1

MINIMALA Simplified General Equilibrium Model

Model MINIMAL (1)

Model MINMAL w stosunku do modelu

„wymiany z produkcją” rozszerzony jest o:

• nakłady materiałowe,• nakłady materiałowe,

• handel zagraniczny (eksport i import),

• dodatkowe elementy popytu finalnego

(spożycie rządowe, inwestycje),

• podatki i cła.

Model MINIMAL (2)

• Model MINIMAL, w odróżnieniu od

modelu „wymiany z produkcją”, wyróżnia

tylko jedno reprezentatywne tylko jedno reprezentatywne

gospodarstwo domowe.

• Możliwa interpretacja – wszystkie

gospodarstwa są jednakowe (mają

jednakowe udziały we własności czynników

produkcji). Nie da się badać efektów

redystrybucyjnych.

Model MINIMAL (3)

• Bazą danych modelu jest tablica

przepływów międzygałęziowych

(input-output).(input-output).

Gałęzie/produkty

• W modelu MINIMAL występuje 7 gałęzi

(AgricMining, Manufacture, Utilities,

Construction, TradeTranspt, FinanProprty, Construction, TradeTranspt, FinanProprty,

Services) i tyle samo produktów.

• Zbiór gałęzi: IND; zbiór produktów: COM.

• Każda gałąź wytwarza tylko jeden rodzaj

produktów.

Czynniki produkcji

• Kapitał.

• Praca.

• Materiały (produkty).• Materiały (produkty).

Kapitał i praca to tzw. pierwotne czynniki

produkcji (primary factors).

Elementy popytu

• Popyt finalny:

– popyt inwestycyjny (2),

– konsumpcja gospodarstw domowych (3),

Nr kategorii

popytu w

oznaczeniach

zmiennych

– konsumpcja gospodarstw domowych (3),

– eksport (4)

– konsumpcja rządowa (5)

• Popyt pośredni (zużycie pośrednie) (1)

8

Excerpt 1a: Sets for users

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 !

IMPUSER # Non-export demanders: users of imports #IMPUSER # Non-export demanders: users of imports #

(AgricMining, Manufacture, Utilities, Construction,

TradeTranspt, FinanProprty, Services, Investment,

Households, Government);

Subset

IMPUSER is subset of USER;

IND is subset of IMPUSER;

9

Excerpt 1a: Sets for users

FINAL

Investment

Households

AgricMining

Manufacture

IMPUSER

USER

FINAL

USERIND

Households

Government

Exports

Manufacture

Utilities

Construction

TradeTranspt

FinanProprty

Services

1

0

Model DatabaseAbsorption Matrix

1 2 3 4 5

Producers Investors Household Export Government Total Sales

Size ← I → ← 1 → ← 1 → ← 1 → ← 1 →

DomesticFlows

↑C

↓

USE(commodity,"dom",user)

Imported↑C USE(commodity,"imp",user)

memorize

numbers

ImportedFlows

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

1

1MINIMAL

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

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

1

2

Excerpt 1b: Other sets; Flows DataSet ! 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 !

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,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

USE from file BASEDATA header "USE";

FACTOR from file BASEDATA header "1FAC";

V0MTX from file BASEDATA header "0TAR";

V1PTX from file BASEDATA header "1PTX";

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3

Excerpt 2: Useful aggregates of the dataCoefficient

(all,c,COM)(all,u,USER) USE_S(c,u) # USE matrix, dom+imp

together#;

(all,u,USER) USE_CS(u) # Total user expenditure on goods #;

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

Formula

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

(all,u,USER) USE_CS(u) = sum{c,COM,USE_S(c,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,USE_S(c,i)};

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

1

4

Excerpt 3: Total Demands for commodities

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 #;

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

In the levels: X0(c,s) = ΣΣΣΣ X(c,s,u)

Percent change: X0(c,s)*x0(c,s) = ΣΣΣΣ X(c,s,u)*x(c,s,u)

