Why complex, data demanding and difficult to estimate agent based models? Lessons from a decades long research program

In the wake of the Keynesian revolution, large-scale macroeconometric modelling became the big business of the economics profession. There were business cycle macro models, and input-output sector models of the Keynesian & Leontief (K&L) type driven by demand, the ultimate manifestation of which was perhaps the Brookings Model of the 1970s, managed by Prize winner Lawrence Klein. This model was eventually linked up with a collection of other national and similarly structured models to an enormous global model.

It did not take long, however, for critical comments to emerge, notably about the unclear microfoundations of such macro models, the wasteful neglect of existing microdata that came with aggregation, and in general their empirical credibility and meaningfulness. What could they really be used for?

The microsimulation approach pioneered by Orcutt (1957, 1960, 1980) was one response to this critique. Orcutt’s disapproved of the erroneous assumptions underlying macro modelling. Only under extreme and unworldly assumptions about “elemental decision-making units” would macro relationships be theoretically acceptable, but those aggregates meant “a disastrous loss of accuracy of representation”. Klevmarken (1978, 1983) also regretted the unnecessary loss of available microinformation that came with aggregation for macro modelling, and that simulation experiments on the Swedish agent-based macroeconomic model, referred to as the “Reference model” in what follows (Section 2), already at that time had obviated. This critique was reiterated in the 1977 Stockholm microsimulation conference, perhaps the first ever, where Bergmann, Eliasson, and Orcutt (1980) stated “that a criterion of good theory in economics can only be how well-grounded in relevant, empirical facts it is” (op. cit. p. 12), and the obvious fact is that economic agents such as individuals, households and business firms are different, and that the role of this heterogeneity should be recognized in good modelling. On this Citro & Hanushek (1997) argued that sufficient knowledge of micro unit behaviour (in their case households) was not yet available for accurate specification of Micro based Macro systems models. Research should, therefore, focus on obtaining better data and estimation procedures, and less on modelling based on assumptions.

Empirically well-grounded economic systems models featuring heterogeneous agents competing in dynamic markets, and growth through endogenous entry and exit (“selection”) soon run up against difficult problems of achieving statistically controlled parameter estimates. The modeller therefore often chooses to simplify the model, and instead faces the perhaps even more serious problem of mis-specification. With sufficient data and enormous future computer capacity the estimation problems of complex, selection based and non-linear models should, however, in principle be solvable. A richly parameterised model would therefore be the right reference for empirically credible and open-minded theorising (see Section 5 on Surprise Economics). Then, there would be no need for macro models at all, since the process of aggregating behaviour in markets would be endogenised within the micro-based model, and aggregation would be reduced to summing up the outputs at the end. There would even be reasons to expect that most macroeconomic relationships would not be compatible with the inherent relationships of an empirically well-grounded micro-based economic systems model (see Section 3). However, the ambition of empirical credibility may still be out of reach as of today, implying a need to state objectively how to make empirical sense of less than perfectly calibrated complex models (Eliasson, 2016, 2017a; Hansen & Heckman, 1996).

The Citro & Hanushek (1997) observation of lack of knowledge about household behaviour was even more appropriate for the state of knowledge about business firm behaviour. While the birth, the life and the death of individuals concern well-defined entities, the life of business firms is that of constant structural transformation through mergers, acquisitions and divestitures. And indeed, demand for a better understanding of the nature and roles played by business firms in long-term economic development was the chief reason for initiating the project that led up to the Reference model of this essay (Section 2). Likewise, early on questions were asked about the economy-wide, long-term consequences of micro-interventions in the economy, and prompted the quantitative inquiry into the Swedish industrial support program of the 1970s and 1980s, that was based on the Reference model (Section 6). In a historical perspective, seemingly minor occurrences in the distant past, like a clustering of successful entrepreneurial activities, or the establishment of a new institution that improved the allocative performance of markets, may have nudged the entire economic system onto a different historical trajectory than it would otherwise have taken (Section 7). The Reference model described in the next section (Section 2) has been found to be appropriate for the quantitative study of the economic systems consequences such very long-term courses of irreversible events between consequences and such.

During the more than 40 years course of the project leading up to the Reference model, we have studied how heterogeneous and quite ignorant agents (firms) compete in more or less open markets, thereby dynamically coordinating the evolution of the model economy along growth trajectories, the successful outcomes of which depend significantly on how agents are born (entrepreneurial entry) and die (exit) along the way to form more or less successful business clusters. These growth dynamics involve integrating familiar, often trivially true principles of economics. I conclude below that understanding such economic systems dynamics is not possible without understanding that market-based integration, and to do that mathematical simulation is the appropriate analytical tool. Even though simulation is a concept that has been subject to a large philosophical literature as computers have become increasingly capable (Fontana, 2006), for me mathematical simulation is a branch of mathematics that is particularly suitable for addressing complex theoretical and empirical economic systems problems.

