International Monetary Theory: Mundell Fleming Redux...v International Monetary Theory: Mundell...

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Brunnermeier & Sannikov International Monetary Theory: Mundell Fleming Redux by Markus K. Brunnermeier and Yuliy Sannikov Princeton and Stanford University Princeton Initiative Princeton, Sept. 9 th , 2017

Transcript of International Monetary Theory: Mundell Fleming Redux...v International Monetary Theory: Mundell...

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International Monetary Theory:Mundell Fleming Redux

by

Markus K. Brunnermeier and Yuliy SannikovPrinceton and Stanford University

Princeton Initiative Princeton, Sept. 9th, 2017

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Motivation

Global currency spilloversβ€’ β€œFlight to safety” - Dollar appreciation when risk rises

β€’ Local currency: good store of value/hedge for idiosyncratic risk

β€’ Global currency: good hedge for international competitiveness risk

When to peg to world currency? When to dollarize?

MoPo space: β€œNuanced Mundell-Fleming Trilemma”‒ Local and global money have different risk profile (imperfect substitutes)

β‡’ increases MoPo space

‒ Too high inflation: local citizens substitute local currency for global currency⇒ limits MoPo space

Reserve currency management – Irrelevance theorem

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Modelling Framework

Closed economy Open Economy

Static Hick’s IS-LM Mundell-Fleming

DynamicImpulse response

New Keynesian Obstfeld-Rogoff

Risk & Dynamicfinancial frictions

Samuelson BewleyDiamond Aiyagari X

I Theory of Money

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Modelling Framework

Closed economy Open Economy

Static Hick’s IS-LM Mundell-Fleming

DynamicImpulse response

New Keynesian Obstfeld-Rogoff

Risk & Dynamicfinancial frictions

Samuelson BewleyDiamond Aiyagari X

I Theory of Money

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Modelling Framework

\Friction OLG Incomplete Markets + idiosyncratic risk

Risk deterministic endowment riskborrowing constraint

investment risk

Only money Samuelson Bewley

Basic β€œI Theory”

With capital Diamond Aiyagari

𝑓′ π‘˜βˆ— = π‘Ÿβˆ—, Dynamic inefficiencyπ‘Ÿ < π‘Ÿβˆ—, 𝐾 > πΎβˆ—

Inefficiencyπ‘Ÿ < π‘Ÿβˆ—, 𝐾 > πΎβˆ—

Pecuniary externalityInefficiencyπ‘Ÿ > π‘Ÿβˆ—, 𝐾 < πΎβˆ—

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Frictions

Incomplete marketsβ€’ Within country

only w.r.t. idiosyncratic risk 𝑑 ෨𝑍𝑑𝑖

(other risks can be shared within national economy)

β€’ Across countries Only global money can be traded

Money is a bubble Like in Samuelson, Bewley

Price are fully flexible

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International setting

Small Economy

β€’ Local currency Store of value Hedge against idiosyn-

cratic risk

β€’ Consumption basket Non-tradable local good π‘ŽπΎπ‘‘ tradable good 1 𝑏1,𝑑𝐾𝑑 tradable good 2

Large Economy*

β€’ Global currency* $ … Hedge for SOE’s citizens against

β€œinternational competitive risk”

β€’ Consumption basket* Non-tradable good* π‘Žβˆ—πΎπ‘‘

βˆ—

tradable global good 1 𝑏1,π‘‘βˆ—πΎπ‘‘

βˆ—

tradable global good 2 𝑏2,π‘‘βˆ—πΎπ‘‘

βˆ—

Exchangerate

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Large Economy*

β€’ Global currency* $ … Hedge for SOE’s citizens against

β€œinternational competitive risk”

β€’ Consumption basket* Non-tradable good* π‘Žβˆ—πΎπ‘‘

βˆ—

tradable global good 1 𝑏1,π‘‘βˆ—πΎπ‘‘

βˆ—

tradable global good 2 𝑏2,π‘‘βˆ—πΎπ‘‘

βˆ—

International setting

Small Economy

β€’ Local currency Store of value Hedge against idiosyn-

cratic risk

β€’ Consumption basket Non-tradable local good π‘ŽπΎπ‘‘ tradable good 1 𝑏1,𝑑𝐾𝑑 tradable good 2 𝑏2,𝑑𝐾𝑑 𝑏2,𝑑

𝑏1,𝑑<𝑏2,π‘‘βˆ—

𝑏1,π‘‘βˆ—

Exchangerate

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Intuition

Purchase good 2 in exchange of good 1 (depends on ToT)