X common price: P(c,s)*X0(c,s)*x0(c,s) = ΣΣΣΣ P(c,s)*X(c,s,u)*x(c,s,u)

Finally: SALES(c,s)*x0(c,s) = ΣΣΣΣ USE(c,s,u)*x(c,s,u)

1

5

Excerpt 4: Imported/domestic Substitution

KEY

Inputs or

Outputs

Functional

Form

CESCES

up to Good CGood 1

Bottom level of nesting structure is same for all local users

CESCES

Imported

Good C

Domestic

Good C

Imported

Good 1

Domestic

Good 1

Nowe mechanizmy* (1)

Nakłady materiałowe (zużycie pośrednie).

• Zapotrzebowanie na materiały w danej

gałęzi proporcjonalne do jej produkcji.gałęzi proporcjonalne do jej produkcji.

* Nowe w „stosunku do modelu wymiany z produkcją”.

Nowe mechanizmy (2)

Substytucja dóbr krajowych i importowanych.

• Odbiorcy (gospodarstwa domowe, producenci,

inwestorzy, rząd) zgłaszają popyt na „kompozyty”

produktów.produktów.

• Skład kompozytu (tj. udział dóbr krajowych i

importowanych) zmienia się pod wpływem zmian

relacji cen produktów krajowych i

importowanych.

• Możliwości substytucji opisuje funkcja CES.

Nowe mechanizmy (3)

Eksport.

• Popyt zagranicy na dobra krajowe jest funkcją

relacji cen produktów krajowych do światowych

cen tych samych produktów.cen tych samych produktów.

• Siłę wpływu relatywnych cen na eksport wyrażona

jest za pomocą (stałej) elastyczności.

• Eksport może zmieniać się też niezależnie od cen,

np. pod wpływem zmian koniunktury na świecie

(zmienne f4q).

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9

Variable

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

(all,c,COM)(all,u,IMPUSER) p_s(c,u) # user price of composite good c #;

(all,c,COM)(all,u,IMPUSER) x_s(c,u) # use of composite good c #;

Coefficient

(all,c,COM) SIGMA(c) # elasticity of substitution: domestic/imported #;

(all,c,COM)(all,s,SRC)(all,u,IMPUSER) SRCSHR(c,s,u) # imp/dom shares #;

Read SIGMA from file BASEDATA header "ARM";

Formula (all,c,COM)(all,s,SRC)(all,u,IMPUSER)

Excerpt 4: CES Imported/domestic Substitution

Formula (all,c,COM)(all,s,SRC)(all,u,IMPUSER)

SRCSHR(c,s,u) = USE(c,s,u)/USE_S(c,u);

Equation E_x

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

x(c,s,u) = x_s(c,u) - SIGMA(c)*[p(c,s) - p_s(c,u)];

Equation E_p_s

(all,c,COM)(all,u,IMPUSER) p_s(c,u) = sum{s,SRC, SRCSHR(c,s,u)*p(c,s)};

xs = xaverage - σσσσ[ps - paverage]

paverage = ΣΣΣΣSs.ps

•

2

0Excerpt 4: Numerical Example of CES demands

p = Sdpd + Smpm average price of dom and imp Manufactures

xd = x - σσσσ(pd - p) demand for domestic Manufactures

xm = x - σσσσ(pm - p) demand for imported Manufactures

Let pm=-10%, x=pd=0

σσ

•

m d

Let Sm=0.3 and σσσσ=2. This gives:

p = -0.3*10 = -3

xd = - 2(- -3) = -6

xm = -2(-10 - - 3) = 14

Cheaper imports cause 14% increase in import volumes

and 6% fall in domestic demand.

Effect on domestic sales is proportional to both Sm and σσσσ.

