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Endogenous growth in production networks

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Abstract

We investigate the interplay between technological change and macro- economic dynamics in an agent-based model of the formation of production networks. On the one hand, production networks form the structure that determines economic dynamics in the short run. On the other hand, their evolution reflects the long-term impacts of competition and innovation on the economy. We account for process innovation via increasing variety in the input mix and hence increasing connectivity in the network. In turn, product innovation induces a direct growth of the firm’s productivity and the potential destruction of links. The interplay between both processes generates complex technological dynamics in which phases of process and product innovation successively dominate. The model reproduces a wealth of stylized facts about industrial dynamics and technological progress, in particular the persistence of heterogeneity among firms and Wright’s law for the growth of productivity within a technological paradigm. We illustrate the potential of the model for the analysis of industrial policy via a preliminary set of policy experiments in which we investigate the impact on innovators’ success of feed-in tariffs and of priority market access.

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Notes

  1. Here and in the following, we always consider implicitly that the vector (μinc,μim,μrad) is normalized so that μrad + μinc + μim = 1

  2. A cautionary note in this respect is that, as argued by Lamperti et al. (2015), market-based policies may not be sufficient to prevent environmental disasters while Command-and- Control policies are fully effective.

  3. In fact, everything goes as if the economy were receiving an external subsidy.

References

  • Acemoglu D, Carvalho VM, Ozdaglar A, Tahbaz-Salehi A (2012) The network origins of aggregate fluctuations. Econometrica 80(5):1977–2016. http://ideas.repec.org/a/ecm/emetrp/v80y2012i5p1977-2016.html

    Article  Google Scholar 

  • Addison DM (2003) Productivity growth and product variety: gains from imitation and education world bank policy research paper 3023. Technical report, The World Bank

  • Aghion P, Howitt P (1992) A model of growth through creative destruction. Econometrica 60(2):323–351

    Article  Google Scholar 

  • Aghion P, Howitt P (1998) Endogenous growth theory. MIT Press, Cambridge

  • Aghion P, Akcigit U, Howitt P (2013) What do we learn from schumpeterian growth theory? Technical report, National Bureau of Economic Research

  • Amiti M, Konings J (2007) Trade liberalization, intermediate inputs, and productivity: evidence from indonesia. Am Econ Rev 97(5):1611–1638

    Article  Google Scholar 

  • Arrow KJ (1962) The economic implications of learning by doing. Rev Econ Stud 29(3):155–173

    Article  Google Scholar 

  • Auerswald P, Kauffman S, Lobo J, Shell K (2000) The production recipes approach to modeling technological innovation: an application to learning by doing. J Econ Dyn Control 24(3):389–450

    Article  Google Scholar 

  • Axtell RL (2001) US firm sizes are zipf distributed. Science 93:1818–1820

    Article  Google Scholar 

  • Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: an explanation of the 1/f noise. Phys Rev Lett 59(4):381

    Article  Google Scholar 

  • Battiston S, Gatti DD, Gallegati M, Greenwald B, Stiglitz JE (2007) Credit chains and bankruptcy propagation in production networks. J Econ Dyn Control 31 (6):2061–2084. http://ideas.repec.org/a/eee/dyncon/v31y2007i6p2061-2084.html

    Article  Google Scholar 

  • Bottazzi G, Secchi A (2006) Explaining the distribution of firm growth rates. RAND J Econ 37(2):235–256

    Article  Google Scholar 

  • Cabral LMB, Mata J (2003) On the evolution of the firm size distribution: facts and theory. Am Econ Rev 98(1):1075–1090

    Article  Google Scholar 

  • Carvalho VM (2014) From micro to macro via production networks. J Econ Perspect 28(4):23–47

    Article  Google Scholar 

  • Carvalho VM, Voigtländer N (2014) Input diffusion and the evolution of production networks. Technical report, National Bureau of Economic Research