Hold global money as Net Foreign Asset Position

Value of money – money is safe assetβ€’ Local money is store of value with nice hedge against

idiosyncratic risk

β€’ Global money ($) hedges better β€œexport risk” (competitiveness = ToT + productivity)

β€’ 2 money can coexist (even though both are β€œbubbles”) Different return-risk profile

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Overview

Large countryβ€’ Portfolio choice between

Physical capital π‘˜π‘‘βˆ—

US Dollar, $ – β€œbubble in positive net supply”

β€’ No state variable: due to scale invariance

Small countryβ€’ Portfolio choice between

Physical capital π‘˜π‘‘ Peso β€œhedge against idiosyncratic shocks”

US Dollar, $ β€œhedge against ToT + export productivity shocks”

β€’ State variable πœˆπ‘‘:Accumulation dynamics of foreign asset position (in $)

πœ‡π‘‘π‘₯ = πœ‡π‘₯ πœˆπ‘‘ , πœŽπ‘‘

π‘₯ = 𝜎π‘₯(πœˆπ‘‘)

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Large country

𝐸 ࢱ0

∞

π‘’βˆ’πœŒπ‘‘ log π‘π‘‘βˆ— 𝑑𝑑

Consumption Cobb-Douglas preferences(over 1 non-tradable one 2 tradable goods)

𝑐0,π‘‘βˆ— (1βˆ’π›Ό)

(𝑐1,π‘‘βˆ— )𝛽(𝑐2,𝑑

βˆ— )(1βˆ’π›½)𝛼

Investment rate πœ„βˆ— in terms of non-tradable local good

Evolution of physical capital stockπ‘‘π‘˜π‘‘

βˆ—

π‘˜π‘‘βˆ— = Ξ¦ πœ„βˆ— βˆ’π›Ώ 𝑑𝑑

Output shocks per unit of capital π‘Žβˆ—, 𝑏1,π‘‘βˆ— , or 𝑏2,𝑑

βˆ—

β€’ Determines relative pricesβ€’ … has to be indifferent Ito-processes

Idiosyncratic real cash flow shocks πœŽπ‘˜π‘‘βˆ—π‘‘ ෨𝑍𝑑

π‘–βˆ—

Net worth dynamics: 𝑑𝑛𝑑

βˆ—

π‘›π‘‘βˆ— = πœƒπ‘‘

βˆ—π‘Ÿπ‘€βˆ—π‘‘π‘‘ + (1 βˆ’ πœƒπ‘‘)π‘ŸπΎβˆ—π‘‘π‘‘ βˆ’

π‘π‘‘βˆ—

π‘›π‘‘βˆ— 𝑑𝑑 + 𝜎

π‘˜π‘‘βˆ—

π‘›π‘‘βˆ— 𝑑 ෨𝑍𝑑

π‘–βˆ— +πœπ‘‘βˆ—

π‘›π‘‘βˆ— 𝑑𝑑

Value of output of all goods produced π‘Žβˆ—πΎπ‘‘βˆ— N

um

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no

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able

loca

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od

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Non-tradeable to consumption basket

Tradeable, non-tradeable good 1 and 2β€’ π‘Žβˆ— units of non-tradeable good buy

𝑏1,π‘‘βˆ— of tradeable good, or

π‘Žβˆ— 1βˆ’π›Ό 𝑏1,π‘‘βˆ— 𝛼𝛽

𝑏2,π‘‘βˆ— 𝛼(1βˆ’π›½)

units of the β€œaggregate good” (consumption basket).

β€’ Hence, production of consumption basket is

π‘Žβˆ— βˆ’ πœ„π‘‘βˆ— 𝑏𝑑

βˆ— π›ΌπΎπ‘‘βˆ—, with 𝑏𝑑

βˆ— =𝑏1,π‘‘βˆ— 𝛽

𝑏2,π‘‘βˆ— 1βˆ’π›½

π‘Žβˆ—

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Return on global money ($)

In terms of non-tradable local good (as numeraire)(which is used for investment rate πœ„π‘‘

βˆ—)

π‘Ÿβˆ—π‘‘π‘‘ = Ξ¦ πœ„βˆ— βˆ’ 𝛿 𝑑𝑑 is risk free

Change of numeraireIn terms of tradable basket (change of numeraire)

