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Does inequality hamper innovation and growth? An AB-SFC analysis


We propose to analyze the relationship between inequality and economic development by means of an Agent Based-Stock Flow Consistent model where workers have been differentiated into four classes competing on segmented labor markets, and where firms’ demand for each type of worker is affected by their hierarchical organization. In order to account for the impact of income and wealth distribution on consumption patterns, worker classes have diversified average propensities to consume and save. Finally, firms in the capital sector invest in R&D, thus possibly coming to produce more productive vintages of machineries, which affect the evolution of labor productivity in the consumption sector. The model is calibrated using realistic values for the income and wealth distribution across different income groups and their average propensities to consume. Results of the simulation experiments suggest that more progressive tax schemes and measures that sustain the dynamics of wages of low and middle level workers concur to foster economic development and to reduce inequality. However, the latter seem to be more effective under both respects. Therefore, the model results are broadly in line with the literature suggesting the prevalence of wage-led growth regimes in closed economic systems. In the conclusions we discuss current limitations and future development of the present research.

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Fig. 1
Fig. 2: Baseline Run 1
Fig. 3: Impact of 𝜃 on groups’ tax rates (left) and tax burdens (right):
Fig. 4: Different tax schemes:
Fig. 5: Different tax schemes:
Fig. 6: Different tax schemes:
Fig. 7: Labor market experiment - low-middle tiers workers only:
Fig. 8: Labor market experiment - low-middle tiers workers only:
Fig. 9: Labor market experiment - low-middle tiers workers only:


  1. As highlighted by Lavoie and Stockhammer (2012), the benefits of a wage-led growth strategy have been resurrected and formalized by several authors in the field of post-Keynesian and Kaleckian economics, starting from the seminal contributions of Rowthorn (1981), Taylor (1983), and Dutt (1987).

  2. In an open economy context, total demand may be profit-led due to the prevailing effect of net export over domestic demand. For instance, global demand remains wage-led for European countries and the US, while it becomes profit-led for China (Onaran and Galanis 2012).

  3. This is even more evident if we include “business income” (as profits from sole proprietorships, partnerships and S-corporations) in the labor income category (Jones and Kim 2014).

  4. Moreover, inequality may rise due to the impact of general purpose technologies, by favoring workers who are able to adapt faster than others (Aghion and Howitt 1997).

  5. Fana et al. (2015), based on empirical assessment of the effects of the recent Italian reform of the labor market, the so called “Jobs Act”, comes to similar conclusions.

  6. The source code can be found at:

  7. Indeed, for simplicity reasons, we abstract from innovation processes affecting labor productivity employed in the capital good sector.

  8. For the consumption and credit markets, where the price and the interest rate express a disbursement from the demander, the probability of switching to the new partner is decreasing with the difference between pold and pnew:

    The same specification is employed for capital goods, though with the prices being replaced by the synthetic indexes of attractiveness associated with each vintage. On the deposit market, where interest rates generates an income for the depositor, the probability of switching is instead:

  9. All agents share the same simple adaptive scheme to compute expectations for a generic variable z:

    $$\begin{array}{@{}rcl@{}} {z^{e}_{t}}=z^{e}_{t-1}+\lambda(z_{t-1}-z^{e}_{t-1}) \end{array} $$
  10. Notice that \(\overline {l_{k}}\) indicates the ratio between capital units and workmen required to employ them in the production process. The overall capital-labor ratio, accounting for office workers and managers as well, can then be approximated by \(\overline {l_{k}} share_{w}\) which is multiplied in the denominator of Eq. 3.14 to obtain the value of labor productivity associated with a certain vintage.

  11. Conversely, if \(g^{D}_{ct}<0\), implying that current capacity is greater than desired, they may abstain from investing or replace only partially capital units reaching obsolescence.

  12. As the number of researchers that capital firms want to hire is a constant share of workmen required for production, R&D investment eventually depends upon planned production levels, which are a function of expected real sales.

  13. For tractability reasons, we assume that the stock of unsold inventories is updated at the new productivity level.

  14. In accordance with standard accounting rules, firms’ inventories are evaluated at the firms’ current unit cost of production. As a consequence, the value of inventories may vary due to variation of either their quantity or of their productive costs.

  15. Formally, consumption firms’ credit demand can be expressed as:

    $$\begin{array}{@{}rcl@{}} L_{ct}^{D} = I^{D}_{ct}+Div^{e}_{ct}+ \sigma W^{e}_{ct}N^{D}_{ct} - OCF^{e}_{ct} \end{array} $$

    where \(Div^{e}_{ct}\) is the expected disbursement for dividends (based on expected profits) and ID is desired nominal investment. The equation of credit demand for capital firms can be obtained from Eq. 3.18 by simply omitting ID.

  16. Loans last for η = 20 periods (i.e. 5 years): in each period firms repay a constant share (1/η) of the principal.

  17. Yet, banks’ capital ratio has a mandatory lower bound (6%).

  18. The values of these parameters (see Table 1) were set so that, at initial conditions, the probability of defaulting associated with capital and consumption firms (respectively, \(pr^{D}_{c0}\) and \(pr^{D}_{k0}\)) are both equal to 1%.

  19. Whenever the liquidity ratio falls below the mandatory threshold, banks apply for cash advances to the Central Bank (see Section 3.5).

  20. However, the 1-to-1 replacement hypothesis, quite common in the AB literature, does not imply that there is no industry dynamics since it does not prevent firms from differentiating from each other. On the contrary, firms tend to be highly heterogeneous, and the distribution of firm size, both in terms of productive capacity and real sales, displays fat tails.

  21. Obviously consumption by households can still be financially constrained, so that \(c^{D}_{ht}\) might end up being unfeasible.