2

1KEY

Inputs or

Outputs

Functional

Form

Leontief

up to Primary

Factors

Good CGood 1

Output

Nested Structure of Production

CESCESCES

CapitalLabour

Factors

Imported

Good C

Domestic

Good C

Imported

Good 1

Domestic

Good 1

2

2Demands for primary factors

Choose inputs of labour and capital, X1LAB(i) and X1CAP(i),

to minimize primary factor cost, P1LAB*X1LAB(i) + P1CAP(i)*X1CAP(i)

where X1PRIM(i) = CES[ X1LAB(i), X1CAP(i) ],

regarding as fixed: P1LAB and P1CAP(i) and X1PRIM(i).

Answer: (all,i,IND)

x1lab(i) = x1prim(i) - SIGMA1PRIM(i)*[p1lab-p1prim(i)];x1lab(i) = x1prim(i) - SIGMA1PRIM(i)*[p1lab-p1prim(i)];

x1cap(i) = x1prim(i) - SIGMA1PRIM(i)*[p1cap(i)-p1prim(i)];

V1PRIM(i)*p1prim(i) =FACTOR("Labour",i)*p1lab + FACTOR("Capital",i)*p1cap(i);

Could write

p1prim(i) = S1LAB(i)*p1lab + S1CAP(i)*p1cap(i),

x1prim(i) = S1LAB(i)*x1lab(i) + S1CAP(i)*x1cap(i)

S1LAB and S1CAP are shares of labour and capital in primary factor cost.

2

3Excerpt 5: Demands for capital and labourVariable

(all,i,IND) x1prim(i) # Industry demand for primary-factor composite #;

(all,i,IND) p1prim(i) # Price of primary factor composite #;

(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 #;

Coefficient (all,i,IND) SIGMA1PRIM(i) # CES substitution, primary factors #;

Read SIGMA1PRIM from file BASEDATA header "P028";Read SIGMA1PRIM from file BASEDATA header "P028";

Equation E_x1lab

(all,i,IND) x1lab(i) = x1prim(i) - SIGMA1PRIM(i)*[p1lab-p1prim(i)];

Equation E_x1cap

(all,i,IND) x1cap(i) = x1prim(i) - SIGMA1PRIM(i)*[p1cap(i)-p1prim(i)];

Equation E_p1prim

(all,i,IND) V1PRIM(i)*p1prim(i)

= FACTOR("Labour",i)*p1lab + FACTOR("Capital",i)*p1cap(i);

2

4Excerpt 6: Top level industry demands

X_S(c,i) = A_S(c,i).X1TOT(i), i∈∈∈∈IND, c∈∈∈∈COM

X1PRIM(i) = A1PRIM(i).X1TOT(i), i∈∈∈∈IND

Variable

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

(all,i,IND) a1prim(i) # All primary-factor augmenting technical change #;

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

Equation E_x1 # demand for commodity composites #

(all,c,COM)(all,i,IND) x_s(c,i)= x1tot(i);

Equation E_x1prim # demand for primary-factor composites #

(all,i,IND) x1prim(i) = a1prim(i) + x1tot(i);

Materials and primary factors used in proportion to X1TOT(i).

A_S(c,i) = amount of composite good c used per unit of output (constant).

A1PRIM(i) = amount of primary-factor needed to make unit of output.

1% decrease in A1PRIM(i) implies a 1% increase in factor productivity

2

5Excerpt 6: Cost of production

Levels: V1TOT(i) = sum{c,COM, sum{s,SRC, USE(c,s,i)}}

+ FACTOR("Labour",i) + FACTOR("Capital",i);

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

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

Right hand terms = 100 times the change in expenditure on some input.

Left hand side = 100 times the change in total costs.

Change in the value of output, V1TOT(i)

= sum of the changes in expenditure on materials and primary factors.

2

6

KEY

Inputs

Outputs

Functional

Form

Cobb-Douglas

up to Good CGood 1

Utility

Structure of Consumer Demand

CESCES

Imported

Good C

Domestic

Good C

Imported

Good 1

Domestic

Good 1

2

7Excerpt 8: Export demands

Levels X(c,"dom","Exports") = F4Q(c)[ ]-EXP_ELAST(c)

Exports of each good c are a declining function of:price in foreign currency, P(c,"dom")/PHIrelative to the world price PWORLD(c).

