Introduction to Agent Based Modelling Tommaso Ciarli SPRU, - PowerPoint PPT Presentation

Introduction Learning outcomes Outline Literature Evolutionary modelling Dawid, H. (2005), Agent–Based Models of Innovation and Technical Change, in Leigh Tesfatsion & K. L. Judd, ed., Handbook of Computational Economics, Volume 2: Agent-Based Computational Economics, North–Holland Safarzyńska, K. & van den Bergh, J. C. J. M. (2010), ’Evolutionary models in economics: a survey of methods and building blocks’, Journal of Evolutionary Economics 20(3), 329-373 Macro Silverberg, G. & Verspagen, B. (2005) Evolutionary Theorizing on Economic Growth in Dopfer, K. (ed.) The Evolutionary Foundations of Economics, Cambridge University Press, 506-539 Verspagen, B. (2006), Innovation and Economic Growth, in Jan Fagerberg; David C. Mowery & Richard R. Nelson, ed., The Oxford Handbook of Innovation, Oxford University Press, Oxford, pp. 487-513. 21 / 96

Introduction Learning outcomes Outline Literature ABM Macro Nelson, R. R. & Winter, S. G. (1982), An Evolutionary Theory of Economic Change, Harvard University Press, Cambridge, MA. Ch 12 & 14 Ciarli, T. (2012), ’Structural interactions and long run growth: An application of Experimental Design to Agent Based Models’, Revue de l’OFCE, Debates and policies 124(5), 295-345. Lorentz, A., T. Ciarli, M. Savona, and M. Valente. 2016. ‘The Effect of Demand-Driven Structural Transformations on Growth and Technological Change.’ Journal of Evolutionary Economics 26(1):219–246. Ciarli, T., and M. Valente. 2016. ‘The complex interactions between economic growth and market concentration in a model of structural change.’ Structural Change and Economic Dynamics forthcomin. Ciarli T., A. Lorentz, M. Savona, and M. Valente. 2016. ‘Growth Regimes and Structural Change’ mimeo. Colander, D.; Howitt, P .; Kirman, A.; Leijonhufvud, A. & Mehrling, P . (2008), ’Beyond DSGE models: toward an empirically based macroeconomics’, American Economic Review 98(2), 236–240. 22 / 96 Dosi, G.; Fagiolo, G. & Roventini, A. (2010), ’Schumpeter Meeting Keynes: A Policy–Friendly Model of Endogenous Growth and Business Cycles’, Journal of Economic Dynamics and Control 34, 1748-1767.

Introduction CS CS Properties ACE Discussion LSD Part I Agent Based Modelling in the social sciences 23 / 96

Introduction CS CS Properties ACE Discussion LSD Standard economics Main features of standard economic theory Rationality: fully rational agents Infinite computation and memory Know the model of the world Know that all other agents are also fully rational No need for learning Interactions Information, knowledge and goods flow through individuals: all connected, no frictions Macro: no interactions Game theory: interactions with all other individuals 24 / 96

Introduction CS CS Properties ACE Discussion LSD Standard economics Main features of standard economic theory Heterogeneity Homogeneous Heterogeneity does not change results Average behaviour = behaviour of the average (normal/symmetric distribution) Time and aggregation Economy always in equilibrium: all micro and macro forces compensate, in short and long run No crucial time dimension: infinitely lived agents Repeated static models GE , Microfoundations , Game Theory 25 / 96

Introduction CS CS Properties ACE Discussion LSD Definition Characteristics of a complex system (Page, 2015) Interaction structure (facebook) Interdependent: people influence each other (fads) Learning and adaptation: change, behaviour, connections and interdependency Selection (and variation) Heterogeneity: initial, as a process of adaptation, or innovation 26 / 96

Introduction CS CS Properties ACE Discussion LSD What does empirical evidence suggests about Information and uncertainty Rationality Interactions Heterogeneity Time and dynamics Emergence? 27 / 96

