The Eurodiffusion project

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The Eurodiffusion project
Piet van Blokland, Lorna Booth, Kirankumar
Hiremath, Michiel Hochstenbach, Ger Koole, Sorin
Pop, Marieke Quant, Djoko
Wirosoetisno February 22, 2002
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Research Questions

• How to model diffusion of Eurocoins?
• Is the data on the Eurodiffusion web site
  reliable?
• Can we estimate the rate of diffusion of
  Eurocoins?
• How much time before half your wallet is foreign?

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Basic facts

• 12 countries, 8 denominations
• Grand total of 64.9 Gigacoins (GC)
• NL 3.3 GC, 1.6 GC in circulation as of Jan 1
• ? 100 MC added every month (savings)
• equilibrium 50-100 MC added per year (wastage)
• Number of coins per country not in proportion to
  population
• E.g. France 190 p.p., NL 200, Germany 280

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Basic facts

• Average Dutch wallet (in guilder era) 15 coins
• In Dutch wallets 1516240 MC, 15 of 1.6 GC in
  circulation!
• Other 85 at banks and check outs
• No info on in circulation for other countries
• Possible assumptions
• fixed ratio to population
• fixed ratio to total number of coins made

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Basic facts

• Banks are free to buy Eurocoins wherever they
  want
• E.g., bank in Maastricht buying coins in D or B
  instead of going to DNB warehouse in Eindhoven
• Result National banks have no idea of net flows
  of Eurocoins
• Assumption net flow 0 for any 2 countries

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Data

• Measurements on Eurodiffusion site
• not guaranteed to
• be unbiased
• participants not
• aselect

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Data

• Eurometers 46, 167, 510
• large groups,
• 3 measurements
• assumed to be more
• reliable
• 91-98 Dutch
• Contrast with overall
• measurement

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Data

• Our measurements (19, 20 Feb)
• Best guess 4 diffusion per month in NL

Lunch students Lorna KdV check
out NL 93.1 98.4
94.7 .
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Models

• Models need to be
• dynamic stochastic
• non-homogeneous (e.g., no Brownian motion)
• Choice Markov chains
• Modeling the movement of 1 coin
• States representing location of coin
• Flexible from 2 to any number of states
• (for countries, regions, wastage, savings,
  etc.)

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Analysis of 2-state Markov chain

• Discrete-time, time unit 1 month
• Transition probability NL ? abroad 0.04
• Transition prob. abroad ? NL from
• net-flow balance

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Analysis of 2-state Markov chain
Flow out
Flow in

• Monthly flow out 0.04 3.3 GC
• Monthly flow in p 61.6 GC
• Thus p tr.prob. abroad ? NL ? 0.002

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Analysis of 2-state Markov chain

• Neglected following aspects
• diffusion depends on country and region
• savings and wastage
• holiday effects (2/3 on holidays diffusion 10)
• collectioners
• Considered only NL vs. rest Europe

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Results 2-state Markov chain

• Situation after 12 months including holiday
  effects corresponds to situation after 15 with
  rate 0.04
• Results after 15 (17) months 55 (50)
• Conclusion after 1 year around half of coins in
  NL are foreign
• Results strongly depend on assumptions and rate

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Data and Markov chains

• After March 1 measurement need to estimate
  diffusion rate on the basis of Q and QQ
• Approach maximum likelihood

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Further work and conclusion

• To do
• Analyse models with gt2 states
• Conclusions
• In about 1 year half of coins in our wallet is
  foreign
• Very nice study week

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Questions