2.1 The Happy Childhood of Macroeconomics

Roughly speaking, macroeconomics first saw the light of day with Keynes. For sure, enlightening analyses came before, including Wicksell’s, but the distinctiveness of macro levels of interpretation came with him. Indeed, up to the 1970s, there were basically two ‘macros’.

One was equilibrium growth theories. While it is the case that, for example, models á la Solow invoked maximising behaviours in order to establish equilibrium input intensities, no claim was made that such allocations were the work of any ‘representative agent’ in turn taken to be the ‘synthetic’ (??) version of some underlying General Equilibrium (GE). By the same token, the distinction between positive (that is, purportedly descriptive) and normative models, before Lucas and his companions, was absolutely clear to the practitioners. Hence, the prescriptive side was kept distinctly separated. Ramsey (Reference Ramsey1928) – type models, asking what a benevolent central planner would do, were reasonably kept apart from any question on the ‘laws of motion’ of capitalism, á la Harrod (Reference Harrod1939), Domar (Reference Domar1946), Kaldor (Reference Kaldor1957), and indeed Solow (Reference Solow1956). Finally, in the good and in the bad, technological change was kept separate from the mechanisms of resource allocation: the famous ‘Solow residual’ was, as is well known, the statistical counterpart of the drift in growth models with an exogenous technological change.

Second, in some fuzzy land between purported GE ‘microfoundations’ and equilibrium growth theories, lived for at least three decades a macroeconomics sufficiently ‘Keynesian’ in spirit and quite neoclassical in terms of tools. It was the early ‘neo-Keynesianism’ (also known as the Neoclassical Synthesis) – pioneered by Hicks (Reference Hicks1937), and shortly thereafter by Modigliani, Samuelson, Patinkin, and a few other American ‘Keynesians’ – whom Joan Robinson contemptuously defined as ‘bastard Keynesians’. It is the short-term macro which students used to learn up to the 1980s, with IS-LM curves, which are meant to capture the aggregate relations between money supply and money demand, interest rates, savings, and investments; Phillips curves on the labour market; and a few other curves as well. In fact, the curves were (are) a precarious compromise between the notion that the economy is supposed to be in some sort of equilibrium – albeit of a short-term nature – and the notion of a more ‘fundamental’ equilibrium path to which the economy is bound to tend in the longer run.

That was a kind of mainstream, especially on the other side of the Atlantic. There was also a group of thinkers whom we could call (as they called themselves) genuine Keynesians. They were predominantly in Europe, especially in the UK and in Italy: see Pasinetti (Reference Pasinetti1974), (Reference Pasinetti1983) and Harcourt (Reference Harcourt2007) for an overview.Footnote ⁵ The focus was only on the basic laws of motions of capitalist dynamics. They include the drivers of aggregate demand; the multiplier leading from the ‘autonomous’ components of demand such as government expenditures and exports to aggregate income; the accelerator, linking aggregate investment to past variations in aggregate income itself; and the relation between unemployment, wage/profits shares, and investments.Footnote ⁶ Indeed, such a stream of research is alive and progressing, refining upon the modelling of the ‘laws of motion’ and their supporting empirical evidence: see Lavoie (Reference Lavoie2009); Lavoie and Stockhammer (Reference Lavoie and Stockhammer2013); and Storm and Naastepad (Reference Storm and Naastepad2012a, Reference Storm and Naastepad2012b), among quite a few others.

Indeed, a common characteristic of the variegated contributions from ‘genuine Keynesianism’, often known also as post-Keynesian, is the scepticism about any microfoundation, to its own merit and also to its own peril. Part of the denial comes from a healthy rejection of methodological individualism and its axiomatisation as the ultimate primitive of economic analysis. Part of it, in our view, comes from the misleading notion that microfoundations necessarily mean methodological individualism (as if the interpretation of the working of a beehive had to necessarily build upon the knowledge of ‘what individual bees think and do’, or indeed ‘should do’). On the contrary, microfoundations might well mean how the macro structure of the beehive influences the distribution of the behaviours of the bees, a sort of macrofoundation of the micro. All this entails a major terrain of dialogue between the foregoing stream of Keynesian models and agent-based ones.

Now, back to the roots of modern macroeconomics. The opposite extreme to ‘bastard Keynesianism’ was not Keynesian at all, even if it sometimes took up the IS-LM-Phillips discourse. The best concise synthesis is Friedman (Reference Friedman1968). Historically it went under the heading of monetarism, but basically it was the pre-Keynesian view that the economy left to itself travels on a unique equilibrium path in the long- and short-run. Indeed, in a barter, pre-industrial economy where Say’s law and the quantitative theory of money hold, monetary policy cannot influence the interest rate and fiscal policy completely crowds out private consumption and investment: ‘there is a natural rate of unemployment which policies cannot influence’; see the deep discussion in Solow (Reference Solow2018). Milton Friedman was the obvious ancestor of Lucas and his companions, but he was still too far from the subsequent axioms, awaiting any empirical proof of plausibility.Footnote ⁷

2.2 ‘New Classical (??)’ Talibanism and Beyond

What happened next? Starting from the beginning of the 1970s, we think that everything which could get worse got worse and more: accordingly, we agree with Krugman (Reference Krugman2011) and Romer (Reference Romer2016) that macroeconomics plunged into a Dark Age.Footnote ⁸

First, ‘new classical economics’ (even if the reference to the Classics could not be further far away) fully abolished the distinction between the normative and positive domains – between models á la Ramsey and models á la Harrod-Domar, Solow, and so on (notwithstanding the differences amongst the latter ones). In fact, the striking paradox for theorists who are in good part market talibans is that they start with a model which is essentially of a benign, forward-looking, central planner, and only at the end, by way of an abundant dose of hand-waving, claim that the solution of whatever intertemporal optimisation problem is in fact supported by a decentralised market equilibrium.

Things could be much easier for this approach if one could build a genuine ‘general equilibrium’ model (that is, with many agents, heterogeneous at least in their endowments and preferences). However, this is not possible for the well-known, but ignored Sonnenschein (Reference Sonnenschein1972), Mantel (Reference Mantel1974), and Debreu (Reference Debreu1974) theorems (more in Kirman, Reference Kirman1989). Assuming by construction that the coordination problem is solved by resorting to the ‘representative agent’ fiction is simply a pathetic shortcut which does not have any theoretical legitimacy (Kirman, Reference Kirman1992).

Anyhow, the ‘New Classical’ restoration went so far as to wash away the distinction between ‘long-term’ and ‘short-term’ – with the latter as the locus where all ‘frictions’, ‘liquidity traps’, Phillips curves, some (temporary!) real effects of fiscal and monetary policies, and so on had precariously survived before. Why would a representative agent endowed with ‘rational’ expectations able to solve sophisticated inter-temporal optimization problems from here to infinity display any friction or distortion in the short-run, if competitive markets always clear? We all know the outrageously silly propositions, sold as major discoveries, also associated with an infamous ‘rational expectation revolution’ concerning the ineffectiveness of fiscal and monetary policies and the general properties of markets to yield Pareto first-best allocations. (In this respect, of course, it is easier for that to happen if ‘the market’ is one representative agent: coordination and allocation failures would involve serious episodes of schizophrenia by that agent itself!).

While Lucas and Sargent Reference Lucas and Sargent1978 wrote an obituary of Keynesian macroeconomics, we think that in other times, nearly the entire profession would have reacted to such a ‘revolution’ as Bob Solow once did when asked by Klamer (Reference Klamer1984) why he did not take the ‘new Classics’ seriously:

The reasons why the profession, and even worse, the world at large took these ‘Napoleons’ seriously, we think, have basically to do with a Zeitgeist where the hegemonic politics was that epitomized by Ronald Reagan and Margaret Thatcher, and their system of beliefs on the ‘magic of the market place’, ‘society does not exist, only individuals do’, et similia. And, tragically, this set of beliefs became largely politically bipartisan, leading to financial deregulation, massive waves of privatisation, tax cuts and surging inequality, and so on. Or think of the disasters produced for decades around the world by the IMF-inspired Washington Consensus or by the latest waves of austerity and structural-reform policies in the European Union as another such creed on the magic of markets, the evil of governments, and the miraculous effects of blood, sweat, and tears (Fitoussi & Saraceno, Reference Fitoussi and Saraceno2013, refers to this as the Berlin–Washington consensus). The point we want to make is that the changes in the hegemonic (macro) theory should be primarily interpreted in terms of the political economy of power relations among social and political groups, with little to write home about ‘advancements’ in the theory itself ... On the contrary!

The Mariana Trench of fanaticism was reached with Real Business Cycle (RBC) models (Kydland & Prescott, Reference Kydland and Prescott1982) positing optimal Pareto business cycles driven by economywide technological shocks [sic]. The natural question immediately arising concerns the nature of such shocks. What are they? Are recessions driven by episodes of technological regress (e.g. people going back to wash clothes in rivers or suddenly using candles for lighting)? The candid answer provided by one of the founding fathers of RBC theory is that: ‘They’re that traffic out there’ (‘there’ refers to a congested bridge, meaning some mysterious crippling of the ‘invisible hand’, as cited in Romer, Reference Romer2016: p. 5). Needless to say, the RBC propositions were (and are) not supported by any empirical evidence. But the price paid by macroeconomics for this sort of intellectual trolling was and still is huge!

2.3 New Keynesians, New Monetarists and the New Neoclassical Synthesis

Since the 1980s, ‘New Keynesian’ economists, instead of following Solow’s advices,Footnote ⁹ basically accepted the New Classical and RBC framework and worked on the edges of auxiliary assumptions. So, they introduced monopolistic competition and a plethora of nominal and real rigidities into models with representative-agent cum rational-expectations microfoundations. New Keynesian models restored some basic results which were undisputed before the New Classical Middle Ages, such as the non-neutrality of money. However, the price paid to talk just to ‘New Classicals’ and RBC talibans was tall. The methodological infection was so deep that Mankiw and Romer (Reference Mankiw and Romer1991) claimed that New Keynesian macroeconomics should be renamed New Monetarist macroeconomics, and De Long (Reference De Long2000) discussed ‘the triumph of monetarism’. ‘New Keynesianism’ of different vintages represents what we could call homeopathic Keynesianism: the minimum quantities to be added to the standard model, sufficient to mitigate the most outrageous claims of the latter.

Indeed, the widespread sepsis came with the appearance of a New Neoclassical Synthesis (NNS) (Goodfriend, Reference Goodfriend2007), grounded upon DSGE models (Clarida, Galí, & Gertler, Reference Clarida, Galí and Gertler1999; Woodford, Reference Woodford2003; Galí & Gertler, Reference Galí and Gertler2007). In a nutshell, such models have a RBC core supplemented with monopolistic competition, nominal imperfections, and a monetary policy rule, and they can accomodate various forms of ‘imperfections’, ‘frictions’, and ‘inertias’. To many respects DSGE models are simply the late-Ptolemaic phase of the theory: add epicycles at full steam without any theoretical and empirical discipline in order to better match a particular set of the data. Of course, in the epicycles frenzy one is never touched by a sense of the ridiculous in assuming that the mythical representative agent at the same time is extremely sophisticated when thinking about future allocations, but falls into backward-looking habits when deciding about consumption or, when having to change prices, is tangled by sticky prices! (Caballero, Reference Caballero2010: offers a thorough picture of this surreal state of affairs.) Again, Bob Solow gets straight to the point:Footnote ¹⁰

Not all New Keynesian economists deliberately choose to step out of economics. Indeed, ‘New Keynesianism’ is a misnomer, in that sometimes it is meant to cover also simple but quite powerful models whereby Keynesian system properties are obtained out of otherwise standard microfoundations, just taking seriously ‘imperfections’ as structural, long-term characteristics of the economy. Pervasive asymmetric information requires some genuine heterogeneity and interactions among agents (see Akerlof & Yellen, Reference Akerlof and Yellen1985; Greenwald & Stiglitz, Reference Greenwald and Stiglitz1993a, Reference Greenwald and Stiglitz1993b; Akerlof, Reference Akerlof2002, Reference Akerlof2007, among others) yielding Keynesian properties as ubiquitous outcomes of coordination failures (for more detailed discussions of Stiglitz’s contributions, see Dosi & Virgillito, Reference Dosi and Virgillito2017).Footnote ¹¹ All that, still without considering the long-term changes in the so-called fundamentals, technical progress, and so on.

2.4 What about Innovation Dynamics and Long-Run Economic Growth?

We have argued that even the coordination issue has been written out of the agenda by assuming it as basically solved by construction. But what about change? What about the ‘Unbound Prometheus’ (Landes, Reference Landes1969) of capitalist search, discovery, and indeed destruction?

In Solow (Reference Solow1956) and subsequent contributions, technical progress appears by default, but it does so in a powerful way as the fundamental driver of long-run growth, to be explained outside the sheer allocation mechanism.Footnote ¹² On the contrary, in the DSGE workhorse, there is no Prometheus: ‘innovations’ come as exogenous technology shocks upon the aggregate production function, with the same mythical agent optimally adjusting its consumption and investment plans. And the macroeconomic time series generated by the models are usually de-trended to focus on their business cycle dynamics.Footnote ¹³ End of the story.

The last thirty years have seen also the emergence of new growth theories (see e.g. Romer, Reference Romer1990; Aghion & Howitt, Reference Aghion and Howitt1992), bringing – as compared to the original Solow model – some significant advancements and, in our view, equally significant drawbacks. The big plus is the endogenisation of technological change: innovation is endogenised into economic dynamics. But that is done just as either a learning externality or as the outcome of purposeful expensive efforts by profit-maximising agents. In the latter case, the endogenisation comes at what we consider the major price (although many colleagues would deem it as a major achievement) of reducing innovative activities to an equilibrium outcome of optimal intertemporal allocation of resources, with or without (probabilisable) uncertainty. Hence, by doing that, one loses also the genuine Schumpeterian notion of innovation as a disequilibrium phenomenon (at least as a transient!).

Moreover, ‘endogenous growth’ theories do not account for business cycles’ fluctuations. This is really unfortunate, as Bob Solow (Reference Solow2005) puts it:

And the separation between growth and business cycle theories is even more problematic given the bourgeoning new empirical literature on hysteresis (among many others, see Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2018a; Cerra, Fatás, & Saxena Reference Cerra, Fatás and Saxena2023, and the literature cited therein), which convincingly shows the existence of many interlinkages between short-run and long-run phenomena. In particular, in the presence of hysteresis, recessions can permanently depress output, thus undermining the very growing capabilities of economies. On the policy side, this calls for a more active role of fiscal and monetary interventions during downturns, and, more generally, to consider the impact of policies across the whole spectrum of frequencies. On the theoretical side, hysteresis is not due to market imperfections, but rather to the very functioning of decentralised economies characterised by coordination externalities and dynamic increasing returns. In that respect, this Element shows that evolutionary agent-based models are genuinely able to account for the emergence of hysteresis, while providing a unified analysis of technological change and long-run growth together with coordination failures and business cycles.

