmSpecificTP model with and without an increase in demand

Fig. 18 Entry of firms FirmSpecificTP model: positive demand shock

Fig. 19 Total vacancies FirmSpecificTP model with and without an increase in demand

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Fig. 20 Total unemployment rate FirmSpecificTP model with and without an increase in demand

Fig. 21 Average wages for the NR and R workers FirmSpecificTP model with and without an increase indemand

the value observed for the entire period is 4.9%. This rate of 6.8% results from unem-ployment rates of 6.95 and 6.7% for routine and non-routine workers, respectively.

Increase in the demand We also consider the impact of an increase in demand. Fig-ure 17 gives the evolution of the average fitness of the incumbent firms. This averagefitness deteriorates slightly after the shock. It seems that the increase in demand allowsless fit firms, that would otherwise leave the industry, to survive longer.

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Fig. 22 Relative wage FirmSpecificTP model with and without an increase in demand

Table 4 Average final periodsimulation results: positivedemand shock

Variables Firm specific Firm specificno shocks demand reduction

Average fitness 0.085 (0.001) 0.092 (0.001)


Avg_r_NR 0.814 (0.004) 0.831 (0.004)

Avg_r_R 0.820 (0.005) 0.834 (0.005)




AverageWages_NR 0.314 (0.000) 0.339 (0.000)

AverageWages_R 0.111 (0.000) 0.111 (0.000)

RelativeWage 3.069 (0.005) 3.065 (0.005)

The turbulence in the market is smaller than in the configuration without shocks,as shown by the number of entries (Fig. 18). In fact, the turnover of firms decreasessubstantially after the shock: the average turnover is 0.4 for the entire period withoutshocks, and only 0.29 for the entire period considering the shock (0.21 for the periodafter the shock only).

In terms of labour market dynamics, the number of vacancies is slightly higher afterthe shock (see Fig. 19). Therefore, the unemployment rates are somewhat lower thanin the model with no shock, as shown in Fig. 20.

The increase in demand does not lead to an increase in wages. In fact, in oureconomy the adjustment of the labour demand is not automatic. Firms interact withworkers through matching and bargaining processes where the bargaining power issplit between the actors. Our simulation results show that, after the shock, non-routineand routine wages have a relatively stable behaviour (Fig. 21).

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Tabl

e5

Lis

tof

vari

able

san

dpa

ram

eter

spe

rob

ject

Obj

ectm

arke

tO

bjec

tind

ustr

yO

bjec

tfirm

Obj

ectl

abou

rO

bjec

tNR

_Wor

ker

Obj

ectR

_Wor

ker

Supp

ly(0

)N

umbe

rFir

ms

(P)

Firm

_ID

(P)

Sum

Con

tWag

es(0

)N

R_W

_ID

(P)

R_W

_ID

(P)

Dem

and

(0)

Hig

hest

Firm

ID(P

)Q

uant

ity(1

)Su

mC

ontW

ages

NR

(0)

NR

_W_S

atW

age

(1)

R_W

_Sat

Wag

e(1

)

Pric

e(0

)A

vgFi

tnes

s(0

)Pr

ofits

(4)

Sum

Con

tWag

esR

(0)

NR

_W_R

esW

age

(P)

R_W

_Res

Wag

e(P

)

Mat

chin

g(0

)A

h(1

)C

osts

(0)

Num

berN

R(P

)N

R_W

_Con

tWag

e(0

)R

_W_C

ontW

age

(0)

Sum

Qua

ntity

(0)

Fitn

ess

(0)

Num

berR

(P)

NR

_W_I

D(1

)R

_W_I

D(1

)

Bar

gPow

er_N

R(P

)A

lpha

Firm

(1)

Tota

lW(P

)

Bar

gPow

er_R

(P)

Bet

a1(P

)To

talU

nem

p(0

)

Tota

lVac

(0)

Bet

a2(P

)U

nem

pNR

(0)

Tota

lVac

_NR

(0)

A(1

)U

nem

pR(0

)

Tota

lVac

_R(0

)F_

Sat_

Wag

e_N

R(1

)To

talU

nem

pRat

e(0

)

Avg

_r_N

R(0

)F_

Sat_

Wag

e_R

(1)

Tota

lUne

mpR

ateN

R(0

)

Avg

_r_R

(0)

F_C

ont_

Wag

e_N

R(1

)To

talU

nem

pRat

eR(0

)

Alp

ha(P

)F_

Con

t_W

age_

R(1

)

Exi

t(0)

F_To

talV

ac(1

)

Ent

ry(0

)F_

Vac

_NR

(0)

InvH

erf

(0)

F_V

ac_R

(0)

Ro_

NR

(P)

Ro_

R(P

)

r_N

R(P

)

r_R

(P)

L(1

)

LN

R(1

)

LR

(1)

123


Tabl

e5

cont

inue

d

Obj

ectm

arke

tO

bjec

tind

ustr

yO

bjec

tfirm

Obj

ectl

abou

rO

bjec

tNR

_Wor

ker

Obj

ectR

_Wor

ker

MSh

are

(2)

Rnd

Alp

haFi

rm(0

)

Des

ired

Alp

haFi

rm(0

)

A_F

it_C

oeff

(P)

A_L

NR

_val

ue

*In

pare

nthe

ses

we

have

the

lette

r“P

”w

hen

the

resp

ectiv

ela

bel

corr

espo

nds

toa

para

met

erin

the

mod

el.