Introduction CS CS Properties ACE Discussion LSD Knightian uncertainty Uncertainty Risk: when we know the probability distribution of future events Incremental innovation Knightian Uncertainty: when the risk cannot be measured Radical innovation: future directions and trajectories of technologies? E.g. environmental impact of innovations Returns from investment in innovations? e.g. pharma before biotech ⇒ procedural, bounded rationality to make decisions (incremental): routinised behaviour ⇒ no Bayesian agent with a clear set of possible outcomes (radical): innovation as a guess, requires intuition, animal spirits 28 / 96

Extreme losses and gains (with non-negligible probability) Source : Levy (1998) S&P 500 1 minute rate of return distribution (90-95)

Technology per se drives uncertainty Source : Little green blog “dishwasher versus hand washing”: Aproximadamente 855.000 resultados (0,39 segundos)

Introduction CS CS Properties ACE Discussion LSD Rationality Micro entities with simple and routinised behaviour Experimental evidence from cognitive Psychology: Kahneman, Tversky, Gigerenzer, etc Difference between Risk and Uncertainty Inherent difficulty in dealing with uncertainty and probability Different risk aversion for gains and losses Bayesian VS frequentist approaches Cognitive biases People take decisions in a relative way, comparing local options 31 / 96

Introduction CS CS Properties ACE Discussion LSD Rationality Risk aversion Problem A (win): an individual is given $1,000 A1: Win $1,000 with 50% probability (0 otherwise) A2: Win $500 with certainty Problem B (loss): an individual is given $2,000 B1: Loose $1,000 with 50% probability (0 otherwise) B2: Loose $500 with certainty Rational choice In both cases the expected outcome is $1500 Depending on risk aversion, if the rational individual chooses A1(A2), she should also choose B1(B2) 32 / 96

Introduction CS CS Properties ACE Discussion LSD Rationality Risk aversion Lab experiment: A statistically significant majority of individuals choose A2 and B1 ⇒ Individuals are risk lovers for losses and risk averse for gains ⇒ The structure of the problem (decision making) affects the choice 33 / 96

Introduction CS CS Properties ACE Discussion LSD Rationality Relative decision making Economist.com subscription: real world experiment Consumers have the following choices 1 Internet only option: $59 2 Print only option: $125 3 Print and Internet option: $125 Result: 16% (1), 0% (2), 84% (3) Consumers have the following choices 1 Internet only option: $59 2 Print and Internet option: $125 Result: 68% (1), 32% (2) 34 / 96

Introduction CS CS Properties ACE Discussion LSD Rationality Micro entities with simple and routinised behaviour ⇒ Difficult to maximise: individuals are not ready to make all necessary calculations leading to the optimal choice, even if they had all the required information. Adaptive trial and error behavioural rules (Gigerenzer heuristics: simple heuristics more efficient to resolve complex problems) Individuals tend to use first known routines, and if these are not successful they will use calculations. 35 / 96

Introduction CS CS Properties ACE Discussion LSD Rationality Expectations Use of imperfect knowledge on the past Experimental evidence on adaptive expectations ⇒ difficult to be rational and predict the preference of other individuals (preferences do change over time) 36 / 96

Introduction CS CS Properties ACE Discussion LSD Heterogeneity Heterogeneity Distribution of Consumers: wealth, income, wages, preferences Firms: size, growth rates, productivity Markets: prices, institutions, organisation, peers All scale free distributions (Pareto): variance tends to infinite Meaning of an average? 47 / 96

Introduction CS CS Properties ACE Discussion LSD Heterogeneity World income distribution Source : Ortiz and Cummins (2011) 48 / 96

Introduction CS CS Properties ACE Discussion LSD Heterogeneity Skewed distribution of innovation by size Not all innovations are equally relevant Citations, value, returns to investment Returns to innovation are also fat tailed (high kurtosis): variance is not finite ⇒ SO is the risk of of returns 49 / 96