2.5 From the ‘Great Moderation’ to the Great Recession

In the beginning of this century, under the new consensus reached by the New Neoclassical Synthesis (NNS), Robert E. Lucas, Jr, (Reference Lucas2003) without any embarrassment, declared ‘The central problem of depression prevention had been solved’, and Prescott religiously believed that: ‘This is the golden age of macroeconomics’.Footnote ¹⁴ Moreover, a large number of NNS contributions claimed that economic policy was finally becoming more of a science (!?), (Galí & Gertler, Reference Galí and Gertler2007; Goodfriend, Reference Goodfriend2007; Mishkin, Reference Mishkin2007; Taylor, Reference Taylor2007).Footnote ¹⁵ This was made possible by the ubiquitous presence of DSGE models in academia and a universe of politicians and opinion-makers under the ‘free market’ / ‘free Wall Street’ globalization spell,Footnote ¹⁶ and helped by the ‘divine coincidence’, whereby inflation targeting, performed under some form of Taylor rule, appeared to be a sufficient condition for stabilising the whole economy. During this Panglossian period, some economists went as far as claiming that the ‘scientific approach’ to macroeconomics policy incarnated in DSGE models was the ultimate cause of the so-called Great Moderation (Bernanke, Reference Bernanke2004), namely the fall of GDP volatility experienced by most developed economists since the beginning of the 1980s, and that only minor refinements to the consensus workhorse model were needed.

Unfortunately, as happened with the famous statement made by Francis Fukuyama (Reference Fukuyama1992) about an alleged ‘end of history’,Footnote ¹⁷ these positions have been proven to be substantially wrong by subsequent events. Indeed, a relatively small ‘micro’ event, the bankruptcy of Lehman Brothers in 2008, triggered a major financial crisis which caused the Great Recession, the deepest downturn experienced by developed economies since 1929.

In that respect, the Great Recession turned out to be a ‘natural experiment’ for economic analysis, showing the inadequacy of the predominant theoretical frameworks. Indeed, as Krugman (Reference Krugman2011) points out, not only did DSGE models not forecast the crisis, but they did not even admit the possibility of such an event and, even worse, they did not provide any useful advice to policymakers on how to put the economy back on a steady growth path (see also Turner, Reference Turner2010; Stiglitz, Reference Stiglitz2011, Reference Stiglitz2015; Bookstaber, Reference Bookstaber2017; Caverzasi & Russo, Reference Caverzasi and Russo2018; Haldane & Turrell, Reference Haldane and Turrell2019).

Scholars of DSGE have reacted to such a failure by trying to amend their models with a new legion of epicycles; for example, financial frictions, homeopathic doses of agent heterogeneity, bounded rationality, and exogenous fat-tailed shocks (see e.g. Lindé, Smets, & Wouters, Reference Lindé, Wouters, Taylor and Uhlig2016, and the discussion in Section 3.4). Conversely, an increasing number of economists have claimed that the 2008 ‘economic crisis is a crisis for economic theory’ (Colander et al., Reference Colander, Folmer and Haas2009; Farmer & Foley, Reference Farmer and Foley2009; Krugman, Reference Krugman2009, Reference Krugman2011; Caballero, Reference Caballero2010; Kirman, Reference Kirman2010b, Reference Kirman2016; Kay, Reference Kay2011; Stiglitz, Reference Stiglitz2011, Reference Stiglitz2015; Dosi, Reference Dosi2014; Romer, Reference Romer2016; Stiglitz, Reference Stiglitz2017). Indeed, history is the smoking gun against the deeply flawed basic assumptions of mainstream DSGE macroeconomics, for example rational expectations and representative agents, which prevents, by construction, the understanding of the emergence of deep downturns together with standard fluctuations (Stiglitz, Reference Stiglitz2015) and, more generally, the very dynamics of economies. Indeed, resorting to representative-agent microfoundations, how can one understand central phenomena such as rising inequality, bankruptcy cascades and systemic risks, innovation, structural change, and their co-evolution with climate dynamics?

3.1 Theoretical Issues

As already mentioned previously, DSGE models suffer the same well-known problems as Arrow–Debreu general-equilibrium models (see Kirman, Reference Kirman1989: for a classical reference) and more. Neglecting them does not mean solving them. On the contrary!

More specifically, the well-known Sonnenschein (Reference Sonnenschein1972), Mantel (Reference Mantel1974), and Debreu (Reference Debreu1974) theorems show that neither the uniqueness nor, and even less so, the stability of the general equilibrium can be attained, even if one employs stringent and unrealistic assumptions about agents, even under amazing information requirements. Indeed, Saari and Simon (Reference Saari and Simon1978) show that an infinite amount of information is required to reach the equilibrium for any initial price vector.

The representative agent (RA) shortcut has been taken to circumvent any aggregation problem. The RA assumption implies that there is isomorphism between micro- and macro-economics, with the latter shrunk to the former. This, of course, is far from being innocent: there are (at least) four reasons for which it cannot be defended (Kirman, Reference Kirman1992).Footnote ¹⁹

First, individual rationality does not imply ‘aggregate rationality’: one cannot provide any formal justification to support the assumption that the macro level behaves as a maximising individual.

Second, even if one forgets also that one cannot safely perform policy analyses with RA macro models, the reactions of the representative agent to shocks or parameter changes may not coincide with the aggregate reactions of the represented agents.

Third, the lack of micro/macro isomorphism is revealed even in terms of aggregation of preferences: the representative agent might appear to prefer $a$ , even if all the ‘represented’ individuals might well prefer $b$ .

Fourth, the RA assumption also induces additional difficulties on testing grounds, because whenever one tests a proposition delivered by a RA model, one is also jointly testing the very RA hypothesis. Hence, one tests the rejection of the latter together with the rejection of the specific model proposition (more on that in Forni & Lippi, Reference Forni and Lippi1997, Reference Forni and Lippi1999; Pesaran & Chudik, Reference Pesaran and Chudik2014).

Finally, the last theoretical issue concerns the existence and determinacy of the system of rational-expectation equilibrium conditions of DSGE models. If the exogenous shocks and the fluctuations generated by the monetary policy rule are ‘small’, and the ‘Taylor principle’ holds, the rational-expectation equilibrium of the DSGE model exists and is locally determinate (Woodford, Reference Woodford2003). This result allows one to compute impulse-response functions in the presence of ‘small’ shocks or parameter changes and to safely employ log-linear approximations around the steady state. Unfortunately, the existence of a local determinate equilibrium does not rule out the possibility of multiple equilibria at the global level (see e.g. Schmitt-Grohè & Uribe, Reference Schmitt-Grohé and Uribe2000; Benhabib, Schmitt-Grohè, & Uribe, 2001; Ascari & Ropele, Reference Ascari and Ropele2009). This is a serious issue because there is always the possibility, for example if the laws of motion of the shocks are not properly tuned, that the DSGE model enters in an explosive path, thus preventing the computation of impulse-response functions and the adoption of the model for policy analysis exercises.

3.2 Empirical Issues

Even neglecting the theoretical absurdities of the basic DSGE edifice, already mentioned previously, equally serious pitfalls concern their empirical use.

The estimation and testing of DSGE models are usually performed assuming that they represent the ‘true’ data generating process (DGP) of the observed data (Canova, Reference Canova, Mills and Patterson2008). This implies that the ensuing inference and policy experiments are valid only if the DSGE model mimics the unknown DGP of the data.Footnote ²⁰ Notice that such an epistemology widespread in economics but unique to it (and to theology!), assumes that the world is ‘transparent’ and thus the ‘model’ faithfully reflects it. This is well epitomised by the grotesque Scientology-like remark of Sargent about rational expectations: ‘All agents inside the model, the econometrician, and God share the same model’ (Sargent, Reference Sargent2005). All other scientific disciplines are basically there to conjecture, verify, and falsify models of the world. Not our own! So, also concerning DSGE models, their econometric performance is assessed along the identification, estimation, and evaluation dimensions (Fukac & Pagan, Reference Fukac and Pagan2006).

Given the large number of non-linearities present in the structural parameters, DSGE models are hard to identify (Canova, Reference Canova, Mills and Patterson2008). This leads to a large number of identification problems, which can affect the parameter space either at the local or at the global level.Footnote ²¹ Identification problems lead to biased and fragile estimates of some structural parameters and do not allow one to rightly evaluate the significance of the estimated parameters applying standard asymptotic theories. This opens a ridge between the real and the DSGE DGP, depriving parameter estimates of any economic meaning and making policy analysis exercises useless (Canova, Reference Canova, Mills and Patterson2008).

Such identification problems also affect the estimation of DGSE models. Bayesian methods apparently address the estimation (and identification) issues by adding a prior function to the (log) likelihood function in order to increase the curvature of the latter and obtain a smoother function. However, this choice is not harmless: if the likelihood function is flat – and thus conveys little information about the structural parameters – the shape of the posterior distribution resembles the one of the prior, reducing estimation to a more sophisticated calibration procedure carried out on an interval instead of on a point (see Fukac & Pagan, Reference Fukac and Pagan2006; Canova, Reference Canova, Mills and Patterson2008). Indeed, the likelihood functions produced by most DSGE models are quite flat (see e.g. the exercises performed by Fukac & Pagan, Reference Fukac and Pagan2006).Footnote ²²

Evaluating a DSGE model, as well as any other models, implies in principle assessing its capability to reproduce a large set of stylized facts, in our case macroeconomic ones (microeconomic regularities cannot be attained by construction given the representative-agent assumption). Fukac and Pagan (Reference Fukac and Pagan2006) performed such exercises on a popular DSGE model with disappointing results. Moreover, DSGE models might seem to do well in ‘normal’ time, but they cannot account even in principle for crises and deep downturns (Stiglitz, Reference Stiglitz2015), even when fat-tailed shocks are assumed (Ascari, Fagiolo, & Roventini, Reference Ascari, Fagiolo and Roventini2015).Footnote ²³

The results just described seem to support Favero’s (Reference Favero2007) claim that modern DSGE models are exposed to the same criticisms advanced against the old-fashioned macroeconometric models belonging to the Cowles Commission tradition: they pay too much attention to the identification of the structural model (with all the problems described earlier) without testing the potential misspecification of the underlying statistical model (see also Johansen, Reference Johansen and Colander2006; Juselius & Franchi, Reference Juselius and Franchi2007). If the statistical model is misspecified, policy analysis exercises lose significance, because they are carried out in a ‘virtual’ world whose data-generating process is different from the one underlying observed time-series data.

More generally, the typical assertion made by DSGE modelers that their theoretical frameworks are able to replicate real-world evidence is at odds with a careful scrutiny of how the empirical evaluation of DSGE models is actually done. Dynamic Stochastic General Equilibrium modelers, indeed, typically select ex ante the set of empirical criteria that their models should satisfy in such a way as to be sure that these restrictions are met. However, they usually refrain from confronting their models with the wealth of fundamental features of growth over the capitalist business cycles, which DSGE models are not structurally able to replicate.

3.3 Political-Economy Issues

Given the theoretical problems and the puny empirical performance of DSGE models, their assumptions cannot be defended by invoking arguments either of parsimonious modelling or data matching. This opens a Pandora’s box on the links between the legion of assumptions of DSGE models and their policy conclusions. But behind all that, one of the crucial issues concerns the relationship between the information the representative agent is able to access, ‘the model of the world’ she has, and her ensuing behaviours.

Dynamic Stochastic General Equilibrium models assume a very peculiar framework, whereby representative agents are endowed with a sort of ‘olympic’ rationality, and have free access to an unbounded information set.Footnote ²⁴ Moreover, rational expectation is the common shortcut employed by DSGE models to deal with uncertainty. Such utterly strong assumptions, however, raise more question marks than answers.

First, even assuming individual rationality, how does it carry over through aggregation, yielding rational expectations (RE) at the system level? For sure, individual rationality is not a sufficient condition for letting the system converge to the RE fixed-point equilibrium (Howitt, Reference Howitt2012). Relatedly, while it is in general unreasonable to assume that agents possess all the information required to attain the equilibrium of the whole economy (Caballero, Reference Caballero2010), this applies even more so to periods of strong structural transformation, like the Great Recession, that require policies never tried before (e.g. quantitative easing; see Stiglitz, Reference Stiglitz2011, Reference Stiglitz2015).

Second, agents can also have the ‘wrong’ model of the economy, but available data may corroborate it (see the seminal contribution of Woodford, Reference Woodford1990: among the rich literature on sunspots).

Third, as Hendry and Minzon (Reference Hendry and Minzon2010) point out, when ‘structural breaks’ affect the underlying stochastic process that governs the evolution of the economy, the learning process of agents introduces further non-stationarity into the system, preventing the economy from reaching an equilibrium state, if there is one. More generally, in the presence of genuine uncertainty (Knight, Reference Knight1921; Keynes, Reference Keynes1936), ‘rational’ agents should follow heuristics, as they always outperform more complex expectation formation rules (Gigerenzer & Brighton, Reference Gigerenzer and Brighton2009; Dosi et al., Reference Dosi, Napoletano, Roventini, Stiglitz and Treibich2020a). But, if this is so, then the modelers should assume that agents behave according to how the psychological and sociological evidence suggests that they actually behave (Akerlof, Reference Akerlof2002; Akerlof & Shiller, Reference Akerlof and Shiller2009). Conversely, given such circumstances, it is no wonder that empirical tests usually reject the full-information, rational expectation hypothesis (see e.g. Coibion & Gorodnichenko, Reference Coibion and Gorodnichenko2015; Gennaioli, Ma, & Shleifer, Reference Gennaioli, Ma and Shleifer2015).

The representative-agent (RA) assumption prevents DSGE models from reaching any distributional issue, even if they are intertwined with the major causes of the Great Recession and, more generally, they are fundamental for studying the effects of policies. So, for example, increasing inequalities in income (Atkinson, Piketty, & Saez, Reference Atkinson, Piketty and Saez2011) and wealth inequalities (Piketty & Zucman, Reference Piketty and Zucman2014) might have contributed to inducing households to hold more and more debt, paving the way to the subprime mortgage crisis (Fitoussi & Saraceno, Reference Fitoussi and Saraceno2010; Stiglitz, Reference Stiglitz2011). Redistribution matters and different policies have a different impact on the economy according to the groups of people they are designed for (e.g. unemployed benefits have larger multipliers than do tax cuts for high-income individuals; see Stiglitz, Reference Stiglitz2011). However, the study of redistributive policies requires models with heterogeneous agents.

