Exploitation, Exploration and Innovation in a Model of Endogenous Growth with Locally Interacting Agents

Transcription

1 DIMETIC Doctoral European Summer School Session 3 October 8th to 19th, 2007 Maastricht, The Netherlands Exploitation, Exploration and Innovation in a Model of Endogenous Growth with Locally Interacting Agents Giorgio Fagiolo Sant Anna School of Advanced Studies, Pisa (Italy) giorgio.fagiolo@sssup.it

2 The Islands Model (Fagiolo and Dosi, 2003) Background Acknowledging with Dick Nelson that there still is a large gap between: What we know about the sources of growth, technological progress, innovation, learning, etc. from empirical research How we inject this knowledge in standard models of growth Theories of Growth vs. Micro/Macro SFs Empirical analyses of technological change and innovation (Cf. Stoneman, 1995; Freeman, 1994; Nelson, 1995 and 1998) New Empirics of Economic Growth and Development (Cf. Durlauf and Quah, 1998; McGrattan and Schmitz, 1998)

3 Motivations (1/2) The role of assumptions Asking Dick Day s question: Can one do good science by using models based on assumptions which are clearly at odds with any empirical evidence about micro behavior? Modeling the economy as a complex evolving system ACE/Evolutionary approach Allows one to be flexible as far as assumptions on individual behavior, interactions, etc. are concerned Highly-parameterized model: trade-off between realistic assumptions, analytical solvability and sharpness of implications

4 Motivations (2/2) Building a dynamic model of growth that Is able (as a plausibility check) to reproduce the fundamental statistical properties of GDP time series Allows one to disentangle the role of the basic sources of growth on the technological side Growth as the result of exploration-exploitation trade-off driven by Technological opportunities Path dependency in technological accumulation Degree of locality / globality of information diffusion Increasing returns to knowledge base exploitation Willingness to explore/exploit

5 The Islands Metaphor Technological Space Technology Output Firms Production Technological Search Innovation Technological Diffusion Imitation Technological Difference Notionally Unbounded Sea Island ( mine ) Homogeneous Good Stylized Entrepreneurs Mining/Extracting the Good Exploration of the Sea Discovering a new island Spreading knowledge from islands Traveling between already known islands Distance between Islands

6 The Model (1/2) Basic ingredients Time is Discrete Finite, constant population of stylized firms I={1,2,,N} Notionally endless, discrete set of technologies (islands) Homogeneous good Islands Stochastically distributed on a bi-dimensional lattice Each node of the lattice can be an island with probability π ( sea with probability 1-π) Each island (x,y) is characterized by a productivity coefficient s(x,y)= x + y

7 The Model (2/2) Initial Conditions Set of initially known islands (exploited technologies) All N firms mining on them (randomly allocated) Each firm working in island (x,y) produces output s.t q( x, y) = s( x, y) n( x, y) α where n(x,y) number of firms currently working on (x,y) α>1 increasing returns-to-scale coefficient

8 Example: 3 initial islands, 10 firms 5 3 2

9 Example: 3 initial islands, 10 firms 5 3 2

10 Dynamics (1/4) Exploration In each t, a miner becomes explorer with probability ε Constant willingness to explore Explorers move around randomly in each period

11 Dynamics (2/4) Innovation In each exploration period, explorers find a new island with a probability π The productivity of the newly discovered island is s* = s(x*,,y*) = (1+W) { [ x* + y* ] + ϕ q i,τ + ξ } Distance from Poisson (λ) Random Variable (Low probability high jumps) the Origin Cumulative Learning Effect: Agents Zero-Mean Random Variable (High Probability Low Jumps) carry with them their previous skills

12 Example: Exploration 5 3 2

13 Example: Exploration 4 3 2

14 Example: Exploration

15 Example: Exploration

16 Dynamics (3/4) Imitation In each t, from any currently exploited island (with at least one miner on it) a signal about current island s productivity is released Any miner currently working on (x,y) receives and follows the signal with a probability proportional to: the productivity of the island the signal comes from the exp of minus the distance between island and miner q( x, y) exp{ ρ d(island,miner)} The higher (smaller) ρ the more global (local) is information and knowledge diffusion Imitators move toward the imitated island following the shortest path leading to it (one step per period)

17 Example: Imitation

18 Example: Imitation

19 Example: Imitation

20 Dynamics (4/4) Dynamics of agents states: summing up In probability, if reached by information on a more productive island Miners Reaching an island With prob. ε i =ε Imitators Explorers In probability, if reached by information on a more productive island

21 Timing and Aggregate Variables Miners update output Miners become explorers Explorers look around Imitators approach islands Information diffusion Miners and explorers collect signals Imitation decisions Time t 1 Time t Given t 1 micro & macro variables Update time t micro & macro variables; next iteration starts Focus on Aggregate output (sum of firms output) and growth rates Number of explorers, imitators, miners

22 Timing and Aggregate Variables Model s parameters ρ : globality of information diffusion ϕ : path-dependency in learning λ : likelihood of radical innovations π : baseline opportunity conditions α : increasing returns to scale in exploitation ε : willingness to explore N : population size T : time horizon

23 Analyzing simulation output Initial Conditions: ( xi,0 ) Micro & Macro Pars: (θi ), Θ Generate Time-Series through Simulation {( xi,t ), t =1,,T} { Xt, t =1,,T} Compute a Set of Statistics S= {s1, s2, } on micro/macro Time-Series Repeat M ind. times Generate Montecarlo Distribution for each Statistics in S= {s1, s2, } Studying how Montecarlo Distributions of Statistics in S= {s1, s2, } behave as initial conditions, micro and macro parameters change Statistical Tests for difference between moments

24 A first question Under which general conditions is the economy able to generate self-sustaining growth as the outcome of the joint processes of exploitation and exploration?