  • Ciarli T, Lorentz A, Savona M, Valente M (2010) The effect of consumption and production structure on growth and distribution. A micro to macro model. Metroeconomica 61(1):180–218

    Article  Google Scholar 

  • Coad A (2009) The growth of firms: a survey of theories and empirical evidence. Edward Elgar Publishing, Cheltenham

    Book  Google Scholar 

  • d’Autume A, Michel P (1993) Endogenous growth in arrow’s learning by doing model. Eur Econ Rev 37(6):1175–1184

    Article  Google Scholar 

  • Dawid H, Gemkow S, Harting P, van der Hoog S, Neugart M (2011) The eurace@ unibi model: an agent-based macroeconomic model for economic policy analysis. Technical Report, Working Paper. Universität Bielefeld

  • Dawid H, Harting P, Neugart M (2014) Economic convergence: policy implications from a heterogeneous agent model. J Econ Dyn Control 44:54–80

    Article  Google Scholar 

  • Dosi G (1982) Technological paradigms and technological trajectories: a suggested interpretation of the determinants and directions of technical change. Res Policy 11 (3):147–162

    Article  Google Scholar 

  • Dosi G, Nelson RR (2010) Technical change and industrial dynamics as evolutionary processes. Handbook of the Economics of Innovation 1:51–127

    Article  Google Scholar 

  • Dosi G, Fagiolo G, Roventini A (2010) Schumpeter meeting keynes: a policy-friendly model of endogenous growth and business cycles. J Econ Dyn Control 34(9):1748–1767. http://ideas.repec.org/a/eee/dyncon/v34y2010i9p1748-1767.html

    Article  Google Scholar 

  • Dosi G, Fagiolo G, Napoletano M, Roventini A (2013) Income distribution, credit and fiscal policies in an agent-based Keynesian model. J Econ Dyn Control 37 (8):1598–1625

    Article  Google Scholar 

  • Dosi G, Fagiolo G, Napoletano M, Roventini A, Treibich T (2015) Fiscal and monetary policies in complex evolving economies. J Econ Dyn Control 52:166–189

    Article  Google Scholar 

  • Ethier WJ (1982) National and international returns to scale in the modern theory of international trade. Am Econ Rev 72(3):389–405

    Google Scholar 

  • Fagiolo G, Dosi G (2003) Exploitation, exploration and innovation in a model of endogenous growth with locally interacting agents. Struct Chang Econ Dyn 14 (3):237–273

    Article  Google Scholar 

  • Feenstra RC, Madani D, Yang T -H, Liang C -Y (1999) Testing endogenous growth in South Korea and Taiwan. J Dev Econ 60(2):317–341

    Article  Google Scholar 

  • Frenken K (2006a) A fitness landscape approach to technological complexity, modularity, and vertical disintegration. Struct Chang Econ Dyn 17(3):288–305

  • Frenken K (2006b) Technological innovation and complexity theory. Econ Innov New Technol 15(2):137–155

  • Frensch R, Wittich VG (2009) Product variety and technical change. J Dev Econ 88(2):242–257

    Article  Google Scholar 

  • Funke M, Ruhwedel R (2001) Product variety and economic growth: empirical evidence for the oecd countries. IMF Staff Pap 48(2):225–242

    Google Scholar 

  • Gualdi S, Mandel A (2015) On the emergence of scale-free production networks. J Econ Dyn Control 73:61–77

    Article  Google Scholar 

  • Jackson MO, Rogers BW (2007) Meeting strangers and friends of friends: how random are social networks?. Am Econ Rev 97(3):890–915

    Article  Google Scholar 

  • Kauffman S (1993) The origins of order: self organization and selection in evolution. Oxford University Press, USA

    Google Scholar 

  • Kauffman S, Lobo J, Macready WG (2000) Optimal search on a technology landscape. J Econ Behav Organ 43(2):141–166

