A Model of Commodity Money with Minting and Melting€¦ · Model Results Historical applications Conclusions/Further research Two major changes to European monetary systems: Debasement

IntroductionModel

ResultsHistorical applications

Conclusions/Further research

A Model of Commodity Moneywith Minting and Melting

Angela RedishWarren Weber

February 16, 2012

Commodity money 1

IntroductionModel



Any study of the money supply [of medieval Europe] needs to takeaccount not only of the total face value of the currency, but also ofthe metals and denominations of which it is composed.

(Mayhew 2004)

Commodity money 2

IntroductionModel



What were these denominations?

800-1200 A.D. most European states issued only one cointype - a penny containing ∼ 1.7 gms fine silver

Commodity money 3

IntroductionModel



Two major changes to European monetary systems:

Debasement of the penny - to a varying extent across mints

In England - in 1160, still ∼ 1.4 gmsIn Venice - in 1160, ∼ 0.10 gms

Introduction of a larger coin - at different times across mints

In Venice - grosso 1194: 2.18 gms (26d)in England - groat 1351: 4.66 gms (4d)

Commodity money 4

IntroductionModel



What drove the changes?

Conventional view - debasement:

debasements were revenue generatorsdebasements created more units of money so facilitated moreexchange

Conventional view - larger coins:

large coins were needed to pay urban workers

Our view

changes in coin types were consistent with welfare increasingresponses to change in the economic environment

Commodity money 5

IntroductionModel



What drove the changes?

we build a random matching model to assess these views

the paper extends existing search models:

to allow for multiple coinsto allow for an endogenous quantity of money

Commodity money 6

IntroductionModel



Preview of results

We find that:

the size of a coin affects social welfare

the size of a coin has distributional consequences

the frequency of trade affects the optimal coin size

the stock of monetary metal affects optimal coin size

permitting minting of two types of coin may raise socialwelfare

Commodity money 7

IntroductionModel



Preview of results

We use these results to reconsider the motives for coinage changes:

debasement may have been a response to urbanization ratherthan (only) generating revenue or making ’more’ units of themedium of exchange

large coins may have been a response to silver discoveriesrather than a response to urbanization

Commodity money 8

IntroductionModel



Outline of talk

Model

Results

Apply model to historical choices of denomination

Conclude/further research

Commodity money 9

IntroductionModel



Environment

Time discrete and infinite

One nonstorable, perfectly divisible consumption good

One storable metal (silver) in fixed supply (m)

Commodity money 10

IntroductionModel



Environment

Silver can be held as coins or jewelry (bullion)

Silver coins are indivisible, but can be minted or melted

Silver coin contains b1 ounces of silver

possible second silver coin contains b2 = ηb1 ounces of silver

Commodity money 11

IntroductionModel



Environment

Agents hold

s1 small silver coinss2 large silver coinsj units silver jewelry

V Only coins can be used in trade

V Only jewelry yields utility (similar to Velde-Weber)

Commodity money 12

IntroductionModel



Agents

[0, 1] continuum, infinitely-lived

Preferences:

u(c)− q + µ(b1j)− γ(s1 + s2)

u(0) = 0, u′ > 0, u′(0) =∞, u′′ < 0

γ utility cost of holding a coin

Maximize expected discounted (β) lifetime utility

θ prob of a being a buyer or seller in a single coincidencematch

Commodity money 13

IntroductionModel



Trade

Each period has two subperiods1 First subperiod: decentralized trade in bilateral matches

Preference assumption rules out double coincidence matchespast trading histories private (no monitoring or commitmenttechnology) - rules out gift-giving equilibriumagents are anonymous - rules out credit

2 Second subperiod: agents can alter coin/jewelry portfolio byminting or melting

Can change how metal stocks held – no change in quantity ofsilver

Commodity money 14

IntroductionModel



Choices

1st sub period

Single coincidence matches: potential consumer makes TIOLIoffer (q, p1, p2)

Buyer ‘sees’ seller’s portfolio

2nd sub period

Agents make portfolio adjustment after trade (z1, z2)

zi is the amount of coins minted (melted if negative)

Commodity money 15

IntroductionModel



Model: Value functions

Expected value of holding yt = (s1t , s2t , jt) beginning secondsubperiod

vt(yt) = maxz1t ,z2t

{βwt+1(s1t + z1t , s2t + z2t , jst − z1t − ηz2t)

−S(z1t , z2t ; jt)}

S(z1t , z2t ; jt) is seigniorage

Commodity money 16

IntroductionModel



Model: Value functions

Expected value of holding yt beginning of first subperiod

wt(yt) = θ∑yt

πt(yt) maxΛ

[u(qt) + vt(s1t − p1t , s2t − p2t , jt)]

