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Macroeconomics with heterogeneous agent models: fostering transparency, reproducibility and replication

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Abstract

This paper provides a detailed description of the Eurace@Unibi model, which has been developed as a versatile tool for macroeconomic analysis and policy experiments. The model explicitly incorporates the decentralized interaction of heterogeneous agents across different sectors and regions. The modeling of individual behavior is based on heuristics with empirical microfoundations. Although Eurace@Unibi has been applied successfully to different policy domains, the complexity of the structure of the model, which is similar to other agent-based macroeconomic models, makes it hard to communicate to readers the exact working of the model and enable them to check the robustness of obtained results. This paper addresses these challenges by describing the details of all decision rules, interaction protocols and balance sheet structures used in the model. Furthermore, we discuss the use of a virtual appliance as a tool allowing third parties to reproduce the simulation results and to replicate the model. The paper illustrates the potential use of the virtual appliance by providing some sensitivity analyses of the simulation output carried out using this tool.

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Notes

  1. Recent contributions include (Ashraf et al. 2016; Dawid et al. 2014; Dosi et al. 2015; Mandel et al. 2015; Russo et al. 2016; Sinitskaya and Tesfatsion 2015; Seppecher and Salle 2015). See also the survey by Dawid and Delli Gatti (2018).

  2. See e.g. Arifovic et al. (2013), Assenza and Delli Gatti (2013), and De Grauwe and Macchiarelli (2015).

  3. Apart from the Eurace@Unibi model covered in this paper, the main representatives of this type of models are the ’Schumpeter meeting Keynes’ model (Dosi et al. 2010; Dosi et al. 2015) and the Lagom model by Mandel et al. (2010).

  4. Recent contributions addressing such issues are Grazzini and Richiardi (2015), Barde (2016), Barde (2017), Barde and Van der Hoog (2017), and van der Hoog (2018b).

  5. For example, Camerer et al. (2016) report that for only 11 out of 18 experimental results published in top five economics journals the results could be independently reproduced by third parties.

  6. A detailed documentation of the implementation of (a previous version of) the model is provided in Dawid et al. (2011).

  7. Parts of Section 2, in particular Sections 2.1 and 2.3 have already been formulated for the description of the Eurace@Unibi model in Dawid et al. (2018a). Parts of Section 3, in particular Section 3.4 on the credit market, has already been developed and used in van der Hoog and Dawid (2018) and in van der Hoog (2018a).

  8. In this respect, our modelling approach builds on a rich literature starting with work of Herbert Simon (Simon 1959).

  9. Empirical evidence that firms’ technology choices are indeed influenced by the skill level of their work force can, for example, be found in Piva and Vivarelli (2009).

  10. A slightly altered dividend rule is used if a firm is hoarding cash. If its payment account exceeds a certain threshold level \(\bar {m}\) that depends on the average revenues over the last four months, \(\bar {m}= 0.25 {\sum }_{\tau = 1}^{4} R^{f}_{t-\tau }\), the dividend rate is given by \(d^{\star }=d\cdot {\mathbb I}[ M_{i,t}\leq \bar {m}] + 1\cdot {\mathbb I}[M_{i,t} > \bar {m}]\). This rule states that if the payment account of the firm is below the threshold level \(\bar {m}\) then it pays out the default dividend rate d = 0.70, while if the payment account exceeds the threshold level \(\bar {m}\) then the firm’s dividend payout equals 100% of it’s average net earnings over the last four months. This rule was installed in order to prevent firms from hoarding money on their payment account, which led to detrimental economic performance due to the absence of a back-channelling of the profits to households.

  11. Note that we index the loans by k and not by i, implying that a firm may have a portfolio of loans, possibly with different banks. The probability of default (PD) refers to the default on a specific loan k, not necessarily to the default of the entire firm i.

  12. A similar specification for the interest rate rule can be found in Delli Gatti et al.(2011, p. 67). The difference with our specification is that we use the probability of default of the firm, while they use the leverage ratio of the bank. Such an interest rate rule could lead to the unfortunate situation that a bank with a worsening financial position, i.e., a higher leverage ratio, will price itself out of the market by asking a higher interest rate.

  13. This rule will be denoted as the “full rationing” rule. An alternative behavioral rule for the bank that we have tested is the “partial rationing” rule: when the credit risk exceeds the risk exposure budget Vb, the firm i would only receive a proportion of its credit request, exactly filling-up the bank’s constraint. This rule would imply that the bank would always exhaust its “excess risk exposure”-budget in Eq. 67. This does not result in a viable economy. It leads to more credit rationing rather than less, since firms requesting credit from the bank after a high-risk firm has already secured a loan will not be able to receive any credit since the bank has already exhausted its entire risk budget. Hence, in the interest of macrofinancial stability, we have opted for applying the “full rationing” rule in relation to the excess exposure budget \({V^{b}_{t}}\).