With this paper I, therefore, start afresh from the ambitions voiced at the 1977 conference that I was myself involved in formulating: (1) one theoretical, emphasising the need for empirically well-grounded prior theory, and (2) another, concerned with the unavoidably “false” assumptions underlying macro theory (Section 3). I will ask: what kind of theoretical foundation should a relevant micro-based economic systems model stand on? How should aggregation over markets of micro behaviour be made a natural part of total economic systems dynamics? How intellectually restrictive is the economist’s standard mathematical toolbox, the calculus of optimisation? What analytical potential does simulation mathematics offer in enhancing the understanding of economic behaviour? How can existing, often diverse and taxonomically incompatible microdata be combined for maximum information access? Perhaps most important of all: what usefulness is added by those complex, analytically non-transparent and difficult to estimate micro-based economic systems models when there are so many analytically transparent and familiar partial models, the parameters of which can be readily estimated?

In the choice between well-grounded, and easy to estimate models, complexity therefore often becomes an accepted excuse to simplify the model on a “false” partial, static or linear format, resulting in an unclear mixture of inaccurate specification, badly defined behavioural parameters, and doubtful empirical credibility about what the analysis has to say.

What kind of trade-off is there between perfectly estimating the wrong model, and imperfectly estimating (“calibrating”) a Micro based Macro economic systems model, that is based on empirically well-grounded prior assumptions?

One example: Currently worries of technological mass unemployment, or “The March of the Machines” has returned in the economic debate. This time artificial intelligence (AI) causes worry (The Economist, 2016). Some 40 years ago, however, mass unemployment caused by the then new micro-electronics technologies worried even famous economists (Leontief, 1982). Since the workers destroyed the textile machines during the early industrial revolution, every half-century or so has seen technological unemployment return for debate. Since “job destruction” and “new job creation” usually occur in different industries, at different places and with a time lag, compared to the firms laying off workers because of technological advance, narrowly defined partial and static sector or macro models have little to tell on this issue. The first serious use of the Reference model occurred when the Swedish Government Committee on Computers and Electronics (DEK) asked the Industrial Institute for Economic and Social Research (IUI, now IFN), of which I had just become the director, to calculate the economy-wide long-term employment consequences under different labour market regimes, of the introduction of new microelectronic technologies (Eliasson, 1979). The conclusion was that technologically laid off labour would soon be employed elsewhere, and the socially by far most costly policy (in terms of lost output) was to prevent the introduction of new technologies and/or delay the immediate unemployment effects caused by them.

I will proceed in the next section to introduce the Reference model, a complex, evolutionary economic systems model on which the economy-wide long-term consequences of the endogenous “birth, life and death of business agents” can be studied. I will then choose four case illustrations, among many possible, the understanding of which requires such a model as a minimum, and for the study of which the Reference model has been applied. I address them in order of what I regard as important and representing great opportunities in agent-based economic modelling: (1) to evaluate the empirical credibility of “surprise outcomes” of simulations, not yet observed, or not yet thought of, because they are not subsumed within traditional and more narrowly defined partial, static, linear and/or macro models; (2) to quantify the long-term costs and benefits of large structure changing micro-interventions in the economy; (3) to study the micro origin of long-term historic evolutions of an economic system, that is addressing the question: what would have happened under alternative initial circumstances?; (4) to support generalising from case study observations.

I consider the first theoretical application especially intriguing, the upshot being that good economic theory and good models, besides being empirically credible, should comprise surprise analytical outcomes. From the beginning in 1974 the Reference model also had a dominant theoretical orientation with a strong, but novel basis in traditional economic principles. The focus was on the complex economic systems consequences of the integration of those principles, which were studied numerically using simulation mathematics. The unique dynamic properties of the Reference model originate in the integration of Schumpeterian entrepreneurial economics with the dynamics of sequential feedback of the Wicksellian/Stockholm School emphasising the difference between ex ante plans and ex post outcomes, Keynesian demand feedback of all income (wages and profits) conveyed to the household sector and taxes collected by the public sector, with a touch of Kaldorian technical change. In fact, I will argue in Section 2 that the integration of those principles in the three markets of the model is what makes up an evolutionary model.

My conclusions will also be that the use of mathematical simulation to study complex economywide dynamic agent-based economic systems theoretically and empirically is a neglected field in mainstream economics and deserves much-increased attention there.

The Reference model has been extensively published over the years. Since recent presentations can be easily accessed, details need not be repeated here. I give a brief overview, and background on some specifics related to the four applications chosen. There are also some pertinent links to the literature of economic doctrines. Since many people have been involved in the modelling project over its soon 45-year lifespan, the reader has to excuse me for being somewhat personal at places.