The RA assumption coupled with the implicit presence of a Walrasian auctioneer, which sets prices before exchanges take place, rules out by construction the possibility of interactions among heterogeneous individuals. This prevents DSGE models also from accurately studying the dynamics of credit and financial markets. Indeed, the assumption that the representative agent always satisfies the transversality condition removes the default risk from the models (Goodhart, Reference Goodhart2009). As a consequence, agents face the same interest rate (no risk premia) and all transactions can be undertaken in capital markets without the need of banks. Abstracting from default risks prevents DSGE models from contemplating the conflict between price and financial stability faced by central banks (Howitt, Reference Howitt2012). As they do not consider the huge costs of financial crises, they deceptively appear to work fine only in ‘normal’ times (Stiglitz, Reference Stiglitz2011, Reference Stiglitz2015); basically when one does not need them!

In the same vein, DSGE models are not able to account for involuntary unemployment. Indeed, even if they are meant to study the welfare effects of macroeconomic policies, unemployment is not present or, when it is, it only stems from frictions in the labour market or from wage rigidities. Such explanations are especially hard to believe during deep downturns like, for example, the Great Recession. In DSGE models, the lack of heterogeneous, interacting firms and workers/consumers prevents the study of the possibility of massive coordination failures (Leijonhufvud, Reference Leijonhufvud1968, Reference Leijonhufvud2000; Cooper & John, Reference Cooper and John1988), which could lead to an insufficient level of aggregate demand and to involuntary unemployment.

In fact, the macroeconomics of DSGE models does not appear to be genuinely grounded on any microeconomics (Stiglitz, Reference Stiglitz2011, Reference Stiglitz2015) they do not even take into account the micro and macro implications of imperfect information, while the behaviour of agents is often described with arbitrary specifications of the functional forms (e.g. Dixit–Stiglitz utility function, Cobb–Douglas production function).

More generally, DSGE models suffer from a sort of internal contradiction. On the one hand, strong assumptions such as rational expectations, perfect information, and complete financial markets are introduced ex ante to provide a rigorous and formal mathematical treatment and to allow for policy recommendations. On the other hand, many imperfections (e.g., sticky prices, rule-of-thumb consumers) are introduced ex post without any theoretical justification only to allow the DSGE model to match the data (see also the discussion later in this Element). Along these lines Chari et al. (Reference Chari, Kehoe and McGrattan2009) argue that the high level of arbitrariness of DSGE models in the specifications of structural shocks may leave them exposed to the so-called Lucas critique, preventing them from being usefully employed for policy analysis.

An assumption of DSGE models is that business cycles stem from a plethora of exogenous shocks. As a consequence, DSGE models do not explain business cycles, preferring instead to postulate them as a sort of deus ex machina mechanism. This could explain why even in ‘normal times’ DSGE models are not able to match many business cycle stylized facts or need to assume serially correlated shocks to produce fluctuations resembling the ones observed in reality (cf. Zarnowitz, Reference Zarnowitz1985, Reference Zarnowitz1997; Cogley & Nason, Reference Cogley and Nason1993; Fukac & Pagan, Reference Fukac and Pagan2006). Even worse, phenomena like the subprime mortgage crisis clearly show how bubbles and, more generally, endogenously generated shocks are far more important for understanding economic fluctuations (Stiglitz, Reference Stiglitz2011, Reference Stiglitz2015).

Moving to the normative side, one supposed advantage of the DSGE approach is the possibility of deriving optimal policy rules. However, when the ‘true’ model of the economy is not known, rule-of-thumb policy rules can perform better than optimal policy rules (Brock et al., Reference Brock, Durlauf, Nason and Rondina2007; Orphanides & Williams, Reference Orphanides and Williams2008). Indeed, in complex worlds with pervasive uncertainty (e.g. in financial markets), policy rules should be simple (Haldane, Reference Haldane2012), while ‘redundancy’ and ‘degeneracy’ (Edelman & Gally, Reference Edelman and Gally2001) are required to achieve resiliency.

3.4 Post-Crisis DSGE Models: Some Fig Leaves Are Not a Cloth

The failure of DSGE models to account for the Great Recession sparked the search for refinements, which were also partly trying to address the critiques discussed in the previous three sections. More specifically, researchers in the DSGE camp have tried to include a financial sector into the barebones model, consider some forms of (very mild) heterogeneity and bounded rationality, and explore the impact of rare exogenous shocks on the performance of DSGE models.

Let us provide a bird’s-eye view of such recent developments. (Another overview is Caverzasi & Russo, Reference Caverzasi and Russo2018.)

The new generation of DSGE model with financial frictions are mostly grounded on the so-called financial accelerator framework (Bernanke, Gertler, & Gilchrist, Reference Bernanke, Gertler, Gilchrist, Taylor and Woodford1999), which provides a straightforward explanation why credit and financial markets can affect real economic activity. The presence of imperfect information between borrowers and lenders introduces a wedge between the cost of credit and those of internal finance. In turn, the balance-sheets of lenders and borrowers can affect the real sector via the supply of credit and the spread on loan interest rates (see Gertler & Kiyotaki, Reference Gertler, Kiyotaki, Friedman and Woodford2010: for a survey). For instance, Curdia and Woodford (Reference Curdia and Woodford2010) introduce patient and impatient consumers to justify the existence of a stylized financial intermediary, which copes with default risk charging a spread on its loan subject to exogenous, stochastic disturbances. From the policy side, they conclude that central banks should keep on controlling the short-term interest rate (see also Curdia & Woodford, Reference Curdia and Woodford2016). In the model of Gertler and Karadi (Reference Gertler and Karadi2011), households can randomly become workers or bankers. In the latter case, they provide credit to firms, but as they are constrained by deposits and the resources they can raise in the interbank market, a spread emerges between loans’ and deposits’ interest rates (see also Christiano, Motto, & Rostagno, Reference Christiano, Motto and Rostagno2013). They find that during (exogenous) recessions, unconventional monetary policy (i.e. the central bank providing credit intermediation) is welfare enhancing (see also Gertler and Kiyotaki, Reference Gertler, Kiyotaki, Friedman and Woodford2010 and Curdia and Woodford, Reference Curdia and Woodford2011 for other types of credit policies).

The foregoing contributions allow for some form of mild heterogeneity among agents. Some DSGE models consider two classes of agents in order to explore issues such as debt deflations or inequality. For instance, Eggertsson and Krugman (Reference Eggertsson and Krugman2012) introduce patient and impatient agents and expose the latter to exogenous debt limit shocks, which force them to deleverage. In such a framework, there can be debt deflations, liquidity traps, and fiscal policies can be effective. Kumhof, Ranciere, and Winant (Reference Kumhof and Rancière2015) try to study the link between rising inequality and financial crises employing a DSGE model where exogenously imposed income distribution guarantees that top earner households (5% of the income distribution) lend to the bottom ones (95% of the income distribution). Exogenous shocks induce low-income households to increase their indebtedness, raising their ‘rational’ willingness to default and, in turn, the probability of a financial crisis. More recent works consider a continuum of heterogenous households in an incomplete market framework. For instance, in the Heterogenous Agent New Keynesian (HANK) model developed by Kaplan, Moll, and Violante (Reference Kaplan, Moll and Violante2018), the assumptions of uninsurable income shocks and multiple assets with different degrees of liquidity and returns lead to wealth distributions and marginal propensities to consume more in tune with the empirical evidence. In this framework, monetary policy is effective only if it provokes a general-equilibrium response of labour demand and household income, and as the Ricardian equivalence breaks down, its impact is intertwined with fiscal policy.

An increasing number of DSGE models allow for various forms of bounded rationality (see Dilaver, Jump, & Levine, Reference Dilaver, Jump and Levine2018 for a survey) albeit to homeopathic degrees. In one stream of literature, agents know the equilibrium of the economy and form their expectations as if they were econometricians, by using the available observations to compute their parameter estimates via ordinary least square (in line with Evans & Honkapohja, Reference Evans and Honkapohja2001). Other recent contributions have relaxed the rational expectations assumption preserving maximisation (Woodford, Reference Woodford2013). For instance, an increasing number of works assume ‘rational inattention’, that is, optimising agents rationally decide not to use all the available information because they have finite processing capacity (Sims, Reference Sims, Friedman and Woodford2010). Along this line, Gabaix (Reference Gabaix2014) models ‘bounded rationality’, assuming that agents have a simplified model of the world, but, nonetheless, they can jointly maximise their utility and their inattention. Drawing inspiration from artificial intelligence programs, Woodford (Reference Woodford2018) develops a DSGE model where rational agents can forecast up to $k$ steps ahead. Finally, building on Brock and Hommes (Reference Brock and Hommes1997), in an increasing number of DSGE models, agents can form their expectations using an ecology of different learning rules, usually fundamentalist versus extrapolative rules (see e.g. Branch & McGough, Reference Branch and McGough2011; De Grauwe, Reference De Grauwe2012; Anufriev et al., Reference Anufriev, Assenza, Hommes and Massaro2013; Massaro, Reference Massaro2013). As the fraction of agents following different expectations rules changes over time, ‘small’ shocks can give rise to persistent and asymmetric fluctuations and endogenous business cycles may arise.

Finally, a new generation of DSGE models try to account for deep downturns and disasters. Curdia, Del Negro, and Greenwald (Reference Curdia, Del Negro and Greenwald2014) estimate the Smets & Wouters (Reference Smets and Wouters2007) model, assuming Student’s $t$ -distributed shocks. They find that the fit of the model improves and rare deep downturns become more relevant (see also Fernandez-Villaverde & Levintal, Reference Fernandez-Villaverde and Levintal2018: for a DSGE model with exogenous time-varying rare disaster risk). A similar strategy is employed to Canzoneri et al. (Reference Canzoneri, Collard, Dellas and Diba2016) to allow the effects of fiscal policies to change over time and get state-dependent fiscal multipliers higher than one in recessions.

4.1 The Basics

Every macroeconomic ABM typically possesses the following structure. There is a population – or a set of populations – of heterogenous agents (e.g., consumers, firms, banks), possibly hierarchically organised, whose size may change or not in time. The evolution of the system is observed in discrete time steps, $t=1,2,\dots$ . Time steps may be days, quarters, years, and so on. At each $t$ , every agent $i$ is characterised by a finite number of microeconomic variables ${\underset{\_}{x}}_{i,t}$ which may change across time (e.g., production, consumption, wealth) and by a vector of microeconomic parameters ${\underset{\_}{\theta }}_i$ (e.g., mark-ups, propensity to consume). In turn, the economy may be well characterised by some macroeconomic (fixed) parameters $\Theta$ (even mimicking policy like tax rates, the Basel capital requirements, etc.).

Given some initial conditions ${\underset{\_}{x}}_{i,0}$ (e.g., wealth, technology) and a choice for micro and macro parameters, at each time step, one or more agents are chosen to update their microeconomic variables. This may happen randomly or can be triggered by the state of the system itself. Agents picked to perform the updating stage might collect their available information (or not) about the current and past states (i.e., micro-economic variables) of a subset of other agents, typically those they directly interact with. They typically use their knowledge about their own history, their local environment, as well as, possibly, the (limited) information they can gather about the state of the whole economy, and feed them into their heuristics, routines, and other algorithmic behavioural rules. Interactions occur within the population of heterogenous agents. Interactions can involve different agents of the same type (e.g., firms from the same industry) or entities from different types (e.g., trading relationship between firms and consumers in the good market). Such a stream of interactions leads to the emergence of a multi-layer network structure that endogenously evolves over time. At the same time, in truly evolutionary environments, technologies, organisations, behaviours, and markets collectively co-evolve.

After the updating round has taken place, a new set of microeconomic variables is fed into the economy for the next-step iteration: aggregate variables ${\underset{\_}{X}}_t$ are computed by simply summing up or averaging individual characteristics. Once again, the definitions of aggregate variables closely follow those of statistical aggregates (i.e., GDP, unemployment).

4.2 Emergence and Validation

The stochastic components possibly present in decision rules, expectations, and interactions in turn requires that the dynamics of micro and macro variables ought to be typically described by some stochastic processes. The non-linearities which are typically present in the dynamics of agent-based systems make it hard to analytically derive closed-form properties of their laws of motion. Together, their stochastic version might well entail instances of non-ergodicity. This suggests that the researcher must often resort to computer simulations in order to analyse the behaviour of the ABM at hand. And even there, the detection of such ‘laws of motion’ is no simple matter, as history counts, even in the longer term.

How are simulations carried out in agent-based economics? A possible procedure that can be implemented to study the output of simulation is synthetically depicted in Figure 1. Given some choice for initial conditions, micro and macro parameters, the system can be run until it reaches some stable behaviour (i.e., for at least $T>T^{*}$ time steps). Suppose one is interested in a set $S=s1,s2,...$ of statistics to be computed on micro and macro simulated variables (e.g. average GDP growth rates, unemployment rates, distributions of firm sizes, productivities and profitabilities). Given the stochastic nature of the process, each run will output a different value for the statistics of interest. Therefore, after having produced $M$ independent runs, which we refer to as Monte Carlo simulations, one has a distribution for each statistic containing $M$ observations, which can be summarised by computing its moments. Recall, however, that moments will depend at least on the choice made for initial conditions and parameters (and not only on them if history really counts). By exploring a sufficiently large number of points in the space where initial conditions and parameters are allowed to vary, computing the moments of the statistics of interest at each point, and by assessing how moments depend on parameters, one might get a quite deep descriptive knowledge of the behaviour of the system (see Figure 1).

Figure 1 A schematic procedure for studying the output of an agent-based model.

Source: Fagiolo and Roventini (Reference Fagiolo and Roventini2012).

Simulation exercises allow one then to study long-run statistical distributions, patterns, and emergent properties of micro and macro dynamics. For instance, a macro agent-based model can endogenously generate apparently ordered patterns of growth together with business cycles and deep crises. In that ABMs provide a direct answer to Solow and Stiglitz’s plea for macroeconomic models that can jointly account for long-run trajectories, short-run fluctuations, and deep downturns (see Section 1). At the same time, such models deliver a wealth of emergent properties ranging from macroeconomic relationships such as the Okun and Phillips curves to microeconomic distributions of, for example, firm size and growth rates, and so on. Moreover, as with every complex system, after crossing some critical threshold or tipping point the economy can self-organise along a different statistical path. This allows one to straightforwardly study phenomena like hysteresis in unemployment and GDP, systemic risk in credit, and financial markets, climate-change tipping points, and others.

More generally, the very structure of ABMs naturally allows one to take the model to the data and validate it against observed real-world observations. Most ABMs follow what has been called an indirect calibration approach (Windrum & Moneta, 2007; Fagiolo et al. 2017) which indeed represents also a powerful form of validation: the models are required to match a possibly wide set of micro and macro empirical regularities. An impressive list of micro and macro stylized facts jointly accounted by macro agent-based models is presented in Section 6; more in Haldane and Turrell (Reference Haldane and Turrell2019), Dosi et al. (Reference Dosi, Napoletano, Roventini and Treibich2016a) and Dosi et al. (Reference Dosi, Pereira, Roventini and Virgillito2020) among others. For instance, at the macro level, ABMs are able to match the relative volatility and comovements between GDP and different macroeconomic variables, the interactions between real, credit, and financial aggregates (including the emergence of deep banking crises), fat-tailed GDP growth-rate distributions, and so on. At the microeconomic level, macro agent-based models are able to reproduce firm size and growth rate distributions, heterogeneity and persistent differentials among firm productivity, lumpy investment patterns, and so on.