Introduction CS CS Properties ACE Discussion LSD Heterogeneity Computed Tomography scanner patents 80 Quantile-Quantile Plot 200 60 150 Citations Patents 40 100 20 50 0 0 0 50 100 150 200 0 20 40 60 80 Patents Citations (a) Linear scale (b) Q-Q Plot Source : Trajtenberg (1990) 50 / 96

Introduction CS CS Properties ACE Discussion LSD Heterogeneity Innovation size distributions (Pareto Plots) based on patent citations Source : Gerry Silverberg EPO 1989 patent citations (left) and USPTO 1989 patent citations (right) 51 / 96

Pareto distributions are a feature of complex system Source : Mitzenmacher (2004)

Introduction CS CS Properties ACE Discussion LSD Heterogeneity Heterogeneity in firms and innovation Distribution of firm size in an industry is heavily skewed (Simon and Bonini, 1958) Firms’ heterogeneity persists through time (technology, productivity, profits, growth) (Dosi et al., 2010b) Large differences across sectors and small differences across countries within sectors in firm’s demography (Breschi et al., 2000) Size of innovation is also drawn from a very skewed distribution (Silverberg and Verspagen, 2007) 53 / 96

Introduction CS CS Properties ACE Discussion LSD Heterogeneity Heterogeneity is a relevant property Many economic phenomena are driven by heterogeneity: diffusion curves, business fluctuations, pricing 54 / 96

Introduction CS CS Properties ACE Discussion LSD Heterogeneity Heterogeneity in the aggregate? Heterogeneity does not cancel out in the aggregate, unless characteristics are normally distributed. Some components dominate (e.g. the financial crisis does not occur because a couple of small firms fail) Imitation and avalanches in networks ⇒ Structural change ⇒ Changing shares of populations Aggregate properties may differ from individual properties: many times impossible to predict from individual behaviour Path dependency and non ergodic systems – stochastic process is time variant Cumulative process: persistent heterogeneity (e.g. Diamond, 1997) 55 / 96

Introduction CS CS Properties ACE Discussion LSD Interactions Interactions and networks Social sciences are all about interactions Trade Information and knowledge Expectations Social relations: e.g. six degrees of separation Neighbourhoods Most natural, technological and social interactions can be described as networks Most real networks have very similar properties: complex systems 56 / 96

Introduction CS CS Properties ACE Discussion LSD Interactions Social networks (a) Facebook connections (b) Twitter followers 57 / 96

Business collaborations: internet industry Source : http://www.orgnet.com/netindustry.html 250 companies: announced joint ventures, strategic alliances, other partnership

Business informal relations Source : http://blog.kiwitobes.com 400 largest US companies: shared board members

Combined knowledge in research: citation networks Source : (Rafols et al., 2012) Disciplines of study (publications) at the Institute of the Study of Science Technology and Innovation (ISSTI), Edinburgh

Introduction CS CS Properties ACE Discussion LSD Interactions Network and complexity Network as constraints Behaviour of a node depends on all others: interdependence Networks define the order of a complex system 61 / 96

The aggregate effect of social influence Source : Salganik et al. (2006) A: songs ordered randomly. C: songs ordered by downloads ⇒ Path dependence and cumulation

Introduction CS CS Properties ACE Discussion LSD Interactions Example 1: NK (Kauffman and Levin, 1987) Complexity is the product of interactions The fitness of a system F depends only on the interaction structure among its N nodes (and their mutation strategy) Each node i ∈ N is connected to K other nodes Each node i has a fitness contribution f given by a string of K + 1 binary values Independent from other nodes ( K = 0 ) Dependent on other nodes’ string value ( K > 0 ) K (interactions) defines complexity (product decomposability (Simon, 2002)) 63 / 96

Introduction CS CS Properties ACE Discussion LSD Interactions Example 2: Business Fluctuations (Ciarli and Valente, 2007) See also Weisbuch and Battiston (2005) and Carvalho (2014). How do micro shocks affect the system fluctuation Production: Input-Output structure Identical firms with iid shocks Consecutive decisions in adjusting a small shock in the final demand generates fluctuations ⇒ Attempts to smooth business cycles generate business cycles Fast adjustments in the demand for inputs create hysteresis Micro volatility is always smaller than aggregate volatility 64 / 96