2.1 Origin and background

The origin of the Reference model dates back to late 1974 when I was approached by Thomas Lindberg, then a director at IBM Sweden, who wondered why so little attention was being paid to large-scale economic modelling in Sweden and asked me to consider setting up such a model for the Swedish economy. I was at the time involved in a study on economic planning and budgeting in large western companies (published as Eliasson, 1976a) and had a pretty good idea of how to structure a model of firm decision making. My condition for engaging in such an academic modelling venture was that the model be micro firm based, explicitly representing aggregation in markets up to the macro level, and be capable of portraying the dynamics of an evolving capitalist market economy. IBM took me around the academic world to check up on what was going on in the field, visits notably reaching out from IBM’s own research centres with a social science orientation in San Jose (USA), Pisa (Italy), and Peterlee (England). One desideratum was that the model venture should not be a replication of something already achieved. There was a general agreement that this was an obvious novel approach to take. The study trips confirmed that there was no such project, excepting Barbara Bergmann’s Transactions Model of the US economy, in the research pipeline at the time. I am particularly grateful to Kenneth Arrow who helped me to get in contact with unorthodox economists in the US. Those contacts led me to Barbara Bergmann and Guy Orcutt in particular, but also to several heretic theoretical economists, among them Richard Day, Harvey Leibenstein, Herbert Simon and Sidney Winter. Winter (1964) was especially supporting in my ambition to begin building an economy wide systems model from a micro firm platform, and with a Darwinian orientation.

The deal with IBM was unlimited programming and computer support for two years. The IBM view was that computer simulation would eventually, if not soon, become the dominant mathematical tool in economics, as it was already becoming in natural sciences and engineering. I was then the head of the Economic Policy Department, and the Chief Economist of the Federation of Swedish Industries, which meant that I had a budget for statistical studies, mostly to support economic forecasting. Even though we soon realised that business cycle forecasting would not be an interesting application of this model, interest in the business community was very positive because the model, contrary to the then all pervasive macroeconomic models of academia and government, promised to confer an explicit role in the industrial and economic analysis to entrepreneurs and businesses.

The preference of the sponsors was that the model is empirically based. And I realized from the beginning that it would not be possible to secure academic funding for such a project in Sweden, so this was an opportunity not to be missed. The project so conceived was of course a reckless venture. I secured an OK from the then President of the Federation of Swedish Industries, Axel Iveroth, to proceed, and to integrate the modelling project with the business forecasting activities of my department. The University of Uppsala, and my previous professor Ragnar Bentzel, became the third party in the modelling venture.

Thanks to IBMs very effective research management practice of assigning at least one highly educated staff member on the task of being “actively interested in the project”, the IBM part of the project was successfully concluded within the two year period.¹ I was especially intrigued by the ease with which I could discuss empirical relevance and technical problems of the model with IBM staff with an engineering degree. While the endogenous growth generating micro core of the model, as specified in Eliasson (1976b), has needed few modifications, the modular design of the entire model has allowed a naturally integrated extended superstructure to be built around it (see Figure 1), the monetary system being one example, later extended with an integrated stock and financial derivatives market, and a rudimentary venture capital market, as a first step towards modelling a complete innovation commercialising process, a competence bloc (Ballot, Eliasson, & Taymaz, 2006; Taymaz, 1999, and see Section 5.1).

Figure 1

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The Reference model described in this article is constructed from bottom up on the basis of empirical evidence on the behaviour of firms collected by myself and documented in Eliasson, (1976a), which not only provided the specification of a firm model (op. cit. Chapter XI) but also the taxonomy of the consistent Micro to Macro database needed (see Albrecht et al., 1992). To feed the Reference model with a high quality microdata foundation, my department at the Federation launched what we called the “Planning Survey” to all large Swedish manufacturing firms and some smaller ones, together covering more than 80 percent of Swedish manufacturing output. Questions were formulated to be compatible with both the firm decision model and with the taxonomy of the internal statistical systems of firms, as I had learnt and documented in Eliasson (1976a). The Planning Survey also became very useful for the Federation, and the backbone of its economic forecasting activity.

Thanks to two (one after the other) very skilled computer engineers at IBM, Mats Heiman and Gosta Olavi, the model was coded (in APL) and up and running on synthetic data already in 1975, and loaded with real firm data from the Planning Survey of the Federation of Swedish Industries in 1976. The first data set 1974–1976 was published in Virin (1976), and used to run the model for my 1977 article on the economy wide consequences of regulations and competition processes in the labour market. When I became the Director of the IUI (now IFN) in 1977 the resources of the research institute became available, and over the years several researchers at the institute have on and off worked with the Reference model and its database, among them I should mention Jim Albrecht, Ken Hanson, Thomas Lindberg, and most important Gerard Ballot, Bo Carlsson and Erol Taymaz. The model was soon ready and set up for experimental, “semi empirical” applications, and continued work would largely be supported by external funding, notably for Government committee projects. The Federation, however, continued to conduct the annual Planning Survey, for its own business cycle forecasting activity.