We do consider the ability of ABMs to jointly account for a huge ensemble of both micro and macro stylised facts under a wide range of parameterisations as the primary validation of their strength and robustness. In fact, it is relatively easy to ‘prove’ any model, no matter how far-fetched, concerning any one empirical regularity, in violation of all the rest we know about that particular phenomenon. So, for example, in the Middle Ages, there were astronomical theories apparently quite apt to ‘explain’ the day and the night in terms of God opening and closing the curtains of the universe. The analogy with DSGE models is striking indeed! However, the ABM perspective has accepted also such an epistemologically twisted comparative challenge and has made much progress even in terms of validation against a single time-series. A detailed survey with the most recent developments is provided in Fagiolo, Guerini, Lamperti et al. (Reference Fagiolo, Guerini, Lamperti, Moneta, Roventini, Beisbart and Saam2017).

On the ‘input side’, that is, modelling assumptions about individual ‘behaviours’ and interactions have been refined on laboratory experiments (Hommes, Reference Hommes2013; Anufriev, Bao, & Tuinstra, Reference Anufriev, Bao and Tuinstra2016), business practices (Dawid et al. Reference Dawid, Harting, van der Hoog and Neugart2019) and, more generally, microeconomic empirical evidence (Dosi et al., Reference Dosi, Napoletano, Roventini and Treibich2016a).Footnote ³¹ ABMs can also be validated on the output side, by explaining the space of parameters and initial conditions in terms of the range of values which allow the model to replicate the stylised facts of interest. For instance, Barde (Reference Barde2016) and Lamperti (Reference Lamperti2018) attempt to validate the output of agent-based models according to the replication of time-series dynamics, while Guerini and Moneta (Reference Guerini and Moneta2017) explore how a macro ABM matches the apparent causal relations in the data. Some works estimate ABMs via indirect inference (see e.g. Alfarano, Lux, & Wagner, Reference Alfarano, Lux and Wagner2005; Winker, Gilli, & Jeleskovic, Reference Winker, Gilli and Jeleskovic2007; Grazzini, Richiardi, & Sellad, Reference Grazzini, Richiardi and Sellad2013; Grazzini & Richiardi, Reference Grazzini and Richiardi2015) or Bayesian methods (Delli Gatti & Grazzini, Reference Delli Gatti and Grazzini2020; Grazzini, Richiardi, & Tsionas, Reference Grazzini, Richiardi and Tsionas2017). Finally, a new strand of research assesses the forecasting capabilities of ABMs vis-à-vis DSGE and VAR models (Poledna et al., Reference Poledna, Miess, Hommes and Rabitsch2023).

In any case, there is a fundamental distinction, often neglected by economists, between explanation and forecasting. One may well use clearly wrong theories in order to predict especially in the short term, and they might well be the ground for powerful heuristics for decision. Agent-based models of the K+S kind are primarily there with the ambition to explain. Together, they are also instrumental in showing the power of wrong models of prediction as robust guidance to behaviours in complex evolving environments. So in Dosi et al. (Reference Dosi, Napoletano, Roventini, Stiglitz and Treibich2020a), for example, one shows that the prediction rule ‘tomorrow will be likely today’ turns out to be a much more effective guidance for individual behaviours in complex and changing worlds than any more sophisticated inferential rule.

No matter the empirical validation procedures actually employed, an important domain of analysis regards the sensitivity of the model to parameter changes through different methods including Kriging meta-modeling (Salle & Yıldızoğlu,; Dosi, Pereira, & Virgillito, Reference Dosi, Pereira and Virgillito2017; Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2018a, Reference Dosi, Pereira, Roventini and Virgillito2018b; Bargigli et al., Reference Bargigli, Riccetti, Russo and Gallegati2020) and machine-learning surrogates (Lamperti, Roventini, & Sani, Reference Lamperti, Roventini and Sani2018). Such methodologies provide detailed sensitivity analyses of macro ABMs, allowing one to get a quite deep descriptive knowledge of the behaviour of the system, even concerning variables far from crucial for the general interpretative power of ABMs themselves. In this respect, however, note that, contrary to common wisdom, the most ‘important’ variables, whatever it means in a system rich of inter-relatedness, are those which are most insensitive to changes in parameterisations. What counts is primarily their presence or absence. This is the case, for example, of an innovation process of whatever kind, or a mechanism of demand generation, or a fiscal policy, again of whatever kind.

4.3 Policy Analysis

If empirically sound, agent-based models represent a very powerful device able to address policy questions under more realistic, flexible, and modular set-ups. Indeed, in contrast to DSGE models, they do not impose any strong theoretical consistency requirements (e.g., equilibrium, representative individual assumptions, rational expectations) and allow for behavioural assumptions which can be replaced in a modular way, without impairing the analysis of the model.Footnote ³² Moreover, as already mentioned earlier, agent-based models are able to jointly match a rich ensemble of macro and micro empirical regularities.This is a major advantage of ABMs vis-à-vis, for example, DSGE ones, which are typically built – in order to retain analytical solvability – to explain very few macro-stylised facts, and cannot replicate by construction any micro empirical regularities, given their representative-agent assumption.

But how can one actually conduct policy experiments in ABMs? In a very natural way, indeed. Take again the procedure for ABM descriptive analysis outlined in Figure 1. Micro and macro parameters can be designed in such a way to mimic real-world key policy variables like tax rates, subsidies, and others. Moreover, initial conditions might play a relevant role (somewhat equivalent to initial endowments in standard models) and describe different distributional set-ups concerning, for example, incomes or technologies. In addition, interaction and behavioural rules employed by economic agents can be easily devised so as to represent alternative institutional, market, or industry set-ups. Since all these elements can be freely interchanged, one can investigate a huge number of alternative policy experiments and rules, the consequences of which can be assessed either qualitatively or quantitatively (e.g., by running standard statistical tests on the distributions of the statistics in $S$ ). For example, one might statistically test whether the effect on the moments of the individual consumption distribution will be changed (and if so, by how much) by a percentage change in any given consumption tax rate. Most importantly, all this might be done while preserving the ability of the model to replicate existing macroeconomic stylized facts, as well as microeconomic empirical regularities, which by construction cannot be matched by DSGE models.

4.4 Conclusions

The number of macroeconomic agent-based models has steadily increased in the last decades, and this trend received a new impulse after the Great Recession uncovered many weaknesses of DSGE models. For instance, in their survey Dawid and Delli Gatti (Reference Dawid, Delli Gatti, Hommes and LeBaron2018) discuss eight families of macroeconomic agent-based models: the model of Ashraf, Gershman, and Howitt (Reference Ashraf, Gershman and Howitt2017), the Ancona–Milano approach (Delli Gatti et al., Reference Delli Gatti, Di Guilmi, Gaffeo, Giulioni, Gallegati and Palestrini2005; Assenza, Delli Gatti, & Grazzini, Reference Assenza, Delli Gatti and Grazzini2015), the Eurace@Unibi model (Dawid et al., Reference Dawid, Gemkow, Harting, van der Hoog, Neugart, Chen and Kaboudan2014a; Dawid, Harting, & Neugart, Reference Dawid, Harting and Neugart2014b, Reference Dawid, Harting and Neugart2018), the Eurace simulator developed in Genoa (Cincotti, Raberto, & Teglio, Reference Cincotti, Raberto and Teglio2010; Raberto et al., Reference Raberto, Ozel, Ponta, Teglio and Cincotti2019; Teglio et al., Reference Teglio, Mazzocchetti, Ponta, Raberto and Cincotti2019), the JAMEL model (Salle & Seppecher, Reference Salle and Seppecher2018; Seppecher, Reference Salle and Seppecher2018), the Keynes meeting Schumpeter model (Dosi, Fagiolo, & Roventini, Reference Dosi, Fagiolo and Roventini2010), the LAGOM model (Mandel, Jaeger, Fuerst et al., Reference Mandel, Jaeger, Fuerst, Lass, Lincke, Meissner, Pablo-Marti and Wolf2010; Wolf, Furst, Mandel et al., Reference Wolf, Furst, Mandel, Lass, Lincke, Pablo-Marti and Jaeger2013), and the model developed by Lengnick (Reference Lengnick2013). The list is not completely exhaustive. Among a burgeoning line of research, one should consider, for instance, the stock-flow consistent model by Caiani et al. (Reference Caiani, Godin, Caverzasi, Gallegati, Kinsella and Stiglitz2016), and the multi-industry models developed independently by Ciarli et al. (Reference Ciarli, Lorentz, Valente and Savona2019), Dosi, Roventini, and Russo (Reference Dosi, Roventini and Russo2019, Reference Dosi, Roventini and Russo2020), and Poledna et al. (Reference Poledna, Miess, Hommes and Rabitsch2023).

The surveys of Fagiolo and Roventini (Reference Fagiolo and Roventini2012, Reference Fagiolo and Roventini2017), Napoletano (Reference Napoletano2018), and Dawid and Delli Gatti (Reference Dawid, Delli Gatti, Hommes and LeBaron2018) show how macroeconomic agent-based models can succesfully address fiscal policy, monetary policy, macroprudential policy, labour-market governance, regional and cohesion policies, innovation and industrial policies, climate-change policies,Footnote ³³ and different combinations of such public interventions. In that, ABMs are a valuable tool in the model portfolio available for policymakers as discussed by Haldane and Turrell (Reference Haldane and Turrell2019). An overview of such models is beyond the scope of the Element. On the contrary, in the next section, we will introduce the family of Keynes meeting Schumpeter models refining upon Dosi, Fagiolo, and Roventini (Reference Dosi, Fagiolo and Roventini2010), which can be considered our workhorse ABM accounting for macro and micro dynamics, as well as for testing the impact of different combinations of microeconomic and macroeconomic policies.

5.1 The Timeline of Events

As already mentioned, our simple economy is composed of a machine-producing sector made of $F_1$ firms (denoted by the subscript $i$ ), a consumption-good sector made of $F_2$ firms (denoted by the subscript $j$ ), $L^S$ consumers/workers, and a public sector. Before accurately describing the K+S model (Dosi, Fagiolo, & Roventini, Reference Dosi, Fagiolo and Roventini2010), we briefly provide the timeline of events occurring in each time step ( $t$ ).

1. 1. Machine-tool firms perform R&D trying to discover new products and more efficient production techniques and to imitate the technology and the products of their competitors.

2. 2. Capital-good firms advertise their machines with consumption-good producers.

3. 3. Consumption-good firms decide how much to produce and invest. If investment is positive, consumption-good firms choose their supplier and send their orders, for their planned expansion, and, possibly, also to replace some older equipments.

4. 4. In both industries firms hire workers according to their production plans and start producing.

5. 5. Imperfectly competitive consumption-good market opens. The market shares of firms evolve according to their ‘competitiveness’ based on prices and possibly other variables such as any unfilled demand.

6. 6. Entry and exit take places. In both sectors firms with near-zero market shares and negative net liquid assets are eschewed from the two industries and replaced by new firms.

7. 7. Machines ordered at the beginning of the period are delivered and become part of the capital stock at time $t+1$ .

At the end of each time step, aggregate variables (e.g. GDP, investment, employment) are computed, summing over the corresponding microeconomic variables.

Let us now turn to a more detailed description of the model and of the agents’ behaviours, which – to repeat –we try to keep as close as we can to what we know they actually do as distinct from what they ought to do under more perfect informational circumstances.

5.2 The Capital-Good Industry

The technology of a capital-good firm is $(A_i^{\tau },B_i^{\tau })$ , where the former coefficient stands for the labour productivity of the machine-tool manufactured by $i$ for the consumption-good industry (a rough measure of producer quality), while the latter coefficient is the labour productivity of the production technique employed by firm $i$ itself. The positive integer $\tau$ denotes the current technology vintage. Given the monetary wage $w$ , the unit cost of production of capital-good firms is:

$c_i\left(t\right)=\frac{w\left(t\right)}{B_i^{\tau }}.$(1)

With a fixed mark-up ( ${\mu }_1>0$ ) pricing rule,Footnote ³⁵ prices ( $p_i$ ) are defined as:

$p_i\left(t\right)=(1+{\mu }_1)c_i\left(t\right).$(2)

The unit labour cost of production in the consumption-good sector associated with each machine of vintage $\tau$ , produced by firm $i$ is:

$c(A_i^{\tau },t)=\frac{w\left(t\right)}{A_i^{\tau }}.$

Firms in the capital-good industry ‘adaptively’ strive to increase their market shares and their profits trying to improve their technology both via innovation and imitation. Both are costly processes: firms invest in R&D a fraction of their past sales ( $S_i$ ):

$R{D}_i\left(t\right)=\nu S_i(t-1),$(3)

with $0<\nu <1$ . R&D expenditures are employed to hire researchers paying the market wage $w\left(t\right)$ .Footnote ³⁶ Firms split their R&D efforts between innovation ( $IN$ ) and imitation ( $IM$ ) according to the parameter $\xi \in [0,1]$ :

$\begin{array}{c}I{N}_i\left(t\right)=\xi R{D}_i\left(t\right),\\ I{M}_i\left(t\right)=(1-\xi )R{D}_i\left(t\right).\end{array}$

We model innovation as a two-step process. The first one determines whether a firm obtains or not an access to innovation – irrespectively of whether it is ultimately a success or a failure – through a draw from a Bernoulli distribution, whose parameter ${\theta }_i^{in}\left(t\right)$ is given by:

${\theta }_i^{in}\left(t\right)=1-e^{-{\zeta }_{1}I{N}_i\left(t\right)},$(4)

with capturing firms’ search capabilities. Note that according to (4), there are some scale-related returns to R&D investment: access to innovative discoveries is more likely if a firm puts more resources into R&D. If a firm innovates, it may draw a new machine embodying technology $(A_i^{in},B_i^{in})$ according to:

$\begin{array}{c}{A}_i^{in}\left(t\right)=A_i\left(t\right)(1+x_i^A(t\left)\right),\\ B_i^{in}\left(t\right)=B_i\left(t\right)(1+x_i^B(t\left)\right),\end{array}$

where $x_i^A$ and $x_i^B$ are two independent draws from a Beta( ${\alpha }_1,{\beta }_1$ ) distribution over the support $[{\underset{\_}{x}}_1,{\bar{x}}_1]$ with ${\underset{\_}{x}}_1$ belonging to the interval $[-1,0]$ and ${\bar{x}}_1$ to $[0,1]$ . Note that the notional possibilities of technological advance – namely technological opportunities (Dosi, Reference Dosi2023) – are captured by the support of the Beta distribution and by its shape. So, for example, with low opportunities the largest probability density falls over ‘failed’ innovations – that is, potential capital goods which are ‘worse’ in terms of costs and performances than those already produced by the searching firm. Conversely, under a condition of rich opportunities, innovations which dominate incumbent technologies will be drawn with high probability. As we shall show later in the Element, a crucial role of ‘Schumpeterian’ technology policies is precisely to influence opportunities and micro capabilities.

