Mukund Moorthy 2nd February 1999

Mixed Structural and Mixed Structural and Behavioral Models for Behavioral Models for Predicting the Future Predicting the Future

Behavior of some Aspects Behavior of some Aspects of the Macroeconomyof the Macroeconomy

Mukund MoorthyMukund Moorthy

2nd February 19992nd February 1999

ContentsContents

Economic ModelingEconomic Modeling System DynamicsSystem Dynamics Fuzzy Inductive ReasoningFuzzy Inductive Reasoning Proposed Macroeconomic ModelProposed Macroeconomic Model Food Demand ModelingFood Demand Modeling ConclusionConclusion

Economic ModelingEconomic Modeling

Economic Forecasting TechniquesEconomic Forecasting Techniques

– Time Series DataTime Series Data

– Neural NetworksNeural Networks

Time Series DataTime Series Data Time Series ComponentsTime Series Components

– Trend ( T )Trend ( T )– Cyclical ( C )Cyclical ( C )– Seasonal ( S )Seasonal ( S )– Irregular ( I )Irregular ( I )

Curve FittingCurve Fitting

Linear Trend EquationLinear Trend Equation

Curve FittingCurve Fitting Exponential Trend EquationExponential Trend Equation

Polynomial Trend EquationPolynomial Trend Equation

Smoothing TechniquesSmoothing Techniques

Moving AverageMoving Average

– each point is average of N pointseach point is average of N points

Exponential SmoothingExponential Smoothing

Time Series ForecastingTime Series Forecasting

Box-Jenkins MethodBox-Jenkins Method

Economic ForecastingEconomic Forecasting

Step-wise Auto-regressive methodStep-wise Auto-regressive method

Neural NetworksNeural Networks

System DynamicsSystem Dynamics

Modeling Dynamic SystemsModeling Dynamic Systems– Information feedback loopsInformation feedback loops


– LevelsLevels

– Flow RatesFlow Rates

– Decision FunctionsDecision Functions


Levels and RatesLevels and Rates

Laundry ListLaundry List

Levels Rates Inflows Outflows

Population Birth Rate Death RateMoney Income ExpensesFrustration Stress AffectionLove Affection FrustrationTumor Cells Infection TreatmentInventory on Stock Shipments SalesKnowledge Learning Forgetting

Birth Rate:

• Population• Material Standard of Living• Food Quality• Food Quantity• Education• Contraceptives• Religious Beliefs

Structure DiagramStructure Diagram

Forrester’s World ModelForrester’s World Model

PopulationPopulation Capital InvestmentCapital Investment Unrecoverable Natural ResourcesUnrecoverable Natural Resources Fraction of Capital Invested in the Fraction of Capital Invested in the

Agricultural SectorAgricultural Sector PollutionPollution

Structure Diagram of Structure Diagram of Forrester’s World ModelForrester’s World Model

Shortcomings of the Shortcomings of the World ModelWorld Model

Levels and RatesLevels and Rates

Laundry ListLaundry List

Fuzzy Inductive Fuzzy Inductive ReasoningReasoning

Discretization of quantitative information Discretization of quantitative information (Fuzzy Recoding)(Fuzzy Recoding)

Reasoning about discrete categories Reasoning about discrete categories (Qualitative Modeling)(Qualitative Modeling)

Inferring consequences about categories Inferring consequences about categories (Qualitative Simulation)(Qualitative Simulation)

Interpolation between neighboring Interpolation between neighboring categories using fuzzy logic categories using fuzzy logic (Fuzzy (Fuzzy Regeneration)Regeneration)

Fuzzy Inductive Fuzzy Inductive ReasoningReasoningMixed Quantitative/Qualitative Modeling

Quantitative Subsystem

Recode FIR Model

Regenerate

Quantitative Subsystem

Recode

FIR Model

Regenerate

FuzzificationFuzzification

Inductive ModelingInductive Modeling

Inductive SimulationInductive Simulation

Modeling the ErrorModeling the Error

Making predictions is easy!Making predictions is easy!

Knowing how good the predictions are: Knowing how good the predictions are: That is the real problem!That is the real problem!

A modeling/simulation methodology that A modeling/simulation methodology that doesn’t assess its own error is worthless!doesn’t assess its own error is worthless!

Modeling the error can only be done in a Modeling the error can only be done in a statistical sense … because otherwise, the statistical sense … because otherwise, the error could be subtracted from the error could be subtracted from the prediction leading to a prediction without prediction leading to a prediction without the error.the error.

Food Demand ModelFood Demand Model

Naïve ModelNaïve Model Enhanced Macroeconomic ModelEnhanced Macroeconomic Model

Naïve ModelNaïve Model

Population DynamicsPopulation Dynamics

Population Dynamics

Macroeconomy

Food Demand

Food Supply


Predicting Growth FunctionsPredicting Growth Functions

k(n+1) = FIR [ k(n), P(n), k(n-1), P(n-1), … ]

Population Dynamics

Macroeconomy

Food Demand

Food Supply


Population Dynamics

Macroeconomy

Food Demand

Food Supply

MacroeconomyMacroeconomy

Population Dynamics

Macroeconomy

Food Demand

Food Supply

Food Food Demand/SupplyDemand/Supply

Population Dynamics

Macroeconomy

Food Demand

Food Supply

Enhanced Macroeconomic Enhanced Macroeconomic ModelModel

Population LayerPopulation Layer

Economy LayerEconomy Layer

Food Demand/Supply Food Demand/Supply LayerLayer

ResultsResults

Annual / Quarterly DataAnnual / Quarterly Data Layer One - Population LayerLayer One - Population Layer Layer two - Economy LayerLayer two - Economy Layer Layer three - Food Demand LayerLayer three - Food Demand Layer Layer Four - Food Supply LayerLayer Four - Food Supply Layer OptimizationOptimization


Population Dynamics

Macroeconomy

Food Demand

Food Supply

Economy LayerEconomy Layer

Population Dynamics

Macroeconomy

Food Demand

Food Supply

Food Supply LayerFood Supply Layer

Population Dynamics

Macroeconomy

Food Demand

Food Supply

Food Demand LayerFood Demand Layer

Population Dynamics

Macroeconomy

Food Demand

Food Supply

OptimizationOptimization

Conclusion and Future Conclusion and Future WorkWork

Mixed SD/FIR Mixed SD/FIR offers the best of both worlds.offers the best of both worlds.

Application to any U.S. industry with change of Application to any U.S. industry with change of demand and supply layers alone.demand and supply layers alone.

Application to any new country or region with Application to any new country or region with new data for layers 1 and 2.new data for layers 1 and 2.

Fuzzy Inductive Reasoning Fuzzy Inductive Reasoning features a features a model model synthesissynthesis capability rather than a capability rather than a model learningmodel learning approach. It is therefore quite fast in setting up approach. It is therefore quite fast in setting up the model.the model.

Conclusion and Future Conclusion and Future WorkWork

Fuzzy Inductive Reasoning Fuzzy Inductive Reasoning is highly robust is highly robust when used correctly.when used correctly.

Fuzzy Inductive Reasoning Fuzzy Inductive Reasoning offers a offers a self-self-assessmentassessment feature, which is easily the most feature, which is easily the most important characteristic of the methodology.important characteristic of the methodology.

OptimizationOptimization with data collected at more with data collected at more frequent intervals.frequent intervals.

Mukund Moorthy 2nd February 1999

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