IBM now appears to have largely abandoned its ambitions in the social science modelling field, and micro firm based economic systems modelling has taken a long-term to catch on in academia (see Section 4). The Reference model has, however, survived thanks to a number of academic researchers that have improved upon its modular structure, and used it for empirical inquiries. Gerard Ballot, Bo Carlsson, Dan Johansson and Erol Taymaz should be particularly mentioned.

Interestingly, after the IBM period the Reference model has not had a separate budget, but has been largely self-financed through government committee work and related data gathering projects. The model has found a number of useful applications, from a study for DEK, in a joint project between IVA and IUI, financed by the Swedish Board of Technical Development (STU) (Carlsson, 1981; Carlsson, Dahmén, Grufman, Josefsson, & Örtengren, 1979), which also provided a critical dataset on global best practice technology for the model, to analytical work for the DEK (Eliasson, 1979, 1980a, 1980b, 1981), to the ambitious cost benefit study on the industrial support program that will be presented in some detail below, and to several OECD studies (Carlsson, 1991; Eliasson, 1987, 1997). For several years, IUI had three economy wide models up and running; the Reference model, one highly aggregated monetary model and a Keynes & Leontief sectoral model. Since the two last models could be derived as special cases of the Reference model by aggregating up to sector levels and shutting down all the Stockholm School ex ante plans ex post outcomes dynamics, it was interesting for the long-term analysis of the Swedish economy published in 1979 (IUI, 1979) to ask the same questions to all three models and then identify the reasons for the different answers.

The most important insight, which should not come as a surprise, was the sensitivity of long-term growth trajectories to the choice of model (read its prior assumptions). While the long-term economic systems trajectories depended critically on the parameters governing market resource allocations in the Reference model, this was not the case for the other two essentially equilibrium models (IUI, 1979, pp. 52–60).² Another insight concerned economic systems controllability. While the Reference model economy was difficult to control through available policy parameters, simulating the other two models conveyed the illusion of being in full control of the economy. Thus, for instance, pushing the Reference model economy too fast, and too far to lower unemployment, soon began to disturb the market coordination of production and investment, and resulted in worse countervailing labour market disturbances.

Even though a de-identified firm database for the year 1982 for external academic use was made available by IUI in 1992 (see Taymaz, 1992), external academic users have not been that many. Broström (2003), who set the model up for a study of the reliability of the Capital Asset Pricing Model (CAPM) under different economic systems conditions for a master’s thesis at the University of Linkoping, however, demonstrated that the model was not that technically difficult to operate. The database work for the model, notably the Planning Survey and the complete stock and flow consistent micro-based National Accounts statistics put together for one initial year, that is 1982 (Albrecht et al., 1992), furthermore, has been found useful in other unrelated research projects. Bergholm (1985) simulated the pull effects of the small number of very large and dominant engineering firms on the Swedish economy, and its exposure to possible negative market experiences of some of these firms. Dan Johansson used the model in his doctorate thesis 2001 at the Royal Institute of Technology (KTH), which was in part a study on the exposure of the Swedish economy to information and communications technologies for the Swedish Agency for Civilian Emergency Planning. In return a new firm based computer and communications (C&C) industry was introduced in the model (see Eliasson & Johansson, 1999; Johansson, 2001, 2005). Most important, however, is the capacity of theoretical reasoning offered by the Reference model. The discussion in Section 4 illustrates that complex high dimensional models of the Reference model type constantly come up with surprise phenomena that have not before been observed, but that may occur suddenly, that cannot be derived from within the confined neoclassical structures, or ideas about what may have happened that you may go and look for. My conceptualisation of an “Experimentally Organized Economy” dawned upon me during repeated simulation studies on the model, and its foundation in Stockholm School ex ante plans, ex post outcomes analysis, featuring the prevalence of more or less mistaken decisions at the micro-level, and the general ignorance of economic actors of circumstances that may challenge their very economic existence (Eliasson, 1987, 2015). Since an eleven sector computable general equilibrium (CGE) model and a Leontief & Keynesian (L&K) model can be demonstrated (see below) to be special cases of the Reference model, any user of that model can easily relate to those more familiar models, and identify and evaluate the origin of unfamiliar surprise outcomes.

