Master Économie et Affaires Internationales Cours “Modèles de Simulation” Paris Dauphine –Septembre – October 2010 Prof. Ramón Mahía Applied Economics Department SIMULATION MODELS: SOME BASICS

STRUCTURE OF THE PRESENTATION  WHAT DOES SIMULATION MEAN?  WHY DO WE NEED SIMULATION MODELS?  BRIEF EXAMPLES OF REAL SIMULATION MODELS  BASIC ELEMENTS, STAGES AND ADVICES FOR BULDING UP A SIMULATION MODEL

SIMULATION MODELS: SOME BASICS WHAT DOES SIMULATION MEAN? A simulation model is a kind of technical tool that help us to understand and take decisions in real complex systems.

SIMULATION MODELS: SOME BASICS WHAT DOES SIMULATION MEAN?  Using a simulation tool, we can experiment in real systems:  To Understand how the system works  To Evaluate alternative decisions  ….or to find the best decision for achieving a particular result / goal(optimization)….

SIMULATION MODELS: SOME BASICS WHY DO WE NEED SIMULATION MODELS?  A real system use to be complex (not chaotic) : different “agents” affecting lots of variables (elements) greatly interrelated in a way that …  It seems difficult or impossible to anticipate the result of a given decision relying on past, experience or theoretical conceptions.  Thus, for understanding the system and/or evaluating decision’s outputs, IDEALLY we would need to “try out”, to experiment with reality.

SIMULATION MODELS: SOME BASICS WHY DO WE NEED SIMULATION MODELS?  Obviously, most of the times we CAN’T make real tries for evaluating alternative decisions because it is simply impossible or very risky and/or expensive:  A Macro example: Which is the impact of different immigration scenarios in pension system in 2025 for Spain?  A Micro example: How will it change (most likely) our market competitors response, and thus, our market share for two different price and distribution strategies

SIMULATION MODELS: SOME BASICS MORE ON SIMULATION DEFINITION  Simulations Vs. Optimization  There are not Simulation Vs Optimization models but different ways of use.  Optimization systems concentrates mainly on reaching a well predefined objective given a set of restrictions.  Simulation is an open strategy that use the links between inputs and outputs without setting a priori what must be considered an optimum solution.  That’s why we usually say that simulation models are “runned” and optimization models are “solved”.

SIMULATION MODELS: SOME BASICS MORE ON SIMULATION DEFINITION  Example: Simulations Vs. Optimization: Replace a quota regime by a tariff only system 1.- OPTIMIZATION LIKE: Which are the tariff level equivalent to an existing quota regime 2.- SIMULATION LIKE: Which are the effects of different tariff levels on prices and trade flows. ….. Most of the times, simulation looks like a natural previous stage for optimization….

SIMULATION MODELS: SOME BASICS WHY DO WE NEED SIMULATION MODELS?  In social sciences, simulation models are extremely useful for understanding systems because of:  The theoretical basis of the system are uncertain or inaccurate: the absence or, at the contrary, the multiplicity of theoretical models that “really” fit “real” systems.  The degree of complexity and uncertainty in the behavior of individuals (elements) and its inter-connections.  The importance of aggregation of phenomena: social phenomena “emerge” from individual action but it has its own dynamics (in part, because the complex interrelations influence individual decisions)  The importance of dynamics of phenomena (playing with time): passing of time affects to the evolution of a system: there are short, medium and long term different effects.

SIMULATION MODELS: SOME BASICS 3 REAL EXAMPLES  Forecasting the impact of migration on pension system by 2025 (CES Project ) :  Very complex and simultaneous interrelations between migration, native demographical trends, economic conditions,..politics  Once again,… impossible to try out and impossible to risk a single forecast output.  Lack of a single theoretical framework to be applied  Individuals (or families) experience and take migration decisions in a different way  Very rich migration time dynamics  Different qualitative issues (politics) to be considered: migration policy design and application, future welfare state design …..