Introduction CS CS Properties ACE Discussion LSD Interactions Diffusion of goods and technologies Is influenced by social networks “In 1953, a young female Macaque monkey in the south of Japan washed a muddy sweet potato in a stream before eating it. This obvious improvement in food preparation was imitated quickly by other monkeys and in less than 10 years it became the norm in her immediate group; by 1983, the method had diffused completely” (Hall, 2006, p. 459) ⇒ Some contagion effect: learn about the new technology from somewhere ⇒ Time to diffuse 65 / 96

Introduction CS CS Properties ACE Discussion LSD Interactions Contagion is the simpler way to explain diffusion Source : VisializingEconomics Contagion models: each user contacts a non adopter with some probability (Geroski, 2000) 66 / 96

Introduction CS CS Properties ACE Discussion LSD Equilibrium Equilibrium Evolutionary dynamics Each time period a process of adaptation, change in population, emergence of novelty Path dependent cumulative causation Even assuming equilibrium, need to know how it is reached: shocks, transitions, adjustments? 67 / 96

Introduction CS CS Properties ACE Discussion LSD Summing up Comparing Economic models and Complex Systems Standard Economic models Complex Evolving Systems Individuals 1,2 or infinite, fully rational, N large but finite, simple en- sophisticated learning tities, adaptive, routinary be- haviour Interactions Extreme cases, trivial pat- Non trivial patterns, local in- terns (full or empty/star teractions with subset of other graphs) agents Diversity Possibly heterogeneous, but Persistently heterogeneous, diversity does not matter for diversity matters for aggre- aggregate dynamics gate dynamics Time and Static (not truly dynamic) Truly dynamic systems, Aggregate models, only equilibrium equilibria possibly irrele- Dynamics states count vant, meta-stable states and emergent (self-organized) properties 68 / 96

Introduction CS CS Properties ACE Discussion LSD Summing up Empirical evidence: complex system features of social systems No evidence of purely rational behaviour Plenty of evidence of direct interactions within and between different populations Plenty of evidence on heterogeneity Little evidence of equilibria , only temporary (a particular condition) Macro as aggregation of micro properties and dynamics 69 / 96

Introduction CS CS Properties ACE Discussion LSD Summing up Given the knowledge gained from empirical observations in different sciences “Can one do good science based on models whose assumptions are clearly at odds with empirical evidence?” (Dick Day, 2003) Wouldn’t economics make more empirical sense if it were based on how do people actually behave, interact, etc, rather than how people should behave, interact, etc? (Miller and Page, 2007) “Water which is too pure has no fish” 70 / 96

Introduction CS CS Properties ACE Discussion LSD Why Why simulations? In order to analyse complex social problems (i.e. development and environmental sustainability) we need a different class of models that can Embed realistic assumptions into micro and macro models: uncertainty, procedural decision, heterogeneity, local interactions, non-equilibrium Replicate some of the empirical evidence discussed Include structural changes Do not assume macro dynamics 71 / 96

Introduction CS CS Properties ACE Discussion LSD Why Why simulations? Interaction of objects (agents) as a complex problem �→ no analytical solution Social interaction as a complex problem with individual behaviour (less straightforward then physical behaviour) No closed system Interaction of heuristics and reaction heuristics “I can calculate the motion of heavenly bodies, but not the madness of people” (I. Newton) Simple interactions can lead to complex outcomes (Arthur, 1994; Schelling, 1971) Minority games, urban segregation, choice of a technology The place where you are sitting now 72 / 96

Introduction CS CS Properties ACE Discussion LSD Why Schelling segregation model: explaining segregation Micromotives and Macrobehaviour (Schelling, 1978): segregation can be explained by simple individual choices (no racism...) (a) Stay if at least 1/3 of (b) Move to random location otherwise neighbours are ‘kin’ Source : L-E Cederman 73 / 96