EXP_ELAST(c) = the +ve elasticity of export demand Suppose = 5,1% increase in price would cause a 5% fall in foreign demand.Shift variable F4Q could be used to simulate exogenous shifts in foreign demands.

P(c,"dom")PHI*PWORLD(c)

demands.

Variable(all,c,COM) pworld(c) # World prices, measured in foreign currency #;(all,c,COM) f4q(c) # Quantity shift in foreign demand #;

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

Coefficient (all,c,COM) EXP_ELAST(c) # Export demand elasticities #;Read EXP_ELAST from file BASEDATA header "P018";

Equation E_x4a (all,c,COM) x(c,"dom","Exports") =f4q(c)-EXP_ELAST(c)*[{p(c,"dom")-phi}- pworld(c)];

Equation E_x4b (all,c,COM) x(c,"imp","Exports") = 0;

2

8Excerpt 9: Domestic market clearing and prices

Subset COM is subset of IND;

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

Variable (change)

(all,c,COM) Delptxrate(c) # Ordinary change in rate of domestic tax #;

Equation E_pA (all,c,COM)

p(c,"dom") = p1tot(c) +100*[V1TOT(c)/(V1TOT(c)+V1PTX(c))]*Delptxrate(c);

E_x1tot says: Output of each industry, X1TOT(i) =total demand for the domestically produced commodity,

X0(c,"dom").

User price = production cost + taxP(c,"dom") = P1TOT(c)*[1 + PTXRATE(c)]

Rule: %Change A = 100.∆∆∆∆A/A

So: %Change [1+A] = 100.∆∆∆∆A/[1+A]1/[1 + PTXRATE(c)] = share of production cost in user price

= V1TOT(c)/[V1TOT(c)+V1PTX(c)]

2

9Excerpt 10: Prices of imports

Levels: P(c,"imp") = PHI*PWORLD(c)*[1 + MTXRATE(c)]

Variable

(change)(all,c,COM) Delmtxrate(c)

# Ordinary change in rate of import tax #;

Equation E_pBEquation E_pB

(all,c,COM)

p(c,"imp") = pworld(c) + phi +100*[V0CIF(c)/SALES(c,"imp")]*Delmtxrate(c);

share of border cost in

user price

3

0Excerpt 11a GDP from income sideVariable w0gdpinc # Nominal GDP from income side #;

Coefficient V0GDPINC # GDP from income side #;

Formula V0GDPINC = sum{i,IND, V1PTX(i)+sum{f,FAC, FACTOR(f,i)}}

+ sum{c,COM,V0MTX(c)};

Equation E_w0gdpinc

V0GDPINC*w0gdpinc =

sum{i,IND, FACTOR("Labour",i)*[p1lab + x1lab(i)]}sum{i,IND, FACTOR("Labour",i)*[p1lab + x1lab(i)]}

+sum{i,IND, FACTOR("Capital",i)*[p1cap(i) + x1cap(i)]}

+sum{c,COM, 100*V0CIF(c)*Delmtxrate(c)

+ V0MTX(c)*[x0(c,"imp") + pworld(c )+ phi]}

+sum{c,COM, 100*V1TOT(c)*Delptxrate(c) + V1PTX(c)*[x1tot(c)+p1tot(c)]};

Each term = 100 times ordinary change

100 ×××× change in tax rate

×××× the original tax base

original tax revenue

×××× percent change in tax base

3

1

Excerpt 11b GDP from expenditure sideGDP = C+I+G+X-M

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)}}-

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

3

2Excerpt 13a More macro variablesVariablex4tot # Export volume index #;p4tot # Export price index #;p2tot # Investment price index #;x0cif_c # Import volume index, CIF prices #;

Equation E_x4totsum{c,COM, USE(c,"dom","Exports")*[x4tot - x(c,"dom","Exports")]} = 0;

Equation E_p4totsum{c,COM, USE(c,"dom","Exports")*[p4tot - p(c,"dom")]} = 0;