π‘Ÿπ‘‘πΊ ≑ π‘Ÿβˆ—π‘‘π‘‘ + 𝑑𝑏𝑑

βˆ—

π‘π‘‘βˆ—

β€’ Where price of non-tradable good in terms of tradable basket

π‘π‘‘βˆ— =

𝑏1,π‘‘βˆ— 𝛽

𝑏2,π‘‘βˆ— 1βˆ’π›½

π‘Žβˆ—

β€’ Special case: 𝑏1,π‘‘βˆ— 𝛽

𝑏2,π‘‘βˆ— 1βˆ’π›½

and hence π‘π‘‘βˆ— is constant

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Solving

1. Postulateβ€’ Price processes 𝑑𝑝𝑑

βˆ—/π‘π‘‘βˆ— = πœ‡π‘‘

π‘βˆ—π‘‘π‘‘ + πœŽπ‘βˆ—π‘‘π‘π‘‘

βˆ—, π‘‘π‘žπ‘‘βˆ—/π‘žπ‘‘

βˆ—= β‹―β€’ Portfolio processes π‘‘πœƒπ‘‘

βˆ—/πœƒπ‘‘βˆ—

2. Derive return processesβ€’ π‘‘π‘ŸπΎβˆ— = Ξ¦ πœ„βˆ— βˆ’ 𝛿 𝑑𝑑 + π‘Žβˆ—βˆ’πœ„βˆ—

π‘žπ‘‘π‘‘ + 𝜎

π‘žπ‘‘ ෨𝑍𝑑

β€’ π‘‘π‘Ÿπ‘€βˆ— = Ξ¦ πœ„βˆ— βˆ’ 𝛿 𝑑𝑑 βˆ’ (πœ‡π‘€βˆ—βˆ’πœ‡π‘€π‘–βˆ—)𝑑𝑑

3. Optimality conditions & Market clearing conditions

4. Solve β€œundetermined coefficients” (πœ‡π‘₯ 𝑠𝑑 , 𝜎π‘₯(𝑠𝑑))

β€’ Solving ODE with boundary conditionsβ€’ For large country: simply solve for constants

money supply growth rate that is NOT distributed via interest payment

Set πœ‡π‘€π‘–βˆ— = 0

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Solving

1. Postulateβ€’ Price processes 𝑝𝑑

βˆ—, π‘žπ‘‘βˆ—

β€’ Portfolio processes πœƒπ‘‘βˆ—

2. Derive return processesβ€’ π‘‘π‘ŸπΎβˆ— = Ξ¦ πœ„βˆ— βˆ’ 𝛿 𝑑𝑑 + π‘Žβˆ—βˆ’πœ„βˆ—

π‘žπ‘‘π‘‘ + 𝜎

π‘žπ‘‘ ෨𝑍𝑑

β€’ π‘‘π‘Ÿπ‘€βˆ— = Ξ¦ πœ„βˆ— βˆ’ 𝛿 𝑑𝑑 βˆ’ (πœ‡π‘€βˆ—βˆ’πœ‡π‘€π‘–βˆ—)𝑑𝑑

3. Optimality conditions & Market clearing conditions

4. Solve β€œundetermined coefficients” (πœ‡π‘₯ 𝑠𝑑 , 𝜎π‘₯(𝑠𝑑))

β€’ Solving ODE with boundary conditionsβ€’ For large country: simply solve for constants

Simply constants for large country

money supply growth rate that is NOT distributed via interest payment

Set πœ‡π‘€π‘–βˆ— = 0

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Optimality (=) & market clearing (=)

Investment rate, πœ„βˆ—

β€’ Tobin’s q: Ξ¦β€² πœ„βˆ— =1

π‘žβˆ—(static problem)

For Ξ¦ πœ„βˆ— = 1

πœ…log(πœ…πœ„βˆ— + 1) β‡’ πœ…πœ„βˆ— = π‘žβˆ— βˆ’ 1

Portfolio choice, πœƒβˆ—

β€’ 𝐸 π‘‘π‘ŸπΎβˆ— βˆ’ π‘‘π‘Ÿπ‘€βˆ— /𝑑𝑑 = πΆπ‘œπ‘£[π‘‘π‘ŸπΎβˆ— βˆ’ π‘‘π‘Ÿπ‘€βˆ—,ด𝑑𝑛𝑑

