Advances in Complex Systems

This paper presents a view of the economy as a complex system with heterogeneous interacting agents who collectively organize themselves to generate aggregate phenomena which cannot be regarded as the behavior of some average or representative individual. There is an essential difference between the aggregate and the individual and such phenomena as bubbles and crashes, herd behavior, the transmission of information and the organization of trade are better modeled in the sort of framework suggested here than in more standard economic models.

In this paper, we present an agent-based, evolutionary, model of output- and labor-market dynamics. Firms produce a homogeneous, perishable good under constant returns to scale using labor only. Labor productivities are firm-specific and change stochastically due to technical progress. The key feature of the model resides in an explicit microfoundation of the processes of : (i) matching between firms and workers, (ii) job search, (iii) wage setting, (iv) endogenous formation of aggregate demand, and (v) endogenous price formation. Moreover, we allow for a competitive process entailing selection of firms on the basis of their revealed competitiveness. Simulations show that the model is able to robustly reproduce Beveridge, Wage and Okun curves under quite broad behavioral and institutional settings. The system generates endogenously an Okun coefficient greater than one even if individual firms employ production functions exhibiting constant returns to labor. Monte Carlo simulations also indicate that statistically detectable shifts in Okun and Beveridge curves emerge as the result of changes in institutional, behavioral, and technological parameters. Finally, the model generates sharp predictions about how system parameters affect aggregate performance (i.e. average GDP growth) and its volatility.

The matching function has become a popular tool in labor economics. It relates job creation (a flow variable) to two stock variables: vacancies and job searchers. In most studies the matching function is considered to be exogenous and assumed to have certain properties. The present study, instead, looks at the properties of an endogenous matching function. For this purpose we have programmed an agent-based computational labor market model with endogenous job creation and endogenous job search behavior. Our~simulations suggest that the endogenous matching technology is subject to decreasing returns to scale. The Beveridge curve reveals substitutability of job searchers and vacancies for a small range of inputs, but is flat for relatively high numbers of job searchers and vertical for relatively high numbers of vacancies. Moreover, the matching technology changes with labor market policies. This raises concerns about the validity of labor market policy evaluations conducted with flow models of the labor market that employ exogenous matching functions.

An urn-ball probabilistic model of the labor market is developed. Agents can be employed (voluntarily or involuntarily) unemployed, or entrepreneurs. The analytical long-run equilibrium probabilities for each state and the matching function are derived. In equilibrium, a higher reservation wage increases the number of start-ups, but has an overall negative impact on the unemployment rate. A more buoyant economy (higher average growth rate and higher average wages) is shown to be associated with a lower unemployment rate. Higher start-up costs discourage entrepreneurship and increase unemployment. More active search behavior leads first to a decrease in the unemployment rate, and then to a small increase, due to increased coordination failure induced by the higher number of applications sent by job seekers. The out-of-equilibrium dynamics are investigated through an agent-based simulation, which also provides results on firm demography. Important empirical regularities such as the Beveridge and the Okun curve are recovered. Finally, the simulation model is used to investigate departures from maximizing individual behavior and the effects of more realistic assumptions about profits and the business cycle.

Power law behavior is an emerging property of many economic models. In this paper we emphasize the fact that power law distributions are persistent but not time invariant. In fact, the scale and shape of the firms' size distribution fluctuate over time. In particular, on a log–log space, both the intercept and the slope of the power law distribution of firms' size change over the cycle: during expansions (recessions) the straight line representing the distribution shifts up and becomes less steep (steeper). We show that the empirical distributions generated by simulations of the model presented in Ref. 11 mimic real empirical distributions remarkably well.

Alternative pension schemes, and early retirement provisions in particular, can produce different effects on retirement behavior, with significant economic consequences. This paper presents new evidence on the effect of different seniority pension reforms, considering the evolution of an agent-based economy in Italy, with heterogeneous workers whose retirement age depends on expected lifetime incomes. Using dynamic aging methods, we examine behavioral changes along proposed pension reform paths. Our model — calibrated to replicate the main demographic and economic features and retirement dynamics of the Italian economy — is used to estimate the age of retirement, total pension expenditures, pension benefits and the trend of inequality and poverty among pensioners under different policy scenarios. More precisely, we compare the current state of affairs (B) with a reform proposed by the Italian Welfare Minister (M) and with an early introduction of a mixed regime for seniority pensions (A) according to two limiting "retirement behavioral rules." Under the individual rationality hypothesis, M produces slightly higher savings with minor redistributive effects; although it leads to an increase in income concentration, M mitigates poverty problems after 2008. The reform is more effective under family-bounded rationality, but it leads to permanent and more significant increases in income concentration and aggravates the diffusion and intensity of poverty.

The clustering of agents in the market is a typical problem dealt with in recent approaches to macroeconomic modeling, describing macroscopic variables in terms of the behavior of a large collection of microeconomic entities. Clustering is subject to many economic interpretations, often described by the Ewens Sampling Formula (ESF). In contrast with the usual complex derivations, we suggest a finitary characterization of the ESF pointing to real economic processes. Our approach is finitary in the sense that we provide a probabilistic description of a system of n individuals considered as a closed system, a population, where individuals can change attributes over time. The probability is understood as the fraction of time the system spends in the considered partition. As the ESF represents an equilibrium distribution satisfying detailed balance, some properties difficult to prove are derived in a simple way. Besides the mean distribution of the cluster sizes, we study the probabilistic time behavior of clusters, in particular the mean survival as a function of the actual size and the correlation between size and age.

The preceding papers have shown the impressive versatility and potential of agent-based modeling in developing an understanding of industrial and labor dynamics. The main attraction of agent-based models is that the actors — firms, workers, and networks — that are the objects of study in the 'real world,' can be represented directly in the model. This one-to-one correspondence between model agents and economic actors provides greater clarity and more opportunities for analysis than many alternative modeling approaches. However, the advantages of agent-based modeling have to be tempered by disadvantages and as yet unsolved methodological problems. In this brief summary drawn from the discussion at the closing session of WILD@ACE, we review three of these open problems in the context of the papers presented at the conference: How can agent-based models be empirically validated? What criteria should be used to evaluate the explanatory success of agent-based models? And how can the conclusions of research on similar topics be integrated?