Equation E_p2totEquation E_p2totsum{c,COM, sum{s,SRC, USE(c,s,"Investment")*[p2tot - p(c,s)]}} = 0;

Equation E_x0cif_csum{c,COM, V0CIF(c)*[x0cif_c - x0(c,"imp")]}=0;

Equation E_x4tot might have been written:

sum{c,COM,USE(c,"dom","Exports")}*x4tot =

sum{c,COM,USE(c,"dom","Exports")*x(c,"dom","Exports")};

3

3

Excerpt 13b Balance of Trade/GDP

Variable (change) delB # (Balance of trade)/GDP #;

Equation E_delB 100*V0GDPEXP*delB=

sum{c,COM, USE(c,"dom","Exports")*

[p(c,"dom")+x(c,"dom","Exports") - w0gdpexp]

- V0CIF(c)*[x0(c,"imp")+ pworld(c)+phi - w0gdpexp]};

B = [X-M]/GDP

B*GDP = [X-M]B*GDP = [X-M]

GDP*∆∆∆∆B + B*∆∆∆∆GDP = ∆∆∆∆[X-M]

100*GDP*∆∆∆∆B + 100*B*∆∆∆∆GDP = 100*∆∆∆∆[X-M]

100*GDP*∆∆∆∆B + B*GDP*gdp = Xx -Mm

100*GDP*∆∆∆∆B + [X-M]*gdp = Xx - Mm

100*GDP*∆∆∆∆B = X[x-gdp] - M[m-gdp]

3

4Excerpt 14: Factor market variables

Variable realwage # Wage rate deflated by CPI #;employ # Aggregate employment #;

(all,i,IND) gret(i) # Gross rate of return #;

Equation E_realwage realwage = p1lab - p3tot;

Equation E_employ sum{i,IND, FACTOR("Labour",i)*[employ - x1lab(i)]}=0;

Equation E_gret (all,i,IND) gret(i) = p1cap(i) - p2tot;Equation E_gret (all,i,IND) gret(i) = p1cap(i) - p2tot;

REALWAGE = P1LAB/P3TOT constant in sticky labour markets.employ = % index of aggregate employment, with wage-bill weights

GRET(i) = P1CAP(i)/P2TOT

P1CAP = annual revenue from unit of capitalP2TOT = cost of creating new unit of capitalGRET = gross rate of return on a unit of new capital: stable in long run

3

5Excerpt 15: Updating the flows data

Updates tell GEMPACK how to make post-simulation or updated database.

Product updates:

Formula: USE(c,s,u) = P(c,s)*X(c,s,u) c∈∈∈∈COM, s∈∈∈∈SRC, u∈∈∈∈USER

Update: USE(c,s,u) →→→→ USE(c,s,u)*[1+0.01*p(c,s)+0.01*x(c,s,u)]

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

Change updates: explicit formulae for ordinary change

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

V0CIF(c)*Delmtxrate(c) + 0.01*V0MTX(c)*[x0(c,"imp")+ pworld(c)+phi];

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

V1TOT(c)*Delptxrate(c) + 0.01*V1PTX(c)*[x1tot(c)+ p1tot(c)];

change in tax rate

×××× the original tax base

original tax revenue

×××× proportional change (=%/100) in tax base

3

6Excerpt 16: Creating a data summary file

check that the input data adds up properly: assist in explaining results.

File (new) SUMMARY # output file for summary data #

Coefficient (all,c,COM) CHECK(c) # (costs + tax) - sales : should = 0 #;Formula (all,c,COM) CHECK(c) =V1TOT(c) +V1PTX(c) -SALES(c,"dom");

Set COSTCAT # cost categories # = SRC union FAC;Coefficient

(all,c,COSTCAT)(all,i,IND) COSTMAT(c,i) # Summary of industry costs #;

FormulaFormula

(all,i,IND)(all,s,SRC) COSTMAT(s,i) = sum{c,COM,USE(c,s,i)};

(all,i,IND)(all,f,FAC) COSTMAT(f,i) = FACTOR(f,i);

Coefficient (all,i,IND) CAPSHR(i) # Share capital in primary factor costs #;

Formula (all,i,IND) CAPSHR(i) = FACTOR("capital",i)/V1PRIM(i);

Coefficient (all,c,COM) IMPSHR(c) # Share imports in local purchases #;

Formula (all,c,COM) IMPSHR(c) = sum{u,IMPUSER,USE(c,"imp",u)}/sum{u,IMPUSER,USE_S(c,u)};

3

7Closing the model

Each equation explains a variable.