βˆ—

π‘›π‘‘βˆ—

π‘‘π‘Ÿπ‘€βˆ—+(1βˆ’πœƒβˆ—) π‘‘π‘ŸπΎβˆ—βˆ’π‘‘π‘Ÿπ‘€βˆ—

] = (1 βˆ’ πœƒβˆ—)( πœŽβˆ—/π‘ž)2

1 βˆ’ πœƒβˆ— =𝐸 π‘‘π‘ŸπΎβˆ—βˆ’π‘‘π‘Ÿπ‘€βˆ— /𝑑𝑑

(πœŽβˆ—/π‘žβˆ—)2= (π‘Žβˆ—βˆ’πœ„βˆ—)/π‘žβˆ—+πœ‡π‘€βˆ—

(πœŽβˆ—/π‘žβˆ—)2= π‘žβˆ—

π‘žβˆ—+π‘βˆ—

β€’ Dividend yield on capital must be 𝜌

Consumptionβ€’ Demand πœŒπ‘π‘‘

βˆ— = 𝜌 π‘žβˆ— + π‘βˆ— πΎπ‘‘βˆ— = π‘Žβˆ— βˆ’ πœ„βˆ— 𝐾𝑑

βˆ— Supply

π‘žβˆ— =π‘žβˆ—

π‘žβˆ— + π‘βˆ—

=1βˆ’πœƒβˆ—

(π‘Žβˆ— βˆ’ πœ„βˆ—)/𝜌

Output market clearing

Capital market clearing

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Equilibrium

where ΖΈπœ‡π‘€βˆ— = 1 βˆ’ πœƒβˆ—

π‘π‘œπ‘Ÿπ‘‘π‘“π‘œπ‘™π‘–π‘œ π‘ β„Žπ‘Žπ‘Ÿπ‘’

πœ‡π‘€βˆ— (monotone transformation)

Numeraire is local good

Moneyless equilibrium Money equilibrium

𝑝0βˆ— = 0 π‘βˆ— = πœŽβˆ—(1+πœ…πœŒ)

𝜌+ΰ·πœ‡π‘€βˆ—βˆ’(1+πœ…π‘Žβˆ—)

π‘ž0βˆ— = πœŽβˆ—

𝜌+ΰ·πœ‡π‘€βˆ—π‘žβˆ— = 1+πœ…π‘Žβˆ— βˆ’

πœ…πœŒπœŽβˆ—

𝜌+ΰ·πœ‡π‘€βˆ—>

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Optimal Monetary Policy

Money growth πœ‡ affects inflation in two ways

πœ‹ = πœ‡π‘€βˆ— βˆ’ (Ξ¦ πœ„βˆ— πœ‡π‘€βˆ— βˆ’ πœ‡π‘€,π‘–βˆ— βˆ’ 𝛿)

𝑔

MoPo can correct pecuniary externality β€’ Citizens take real interest rate as given

when choosing their portfolio between money & physical capitalβ€’ Money exists for πœŽβˆ— > πœŒβ€’ Money growth > 0 is optimal for πœŽβˆ— > 2 𝜌 (for πœ… = 0)

β€’ MoPo improves insurance provided by β€œsafe asset” Constrained optimal! Incentive compatible

Money is neither neutral nor super-neutral (no price stickiness)

boosts growth like in Tobin (1965)

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Overview

Large countryβ€’ Portfolio choice between

Physical capital π‘˜π‘‘βˆ—

US Dollar, $ – β€œbubble in positive net supply”

β€’ No state variable: due to scale invariance

Small countryβ€’ Portfolio choice between

Physical capital π‘˜π‘‘ Peso β€œhedge against idiosyncratic shocks”

US Dollar, $ β€œhedge against ToT + export productivity shocks”

β€’ State variable πœˆπ‘‘:Accumulation dynamics of foreign asset position (in $)

πœ‡π‘‘π‘₯ = πœ‡π‘₯ πœˆπ‘‘ , πœŽπ‘‘

π‘₯ = 𝜎π‘₯(πœˆπ‘‘)

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Small country

Small country cannot produce tradable good 2

tradable basket can be traded for global good 1 at rate

𝑏𝑑 ≔ ด𝑏1,𝑑Productivity

𝑏2,π‘‘βˆ— /𝑏1,𝑑

βˆ— 1βˆ’π›½

Terms of Trade

=𝑏1,𝑑𝑏1,π‘‘βˆ— ( 𝑏1,𝑑

βˆ— 𝛽𝑏2,π‘‘βˆ— 1βˆ’π›½

)

β€’ Short-cut thinking:one unit of capital produces 𝑏𝑑 units of tradable basket(while actually it produces only good 1 at rate 𝑏1 and trades some of them for tradable good 2)

𝑑𝑏𝑑

𝑏𝑑= πœ‡π‘π‘‘π‘‘ + πœŽπ‘π‘‘π‘π‘‘

since all 𝑏1,𝑑, 𝑏2,π‘‘βˆ— , 𝑏1,𝑑

βˆ— are (correlated) geometric Brownian.

