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An agent-based model for Secular Stagnation in the USA: theory and empirical evidence

Journal of Evolutionary Economics volume 32, pages 1345–1389 (2022)Cite this article

Abstract

This paper deals with the Secular Stagnation in productivity growth that marks the US economy since the end of the Golden Age. I contribute to the understanding of this phenomenon proposing a theoretical and empirical analysis. On the theoretical side, I develop an agent-based, stock-flow consistent model to investigate the deep relationship between functional income distribution and productivity through the channel of innovation. Findings suggest that the continuous shift of income from wages to profits may have resulted in a smaller incentive to invest on R&D, with the corresponding decline in productivity growth that characterizes US Secular Stagnation. In this respect, a social compromise between workers and capitalists in terms of higher wages helps foster innovation and economic growth, but it does not necessarily entail significant improvements in terms of income concentration, because of higher unemployment rates. Additionally, I question the neoclassical belief on the negative interest-elasticity of investments, since decreases in the rate of interest are not associated with increases in capital accumulation, but they decrease income inequality through higher employment rates. On the empirical side, this paper presents a panel cointegration analysis on US manufacturing industries for the period 1958–2011. If, on the one hand, the linkage between R&D and wages is corroborated, on the other hand, I find the lack of any long-run relationship between innovative search and the rate of interest, which does not necessarily conflict with theoretical predictions.

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Source: see Supplementary Material

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Data availability

The .R codes and data that support the findings of this study are available from the corresponding author upon request.

Notes

  1. A major attempt to provide the topic with a formal treatment is Eggertsson et al. (2019), whose aim consists of contextualizing Summers (2014a, b) in the New-Keynesian framework. However, the overall framework suffers from important limitations: see Pyka and Fagiolo (2005), Fagiolo and Roventini (2016), and Di Bucchianico (2020).

  2. Among the reasons to adopt this framework, I devise macro-to-micro and micro-to-macro channels. On the one hand, crucial macroeconomic phenomena, e.g., the social conflict between workers and capitalists or the final demand from households influence entrepreneurial decisions about innovative search, employment, and competitiveness. On the other hand, the market structure, its evolution, and firms size distribution steer the aggregate dynamics of innovation and productivity which are central to my definition of Secular Stagnation.

  3. For a thorough historical analysis on why we should consider productivity aspects of Secular Stagnation, see Borsato (2021).

  4. See online Supplementary Material for definitions and details.

  5. I recognise that the Golden Age in US was a particular period marked by the necessity of winning the Cold War against the Soviet Union. It would explain why, for instance, space expenditure growth rates surged toward extraordinary values until the end of the Sixties and then fell sharply after the first moon landing. Further evidence and comments in the online Supplementary Material.

  6. Therefore, aggregate labour demand is never above aggregate labour supply, but equal at most. Though this assumption could be thought of as reasonable, recent evidence suggests a shortage of workers in some sub-sectors of the US economy.

  7. Even if production adapts to demand, firms maintain excess capacity, and this excess does not reflect a wrongful process of expectations formation, but rather the rational decision of the firm to be able to accommodate fluctuations in demand (Ciccone 1986). In what follows, lower case letters denote microeconomic variables and parameters while capital letters refer to aggregate variables. Subscripts j and i set the focus on the single firm and the single individual, respectively.

  8. The introduction of the cost component responds to two further reasons. First, it counterbalances the intrinsic instability that an accelerator-like schedule would implicate. Second, there is a broad literature emphasizing that periods of economic stagnation in early-stage capitalism were the result of investments led by profit-seeking behaviour and not (yet) by final demand (Kaldor 1957, 1961). Dutt (2006), Hicks (1963), Marx (1976) and Hein (2012) provide further details.

  9. For simplicity, I posit that firms do not go bankrupt. Moreover, any time they have sufficient means not to incur further debt, i.e., \(\mathrm{d}{ld}_{j,t}<0\), they use those resources to repay (part of) past debt.

  10. In which \({\sigma }_{i,t}^{mh} = \frac{{m}_{i,t}^{h}}{{M}_{h,t}}\), being \({m}_{i,t}^{h}\) and \({M}_{h,t}\) the individual and the aggregate wealth, respectively.

