Modelisation economique Introduction

Transcription

Modelisation economique
Introduction
Antoine Bouet
Introduction
• Interet de la modelisation
– Pour la recherche economique : modele MIRAGE /
modele INGENUE / modele PEP…
– Pour une utilisation dans les entreprises,
banques… : optimisation d’un flux de transport,
composition optimale d’un portefeuille, modele
de production et de commercialisation d’un
produit…
• Modele simple implementable sous Excel
• Modele plus complique sous GAMS
Introduction
• Modele simple
• P est le prix d’un bien ; QS son offre ; QD sa
demande ; a, b, c et d des constantes
positives.
Introduction
• Concepts-cle de la modelisation
– Parametres
– Variables exogenes
– Variables endogenes
– Equations
– Calibrage et Resolution
• Modelisation
economique
Introduction
• Classification des
modeles
Introduction
• Construction d’un modele sous Excel
• Utiliser la fonction Solver dans le menu Data
• Si modele precedent :
– Parametres = a, b, c et d
– Pas de variable exogene
– Variables endogenes = QS, QD et P
– Distinction valeurs initiales / valeurs finales
– Trois equations = demande / offre / equilibre
Introduction
• Modele d’equilibre partiel P1
• Pb avec / sans optimisation
• Distinction valeur finale / valeur courante
• Algorithme de Newton
Introduction
• Optimisation lineaire
• Exemple d’une entreprise agroalimentaire :
objectif de minimisation de cout total de
transport (des asperges !)
• 2 fermes : Seattle (Se), San Diego (SD)
• 3 centres urbains: Chicago (Ch), New York
(NY), Topeka (To)
Introduction
• Donnees en tonnes
– Offres : Seattle (350) / San Diego (600)
– Demandes : New York (325) / Chicago (300) /
Topeka (275)
– Cout du fret = 90
– Distances en milliers de kms
Introduction
• Modelisation :
• Soit xij les acheminements de i a j ; dj les
demandes ; si les offres ; f le cout du fret ; TC
le cout total de transport (en milliers de USD)
Introduction
Introduction
Variables endogenes
Initial Current
Equations
Initial
Current
sSe
350
xSeNY
325.00
sSD
600
xSeCh
25.00
dNY
325
xSeTo
-
dCh
300
xSDNY
-
275.00 demandNY
325
dTo
275
xSDCh
275.00
- demandCh
300
distSeNY
2.5
xSDTo
275.00
275.00 demandTo
275
distSeCh
1.7
TC
156.15
distSeTo
1.8
distSDNY
2.5
Resultats
distSDCh
1.8
Economie de cout par jour
distSDTo
1.4
En %
f
90
Economie par mois
$
2,475.00
1.6%
$ 54,450.00
50.00 cost
153.68
300.00 supplySe
350
- supplySD
550
153.675 posxSeNY
50.00
posxSeCh
300.00
posxSeTo
-
posxSDNY
275.00
posxSDCh
-
posxSDTo
275.00
Introduction
• Etude d’un modele de portefeuille
• Investisseur doit gerer un portefeuille a partir
de 4 titres :
– Hardware hw
– Software sw
– Showbiz sb
– T-Bonds (obligations du Tresor) tb
Introduction
• Rendements moyens:
–
–
–
–
hw: 8 (%)
sw: 9
sb: 12
tb: 7
• Interet de diversifier son portefeuille: les titres ne sont
pas parfaitement correles donc on peut les combiner
pour un portefeuille
– Dont le rendement espere sera superieur pour un risque
constant;
– Dont le risque sera inferieur pour un rendement espere
constant.
Introduction
• Soit xi la part (en %) du
titre i dans le
portefeuille;
• On demande a
l’investisseur un
portefeuille d’esperance
de rendement 10% en
minimisant le risque
associe.
Introduction
Introduction
Introduction
• FormVariance=$H3*SUMPRODUCT($H3:$H6,$
F7:$F10)+$H4*SUMPRODUCT($H3:$H6,$F11:
$F14)+$H5*SUMPRODUCT($H3:$H6,$F15:$F1
8)+$H6*SUMPRODUCT($H3:$H6,$F19:$F22)
Introduction
Parametres
Variables exogenes
Variables endogenes
Equations
Initial Current
Initial Current
Initial
Current
Target
10
10 mhw
8
8 xhw
25.0%
30.3% xsum
msw
9
9 xsw
25.0%
8.7% portmean
msb
12
12 xsb
25.0%
50.5% posxhw
mtb
7
7 xtb
25.0%
10.6% posxsw
vhwhw
4
4 variance
1.63
2.90 posxsb
vhwsw
3
3
posxtb
vhwsb
-1
-1
vhwtb
0
0
vswhw
3
3
vswsw
6
6
vswsb
1
1
vswtb
0
0
vsbhw
-1
-1
vsbsw
1
1
vsbsb
10
10
vsbtb
0
0
vtbhw
0
0
vtbsw
0
0
vtbsb
0
0
vtbtb
0
0
1.00
10
0.30
0.09
0.50
0.11
Introduction
• On modelise maintenant un modele en equilibre
partiel
• Liberalisation du secteur du ble en Chine
• Donnees 2010
• Demande : QD = 7.8 Mios de USD
• Production : QS = 6.373 Mios de USD
• Surplus de demande MD est importee