Like innovation search, imitation follows a two-step procedure. The possibilities of accessing imitation come from sampling a Bernoulli, ( ${\theta }_i^{im}\left(t\right)$ ):

$\begin{array}{c}{\theta }_i^{im}\left(t\right)=1-e^{-{\zeta }_{2}I{M}_i\left(t\right)},\end{array}$(5)

with $0<{\zeta }_2⩽1$ . Firms accessing the second stage are able to copy the technology of one of the competitors $(A_i^{im},B_i^{im})$ . We assume that firms are more likely to imitate competitors with similar technologies and we use a Euclidean metric to compute the technological distance between every pair of firms to weight imitation probabilities. Such appropriability conditions stem from the tacit nature of knowledge embodied in the technology, even in the presence of explicit intellectual properties rights (which, however, can be easily modeled in our framework).

All firms which draw a potential innovation or imitation have to put it on production or keep producing the incumbent generation of machines. Comparing the technology competing for adoption, firms choose to manufacture the machine characterised by the best trade-off between price and efficiency. More specifically, knowing that consumption-good firms invest following a payback period routine (see Section 5.3), capital-good firms select the machine to produce according to the following rule:

(6)

where $b$ is a positive payback period parameter (see Eq. 10). Once the type of machine is chosen, we capture the imperfect information pervading the market, assuming that each firm sends a ‘brochure’ with the price and the productivity of its offered machines to both its historical ( $H{C}_i$ ) clients and to a random sample of potential new customers ( $N{C}_i$ ), whose size is proportional to $H{C}_i$ (i.e., $N{C}_i\left(t\right)=\gamma H{C}_i\left(t\right)$ , with $0<\gamma <1$ ).

5.3 The Consumption-Good Industry

Consumption-good firms produce a homogenous goods using capital (i.e. their stock of machines) and labour under constant returns to scale. Firms plan their production ( $Q_j$ ) according to adaptive demand expectations ( $D_j^e$ ):

$D_j^e\left(t\right)=f\left(D_j\right(t-1),D_j(t-2),\dots ,D_j(t-h\left)\right),$(7)

where $D_j(t-1)$ is the demand actually faced by firm $j$ at time $t-1$ ( $h$ positive integer).Footnote ³⁷ The desired level of production ( $Q_j^d$ ) depends on the expected demand as well as on the desired inventories ( $N_j^d$ ) and the actual stock of inventories ( $N_j$ ):

$Q_j^d\left(t\right)=D_j^e\left(t\right)+N_j^d\left(t\right)-N_j(t-1),$(8)

with $N_j^d\left(t\right)=\iota D_j^e\left(t\right),\iota \in [0,1]$ . The output of consumption-good firms is constrained by their capital stock ( $K_j$ ). If the desired capital stock ( $K_j^d$ ) – computed as a function of the desired level of production – is higher than the current capital stock, firms invest ( $E{I}_j^d$ ) in order to expand their production capacity:Footnote ³⁸

$E{I}_j^d\left(t\right)=K_j^d\left(t\right)-K_j\left(t\right).$(9)

The capital stock of each firm is obviously composed of heterogenous vintages of machines with different productivity. We define ${\Xi }_j\left(t\right)$ as the set of all vintages of machine-tools belonging to firm $j$ at time $t$ . Firms scrap machines following a payback period routine. Consequently, technical change and equipment prices influence the replacement decisions of consumption-good firms.Footnote ³⁹ More specifically, firm $j$ replaces machine $A_i^{\tau }\in {\Xi }_j\left(t\right)$ according to its technology obsolescence as well as the price of new machines:

$R{S}_j\left(t\right)=\left(A_i^{\tau }\in {\Xi }_j\left(t\right):\frac{p^{*}\left(t\right)}{c(A_{i,\tau },t)-c^{*}\left(t\right)}\le b\right),$(10)

where $p^{*}$ and $c^{*}$ are the price and unit cost of production upon the new machines. Firms compute their replacement investment by summing up the number of old machine-tools, satisfying Eq. 10. Moreover, they also scrap the machines older than $\eta$ periods (with $\eta$ being a positive integer).

Consumption-good firms choose their capital-good supplier by comparing the price and productivity of the currently manufactured machine-tools they are aware of. As we mentioned earlier (see Section 5.2), the capital-good market is systematically characterised by imperfect information. This implies that consumption-good firms compare ‘brochures’ describing the characteristics of machines only from a subset of equipment suppliers. Firms then choose the machines with the lowest price and unit cost of production (i.e., $p_i\left(t\right)+bc(A_i^{\tau },t))$ and send their orders to the corresponding machine manufacturer. Machine production is a time-consuming process: capital-good firms deliver the ordered machine-tools at the end of the period.Footnote ⁴⁰ Gross investment of each firm ( $I_j$ ) is the sum of expansion and replacement investment. Pooling the investment of all consumption-good firms, one gets aggregate investment ( $I$ ).

Consumption-good firms have to finance their investments, as well as their production, as they advance worker wages. In line with any empirical observation and also a growing number of theoretical and empirical papers (e.g. Stiglitz & Weiss, Reference Stiglitz and Weiss1992; Greenwald & Stiglitz, Reference Greenwald and Stiglitz1993a; Hubbard, Reference Hubbard1998), we assume imperfect capital markets. This implies that the financial structure of firms matters (external funds are more expensive than internal ones) and firms may be credit rationed. More specifically, consumption-good firms finance production using their stock of liquid assets ( $N{W}_j$ ). If liquid assets do not fully cover production costs, firms borrow the remaining part, paying an interest rate $r$ up to a maximum debt/sales ratio of $\Lambda$ . Only firms that are not production-rationed can try to fulfill their investment plans by employing their residual stock of liquid assets first and then their residual borrowing capacity.Footnote ⁴¹

Given their current stock of machines, consumption-good firms compute average productivity ( ${\pi }_j$ ) and unit cost of production ( $c_j$ ). Prices are set applying a variable mark-up ( ${\mu }_j$ ) on unit costs of production:

$p_j\left(t\right)=(1+{\mu }_j(t\left)\right)c_j\left(t\right).$(11)

Mark-up variations are regulated by the evolution of firm market shares ( $f_j$ ):Footnote ⁴²

${\mu }_j\left(t\right)={\mu }_j(t-1)\left(1+\upsilon \frac{f_j(t-1)-f_j(t-2)}{f_j(t-2)}\right),$(12)

with $0⩽\upsilon ⩽1$ .

The consumption-good market too is characterized by imperfect information (antecedents in the same vein are Phelps and Winter, Reference Phelps, Winter and Phelps1970; Klemperer, Reference Klemperer1987; Farrel & Shapiro, Reference Farrel and Shapiro1988; see also the empirical literature on consumers’ imperfect price knowledge surveyed in Rotemberg, Reference Rotemberg2008). This implies that consumers do not instantaneously switch to products made by more competitive firms. However, prices are clearly one of the key determinants of firms’ competitiveness ( $E_j$ ). The other component is the level of unfilled demand ( $l_j$ ) inherited from the previous period:

$E_j\left(t\right)=-{\omega }_1{p}_j\left(t\right)-{\omega }_2{l}_j\left(t\right),$(13)

where ${\omega }_{1,2}$ are positive parameters.Footnote ⁴³ Weighting the competitiveness of each consumption-good firm by its past market share ( $f_j$ ), one can compute the average competitiveness of the consumption-good sector:

$\bar{E}\left(t\right)=\underset{j=1}{\sum ^{F_2}}{E}_j\left(t\right)f_j(t-1).$

This variable represents also a moving selection criterion driving, other things being equal, expansion, contraction, and extinction within the population of firms. We parsimoniously model this market set-up, letting firm market shares evolve according to a ‘quasi’ replicator dynamics (for antecedents in the evolutionary camp see Metcalfe, Reference Metcalfe1994a; Silverberg, Dosi, & Orsenigo, Reference Silverberg, Dosi and Orsenigo1988):

$f_j\left(t\right)=f_j(t-1)\left(1+\chi \frac{E_j\left(t\right)-\bar{E}\left(t\right)}{\bar{E}\left(t\right)}\right),$(14)

with $\chi >0.$ Footnote ⁴⁴

The profits ( ${\Pi }_j$ ) of each consumption-good firm reads:

${\Pi }_j\left(t\right)=S_j\left(t\right)-c_j\left(t\right)Q_j\left(t\right)-rDe{b}_j\left(t\right),$

where $S_j\left(t\right)=p_j\left(t\right)D_j\left(t\right)$ and $Deb$ denotes the stock of debt. The investment choices of each firm and its profits determine the evolution of its stock of liquid assets ( $N{W}_j$ ):

$N{W}_j\left(t\right)=N{W}_j(t-1)+{\Pi }_j\left(t\right)-c{I}_j\left(t\right)\text{,}$

where $c{I}_j$ is the amount of internal funds employed by firm $j$ to finance investment.

5.4 Schumpeterian Exit and Entry Dynamics

At the end of each period, we let firms with (quasi) zero market shares or negative net assets die and we allow a new breed of firms to enter the markets. In many of our models, we keep the number of firms fixed, hence any dead firm is replaced by a new one (this simplifying assumption is, however, by no means a necessary one).

In line with the empirical literature on firm entry (Caves, Reference Caves1998; Bartelsman, Scarpetta, & Schivardi, Reference Bartelsman, Scarpetta and Schivardi2005), we assume that entrants are on average smaller than incumbents, with the stock of capital of new consumption-good firms and the stock of liquid assets of entrants in both sectors being a fraction of the average stocks of the incumbents. More specifically, the stock of capital of a new consumption-good firm is obtained by multiplying the average stock of capital of the incumbents by a random draw from a Uniform distribution with support $[{\varphi }_1,{\varphi }_2],0<{\varphi }_1,<{\varphi }_2⩽1$ . In the same manner, the stock of liquid assets of an entrant is computed by multiplying the average stock of liquid assets of the incumbents of the sector by a random variable distributed according to a Uniform distribution with support $[{\varphi }_3,{\varphi }_4],0<{\varphi }_3,<{\varphi }_4⩽1$ .

Concerning the technology of entrants, new consumption-good firms select amongst the newest vintages of machines according to the ‘brochure mechanism’ described earlier. The process- and product-related knowledge of new capital-good firms is again drawn from a Beta distribution, whose shape and support are shifted and ‘twisted’ according to whether entrants enjoy an advantage or a disadvantage vis-à-vis incumbents. More precisely, the technology of capital-good firms is obtained by applying a coefficient extracted from a Beta( ${\alpha }_2,{\beta }_2$ ) distribution to the endogenously evolving technology frontier ( $A^{max}\left(t\right),B^{max}\left(t\right))$ , where $A^{max}\left(t\right)$ and $B^{max}\left(t\right)$ are the best technology available to incumbents. In fact, the distribution of opportunities for entrants versus incumbents is a crucial characteristic of different sectoral technological regimes (a particular case of that is the distance from the technological frontier of entrants discussed in Aghion & Howitt, Reference Aghion and Howitt2007).

5.5 The Labour Market

The labour market is certainly not Walrasian: real wages not claring the market and involuntary unemployment as well as labour rationing are the rules rather than the exceptions. The aggregate labour demand ( $L^D$ ) is computed by summing up the labour demand of capital- and consumption-good firms. The aggregate supply ( $L^S$ ) is exogenous and inelastic. Hence aggregate employment ( $L$ ) is the minimum between $L^D$ and $L^S$ .

The wage rate is determined by institutional and market factors. In the simplest case, which we use in our baseline version, wages are determined at the macro level via indexation mechanisms upon consumption prices and average productivity, on the one hand, and adjustments to unemployment rates, on the other:

$w\left(t\right)=w(t-1)+\left(1+{\psi }_1\frac{\Delta \overline{AB}\left(t\right)}{\overline{AB}(t-1)}+{\psi }_2\frac{\Delta cpi\left(t\right)}{cpi(t-1)}+{\psi }_3\frac{\Delta U\left(t\right)}{U(t-1)}\right),$(15)

where $\overline{AB}$ is the average labour productivity, $cpi$ is the consumer price index, and $U$ is the unemployment rate. Variations may be experimented with, mimicking different regimes for the labour market, by changing the system parameters ${\psi }_{1,2,3}$ . However, more adequate representations of different regimes in a genuine ABM spirit are required. We present some promising attempts in Section 5.8. In any case, note that the analogy between Eq. 15 and any form of ‘Phillips curve’ is only superficial. Indeed, our results hold even if the coefficient on the unemployment term is set to zero. The importance of the relation is in terms of the transmission process from productivity to wages (or the absence thereof).

5.6 Consumption, Taxes, and Public Expenditures

An otherwise black-boxed public sector levies taxes on firm profits and worker wages or on profits only and pays to unemployed workers a subsidy ( $w^u$ ) that is a fraction of the current market wage (i.e., $w^u\left(t\right)=\phi w\left(t\right)$ , with $\phi \in (0,1)$ ). In fact, taxes and subsidies are the fiscal leverages that contribute to the aggregate demand management regimes (we shall explore this issue in more detail later). Note that a ‘zero tax, zero subsidy’ scenario is our benchmark for a pure Schumpeterian regime of institutional governance (see the experiments in Section 7).

Aggregate consumption ( $C$ ) is computed by summing up over the income of both employed and unemployed workers:

$C\left(t\right)=w\left(t\right)L^D\left(t\right)+w^u(L^S-L^D(t\left)\right).$(16)

The model satisfies the standard national account identities: the sum of value added of capital- and consumption goods firms ( $GDP$ ) equals their aggregate production since in our simplified economy there are no intermediate goods, and that in turn coincides with the sum of aggregate consumption, investment, and change in inventories ( $\Delta N$ ):

$GD{P}_t\equiv \underset{i=1}{\sum ^{F_1}}{Q}_i\left(t\right)+\underset{j=1}{\sum ^{F_2}}{Q}_j\left(t\right)\equiv C\left(t\right)+I\left(t\right)+\Delta N\left(t\right).$

The dynamics generated at the micro level by decisions of a multiplicity of heterogenous, adaptive agents and by their interaction mechanisms is the explicit microfoundation of the dynamics for all aggregate variables of interest (e.g. output, investment, employment). However, as the model amply demonstrates, the aggregate properties of the economy do not bear any apparent isomorphism with the micro adjustment rules outlined earlier. Needless to say, a fundamental consequence is also that any ‘representative agent’ compression of micro heterogeneity is likely to offer a distorted account of both what agents do and the collective outcomes of their actions – more in Dosi (Reference Dosi2023), indeed, well in tune with the arguments of Kirman (Reference Kirman1992) and Solow (Reference Solow2008).