More variables than equations.

Endogenous variables: explained by model

Exogenous variables: set by user

Closure: choice of exogenous variables

Many possible closures

Number of endogenous variables = Number of equations

One way to construct a closure:

(a) Find the variable that each equation explains; it is endogenous.

(b) Other variables, not explained by equations, are exogenous.

MINIMAL equations are named after the variable they SEEM to explain.

3

8

The ORANI short-run closure

Variable Size Descriptionphi 1 Exchange rate $A/$USx_s(COM,"Investment") COM Investment demandsx_s(COM,"Government") COM Government demandsx1cap IND Current capital stocksrealwage 1 Real wagex3tot 1 Real household

consumptionconsumptiona1prim IND Factor-using technical

changepworld COM World prices $USf4q COM Export demand shiftDelmtxrate COM Tax rate on importsDelptxrate COM Tax rate on production

Industry capital stocks, real wages and absorption fixed

"Shortrun" might be 2 years

3

9A possible long-run closure

Variable Size Description

phi 1 Exchange rate $A/$US

x_s(COM,"Investment") COM Investment demands

x_s(COM,"Government") COM Government demands

gret IND Rates of return on capital

employ 1 Aggregate employmentDelB 1 Balance of trade/GDP

a1prim IND Factor-using technicala1prim IND Factor-using technicalchange

pworld COM World prices, $US

f4q COM Export demand shift

Delmtxrate COM Tax rate on imports

Delptxrate COM Tax rate on production

•••• Capital stocks adjust in such a way to maintain fixed rates of return (gret).

•••• Aggregate employment is fixed and the real wage adjusts.

•••• DelB fixed instead of x3tot (real household consumption)

4

0Different closures

Many closures might be used for different purposes.

No unique natural or correct closure.

Must be at least one exogenous variable measured in local

currency units.

Normally just one — called the numeraire.Normally just one — called the numeraire.

Often the exchange rate, phi, or p3tot, the CPI.

Some quantity variables must be exogenous, such as:

•••• primary factor endowments

•••• final demand aggregates

4

1Three Macro Agnostics

4

2Three Macro Don't Knows

•••• ΑΑΑΑbsolute price level. Numeraire choice determines

whether changes in the real exchange rate appear as

changes in domestic prices or in changes in the exchange

rate. Real variables unaffected.

•••• Labour supply. Closure determines whether labour •••• Labour supply. Closure determines whether labour

market changes appear as changes in either wage or

employment.

•••• Size and composition of absorption. Either exogenous or

else adjusting to accommodate fixed trade balance.

Closure determines how changes in national income

appear.

4

3Illustrative simulation

10% increase in agregate real household consumption, x3tot.

Standard ORANI shortrun closure, fixed• Investment demands

• Government demands

• Current capital stocks

• Real wage

• Technical change• Technical change

• World prices

• Export demand shift

• Tax rates

• Exchange rate

Gragg 2-4-6 extrapolation solution method (accurate method)(accurate method).

Why? Perhaps tax cut.

4

4Illustrative simulation

Results: GDP up, price level up, real appreciation.

Consumption is 60% of GDP, but GDP up only 1%

Leakage: exports down, imports up

Increased output prices cause exports to fall.Increased output prices cause exports to fall.

and imports expand at the expense of domestic sales.