The Reference model is essentially deterministic, and features phases of deterministic economic systems chaos. We have tried to keep stochastic specifications at a minimum, even though stochastic specifications were unavoidable in two places of importance: (1) the assigning of priority order in which firms search each quarter for labour in the market, including poaching on other firms, by offering higher wages, and (2) the assignment of productivity and other characteristics of new firms entering markets as drawings from empirically studied distributions of such firms.

The Reference model began life soon 45 years ago as a bottom-up open economy construct, with locally interacting (competing) heterogeneous firms, in principle across the entire economy and over time; a complex mathematical structure beyond traditional analytical tractability. Richiardi (2017) distinguishes between such models, and the more simple, partial simulation models often related to some external equilibrium skeleton that make them analytically tractable. This essay can be seen as an argument against the latter, and for the need of the former to address a number of urgent social economic problems credibly, for instance the four examples in this document. I will also make the point that simulation is a highly sophisticated mathematical tool that today makes it unnecessary to hold on to wrongly specified models to be able to use the old toolbox of economists. The Eurace@Unibi model appears to be of the new complex agent-based kind that I advocate (see for instance Dawid, Harting, Van der Hoog, & Neugart, 2016), that also incorporates many features of the original Reference model.

The main reasons for the previous limited external academic interest in models of this type are (1) their complexity, need for new methodological skills, and demands for resources, that for a long time took such modelling beyond the budgets of academic computing, (2) their demands on unique statistical data availability, and most importantly (and unfortunately), (3) not being structurally and methodologically of the kind familiar to the profession. This has also made both replication of studies, and compact article writing on the results, difficult, even though a version of the model based on a de-identified database, was made available since the early 1990s for anyone wanting to replicate the experiments.³ Early support by IBM, the Federation of Swedish Industries, and IUI made it possible to overcome most of those difficulties. However, as I will argue extensively in the main text, and have in other publications, this is the way good empirical projects in economics should be organised, will have to be conducted in the future, and I would not do it differently, should I do it again.

Microsimulation is an apt term for the ambitions I will be advocating, but the microsimulation field has unfortunately branched out in several, sometimes incompatible, directions, some of them voiced in the 1977 Stockholm conference.

The study of “micro-based dynamic economic systems theory and modelling” is my preferred general term. Simulation in the sense of this paper is a mathematical tool for the analysis of complex economic systems, in particular aimed at understanding the long-term evolution of entire economies. Microsimulation, on its side, has become a recognised term both for a method of analysis, and for the study of a particular class of economic models. The latter interpretation therefore understands microsimulation as commonly practiced to be a special branch of Micro to Macro economic systems modelling, or the wider field of economic modelling that we envisioned at the time of the 1977 Stockholm conference. That branch starts from Orcutt’s concept that each micro agent conducts a stochastic experiment, with empirical applications dominated by the study of the distributional consequences for the household sector, notably of tax changes. Market intermediated interactions between those agents are rarely modelled, if at all. Few of the large number of such microsimulation studies have exhibited an interest in the macro outcomes.

The second branch is represented by the Eliasson (1976b, 1977) micro- (firm) based self-coordinated economic systems model presented as the Reference model in the previous section, and Bergmann’s (1974) “transactions” model. Both have economy wide ambitions, as their distinguishing feature, and more importantly, they model the interaction (competition) of heterogeneous agents in explicit markets, and have a theoretical focus on the dynamics of the evolution of complex economic systems. Eliasson has often expressed his goal (for instance Eliasson, 2005b) as that of studying the economy wide consequences of “the birth, the life and the death of firms”, as they compete with each other in product markets, and for resources in labour and financial markets.

Firms are modelled to design business experiments to be tested in competition with other firms in markets, and to react to experiences from realised ex post outcomes, that diverge from ex ante plans, experiences that are fed back through markets to affect next period’s plans. Concerns about a realistic representation of firm behaviour are supported by references both to the Eliasson (1976a) study of business planning practices, as the prototype of their behaviour in the model, and to the specially designed survey to real Swedish firms to obtain a database for the model, including explicitly measured initial conditions for the quarter model simulations. The initial conditions measured are then endogenously updated from quarter to quarter.¹⁷ How aggregation of firms’ behaviour up to macro is intermediated in those markets is explicitly modelled.

The 1990s has witnessed a third branch of Micro to Macro economic systems modelling: agent-based modelling (ABM). As far as the ambition has been to model entire economic systems, for instance the Eurace model (Dawid et al., 2016), it comes close to the Bergmann (1974), Bergmann et al. (1980) and Eliasson (1976b, 1977) models. Both Ballot, Mandel, & Vignes (2015) and Richiardi (2013) classify the latter two models as the first economic ABMs, and they are right. The origin of ABM in general is however unclear, but seems not to be economics but rather computer based studies of the behaviour of ant colonies (The Economist, 2013). Fontana (2006) draws the lineage back to von Neumann, cellular automata and the Santa Fe Institute founded in 1984 to advance the understanding of complex multidisciplinary systems (Arthur, 1999), the interaction of heterogeneous micro agents in complex economic systems being one example, very much of what has been going on in the Reference model. When touching down in economics in the 1990s, ABM has been announced as a “new separate” branch of economics. The question therefore is if that literature offers more than a new name for Micro to Macro economic systems modelling published decades earlier.