Return on global money can be written as

π‘‘π‘Ÿπ‘‘πΊ = πœ‡πΊπ‘‘π‘‘ + πœŽπΊπ‘‘π‘π‘‘ + 𝜎𝐺,βˆ—π‘‘π‘π‘‘

βˆ—

call prefer

Ito product rule: 𝑑 π‘‹π‘‘π‘Œπ‘‘ = π‘‘π‘‹π‘‘π‘Œπ‘‘ + π‘‹π‘‘π‘‘π‘Œπ‘‘ + πœŽπ‘‹πœŽπ‘Œπ‘‘π‘‘

Part of π‘π‘‘βˆ— which is orthogonal to 𝑏𝑑

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Small country

Same preferences:

β€’ 𝐸 0βˆžπ‘’βˆ’πœŒπ‘‘ log 𝑐𝑑 𝑑𝑑

β€’ 𝑐0,𝑑(1βˆ’π›Ό)

𝑐1,𝑑𝛽𝑐2,𝑑1βˆ’π›½ 𝛼

ΰ·œπ›Όπ‘‘πΎπ‘‘ devoted to produce tradable good 1β€’ Can be traded for tradable basket since

small county can’t produce tradable good 2 itself

πœ‰π‘‘π‘π‘‘πΎπ‘‘ consumption of tradable goods basket

( ΰ·œπ›Όπ‘‘βˆ’πœ‰π‘‘)𝑏𝑑𝐾𝑑 trade-imbalance (net export)

𝐺𝑑 > 0 Net foreign asset position (only global money)

(in tradable goods basket)

𝑑𝐺𝑑𝐺𝑑

= π‘‘π‘Ÿπ‘‘πΊ + (ΰ·π›Όπ‘‘βˆ’πœ‰π‘‘)𝑏𝑑𝐾𝑑

𝐺𝑑𝑑𝑑

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State variable

Equilibrium is a map

Histories of shocks prices π‘žπ‘‘ , 𝑝𝑑, allocationπ‘πœ, π‘πœ

βˆ—, 0 ≀ 𝜏 ≀ 𝑑 ΰ·œπ›Όπ‘‘, πœ„π‘‘, πœ‰π‘‘ & portfolio (1 βˆ’ πœƒπ‘‘ βˆ’ πœπ‘‘, πœƒπ‘‘, πœπ‘‘)

net foreign asset position to tradable production potential

πœˆπ‘‘ =𝐺𝑑

𝑏𝑑𝐾𝑑

Evolution

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Portfolio choice & Asset pricing

Portfolio share (processes)

β€’ Local moneyπ‘‘πœƒπ‘‘πœƒπ‘‘

=πœ‡π‘‘πœƒπ‘‘π‘‘+πœŽπ‘‘

πœƒπ‘‘π‘π‘‘+πœŽπ‘‘πœƒ,βˆ—π‘‘π‘π‘‘

βˆ—

β€’ Global moneyπ‘‘πœπ‘‘

πœπ‘‘= πœ‡π‘‘

πœπ‘‘π‘‘ + πœŽπ‘‘

πœπ‘‘π‘π‘‘ + πœŽπ‘‘

𝜁,βˆ—π‘‘π‘π‘‘

βˆ—

Returns expressed with country networth, 𝑁𝑑, as numeraireβ€’ Return on individual networth π‘‘π‘Ÿπ‘‘

𝑛 = πœŒπ‘‘π‘‘ + (1 βˆ’ πœƒπ‘‘ βˆ’ πœπ‘‘)πœŽπ‘›

𝜎(π‘žπ‘‘)

β€’ Return on local money π‘‘π‘Ÿπ‘‘π‘€πΏ =

π‘‘πœƒπ‘‘

πœƒπ‘‘

β€’ Return on global money ($) π‘‘π‘Ÿπ‘‘π‘€πΊ =

ΰ·π›Όπ‘‘βˆ’πœ‰π‘‘

πœˆπ‘‘π‘‘π‘‘ +

π‘‘πœπ‘‘

πœπ‘‘

Asset pricing equation (due to log utility)

𝐸 π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐺 = πΆπ‘œπ‘£[π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐺 , π‘‘π‘Ÿπ‘‘π‘›] β‡’ 𝜌 βˆ’