+(1− θ)vt(yt) + µ(b1jt)− γ(s1t + s2t)

where:

Λ = set of all feasible TIOLI offersπt(yt) = fraction of agents with yt beginning first subperiody denotes seller portfolios

Commodity money 17

IntroductionModel



Model: Equilibrium

Steady state symmetric equilibrium:

Value functions w , v ; asset holdings π; and quantitiesp1, p2, z1, z2, q that satisfy

1 Bellman equations2 asset transitions3 market clearing

Commodity money 18

IntroductionModel



Social Welfare depends on coin sizeWelfare distribution depends on coin sizeOptimal coin size depends on trading frequencyOptimal coin size depends on quantity of metalAdding a second coin type may increase welfare

Results

Numerical – analytic results not possible

Assume:

β = 0.9σ = 0.04γ = 0.001u(q) = q1/4

µ(b1j) = 0.05(b1j)1/2

Base case:

θ = 13

m = 0.1

Commodity money 19

IntroductionModel




Single coin: Welfare effect of changing coin size

1.46

1.48

1.50

1.52

1.54

1.56

0.000 0.005 0.010 0.015 0.020

ex antewelfare

silver coin size

Commodity money 20

IntroductionModel




Single coin: Distribution of coin and jewelry holdings

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25 30 35

fraction ofagents

units of silver held in terms of coins

0 coins1 coin2 coins3 coins4 coins5 coins6 coins

Commodity money 21

IntroductionModel




Distribution of welfare

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5

fraction ofagents

welfare

b1=0.009

b1=0.015

Commodity money 22

IntroductionModel




Optimal coin size depends on trading frequency

0

0.003

0.006

0.009

0.012

0.015

0.018

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

optimal b1

theta

Commodity money 23

IntroductionModel




Optimal coin size depends on quantity of metal

1.45

1.50

1.55

1.60

1.65

0.000 0.005 0.010 0.015 0.020 0.025

ex antewelfare

silver coin size

m=0.2

m=0.1

m=0.05

Commodity money 24

IntroductionModel




Adding a second coin type may increase welfare

1.52

1.54

1.56

1.58

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

ex antewelfare

original silver coin size

one coin

two coins, η = 3

Commodity money 25

IntroductionModel



Debasement - or smaller coin sizesIntroduction of grossi and groats

Shift to smaller coins

Pennies in 800 A.D. were ∼ 1.7 gms of fine silver

By 1160

In England still ∼ 1.4 gmsIn Venice ∼ 0.10 gms

Commodity money 26

IntroductionModel




Motives for smaller coins

The model suggests that optimal coin size depends on tradingfrequency

Venice urbanized earlier and much more than England

Venice urbanized from 1000 ADEnglish market towns grew especially after 1250

This difference in debasement policy is consistent with asocial welfare maximizing response to urbanization

Commodity money 27

IntroductionModel




Introduction of grossi and groats

In 1194 Venice introduced large silver coins

grossi weighing 2.18 gms of 96.5% fine silvercontained the same fine silver as about 26 denari

Not until 1351 did the English produce large silver coins

groats weighing 4.66 gms of 92.5% fine silvercontained the same fine silver as 4 pence.

Commodity money 28

IntroductionModel




Silver flows

The model suggests that larger stocks of silver imply largeroptimal coin size

The late 12th century saw large increases in silver

1160-1320 known for the large amounts of silver minedFlows (from Saxony) went first to Venicein England inflows came later

The introduction of grossi and groats may have beenmotivated by the larger silver stocks

Commodity money 29

IntroductionModel




Money stock in England

0

20

40

60

80

100

1240 1270 1300 1330 1360

Pence per capita

Commodity money 30

IntroductionModel




Two coins with varying metal stocks

1.66

1.68

1.70

1.72

1.74

1.76

1.78

1.80

0.000 0.005 0.010 0.015 0.020 0.025

ex antewelfare

single coin size

two coins (ms=.2,η = 3)

single coin (ms=.2)

two coins (ms=.1,η = 3)

single coin (ms=.1)

Commodity money 31

IntroductionModel



Conclusion

Coin size/type affects welfare in the economy

Debasement of the penny is consistent with a monetary policythat valued social welfare

Silver inflows in the 13th century give a rationale forincreasing coin sizes

Commodity money 32

IntroductionModel



Next direction - outstanding issues

Why debase rather than introduce a second (smaller) coin?

Build a model where agents benefit from a large gold coin

Commodity money 33

Documents

A Model of Commodity Money with Minting and Melting€¦ · Model Results Historical applications Conclusions/Further research Two major changes to European monetary systems: Debasement