  11. A well-established evolutionary tradition models firms' innovative activity as a two-step stochastic process (Dosi and Nelson 2010; Nelson and Winter 1982). Although I imagine innovation as it took place with the hiring of researchers, I depart from that tradition for two reasons: firstly, I want to keep the model as simple as possible; secondly, I want to respect some empirical regularity in the innovation process in terms of creation and diffusion of novelties (Tarde 2013).

  12. In which \({\sigma }_{j,t}^{ld}=\frac{l{d}_{j,t}}{{L}_{d,t}}\); \({L}_{d,t}\) is the aggregate amount of loans.

  13. The presence of a passive bank is a limitation but not a major problem. Albeit this assumption does not allow to study the relationship households’ and corporates’ debt has with growth, this is not the object of the present paper, and an active banking system would only add further complexity. Additionally, opting for a passive banking sector is not uncommon, even when the interactions between stocks and flows require the crucial presence of a banking system: recent examples from the literature are Brochier and Macedo e Silva (2019), and Missaglia and Botta (2020).

  14. \({Y}_{t}\) is aggregate production.

  15. As clarified by Sawyer and Passarella (2021), regressive expectations provide a more accurate approximation of how economic agents make their decision in the real worlds. Moreover, “Unlike adaptive expectations, regressive expectations are not systematically wrong” (ibid., p. 393). Yet, that of expectations formation is a hot debate in the literature: see Assenza et al. (2014), Coibon and Gorodnichenko (2015), Coibon et al. (2018), Sorić et al. (2020), and Hommes (2021).

  16. Simulations show the long and gradual convergence of capacity utilization toward an average 70 percent. Details available upon request.

  17. The cyclicality of R&D fuels an interesting debate in the literature and the empirical evidence is mixed: details in Aghion et al. (2010, 2012), Chiao (2001), and Rafferty and Funk (2004).

  18. As above, the random pattern of interaction in the market for “capital” goods leads every firm to produce and sell an amount of goods to the other firms equal to the average. This simplification does not contrast with a log-Gaussian distribution, for firms differ in how they perform on the “consumption” good market in terms of sales and employment. Therefore, this market acts as an important source of heterogeneity.

  19. Representativeness concerns to evidence of lumpiness only and does not extend to other features.

  20. We should not forget the Structuralist perspective, which aims at studying the long-run outcome of short-term interactions between growth and distribution (Barbosa-Filho and Taylor 2006; Rezai 2012; Di Matteo and Sordi 2015; Taylor 2021). Within the evolutionary tradition, a variety of research joins the analysis of innovation creation to the surge of growth cycles (Silverberg and Verspagen 1995; Perez 2003; Fatás-Villafranca et al. 2012; Dosi et al. 2015; Spinola 2021).

  21. A lower amount of Monte Carlo runs with respect to the baseline case does not alter the general properties of the model. See Supplementary Material for details.

  22. The fact that in the model there is not such a clear and well-established influence of the interest rate on investments could be also the consequence of a banking system providing all the demanded credit at a given interest rate. Different results might arise with some sort of endogenous movement of the interest rate on loans as outcome of monetary contractions and credit rationing. In this case, an interest rate hike could constrain investment choices and decrease the investment rate. I will focus on it in future research.

  23. The configuration of parameters in the baseline scenarios with its specific wage rate shows that the decreasing and convergent pattern followed by the wage share does not reduce productivity growth. The reason lies in the increased normal profit rate which keeps feeding entrepreneurial willingness to undertake innovative search. Moreover, the increase in the investment expenditure does not lead automatically to a positive spiral in the need of workers. The skewness in firms’ size distribution shows indeed that, even though they attract a higher level of demand, large firms benefit from productivity gains because they are involved in a more intensive innovative search. Smaller firms, in contrast, will experience a decrease in the target capital stock, because of a lower market share: in this case, investment would decline and the need of workers as well.

  24. The presence of Secular Stagnation in productivity, R&D, and wage share is visible at the industrial level too. Details in the online Supplementary Material.