ΰ·π›Όπ‘‘βˆ’πœ‰π‘‘

πœˆπ‘‘βˆ’ πœ‡π‘‘

𝜁= πœŽπ‘› 2

𝐸 π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐿 = πΆπ‘œπ‘£[π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐿 , π‘‘π‘Ÿπ‘‘π‘›] β‡’ 𝜌 βˆ’ πœ‡π‘‘

πœƒ = πœŽπ‘› 2

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Portfolio choice & Asset pricing

Portfolio share (processes)

β€’ Local moneyπ‘‘πœƒπ‘‘πœƒπ‘‘

=πœ‡π‘‘πœƒπ‘‘π‘‘+πœŽπ‘‘

πœƒπ‘‘π‘π‘‘+πœŽπ‘‘πœƒ,βˆ—π‘‘π‘π‘‘

βˆ—

β€’ Global moneyπ‘‘πœπ‘‘

πœπ‘‘= πœ‡π‘‘

πœπ‘‘π‘‘ + πœŽπ‘‘

πœπ‘‘π‘π‘‘ + πœŽπ‘‘

𝜁,βˆ—π‘‘π‘π‘‘

βˆ—

Returns expressed with country net worth 𝑁𝑑 as numeraireβ€’ Return on individual net worth π‘‘π‘Ÿπ‘‘

𝑛 = πœŒπ‘‘π‘‘ + (1 βˆ’ πœƒπ‘‘ βˆ’ πœπ‘‘)πœŽπ‘›

𝜎(π‘žπ‘‘)

β€’ Return on local money π‘‘π‘Ÿπ‘‘π‘€πΏ =

π‘‘πœƒπ‘‘

πœƒπ‘‘

β€’ Return on global money ($) π‘‘π‘Ÿπ‘‘π‘€πΊ =

πœ‰π‘‘βˆ’ΰ·π›Όπ‘‘

πœˆπ‘‘π‘‘π‘‘ +

π‘‘πœπ‘‘

πœπ‘‘

Asset pricing equation (due to log utility)

𝐸 π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐺 = πΆπ‘œπ‘£[π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐺 , π‘‘π‘Ÿπ‘‘π‘›] β‡’ 𝜌 βˆ’

ΰ·π›Όπ‘‘βˆ’πœ‰π‘‘

πœˆπ‘‘βˆ’ πœ‡π‘‘

𝜁= πœŽπ‘› 2

𝐸 π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐿 = πΆπ‘œπ‘£[π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐿 , π‘‘π‘Ÿπ‘‘π‘›] β‡’ 𝜌 βˆ’ πœ‡π‘‘

πœƒ = πœŽπ‘› 2

Money worth πœƒ net worths

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Portfolio choice & Asset pricing

Portfolio share (processes)β€’ Local money

π‘‘πœƒπ‘‘πœƒπ‘‘

=πœ‡π‘‘πœƒπ‘‘π‘‘+πœŽπ‘‘

πœƒπ‘‘π‘π‘‘+πœŽπ‘‘πœƒ,βˆ—π‘‘π‘π‘‘

βˆ—

β€’ Global moneyπ‘‘πœπ‘‘

πœπ‘‘= πœ‡π‘‘

πœπ‘‘π‘‘ + πœŽπ‘‘

πœπ‘‘π‘π‘‘ + πœŽπ‘‘

𝜁,βˆ—π‘‘π‘π‘‘

βˆ—

Returns expressed with country net worth 𝑁𝑑 as numeraireβ€’ Return on individual

net worth π‘‘π‘Ÿπ‘‘π‘› = πœŒπ‘‘π‘‘ + 1 βˆ’ πœƒπ‘‘ βˆ’ πœπ‘‘

πœŽπ‘›

𝜎 π‘žπ‘‘ 𝑑 ෨𝑍𝑑

β€’ Return on local money π‘‘π‘Ÿπ‘‘π‘€πΏ =

π‘‘πœƒπ‘‘

πœƒπ‘‘

β€’ Return on global money ($) π‘‘π‘Ÿπ‘‘π‘€πΊ =

πœ‰π‘‘βˆ’ΰ·π›Όπ‘‘

πœˆπ‘‘π‘‘π‘‘ +

π‘‘πœπ‘‘

πœπ‘‘

Asset pricing equation (due to log utility)

𝐸 π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐿 = πΆπ‘œπ‘£[π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐿 , π‘‘π‘Ÿπ‘‘π‘›] β‡’ 𝜌 βˆ’ πœ‡π‘‘

πœƒ = πœŽπ‘› 2

𝐸 π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐺 = πΆπ‘œπ‘£[π‘‘π‘Ÿπ‘‘π‘› βˆ’ π‘‘π‘Ÿπ‘‘

