The 1-2-3 Model:Tradables, Non-tradables, and

Semi-tradables inTrade Models

Shantayanan DevarajanJeffrey D. LewisJaime de Melo

Sherman Robinson

2

Macroeconomic Adjustment

GDP = C + I + G + E - MGDP + (M – E) = C + I + Gproduction + trade balance = absorption

Trade shocks and structural adjustment:“Expenditure reduction” versus“Expenditure switching”

3

Modeling Issues

• The specification of goods as tradable, nontradable, traded, and nontraded.– The Armington specification in CGE

models. • The role of the exchange rate in CGE

models. – Real versus “financial” exchange rate.

4

Purchasing Power Parity:PPP Exchange Rate

( )π

π

π

ˆˆˆ0ˆ

ˆˆˆˆ

−=⇒=

−+=

=

PRR

PRRP

RR

r

r

r

5

PPP Exchange Rate

• R has units of domestic currency per $US.

• R↑ is a depreciation of the exchange rate.

6

Problems

• If all goods are tradable, then PPP is trivial. All prices set by world prices. – Law of One Price.

• PPP must measure relative prices of tradables and nontradables.– Harberger, Edwards, Srinivasan.

• Underlying Salter-Swan model.

7

Salter-Swan Model

Non-tradables

Tradables

Borrowing

A

B

C

N1N2

T1

T3

T2

T1 T3 absorption cut

T3 T2 structural adjustment

N1 N2 structural adjustment

8

Problems

• Hard to define tradables and nontradables empirically.– Most sectors have some trade.– Purely nontraded goods are a very small

share of GDP. • Requires dichotomous classification of

goods: purely tradable or nontradable.

9

Law of One Price

• Given commodity arbitrage, all traded goods will have the same price in all markets.

• Very powerful assumption. Common in neoclassical trade theory.– Project analysis.– Theory of comparative advantage.

10

Law of One Price

1. All domestic prices of tradables are set by world prices.

2. Any change in the price of an import is immediately transmitted to price of corresponding domestic good.

3. Tariff policy is very powerful. Immediately affects price of domestically produced goods.

11

Law of One Price

4. Should observe extreme specialization in production.

5. Should never observe two-way trade (cross hauling).

6. Trade shares are not important. Only tradablility matters.

12

Problems

• Implications of Law of One Price are all false empirically.

• Changes in world prices and tariffs are only weakly transmitted to domestic markets.

• Do not observe extreme specialization.

13

Problems

• Observe two-way trade in most sectors, and at very fine levels of disaggregation.

• Trade shares are clearly important. Sectors with large trade shares are more affected by changes in world markets.

14

Armington Insight

• Specify traded goods as imperfect substitutes for domestic goods with the same sector classification.

• Allow degrees of “tradability” rather than dichotomous classification.

• Armington model provides a good theoretical and empirical framework for analyzing trade policy.

15

1-2-3 Model

• 1 country, 2 activities, 3 commodities• 2 activities, producing D and E.

– E not consumed domestically.• Additional commodity, M, consumed

domestically but not produced.

16

1-2-3 Model

• Aggregate GDP (X) is fixed.– Full employment model.

• Trade balance set exogenously.• World prices of M and E are fixed.• Total absorption (Q) is endogenous.

17

Basic 1-2-3 CGE Model

( )( )

( )

( )

2

2

Flows

1. , ;

2. , ;

3.

4. ,

5. ,

6.

S

S D

Dq

e dS

m dD

x

X G E D

Q F M D

YQP

E g P PDM f P PD

Y P X R B

σ

= Ω

=

=

=

=

= +

( )( )

1

1

Prices7. 8.