SIMULATION MODELS: SOME BASICS 3 REAL EXAMPLES  Removal of trade barriers in an EU import market (implications on world trade prices and trade yields for different countries):  Lack of a reliable and realistic theoretical framework (imperfect competition, market power, …)  Different strategies in different countries could be taken in new scenarios (lots of agents involved on decisions)  Importance of dynamics

SIMULATION MODELS: SOME BASICS 3 REAL EXAMPLES  Forecasting natural gas demand (national and regional distribution) for the next 24 months:  Impossible to give a single forecast (different scenarios have to be considered) because…  Lots of elements / interrelations (different scenarios) in different time dimensions: Short term: seasonal elements such as weather conditions (hardly foreseeable) that affects Energy MIX and intensity of consumption. Medium term (economic conditions) Long term: Policy related issues (Regulatory elements, “Kyoto Protocol” strategies to be adopted, new future competitors, new rules…..)  …crossed with specific regional dynamics

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS & STAGES FOR BIUILDING UP A SIMULATION MODEL  (i) Real system “draft”  (ii) Operative system “representation” (design)  (iii) Different type of variables (parts)  (iv) Simulation flow structure (links)  (v) Technical Structure (computation)  (vi) Interface (platform of use)  (vii) Results (use of the model)

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS & STAGES FOR BIUILDING UP A SIMULATION MODEL  (i) Real (whole) system to be analyzed: The collection of elements and interactions to be analysed by means of the simulation.  In a very first stage, start drawing a broad definition, a framework of the whole system: different parts (sub- systems) should be recognized, every element should be identified and every relevant connection should be properly acknowledged even if your fundamental interest is focused in just a single part. (see next)

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS & STAGES FOR BIUILDING UP A SIMULATION MODEL  (i) Real (whole) system to be analyzed (cont):  The largest part of the technical decisions regarding the estimation, calibration, design of scenarios and interface design rely on and are conditioned by a good comprehension of the elements and interrelations of the whole system to be analysed.

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS & STAGES FOR BIUILDING UP A SIMULATION MODEL  (ii) System “representation”: Simplified and limited version of the real system  Then, in a second stage, start to identify the “reduced” representation of the system that best fit YOUR simulation aims: leave out some complete parts, reduce elements of interest and drop useless relationships (never forget, of course, those rejected variables and links, in case you need them later on, and bear them always in mind for a broad and wide range comprehension of the final results).

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS & STAGES FOR BIUILDING UP A SIMULATION MODEL  (iii) Type of variables:  Inputs:  (***) Stimulus Inputs (decision or critical): main variables to be changed for simulation  Exogenous Inputs (out of model, usually fixed or very limited, frequently qualitative, ideally not critical,..)  Outputs :  Intermediate outputs (state and auxiliary variables, or estimated parameters)  (***) Final outputs

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS & STAGES FOR BIUILDING UP A SIMULATION MODEL  (iv) Simulation flow structure: Structured scheme that illustrate the connection between different variables: cause – effect chains  Simplify the flow along the cause – effect chains (reduce dimensionality, look for a semi - linear design)  Rationalize chain flows: prioritize inputs and outputs, give them hierarchical order, and then…  Divide the system in homogeneous parts for planning the work across areas. Locate the links between the different areas and order the stages, identifying the priorities and crucial points.

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS & STAGES FOR BIUILDING UP A SIMULATION MODEL  (iv) Simulation flow structure: (cont.)..  Identify the sequences of work, bottle – necks, critical crossing points,…  Plan a preliminary time work modeling schedule according to:  “In model” factors: the previous identification of lines, crossing points and bottlenecks  “Out of model” factors: existing organization of areas, the resources available, the difficulty of different tasks

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS tt+1t+2t+3t+4t+5t+6t+7t+8

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS  (v) Technical Structure: Quantitative definition of elements (variables) and links between them (equations) 1.- Collection of data for every variable (element) 2.- Mathematical (for deterministic links) and/or statistical models (for randomness) 3.- Mathematical and/or statistical algorithms to describe and validate convergence and/or equilibrium of simulation or optimization solutions.

