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Master Économie et Affaires InternationalesCours “Modèles de Simulation”
Paris Dauphine –Septembre – October 2010
Prof. Ramón MahíaApplied Economics Department
www.uam.es/ramon.mahia
SIMULATION MODELS: SOME BASICS
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 2007-08) : 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 BASICSBASIC 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 BASICSBASIC 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 BASICSBASIC 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 BASICSBASIC 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 BASICSBASIC 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 BASICSBASIC 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 BASICSBASIC 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
t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8
SIMULATION MODELS:
SOME BASICSBASIC 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 BASICSBASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS
NATIONAL PRODUCERS YIELDS
TARIFFS
IMPORT PRICES
IMPORT DEMANDDOMESTIC
GROWTH
ECONOMETRIC MODEL
DOMESTICDEMAND
SUBSIDIES
DOMESTICPRICES
ECONOMETRIC MODEL
IDENTITY
REST OF THE MODEL
SIMULATION MODELS:
SOME BASICSBASIC STAGES FOR BIUILDING A SIMULATION MODEL: ELEMENTS AND DECISIONS
(v) Technical Structure: (Cont.) (Example of an
optimization algorithm for an international trade model)
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Ad-Quantum Tariff Matrix
Ad-Valorem Tariff Matrix
Import Inverse
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Export Inverse
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Existing Quota
Regimes
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• Equilibrium is reached making equal the inverse functions
of imports and exports revenues
SIMULATION MODELS:
SOME BASICSBASIC 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 BASICSBASIC 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 BASICSBASIC 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 BASICSBASIC 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:
INPUTS VALUESHost country demographics High fertility variant
Medium fertility variant
Low fertility variantHost country economic growth High growth Medium growth Poor growth CrisisImmigration restrictions None Medium HighTime Short term Medium term Long termTOTAL SCENARIOS 108
Time Demographics Economic growth Restrictions ScenarioShort term Medium Medium None 1 Poor Medium 2Medium Term Medium Medium None 3 Poor Medium 4 Crisis Medium 5 High 6Long Term High High None 7 Medium Medium None 8 Low Poor Medium 9 Crisis Medium 10 High 11
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.