Introduction to Economic Modeling

D. K. Twerefou

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Major Economic and CC Questions

• Why rate of growth of income are different over time and in different countries?

• How do households and firms make their consumption and investment decisions?

• What factors affect household decision to adapt or not adapt to climate change

• What is the relationship between land value and climatic variable?

• What is the relationship between plant growth and changes in climatic variable?

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What is an Economic Model?• An abstract map of an economy • Way of systematic thinking on

– how the value of one variable determines the value of another variable.

– How one set of variables determine another set of variables

• Language that economists speak

Uses of Models

–Analysis of behaviour, facts –Evaluation of a policy–Analysis of impacts –Analysis of the interrelationships

between variable

Components of a Model

– Endogenous variables– Exogenous variables– Parameters– Assumptions– Solutions

Example of a model-1

• Endogenous Variable -variables determined within a given model -Y -endogenous - determined by given values of X.

• Exogenous Variable - X1 and X2 - exogenous determined outside the model.

• Parameters- constants whose values are fixed in a given model. Eg. B0 ,B1 and B2 are parameters.

0 1 2 2iY X X u

Example of a model-2

• Models are abstract representation of reality, there is the need to make some assumptions about the behaviour of the model.

• Why? necessary to ensure that model is concise and yield meaningful analysis.

Representation of model

• Diagrams and equations– linear or non-linear, – Single or multiple equations, – static or dynamic or strategic

Single Linear/ Non-linear

• A linear model is a model without polynomial terms.

• A non-linear is a model expressed in terms of polynomial

0 1 1 2 2Y X X u

20 1 1 2 2Y X X u

Multiple (simultaneous) equations

• More than one equation with the same variables.

• Y = C + I + G ; • C = a0 + a1(Y-T)

Static or Dynamic • Static model -Explains the behavior of a

phenomenon/activity within a specific point in time.

• A dynamic model - explains the behaviour of a phenomenon over a some period of time.

- model deforestation using a dynamic model. - deforestation occurs over a period of time

• Yt= Ct + It + Gt • Current consumption depends on past income• Ct =200 + 0.8*(Yt-1 -Tt-1)

What determined GDP growth?

Determinants of Economic Growth and CO2 emissions

0 1 2 3 4GDP Labor Capital FDI ODA u

What determined CO2 emissions?

What determines CO2 emissions

• What factors account for the rate of carbon emissions into the atmosphere in a given country????

– Linear or Non-linear?– Exogenous/Independent variables– Endogenous/Dependent Variables– Parameters– Dynamic or static?– Linear non –linear

2 0 1 2 3 4. .CO GDP Industrialization ind Effic Pop u

Determinants of Deforestation

• What factors account for the rate of deforestation?

• Why do we introduce a non-linear element into the equation?????

20 1 2 3 4_DEF GDP GDP Agric landuse Urbanisation u

Quiz

Identify the : - endogenous variables– exogenous variables– Parameters– Assumptions– In the equations

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Keynesian Static Model of National Income -1

Y = C + I + G ; C = a0 + a1(Y-T)

Endogenous variables - Y, C Exogenous variables - G, IParameters- a0 and a1.

C =200 + 0.8*(Y-T) T =20; G=20; I =30

Keynesian Static Model of National Income -2

• Solving the model: Y = (a0 - a1T+I+G)/(1-a1)• Y =200 +0.8*(Y-T) +I +G• Y-0.8Y = 200 -0.8*(20) +30+20• 0.2 Y =200-16 +50• Y =234/0.2 = 5*(234) = 1170• C = 200+0.8*(1170-20) = 1120• Checking the validity of the solution:• Y =1170 =1120+20+30 = C + I + G• MULTIPLIER = (1/(1-0.8))=5

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Keynesian Dynamic Model of National Income

Yt= Ct + It + Gt Current consumption depends on past incomeCt =200 + 0.8*(Yt-1 -Tt-1)Tt-1 =20; Gt =20; It =30; Yt-1 = 500 Yt =200 +0.8*(500-20) +30 +20Yt = 200 +384 +30+20Yt =200+384 +50 = 634Assume Tt, It , Gt remain same for all years

Yt+1 = 200 +0.8*(634-20) +30 +20 = 741Solve this model for another 20 years.

Thanks you

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Economy(p, w, y, c, l, L)

Firms (producers) Max π(LS)

Households (consumers)Max U(C,L)

Labour supply, L

Wage payment, wL

Supply of Goods

Payments for goods, p.y

1lcUMax1 LSlwLSpc

0;0;0 LSlc

wLDpyMax LDy

0;0 LDy

Market p and w such thatY = CLD = LSLS +l = L

Micro-Foundation to Macro VariablesGeneral Equilibrium with a representative household and firm