• Droit de douane de 10.3%
• Cout de transport de 27.6%
Introduction
• On supposera que offre et demande de ble en
Chine suivent des fonctions isoelastiques
definies par rapport au prix interieur P avec
elasticites respectives es=3 et ed=-1.5
• Chine est un grand pays et offre d’importation
suit une fonction isoelastique d’elasticite
em=15
Introduction
Introduction
• Calibrage:
– Hypothese P=1 (changement d’unite)
– Donc : P*=1/(1+t+w)
– KD=…
– KS=…
– KM=…
Introduction
Introduction
Parameters
Exogenous variables
IV
IV
Endogenous variables
Initial value
CV
Eqn
Current value
ed
-1.5
t
10.3%
0.0%
QS
6373
5682.718412
EQS
5,682.72
es
3
w
27.6%
27.6%
QD
7800
8260.160645
EQD
8,260.16
ems
15
P
1.000
0.963
KD
7,800.00
P*
0.725163162
6,373.00
176965.239
M
1427
KS
KMS
calibration
Domestic supply
EP
0.96250739
0.754316136
EPstar
2577.442233
2577.442233
EM
2577.442233
Variation
-10.8%
scaling demand
7,800.00
Domestic demand
5.9%
scaling supply
scaling imports
6,373.00
176965.239
to be copied
in B8:B10
Domestic price
Foreign price
-3.7%
4.0%
Imports
80.6%
Introduction
* A 2 markets 2 regions partial equilibirum model:
* Inspired by V.O.Ronningen, 1997, Multi-Market,
Multi-Region Partial Equilibrium Modeling, in J.F.
Francois and K.A. Reinert, eds, Applied methods for
trade policy analysis, Cambridge, Cambridge
Universirt Press
12/8/2011
Initiation to economic modeling - M2 EAEI
Introduction
• * A 2 markets 2 regions partial equilibirum
model:
• Market 1/ Market 2 ; Meat and Coarse grains
• Supply of meat depends on meat price and
coarse grains price
• Demand for coarse grains depends price of
coarse grains and meat supply
12/8/2011
Introduction
•
•
•
•
•
•
•
•
•
•
•
•
Countries r /1,2/ ;
Variables
pmt(r)
domestic price of meat in r
pcg(r)
domestic price of coarse grain in r
wpmt
world price of meat
wpcg
world price of coarse grain
smt(r)
supply of meat in r
dmt(r)
demand of meat in r
scg(r)
supply of coarse grain in r
dcg(r)
demand of coarse grain in r
netmt(r)
excess supply of meat in r
netcg(r)
excess supply of coarse grain in r ;
•
On va appeler les variables dependant de r pmt1, pmt2, pcg1, pcg2,….
12/8/2011
Introduction
• Model
•
•
Relation between domestic price of meat and world price of meat
pmt(r) = cpmt(r) + wpmt + ddmt(r) ;
•
•
Supply of meat
smt(r) = csmt(r)*(pmt(r)**esmt(r))*(pcg(r)**escrmt(r)) ;
•
•
Demand for meat
dmt(r) = cdmt(r)* (pmt(r)**edmt(r));
•
•
Excess supply of meat
netmt(r) = smt(r) - dmt(r) ;
12/8/2011
Introduction
•
•
Relation between domestic price of coarse grain and world price of coarse grain
pcg(r) = cpcg(r) + wpcg + ddcg(r) ;
•
•
Supply of coarse grain
scg(r) = cscg(r)*(pcg(r)**escg(r)) ;
•
•
Demand for coarse grain
dcg(r) = cdcg(r)* (pcg(r)**edcg(r))*(smt(r)**edcrcg(r)) ;
•
•
Excess supply of coarse grain
netcg(r) = scg(r) - dcg(r) ;
12/8/2011
Introduction
• World trade of meat
• sum(r,netmt(r)) = 0 ;
• World trade of coarse grain
• sum(r,netcg(r)) = 0 ;
12/8/2011
Introduction
•
•
•
•
•
•
•
•
•
Elasticities
Supply meat /own price
Supply meat /price of grain
Demand for meat
Supply grains/own price
Demand for grains/ meat sup.
Demand for grains
;
12/8/2011
1
0.7
-0.2
-0.6
0.6
0.7
-0.8
2
0.5
-0.1
-0.8
0.4
0.3
-0.5
Introduction
•
•
•
•
•
•
•
•
•
•
•
•
World price of meat
World price of coarse grain
•
What is the impact of the removal of tariff on meat and tariff on grains?
Tariff on meat
Tariff on grains
Dom. Price of meat
Dom. Price of grains
Supply of meat
Demand for meat
Supply of grains
Demand for grains
;
12/8/2011
2000
100
1
600
0
2600
100
30259
37847
208033
170846
2
0
50
2000
150
64979
57391
233840
271027
Partial / General equilibrium analysis/Spatial-non spatial
models
• Analytical methodologies of international
trade
– Non spatial Partial equilibrium model
– Spatial Partial equilibrium model
– Single country GE trade model
– Multi - country GE trade model
• Multi country CGEM
• Gravity equations
12/8/2011
models
trade
– Non spatial Partial equilibrium model
• it does not consider equilibrium on all markets in order
to focus on one or several markets
• increased tractability or allows for more analytical
