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The creative response and the endogenous dynamics of pecuniary knowledge externalities: an agent based simulation model

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Abstract

The paper elaborates an agent based simulation model (ABM) to explore the endogenous long-term dynamics of knowledge externalities. ABMs, as a form of artificial cliometrics, allow the analysis of the effects of the reactivity of firms caught in out-of-equilibrium conditions conditional on the levels of endogenous knowledge externalities stemming from the levels of knowledge connectivity of the system. The simulation results confirm the powerful effects of endogenous knowledge externalities. At the micro-level, the reactions of firms caught in out-of-equilibrium conditions yield successful effects in the form of productivity enhancing innovations, only in the presence of high levels of knowledge connectivity and strong pecuniary knowledge externalities. At the meso-level, the introduction of innovations changes the structural characteristics of the system in terms of knowledge connectivity that affect the availability of knowledge externalities. Endogenous centrifugal and centripetal forces continually reshape the structure of the system and its knowledge connectivity. At the macro system level, an out-of-equilibrium process leads to a step-wise increase in productivity combined with non-linear patterns of output growth characterized by significant oscillations typical of the long waves in Schumpeterian business cycles.

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Notes

  1. We define the equilibrium cost of knowledge as the cost of a standard divisible input, traded in a competitive market, that can be fully appropriated, wear and tear because has a clear exhaustibility, and is used to produce an output that is traded in a competitive market.

  2. NK models assume the reverse, defining density of the components in the landscape, and their knowledge to be exogenous (Levinthal 1997).

  3. See “Appendix A” for detailed presentation of the pseudo code of the model, “Appendix B” for the parameters of the model, “Appendix C” for the parameters of the simulation.

  4. See Antonelli and Ferraris (2011, 2017) for other complementary specifications of this simulation model.

  5. Note that the system is analytically consistent. Naming \(\prod \) the profit of a generic enterprise and D the dividend it will pay to its shareholders, and remembering Eqs. 1,  2 and 5 it is possible to write the following equations:

    $$\begin{aligned} \hbox {D}_{\mathrm{i}} = \prod \nolimits _{\mathrm{i}} = \hbox {pO}_{\mathrm{i}} - \hbox {W}_{\mathrm{i}} \end{aligned}$$
    (15)

    where D could be less than zero if a loss had to be reintegrated. The amount of dividends paid to the whole systems is:

    $$\begin{aligned} \hbox {D} = \sum \hbox {D}_{\mathrm{i}.} \end{aligned}$$
    (16)

    At the aggregate level the system could be resumed as follows:

    $$\begin{aligned} \hbox {Y} = \sum \hbox {W}_{\mathrm{i}} + \sum \hbox {D}_{\mathrm{i}.} \end{aligned}$$
    (17)

    By specifying \(\hbox {D}_{\mathrm{i}}\) using Eq. (16) it is possible to obtain:

    $$\begin{aligned} \hbox {Y} = \sum \hbox {W}_{\mathrm{i}} + \sum \hbox {pO}_{\mathrm{i}} - \sum \hbox {W}_{\mathrm{i}.} \end{aligned}$$
    (18)

    By operating simple compensations Eq. (18) becomes:

    $$\begin{aligned} \hbox {Y} = \sum \hbox {pO}_{\mathrm{i}.} \end{aligned}$$
    (19)

    Recalling expression (2) it is evident that the whole system can reach equilibrium and the amount of money into the system remains always constant.

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Acknowledgements

The authors acknowledge the financial support from the European Commission DG Research under Grant Number 266959 for the ‘Policy Incentives for the Creation of Knowledge: Methods and Evidence’ (PICK-ME) project, as part of the Cooperation Programme/Theme 8/Socio-economic Sciences and Humanities (SSH), of the Collegio Carlo Alberto, and the University of Torino project IPER.

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Authors and Affiliations

  1. Dipartimento di Economia, Università di Torino, Turin, Italy

    Cristiano Antonelli

  2. BRICK, Collegio Carlo Alberto, Turin, Italy

    Cristiano Antonelli & Gianluigi Ferraris

Authors
  1. Cristiano Antonelli
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  2. Gianluigi Ferraris
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Correspondence to Cristiano Antonelli.

Appendices

Appendix A: The pseudo code of the model

(Parameter of the simulation are written in italic bold)

figure a
figure b

Appendix B: Parameters of the model and set up for the different simulations

In order to control the simulations and allow configuration of a wide set of different scenarios, a reach set of parameters has been provided to bias both the behaviour of agents (firms) and the structure of the economic at system macro level and common macro level too. In the simulations of to this paper few of the available parameters vary, their number has been set to support further evolutions of the research, so many parameters have had the same value for all the simulations presented in the paper, related to those parameter no sensitivity analysis, neither specific simulations have been done due to the fact their values were always the same for each simulations or scenario. Models based on the Swarm protocol distinguish two different object devoted to control the simulation: the Observer that is charged to collect and report the results emerging during the simulation the Model that is charge to build all the objects to populate the model and schedule the activity of those ones. Both Observer and Model give the possibility to specify customized parameters,

The observer uses a first set of two parameter to determine the output shape and update:

  • displayFrequency set up the interval, in model steps, between each refresh of the graphs. Because the presented simulation was devoted to study the dynamic of the system, this parameter has been set to 1 (i.e. graphs are redrawn at each simulation step) to fully report variations in the observed quantities.