5.7 The Credit Market Extensions

Building on the initial set-up presented and tested in Dosi, Fagiolo & Roventini (Reference Dosi, Fagiolo and Roventini2010), the model has been extended (Dosi et al., Reference Dosi, Fagiolo, Napoletano and Roventini2013, Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015), introducing a credit market populated by heterogenous banks in order to study the possible interplays between the real and financial sectors. Such addition allows us to investigate the role of credit in amplifying and triggering macroeconomic fluctuations, possibly leading to the emergence of bank and sovereign debt crises and deep downturns that could affect the long-run performance of the economy (see Levine, Reference Levine1997: explicitly opposing Schumpeter’s view on that). The credit sector is populated by $B$ heterogenous banks, which gather deposits, distribute loans, and own sovereign bonds. In addition, a central bank now sets the baseline interest rate following a Taylor rule.

Banks are heterogenous in their number of clients (drawn from a Pareto distribution). Credit supply is constrained by capital adequacy requirements inspired by Basel-framework rules. Besides the regulatory limit, we assume that banks maintain a buffer over the regulatory capital level, as indicated by the empirical evidence (BIS, 1999). The size of such buffers evolves strategically in order to offset bank financial fragility along the business cycle, and it is proxied by the ratio between accumulated bad debt (i.e. loans in default) and bank assets (i.e. sum of the stocks of loans, sovereign bonds, and reserves held by the bank), $Bd{a}_{k,t}$ . Total credit supply available from bank $k$ at time $t$ therefore is as follows:

$T{C}_{k,t}=\frac{N{W}_{k,t-1}^b}{{\tau }^b(1+\beta Bd{a}_{k,t-1})},$(17)

where $\beta >0$ is a parameter that measures the banks’ speed of adjustment to its financial fragility, and ${\tau }^b$ is the macroprudential regulatory parameter. Credit supply therefore decreases in $\beta$ and $\tau$ and is positively affected by banks’ equity.

Banks allocate credit across firms by ranking them according to their creditworthiness, proxied by the ratio between firms’ past net worth and sales. Loans are granted to firms as long as credit supply is not exhausted. As a consequence, consumption-goods firms may be credit-rationed. Firms’ probability to get a loan depends on their credit ranking as well as on the financial health of their bank. Note that the lower performance of other clients improves firms’ relative ranking, but also has a negative impact on total credit availability, because firms’ defaults weaken the equity of their bank, thus reducing the supply of credit.

We assume that the central bank follows a Taylor rule, which adjusts the interest rate to changes in inflation and, under some revealing policy scenarios, to unemployment, relative to their target levels:

$r_t=r^T+{\gamma }_{\pi }({\pi }_t-{\pi }^T)+{\gamma }_U(U^T-U_t),{\gamma }_{\pi }>1,{\gamma }_U\ge 0,$(18)

where ${\pi }_t$ is the inflation rate of the period, $U_t$ the unemployment rate, and $r^T,{\pi }^T,U^T$ are the target interest, inflation, and unemployment rates, respectively. Banks fix the interest rate on loans by applying a risk premium on the policy rate.

Bank revenues are composed of interests from loans, deposits at the central bank, and sovereign bonds. Gross profits are taxed at the rate $tr$ . Massive loan losses may turn profits negative, reducing the equity of banks and their credit supply. A bank goes bankrupt if firm bankruptcy shocks turn its net worth negative. In such a case, the government steps in and recapitalizes the bank. The public bailout entails a cost ( $Gbailou{t}_{t,k}$ ), equal to the difference between the equity of the failed bank before and after the intervention, which affects the public budget.

Given government tax revenues ( $Ta{x}_t$ ) and expenses, public deficit reads:

$De{f}_t=Deb{t}_t^{cost}+Gbailou{t}_t+G_t-Ta{x}_t,$(19)

where $G_t$ are unemployment subsidies and $Deb{t}_t^{cost}$ is the cost of sovereign debt. Deficits are financed on the bonds market, where banks buy the bonds issued by the government. Banks buy bonds with their net profits; if the total bank savings are lower than the stock of sovereign debt that needs to be refinanced, the central bank buys the residual part.

5.8 The Labour-Market Extension

A series of our contributions (Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2017, Reference Dosi, Pereira, Roventini and Virgillito2018a, Reference Dosi, Pereira, Roventini and Virgillito2018b, Reference Dosi, Pereira, Roventini and Virgillito2019, Reference Dosi, Freeman, Pereira, Roventini and Virgillito2021) have extended the K+S model, accounting for decentralised interactions in the labour market between heterogenous workers and firms. Such interactions occur within different institutions characterising wage-setting rules and labour markets, for example the presence (or not) of minimum wage, unemployment subsidy, firing rules, and so on.

The aggregate supply of labour $L^S$ is still fixed, while the desired labour demand $L_{j,t}^d$ by any consumption-good firm $j$ is determined by the ratio between the desired production $Q_{j,t}^d$ and the average productivity of its current capital stock $A_{j,t}$ (see Section 5.3):

$L_{j,t}^d=\frac{Q_{j,t}^d}{A_{j,t}}.$(20)

A similar process is performed by firms $i$ in the capital-good sector to define $L_{i,t}^d$ , considering effective orders $Q_{i,t}$ and labour productivity in the current machine-producing technique $B_{i,t}$ .Footnote ⁴⁵ Given the existing labour force of the firm $L_{j,t-1}$ , the desired variation of employment $\Delta L_{j,t}^d$ is then calculated as follows:

$\Delta L_{j,t}^d=L_{j,t}^d-L_{j,t-1}.$(21)

Each firm $j$ gets, in probability, a fraction of the applicant workers in its ‘candidates queue’, proportional to its market share $f_{j,t-1}$ :

$\text{E}\left(L_{j,t}^s\right)=\varpi L^S{f}_{j,t-1},$(22)

where $\omega \in R^{+}$ is a parameter defining the number of job ‘queues’ each seeker joins, in average, and $\text{E}\left(L_{j,t}^s\right)$ is the expected number of workers in the queue of firm $j$ . As workers can apply to more than one firm at a time, firms may not be able to hire all workers in their queue, even when they mean to. Considering the set of workers in the candidates queue $\left\{{\ell }_{j,t}^s\right\}$ , each firm has to select to whom to make a job (wage) offer. The set of desired workers $\left\{{\ell }_{j,t}^d\right\}$ , among those in the queue $\left\{{\ell }_{j,t}^s\right\}$ , is defined as:

$\left\{{\ell }_{j,t}^d\right\}=\{{\ell }_{j,t}\in \{{\ell }_{j,t}^s\}:w_{\ell ,t}^r<w_{j,t}^o\text{and}\#\{{\ell }_{j,t}^d\}\le \Delta L_{j,t}^d\},$(23)

that is, the firm targets workers that would accept its wage offer $w_{j,t}^o$ , considering the wage $w_{\ell ,t}^r$ requested (if any), up to its demand of workers $\Delta L_{j,t}^d$ . Therefore, the number of effectively hired workers (the size of set $\left\{{\ell }_{j,t}^h\right\}$ ) is:

$\#\left\{{\ell }_{j,t}^h\right\}=\Delta L_{j,t}\le \Delta L_{j,t}^d\le L_{j,t}^s=\#\left\{{\ell }_{j,t}^s\right\},\Delta L_{j,t}=L_{j,t}-L_{j,t-1}.$(24)

The model allows for different institutional regimes in the labour market. In the first one, which we call ‘Fordist’, there is an implicit pact among firms and workers, implying that the latter never voluntarily quit their jobs, while firms fire employees ( $\Delta Q_{j,t}^d<0$ ) only when experiencing negative profits ${\Pi }_{j,t-1}$ and shrinking production $\Delta Q_{j,t}^d$ . Of course, firms exiting the market always fire all their workers. Conversely, only unemployed workers search for jobs.Footnote ⁴⁶

Wages are not bargained. Firm $j$ unilaterally offers a wage $w_{j,t}^o$ based on past offers according to the following rule:

$w_{j,t}^o=w_{j,t-1}^o[1+max(0,W{P}_{j,t}\left)\right].$(25)

The wage premium $W{P}_{j,t}$ is defined as:

$W{P}_{j,t}={\psi }_4\frac{\Delta A_t}{A_{t-1}}+{\psi }_5\frac{\Delta A_{j,t}}{A_{j,t-1}},{\psi }_2+{\psi }_4\le 1,$(26)

with $A_t$ being the aggregate labour productivity, $A_{j,t}$ the firm-specific productivity, and ${\psi }_4,{\psi }_5\in [0,1]$ the parameters. The gains in labour productivity are then passed to workers via wage increases. Moreover, wages are linked not only to firm-specific performance but also to the aggregate productivity dynamics of the economy. Finally, note that $w_{j,t}^o$ is simultaneously applied to all existing workers of firm $j$ , so there is no intra-firm differential in wages.Footnote ⁴⁷

Another archetype we study is the ‘Competitive’ regime, which can result from the introduction of structural reforms to spur flexibility in the labour market. In the new setting, wages adjust to labour market conditions: firms freely hire and fire in each period, and employees can actively search for better jobs all the time.

The wage $w_{\ell ,t}^r$ requested by worker $\ell$ is a function of the individual unemployment condition and the past wage history. If the worker was unemployed in the previous period, the requested $w_{\ell ,t}^r$ shrinks. More specifically, she will ask for the maximum between the unemployment benefit $w_t^{un}$ (if available) and her own satisfying wage $w_{\ell ,t}^s$ :

$w_{\ell ,t}^r=\left(\begin{array}{cc}max(w_t^{un},w_{\ell ,t}^s)& if\ell isunemployedint-1\\ w_{\ell ,t-1}(1+ϵ)& if\ell isemployedint-1\end{array}\right),$(27)

with the parameter $ϵ\in R^{+}$ . The satisfying wage accounts for the recent wage history:

$w_{\ell ,t}^s=\frac{1}{T_s}\sum _{h=1}^{T_s}{w}_{\ell ,t-h},$

that is, as the moving average salary of the last $T_s\in N^{*}$ periods.

Considering job applications and knowing the required number of workers $\Delta L_{j,t}^d$ to hire, the wage offered by each firm is the minimum that satisfies enough workers in its queue $\left\{{\ell }_{j,t}^s\right\}$ . So, it is the highest wage requested by the cheapest available workers which fulfils $\Delta L_{j,t}^d$ :

$w_{j,t}^o=max{w}_{\ell ,t}^r,\ell \in \left\{{\ell }_{j,t}^s\right\}\text{and}\#\left\{{\ell }_{j,t}^d\right\}\le \Delta L_{j,t}^d.$(30)

Employed workers search for better-paid jobs in each period. If a worker gets an offer from another firm $n$ , she decides whether to quit or not from her current employer $j$ if $w_{n\ne j,t}^o\ge w_{\ell ,t}^r$ . That is, worker $\ell$ quits firm $j$ if she receives a wage offer $w_{n\ne j,t}^o$ from at least one firm $n$ that is equal or higher than her required wage $w_{\ell ,t}^r$ .

Note that, differently from the original version of the K+S model, the market wage is not determined by exogenous institutional factors (see Equation 15), but it is microfounded via the local interactions of heterogeneous firms and workers. The unemployed benefit $w_t^{un}$ is a fraction of the current average wage:

$w_t^{un}=\phi {\bar{w}}_{\ell ,t-1},$(31)

where $\phi \in [0,1]$ is a parameter and ${\bar{w}}_{\ell ,t-1}$ , the past period average wage. The government can also fix an institutional minimum wage $w_t^{min}$ which imposes a lower bound to the firm-specific wage-setting behaviour:

$w_t^{min}=w_{t-1}^{min}(1+{\psi }_6\frac{\Delta A_t}{A_{t-1}}).$(32)

6.1 Macroeconomic Empirical Regularities

The macroeconomic empirical regularities matched by the K+S model are reported in Table 1. First, the generated time series show the emergence of endogenous self-sustained economic growth with persistent fluctuations (SF1, see Figure 3). Business cycles are punctuated by deep downturns (Stiglitz, Reference Stiglitz2014) and, in line with the empirical evidence (e.g. Fagiolo, Napoletano & Roventini Reference Fagiolo, Napoletano and Roventini2008; Ascari, Fagiolo, & Roventini, Reference Ascari, Fagiolo and Roventini2015), the GDP growth-rate distribution exhibits fat tails (SF2, see Figure 4), revealing the coexistence of mild and deep downturns. Moreover, most recessions are short-lived; few last for long periods of time. The distribution of the duration of recessions generated by the model is exponential (SF3, see Figure 5), as found in empirical data (Ausloos, Miskiewicz, & Sanglier, Reference Ausloos, Miskiewicz and Sanglier2004; Wright, Reference Wright2005).

Figure 3 Output, consumption, and investment time series; top: logs; bottom: bandpass-filtered (6,32,12) series, reproduced from Dosi et al. (Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015).

Figure 4 Distribution of real GDP growth rates: binned simulated densities (250 bins, 59,900 observations, circles) vs. normal fit (Dosi et al., Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015).

Figure 5 Exponential fit of recession durations (Dosi et al., Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015).

We then de-trend the macroeconomics series to study their behaviour at the business cycle frequencies. Well in tune with the empirical evidence (e.g. Stock & Watson, Reference Stock, Watson, Taylor and Woodford1999; Napoletano, Roventini & Sapio, Reference Napoletano, Roventini and Sapio2006), the fluctuations of aggregate consumption are smoother than those of GDP, whereas investment is more volatile than output (SF4, see Figure 3, bottom). Moreover, the co-movements between GDP and the most important macroeconomic variables are in line with what is found in real data (SF5, see Table 3): consumption is pro-cyclical and coincident; net investment, changes in inventories, productivity, nominal wages, and inflation are pro-cyclical; unemployment, prices, and mark-ups are counter-cyclical; the real wage is acyclical.Footnote ⁵¹ Finally, R&D investment is pro-cyclical (SF6; see e.g. Walde & Woitek, Reference Walde and Woitek2004).

The K+S models with heterogenous banks (Dosi et al., Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015) match additional stylized facts concerning credit dynamics and banking crises. To begin with, we find that bank profits as well as firms’ total debt are pro-cyclical, while loan losses are counter-cyclical (SF7, see e.g. Lown & Morgan, Reference Lown and Morgan2006; Leary, Reference Leary2009). Moreover, in line with the empirical evidence (Mendoza & Terrones, Reference Mendoza and Terrones2012), we find that credit surges anticipate banking crises: banks’ loan losses are positively correlated with a lag with firm debt, suggesting that higher levels of credit precede bad debt, further depressing banks’ equity (SF8, Foos, Norden, & Weber, Reference Foos, Norden and Weber2010). Finally, the duration of banking crises, defined as a period in which at least one bank fails, has similar qualitative properties as the empirical one (SF9, see Figure 6, as well as Reinhart & Rogoff, Reference Reinhart and Rogoff2009) and the distribution of the ratio of fiscal costs of banking crises to GDP is characterised by excess kurtosis and heavy tails (SF10).