Introduction CS CS Properties ACE Discussion LSD Why Schelling segregation model: set-up N agents located on a 2-dimensional grid (torus) of LxL cells. Types: Each agent can be either RED or GREEN Only a percentage p of cells is occupied: N < LxL Agents are initially located on the grid at random In each time period, agents may be happy or unhappy Agent cares about the proportion q of other agents of same colour in its Moore neighbourhood of radius 1 Agents are unhappy if q is below a certain critical threshold (parameter of the model) and happy otherwise In each iteration of the model one unhappy agent is randomly selected to move to a random empty cell in the lattice 74 / 96

Introduction CS CS Properties ACE Discussion LSD Why Schelling segregation model: experiments Source : Izquierdo et al. (2009) http://jasss.soc.surrey.ac.uk/12/1/6/appendixB/ Schelling1969.html 75 / 96

Introduction CS CS Properties ACE Discussion LSD Why Schelling segregation: Chicago 1940 Source : Möbius and Rosenblat (2001) Percentage of blacks: 1-5% yellow; 5-10% pink; 10-25% orange; 25-50% red; 50-75% dark red; 75-95% brown; > 95% black 76 / 96

Introduction CS CS Properties ACE Discussion LSD Why Schelling segregation: Chicago 1950 Source : Möbius and Rosenblat (2001) Percentage of blacks: 1-5% yellow; 5-10% pink; 10-25% orange; 25-50% red; 50-75% dark red; 75-95% brown; > 95% black 77 / 96

Introduction CS CS Properties ACE Discussion LSD Why Schelling segregation: Chicago 1960 Source : Möbius and Rosenblat (2001) Percentage of blacks: 1-5% yellow; 5-10% pink; 10-25% orange; 25-50% red; 50-75% dark red; 75-95% brown; > 95% black 78 / 96

Introduction CS CS Properties ACE Discussion LSD What ACE: Definition ACE Agent–Based Computational Economics: “the computational study of economic processes modelled as dynamic systems of interacting agents” (L. Tesfatsion) Modeller constructs a virtual economic world populated by various agent types (economic, institutional, social, biological, physical) Modeller sets initial world conditions Modeller then steps back to observe how the world develops over time (no further intervention by the modeller is permitted) World events are driven by agent interactions 79 / 96

Introduction CS CS Properties ACE Discussion LSD What Main properties of ACE Population of heterogeneous (economic) ‘agents’ Agents live in complex systems evolving through time (Kirman, 1998). True dynamics: non reversible “Hyper-rationality” not viable (Dosi et al., 1996): internal states, rules of behaviour, and adaptive expectations Agents are autonomous or semi–autonomous Agents interact with one another and possibly with an environment (local/social interactions) Endogenous and persistent novelty (technological change): open-ended spaces Aggregate structure emerges from agent interactions (Tesfatsion, 1997) Generations of agents emerge from the interactions of their ancestors (selection, retention, innovation �→ evolution) (Nelson and Winter, 1982) 80 / 96

Introduction CS CS Properties ACE Discussion LSD What Micro and macro interactions Source : Page (2015) 81 / 96

Introduction CS CS Properties ACE Discussion LSD Implementation and analysis Structure of ABM Time Discrete t = 0 , 1 , 2 , ..., ( T ) Sets of Agents Often N t = N I t = 1 , 2 , ..., N t Sets of Micro States Firm’s output i → x i , t Vectors of Micro-Parameters Res. Wage i → θ i Vector of Macro-Parameters Min. Wage Θ ∈ ℜ m Interaction Structures Networks G t ∈ ℘ ( I t ) Micro Decision Rules Innovation rule R i , t ( ·|· ) Aggregate variables GNP X t = f ( x 1 , t , ..., x N t , t ) 82 / 96