4

5Table1 : Consumption increase: macro results

Variable Description % changeemploy Aggregate employment 111...222444p1lab Economy-wide wage rate 7.69p3tot Consumer price index 7.69phi Exchange rate, (local $)/(foreign $) 0.00realwage Wage rate deflated by CPI 0.00w3tot Nominal total household consumption 18.46x3tot Real household consumption 10.00x3tot Real household consumption 10.00w0gdpexp Nominal GDP from income side 9.23w0gdpinc Nominal GDP from expenditure side 9.23p0gdpexp GDP price index, expenditure side 8.20x0gdpexp Real GDP from expenditure side 000...999555x4tot Export volume index ---111999...777111p4tot Export price index 4.49p2tot Investment price index 5.71x0cif_c Import volume index, CIF prices 111222...555111delB Ordinary change, (Balance of trade)/GDP ---000...000444

4

6Causation in Short-run Closure

Real Wage

Capital StocksTech Change

Rate of

return on

capital

EndogenousExogenous

Private

ConsumptionInvestment

Government

Consumption

Capital StocksTech Change

Trade

balance

Employment

GDP = +++

4

7

Why higher prices?ShortShort--run: industry capital stocks fixedrun: industry capital stocks fixedTo increase output, must hire more labour.

Additional units of labour are less productive

Unit costs increase with output.

Supply curve are upward-sloping.

The more capital-intensive the sector, the steeper is supply curveThe more capital-intensive the sector, the steeper is supply curve

Largest price rise is for FinanProprty.

Circle of price risesCircle of price risesIncreases in output price in one industry raises input costs in others

Higher consumer prices increase the nominal wage because real wage rate is fixed.

All domestic prices rise.

4

8Effect of demand increasePrice

Demand

price rise

Capital stocks fixed

To increase output, must hire more labour.

Additional units of labour are less productive

Quantity

Demand shifts right5%

output upSupply

productive

Unit costs increase with output.

Supply curves are upward-sloping.

4

9

Variable Description Servicesp1cap Rental price of capital 15.25p1lab Nominal Wage (CPI-linked) 7.69p1tot Cost of output 7.92x1lab Employment 3.45x1tot Industry output 3.11

x(part) Exports -31.69x0(imp) Total imports 18.33

Effect on Services industry

p(imp) User price of imports 0.00

Output up, employment up more, implies p1cap>p1lab

p1cap, p1lab both up, so p1tot up

so imports grow more than domestic output

and exports down

5

0Effects of increased input costs

Non-traded sectors: inelastic demand,

pass on higher costs without losing sales.Price

InelasticDemand Supply curve

shifts up

large price rise

Price

ElasticDemand

Supply curveshifts up

small price rise

Export-oriented industries, such as AgricMining, are not able to do so. Import-competers, such as Manufacture, are also vulnerable.

Not shown: right shifts in demand for consumer goods:

Manufacture, TradeTranspt, FinanProprty, and Services

Quantity

small outputfall

large price rise

Quantity

large output fall

5

1GDP IdentityRealGDP = F(Capital,Labour) approximate aggregate relation

GDP from income side:• gdp = Skk + Sll k=0• gdp = Sll

• 0.95 = (approx) (0.68)*1.24 = 0.84

GDP from expenditure side: • RealGDP = C + I + G + (X-M)• RealGDP = C + I + G + (X-M)• I, G fixed, C exogenously increased (by 6% of GDP).• (X-M) changes to make income GDP = expenditure GDP

Why is the change in GDP 1 percent and not 6 percent? GDP = C + I + G + (X-M); Exogenous %∆∆∆∆C= 10; %∆∆∆∆I, %∆∆∆∆G = 0.