Alte

rnat

ivel

y,th

ela

bels

that

corr

espo

ndto

vari

able

sha

vein

pare

nthe

ses

anin

tege

rth

atde

note

sth

ela

gged

time

asso

ciat

edw

ithea

chof

them

123


Table 6 Initial valuesconfiguration

Market NR_Worker R_Worker

Supply 59.756580 SatWage 0.36 SatWage 0.13

Demand 140.000000 ResWage 0.30 ResWage 0.10

Price 2.342838

The relative wage continues to increase after the shock, although at a slower pace,as seen in Fig. 22. This can also be seen in Table 4, which presents the average finalperiod simulation results. To understand the behaviour of the wages, we must considerthe ability of the firms to fill their vacancies. In order to do that, we must analyze theeffective ratios of filled vacancies (r_NR and r_R), for the configurations with andwithout shocks.

In Table 4, we can see that these two variables are somewhat improved when com-pared with the situation without shocks. This means that, on average, firms fill a largerproportion of their vacancies, so there are fewer ex-post vacancies. According to ourmodel, this means that firms do not have to increase their wages in order to attractworkers to their queues. Nevertheless, the wages of non-routine workers increase morethan in the set without shocks, whereas wages for routine workers have a very similarbehaviour in both sets (see Table 4).

In a period of expansion, the firms’ efforts to fulfil rising demand mean they willpay relatively more to non-routine workers, who not only are more productive, butalso have a greater bargaining power. The average wage for non-routine workers is0.346 after the demand increase, and only 0.314 and 0.339 for the model with no shock,and the entire period in the model with a demand shock, respectively. For routine work-ers, the average wage is 0.111 for all these three cases. The relative wage is higher forthe post-shock period (3.17), than for the entire period both with and without shocks(3.069 and 3.065, respectively).

4 Conclusion

In this paper, we proposed an evolutionary model where heterogeneous firms and work-ers interact and co-evolve, which accounts for some key features of the job search,bargaining and matching literature. Within a micro-meso perspective, the model high-lights the influence of firms’ “institutional settings” on industry dynamics. Thesesettings are formalized as the firms’ labour choices.

The results obtained by means of computer simulation robustly show that, in astable environment, there is a clear initial improvement in the average fitness of theincumbent firms’ population, which then evolves around an evolutionary stationarythreshold. The introduction of endogenous matching and bargaining processes in thelabour market leads to important frictions, as shown by the existence of ex-post vacan-cies and unemployment. Furthermore, there is increasing wage inequality between thetwo types of workers considered in the model. It is important to stress that this out-come occurs in a scenario where technological progress is neutral. Therefore, wageinequality does not derive exclusively from biased technological change as most of the

123


Tabl

e7

Initi

alva

lues

confi

gura

tion—

firm

s

ID1

23

45

67

89

10

Alp

haFi

rm0.

4043

340.

3116

810.

8142

290.

0777

610.

5125

650.

8536

560.

6586

920.

7614

950.

0682

120.

9724

33

Est

imat

edL

NR

17,3

86.3

6013

,402

.280

35,0

11.8

5033

,437

.360

22,0

40.3

0036

,707

.210

28,3

23.7

6032

,744

.290

2,93

3.13

341

,814

.620

Est

imat

edL

R25

,613

.640

29,5

97.7

207,

988.

153

39,6

56.2

6020

,959

.710

6,29

2.79

214

,676

.240

10,2

55.7

2040

,066

.870

1,18

5.38

1

LN

R16

1333

321

3526

313

39

LR

2730

1140

229

1713

406

L43

4344

4343

4443

4443

45

Tota

Vac

5644

5149

6871

4464

5749

r0.

7678

570.

9772

730.

8627

450.

8775

510.

6323

530.

6197

180.

9772

730.

6875

000.

7543

860.

9183

67

A0.

3503

970.

3333

490.

3101

820.

2903

080.

3656

880.

3029

270.

3388

010.

3198

850.

2885

510.

2810

72

Bet

a10.

30.

30.

30.

30.

30.

30.

30.

