Topic 3 - Mundell's 2 country model / interdependence -

Why do we care about interdependence

We are motivated by spillover effects of a shock in 1 country on another

• e.g. financial crisis

Assumptions of Interdependence model

2 symmetric countries → H & F

Perfect Capital mobility → UIP holds

Adoptive expectations → expected change in ER = 0

• makes model static

Fixed prices → S & Q move together

Marshall-Lerner condition is satisfied

• Real depreciation → rise in NX

Output determined by Demand

Channels of interdependence

Marginal propensity to import (MPI)

• AD changes affecting trading partner

• AD UP leads to increased imports and higher NX in F

Interest rates (i)

• i change may affect i*

Exchange rate (when flexible)

• If p fixed, then a change to nom ER (S) will affect relative p and lead to expenditure switching

• If S increases -> depreciation -> dom good relatively cheaper -> dom output may increase

H output equation - Flexible ER

H Money Market equation - Flexible ER

M = M^S

RHS - M^D (as a function of i & y)

• no P as Fixed P so we say p=0

M is a level so not log transformed

UIP with adoptive expectations

i = i*

what is the term u

Captures FP or government spending

What relationship do i & y have

if real i increases then I falls -> AD falls -> output falls

-              Negative relationship of i & y

What relationship do s & y have

s increases (nom depreciation) -> q changes -> relative p changes -> NX increase -> y increase

• If ML condition holds which we assume

-              Positive relationship between s & y

Endogenous variables - Flexible ER

M & u

• Used for FP & MP + shocks

Relationship between y & y*

MPI drives y* effect

y* increase -> higher D for imports → H exports increase -> NX increase → y increase

-              Positive relationship between y & y*

Relationship between u & y

u increases -> AD increases -> y increases

-              Positive relationship between y & u

M & CB balance sheet

M = D + F

• D - CB holding of govt bonds

• F - Foreign exchange reserves

F output & money market equation - Flex ER

Conversion into y, y* space - Combine IS

Incorporate i = i*

Sum IS + IS* = IS^W

Conversion into y, y* space - Combine IS & LM

Combine IS^W with LM curves 

If FF_FL slope < 1 - diagram

g

MPI

<1 as only part of the increase falls in increased imports

• Therefore slope in HH_FL < 1 in absolute terms

• As denominator > 1

Why is HH_FL & FF_FL equilibrium on 45^o

countries identical / symmetrical initially

HH_FL slope vs FF

Inverse

• -0.5 = -2

Negative shock in Foreign Money supply - graph

-              M* only part of intercept term in FF_FL not the slope  -> shifts curve

-              not in HH_FL at all    ->     no shift

Positive shock in foreign FP or GS

u*

-              in both FF_FL & HH_FL intercept term  -> shifts both curves

-              stays on 45^o line (increase in y = increase in y*)

Breakdown of channels from u* increase

MPI - expansionary

• u* increase → AD_F increase → D for imports increase → X_H increase

• y* increase = y increase

• Relatively small impact as g < 1

Interest rate - Contractionary

• M exogenous so fixed

• To balance money market equilibrium as y* rises, i* must rise too

• i = i* because of UIP (nom & real i rise as inflation rate = 0 from fixed prices)

• i increase → I decrease → y decrease

Exchange rate channel - Expansionary

• i has fallen + g < 1

• To keep equilibrium s needs to rise to match fall in i

• s rises → depreciation

• As p is fixed, real ER falls as well (nom = real depreciation)

• NX rises from ML condition → AD rises

Fixed ER - CB intervention

CB needs to intervene to correct currency if there is a shock

-              Using F reserves

M^s becomes endogenous

Home / F output equation - Fixed ER

Money market equation - H - Fixed ER

Variables with * for F version

M becomes endogenous under fixed ER

Are F reserves endogenous under fixed ER

Yes

• Add together to get World reserves

F + F* = F^W

Conversion into y, y* space - fixed ER

incorporate i = i*

Sum LM + LM* = LM^W

Combine LM^W with Dom & F IS

Graph if FF_FX slope > 0

g<1 so slope<1 → crosses 45^o

HH_FX is inverse and symmetrical

• equilibrium at 45^o

Graph if FF_FX slope < 0

-k > RHS

absolute value still < 1

• FF_FX still flatter than 45^o

Negative shock to Foreign Govt bonds - Fixed ER - slope > 0

D* down = decrease in OMOs in F
- affects both HH & FF so both shift

Positive shock to Foreign FP or GS - Fixed ER - slope > 0

U* change

-              Only affects FF

Positive shock to Foreign FP or GS - Fixed ER - slope < 0

u* change only affects FF

-              However, it has flipped the sign on effect on y

Negative shock to Foreign Govt bonds - Fixed ER - slope < 0

D* change affects both HH & FF

• y* falls → y fall from MPI (contractionary effect)

• no ER effect as fixed ER

• y* falls → g < 1 so not full effect → i rises to correct → y falls (contractionary effect)

Effects of larger g

g - MPI

larger g means greater impact on domestic output for any F shock

as g increases → higher chance of positive impact of F positive shock