C/GDP = 0.6 ⇒⇒⇒⇒%∆∆∆∆GNP = 0.6××××10 = 6% if trade balance unchanged. BUT TRADE BALANCE IS ENDOGENOUS

Real appreciation ⇒⇒⇒⇒ X↓↓↓↓ and M↑↑↑↑. (“LeakageLeakage”)

5

2Consumption increase: sectoral results

Description AgricMining Manufacture Utilities Construction TradeTranspt FinanProprty Services

Rental price of capital -8.42 6.27 18.78 7.83 9.49 18.47 15.25

Price, factor composite -0.73 7.37 13.66 7.71 8.10 14.40 8.40

Cost of output 2.09 5.59 10.76 6.65 7.96 12.71 7.92

Employment -7.78 -0.66 5.02 0.06 0.83 4.89 3.45

Use of factor composite -3.95 -0.52 2.23 0.06 0.64 1.76 3.11

Industry output -3.95 -0.52 2.23 0.06 0.64 1.76 3.11

Exports -9.81 -23.83 -40.01 -27.53 -31.8 -45.01 -31.69

Gross rate of return -13.37 0.52 12.36 2.00 3.57 12.06 9.03

Total imports 5.54 11.34 25.51 14.05 20.72 27.58 18.33Total imports 5.54 11.34 25.51 14.05 20.72 27.58 18.33

Domestic user prices 2.09 5.59 10.76 6.65 7.96 12.71 7.92

User price of imports 0.00 0.00 0.00 0.00 0.00 0.00 0.00

AgricMining: large export share (elastic) restrains price rise

Manufacture: import competition restrains price rise

Others: little trade, prices rise more

labour-intensive selling to household do best (Services)

5

3Some Database Shares

AgricMining Manufacture Utilities Construction TradeTranspt FinanProprty Services AverageCost shares

Dom goods 0.41 0.60 0.47 0.49 0.39 0.32 0.31 0.43Imp goods 0.04 0.14 0.02 0.07 0.04 0.02 0.06 0.07

Labour 0.27 0.20 0.24 0.39 0.44 0.25 0.57 0.34Capital 0.28 0.06 0.28 0.06 0.13 0.42 0.06 0.16

Total 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00Sales shares

Intermediate 0.51 0.53 0.77 0.07 0.41 0.49 0.09 0.39Investment 0.01 0.08 0.00 0.84 0.05 0.03 0.00 0.11

Households 0.05 0.30 0.22 0.00 0.43 0.45 0.36 0.31Government 0.02 0.00 0.01 0.09 0.01 0.02 0.55 0.11

Exports 0.42 0.08 0.00 0.00 0.10 0.01 0.00 0.09Exports 0.42 0.08 0.00 0.00 0.10 0.01 0.00 0.09Total 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Import share 0.08 0.27 0.00 0.00 0.03 0.02 0.03Capital share 0.51 0.22 0.54 0.13 0.23 0.63 0.10Output 40513 110420 15275 38733 81013 69380 76593

5

4Comparative-static interpretation of results

Employment

Change

C

Results refer to changes at some future point in time.

0 T

A

years

B

5

5

Length of run ,T

T is related to our choice of closure.

With shortrun closure we assume that:

•••• T is long enough for price changes to be transmitted throughout the economy, and for price-induced substitution to take place.

•••• T is not long enough for investment decisions to greatly affect •••• T is not long enough for investment decisions to greatly affect the useful size of sectoral capital stocks.[New buildings and equipment take time to produce and install.]

T might be 2 years. So results mean:

a 10% consumption increase might lead

to employment in 2 years time being 1.24% higher than it would be

(in 2 years time) if the consumption increase did not occur.

5

6

Features of more complex models

•••• more sectors.

•••• more primary factors: land, natural resources, types of labour.

•••• more final demanders: inventories, multiple households

•••• margin flows•••• margin flows

•••• commodity taxes specific to both commodity and user.

•••• multiproduction:one industry makes several commodities, or several industries make the same commodity.

• more technical change variables.

5

7

More features of more complex models

•••• consumption shares that depend on income as well as relative prices.

•••• more complicated production technology, with more types of substitution (eg, between capital and energy).

•••• more macro indices and other variables to help present results.present results.

•••• equations linking investment to profitability in each industry

•••• different investment technology for each industry.

•••• multiple regions (provinces, nations)

•••• multi-period models, which track through time

But still very similar to MINIMAL.