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A classical-evolutionary model of technological change

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Abstract

Technological change is a central concern for evolutionary economics, which combines detailed empirical studies and conceptual frameworks with mathematical modeling, among them the NK model from evolutionary biology. Technological change is also a central concern for classical and Marxian economics, where it is studied under the rubric of “cost share-induced technological change.” Among the contributions from classical economists is a classical-evolutionary model first introduced by Duménil and Lévy. This paper strengthens the classical-evolutionary model’s microeconomic foundations by deriving it from an underlying NK model. The result is an aggregate model suitable for macroeconomic analysis that is grounded in evolutionary microeconomic theory. This explicit micro-to-macro link opens avenues for further research. The paper presents new results for the classical-evolutionary model, including a “generating function” method for creating candidate functional forms, and provides three illustrative applications.

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Notes

  1. Weitzman (1996, 1998) also finds Harrod-neutral change emerging endogenously in a model of innovation. However, the mechanism is quite different: rather than being driven by cost and profitability considerations, diminishing returns are overcome by the combinatorially expanding possibilities opened through successive rounds of innovation.

  2. Evolutionary economics admits the possibility of exploratory but highly uncertain “long-jumps” on rugged fitness landscapes (Levinthal 1997), but that is a quite different process from taking a large step towards a well-defined technological frontier.

  3. An alternative would be to use products, rather than firms or divisions, as the unit of analysis (as in Cantner et al. 2012).

  4. This section treats TFP growth strictly as a measured quantity, with no theoretical commitment to growth accounting. For a critique of growth accounting and the production function approach, see (Felipe and McCombie 2013; Felipe and Fisher 2003).

  5. See https://mathworld.wolfram.com/HeavisideStepFunction.html for more on the Heaviside function.

  6. It is here that changes in the term c in Eq. 1 would appear if, contrary to the assumption in this paper, that term were not constant. The sum would then be over \(\boldsymbol {\sigma }(s^{\prime })\cdot \hat {\boldsymbol {\nu }}(s^{\prime }\rvert s_{k}) h(\boldsymbol {\sigma }(s^{\prime })\cdot \hat {\boldsymbol {\nu }}(s^{\prime }\rvert s_{k}) - {\Delta } c_{k})\).

  7. The underlying NK model has N elements, each with multiple variants. Denoting the number of variants per element by V, there are VN possible combinations. Even for modest numbers that can yield a large value; 10 elements with 5 variants each yields nearly 10 million possible combinations. Yet, even that understates the size of the search space, since those numbers are typical of what (Murmann and Frenken 2006) term the “first-order subsystem technology cycle” (e.g., for early glider design as shown in their Table 3 on page 940). Below that level are second-order subsystems and components, each of which has its own potentially large search space.

  8. The density function can be defined formally as

    $${f}_d^k\left(\hat{\boldsymbol{v}}\right)=\underset{\boldsymbol{\varepsilon} \to \textbf{0}}{\lim}\frac{1}{\prod_{i=0}^n{\varepsilon}_i}\frac{\epsilon_d^k\left({s}_k\right)}{\left|{\mathcal{N}}_d^{k,\textrm{impr}}\left({s}_k\right)\right|}\left|\left\{{s}^{\prime}\in {\mathcal{N}}_d^{k,\textrm{impr}}\left({s}_k\right)\left|\hat{\boldsymbol{v}}-\frac{\boldsymbol{\varepsilon}}{2}\leq\hat{\boldsymbol{v}}\left(\left.{s}^{\prime}\right|{s}_k\right)<\hat{\boldsymbol{v}}+\frac{\boldsymbol{\varepsilon}}{2}\right.\right\}\right|\cdot $$

     

    Due to the granularity of actual innovation processes, the elements of the vector ε cannot in fact be taken arbitrarily close to zero. The assumption is that they can be brought close enough to zero to justify a continuum model for aggregate analysis.

  9. This is also true by construction, since the matrix of second derivatives of a smooth scalar function is symmetric.

  10. This assumption is compatible with using national accounts data for empirical macroeconomic modeling. No matter how disaggregated the input-output table may be, the sectors that enter into it include a very large number of firms with different characteristics. Nevertheless, the sectoral price indices and sector-by-sector technical coefficients are taken to be broadly representative.

  11. Those papers embed technological change within larger agent-based models in order to explore the interaction between Keynesian and Schumpterian dynamics (Dosi et al. 2010) and between inequality and innovation (Caiani et al. 2019). This paper takes inspiration from the way in which they introduced R&D expenditure into their technological change sub-models, but does not explore them further.

  12. There are conditions under which prices or productivities will not stabilize. Hence the claim is that cost share-induced technological change can, but not necessarily will, stabilize prices in a multi-sector economy.

  13. The Scilab script is available from the author upon request.

  14. According to the World Bank’s methodology (World Bank 2011), fossil resource rents are effectively the profits of fossil extractive sectors as a share of GDP.

  15. Data from the Monthly Energy Review can be downloaded from https://www.eia.gov/totalenergy/data/browser/. The heat content of natural gas is available from https://www.eia.gov/dnav/ng/ng_cons_heat_dcu_nus_a.htm. The time series for heat content begin in 2003; the 2003 values were used for earlier years.

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Acknowledgements

The work presented in this paper benefited from the support of the AFD 2050 Facility. The author is grateful to Antoine Godin and Devrim Yilmaz and to two anonymous reviewers for critical comments on the paper.

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Funding was provided by the Agence Française de Développement under the AFD 2050 Facility

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    Eric Kemp-Benedict

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Kemp-Benedict, E. A classical-evolutionary model of technological change. J Evol Econ 32, 1303–1343 (2022). https://doi.org/10.1007/s00191-022-00792-5

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