  25. Interestingly, Fleissig and Strauss (1997) applied the LLC test on real wage panel data finding that real wage innovations for the G7 countries, except for the US, are temporary with half-lives generally less than three years.

  26. Two main messages from Table 9: firstly, since the importance given throughout the analysis to the social conflict and to the distribution of the social product between workers and entrepreneurs, these aspects can be embodied by the influence of unit labour costs on innovative search, the former being a proxy for the wage share at microeconomic level; secondly, this robustness exercise helps understand as the relationship between R&D and wages would not qualitatively change if we switched from labour to unit labour costs.

  27. Table 11 does not distinguish between investments in tangible and intangible capital. I could have alternatively amended the table by creating a new variable for physical investments, say IK, and a new one for R&D investments, say IRD. However, this specification is not very necessary. I assume that firms fund their net investments with their accumulated entrepreneurial profits and out of new loans. There is not such a distinction between sources based on the kind of net investments they are going to fund.

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Acknowledgements

The author is grateful to Alberto Russo, Alessandro Caiani, André Lorentz, Andrea Roventini, Eugenio Caverzasi, Giacomo Rella, Giovanni Bella, Lorenzo Siddi, Marco Veronese Passarella, Maria Savona, Mauro Caminati, Nicolò Gozzi, Riccardo Pariboni, and Tiziano Razzolini for their suggestions during the development of the work. Moreover, I wish to thank the editor and two anonymous referees for their useful and precise comments. This work was supported by University of Siena, the former institution the author belonged to. All errors remain the author’s.

Funding

The author developed the present work when he was a PhD student at the Department of Economics and Statistics at the University of Siena (IT). This work was supported by a three-year PhD scholarship, 2017–2020.

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    Andrea Borsato

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Appendix - Accounting and balance sheets

Appendix - Accounting and balance sheets

This Appendix provides information on the stock-flow consistent properties of the model. Appendix Table 10 concerns to the balance sheet matrix. Financial variable, such as deposits, M, and loans, L, have specular counterpart, with opposite sign, in the sheet of the bank. By contrast, tangible capital, K, does not match with any other liability, but does with households’ positive net worth, Vh, to balance the model.

The transactions-flow matrix in Appendix Table 11 relates some components of NIPA accounts with changes in financial assets and liabilities. Households apart, both production firms and the bank have current and capital accounts. For what regards to the current account of firms, we have the expenditure side of the aggregate production, Y, composed of aggregate consumption, C, and aggregate investment, I. On the other hand, the national product is divided between the wage bill, WB, the entrepreneurial profits, F, the amortization fund, AF, and the interest payments on previous loans, \({r}_{l}\cdot {L}_{t-1}\). The capital account of production firms shows that aggregate investment expenditure is funded through the amortization fund, part of firms accumulated profits, Fu, and out of new loans, \(\Delta L\). Precisely, AF finances the replacement of worn-out capital while Fu and \(\Delta L\) the net investment.Footnote 27 Households consume and save \(\Delta M\). The sources of their expenditure (and savings) are the wage bill, the bank profits as distributed income, and the interest payments on previously accumulated wealth, \({r}_{h}\cdot {M}_{t-1}\). If the household refers to a capitalist, entrepreneurial profits constitute a further source. Finally, the bank records the interest payments on loans and deposits in the respective current account. On the other hand, its capital account registers additions, or subtractions, to assets and liabilities.

Every SFC model has a redundant equation, a relationship that equals the stock of loans, L, to the stock of wealth, M, and closes the model:

$${M}_{t}={L}_{t}$$
(40)

Although the model contains no equilibrium condition which makes M and L equal, they must result identical once the model is solved, in accordance with a Walrasian principle (Godley and Lavoie 2006).

Table 10 Balance sheet matrix
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Table 11 Transactions-flow matrix
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Borsato, A. An agent-based model for Secular Stagnation in the USA: theory and empirical evidence. J Evol Econ 32, 1345–1389 (2022). https://doi.org/10.1007/s00191-022-00772-9

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Keywords

  • Secular Stagnation
  • Innovation Dynamics
  • Agent-based SFC Models
  • Panel Cointegration Analysis

JEL Classification

  • C33
  • O30
  • O43
  • O47