In post times, Kydland and Prescott (1982) DSGE models have sailed up as a fad in academic economics, but then declined in popularity after the crisis of 2008, observes The Economist (2016, p. 65), central banks being early enthusiastic users of DSGE models. These models have been presented as both dynamic and micro-based macro compared to CGE sector models. Compared to the micro firm, or household based macro systems models, just discussed this is going a bit far, even if heralded as something radically new by many economists (for instance Fernandez-Villaverde, 2010). There are no explicit heterogeneous agents and no explicit markets (only an assumed zero transactions costs rational expectations equilibrium), and no dynamics; all markets are (in stochastic market clearing equilibrium), and when it comes to the endogenous growth cycle claimed to be there, Kydland & Prescott (1982) have plugged in an exogenous trend.¹⁸

So this family of economic macro models has little to do with neither economic dynamics nor ABM. Perhaps there is no economics at all in the DSGE model, because assumptions have been substituted for explanation. Day (1996, p. 399) therefore calls such models “statistical characterisations of their trajectories”.¹⁹ “The great recession poses a serious challenge to mainstream macro“(read DSGE models) writes Richiardi (2017). The failure of DSGE models in central banks to predict and to support an understanding of the financial crisis of 2008 seems to have caused interest in such models to cool (Goodhart, Romanidis, Tsomocos, & Shubik, 2016).²⁰

Since both the DSGE and the CGE, as well as the K&L models can be derived as special cases of the Reference model (Eliasson 2017a, p. 362), or similarly structured agent-based models, I see no point in making this a special branch of micro-based economic systems modelling.

There is also a fourth branch of Micro to Macro economic systems models with the specific ambition of clarifying the microeconomic foundations of existing macroeconomic neoclassical and Keynesian models, taking the latter for given. That was also one ambition voiced in the 1977 Stockholm Microsimulation Conference. In the light of this paper, this ambition, however, becomes futile. With Reference type models properly established and estimated there will be no need for a separate macro theory. But some of these studies (for instance Fisher, 1972, 1983, Weintraub, 1979, 1983), are interesting for other reasons, because they clarify indirectly, and sometimes in direct words, the shaky foundations of any macro model. Fisher’s (1972) treatise on “price adjustment without an auctioneer” is interesting, not only because it clarifies that, but also because the profession had not yet in 1972, and still not, taken economics beyond the central planner and auctioneer of Walras who coordinates the economy free of charge.²¹ Weintraub (1983) does not hold back his words when he concludes: Could it be that the Walrasian equilibrium story has exercised such strong influence on a narrow minded profession that “empirical work, ideas and facts and falsification” have been allowed to play “no role at all”?

I will therefore stay with using “Micro to Macro economic systems modelling” as the general term that covers both microsimulation, ABM and the narrow task of clarifying the micro foundations of existing macroeconomic models as special cases. The distinction that should be made is that micro-based economic systems modelling concerns the evolution of an entire economy, featuring deterministic behaviour of heterogeneous agents interacting in markets, incompatible ex ante agent plans that are sorted out by competition and self-coordinate the economic system (without, however, clearing the markets) such that prices and quantities are determined, and realised behaviour fed back sequentially over time. Each agent thus faces the actions of all other agents as a critical part of its economic environment.

Rapid advance in computer capacity and improvements in simulation techniques have gradually made complex models of the Reference model type tractable for mathematical simulation analysis. Only recently, however, has computer capacity and databases for empirically credible estimation of such models began to become available, allowing modelling to move from the low ambition of generating “stylised facts”, by way of the very early, and for the time advanced calibration model of Taymaz (1991b), developed for the Reference model, to not yet achieved proper parameter estimation. The latter should be a priority concern to confer the empirical credibility on these models that they deserve (Eliasson, 2016; Hansen & Heckman, 1996; Richiardi, 2013). The compilation of high-quality databases on taxonomies tailored to the problems addressed probably is the most difficult of the two obstacles to progress. Ultimately, however, there should be little use for a separate branch of economics called macroeconomics.

