Master Économie et Affaires Internationales Cours “Modèles de Simulation” Paris Dauphine –October 2009 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 OF A SIMULATION MODEL  AN EXAMPLE OF A SIMPLE MODEL  MORE ON SIMULATION DEFINITION

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 objective (optimization)….

SIMULATION MODELS: SOME BASICS WHY DO WE NEED SIMULATION MODELS?  A real system use to be complex (not chaotic) : a lot of variables (elements) and interrelations in the working of the system in a way that seems difficult or impossible to anticipate the result of a given decision relying on past, experience or theoretical conceptions.  That means that for understanding and/or evaluating decisions, we should need to “try out”, to experiment with reality.

SIMULATION MODELS: SOME BASICS WHY DO WE NEED SIMULATION MODELS?  Sometimes we CAN’T make real tries on the system for evaluating alternative decisions because it is impossible:  To evaluate the impact of different immigration scenarios in pension system in 2025 in our Country…  To forecast our market share depending on our different strategies and difrerent responses of competitors

SIMULATION MODELS: SOME BASICS WHY DO WE NEED SIMULATION MODELS?  Even if we could really try out, it would be very risky and/or costly (we can try just once and its difficult or costly to back down):  To evaluate the impact of a new promotional strategy  To decide on the best configuration of a new product  To change a tariff level for protecting our domestic market from imports

SIMULATION MODELS: SOME BASICS WHY DO WE NEED SIMULATION MODELS?  In social sciences, simulation models are extremely useful for understanding systems because of:  The absence (or the multiplicity) of accurate theoretical models that “really” fit “real” systems.  The complexity and uncertainty in the behavior of individuals (elements) and its inter-connections.  The importance of dynamics of phenomena (playing with time): how affects passing of time to the evolution of a system  The importance of aggregation of phenomena: how social phenomena “emerge” from individual action

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 for the next 24 months:  Impossible to give a single forecast (different scenarios have to be considered) because:  Lots of elements / interrelations (different scenarios): Economic conditions Weather conditions (that affects Energy MIX and intensity of consumption) Regulatory elements (“Kyoto Protocol” strategies to be adopted, new future competitors, new rules…..)

SIMULATION MODELS: SOME BASICS 3 REAL EXAMPLES  Forecasting the impact of migration on pension system by 2025 :  Once again,… impossible to try out and impossible to risk a single forecast output.  Very complex migration dynamics: lack of theoretical framework to be applied  Very complex and simultaneous interrelations between migration, native demographical trends, economic conditions,..politics  Different qualitative issues to be considered: migration policy design and application, future pension system design …..

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)

SIMULATION MODELS: SOME BASICS BASIC ELEMENTS & STAGES FOR BIUILDING UP A SIMULATION MODEL  (i) Complete system to be analyzed: The collection of elements and its 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 documented

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 right representation of the system that best fit OUR simulation aims: leave out some complete parts, reduce elements of interest and drop useless relationships (never forget, of course, those rejected variables and links, 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:  (***) Decision Inputs: variables to be changed for simulating  Exogenous Inputs (out of model but not necessary fixed)  Outputs :  Intermediate outputs (state and auxiliary) variables  (***) 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 and rationalize the flow along the cause – effect chains representation 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.

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.)..  Plan a preliminary time schedule according to  the previous organization of areas  the resources available  the difficulty of different tasks  Identify the critical lines of work.

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: Mathematical body of the simulation structure used to model the relationships between elements. Includes: 1.- Collection of data for every variable (element) 2.- Mathematical and/or statistical models for linking elements (variables) 3.- Mathematical and/or statistical algorithms for describing 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 IMPORT DEMAND ECONOMETRIC MODEL DOMESTIC DEMAND ECONOMETRIC MODEL IDENTITY

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 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, 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…)… (See more advices at the end of this presentation).

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

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 MORE ON SIMULATION DEFINITION  Deterministic (MKT Mix effects evaluation) Deterministic Inputs (controlled values): Advertising effort Price policy Distribution policy Sales Force  Random (Agricultural Crop Yield) Random Inputs (not controlled values): Climate conditions Plagues

SIMULATION MODELS: SOME BASICS MORE ON SIMULATION DEFINITION  Deterministic + Random (MKT Mix evaluation) Deterministic Inputs (controlled values): Advertising effort Price policy Distribution policy Sales Force Inputs to be randomly modeled (forecasted) MKT Mix of existing or new competitors Economic conditions of country Market Demand (2nd stage input) Regression analysis

SIMULATION MODELS: SOME BASICS MORE ON SIMULATION DEFINITION  Static Vs. Dynamic: Does “passing of time” result in a key variable (even an input) for the simulation system?  Example: Time as a basic input of a simulation system (two real examples):  Economic impact of an immigration flow will not only depend on the amount of immigration, but in the speed of it.  Effects on prices or trade flows of a tariff removal between two areas, would drastically change if you consider a gradual removal or not.

SIMULATION MODELS: SOME BASICS MORE ON SIMULATION DEFINITION  Time as a basic input….. (example from Femise Project)