    Article  Google Scholar 

  • Lamperti F, Napoletano M, Roventini A (2015) Preventing environmental disasters: market-based vs. command-and-control policies. LEM working papers, 34

  • Lancaster KJ (1966) A new approach to consumer theory. J Polit Econ 74 (2):132–157

    Article  Google Scholar 

  • Mandel A, Jaeger C, Fürst S, Lass W, Lincke D, Meissner F, Pablo-Marti F, Wolf S (2010) Agent-based dynamics in disaggregated growth models. Documents de Travail du Centre d’Economie de la Sorbonne 10077, Université Panthéon-Sorbonne (Paris 1) Centre d’Economie de la Sorbonne. http://ideas.repec.org/p/mse/cesdoc/10077.html

  • McNerney J, Farmer JD, Redner S, Trancik JE (2011) Role of design complexity in technology improvement. Proc Natl Acad Sci 108(22):9008–9013

    Article  Google Scholar 

  • Nelson RR, Winter SG (1982) An evolutionary theory of economic change. Harvard University Press, Harvard

  • Romer PM (1990) Endogenous technological change. J Polit Econ 98(5 pt 2):71–102

    Article  Google Scholar 

  • Saviotti P, Pyka A (2008) Product variety, competition and economic growth. J Evol Econ 3(18):323– 347

    Article  Google Scholar 

  • Saviotti P P, et al (1996) Technological evolution, variety and the economy. Books

  • Saxenian AL (1996) Regional advantage. Harvard University Press, Cambridge

    Google Scholar 

  • Silverberg G, Verspagen B (2005) A percolation model of innovation in complex technology spaces. J Econ Dyn Control 29(1):225–244

    Article  Google Scholar 

  • Tàbara J D, Mangalagiu D, Kupers R, Jaeger CC, Mandel A, Paroussos L (2013) Transformative targets in sustainability policy making. J Environ Plan Manag 56(8):1180–1191

    Article  Google Scholar 

  • Utterback JM (1994) Mastering the dynamics of innovation: how companies can seize opportunities in the face of technological change. Harvard Business School Press, Boston. ISBN 0-87584-342-5

    Google Scholar 

  • Weisbuch G, Battiston S (2007) From production networks to geographical economics. J Econ Behav Organ 64(3):448–469

    Article  Google Scholar 

  • Wolf S, Fuerst S, Mandel A, Lass W, Lincke D, Pablo-Marti F, Jaeger C (2013) A multi-agent model of several economic regions. Environ Model Softw 44:25–43. https://doi.org/10.1016/j.envsoft.2012.12.012. ISSN 1364-8152. http://www.sciencedirect.com/science/article/pii/S1364815213000029

    Article  Google Scholar 

  • Wright TP (1936) Factors affecting the cost of airplanes. Journal of the Aeronautical Sciences 3(4):122–128

    Article  Google Scholar 

  • Yang X, Borland J (1991) A microeconomic mechanism for economic growth. J Polit Econ 99(3):460–482

    Article  Google Scholar 

Download references

Funding

This study was funded by the European Commission through the FP7 project IMPRESSIONS (603416) and the H2020 project Dolfins (640772), and through the Agence Nationale de la Recherche via Labex Louis Bachelier (ANR 11-LABX-0019) and Labex OSE (ANR-10-LABX-93-01).

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Correspondence to Antoine Mandel.

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Appendix A: General equilibrium and production networks

Appendix A: General equilibrium and production networks

1.1 A.1 A general equilibrium economy

One can associate to a production network A a general equilibrium economy as follows:

Definition 1

The general equilibrium economy \(\mathcal {E}(A)\)is defined by the given of:

  • A representative household supplying one unit of labor andhaving preferences represented by the Cobb-Douglas utility function\(u(x_{1},\cdots ,x_{m})=\prod _{i = 1}^{m} x_{i}^{\alpha _{0,i}}\)

  • A set of firms M with production functions of the form

    $$ f_{i}(x_{0},(x_{j})_{j = 1,\cdots,n_{i}})= x_{0}^{\alpha} \left( \sum\limits_{j = 1}^{n_{i}} x_{j}^{\theta}\right)^{(1-\alpha)/\theta} $$
    (6)
  • A production network A consistent with Eq. 6in the sense that for alliM,\(\sum _{j = 1}^{m} a_{i,j}=n_{i}\).