The question “What are these complex and difficult to estimate models good for?” is instead a fundamental concern. And it can only be answered with: “What are you interested in?”. There are a number of questions for which a meaningful answer requires the analysis to be based on an economy wide, dynamic and difficult to estimate agent-based model. However, to handle them all within the same general model structure becomes a killing proposition. Economics is a sufficiently large field to make the ambition to put together a universal theoretical construct that holds intelligible answers to all important socioeconomic questions meaningless, not to mention all psychological, sociological and historical dimensions that impinge on the economic system, and that are most often neglected altogether by economists. This is to say that economic models will always be purpose dependent, and require that the researchers present a convincing empirical argument for the prior, and thus always partial model choice they make. This does not exclude that a more general and perhaps verbal “theory” can be used to facilitate that choice, and to help interpret the results achieved on the basis of a partial model. In fact, that prior choice to arrive at an empirically credible partial model for quantitative analysis, is its most important part. It defines the “art of economic analysis” (Eliasson, 1992, 1996, 2005a, 2017b).

Mathematical simulation today effectively frees the theoretical economist of the bounds imposed by the traditional mathematical tools of the profession, and the consequent need to simplify models for less interesting partial analysis. High dimensional complex models with many parameters and variables are rich in empirical content. To the extent the model has an economically and empirically credible foundation its behaviour can be fruitfully explored for interesting and surprising conjectures, sometimes not observed before, and more important in this context, often not before thought of, because they are not part the lower dimensional partial models commonly used. As many of the behaviours originally featured by the Reference model have been subsequently observed, and have been patched onto standard macro models as ad hoc and rarely consistent postfixes, it is legitimate to ask whether these early analytical conjectures could have served as signals of what to go and look for, without the need to learn it the hard way. One problem might have been the empirical credibility of the calibrated parameters of the complex model, and hence the relevance of those “theoretical” results. But using falsely specified, but perfectly estimated models is worse, since then you cannot use your model to identify the reasons for this or that conjecture. Given an assessment of the overall empirical credibility of the model, such conjectures might therefore serve well as warnings of what may come, to be taken as seriously as a common sense appreciation would tell. They could also help empirical researchers to go out to look for new empirical evidence. In retrospect it seems that the worries about miss-calibrated parameters were overstated compared to the risks involved in simplified, partial, and miss-specified models, although those risks are rarely made public in the vast econometric literature (Eliasson, 2016, 2017a).

Questions on the economy wide long-term social costs and benefits of micro interventions in the economy are frequently asked on both invasive and less substantial policies, and on public projects. And whatever the state of the art in empirical economics, economists are happy to provide answers. Estimates of the longer term costs and benefits based on models of the Reference type are however sensitive to the accuracy of initial state measurements, parameter determination and the specification of the policy interface.

Economic historians should happily recognise the potential of high dimensional models with many parameters and variables and sequential market feedbacks, which embody a rich variety of possible historical evolutions of the model economy. Their scientific task has normally been limited to describing ex post the one track historical evolution has in fact followed. To explain why the economy embarked upon a particular track, however, requires an analysis of what alternative histories could have occurred. Identifying the origin of alternative economy wide historic developments furthermore requires that you take the analysis down to the market/agent level. Depending on the initial conditions (a problem of historic measurement), and the parameters of the model that guide the historic evolution (a matter of relevant specification and estimation), something entirely different might have occurred. This defines the difference between measurement without context and historic explanation, which requires a comparison of facts with alternative possibilities. For the latter the historian needs a model capable of generating credible alternative economic historical evolutions.²⁹

There are of course problems associated with attempts to be up to such ambitions. What, for instance, does it mean for understanding and predicting over the longer term that the agents (firms) that dominate the economy today are likely to have been a seemingly insignificant market choice of innovators in the past, a choice that could in no way have been reliably predicted at the time? How should the very long time and bad future consequences of bad policy choices today, that can be discounted away (the political discount rate), be compared with the distress experienced by later generations, when the bad future has materialised? Evolutionary, micro-based economic systems models that are empirically well founded exhibit these properties. None of these historical questions furthermore can be meaningfully raised without the explicit context of such a model. Even though a tall order for the economic historian, complementing the analysis of ex post facts with simulated alternative economic histories should amplify the empirical credibility of the historical analysis. The Reference model of this article can simulate such alternative trajectories in great detail, and their long-term evolution is not, as in neoclassical growth models, governed by an exogenously imposed (assumed) equilibrium trend.³⁰ Should we engage in such number crunching? I think we should, even though there are problems.

First, growth of the Reference model economy is controlled by the most difficult to estimate time reaction parameters, and competition based selection through entrepreneurial entry and exit sometimes makes small circumstances cumulate into major future events. But this is, as we have already discussed, also a typical historical fact, in that what we observe today is almost always the result of historical circumstances that were at the time seemingly insignificant, often produced by chance. Hence, the simulation of alternative histories should be based on models that feature the cumulative importance of such historic choices. For instance, why have some regions, or entire economies, failed to be industrialised, while others have grown successfully for centuries, only to sometimes suddenly collapse and retard into a less advanced state? Literature abounds with alternative historical speculations of historical development, and models of the Reference type would allow evaluating these speculations in a logically consistent way. However, over the longer term, and for the same reason, the economic consequences of small errors in estimated parameters and measured initial conditions may cumulate into significant errors.