  • zoomFactor influence the shape of the graphs produced and updated during the simulation run. Its value is usually set to 2, all the simulations used that value.

The model has been provided a wider set of parameters to make the configuration of different scenario very easy. In details:

  • randomSeed: (any natural number in the interval ]0,\(\infty \)[) it is used to initialize the random seed generator. Useful both to vary the random distributions as well as to ensure the possibility to replicate an experiment with the same random number distribution.

  • Agents: (any natural number in the interval ]0,\(\infty \)[) determines the number of firms that will be put in the simulated economy. The maximum number of firms allowed for a simulation depends on the memory and processing power of the computer used for the simulation.

  • Commons: (any natural number in the interval ]0,\(\infty \)[) specifies how many commons will be generate and used into the simulation. The maximum number of firms allowed for a simulation depends on the memory and processing power of the computer used for the simulation.

  • InitialWealth: (any real number in the interval ]0,\(\infty \)[) specifies the initial endowment of workers they’re going to offer into the market to buy the first productive cycle’s output.

  • StartingProductivity: (any real number in the interval ]0, \(\infty \)[) indicates the upper limit for the interval used to assign each agent an initial productivity, by randomly tossing, for each, a different real number into the interval ]0,startingProductivity[.

  • StartingFactor: (any real number in the interval ]1,\(\infty \)[) specifies the quantity of work units the enterprises will demand on the market and employ for production in the first simulated production cycle.

  • SuccessesThreshold: (any natural number in the interval ]0,\(\infty \)[) specifies how much consecutive successes have to be piled before starting a trial for innovation. A success is achieved every time the own profit of the agent is greater than the average common’s one + a tolerance percentage.

  • FailuresThreshold: (any natural number in the interval ]0,\(\infty \)[),\(\infty \)[) specifies how much consecutive failures have to be piled before starting a trial for innovation. A failure is suffered every time the own profit of the agent is less than the average common’s one—a tolerance percentage.

  • IprDuration: (any natural number in the interval ]0,\(\infty \)[) specifies the number of production cycle the patent rights protect each innovation, during this time the innovation is hidden to the other agents.

  • RevampTime: (any natural number in the interval ]0,\(\infty \)[) specifies the number of production cycle after an agent is gone out of business for having another one keep its place. The name of the parameter is due to the fact that a new agents is only the revamp of the old one, with productivity equal to the average common’s one.

  • FactorUp: (any real number in the interval ]1,\(\infty \)[) is the number used to multiply the previous demand for factor to determine the actual one, by the firms that achieved a profit. Because the base assumption is that profitable firms will expand the production this parameter have to be set at a value greater than one, but close to one; for instance setting factorUp to two would means that enterprises that had a profit will double their demand for factor (work) for the next production cycle.FactorDown: (any real number in the interval ]0,1[) is the number used to multiply the previous demand for factor by the enterprises that just suffered a loss; this parameter has to be set close to one too, even less than one.

  • PotentialPerStep: (any real number in the interval ]0,1[) represents the fraction of the common’s productivity that each agent accumulate in each production cycle due to experience. This parameter has to be set accordingly with the following “Productivity upgrade”, that measure the amount of accumulated experience needed to enhance technology of one unit.

  • ProductivityUpgrade: (any real number in the interval ]0,\(\infty \)[) represents the minimum quantity of accumulated potential that could be transformed in a unit of technological enhancement. Note that transformation can be performed for this amount of cumulated experience at a time only, and gives one unit of technological enhancement.

  • Tolerance: (any real number in the interval ]0,1[), defines the symmetric interval around the average common’s profit used by each firm to decide if take actions to improve its technology. Unless the result (either profit or loss) of an enterprise in a certain production cycle was less than [average common’s results * (1-tolerance)] or was grater than [average common’s results * (1+tolerance)] no improvement on the technological level are tried.

  • MaxLoss: (any real number in the interval ]0,\(\infty \)[), it measures the maximum loss an enterprises can cumulate before going out of business. The meaning is in that if cumulated results of an enterprises reach a negative amount less than (−1)maxLoss it goes immediately out of business and will be replaced, into the same common, by another one after revampTime production cycles.

