Model „Mini-minimal”

Stosowane modele równowagi ogólnej (CGE)

ogólnej (CGE)

Wykład 2

Model „Mini-minimal”

• Uproszczona wersja modelu MINIMAL (dostępnego pod adresem

http://www.monash.edu.au/policy/minimal.htm)

• Na czym polega uproszczenie? Model Mini- minimal nie zawiera m.in. mechanizmów minimal nie zawiera m.in. mechanizmów

substytucji dóbr i czynników produkcji, równań popytu konsumpcyjnego i eksportu.

• Mini-minimal obejmuje m.in. równania produkcji

i cen typu input-output.

MINIMAL

Flows Database (million $ Australian, 1986-87)

All Users

Industries Final Demands

AgricMining Manufacture Utilities Construction TradeTranspt FinanProprty Services Investment Households Exports Government Total Domestic

AgricMining 5502 14658 1839 689 143 52 641 210 2316 18975 705 45730

Manufacture 4587 30009 643 12486 10200 3061 6947 10150 38537 10587 57 127264

Utilities 1345 2045 3261 176 979 2814 2037 0 3573 21 150 16401

Construction 89 55 13 0 438 1708 381 33809 0 29 3679 40201

TradeTranspt 2958 11539 694 3353 8892 3052 5680 4563 38211 9269 582 88793

FinanProprty 1754 6545 622 1886 9623 9819 6111 2412 33641 886 1221 74520

Services 403 1595 92 290 1316 1586 2210 18 28653 345 44293 80801

Imported

AgricMining 233 1677 1 49 7 3 145 9 340 6 2470

Manufacture 1305 12411 184 2518 2322 832 3232 9491 9792 0 42087

Źródło: prezentacja modelu MINIMAL, Monash University

Manufacture 1305 12411 184 2518 2322 832 3232 9491 9792 0 42087

Utilities 1 2 2 0 1 3 2 0 3 0 14

Construction 0 1 0 0 3 0 8 68 0 2 82

TradeTranspt 104 259 11 34 703 142 258 41 1011 36 2599

FinanProprty 90 302 19 29 328 274 209 39 176 4 1470

Services 26 451 7 55 117 66 774 29 706 81 2312

Labour 10779 22512 3594 15008 35532 17095 43346 147866

Capital 11337 6359 4293 2160 10409 28873 4612 68043

Production tax 5217 16844 1126 1468 7780 5140 4208 41783

Total Cost 45730 127264 16401 40201 88793 74520 80801 60839 156959 40112 50816 782436

Tax on imports 497 5787 0 0 0 27 52

Model Database

Absorption Matrix

1 2 3 4 5

Producers Investors Household Export Government Total Sales Size ← I → ← 1 → ← 1 → ← 1 → ← 1 →

Domestic Flows

↑ C

↓

USE(commodity,"dom",user)

Imported

↑

C USE(commodity,"imp",user)

memorize numbers

4

Imported Flows

C

↓

USE(commodity,"imp",user)

Labour

↑ 1

↓

FACTOR (labour)

C= Number of Commodities = 7 I = Number of Industries = 7 Capital

↑ 1

↓

FACTOR (capital)

Output tax

↑ 1

↓

V1PTX

Also V0MTX = Tax on Imports of each commodity

Źródło: prezentacja modelu MINIMAL, Monash University

Model (1)

! Sets and flows data!

Set ! User categories: IO table columns !

IND # Industries # (AgricMining, Manufacture, Utilities, Construction,

TradeTranspt, FinanProprty, Services); ! subscript i ! FINALUSER # Final demanders # (Investment, Households, Government, Exports);

USER # All users #= IND union FINALUSER; ! subscript u ! Set ! Input categories: IO table rows !

Set ! Input categories: IO table rows !

COM # Commodities # (AgricMining, Manufacture, Utilities, Construction,

TradeTranspt, FinanProprty, Services); ! subscript c ! SRC # Source of commodities # (dom,imp); ! subscript s ! FAC # Primary factors # (Labour, Capital); ! subscript f !

Model (2)

Coefficient

(all,c,COM)(all,s,SRC)(all,u,USER) USE(c,s,u) # USE matrix #;

(all,f,FAC)(all,i,IND) FACTOR(f,i) # Wages and profits #;

(all,i,IND) V1PTX(i) # Production tax revenue #;

(all,c,COM) V0MTX(c) # import tax revenue #;

File BASEDATA # Flows Data File #;

Read Read

USE from file BASEDATA header "USE";

FACTOR from file BASEDATA header "1FAC";

V0MTX from file BASEDATA header "0TAR";

V1PTX from file BASEDATA header "1PTX";

Model (3)

! Useful aggregates of the base data ! Coefficient

(all,c,COM)(all,s,SRC) SALES(c,s) # Total value of sales #;

(all,i,IND) V1PRIM(i) # Wages plus profits #;

(all,i,IND) V1TOT(i) # Industry Costs #;

(all,c,COM) V0CIF(c) # Aggregate imports at border prices #;

Formula

(all,c,COM)(all,s,SRC) SALES(c,s) = sum{u,USER,USE(c,s,u)};

(all,c,COM)(all,s,SRC) SALES(c,s) = sum{u,USER,USE(c,s,u)};

(all,i,IND) V1PRIM(i) = sum{f,FAC,FACTOR(f,i)};

(all,i,IND) V1TOT(i) = V1PRIM(i) +

sum{c,COM,sum{s,SRC,USE(c,s,i)}};

