Technological unemployment and income inequality: a stock-flow consistent agent-based approach


The paper presents a stock-flow consistent agent-based model with effective demand, endogenous credit creation, and labor-saving technological progress. The aim is to study the joint dynamics of both personal and functional distribution of income as a result of technological unemployment, together with the effect on household debt. Numerical simulations show the potentially destabilizing effect of technological unemployment and reveal that an increase in the profit share of income amplifies the negative effect of income inequality on the business cycle and growth. The sensitivity analysis provides indications on the effectiveness of possible mixes of fiscal and redistributive policies, but also demonstrates that the effectiveness of policy measures is strongly dependent on behavioral and institutional factors.

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  1. 1.

    Besides allowing for formal Minskyan analyses of debt accumulation and financial fragility (Dos Santos 2005), SFC models have recently been used to study the macroeconomic effects of shareholder value orientation and ‘financialisation’ (Van Treeck 2009), as well as that of household debt accumulation (Kim and Isaac 2010). For an exhaustive survey, see Caverzasi and Godin (2015).

  2. 2.

    See also Riccetti et al. (2013a, b, 2016).

  3. 3.

    We will focus our entire analysis in the region where the economy is not capital-constrained and output is below potential, so that \(\bar {Q}=\gamma K\) and \(Q<\bar {Q}\). Model parameters have been calibrated in the simulations such as to avoid the problem that the capital constraint becomes binding after the burnout phase.

  4. 4.

    See Rowthorn (1982), Dutt (1984) and Taylor (1985) for early models of growth and distribution in this tradition.

  5. 5.

    Since the focus of the paper is systemic financial fragility as the result of households’ leverage, we implicitly assume that the firm sector is fully rationed on the credit market. This assumption does not imply a loss of generality, as a perfectly elastic supply of credit rules out any possible crowding out effect on the credit market.

  6. 6.

    The consumption rule applies to all workers, employed and unempoyed. Therefore it is theoretically possible that an unemployed worker consumes more than an employed one, with a consequent increase in leverage for the former. This simplifying assumption allows for aggregation and closure of the model through the multiplier.

  7. 7.

    The priority given to debt repayment follows from the assumption that money deposits do not hold any interest. Setterfield and Kim (2016) and Lusardi et al. (2011) provide a theoretical explanation for this assumption based on a “pecking order”-type behavior of households.

  8. 8.

    The numerical simulations confirm that, in each period, the accounting consistency is mantained.

  9. 9.

    Due to Eq. 4, the actual inflation is always roughly equal to πe as confirmed by simulations.

  10. 10.

    Given that the main focus of this paper is household leverage in the presence of technological progress, we abstract from unnecessary complications, such as the inclusion of a government budget constraint or the study of the sustainability of public debt. In the simulations, we do not observe in any scenario an explosive dynamic of debt. When its absolute size grows, the system collapses before public debt goes out of control. The introduction of a range in public debt would negatively affect aggregate demand and lead to an earlier collapse, without changing the underlying conclusions and the basic intuitions.

  11. 11.

    Systemic financial fragility can be further analyzed by extending the model to include microfounded firms and banks. However, the introduction of the negative term ϕDt− 1 in Eq. 11 partially addresses this shortcoming. The accumulation of debt progressively reduces consumption and aggregate demand, replicating in substance the effect of a debt default.

  12. 12.

    Equation 31 simply represents the accounting closure of the demand-driven model in order to determine the aggregate level of output as in standard textbook Keynesian models.

  13. 13.

    The generation of macroeconomic patterns more aligned with the empirical evidence would require a specific analysis of real data and the use of more sophisticated calibration techniques which, given the length and the scope of the present paper, we prefer to postpone to future developments of this project.

  14. 14.

    Other agent-based models (for example Caiani et al. 2016; Dosi et al. 2015) use a higher value of 5%. This parameter is not central in our model and its effect is mostly to increase the frequency of fluctuations.

  15. 15.

    This outcome is due to the high heterogeneity of wages and their dynamics. The unemployment benefit is the major factor in reducing the overall income inequality.

  16. 16.

    Also Ciarli et al. (2012) refer to Verdoorn’s law, but only as a positive correlation between output and technical change that they find ex-post in their simulation data, while the determinant of the latter is on the supply side as in the cited Keynes-Schumpeter models and in other Schumpeterian growth models such as Silverberg and Lehnert (1993).

  17. 17.

    For simplicity, we abstract from the cost of innovation because the firm sector is modeled as a single aggregate and the R&D costs for one firm would be the revenue for another in a stock-flow consistent perspective. A more refined modeling of the innovation financing process would imply the modeling of an additional capital or innovation producing sector as in the cited agent-based models or in aggregate models such as Caiani et al. (2014) for example. Since the paper focuses on the effects of technological progress on household income distribution this aspect is left to possible future developments of this research.

  18. 18.

    Such predator-prey dynamics between demand and distribution are studied, for instance, in Skott (1989) and Barbosa-Filho and Taylor (2006).

  19. 19.

    An alternative solution to introduce a more progressive tax system would involve, for example, different rates for brackets of income earners. However, this option would make it impossible to calculate the multiplier and have a neat and simple closure of the model as the one presented in Section 2.5.

  20. 20.

    The toolbox is available at the address

  21. 21.

    The choice of the sub-period depends on the amplitude and frequency of the fluctuations for each value of the parameter and has the aim to isolate the effect of the parameter’s changes.


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We thank Evgeniya Goryacheva for the excellent research assistance. We are also thankful to Andre Diniz and Andre Cieplinski who have helped us for the simulations of previous versions of this model. This paper presents an extension to the models built in Carvalho and Di Guilmi (2014) and Di Guilmi and Carvalho (2017), which themselves have largely benefited from comments from Daniele Tavani and Peter Skott, as well participants at the Eastern Economic Association, World Keynes Conference, FMM Conference, Crisis2016 and numerous seminar/workshop presentations. We also thank two anonymous reviewers whose comments have led to this improved version of the paper. Financial support by the Institute for New Economic Thinking is gratefully acknowledged.


This study was funded by the Institute for New Economic Thinking (INET Grant INO13-00007) and by the Business School of the University of Technology Sydney (grant 2210094).

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Carvalho, L., Di Guilmi, C. Technological unemployment and income inequality: a stock-flow consistent agent-based approach. J Evol Econ 30, 39–73 (2020).

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  • Stock-flow agent-based consistent model
  • Income inequality
  • Functional distribution
  • Technological unemployment
  • Social imitation

JEL Classification

  • C63
  • D31
  • E21
  • E25