  14. Note that, in relation to the “excess liquidity”-budget in Eq. 70, we apply the “partial rationing” rule. Hence, a bank will typically deplete all its excess liquidity and will be “at” the RRR constraint.

  15. This implies the bank behaves as if it believes the reserve requirement is in fact an a priori constraint on its credit supply. An alternative would be to model more explicitly the expected future cash flows that results from supplying a loan, see e.g., Caiani et al. (2016).

  16. The consumption budget could exceed the savings account in case the financial market is illiquid and the household cannot sell enough financial assets if it wants to consume more than its savings account. On the other hand, the consumption budget could also become negative if the last term is negative, i.e. if current financial asset wealth is smaller than the target wealth, and the household wants to invest more in financial assets.

  17. The problem of market illiquidity can be softened somewhat by introducing a market maker into the model, but this does not solve the issue entirely. It could still occur that this market maker is not willing to take the counter-party risk that all market participants are trying to sell.

  18. To derive the household’s orders for shares in the market one could have also followed a more elaborate route and apply the literature on artificial financial markets that use the mean-variance maximization framework of the capital asset pricing model with wealth based portfolio dynamics (Chiarella and He 2003; 2001; Hommes et al. 2006)

  19. See Weddepohl (1995) for a related model with cautious price adjustments in discrete tâtonnement processes, for which it is proven that, under restrictions on the maximal rate of price increases or decreases, the trajectory of prices converges to a neighborhood of an equilibrium. However, still any type of erratic dynamics remains possible, including quasi-periodic and chaotic orbits. Hence, imposing restrictions on the growth rate of prices does not guarantee that prices will converge to a steady state equilibrium.

  20. The VA is available at the dedicated webpage http://www.wiwi.uni-bielefeld.de/lehrbereiche/vwl/etace/Eurace_Unibi/Virtual_Appliance. This webpage also provides an installation guide and user manual for the VA, in which the few steps needed to install the VA are described.

  21. The Simulation GUI allows the user to determine how many cores are used during the simulation.

  22. The intensity of competition parameter is set to γc = 16 in these simulations.

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Acknowledgements

The authors gratefully acknowledge the substantial contributions of Simon Gemkow to the development and implementation of the Eurace@Unibi model and the associated R-scripts and of Gregor Böhl to the development and implementation of the ETACE Virtual Appliance. The paper has profited from helpful comments from two anonymous referees.

Funding

This research has been supported by the European Union Horizon 2020 grant No. 649186 - Project ISIGrowth.

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Authors and Affiliations

  1. Chair for Economic Theory and Computational Economics (ETACE), Department of Business Administration and Economics and Center for Mathematical Economics, Bielefeld University, Universitaetsstr. 25, Bielefeld, D-33615, Germany

    Herbert Dawid

  2. Chair for Economic Theory and Computational Economics (ETACE), Department of Business Administration and Economics, Bielefeld University, Universitaetsstr. 25, Darmstadt, D-33615, Germany

    Philipp Harting & Sander van der Hoog

  3. Department of Law and Economics, Technische Universität Darmstadt, Darmstadt, Germany

    Michael Neugart

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  1. Herbert Dawid
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Correspondence to Herbert Dawid.

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Appendices

Appendix A: Parametrization and initialisation

1.1 A.1 Parametrization

The model hosts a considerable number of agents, variables and parameters, which are listed in Tables 6, 7 and 8. Values of all parameters are chosen to reflect empirical evidence whenever possible. The ratio of the number of households (workers) and firms matches mean firm sizes to be observed in Europe. The innovation probability is chosen to reflect estimates approximating shifts of the technological frontier.

Table 6 List of agent types in the Eurace@Unibi model
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Table 7 List of variables in the Eurace@Unibi model
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Table 8 List of parameters in the Eurace@Unibi model
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Comparable to data reported in Vandenbussche et al. (2006), our calibration yields a growth rate of the technological frontier of around 6% per year if skills were sufficient to fully exploit technological innovations. Wage updates are calibrated to match wage growth in Germany during the decade of full employment in the sixties. The parameter value for the adjustment of the reservation wage is based on reported wage losses of approximately 17% after spells of unemployment in Germany (see Burda and Mertens 2001), and an average duration of unemployment of 30 weeks. As a proxy for the reservation wage we make use of the net replacement rates of unemployment benefit schemes in OECD countries (see Organization for Economic Co-operation and Development 2004). For the marginal propensity to save we chose 0.1, which is close to the savings rate in Germany in previous years. The intensity of the consumer choice stems from estimated multi-nominal logit models of brand selection. Estimates based on market data (Krishnamruthi and Raj 1988) provide a lower bound of six.