(all,c,COM) V0CIF(c) = SALES(c,"imp") - V0MTX(c);

Model (4)

Variable

(all,c,COM)(all,s,SRC)(all,u,USER)

x(c,s,u) # Demand by user u for good c, source s #;

(all,c,COM)(all,s,SRC) x0(c,s) # Total demand for good c, source s #;

(all,c,COM)(all,s,SRC) p(c,s) # User price of good c, source s #;

(all,i,IND) x1lab(i) # Employment by industry #;

p1lab # Economy-wide wage rate #;

(all,i,IND) x1cap(i) # Current capital stock #;

(all,i,IND) p1cap(i) # Rental price of capital #;

(all,i,IND) p1cap(i) # Rental price of capital #;

(all,i,IND) x1tot(i) # Industry output #;

(all,i,IND) p1tot(i) # Unit cost of production #;

(all,c,COM) ptxpow(c) # Power of domestic tax #;

(all,c,COM) mtxpow(c) # Power of import tax #;

(all,c,COM) pworld(c) # World prices, measured in foreign currency #;

phi # Exchange rate, (local $)/(foreign $) #;

Model (5)

! Total demands for commodities ! Equation E_x0

(all,c,COM)(all,s,SRC) SALES(c,s)*x0(c,s)= sum{u,USER,USE(c,s,u)*x(c,s,u)};

! Demands for capital and labour ! Equation E_x1lab

(all,i,IND) x1lab(i) = x1tot(i);

Equation E_x1cap

(all,i,IND) x1cap(i) = x1tot(i);

! Demands for material (intermediate) inputs to production ! Equation E_x1

(all,c,COM)(all,s,SRC)(all,i,IND) x(c,s,i) = x1tot(i);

Model (6)

! Cost-balance equation !

Equation E_p1tot # cost of production = cost of all inputs # (all,i,IND) V1TOT(i)*[p1tot(i)+ x1tot(i)] =

sum{c,COM,sum{s,SRC, USE(c,s,i)*[p(c,s) + x(c,s,i)]}}

+ FACTOR("Labour",i)*[p1lab + x1lab(i)]

+ FACTOR("Capital",i)*[p1cap(i)+ x1cap(i)];

! Market clearing condition ! Subset COM is subset of IND;

Subset COM is subset of IND;

Equation E_x1tot (all,c,COM) x1tot(c) = x0(c,"dom");

! Purchaser's prices ! Equation E_pA

(all,c,COM)

p(c,"dom") = p1tot(c) + ptxpow(c);

Equation E_pB (all,c,COM)

p(c,"imp") = pworld(c) + phi + mtxpow(c);

Model (7)

! Expenditure-side GDP measures ! Variable

w0gdpexp # Nominal GDP from expenditure side #;

p0gdpexp # GDP price index, expenditure side #;

x0gdpexp # Real GDP from expenditure side #;

Coefficient

V0GDPEXP # GDP from expenditure side #;

Formula

V0GDPEXP = sum{c,COM, sum{s,SRC,sum{u,FINALUSER, USE(c,s,u)}} - V0CIF(c)};

Equation E_w0gdpexp V0GDPEXP*w0gdpexp =

sum{c,COM, sum{s,SRC,sum{u,FINALUSER, USE(c,s,u)*[p(c,s)+x(c,s,u)]}}

- V0CIF(c)*[x0(c,"imp")+ pworld(c) + phi]};

Equation E_p0gdpexp

V0GDPEXP*p0gdpexp = sum{c,COM,

sum{s,SRC,sum{u,FINALUSER, USE(c,s,u)*p(c,s)}} - V0CIF(c)*[pworld(c)+phi]};

Equation E_x0gdpexp x0gdpexp = w0gdpexp - p0gdpexp;

Model (8)

! Updating rules ! Update

(all,c,COM)(all,s,SRC)(all,u,USER) USE(c,s,u) = p(c,s)*x(c,s,u);

(all,i,IND) FACTOR("Labour",i) = p1lab*x1lab(i);

(all,i,IND) FACTOR("Capital",i) = p1cap(i)*x1cap(i);

(change)(all,c,COM) V0MTX(c) =

0.01 * [V0CIF(c)+V0MTX(c)]*[x0(c,"imp")+p(c,"imp")]

0.01 * [V0CIF(c)+V0MTX(c)]*[x0(c,"imp")+p(c,"imp")]

-0.01 * V0CIF(c) * [x0(c,"imp")+pworld(c)+phi];

(change)(all,c,COM) V1PTX(c) =

0.01 * [V1TOT(c)+V1PTX(c)]*[x0(c,"dom")+p(c,"dom")]

-0.01 * V1TOT(c) * [x0(c,"dom")+p1tot(c)];

! end of file !

Domknięcie (closure)

• Ile jest zmiennych w modelu?

• Ile jest równań w modelu?

• Zasada:

Liczba zmiennych endogenicznych Liczba zmiennych endogenicznych

= liczba równań

Plik CMF

auxiliary files = minimini;

File BaseData = minimal.har;

updated file BaseData = minimal.upd;

method = euler;

steps = 2 4 6;

Verbal Description= Test simulation;

Exogenous x(COM,SRC,FINALUSER);

Exogenous p1lab; ! 1 Exogenous p1lab; ! 1 Exogenous p1cap; ! IND Exogenous pworld; ! COM Exogenous phi; ! 1 Exogenous ptxpow; ! COM Exogenous mtxpow; ! COM rest endogenous;

shock pworld = uniform 5;