Figure 6 Distribution of banking crisis duration; simulated vs. empirical data. The length of a banking crisis is defined as the number of consecutive years with at least one banking failure in the country (Reinhart & Rogoff, Reference Reinhart and Rogoff2009).

The micro foundation of the labour market structure and dynamics further enriches the list of empirical regularities matched by the model and also debunks the robustness of some other ‘stylised facts’. More specifically, the extended K+S model is able to account for (roughly) the Beveridge curve (i.e. the negative correlation between unemployment and vacancy rates; see Figure 7 showing patterns as rough as the real ones), the Matching function (the positive correlation between vacancy-to-unemployment and job-finding rates; see Figure 8), the Wage curve, and the Okun curve (SF11-14; see Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2017, also for a detailed discussion of the other stylised facts). The model also replicates the analysis performed in Shimer (Reference Shimer2005) concerning the correlation structure between unemployment, vacancy, job finding, separation, and productivity (SF15; see Table 4). On the debunking side, the results from our model add doubts on the robustness of the ‘Phillips curves’ (as already discussed by Solow, Reference Solow1990; see also the recent Ratner & Sim, Reference Ratner and Sim2022), which might indeed be conditional on specific periods and institutional regimes.

Figure 7 Beveridge curve (Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2017).

Figure 8 Matching function (Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2017).

6.2 Microeconomic Empirical Regularities

Beyond accounting for macroeconomic stylised facts, the family of the Schumpeter meeting Keynes models is also able to match the rather long list of microeconomic empirical regularities reported in Table 2.

Let us first consider those concerning the cross-sectional dynamics of firms (Bartelsman & Doms, Reference Bartelsman and Doms2000; Dosi, Reference Dosi, Malerba and Brusoni2007). Rank-size plots and normality tests suggest that cross-section firm (log) size distributions are skewed and not log-normal (SF16; see Figures 9 and 10 and Table 5). Moreover, firm growth-rate distributions are ‘tent-shaped’ (SF17; see Table 6) with tails fatter than the Gaussian benchmark (Table 6; see Bottazzi & Secchi, Reference Bottazzi and Secchi2003, Reference Bottazzi and Secchi2006).

Figure 9 Pooled (year-standardised) capital-good firm sales distributions. Log rank vs. log size plots.

Figure 10 Pooled (year-standardised) consumption-good firm sales distributions. Log rank vs. log size plots.

Turning to firm productivity, again in line with the empirical evidence (Bartelsman & Doms, Reference Bartelsman and Doms2000; Dosi, Reference Dosi, Malerba and Brusoni2007), firms strikingly differ in terms of labour productivity (SF18; compare the standard deviations of labour productivity across firms plotted in Figure 11). Moreover, such productivity differentials persist over time (SF19; see the firm productivity autocorrelations reported in Table 7).Footnote ⁵²

Figure 11 Firms’ Productivity Moments (logs). First panel: capital-good firms. Second panel: consumption-good firms.

The model is also able to generate as an emergent property investment lumpiness SF20; see Doms & Dunne, Reference Doms and Dunne1998; Caballero, Reference Caballero, Taylor and Woodford1999). Indeed, in each time step, consumption-good firms with ‘near’ zero investment coexist with firms experiencing investment spikes (see Figure 12 and relate it to Gourio & Kashyap, Reference Gourio and Kashyap2007).

Figure 12 Investment lumpiness. First panel: share of firms with (near) zero investment; second panel: share of firms with investment spikes.

New microeconomic stylised facts are matched when heterogenous banks and workers are added to the K+S model. Firms’ bankruptcies are counter-cyclical (SF21, see Jaimovich & Floetotto, Reference Jaimovich and Floetotto2008), and the distribution of firms’ bad debt at bankruptcy follows a power law (SF22), in tune with the empirical evidence (Di Guilmi et al., Reference Di Guilmi, Gallegati and Ormerod2004). Finally, the labour-augmented K+S model replicates fat-tailed unemployment time distribution, fat-tailed wage growth rates distributions, and heterogenous worker-skill distributions (SF23–25).

7.1 Tuning the Schumpeterian Engine: Innovation Policy Matters

We start by considering how technology policies concerning firm search capabilities and technological opportunities affect the long-run performance of the economy and also its short-run dynamics (Section 7.1.1). Then we study a set of policies targeting appropriability conditions and the industrial dynamics of the economy (entry and competition; see Section 7.1.2).Footnote ⁵⁴

7.2 Necessity of Keynesian Policies: Demand and Institutions Matter

So far, we have explored the effects of different ‘Schumpeterian’ policies and organisational set-ups over, for example, the rate of growth of the economy, the unemployment rates, and so on. The above sets of experiments clearly indicate that the sources of growth in the model lie in firms’ ability to search efficiently and to develop improved products and processes, significantly affecting also the short-run dynamics of the economy. However, to repeat, such results are conditional on a ‘Keynesian machine’ well in place. What happens if we switch that off?

A first rough but very robust answer comes from the comparison between the foregoing regime with a set-up whereby all ‘Keynesian’ policies are turned off and the system lives under a ‘pure Schumpeterian regime’, holding, however, constant technological opportunities, search rules, and competition dynamics, as in the benchmark model (E7; see also Dosi, Fagiolo, & Roventini, Reference Dosi, Fagiolo and Roventini2010). Turning off the ‘Keynesian’ component implies a major jump to a different phase of the system, characterised by nearly zero growth and enormous fluctuations (see Table 10, column 2). This is because, by sustaining demand during recessions, countercyclical Keynesian policies also smooth investment over the business cycle. Low demand indeed reduces both consumption-goods firms’ investment and capital-goods firms’ R&D expenses, thus rates of innovation and productivity growth. Such a vicious circle of low R&D, low economic growth, and high volatility is in line with previous accounts by Stiglitz (Reference Stiglitz, Shionoya and Perlman1994) and Aghion et al. (Reference Aghion, Askenazy, Berman, Cette and Eymard2008) and Aghion et al. (Reference Aghion, Angeletos, Banerjee and Manova2010), in particular in the presence of credit market imperfections (Aghion, Hemous, & Kharroubi, Reference Aghion, Hemous and Kharroubi2014).

The experiments discussed earlier indicate that Schumpeterian and Keynesian policies affect, together, short-term economic indicators (e.g., output volatility and employment), as well as long-term ones (e.g., GDP growth). Still, these experiments were implemented considering ‘everything else being equal’: an active technology policy was tested, taking as fixed the fiscal side of the model, and the other way round. Could technology policies be a substitute for a lack of fiscal policies? We test this proposition by experimenting with a ‘strong Schumpeterian regime’ (high search capabilities and technological opportunities) combined with a zero fiscal policy scenario (no taxes and unemployment subsidies). Table 10 (column 3) shows that in this case average GDP growth falls by 56% with respect to the baseline. Notice that it is exactly the net effect from both policies. Indeed, the former increases the average GDP growth rate (respectively, by 6% and 25%), while the latter has a negative impact amounting to a 86% cut in the long-run rate of output growth. It follows that Keynesian policies are complementary to Schumpeterian ones, as the latter alone cannot sustain a stable growth path.

In the K+S benchmark model, taxes and unemployment subsidies act as automatic stabilisers, dampening business cycle fluctuations. In experiment E8 (Dosi et al., Reference Dosi, Fagiolo and Roventini2010), we jointly modify the intensity of these stabilisers by altering the tax and subsidy rates $tr$ and $\phi$ (see Section 5.6). Results in Table 10 show the impact of Keynesian fiscal policies upon long-run economic growth and short-run dynamics. In the presence of the ‘good phase’ of the system (to repeat, with positive tax and subsidy; see Figure 13), higher levels of automatic stabilisers do not affect average GDP, but they further stabilise output fluctuations: GDP volatility and unemployment rates fall as taxes and subsidy rates are jointly increased.Footnote ⁵⁷

Figure 13 Fiscal policy experiments (Dosi, Fagiolo, & Roventini, Reference Dosi, Fagiolo and Roventini2010). First panel: average output growth rate. Second panel: bandpass-filtered output standard deviation. Third panel: average unemployment rate (unemp.) and full-employment frequency (full emp.). In such policy experiments, the unemployment subsidy rate ( $\phi$ ) is four times the tax rate.

7.2.1 Fiscal Austerity Rules

Let us now further test the impact of Keynesian fiscal policies by studying the impact of different austerity fiscal rules akin to those implemented in the European Union. We first consider a fiscal rule mimicking the European Stability and Growth Pact (SGP; see Dosi et al., Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015) which constrains the public deficit to 3% of GDP, forcing the government to cut unemployment subsidies until the deficit-to-GDP target is reached. We then introduce the stricter Fiscal Compact (FC) rule, where the the SGP deficit limit is supplemented by a debt-reduction rule: if the ratio of public debt to GDP is over the SGP target of 60%, it should be reduced by 1/ 20th (5%) of the difference between the current and target levels in every year.Footnote ⁵⁸ In both regimes, unemployment benefits are eventually cut to comply with the fiscal rules. In line with the European Union fiscal framework, we introduce escape clauses ( $SG{P}_{ec}$ and $F{C}_{ec}$ ) which freeze austerity rules in case of negative GDP growth. Finally, we account for the possible existence of a positive feedback mechanism going from the level of public debt to its financing cost by adding a risk premium to the interest rate on sovereign bonds. In such a scenario with the FC fiscal rule ( $F{G}_{ec}^{spread}$ ), ‘frugal’ governments should pay a lower interest rate on their stock of public debt.

The results from the fiscal rule experiments (E9; see Table 11) point, again, to the necessity of active fiscal policy to stabilise the economy and achieve steady growth. Indeed, we find that in the ‘harsh’ case, when the $SGP$ fiscal rule is applied, average GDP growth is halved compared to the baseline scenario, and GDP volatility and unemployment are respectively 14 and 5 times higher. Moreover, the public-debt-to-GDP ratio explodes due to the joint expansion of debt and the shrinkage of output, showing the self-defeating effect of fiscal discipline policies. The negative impact of austerity fiscal rules is even more harmful in the Fiscal Compact scenario. When escape clauses are present ( $SG{P}_{ec}$ e $F{C}_{ec}$ ), the long-run harmful effects of fiscal discipline disappear, but volatility and unemployment rates are still significantly higher with respect to the case where fiscal policy is unconstrained (see Table 10). These findings shed light on the non-linear effects of fiscal policies on GDP growth (see Figure 13), as the halt to fiscal support during recessions is likely to transform them in depressions. Finally, the results are also robust when the spread on sovereign bonds is linked to the ratio between public debt and GDP ( $F{G}_{ec}^{spread}$ ): austerity rules worsen both short- and long-run economic dynamics without improving public finances.Footnote ⁵⁹

Table 11 Fiscal policy experiments. Normalised values compared to the benchmark across experiments, for 100 simulation runs. Absolute value of the $t$ -statistic in parentheses; (**) significant at 5 level, (*) significant at 10 level.

Experiment	E9
	SGP	${\text{SGP}}_{\text{ec}}$	FC	${\text{FC}}_{\text{ec}}$	${\text{FC}}_{\text{ec}}^{\text{spread}}$
GDP growth	0.527**	0.995**	0.572**	0.992**	0.997**
	(6.894)	(0.876)	(6.499)	(1.388)	(0.524)
GDP volatility	14.645**	1.408**	16.204**	1.624**	1.530**
	(7.466)	(5.856)	(7.848)	(7.166)	(6.962)
Unemployment	5.692**	5.706**	1.419	1.948**	1.679**
rate	(8.095)	(2.088)	(7.585)	(3.928)	(3.139)
Public Debt/GDP	$+\infty$	1.763**	$+\infty$	4.078**	2.590**
		(0.774)		(2.472)	(1.483)

One of the advantages of employing agent-based models to study economic problems is the possibility of zooming upon the microeconomic level to better understand the emergent properties observed at the macro level. The wealth of microeconomic data generated by the simulations can indeed be employed to build new statistics which can shed light on macroeconomic dynamics. This is what we do with the microeconomic indicators displayed in Table 12, which allow us to study the underlying micro-level mechanisms at the origin of the aggregate outcomes observed when fiscal rules are in place (see Dosi et al., 2016). First, we consider the consumption-good sector. We find that firms’ investment rate falls due to the lower consumption demand. This slows down the diffusion of the new vintages of machines with state-of-the-art technology thus depressing productivity growth. The negative impact of austerity policies percolates to the capital-good sector. There, the lower sales experienced by capital-good firms reduce their R&D investment. As a result, innovation falls, slowing down the productivity growth of the industry (see Table 12). The reduced creation and diffusion of innovations imply that the best vintage stays undisputed for a longer period, and the productivity frontier grows at a slower pace. Indeed, this represents a power evidence of the (virtuous or perverse) feedback between the ‘Keynesian’ demand-generating mechanism and the long-term movement of the technological frontier.

Table 12 Fiscal rule – microeconomic indicators. Normalised values compared to the benchmark across experiments, for 100 simulation runs. Absolute value of the $t$ -statistic in parentheses; (**) significant at 5 level, (*) significant at 10 level.

Experiment	E9 Fiscal rule SGP
Innovation creation in the capital-good sector
Share of successful innovators	0.946**	(2.762)
Productivity growth	0.980**	(2.269)
Productivity dispersion	0.917**	(6.538)
Innovation diffusion in the consumption-goods sector
Productivity growth	0.889**	(3.912)
Productivity dispersion	0.865**	(3.429)
Investment rate	0.973	(1.275)
Duration of best vintage	1.037**	(3.927)
Productivity growth best vintage	0.954**	(34.446)
Relative distance between	0.970**	(2.432)
best and worst vintages

7.2.2 Labour Market Reforms

In contrast to DSGE models, macroeconomic agent-based models can easily test different combinations of policies concerning the labour and credit markets. We undertake two sets of policy experiments. In the first one, we study the interactions between fiscal policies and different labour-market institutions governing wage formation, firm firing rules, etc. (E10). In the next section, we will present the second policy combination scenario, where we interact fiscal policies with monetary policy rules (E11).

How do labour market institutions affect the short- and long-run performance of the economy and interact with fiscal policy rules? In the ‘Fordist’ regime, the labour-augmented K+S model presented in Section 5.8 depicts a scenario where (i) wages are insensitive to the labour-market conditions and indexed to aggregate and firm-specific gains; (ii) there is a sort of covenant between firms and workers concerning ‘long-term’ employment, as firms fire only when their profits get negative, while employed workers do not seek for alternative occupations; (iii) labour market institutions contemplate a minimum wage fully indexed to aggregated economy productivity and unemployment benefits financed by taxes on profits. The ‘Fordist’ regime captures the main features of the Trente Glorieuses (roughly the three decades after World War II) characterised by low probability of workers being fired, wage dynamics mostly rigid to the business cycle, wage growth rate indexed upon productivity growth, a shrinking degree of inequality, and significant, tax-based unemployment benefits.