𝑀𝐺 , π‘‘π‘Ÿπ‘‘π‘›] β‡’ 𝜌 βˆ’

πœ‰π‘‘βˆ’ΰ·π›Όπ‘‘

πœˆπ‘‘βˆ’ πœ‡π‘‘

𝜁= πœŽπ‘› 2

E[net worth – money return]

Price of risk Γ— risk

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Consumption & Investment

Consumption Demand 𝜌 ΰΈ“πΊπ‘‘πœπ‘‘

wealthin trad.basket

= πœ‰π‘‘π‘π‘‘πΎπ‘‘π›Ό

Supply

β€’ Cobb-Douglas β‡’constant consumption expenditure shares

πœ‰π‘‘π‘π‘‘πΎπ‘‘π›Ό

𝑃𝑑𝑔= [ 1βˆ’ΰ·π›Όπ‘‘ π‘Žβˆ’πœ„π‘‘]

1βˆ’π›Όπ‘ƒπ‘‘π‘™

Production allocation

Investment rate πœ„π‘‘β€’ Depends on π‘žπ‘‘

Output of non-tradableConsumption of tradables

Non-tradable

Trade-able

(incl. net exports)

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(Co-)Existence of Money

Proposition 1:β€’ If 𝜎2 > 𝜌 and M ≀ Ξ¦ πœ„πœˆ=0 , then

local money has value and 𝜈 = 0 (no NFAP) is absorbing state

β€’ Otherwise, if 𝜎2 βˆ’ 𝜌 +Mβˆ’Ξ¦ πœ„πœˆ=0 > 0, then global money has value for citizens in small country(and local money may or may not have value)

𝜎2𝜌

M βˆ’Ξ¦ πœ„ =

πœ‡πΊ βˆ’ πœ‡π‘ + πœŽπ‘ βˆ’ 𝜎𝐺 πœŽπ‘

βˆ’Ξ¦ πœ„ + 𝛿attractiveness of globalmoney

ONLYLOCAL MONEYin the long run

GLOBAL MONEY+ possiblyLOCAL MONEY

attractiveness of local money

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Numerical Example

𝜌 = 5%, 𝜎 = .3, 𝛼 = .2, πœ‡π‘ = 1%, πœŽπ‘ = .15, πœ‡πΊ = 2.2%, π‘Ž = .13,𝛿 = 2%, 𝜎𝐺 = 𝜎𝐺,βˆ— = 0, πœ… = 2 β‡’ 𝑀 = .0545, 𝜎𝜈 = .15

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Exchange rate dynamics - UIP

π‘–π‘‘βˆ— βˆ’ 𝑖𝑑 = 𝐸𝑑 Ξ”β„° + πœ“π‘‘

πœ“π‘‘ = ΰΈ–βˆ’πœŽπœƒ

>0

(𝜎𝜁 βˆ’ πœŽπœƒ)>0

(risk premium in terms of Peso)

For 𝑖𝑑 = π‘–π‘‘βˆ— (= 0)

β€’ foreign currency is expected to appreciate relative to local currency (whenever it is held in positive quantity). Local currency is a hedge, it appreciates relative to net worth when 𝜈 drops. Global currency is risky, so to be held in positive amount it must earn a risk

premium

UIP violation, πœ“π‘‘, depends whether money is β€œprinted”‒ to pay interest πœ‡π‘€π‘–

No real changes (portfolio choice is not affected) Higher inflation πœ‹ = πœ‡π‘€π‘– βˆ’ (πœ™ πœ„ βˆ’ 𝛿), 𝐸𝑑 Ξ”β„° = πœ‡π‘€π‘– (dollar appreciates)

β€’ to generate seignorage (redistributed ∝ wealth share) (πœ‡π‘€βˆ’πœ‡π‘€π‘–) Affects portfolio choice, π‘ž, investment rate πœ„, growth rate

risk premium πœ“π‘‘

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Flight to safety (into dollar)

Unanticipated increase in πœŽπ‘

β€’ E.g. ToT becomes more volatile

Portfolio share held in dollars increases Dollar valuation is higher

(increase in volatility of 𝜈)

Transitionβ€’ Start with current (dollar holding) 𝐺

β€’ Recalculate new state variable πœˆπ‘‘β€’ Our full dynamics also includes transition dynamics

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Spillover from lower πœ‡πΊ

β€’ Higher money supply growth πœ‡π‘€βˆ— in large countryβ€’ Lower growth Ξ¦ πœ„βˆ— βˆ’ 𝛿 in large countryβ€’ Loss of competitive edge in global tradable basket