1.2 A.2 Out-of-equilibrium dynamics

For a given network, the dynamics of prices and output follow from the application of simple behavioral rules. More precisely, given a production network A the dynamics of wealth \({w^{t}_{i}} \in {\mathbb {R}}_{+}\), output \({q^{t}_{i}} \in {\mathbb {R}}_{+}\) and prices \({p^{t}_{i}} \in {\mathbb {R}}_{+}\) within period t are determined as follows.

  1. 1.

    Each agent i receives the nominal demand \(\sum _{j \in N} \alpha ^{t}_{i,j} {w^{t}_{j}}\), which is implied by the current structure of the supply network

  2. 2.

    Agents adjust their prices frictionally toward their market-clearing values according to:

    $$ {p_{i}^{t}}=\tau_{p} \overline{p}_{i}^{t}+ (1-\tau_{p}) p^{t-1}_{i} $$
    (7)

    where τp ∈ [0, 1] is a parameter measuring the speed of price adjustment and, given the nominal demand \(\sum _{j \in N} \alpha ^{t}_{i,j} {w^{t}_{j}}\) and the output stock \({q_{i}^{t}}\), \(\overline {p}_{i}^{t}\) is the market clearing price for firm i, that is:

    $$ \overline{p}_{i}^{t}=\frac{\sum_{j \in N} \alpha^{t}_{i,j} {w^{t}_{j}}}{{q_{i}^{t}}}. $$
    (8)
  3. 3.

    Whenever τp < 1 markets do not clear (except if the system is at a stationary equilibrium). In case of excess demand, we assume that clients are rationed proportionally to their demand. In case of excess supply, we assume that the amount \(\overline {q}^{t}_{i}:=\sum _{j \in N} \alpha ^{t}_{i,j} {w^{t}_{j}}/p_{i}^{t}\) is actually sold and that the rest of the output is stored as inventory. Together with production occurring on the basis of purchased inputs, this yields the following evolution of the product stock:

    $$ q^{t + 1}_{i}={q^{t}_{i}}-\overline{q}^{t}_{i} + f_{i}\left( \frac{\alpha^{t}_{0,i}{w^{t}_{i}}}{{p_{0}^{t}}}, \left( \frac{\alpha^{t}_{j,i}{w^{t}_{i}}}{{p_{j}^{t}}}\right)_{j \in \Sigma_{i}(A^{t})}\right) $$
    (9)

    Note that in the case where τp = 1, markets always clear (one has \(\overline {q}^{t}_{i} = {q^{t}_{i}}\)) and Eq. 9 reduces to

    $$ q^{t + 1}_{i}= f_{i}\left( \frac{\alpha^{t}_{0,i}{w^{t}_{i}}}{{p_{0}^{t}}},\left( \frac{\alpha^{t}_{j,i}{w^{t}_{i}}}{{p_{j}^{t}}}\right)_{j \in \Sigma_{i}(A^{t})}\right) $$
    (10)
  4. 4.

    As for the evolution of agents’ wealth, it is determined on the one hand by their purchases of inputs and their sales of output. On the other hand, we assume that the firm sets its expenses for next period at (1 − λ) times its current revenues and distributes the rest as dividends to the representative household. That is one has:

    $$ \forall i \in M,\ w^{t + 1}_{i}=(1-\lambda)\overline{q}^{t}_{i} {p_{i}^{t}} $$
    (11)
    $$ w^{t + 1}_{0}= {q}_{0}^{t} {p_{0}^{t}} +\lambda \sum\limits_{i \in M}\overline{q}^{t}_{i} {p_{i}^{t}} $$
    (12)

    Note that Eq. 12 can be interpreted as assuming that firms have myopic expectations about their nominal demand (i.e they assume they will face the same nominal demand next period) and target a fixed profit/dividend share λ ∈ (0, 1).