Introduction CS CS Properties ACE Discussion LSD Implementation and analysis Implementation of AB computations Each agent is an object instance variables (representing internal states) and methods (representing behavioural routines) The population of agents is also an object �→ Upstream: hierarchies (emergent properties and interactions) Topology of interaction , e.g., a spatial environment or a social network, a market Mechanisms for activating agents: incentives & routines Usually stochastic processes (uncertainty) 83 / 96

Introduction CS CS Properties ACE Discussion LSD Analysis Realisations Highly parametrised: analysis Parameters of interest: functional analysis Whole space / reasonable space Stochastic processes Uncertainty: sequence of stochastic events can have a strong effect on the outcome (e.g. percolation) Analyse distribution of each output variable Each realisation a scenario (consistent with the model and in probability) Analysis of plausible scenarios 84 / 96

Introduction CS CS Properties ACE Discussion LSD Analysis Robustness Calibration Abstract model vs explanation of a phenomenon vs foresight Reproducing empirical evidence, under given parameter values (validation) Robust assumptions 85 / 96

Introduction CS CS Properties ACE Discussion LSD Analysis Procedure of ABM ( x i,0 ) Initial Conditions: ( θ i ), Θ Micro & Macro Pars: Generate Montecarlo Distribution for each Statistics in S = {s 1 , s 2 , … } Generate Time-Series through Simulation {( x i,t ), t =1,…,T} Studying how Montecarlo { X t , t =1,…,T} Distributions of Statistics in S = {s 1 , s 2 , … } behave as initial conditions, micro and macro parameters change Compute a Set of Statistics S = {s 1 , s 2 , … } on micro/macro Time-Series Statistical Tests for difference between moments Repeat M ind. times Source : G. Silverberg 86 / 96

Introduction CS CS Properties ACE Discussion LSD Examples Some applications in economics and business Evolutionary-Games: P . Young, Kandori et al., Blume, Ellison (Local) Interaction Models: Kirman, Weisbuch, Lux Endogenous Network Formation: Vega-Redondo, Cowan, Goyal, Jackson-Watts...) Innovation (Polya-Urn Schemes): Arthur, Dosi, Kaniovski, Lane, Marengo Complexity: Frenken, Valente, Marengo Strategy and organisations: Carley and Pietrula, Lomi and Larsen Technological modularity, firm and industry organisation: Ethiraj et al. (2007); Frenken et al. (1999); Kauffman et al. (2000); Marengo and Dosi (2005); Ciarli et al. (2008) 87 / 96

Introduction CS CS Properties ACE Discussion LSD Examples Some applications in economics and business Growth: Nelson and Winter (1982), Silverberg, Verspagen, Dosi, Howitt, Llerena and Lorentz (2004); Dawid and Fagiolo (2008); Dosi et al. (2010a); Ciarli et al. (2010); Ciarli (2012); Ciarli et al. (2012); Fagiolo and Roventini (2012) Firms location: David et al. (1998) Firms and technological change: Dawid (2006); Teitelbaum and Dowlatabadi (2000); Yildizoglu (2002) Markets: Axtell, Epstein, Tesfatsion, Kirman and Vriend (2000) Electricity markets: Tesfatsion Sectoral studies: Malerba et al Environmental economics: van den Bergh, Safarzynska, Windrum et al. (2009a,b) 88 / 96

Introduction CS CS Properties ACE Discussion LSD Examples Some applications in economics and business Industrial life cycle cycles: Windrum and Birchenhall (2005), Malerba et al Labour market: Tesfatsion, Fagiolo et al. (2004), Richiardi and Leombruni Financial markets (a huge number): Delli Gatti et al. (2004), Delli Gatti and Stiglitz, Cont, econophisycs Macro instability: Bak et al. (1993); Dosi et al. (2006), Weisbuch and Battiston, Ciarli and Valente (2007) Macro: Howitt, Duffy, Arifovic Firms coalition and network formation: Cowan and Jonard, Ozman, Page, Huberman, Axtell, Vega-Redondo, Jackson, Watts Foresight: Lempert Other social sciences: Politics (state cooperation, conflict), Sociology, Anthropology, ... 89 / 96

