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