Second, rather than providing counterfactual histories for the past, simulations can also project the present into the future. This can be a valuable guide for policy makers. Bad outcomes today can be the consequence of bad policies in the past, but the complexity of the economic evolution might prevent policy makers from making sense of it and take appropriate action. Moreover, even when policy makers think they know, correcting the situation through policy may take more time than the political horizon: having a Reference model can help extending such a political horizon. However, forecasts to guide the model economy onto a desired long-term growth path may be impossible because of the immense number of future paths the model economy can take, the near impossibility to simulating them all to make an informed policy choice, and (above all) the bad empirical control of the calibrated parameters. This implies large risks of substantial policy mistakes, if a particular simulated forecast is taken seriously. Device policies that work “on average” will not solve that dilemma. Sensitivity analysis of the calibrated parameters (as in Eliasson & Taymaz, 2000) will indicate the risks associated with a particular policy choice, though.

An interesting and potentially socially valuable application however exists. The potential of the kind of models we discuss, including the Reference model, is to be capable of generating many different economic systems histories. For each of them it is possible to trace ex post and in great detail, as economic historians do, their origin and the details of the historic path the economic system has taken. While trying to police the model economy towards desired long-term outcomes is both futile, and involves significant risk of taking the economy in the wrong direction, trying to avoid bad future outcomes by steering around circumstances that create them makes more sense. In principle, it is possible to explore by simulation a large portion of the near term interior of the economic opportunities space of the model³¹, and to determine circumstantial risk zones that policy makers should try to stay out of to prevent bad long-term outcomes. However, how much credibility should be attached to those calculated risk zones is again a matter of empirical credibility of the model used: (1) its prior specification, (2) the empirical credibility of its parameterisation, on which it might not be possible to reach consensus, and (3), not least important, the quality of measurement of initial conditions. On all three counts policy makers will have to apply both common sense and sound judgement. This second use of the model to help device risk reduction policies, as distinct from forecasting, should however require less in the form of empirically accurate parameterisation. The risk of missing a specific predicted policy target because of errors in parameters, must be larger than that of misguiding the economy with the help of the same model around a simulated undesired event. An analogy could be trying to bring an old car with a loose steering, driven at high speed on a narrow and winding road, to a simulated (“predicted”) Nirvana. That must involve a larger risk of failure than changing the road, if the model suggests the road leads to disaster.

Case observations may be complemented with data on their environmental context (for instance an economy wide model) for an improved understanding of what the case observations mean for the entire economy. Ideally the cases can be entered as exogenous interventions in the markets of the calibrated Reference model, as in the industrial support program of Section 6. Eliasson (1984) also simulates the catastrophic macroeconomic outcome of a single microeconomic event, triggered endogenously by an unhappy constellation of market circumstances, and the economy wide dynamic feedback consequences. Even if the model has not been “credibly calibrated” for such experiments and the ambition is to quantify the macroeconomic circumstances of certain micro interventions in the economy, the logical structure of the Reference model and its database can still be used to validate case study results against external information, as in the Gripen spillover measurements in Eliasson (2010, 2017a), briefly presented in the cost benefit Section 6.

Generalising from case studies to the economy wide level on the basis of an economy wide agent-based model also offers a number of practical opportunities for learning of both business decision makers and policy makers, and theoretical insights for the analyst.

This paper is an argument against excessive parsimony in economic modelling, with the added notice that when you have to cut modelling complexity down, which you always have to, the partialisation arrived at should be argued credibly on empirical grounds, and with reference to the problem being addressed. Since modern mathematical simulation technology has done away with the need for unnecessarily cutting down on complexity to achieve theoretical clarity, there is no insight to be gained from using partial and static macro models to address economy wide long run problems, or linear models to address non-linear phenomena, or macro models to answer questions about the economy wide consequences of micro interventions in an economy.

Economists had to use such misspecifications in the pre-digital age. If they still stick to such practices they have become the prisoners of the old toolbox of the profession. I have gone through four problem areas where large scale economy wide and long run (dynamic) micro agent-based economic systems models are needed to answer a number of commonly asked “what if” questions, and listed the minimum requirement on specification to avoid giving erroneous answers. Empirical credibility of both prior model specification, and estimation has been a key notion.

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Author details

1. Gunnar Eliasson

   Royal Institute of Technology (KTH), Sweden

   For correspondence

   gunnar.elias@telia.com