25 A closed economy without exploration (1/2) Shutting down exploration and innovation A given initial set of islands (e.g, only 2) Firms initially mining on them (50%, 50%) They can only exchange information among the 2 existing technologies (initial set of islands cannot be expanded) Diffusion of information drives growth In this case the model is analytically solvable! Whenever an island manages to capture all agents the growth process stops (growth rates are zero) The process is path-dependent and possibly inefficient (convergence toward an inefficient level of output is a nonzero probability event)

26 A closed economy without exploration (2/2) Growth is always a transitory phenomenon Log of GNP Time 0,4 Growth Rates 0,3 0,2 0,1 0-0,1-0,2-0,3-0,4 Time Lock-in may occur on the ex-ante less efficient island

27 A closed economy with exploration (1/4) Allowing for exploration in a closed box Initial set of islands cannot be expanded (no innovation) Explorers are allowed to search only inside initial box Imitation still occurs as before Diffusion of information still drives growth Process driven by information diffusion Steady states can be destabilized by irrational entrepreneurs who decide to leave their island even if everyone is there

28 A closed economy with exploration (2/4) Absorbing states become basins of attraction: growth is a transitory phenomenon but fluctuations can arise 600 GNP Time

29 A closed economy with exploration (3/4) Two ex-ante equally efficient islands 60 Miners Time

30 A closed economy with exploration (4/4) One ex-ante more efficient island: temporary inefficiency may arise Miners Time

31 Exploration in a Open-Ended Economy In the full-fledged model self-sustaining growth can arise! Log of GNP Time

32 A second question When the economy does generate self-sustaining growth (full-fledged model), do log(gnp) time-series display empirically observed statistical properties?

33 Statistical Properties of Simulated GNP Series Yes, if self-sustaining growth does emerge log(gnp) time series are I(1), i.e. difference-stationary growth rates are positively correlated over short horizons persistence of shocks are in line with empirical evidence Scale-effects are not present As in reality, unlike in many endogenous growth models are! AGR 0.20% 0.15% 0.10% Econometric Sample Size (T) % % Population Size (N)

34 A third question When the economy does generate self-sustaining growth (full-fledged model), what are the roles played by system parameters (i.e. by the sources of growth)?

35 The Sources of Growth (1/4) Average growth rates (AGRs) increasing in path-dependency in knowledge accumulation globality of information diffusion AGR 0,75% 0,55% 0,35% 0,15% -0,05% -1,5-0,5 log 10 (ρ) 0,5 1,5 0,2 0,4 0,6 ϕ as well as in returns-to-scale strength and opportunities

36 The Sources of Growth (2/4) The exploitation-exploration trade-off AGR are maximized only if there is a balance between resources devoted to exploration and resources devoted to exploitation 0,2% AGR 0,1% 0,0% 0,0 0,2 0,4 0,6 0,8 ε

37 The Sources of Growth (3/4) Emergence of thresholds I(1) log(gnp) time-series only emerge if increasing returns to scale, opportunities, path-dependency and globality of information are strong enough! 60% < [% of Acc. ADF(1) Test] < 90 % 30% < [% of Acc. ADF(1) Test] < 60 % [% of Acc. ADF(1) Test] > 90 % ϕ 0.2-1,5-0,5 0,5 1,5 Log 10 ρ 0

38 The Sources of Growth (4/4) Emergence of thresholds and if the exploitation-exploration trade-off is solved 100% % of Acceptance of ADF(1) Test 80% 60% 40% 20% 0% ε

39 A fourth question Does the self-sustaining growth process generated by the model lead to explosive growth patterns? Does the variability of growth rates increase over time and tends to infinity?

40 Time Evolution of GNP Growth Rate Variability Higher growth is always associated to smaller GR variability! Self sustained growth is a self-organized process leading to ordered growth patterns No Growt h Mild Growt h SSG - Low Opp S S G - High Opp Time

41 A final question What happens in we inject in the economy more rational firms?

42 Irrationality as a necessary condition for growth Simple setup CRTS, no info diffusion, no path-dependency Injecting in the economy a representative rational firm (RRF) who decides whether to exploit or explore by maximizing expected returns RRF knows the structure of the economy and the direction where best islands are (but not where they are) 500 GDP 400 Irrational Individuals 300 Rational Individuals Time

43 A laboratory for further research Possible extensions Learning Multi-layer economies Demand side and Keynesian cycles Growth and development Internet resources Go to my web-site Software section Download Islands setup wizard

44 and have fun