  22. See Section 4 for the details regarding the empirical evidence employed to calibrate these parameters.

  23. Public servants are also subject to a turnover 𝜗.

  24. As a matter of example, in the US, traditionally characterized by a significant level of inequality, the bottom 60% of households in the US earns a share of 29% of gross before-tax income, the next 30 percentiles earn approximately 35% of income, and the top 10% earns aproximately 36% of gross income. (Source: supplemental data of the US Congressional Budget Office’s report “The Distribution of Household Income and Federal Taxes, 2011”, 2014, available at

  25. In order not to complicate too much the procedure and without lack of generality, we do not consider interest paid to households by banks, which constitute a negligible portion of households’ gross income.

  26. These values are reasonably similar to empirical ones: Dynan et al. (2004) reports that the lowest quintile has a propensity to save equal to 1.4%, the second 9.0%, the middle quintile equal to 11%, the fourth 17%, and the top quintile equal to 23.6%. Yet, the average saving rate increases significantly for top percentiles as the top 5 and 1% of households save 37.2 and 51.2% of their net income. This suggests that our average propensities to consume may slightly overestimate the empirical equivalent for high-income earners. This is required to avoid putting excessive depressive pressure on our artificial system where savings mostly remain idle, whereas in reality they can circulate again, for example, as inter-generational transfers, or being invested in real estates, or in financial assets.

  27. In this respect we keep the same proportions between sectors employed in Caiani et al. (2016). Workers employed in each sector are then equally distributed across firms.

  28. Notice that, since only workmen are directly employed in the production process, whereas other types of workers are in charge of different functions (supervision and basic management, R&D, strategic management), labor productivity in the capital good sector and the capital-workmen ratio are both significantly higher than the correspondent values in the previous version of the model.

  29. With investment and unemployment volatility being significantly more volatile than real GDP, and consumption being slightly less volatile than output.

  30. In all the experiments performed in the paper, the transition takes approximately 200 periods before the system converges to a quasi-steady trend.

  31. Yet real investment, computed as nominal investment divided by average consumption goods price, is increasing as a consequence of the higher inflation of capital goods prices. This, in turn, can be attributed to the fact that more productive capital goods reduce unit labor costs of consumption firms, on which the markup is applied, thereby dampening inflation. This does not happen for capital firms given their workmen’s constant productivity.

  32. Indeed, for positive values of 𝜃, the higher the average income of a group compared to the global average (i.e. the higher \(\frac {SI_{ht}}{SP_{h}}\)), the higher the share of taxes paid by that group (\({\textit {tax burden}}^{i}_{ht}\)). The same occurs for taxes on wealth.

  33. In addition, Fig. 4 shows that the average trends for the 𝜃 = 0.75 and 𝜃 = 1.0 cases tend to overlap, whereas the latter is slightly lower if we consider the average deviation from the baseline in Table 2.

  34. To be thorough, this does not happen for wealth inequality measures that are consistently decreasing from scenario to scenario.

  35. However, the property observed may be partly connected also to the peculiar configuration of our experiments, where the tax rates of different workers’ groups were computed so to maintain the overall tax load on households unaltered compared to the flat tax rate system. As already discussed, the functions adopted for this sake (6.7) imply that \({\textit {tax burden}}^{i}_{ht}\) is an increasing function of \(\frac {SI_{ht}}{SP_{h}}\), while τiht may be also decreasing if the rise of \({\textit {tax burden}}^{i}_{ht}\) determined by Eqs. 6.3 and 6.5 is less than proportional to the rise of income share held by group h. Therefore, an increase in income polarization, though determining an increase of the tax burden for high-income groups and a correspondent decrease for low-income agents, may be accompanied by a reduction of tax rates for all groups, which softens the redistributive efficacy of the tax scheme.

  36. Among these we mention the progressive reduction of top statutory personal income tax rate and top marginal tax rates for employees occurred since the ’80s. In some countries, such as the US, this drop has been of the order of more than 20% (from 70% in 1981 to 47% after 2007) according to OECD data.

  37. Still, summary results for the tests on the difference between populations, reported in the p < 0.05 and p < 0.10 lines of Table 3, highlight that significant statistical differences between time series in the baseline and the corresponding time series (i.e. obtained with the same pseudo random number generator seed) in the alternative scenarios do exist. However, the low variations of average values observed suggest that the same value of the parameter can affect the dynamics of these variables in opposite directions, depending on stochastic effects.

  38. Given the almost negligible impact on unemployment and real aggregates, these variations are probably due to nominal factors, in particular, to the higher inflation. This in fact increases tax revenues, while reducing the debt burden, and interests payments on past debt especially.

  39. Still, inflation is mild even in this last case, being characterized by an average quarterly rate of approximately 0.79%, which corresponds to an annual rate slighlty above 3%.

  40. The only exception is represented by the class of managers, given the multiplicative effect embedded in the dividend distribution procedure, which allows richer managers’ to increase the share of dividends received from firms and banks.


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This research has benefited from funding of the Institute for New Economic Thinking (INET) and from the European 7th Framework Program under the project “Mathematics of Multilevel Anticipatory Complex Systems (MatheMACS)’, Project Reference: 318723.

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Appendix A: Calibration

Table 1 Parameter values employed in the simulation experiments

Appendix B: Results summary tables

Table 2 Tax progressiveness experiments
Table 3 Labor market experiments

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Caiani, A., Russo, A. & Gallegati, M. Does inequality hamper innovation and growth? An AB-SFC analysis. J Evol Econ 29, 177–228 (2019).

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  • Innovation
  • Inequality
  • Agent based macroeconomics
  • Stock flow consistent models

JEL Classification

  • C63
  • D31
  • E30
  • E25
  • H23