esds Economic and Social Data Service ESDS International Annual Conference LONDON November 30 th, 2009 Giorgio Castagneto Gissey, BSc University of Warwick, MSc Economics and International Finance

The concept of Petri nets has its origin in Carl Adam Petri’s dissertation Kommunikation mit Automaten, submitted in 1962 to the faculty of Mathematics and Physics at the Technische Universität Darmstadt, Germany PETRI NETS

A Petri net is a graphical and mathematical modelling tool A place with 2 tokens A transition (exponential) A transition (immediate) A transition (deterministic) Input arc multiplicity 2 2 2PlacesTransitionsArcs

Petri nets can be used as a visual-communication aid similar to flow charts, block diagrams, and networks graphical tool mathematicaltool It is possible to set up state equations, algebraic equations, and other mathematical models governing the behaviour of systems PETRI NETS

Keynes model is valid only when money issued by the States has a real intrinsic value, while in the case of “chartal” money created and extinguished by the bank system on account of its capital the model can not apply. Therefore, while in the circulation model the quantity of money follows the law of supply and demand with subsequent endogenous adjustment, in a system of fiat money there will be no independent supply function and the supply and demand function can no longer move at steady state.

BANKS Money creation Inflation levels To increase profits Interest rates on lending Interest rates on borrowing

To investigate the role of commercial banks profit margin on inflation and other primary macroeconomic variables By comparing two models: the Petri Net and the Classic Model

A rise in the level of interest receipts causes the money supply to expand, leading to increasing inflation levels and thus a decrease in output. inflation levels and thus a decrease in output.

period of interest is 1997Q4-2008Q2 1997Q4-2008Q2 Origin of the data : Office for National Statistics, Time Series Data, ESDS International, Time Series Data, ESDS International, (Mimas) University of Manchester (Mimas) University of Manchester

i L -i D M CPI GDP t-1 R M t-1 CPI t-1 r c (i L -i D ) t-1 D L BP

If M k is a matrix equation as a m x 1 column vector, the jt h entry of M k denotes the number of tokens in place j immediately after the kt h firing in the firing sequence. Let A denotes the change of the marking as the results of firing transition i, then: M k = M k-1 + A T u k Writing the state equation (1) for I = 1,2,….,d and summing them, we obtain (1) M d = M 0 + A T Σ u k d k=1 (2) The 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 = c 4 + a 42 GDP t -1 + a 43 R t + a 44 M t -1 + a 48 CPI t-1 - a 410 r t – a 411 c t + SD s + b 44 ε t [1]

M t = c 7 + a 72 GDP t -1 + a 73 R t + a 74 (i L - i D ) t -1 + a 75 D t + a 76 L t + a 78 CPI t -1 – a 710 r t – a 711 c t + b 77 ε t M [2] [3] CPI t = c 8 + a 82 GDP t -1 + a 84 (i L - i D ) t -1 + a 85 D t + a 86 L t + + a 87 M t -1 + a 89 BP t – a 810 r t – a 811 c t +SD s + b 88 ε t 00 00CPI 0

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 (i L – i D ) M0 CPI Model R * (0.007) 0.045* (0.017) 0.018* (0.005) Data are expressed as elasticities (%) ± SD. [**] P < 0.01, significant Monte Carlo assessment of goodness-of-fit **

M4 (i L – i D ) M0 CPI Model R (0.021) (0.042) (0.015) Data are expressed as elasticities (%) ± SD. [*] P < 0.05 * *

Profit Margin = INFLATION

The variability of the parameter estimates The variability of the parameter estimates was smaller when the Petri Net Model was used, as shown by a smaller standard deviation and the high goodness of fitting CPI inflation estimated by the classic model was sistematically higher than that computed by the Petri Net model, resulting to be above the 2% target

The estimates of the present model confirm the main hypotheses, entailing a rise in CPI levels following an increase in the spread, and fully represents a major finding of the underlying research, even though the neglected issue of endogeneity cannot successfully approve the estimated results. The Petri Net Model seems to be a better Model to estimate the effect of inflation on macroeconomics

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