9. ,

10. ,

11. 1Equilibrium Conditions12. 013. 014.

m m

e e

x e d

q m d

D S

D S

m e

P R pwP R pw

P g P P

P f P P

R

D DQ Qpw M pw E B

=

=

=

=

≡

− =

− =

− =

18

Basic 1-2-3 CGE Model

Identities15. 16. 17.

x e d S

q S m d D

q D

P X P E P DP Q P M P DY P Q

≡ +

≡ +

≡

19

Basic 1-2-3 CGE ModelEndogenous VariablesE: Export goodM: Import goodDS: Supply of domestic goodDD: Demand for domestic goodQS: Supply of composite goodQD: Demand for composite goodY: Total incomePe: Domestic price of export goodPm: Domestic price of import goodPd: Domestic price of domestic

good

Px: Price of aggregate outputPq: Price of composite goodR: Exchange rate

Exogenous Variablespwe: world price of export goodpwm: world price of import goodB: Balance of tradeσ: Import substitution elasticityΩ: Export transformation elasticity

20

SAM for 1-2-3 Model

Activities Commod Hshld World Activities d DP D eP E Commodities q DP Q Households xP X R B World mP M Total d S eP D P E+ q SP Q Y

E/D = k (PE / PD ) Ω

PE = R·pwe

PD /PE

D

E

M/D = k’(PD / PM)σ

PM = R·pwm

PD /PM

M

D

23

1-2-3 Programming Model

( )

( ) x

Maximize , ;

with respect to: , , ,subject to: Shadow Prices

1. , ; technology /

2.

D S

S x q

Q F M D

M E D D

G E D X P P

σ

λ

=

Ω ≤ =

balance of trade /3. domestic market /

m e b q

D S d d q

pw M pw E B R PD D P P

λ

λ

⋅ ≤ ⋅ + =

≤ =

PD/PE

PMM=PEEPD/PM

E

D

M

D

1-2-3 Model

25

26

27

External Shocks, Structural Adjustment, and the Real

Exchange Rate

Shantayanan DevarajanJeffrey D. Lewis

Sherman Robinson

28

Simple 1-2-3 Model

);,( (1) Ω= EDGX

);,( (2) σMDFQ =

29

2(3) e

d

E PkD P

Ω

=

1(4) d

m

M PkD P

σ

=

1-2-3 Model

30

(6) e eP R π= ⋅

(5) m mP R π= ⋅

1-2-3 Model

(7) m eM Eπ λ π⋅ = ⋅ ⋅

31

Variables and Parameters

• Variables– E, M, D, Q, Pd, Pe, Pm, R

• Parameters or exogenous variables– οm, οe, κ, X, ρ, Ω–

• 8 variables, 7 equations– Choice of numeraire. Often R 1.

( )1 so 0 1eB E Bλ π λ= − = ⇒ =

32

( )( )

mm

ee

em

de

md

RP

RP

EM

PPDE

PPDM

π

π

πλπ

σ

ˆˆˆˆˆˆ

ˆˆˆˆˆ

ˆˆˆˆ

ˆˆˆˆ

+=

+=

++=+

−Ω=−

−=−

Real Exchange Rate Change

33

( ) ( ) ( )1 ˆˆ ˆ ˆ1 1

ˆ1 0

d m eP

R R

σ π π λσ

= − ⋅ + +Ω ⋅ + +Ω

≡ ⇒ =

Equilibrium Domestic Price

34

Case 1

ˆˆ ˆ ˆCase 1: 0, 0ˆ ˆ ˆThen:

PPP calculation is ok.

m e

dR P

π π π λ

π

= = ≠ =

= −

35

Case 2

Case 2: or Model collapses to small open economy with all goods tradable. is tied to world price. dP

σ →∞ Ω→∞

36

Case 3

ˆˆ ˆCase 3: 0, 0ˆImplies: 0

real appreciation"Dutch disease" case.

m e

dP

π π λ= = >

>

37

Case 4

ˆ ˆ ˆCase 4: 0, 0, 0ˆIf 1 0 (depreciation)ˆIf 1 0 (appreciation)

and trade volume falls.

m e

d

d

P

P

λ π π

σ

σ

= > =

< ⇒ <

> ⇒ >

38

Case 5: Lerner Symmetry

( )( )

( )( )

ˆ ˆˆ ˆIf: 0, 0, 01ˆ ˆ ˆ ˆThen:

ˆ ˆˆ ˆIf: 0, 0, 01ˆ ˆ ˆThen:

The effect is symmetric, and Lernersymmetry holds.

m e

d e d m

e m

d e e

R

P P P

R

P P

π π λσ

πσ

π π λσ

πσ

≠ = = =

−− = =

+Ω

≠ = = =

− −− =

+Ω

39

( )

( )

balance de tra ˆ

tradeof terms ˆˆ

inflation worldˆˆ

rate exchange PLD ˆˆ

Ω+−

Ω+−

+

Ω+Ω+⋅

−

=−

σλσ

ππσ

ππσ

em

em

dPR

Equilibrium PLD EXR

40

( )

( )Ω+

−Ω+

−=

Ω+Ω+⋅

−−=

σλ

σππ

σππσ

ˆˆˆ

ˆˆˆˆˆ

em

emdr PRR

Equilibrium Real EXR

Terms of trade Trade balance

Differential inflation

41

Purchasing Power Parity

( )PRRP

RR

r

r

ˆˆˆˆ −+=

=

π

π

42

Offer Curves in the 1-2-3 Model

43

Standard Offer Curve

E

M

πe/ πm

“Offer” of exports for given world prices

44

1-2-3 Model Offer Curve

E

M

σ > 1

σ < 1

σ = 1

45

1-2-3 Model Offer Curve

• Slope of offer curve depends on import substitution elasticity.

• Length of offer curve for a given domain of changes in world prices depends on both import substitution elasticity and export transformation elasticity.

46

1-2-3 CGE Model with Consumption, Government,

and Investment

Shantayanan DevarajanDelfin S. Go

Jeffrey D. LewisSherman Robinson

Pekka Sinko

47

1-2-3 CGE Model

( )( )

( )

( )

2

2

Real Flows

1. , ;

2. , ;

3.

4. ,

5. ,

S

S D

D

e dS

m dD

X G E D

Q F M D

Q C Z GE g P P

DM f P PD

σ

= Ω

=

= + +

=

=

48

1-2-3 CGE Model

( )

6. 7. 8.

9. 1

m m

q q D

y

e e

x q

g

t y

T t R pw Mt P Qt Yt P E

Y P X tr P re RS s Y R B S

C P s t Y

=

+

+

+

= + +

= + +

= − −

49

1-2-3 CGE Model

( )( )( )

( )( )

1

1

Prices

10. 1

11. 1

12. 1

13. ,

14. ,

15. 1

m m m

e e e

t q q

x e d

q m d

P t R pw

P t R pw

P t P

P g P P

P f P P

R

= +

+ =

= +

=

=

≡

50

1-2-3 CGE Model

Equilibrium Conditions16. 017. 018. 19. 020. 0

D S

D S

m e

t

q q g

D DQ Qpw M pw E ft re BP Z ST P G tr P ft R S

− =

− =

− − − =

− =

− − + − =

51

1-2-3 CGE Model

Identities21. 22.

x e d S

q S m d D

P X P E P DP Q P M P D

≡ +

≡ +

52

Endogenous Variables E: Export good M: Import good DS: Supply of domestic good DD: Demand for domestic good QS: Supply of composite good QD: Demand for composite good Pe: Domestic price of export good Pm: Domestic price of import good Pd: Domestic price of domestic good Px: Price of aggregate output Pq: Price of composite good Pt: Sale price of composite good R: Exchange rate T: Tax revenue Sg: Government savings Y: Total income C: Aggregate consumption S: Aggregate savings Z: Aggregate real investment

Exogenous Variables pwe: world price of export good pwm: world price of import good tm: Tariff rate tx: Export tax rate tq: Sales tax rate ty: Direct tax rate tr: Government transfers (real) ft: Foreign transfers to government re: Foreign remittances to private sector s: Average savings rate X: Aggregate output (GDP) G: Real government demand B: Balance of trade σ: Import substitution elasticity Ω: Export transformation elasticity