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS NATIONAL PRODUCERS YIELDS TARIFFS IMPORT PRICES IMPORT DEMAND DOMESTIC GROWTH ECONOMETRIC MODEL DOMESTIC DEMAND SUBSIDIES DOMESTIC PRICES ECONOMETRIC MODEL IDENTITY REST OF THE MODEL

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS  (v) Technical Structure: (Cont.) (Example of an optimization algorithm for an international trade model) Ad-Quantum Tariff Matrix Ad-Valorem Tariff Matrix Import Inverse Function Export Inverse Function Existing Quota Regimes Equilibrium is reached making equal the inverse functions of imports and exports revenues

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS  (v) Technical Structure: (Cont.)  There exists different technical solutions for different objectives (forecasting, evaluating, optimizing, …….)  …. and restrictions given (uncertainty, data available, time, skills, theoretical requirements)…  So choosing the technique wont be easy....  If different alternatives can be technically chosen, let simplicity lead your decision (simplicity of construction, of updating, of use…)…

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS  (v) Technical Structure: (Cont.)  Concentrate on data ( "Measure twice, and cut once“).  Carefully supervise your “raw material”: use homogeneous data, ensure the future availability of them, choose the samples carefully, be extremely scrupulous in the handling of data (check robustness).  Use the data provided by the end user, agree with them if data responds truthfully to “their” reality perception him.  There would exists different technical solutions for the different objectives (forecasting, evaluating, optimizing, …….) …. and restrictions given (uncertainty, data available, time, skills, theoretical requirements)…  …thus choosing the technique wont be easy.... (see next)

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS  (v) Technical Structure: (Cont.)  For choosing the technique:  Explore the analytical - mathematical – statistical procedures that best adapt to the system and your aims.  Try to adapt the analytical technique to the problem and not the other way round (models MUST be useful and suit the problem, not technically attractive or handsome)  If different alternatives can be technically chosen, let simplicity lead your decision. Do not complicate the technical models if it does not lead to clear benefits from the user perspective (“If your intention is to discover the truth, do it with simplicity and lave the elegance for the tailors“)

SIMULATION MODELS: SOME BASICS BASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS  (v) Technical Structure: (Cont.)  What if we need some stochastic (econometric) models?:  If you can, try to avoid critical dependency on stochastic estimations: if inferential statistics are used, not only final, BUT INTERMEDIATE outcomes would vary in a confidence interval so you should carefully check the “sensitivity” of the WHOLE system to EVERY coefficient change ... Think “seriously” if estimations will be static or an automatic re-estimations will be addressed in the model.  Limit or warn (in the interface) the use of the model with “within – sample data” scenarios.  Try (never easy) to offer results in an confidence interval – way (providing values and probabilities).

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS OF A SIMULATION MODEL  (vi) Interface: Platform for using the model  Sometimes is not necessary (self use)  Call for software professionals (if you have lots of money)  Let simplicity guide the design of the interface: The interface is wished for using the model, not for understanding the model: The “model” COULD be COMPLEX, but the interface MUST be FRIENDLY:  Prioritise the wishes of users in all the stages and take their advices  Set different levels of use: Decision makers, medium level technicians, high skilled technical experts, etc... “There is no inept user, only badly designed systems”.

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS OF A SIMULATION MODEL  (vi) Interface: Platform for using the model

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS OF A SIMULATION MODEL  (vi) Interface: Platform for using the model

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS OF A SIMULATION MODEL  (vi) Using the model:  (**) Scenario: a set of inputs and parameters considered for a simulation exercise  When several inputs are taken, lots of potential variant scenarios arises  For reducing dimensionality:  Try to identify tree-structures (if possible) identifying hierarchical connections of different inputs  Pode the tree: Drop impossible, hardly probable, not interesting and not different scenarios.  Order the final list

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS OF A SIMULATION MODEL  (vi) Using the model: INPUTSVALUES Host country demographicsHigh fertility variant Medium fertility variant Low fertility variant Host country economic growthHigh growth Medium growth Poor growth Crisis Immigration restrictionsNone Medium High TimeShort term Medium term Long term TOTAL SCENARIOS108 TimeDemographicsEconomic growthRestrictionsScenario Short termMedium None1 PoorMedium2 Medium TermMedium None3 PoorMedium4 CrisisMedium5 High6 Long TermHigh None7 Medium None8 LowPoorMedium9 CrisisMedium10 High11

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS OF A SIMULATION MODEL  (vi) Using the model:  Give probabilities to different scenarios (use conditional probabilities if a tree scheme is used)  Evaluate the output:  Offer a kind of result that jointly evaluates the probability of the outcome and the magnitude of it  Once you get results for each given scenario, clearly identify the sensitivity of results to changes in every inputs.  Identify (and don’t underestimate) qualitative issues (or simply out of model facts) that could affect results.