30.

30.

3

Bet

a20.

70.

70.

70.

70.

70.

70.

70.

70.

70.

7

Qua

ntity

6.55

9.24

85.

569.

244

7.36

1.96

91.

894.

358

7.78

7.37

57.

054.

379

7.75

4.61

67.

640.

644

1.88

2.89

36.

251.

852

Msh

are

0.10

9766

0.09

3199

0.12

3199

0.03

1701

0.13

0318

0.11

8052

0.12

9770

0.12

7863

0.03

1509

0.10

4622

Bar

gPow

er_N

R0.

40.

40.

40.

40.

40.

40.

40.

40.

40.

4

Bar

gPow

er_R

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

0.6

SatW

age_

NR

0.35

2692

0.30

3248

0.35

1339

0.31

1379

0.31

1652

0.34

9880

0.35

2401

0.34

8272

0.32

8720

0.33

7105

SatW

age_

R0.

1115

020.

1189

490.

1265

410.

1155

820.

1195

460.

1071

330.

1078

740.

1228

660.

1226

010.

1272

76

Con

tWag

e_N

R0.

3570

770.

3372

990.

3565

360.

3405

520.

3406

610.

3559

520.

3569

600.

3553

090.

3474

880.

3508

42

Con

tWag

e_R

0.11

8901

0.12

3369

0.12

7925

0.12

1349

0.12

3728

0.11

6280

0.11

6724

0.12

5720

0.12

5561

0.12

8366

Wag

esN

R5,

713.

229

4,38

4.89

011

,765

.670

1,02

1.65

57,

153.

877

12,4

58.3

209,

280.

970

1,10

1.45

71,

042.

464

13,6

82.8

40

Wag

esR

3,21

0.33

237

,011

.082

1,40

7.17

14,

853.

968

2,72

2.00

71,

046.

518

1,98

4.31

51,

634.

355

5,02

2.42

40.

7701

94

Fitn

ess

0.09

5666

0.18

8319

0.31

4229

0.42

2239

0.01

2565

0.35

3656

0.15

8692

0.26

1495

0.43

1788

0.47

2433

Rev

enue

s15

,367

.260

13,0

47.8

4017

,247

.900

4,43

8.17

418

,244

.560

16,5

27.2

7018

,167

.810

17,9

00.7

904,

411.

313

14,6

47.0

80

Cos

ts10

,980

.380

12,1

34.8

3020

,085

.880

17,9

53.7

5010

,146

.030

21,2

85.2

7014

,677

.160

18,4

01.8

2015

,348

.320

250,

827.

770

Prof

its4,

386.

878

0.91

3009

−2,8

37.9

80−1

0,51

5.60

08,

098.

528

−4,7

58.0

003,

490.

648

−0.5

0102

0−1

0,93

7.00

0−1

0,43

5.70

0

123


literature in this specific research area sustains (e.g., Acemoglu et al. 2001), but rather,it does to some extent depend on the firms’ intrinsic institutional choices regardinglabour. We also analyzed the effect of both positive and negative demand shocks. Theturbulence in the industry increases (decreases) after a negative (positive) demandshock. As expected, the negative demand shock causes a decrease in the number ofvacancies and, consequently, unemployment rates increase considerably. This rise inunemployment, quite surprisingly, goes together with an increase in wages for bothtypes of workers, since the capability of firms to fill their vacancies decreases after theshock. This latter aspect is an emergent property of the model as it results from theinteraction of firms and workers and not from a previously imposed assumption, andmimics quite well the recent experience of some economies, namely, the US, Spain,Portugal, and Greece. After the positive demand shock, firms increase their numberof vacancies slightly, so the unemployment rates are lower than in the model withoutshocks.

We should bear in mind that these results were obtained for a specific model, withina computational simulation setting. Therefore, it is important to highlight the limita-tions of this approach, and caution should be used in interpreting the results. In whatconcerns the theoretical frame, we could explore more realistic assumptions, namelyregarding the duration of jobs and the wage setting mechanism itself. Moreover, wecould endogenize the supply of both types of labour in the model, which would allow usto examine issues related to education, training and employment policies. The explora-tion of ‘occupationally’-biased technological change could also be a interesting topicfor future research.

Appendix: Object structure and initial configuration setting

We assume that 225 workers of each type exist in the economy. A very small numberis initially unemployed: 5 of the non-routine and 10 of the routine workers. The initialnumber of both types of workers allocated to each firm is randomly generated, and theinitial total number of workers is equal for all firms. The desired ratio of filled vacan-cies is initially set, for all firms, at 0.9 for non-routine and 0.85 for routine workers.The initial total vacancies are generated so that the effective ratio of filled vacancies(r) is between 0.6 and 1.0, giving an average of 0.8.

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