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A Mathematical Model and Decision Support System for Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy. Darko Pongrac. Outline. Introduction Mathematical model Heuristic Computational results Conclusions Future research.

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Darko pongrac

A Mathematical Model and Decision Support System for Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

Darko Pongrac


Outline
Outline Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Introduction

  • Mathematical model

  • Heuristic

  • Computational results

  • Conclusions

  • Future research


Introduction situation in croatia
Introduction – situation in Croatia Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Croatian National Bank (CNB) - aims:

    • price stability

    • supporting economic growth

  • Commercial banks – aims:

    • making profit


Introduction situation in croatia1
Introduction – situation in Croatia Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

Commercial banks

  • foreign ownership

  • indebtedness abroad with low interest rate

  • giving loans in Croatia with high interest rate

    easy profit!


Introduction situation in croatia2
Introduction – situation in Croatia Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • commercial banks’ debt abroad increase the Croatian external debt

  • Croatian external debt reached the level which is in the economic theory considered as upper accepted level for external debt of a country

Croatian National Bank (CNB):

  • uses the available instruments and measures to control the external debt


Introduction monetary policy
Introduction – Monetary policy Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • according to our open economy, there exists high possibility for transmitting inflation from abroad (for example: increasing of energy prices on the world market has big influence on domestic prices)

  • transmitting inflation from abroad and high level of foreign debt can effect high disturbance in country economy

  • special attention is focused on the external debt growth

  • historically low level of interest rates on the world capital markets


Introduction monetary policy1
Introduction – Monetary policy Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • CNB has a limited number of available measures and instruments for influencing commercial banks behaviour

    • slow measures

    • fast measures


Introduction monetary policy2
Introduction – Monetary policy Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

Slow measures

  • Reserve requirements

  • Marginal reserve requirements (MRR)

  • Special reserve requirements (SRR)

  • Compulsory central bank bills (CCBB)

These measures were used in the model

developed in this work.


Introduction monetary policy commercial banks objectives
Introduction – Monetary policy Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy– commercial banks’objectives

  • Profit is made from different revenues that can be put into two main categories:

    • interest

    • fees

  • Interest and fee revenues connected to the credit activities are shown through the effective interest rate.

  • Revenues from credit activities are a significant part of commercial banks’ revenues.


Introduction mathematical programming
Introduction – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymathematical programming

  • mathematical programming is in high expansion with evolution of the computers

  • specially expanded in last twenty years

  • we know difference between single level and multilevel mathematical programming

  • Bialas and Karwan described, in 1982., multilevel programming problem which includesn level


Mathematical model
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

Bilevel programming model

  • CNB – leader: minimize the increase in household’s consumption (loans to households)

  • commercial banks – followers: maximize their profits

    Conflict!


Mathematical model1
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

CNB (leader):

  • controls the percentage of marginal reserve requirements (MRR)

  • controls the percentage of special reserve requirements (SRR)

  • regulate conditions on the purchase of the compulsory CNB bills


Mathematical model2
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

Commercial banks’ loans are divided in three main categories:

  • housing loans

  • loans to households

  • loans to enterprises


Mathematical model3
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Indexes

    • i - type of indebtedness

    • j - commercial bank

    • l - type of investment

    • p - marginal reserve requirements

      percentage

    • t - time period of indebtedness

      (macro period)

    •  - time period of investments

      (micro period) St


Mathematical model4
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Parameters

    • op - reserve requirements percentage

    • dlt - minimal demand for credit

    • glt - maximal supply of credit

    • ol - the number of repayments of credit

      instalments

    • bi - the number of repayments of

      indebtedness instalments

    • kit - interest rate of indebtedness

    • mjlt - interest rate of investment

    • xjil0 - bank’s indebtedness at the beginning

      of the observed period

    • Wjl0 - bank’s credit at the beginning of the

      observed period


Mathematical model5
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Variables

    • xjilpt - the amount of bank’s debt in the

      observed period

    • wjl- the amount of bank’s credit in the

      observed period

    • zilpt - 1, if the percentage of marginal/special

      reserve requirements is p; 0 otherwise

    • vjilpt - 1, if bank’s indebtedness is bigger then

      repayment related to the previous

      indebtedness; 0 otherwise

      xjilpt ,wjl≥ 0; zilpt ,vjilpt  {0,1}


Mathematical model6
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Notes

    • yjilpt - the amount that the bank repays for

      previous indebtedness

    • Wjlt - the total amount of bank’s credit in

      themacro period

    • Ujlt - the total amount of clients’

      repaymentsrelated to previous

      credit

    • Qjipt - bank’s debt

    • Rjlt - bank’s credit


Mathematical model7
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Expression for notes:

