ee ssdd ssEconomic and Social Data Service

ESDS International Annual Conference ESDS International Annual Conference

LONDONLONDONNovember 30November 30thth, 2009 , 2009

Giorgio Castagneto Gissey, BSc

University of Warwick, MSc Economics and International Finance

The concept of Petri nets has its origin in The concept of Petri nets has its origin in Carl Adam Petri’s dissertation Carl Adam Petri’s dissertation

Kommunikation mit AutomatenKommunikation mit Automaten, submitted in 1962 , submitted in 1962 to the faculty of Mathematics and Physics to the faculty of Mathematics and Physics

at the Technische Universität Darmstadt, Germanyat the Technische Universität Darmstadt, Germany

PETRI NETSPETRI NETS

A Petri net is a graphical and mathematical A Petri net is a graphical and mathematical modelling tool modelling tool

A placewith 2 tokens

A transition (exponential)

A transition (immediate)

A transition (deterministic)

Input arcmultiplicity 2

22

Places Places TransitionsTransitions ArcsArcs

Petri nets can be used as a Petri nets can be used as a visual-communication aid visual-communication aid

similar to flow charts, block similar to flow charts, block diagrams, and networksdiagrams, and networks

graphical tool graphical tool

mathematical mathematical tooltool

It is possible to set up state It is possible to set up state equations, algebraic equations, equations, algebraic equations, and other mathematical models and other mathematical models

governing the behaviour of systemsgoverning the behaviour of systems

PETRI NETSPETRI NETS

Keynes model is valid only when money issued Keynes model is valid only when money issued by the States has a real intrinsic value, by the States has a real intrinsic value,

while in the case of “chartal” money created and while in the case of “chartal” money created and extinguished by the bank system on account of its extinguished by the bank system on account of its capital the model can not apply. Therefore, while capital the model can not apply. Therefore, while

in the circulation model the quantity of money in the circulation model the quantity of money follows the law of supply and demand with subsequent follows the law of supply and demand with subsequent

endogenous adjustment, in a system of fiat money endogenous adjustment, in a system of fiat money there will be no independent supply function and there will be no independent supply function and

the supply and demand function can no longer the supply and demand function can no longer move at steady state.move at steady state.

BANKSBANKS

Money creationMoney creation

Inflation levelsInflation levels

To increaseTo increaseprofitsprofits

Interest rates Interest rates on lending on lending

Interest rates Interest rates on borrowing on borrowing

To investigate the role of commercial To investigate the role of commercial banks profit margin on inflation and banks profit margin on inflation and

other primary macroeconomic variablesother primary macroeconomic variablesBy comparing two models: By comparing two models:

the the Petri NetPetri Net and and

the the Classic ModelClassic Model

A rise in the level of interest receipts causes A rise in the level of interest receipts causes the the money supply to expandmoney supply to expand, leading to , leading to increasingincreasing

inflation levelsinflation levels and thus a decrease in output. and thus a decrease in output.

period of interest is period of interest is 1997Q4-2008Q21997Q4-2008Q2

Origin of the data : Origin of the data : Office for National Statistics, Office for National Statistics, Time Series Data, ESDS International, Time Series Data, ESDS International, (Mimas) University of Manchester(Mimas) University of Manchester

iiLL-i-iDD MM CPICPI

GDPt-1

R

Mt-1

CPIt-1

r

c

(iL-iD) t-1

D

L

BP

If If MMkk is a matrix equation as a is a matrix equation as a m x 1 m x 1 column vector, thecolumn vector, the jt jthh entry ofentry of M Mkk

denotes the number of tokens in place denotes the number of tokens in place j j immediately after theimmediately after the kt kthh firing firing inin the firing sequence.the firing sequence. Let Let AA denotes the change of the marking as the results of firing transition denotes the change of the marking as the results of firing transition ii,, then:then:

Mk = Mk-1 + ATuk

Writing the state equation (1) for Writing the state equation (1) for I = 1,2,….,d I = 1,2,….,d and summing them, we obtainand summing them, we obtain

(1)

Md = M0 + AT Σ uk

d

k=1(2)

The weight of each arc of the Petri Nets is set equal to 1The weight of each arc of the Petri Nets is set equal to 1

Variables in the system are defined as follows:

(i L –i D)t = c4 + a42 GDPt -1+ a43 Rt + a44 Mt -1+ a48 CPIt-1 -

a410 rt – a411 c t + SDs + b44εt

0 0

00[1]

Mt = c7 + a72 GDPt -1+ a73 Rt + a74 (i L- i D)t -1+ a75 Dt

+ a76Lt + a78 CPIt -1– a710rt – a711ct + b77εt

0 0

0 0 0 M[2]

[3]CPIt = c8 + a82 GDPt -1+ a84(i L- i D)t -1+ a85 Dt + a86 Lt +

+ a87 Mt -1+ a89 BPt – a810 rt – a811 ct +SDs + b88εt

0 0

0 0 CPI0

Monte Carlo procedure was performed to obtain empirical parameter confidence regions.

Monte Carlo hypothesis tests applied to multiple realizations from such models provide appropriate goodness-of-fit tests

regardless of within-model peculiarities.

The unit root null hypothesis for stationarity is not rejected at 5%

for any variable in the model, within the third difference lag.

Furthermore, variables that are originally observed as stationary are the key spread and

both monetary aggregates.

M4

(iL – iD)

M0

CPI

Model R2

0.019*(0.007)

0.045*(0.017)

0.018*(0.005)

0.870

Data are expressed as elasticities (%) ± SD.[**] P < 0.01, significant Monte Carlo assessment of goodness-of-fit

****

M4

(iL – iD)

M0

CPI

Model R2

0.052(0.021)

0.652

0.076(0.042)

0.261

0.035(0.015)

0.711

Data are expressed as elasticities (%) ± SD. [*] P < 0.05

**

**

Profit MarginProfit Margin

==

IINNFFLLAATTIIOONN

The variability of the parameter estimates The variability of the parameter estimates was smaller when the Petri Net Model was smaller when the Petri Net Model

was used, as shown by a smallerwas used, as shown by a smallerstandard deviation and the high goodness standard deviation and the high goodness

of fittingof fitting

CPI inflation estimated by the classicCPI inflation estimated by the classicmodel was sistematically higher than that model was sistematically higher than that computed by the Petri Net model, resultingcomputed by the Petri Net model, resulting

to be above the 2% targetto be above the 2% target

The estimates of the present model confirm the The estimates of the present model confirm the main hypotheses, entailing a rise in CPI levels main hypotheses, entailing a rise in CPI levels following an increase in the spread, and fully following an increase in the spread, and fully represents a major finding of the underlying represents a major finding of the underlying research, even though the neglected issue of research, even though the neglected issue of

endogeneity cannot successfully approve endogeneity cannot successfully approve the estimated results.the estimated results.

The Petri Net Model seems to be a betterThe Petri Net Model seems to be a betterModel to estimate the effect of inflationModel to estimate the effect of inflation

on macroeconomics on macroeconomics

THANK YOUTHANK YOU

FOR YOUR KIND ATTENTIONFOR YOUR KIND ATTENTION