details
12/8/2011
models
•
Non spatial Partial equilibrium model
– Suppose n countries (i=1, 2, …n) with 1 being the domestic country, j = 2, …n is
the index for foreign countries
– imports and domestic goods are imperfect substitutes
– Demand function for domestically produced goods :
Q1D = Q1D ( P1 ; P2 ;...; Pn )
– Demand function for imports
Q Dj = Q Dj ( P1 ; P2 ;...; Pn )
12/8/2011
models
• Non spatial Partial equilibrium model
– Supply of domestic good:
Q1S = Q1S ( P1 )
– Supply of foreign goods:
Q Sj = Q Sj ( P * j )
– Gap between domestic and foreign prices
Pj = P * j .(1 + t j + τ j )
12/8/2011
models
trade
– General equilibrium model
• How is equilibrium determined on all markets
simultaneously?
• Full integration of income and interdependence effects
• Fully consistent, but simultaneously needs simplifying
assumptions on specific elements
12/8/2011
models
• Single country General equilibrium model
– one country and N sectors (k=1, 2…N)
– imported and domestic goods are perfect
substitutes
– no intermediate consumption in production, no
government
– labor is the sole productive factor
– perfect competition
12/8/2011
models
– Demand function of good k
QkD = QkD ( P1; P2 ...PN ; Y ) = QkD ( P; Y )
– Supply of good k
QkS = QkS ( Pk ; w)
– Domestic Excess Demand for good k
EDk = QkD ( P; Y ) − QkS ( Pk ; w)
12/8/2011
models
– Rest of the world’s Excess Supply of good k
ES *k = ES *k ( P*)
– Relation between domestic and world prices
Pk = P *k .(1 + t k )
12/8/2011
models
• Single country General equilibrium
model
– Labor market equilibrium
∑ L (w; P ) = L
D
k
k
k
– National income
Y = wL + ∑ tk P *k EDk
k
– The current account is constant
− ∑ P *k EDk = CA
k
12/8/2011
models
• Identification of economic agents and behaviours that
will be accounted for
• Collecting macroeconomic data
• Econometric estimation of behavioural parameters
(elasticities in particular): they can also be taken from the
literature
• Calibration
• Implementation of shocks
• Study of results
• Sensitivity analysis
12/8/2011
models
• These analytical instruments are complementary, not substitute.
• General equilibrium models account for income effects, interdependence
between factor and product markets.
• They are complex and demanding in terms of statistical information.
• The modeler is bound to simplify theoretical representation.
• Partial equilibrium models give the modeler more freedom to study a
specific aspect of trade liberalization
• Excellent instrument to analyze complex behavior (strategic interaction,
asymmetric information), complex production system or complex policy
instrument
12/8/2011
A simple CGE
• Object: making of a (very) simple CGEM
• Simple economy with one good, two primary factors, labour and capital, a
Cobb-Douglass technology, no relations with abroad.
Y = A0.KDα .LD1−α
W .LD = (1 − α ).P.Y
R.KD = α .P.Y
INC = W .LS + R.KS
P.C = INC
Y =C
LD = LS
KD = KS
12/8/2011
A simple CGE
• Object: making of a (very) simple CGEM
• Note that one equation is not independent:
P.Y = P.C = INC = α .P.Y + (1 − α ).P.Y
So :
R.KD + W .LD = INC
Since : LD = LS , it ensures that : KD = KS
So : KD = KS is implied by other equations
•
This is due to Walras’s law.
Write: KD=KS + Leon
Leon is a new variable, initialized at 0
So 9 variables, 8 equations: introduce a numeraire, P
Since KD=KS is not independent, leon will remain at 0
12/8/2011
A simple CGE
•
•
•
•
•
•
Parameters
LS
KS
;
LS = 7000;
KS = 3000;
• What is the impact of an increase in Labor Supply by
10%?
12/8/2011
Introduction
•
•
•
•
•
•
•
Modele 1-2-3 : modele concu par Devarajan, Go, Lewis, Robinson et Sinko (2007)
Economie du Sri Lanka : modele d’un petit pays avec deux secteurs avec secteur
expose et secteur abrite
Un pays ; deux secteurs ; trois biens
D bien domestique vendu seulement dans l’economie nationale
E bien produit domestiquement et exporte
M importations
Plein emploi des FP et PIB reel constant
12/8/2011
Introduction
Introduction
Introduction
Introduction
Introduction

Modelisation economique Introduction

Transcription

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