    • j,i,l,p,t (a)

    • j,l,t(b)

    • j,l,t (c)

    • j,i,p,t (d)

    • j,l,t(e)


Mathematical model8
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Model:

    with constraints:

    i,l,t (1)

    j

    with constraints :


Mathematical model9
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Model - constraints:

    j,l,t (2)

    j,i,l,p,t (3)

    j,i,l,p,t (4)

    j,i,l,p,t (5)


Mathematical model10
Mathematical model Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Model - constraints:

    j,i,l,p,t (6)

    j,i,l,p,t(7)

    xjilpt ,wjl≥ 0; zilpt ,vjilpt  {0,1},j,i,l,p,t(8)


Mathematical model difference between models
Mathematical model - Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policydifference between models


Heuristic
Heuristic Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • NP-hard problem (Ben-Ayed, Blair, 1989)

  • heuristic

  • nonlinear constraint (2) was relaxed in the way that the binary variablevijlptis fixed to 1 in all observed points (the real situation), and the second binary variable zilptis fixed to 1 for a chosen value of marginal reserve requirements in each observed period


Heuristic1
Heuristic Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • Real situation: j=34, i=2, l=3, p=70, t=12

    171136 0-1 variables

    and constraint (2) is cubic


Heuristic2
Heuristic Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • interest rates for banks’ debt are fixed to the chosen values (euribor+1%,that is 4.5%), interest rates for banks’ loans are known

  • all banks have the same conditions for indebtedness

  • we observe only macro periods

  • we observe the neighbourhood of ±5% of the chosen marginal reserve requirements

  • for a closer look at the changes in banks’ behaviour the neighbourhood changes to ±1%


Heuristic3

Start Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

Read model parameters

Choose initial bank for solving

Choose initial marginal/ special reserve requirement for solving

Solve relaxed linear problem

Choose next marginal/ special reserve requirement for solving

Has the marginal/

special reserve requirement been found for all kinds

of loans?

No

Choose the next bank

for solving

Yes

Have all

the banks been

considered?

No

Yes

Print out the calculated

values for the highest, lowest and mean marginal / special reserve requirement

for the banking system

Stop

Heuristic

  • What does it mean “Choose the next value for MRR”?

  • neighbourhood of ±5%

  • for a closer look, neighbourhood of ±1%


Heuristic4
Heuristic Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

What does it mean “Is the MRR found?”

  • jump!

  • Wjlt - the total amount of bank’s credit in the macro period


Computational results model without ccbb
Computational results – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymodel without CCBB


Computational results model without ccbb1
Computational results – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymodel without CCBB


Computational results model without ccbb2
Computational results – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymodel without CCBB


Computational results model without ccbb3
Computational results – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymodel without CCBB


Computational results model with ccbb
Computational results – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymodel with CCBB


Computational results model with ccbb1
Computational results – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymodel with CCBB


Computational results model with ccbb2
Computational results – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymodel with CCBB


Computational results model with ccbb3
Computational results – Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policymodel with CCBB


Computational results comparison of models
Computational results - Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policycomparisonof models

  • MRR in margin between 10 and 80% have effect on all banks and all types of their loans

  • only 8 banks don’t have housing loans

  • higher effect on housing and enterprises loans, and lower effect on other loans to households in first model

  • almost same effect on all type of loans in second model

model without CCBB model with CCBB


Conclusion
Conclusion Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • according to our numerical analysis the rate of marginal reserve requirements of 55% is an average rate on which banks stop profiting on extending credits to the households, and that is exactly the rate approved by the CNB’s decision

  • based on the results which set the marginal reserve requirements rate of 40% as a rate which starts being unprofitable for banks to extend households credits, we can see why formerly prescribed marginal reserve requirement rates weren’t efficient in stopping the external debt growth


Further research
Further research Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

  • looking into the possibility of introducing some new measures on extending the credits to the households

  • looking for the possibility of introducing variable MRR which would depend on foreign debt changes and the changes in the credits to the households

    -> heuristic based on tabu search


Further research1
Further research Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

Heuristic based on tabu search:

  • trade off between decreasing the foreign loans’ increase (MRR decreases) and increasing the interest rate (demand decreases)

  • the rule of searching the neighbourhood: commercial bank accepts to decrease the foreign debt increase, and the interest rate increases in order to obtain the same profit (0-1 variable becomes 0)

  • interest rate increases, MRR changes(0-1 variable changes)


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