1.2 A.2 Initialization

In general, there are several considerations that constrain the initialization of the agent’s state variables. First and foremost, we cannot initialize the variables completely at random. This would violate the internal logic of the model, since, in order to obtain a working simulation, we have to initialize the agent’s balance sheets according to the criterion of stock-flow consistency. This means that we are constrained to set the initial values such that the balance sheet relationships between agents hold. If the balance sheets would be inconsistent from the start they would remain so throughout the entire simulation.

The second consideration is that we start with plausible values. This is in order to alleviate the initial transient effects that any initialization invariably has. In our experience, large path dependencies can be generated by such initial transients, so it is important to carefully consider the interdependencies between the initial values.

  • capital price: The initial capital price is assumed to be in a fixed relation to the initial wage that is on average paid in the economy. Even if the investment goods firm does not employ workers, it has a memory variable wage offer that is used only for the initialization.

  • unit costs: The price setting of the investment goods firm is a combination of value and cost based pricing. For the cost based price component, the investment goods firm takes virtual unit costs into account, i.e. a variable called unit costs that is a proxy for the costs that would arise in the production process. Since the costs usually change over time (mainly due to increasing labor costs), this change has to be incorporated in the evolution of the unit costs. In order to have a stable capital goods price in the first months, the unit costs have to be initialized at the same level as the initial capital goods price.

  • output: We set the output of a firm at a level such that the total labor demand that is needed for producing the cumulated output would correspond to full employment.

  • total units capital stock: The capital stock is set to have a sufficient capital stock in order that the initial production quantity can be produced without additional capital investments.

  • total value capital stock: This is an asset on the balance sheet of the firm.

  • payment account: The value of the firm’s payment account is set to equal the value of its capital stock, such that the firm has sufficient liquidity in the first month to start repaying the initial loan inherited from historical investments.

  • total value local inventory: The firm has no initial inventory stock.

  • initial loan: We start the firms with an initial loan in order to approximate plausible leverage ratios. This will alleviate initial transient effects. The initial loan is set according to a constant leverage ratio of 2.0. This implies that the initial loan is (2/3) of total assets and equity is (1/3) of total assets.

  • capital financing per month: We assume that the firm has invested in capital during its history before day 0 (the start of the simulation). The investments are exactly that amount necessary to compensate for the monthly depreciation of capital such that the capital stock remains constant. In order to stabilize the simulation with regard to bankruptcies at the beginning, we deviate from the usual assumption that the loan obtained for the investments has to be repaid in the standard repayment period of a loan. Instead we allow the initial loan to be repaid in twice the length of time (24 months).

  • employee firm id: We assume all households are initially unemployed.

  • wage reservation: The reservation wage is set equal to the firms wage offer, such that households accept job offers in the first month.

  • mean net income: Mean net income is set equal to the reservation wage.

  • payment account: Households have an initial payment account equal to 15 monthly wages, to represent a plausible savings buffer.

  • assets owned: The households asset portfolio is scaled to yield a wealth level that is reasonable. Each household is endowed with an equal number of index shares, with a price such that the total value of the initial portfolio is 10 (each household has risky-asset wealth equal to 10 monthly mean wages).

  • wealth: Households’ initial total wealth consists of liquid money holdings in the payment account and illiquid asset holdings. Together with the payment account of 15 monthly wages, the initial total wealth of each household is 25.

  • number of shares: The number of index shares is scaled to the total number of firms and households.

  • weight: The weight of the firms in the index share is uniform. This is needed to compute the dividend per index share from the total dividend payment of the firms.

Appendix B: Eurace@Unibi Model - Function references

In the following we provide a list of functions and a description of what they do as implemented in the C-code (Tables 9, 10, 11, 12, 13, 14, 15, 16 and 17).

1.1 B.1 Firm

Table 9 List of functions for Firm agent
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1.2 B.2 Household

Table 10 List of functions for Household agent
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1.3 B.3 Mall

Table 11 List of functions for Mall agent
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1.4 B.4 Investment Goods Firm

Table 12 List of functions for Investment Goods (IG) Firm agent
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1.5 B.5 Eurostat

Table 13 List of functions for Eurostat agent
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1.6 B.6 Bank

Table 14 List of functions for Bank agent
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1.7 B.7 Government

Table 15 List of functions for Government agent
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1.8 B.8 Central Bank

Table 16 List of functions for Central Bank agent
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1.9 B.9 Clearing House

Table 17 List of functions for Clearing House agent
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Dawid, H., Harting, P., van der Hoog, S. et al. Macroeconomics with heterogeneous agent models: fostering transparency, reproducibility and replication. J Evol Econ 29, 467–538 (2019). https://doi.org/10.1007/s00191-018-0594-0

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