  5. 5.

    As for the evolution of input shares, agents adjust frictionally their input combinations toward the cost-minimizing value according to:

    $$ \alpha_{i}^{t + 1}=\tau_{w} \overline{\alpha}_{i}^{t} +(1-\tau_{w}) {\alpha_{i}^{t}} $$
    (13)

    where τw ∈ [0, 1] measures the speed of technological adjustment and \(\overline {\alpha }_{i}^{t} \in {\mathbb {R}}^{M}\) denotes the optimal input weights for firm i given prevailing prices. Those weights are defined as the solution to the following optimization problem:

    $$ \left\{\begin{array}{cc} \max & f_{i}\left( \frac{\alpha_{0},i}{{p_{0}^{t}}},\left( \frac{\alpha_{j},i}{{p_{j}^{t}}}\right)_{j \in \Sigma_{i}(A^{t})}\right) \\ \text{s.t} & \sum_{j \in \Sigma_{i}(A^{t})} \alpha_{j,i}= 1 \end{array}\right. $$
    (14)

1.3 A.3 Convergence

These behavioral rules in fact define out-of-equilibrium dynamics in the economy \(\mathcal {E}(A)\). Their asymptotic properties are extensively studied in Gualdi and Mandel (2015). In particular, for a fixed network and over a vast region of the parameter space, one observes convergence to a general equilibrium of the underlying economy with a fixed mark-up rate λ. It corresponds to general equilibrium in the common-sense if λ = 0 and is defined as follows:

Definition 2

A λ-mark-up equilibriumof the economy \(\mathcal {E}(A)\)is acollection of prices \((p^{*}_{0},\cdots ,p^{*}_{n}) \in {\mathbb {R}}^{M}_{+}\),production levels \((q^{*}_{0},\cdots ,q^{*}_{n}) \in {\mathbb {R}}^{M}_{+}\)andcommodity flows \((x^{*}_{i,j})_{i,j = 0\cdots n} \in {\mathbb {R}}^{M\times M}_{+}\)such that:

  • Markets clear. That is for all iM,one has

    $$q^{*}_{i} = \sum\limits_{j = 1}^{M} x^{*}_{i,j}. $$
  • The representative consumer maximizes his utility. That is\((q^{*}_{0},(x^{*}_{0,j})_{j = 1,\cdots ,n})\)isa solution to

    $$\left\{\begin{array}{c} \max u_{i}((x_{0,j})_{j = 1,\cdots,n}) \\ \\ \text{s.t } \sum_{j = 1}^{n} p^{*}_{j} x^{*}_{0,j} \leq 1 \end{array}\right. $$

    (with the price of labor normalized to 1)

  • Production costs are minimized. That is for alliM,(xi,j∗)j= 0⋯nis the solutionto

    $$\left\{\begin{array}{cc} \min & \sum_{j \in \Sigma_{i}(A)} p^{*}_{j} x_{j} \\ \text{s.t} & f_{i}(x_{j})\geq q^{*}_{i} \end{array}\right. $$
  • Prices are set as a mark-up over production costs at rate\(\frac {\lambda }{1-\lambda }\). That is one has for alliN :

    $$p^{*}_{i} =\left( 1+ \frac{\lambda}{1-\lambda}\right)\frac{\sum_{j \in \Sigma_{i}(A)} p^{*}_{j} x^{*}_{i,j}}{q^{*}_{i}} $$

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Gualdi, S., Mandel, A. Endogenous growth in production networks. J Evol Econ 29, 91–117 (2019). https://doi.org/10.1007/s00191-018-0552-x

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