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Higher Peso inflation πœ‹π‘‘

seniorage πœ‡π‘€ βˆ’ πœ‡π‘€π‘– is distributed ∝ capital holding

Store of value is less attractive β€’ Pricing equation now

𝜌 + πœ‹π‘‘ βˆ’ πœ‡πœƒ = πœŽπ‘ 2

higher investment πœ„π‘‘ β‡’ boosts growth, but higher idio risk

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Mundell-Fleming Trilemma

Trilemma: Can only pick a 2 desiderata out of 3 –1 side

β€œDilemma”: Pick only 1

Autonomous Monetary Policy

Fixed ex-change rate

Free Capital Flow

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Mundell-Fleming Trilemma

Trilemma: Can only pick a 2 desiderata out of 3 –1 side

β€œDilemma”: Pick only 1

Autonomous Monetary Policy

Fixed ex-change rate

Free Capital Flow

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Floating Exchange Rate

With floating exchange rate & open capital account Still range of Monetary policy, since local and global money are imperfect substitutes

β€’ Inflation boosts growth, but only possible up to a limit ΰ΄€πœ‹(πœ‡πΊ). Beyond ΰ΄€πœ‹(πœ‡πΊ) monetary policy has little bite Global money becomes too attractive

β€’ Range is higher with higher inflation in large country (global money) Large country’s MoPo determines

range for small country

Policy range is largerif local money is backed by taxes(ΰ΄€πœ‹ depends on distribution of seignorage)

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Closed capital account

Range of Monetary policy is much larger,up ΰ΄§πœ‹ = 𝜎2 βˆ’ 𝜌 β‰ˆ 4%(physical capital is risky store of value)

Total money holding is larger with closed capital accountβ€’ Global money would be a better

hedge for β€œexport risk”

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Fixed exchange rate regimes & no MoPo

Dollarization = (fully backed) Currency Board Xx

Exchange rate pegβ€’ Requires strong fiscal backing

(since no backing through holding of global reserves) After a string of adverse shocks, government must tax and use to

proceeds to remove some of the local currency in circulation

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Foreign Currency Reserves

Irrelevance Theorem:β€’ If central bank holds global money (reserves)

β€’ Citizens in small country will hold accordingly less

Remark:β€’ If central banks holds more $-reserves than citizens would like to

hold, then agents borrow foreign currency from abroad.

β€’ If local money is worthless (without foreign reserves), then the value of local money with reserves only derives from the latter (currency board)

β€’ With fiscal backing of the local money, complicates analysis

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Optimal Monetary Policy

LARGE COUNTRYMoPo can correct pecuniary externality β€’ Citizens take real interest rate as given

when choosing their portfolio between money & physical capitalβ€’ Money exists for πœŽβˆ— > πœŒβ€’ Inflation is optimal for πœŽβˆ— > 2 𝜌

β€’ MoPo improves insurance provided by β€œsafe asset” Constrained optimal! Incentive compatible

SMALL COUNTRYβ€’ Additional savings decision due open capital account

Generally, optimal monetary policy depends on control social planner has

(For πœ… = 0, no adjustment costs)

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Conclusion

Endogenous value of money (safe asset) in 2 countriesβ€’ Local currency: better hedge for idiosyncratic risk (non-tradable consumption)

β€’ Global currency: hedge against ToT + export productivity shocks

Spillover effects from US monetary policy

Flight to safety

When to peg? When to dollarize?

β€œNuanced Mundell-Fleming Trilemma”‒ Local and global money have different risk profile (imperfect substitutes)

β‡’ increases MoPo space β€’ Too high Peso inflation:

local citizens substitute local currency for global currency⇒ limits MoPo space

Central Bank’s foreign reserves holding: Irrelevance Result

Optimal Monetary Policy β€’ Idiosyncratic risk – correct pecuniary externality (real interest rate)β€’ International savings


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Mundell-Fleming Presentation

Mundell-Fleming Presentation

The Open Economy Revisited: the Mundell-Fleming Model and ...€¦ · the Mundell-Fleming model (IS -LM for the small open economy) causes and effects of interest rate differentials

The Open Economy Revisited: the Mundell-Fleming Model and ...€¦ · the Mundell-Fleming model (IS -LM for the small open economy) causes and effects of interest rate differentials

The Mundell-Fleming model From IS-LM to Mundell-Fleming Policy in an open economy.

The Mundell-Fleming model From IS-LM to Mundell-Fleming Policy in an open economy.