Introduction CS CS Properties ACE Discussion LSD Some critical aspects Do we really need simulations? It depends on the phenomenon under study See introductory discussion on the crisis, and empirical regularities of complex systems: societies are complex. How reasonable and helpful are the assumptions for what we want to study? 90 / 96

Introduction CS CS Properties ACE Discussion LSD Some critical aspects Critical aspects of simulations See discussions in Windrum (2007); Valente (2007); Windrum et al. (2007); Leombruni and Richiardi (2005) Determinacy of results Sim. models produce all and only whatever you code into them True, but computers help to understand exactly the implications of the assumptions. Think, for example, of models of weather forecasting. The basic physics is trivial, but the aggregate effect is impossible to derive by analytical means, and computers help to fill the gap between the hypotheses (e.g. basic physics) and their implications (forecasting). 91 / 96

Introduction CS CS Properties ACE Discussion LSD Some critical aspects Critical aspects of simulations Empirical validation Are results confirmed empirical observations? (Windrum, 2007) Data replication is useless without understanding their meaning. Worse, there are always a large number of different ways to replicate a data set, only some of which may make sense. → First need to have robust evidence on assumptions on micro ֒ behaviour Results come in the form of distributions, depending on the randomness of initial conditions and on interactions 92 / 96

Introduction CS CS Properties ACE Discussion LSD Some critical aspects Critical aspects of simulations Testing randomness and parameter space Random models/models with many parameters must be adequately tested for the robustness of results: a single random run may be an exceptional case in a distribution Crucial, open issues Pushing policy and design exercises Fostering empirical validation techniques 93 / 96

Introduction CS CS Properties ACE Discussion LSD A short intro Outline for the hands on simulation course Laboratory for Simulation Development: thttp://www.labsimdev.org/Joomla_1-3/ Last version: https://github.com/marcov64/Lsd Objective : learning how to use simulations implemented in LSD to make research in Economics Plan Introduction : goals and plan of the course Definitions : a normal form of a simulation model. Introduction to LSD : equations, structures and configurations of models. Tutorials : implementation of increasingly complex example models. 94 / 96

Introduction CS CS Properties ACE Discussion LSD Broad methodological issues Simulation programme Using a standard programming language the most difficult task is not the coding of the model. Rather it is the coding of ancillary tools necessary to declare the model’s elements, assign initial values, export results, etc. Using LSD, conversely, the modeller focuses only on the model, and the system automatically generates professional tools to control and access any aspect of the model. 95 / 96

Introduction CS CS Properties ACE Discussion LSD Hands on Topics of the course During the course we will approach the following topics: Design : decide what the model should look like, for it to contribute to a research project. Implementation : turning an abstract idea into a working simulation program. Interpretation : extracting knowledge from simulation models. 96 / 96

Backup slides References Introduction General Equilibrium in a slide Key Assumptions Full rationality (fully informed optimizing agents) No time and no dynamics Only equilibrium analysis No interactions (Star Network) Positive questions: equilibrium Existence and Uniqueness Stability 97 / 96

Backup slides References Introduction General Equilibrium: limitations Back Meaning of existence of a social equilibrium (observation?) How can an equilibrium be established (Walrasian auctioneer)? What happens out of equilibrium (a part from instantaneous attraction)? What (or who) is an auctioneer ? Interactions ? How does an economy move from an equilibrium to another one? What happens in between ? Assumptions on micro behaviour and predictive power (e.g. crisis) 98 / 96

Backup slides References Introduction Microfounded macroeconomic models in a slide Example: economic growth Representative firm with a production function: F ( L t , A t K t ) Representative household with utility function: ∫ ∞ U = t =0 e − ρ t u ( C ( t )) L t H dt Both firms and households are fully rational (maximizing) agents, with unbounded computational skills 99 / 96