At the opposite end when the labour market is characterised by the ‘Competitive’ regime, (i) flexible wages respond to unemployment and market conditions; (ii) firms have a stronger bargaining power with regard to wages and employment, which they seamlessly adjust according to the planned production level; (iii) employed workers search for better paid jobs; (iv) the minimum wage and unemployment benefit institutions are weaker or even absent. The Competitive scenario is akin to the labour market presented in introductory-level Neoclassical economics textbooks and it captures the structural reforms suggested by the Washington Consensus and the European Union (Fitoussi & Saraceno, 2013).

We simulate the model in the Fordist and Competitive regimes (see Table 13). Simulation results show that labour market flexibility worsens the performance of the economy both over short- and long-run horizons. Indeed, the unemployment rate is higher in the Competitive regime, while the Fordist regime entails stronger productivity and output growth. Note that the degradation of economic performance increases with the degree of labour-market flexibility: in Dosi et al. (Reference Dosi, Pereira, Roventini and Virgillito2017) we find that in the Competitive scenario nearest to ‘market perfection’ (absence of minimum wage, unemployment benefits, and employment protection rules), the modelled economic system is most of the time near to collapse with basically zero long-term economic growth and extremely high unemployment rates and volatility. This result is in line with those obtained earlier when the Keynesian machine is switched off. Moreover, we find that hysteresis is much more likely to emerge in the Competitive regime, thus worsening macroeconomic dynamics at all frequencies (see Figure 14 and the results in Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2018a).

Table 13 Labour-market reform experiments. Normalised values compared to the benchmark across experiments, for 50 simulation runs. P-values in parentheses; (**) significant at 5 level, (*) significant at 10 level.

Experiment	E10
	Fordist (baseline)	Competitive (ratio)	Competitive & Fiscal Compact (ratio)
GDP growth	0.02	0.78**	0.68**
		(0.01)	(0.00)
GDP volatility	0.11	0.86**	1.19**
		(0.01)	(0.00)
Unemployment rate	0.02	8.93**	10.96**
		(0.00)	(0.00)
Profit share	0.22	1.02**	1.03**
		(0.00)	(0.00)
Income concentration	0.05	3.60**	5.09**
		(0.00)	(0.00)

Figure 14 GDP long-term trend recovery after crisis (Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2019). Typical simulation run. Top: Fordist; middle: Competitive; bottom: Competitive and Fiscal Compact rule. Dashed line: pre-crisis trend | grey boxes: trend recovery period.

The negative impact of the Fiscal Compact rule is magnified when the labour market is characterised by a higher level of flexibility (see Table 13).Footnote ⁶⁰ Indeed, the policy combination of austerity rule and competitive labour-market reforms permanently damage the GDP growth trajectory and spur unemployment, leading to the emergence of super-hysteresis (see Figure 14; Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2018a and Cerra et al., Reference Cerra, Fatás and Saxena2023). Also in this case austerity policies are self-defeating, leading to higher levels of public debt (see the detailed analysis in Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2019). To sum up, our results clearly show that the policy combination grounded on ‘structural reforms’ to increase labour flexibility and austerity fiscal policies (the so called Berlin–Washington consensus; see Fitoussi & Saraceno, Reference Fitoussi and Saraceno2013) have a deeply negative impact on the short- and long-run performance of the economy, and also on public finances.

7.2.3 Monetary Policy

In the foregoing experiments, the central bank followed a ‘conservative’ monetary policy as it applied a standard Taylor rule which adjusts the baseline interest rate only to the inflation gap ( $T{R}_{\pi }$ ; see Eq. 18). In line with the recent monetary policy strategy of the Federal Reserve (Yellen, Reference Yellen2014), we now let the central bank follow a dual-mandate monetary policy ( $T{R}_{\pi ,U}$ ) by including an adjustment to the unemployment gap ( ${\gamma }_U>1$ ), with a 5% unemployment rate target (E11).

Simulation results reported in Table 14 show that when fiscal policy is unconstrained and the central bank commits to both price and employment stabilisation, monetary policy positively affects the performance of the economy. When the SGP fiscal rule is activated, the positive impact of the dual-mandate monetary policy is reinforced, as it contributes to alleviate the pains caused by fiscal-consolidation policies and to stabilise public finance. The dual-mandate Taylor rule dominates the conservative one also in the presence of the FC rule, when fiscal clauses are activated and when the bond-spread channel is taken into account.Footnote ⁶¹

Table 14 Monetary policy experiments. Normalised values compared to the benchmark across experiments, for 100 simulation runs. Absolute value of the $t$ -statistic in parentheses; (**) significant at 5 level, (*) significant at 10 level.

Experiment	E11
	${\text{norule,TR}}_{\pi ,\text{U}}$	${\text{SGP,TR}}_{\pi }$	${\text{SGP,TR}}_{\pi ,\text{U}}$
GDP growth	1.019**	0.527**	1.014
	(3.730)	(6.894)	(1.157)
GDP volatility	0.865**	14.645**	2.760**
	(6.018)	(7.466)	(2.401)
Unemployment rate	0.322**	5.692**	0.909
	(5.903)	(8.095)	(0.555)
Public Debt/GDP	−50.648**	$+\infty$	−45.545**
	(30.377)		(9.011)

The better performance of the $T{R}_{\pi ,U}$ rule over the $T{R}_{\pi }$ depends on the presence of bank credit transmission channels of monetary policy (see e.g. Bernanke, Gertler, & Gilchrist, Reference Bernanke, Gertler, Gilchrist, Taylor and Woodford1999 and Boivin, Kiley, & Mishkin, Reference Boivin, Kiley, Mishkin, Friedman and Woodford2010) due to the interaction of the dual-mandate monetary policy with the Basel rule governing changes in credit supply (see Eq. 17). By reducing the pro-cyclicality of the Basel macroprudential rule, the dual mandate therefore compensates its destabilising effect and provides both banks and firms with a stronger financial record at the eve of an economic crisis. Indeed, with a dual-mandate monetary policy rule, the interest rate goes up during expansions as a response to low unemployment levels. This boosts banks’ profit margin and net worth, while cooling down firms’ borrowing. When the downturn arrives, the interest rate goes down and loan losses increase. However, banks’ capital buffers allow them to better resist the negative shocks and provide more credit vis-à-vis the conservative Taylor rule scenario.

7.3 Income Inequality and Policy Effectiveness: Distribution Matters

In macro agent-based models, policy experiments can be performed in alternative scenarios concerning the structural and institutional characteristics of the economy, as well as with respect to personal and functional income distributions. Admittedly, all the incumbent K+S models are constrained by the assumption of initial levels of mark-ups of the firm which partly ‘anchor’ the average functional income distribution thereafter. This indeed is a drawback to be overcome in the near future. Still, even under this limitation, it is highly informative to study the impact of alternative combination of policies on the level of functional income inequality in the economy (E12), and, even more so, on the personal distribution with respect to wage earners.

The policy experiments performed so far have been carried out for a given level of income inequality. Indeed, the firm-specific mark-ups of consumption-good firms fluctuate around the initial peg; see Eqs. 11 and 12. By tuning up and down the level of the initial mark-up rate, we can (admittedly, still in a rudimentary way) change the long-term functional income distribution. This allows us to study how inequality affects the dynamics of the economy, as well as the results produced by the different mixes of policies spotlighted in the previous section. In Dosi et al. (Reference Dosi, Fagiolo, Napoletano and Roventini2013), we found that a higher level of inequality in the wage/profit distribution increases the effects of fiscal policies. This is in line with many works suggesting that increasing levels of inequality have contributed to depress aggregate demand and to weigh down private indebtedness, thus setting the stage for the Great Recession (Fitoussi & Saraceno, Reference Fitoussi and Saraceno2010; Stiglitz, Reference Stiglitz2012; Kumhof & Rancière, Reference Kumhof and Rancière2015).

Given such premises, let us study how our target variables evolve when we modify the income distribution under the benchmark scenario where fiscal rules are not activated and the central bank follows a conservative Taylor rule. First, rising firm margins, reflected, of course, by higher income inequality, impact aggregate demand, and they thus affect macroeconomic dynamics (see Figure 15). If, on the one hand, the average GDP growth rate is stable for different levels of mark-up, on the other hand, the (slightly) U-shape pattern displayed by GDP volatility, unemployment rates, likelihood of economic crisis and public-debt-to-GDP ratio reveal the existence of two ‘regimes’. When mark-ups are low, firms have a reduced ability to finance their investment with their own accumulated profits and rely more on credit, increasing the size of banks and the cost of banking crises. Therefore the size of the banking sector is negatively associated with the mark-up rate. If mark-ups are too low, firms’ higher failure rates weaken the banking sector, thus curbing the supply of credit. As a consequence, a higher proportion of financially constrained firms reduces production and investment, leading to higher unemployment rates. When income distribution is too skewed towards profits, firms do not invest because demand is too low. This spurs GDP volatility, unemployment, and public debt (Dosi et al., Reference Dosi, Fagiolo, Napoletano and Roventini2013 and Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015).

Figure 15 Income distribution and macroeconomic dynamics (Dosi et al., Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015). Confidence-interval bands are shown in a lighter colour and are computed as plus or minus two Monte Carlo standard errors.

Let us now consider the impact of fiscal rules across different functional inequality scenarios. Income distribution and fiscal policies can interact via two channels. First, tighter limits on budget deficits can further depress aggregate demand, thus worsening firms’ financial constraints and increasing the likelihood of banking crises which require public bailout. Second, when the income distribution is more biased towards profits, fiscal policy is more needed to sustain an (otherwise low) consumption demand (see Dosi et al., Reference Dosi, Sodini and Virgillito2015). Simulation results show that for every level of functional income inequality, the SGP and FC fiscal rules increase the instability of the economy (see Figure 16) and inflate the ratio between public debt and GDP. Moreover, fiscal discipline appears to be more harmful as the income distribution becomes more biased towards profits. Indeed, even if in this regime firms have access to both internal and external financial resources, they do not invest for a lack of aggregate demand, which in turn reduces the average GDP growth rate and leads to the explosion of the public-debt-to-GDP ratio.Footnote ⁶² Further exercises suggest that when the escape clauses are in place, they prevent the activation of fiscal rules up to 40% of the periods (Figure 16, bottom right), thus reducing their negative impact on the dynamics of the economy. Nonetheless, in line with our previous results, the economy keeps on being more unstable and we keep observing a perverse effect of fiscal rules on public debt. Such results are also confirmed in the sovereign bond-spread adjustment scenario.

Figure 16 Fiscal rule experiments (Dosi et al., Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015). Confidence-interval bands are shown in a lighter colour and are computed as plus or minus two Monte Carlo standard errors.

How does monetary policy interact with income inequality? In the presence of unconstrained fiscal policies, the dual-mandate Taylor rule outperforms the ‘conservative’ one for every level of inequality without leading to inflation spirals (see Figure 17). Which mechanisms are responsible for such dynamics? With a dual-mandate Taylor rule, the banking sector performs better, as the economy is characterised by a higher share of investment projects that are financed and implemented and a lower rate of banking failures. Lower unemployment pushes interest rates up, thus increasing banks’ profitability, while tightening firms’ constraints to invest. The increase of the interest rate cools down aggregate demand during booms, while improving the net worth of the banks, leading to a higher supply of credit when the economy experiences a downturn.

Figure 17 Monetary policy experiments (Dosi et al., Reference Dosi, Fagiolo, Napoletano, Roventini and Treibich2015). Confidence-interval bands are shown in a lighter colour and are computed as plus or minus two Monte Carlo standard errors.

Finally, the labour-augmented K+S model allows one to account for the evolution of both functional and personal inequality as heterogeneous workers can earn different wages. We find that the negative impact on economic dynamics of ‘structural reforms’ designed to increase the flexibility of the labour market reflects also in an increase of the profit share and in a higher personal income concentration (see Table 13). This is in line with the recent empirical evidence on the impact of policies to flexibilise the labour market (see, e.g., Hoffmann, Malacrino, & Pistaferri, Reference Hoffmann, Malacrino and Pistaferri2022; Daruich, Di Addario, & Saggio, Reference Daruich, Di Addario and Saggio2023). Not surprisingly, functional and personal inequalities further increase when fiscal austerity rules are applied to economies characterised by ‘Competitive’ labour markets.

7.4 Which Policies for Smooth Inclusive Growth?

The results presented in this section using the Schumpeter meeting Keynes models as a laboratory for simulation experiments illustrate how macreoeconomic agent-based models are a powerful and flexible tool for policy analysis. In particular, ABMs allow one to jointly test different ensembles of public interventions, for example innovation, industrial, fiscal and monetary policies, as well as market reforms. Moreover, the impact of policies can be studied at different frequencies, taking into account both their effect on business cycles and their influence on growth dynamics. Policy exercises can be conditioned to different institutional scenarios as shown by our experiments with alternative labour market regimes and different levels of income inequality. Naturally, actual decision makers can be effectively involved in the process of the design of macro agent-based models for policy evaluation (Moss, Reference Moss2008).

The results of the battery of policy exercises carried out with the K+S models exploit its capability to bridge Schumpeterian theories of technology-driven economic growth with Keynesian theories of demand generation. First, innovation and industrial policies affect both the long- and short-run performance of the economy. However, such policies tuning the ‘Schumpeterian engine’ are not sufficient to maintain the economy on a high-growth/near full-employment path. Indeed, the endogenous innovation engine is able to do that only in the presence of a ‘Keynesian’ demand-generating engine, which requires a policy mix comprising (i) an unconstrained fiscal policy, where automatic stabilisers are free to dampen business cycle fluctuations; (ii) a monetary policy targeting both price and employment stability; (iii) ‘rigid’ labour market institutions (strict firing rules, minimum wage, etc.). Such a policy combination is able to achieve lower unemployment and output volatility cum higher productivity and GDP growth.

More generally, our results dispose of the traditional dichotomy between variables impacting the long run (typically, ‘supply-side’ technology-related changes) and variables with a short-term effect (traditional demand-related variables). On the contrary, technological innovations appear to exert their effects at all frequencies. Conversely, Keynesian demand-management policies do not only contribute to reduce output volatility and unemployment rates, but they affect also long-run growth rates insofar as they contribute to ‘delock’ the economy from the stagnant growth trajectory, which is indeed one of the possible emergent meta-stable states linked to the structural characteristics of the economy such as functional income inequality. In that, the policy analysis exercises carried out with the K+S models are well in tune with the mentioned empirical evidence showing the ubiquitous presence of hysteresis in macroeconomic dynamics (Dosi et al., Reference Dosi, Pereira, Roventini and Virgillito2018a; Cerra et al., Reference Cerra, Fatás and Saxena2023).