  • TransformationCost: (any real number in the interval [0,\(\infty \)[), it measures the amount of work unit an enterprise has to demand on the market to perform a transformation of accumulated experience in technological enhancement.

  • MovingCost: (any real number in the interval [0,\(\infty \)[), it measures the amount of work unit an enterprise has to demand on the market to move from the actual common to another one.

  • SpilloverMinProb: (any real number in the interval [0,1]), is the success base probability assigned to a generic spillover action, the effective probability of success for a spillover action is computed as: (1-spilloverMinProb)(1-delta)+spilloverMinProb), where delta measures the distance between productivity after and before the spillover action.

  • CommonsCost: (any real number in the interval [0,\(\infty \)[), is the amount used to compute the quantity of work each firms has to buy, each production cycle, to get information and manage relation into the commons it belongs to. The costs are the same for each agent into the commons.

In order to manage the simulations, some control parameters have been used:

  • Scenario: (an integer number in the interval [1,5]) specifies the scenario to be executed among: Alpha, Beta, Gamma, Iota and Theta; by choosing one of them the program automatically sets up the core parameters to configure the chosen scenario.

  • Spillover: (an integer number in the interval [0,1]) it is a simple switch that allows or stops the possibility for firms to spill knowledge from other ones into the common.

  • Reinforce: (an integer number in the interval [0,1]) used to turn on or off the effect of the common productivity on the knowledge each enterprise grows up by executing each production cycle.

Finally the old parameters: (i) focused, (ii) explorationRate and (iii) spilloverCostRate are no more used, even still present in the input form.

Appendix C: Parameters’ values for the simulations

The simulations used for the research were based upon different settings of few parameters, as described in chapter four, obtained by biasing a base configuration named alpha scenario. The full parameters setting for each scenario are reported in the following Table 6.

Table 6 Parameters’ setting for each scenario
Full size table

Appendix D: Robustness and sensitivity

1.1 Introduction—pseudo random generators

Several processes in the model are based on random events: (i) technological improvement may fail according to a probability distribution set parametrically, (ii) other firms are picked up randomly among the neighbours to observe and eventually imitate, (iii) enterprises that move decide randomly the new common to enter in, etc. The generation of pseudo random numbers has to be managed with specific care.

In order to guarantee the full independence of each agent, as well as of each environmental component, like commons, market and so on, each object has been provided an own random generator (Ferraris 2006); the control of the random distributions is based on a simple procedure:

  1. (a)

    The modelSwarm object (the main component that is charged to build and activate all the other ones, either agents or environmental institutions, has been provided with an own random generator (named the main generator), whose seed can be fixed by the researcher, simply supplying a value for the parameter “randomSeed”. If the value zero is specified the model tosses a random seed using the standard generator the simulation tool (for this model Swarm) provided.

    Note that this generator is not used to toss random values for parameters expected to vary. In this way it is possible to fix all the random events, even with parameters that are randomly set up.

  2. (b)

    Each component of the model that uses random numbers is given an own random generator, made by the modelSwarm just before building the component, fed with a seed tossed by using the main generator.

Such a architecture allows both: (i) independence of each component even for humongous numbers of requests for random values, (ii) full control of the random generation. In this way the researcher is allowed to:

  1. (a)

    exploit the possibility to replicate a simulation with the same sequence of random numbers,

  2. (b)

    change randomly the sequence,

  3. (c)

    avoid interferences among agents and environmental institutions (or generally speaking components) even with heavy usage of random numbers.

The exploitation of the previous described architecture allowed both robustness and sensitivity tests, whose results are briefly described in the next paragraphs.

1.2 Robustness

To ensure that the results obtained from the simulations were independent from the random distributions, a simple robustness test has been performed:

  1. (a)

    The model has been run for one hundred times with fixed parameters values but randomly changing, each time, the seed of the main generator (recalling the architecture described in F1, this means a different random seed, each time, for the more than one thousand objects involved in each simulations).

  2. (b)

    For each simulation the average values of the productivity are measured at the 2000th production cycles (because each simulations employed one thousand agents, it means 2 million production cycles for each measure, that was based on several millions random tossed values for different decisions).

  3. (c)

    After one hundred values of productivity obtained running the simulations, the mean, variance of the values, a succession has been computed to evaluate the independence of the results from the random seeds distribution.

Table 7 resumes the results: the variance of both productivity and commons dimension is quite low and seems to confirm the simulations results are not determined by employed random distributions, neither Pearson’s r value shows correlation between results and random seeds.

Table 7 Analysis of the results obtained by one hundred simulations with same parameters’ values but different random seed, based upon the alpha scenario
Full size table

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Antonelli, C., Ferraris, G. The creative response and the endogenous dynamics of pecuniary knowledge externalities: an agent based simulation model. J Econ Interact Coord 13, 561–599 (2018). https://doi.org/10.1007/s11403-017-0194-3

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