Including banks in macro models (finally!)

A simple model of credit and banking

Emanuele CampiglioGiovanni Bernardo

New Economics FoundationLondon

8/08/2012

Outline

1. Introduction: the macro modelling research at nef

2. Double-entry bookkeeping and model consistency

3. Another introduction: money, credit and banks

4. Moving away from the money multiplier

5. The theoretical structure of the model

6. Some numerical simulations

7. Conclusions

Emanuele Campiglio – Giovanni Bernardo – New Economics Foundation

nef macro modeling• nef has been developing an understanding of how to model the

macroeconomic system.

• We use a methodology called system dynamics to build theories concerning the dynamic functioning of the system and run numerical simulations of possible macro scenarios.

• This is an ongoing research project, but we feel the modeling tools we have developed are already able to show some original results and contribute to the current economic debate.

• In a previous presentation (LINK) we have presented the general aggregate macro framework of the model, employing it to analyze the debate between Krugman and Keen regarding debt and aggregate demand.

• In this presentation, we deal instead with the way we model the banking system.

http://www.neweconomics.org/blog/2012/07/25/reconciling-krugman-and-keen-using-nefs-model

The structure of the model

Aggregate macroeconomic framework

Sectoral accounts

Demand

Government

Production Employment

Banks Central Bank Gilt sellers Households Non financial firms

The model is composed of two main blocks:1. A macro “core unit” where demand, supply, profits, investments and employment

dynamics are modelled. Have a look here for more details. 2. A set of sectoral accounts, one for each agent that populates the economy. Each

account is built using a double-entry bookkeeping representation in order to ensure consistency.


http://www.slideshare.net/emacampiglio/reconciling-krugman-and-keen-using-nef-model

Including banks in macro models

• Trying to understand the functioning of the banking system and its interaction with the rest of the economy has been one of the main objectives of this research project.

• Economists have been strongly blamed for not having banks, debt and money inside their models: the majority of “mainstream” models has proved unable to foresee the crisis and properly understand its mechanisms.

• Indeed, the macroeconomic models of many central banks (or at least the ones that they publicly share) do not include banks at all. Banks just don’t exist.

• Take a look for yourself:– Quarterly model of the Bank of England

– The suite of models of the European Central Bank

– The FRB model used by the US Federal Reserve

http://www.bankofengland.co.uk/publications/Pages/other/beqm/default.aspx

http://www.ecb.int/home/html/researcher.en.html

http://www.federalreserve.gov/pubs/feds/1996/199642/199642pap.pdf

What we present• As a reaction to this knowledge gap, a lively debate has originated regarding how to innovate

and improve macroeconomic theory so to include banks in the picture.• At nef we have also tried to give our small contribution to the effort, developing an analytical

macro framework able to model banking behavior, or, at least, grasp some of its crucial features.

• Our model, as all models, is a simplification of reality. We are in no way offering an exhaustive representation of the economic system, nor any future forecasts.

• In this presentation:– We present a relatively simple but original macroeconomic model, composed of a macro “core unit” and a

set of sectoral accounts that represent the agents populating the economy (non financial firms, banks, central bank).

– We model the monetary dynamics of the economy as driven by the decisions of the private banking system - rather than by the central bank. We show some evidences supporting our approach and discuss the recent measures of “Quantitative Easing”.

– We show that a strong connection exists between the process of credit creation and the growth experienced by the economy: a confident banking system, willing to grant credit to firms for productive investments, is a necessary prerequisite for the economy to prosper.

– Finally, we present some numerical simulations to show how our model reacts to shocks. The level of confidence of the banking system and the propensity to invest of entrepreneurs appear to be two crucial variables in determining the dynamic of the system.


Model consistency

Balance sheet

Assets Liabilities

Total assets = Total liabilities

Total change in assets = Total change in liabilities

Asset 1

Asset 2

Liability

Net worth


We model every agent in the economy using a double-entry bookkeeping method. Imagine the model as a set of balance sheets, where each agent has some assets and some liabilities that change over time.

• Assets are pictured on the left-hand side of the balance sheet.

• Liabilities are pictured on the right-hand side.

• Net worth, calculated as the difference between assets and liabilities, is what makes the balance sheet balanced.

• In every period assets must be equal to liabilities and, as a consequence, total changes in assets must be equal to the total change in liabilities.

Private banks balance sheet

Private banks Balance sheet

Assets Liabilities


Reserves

Loans

Deposits

Net worth

Private banks in our model have two assets: • Reserves at the Central

Bank;• Loans, the amount of

credit that the rest of the economy (in our case just firms) owes to them.

They have only one liability: • Deposits: the amount of

money that other agents have deposited at the bank is a debt that banks have towards them.

.


Firms balance sheet

Balance sheet

Assets Liabilities


Deposits

Capital stock

Loans

Net worth

Non financial firms have two kinds of assets in our model:• Deposits at banks;• The stock of physical

capital (buildings, machinery etc.). The physical capital then enters the production function as a factor of production.

They have just one liability:• Loans. That is, the

amount of debt they have towards banks.

Central Bank balance sheet

Balance sheetAssets Liabilities


Gilts Reserves

The Central Bank has just one type of asset:• Gilts, as to say, governments

bonds. We assume that the central bank is always able to buy or sell the desired amount of gilts on the secondary market

The central bank has one kind of liability:• Reserves. Reserves are,

basically, accounts that private banks have at the central bank, and therefore appear on the liabilities side of the central bank balance sheet.


Another introduction: money

• Money is a very confusing thing. Everybody would instinctively know how to use it, but little is usually understood regarding what money really is, who creates it and how it circulates.

• There is no single definition of money. A set of monetary aggregates (called M0, M1, M2 and so on) are usually used, which differ depending on the degree of liquidity of money - that is, how easily it can be exchanged in the market.

• The definition of monetary aggregates differs across countries, but in general M0 represents the amount of central bank reserves and physical cash (notes and coins), which are very liquid, while the broader aggregates gradually include less liquid means of payment, such as deposits and other funds.

• For simplicity, in our model we assume that only two kinds of money aggregates exist:

1. M0 (also called monetary base, or narrow money), composed just by Central Bank Reserves. No physical cash exists in the model.

2. M4, or broad money, equal to the monetary base plus the stock of deposits.

Who creates credit?• Broad money is an extremely important variable. It represents the overall

amount of credit existing in the economy. Credit can be exchanged for goods and services and is increasingly used as a means of payment in modern societies.

• Credit is created by private banks: every time that a bank grants a loan it simultaneously creates a corresponding deposit, that can then be used and transferred to buy goods, pay the rent, purchase a car or a house, etc. That is, banks are capable of autonomously expanding their balance sheets by creating new credit.


Berry et al. (2007) Interpreting movements in Broad Money, Bank of England Quarterly Bulletin 2007 Q3

“By far the largest role in creating broad money is played by the banking sector.. When banks make loans they create additional deposits for those that have borrowed.”(Bank of England, 2007)

http://www.bankofengland.co.uk/publications/Documents/quarterlybulletin/qb070302.pdf

How the usual story goesHow are money and credit usually modeled? Textbook economic theory presents an explanation of the functioning of the banking system based on the theory of the money multiplier. This is how the basic story goes:• Suppose a bank has 100£ in deposits (representing the monetary base). It decides to keep 10£ as

reserves and lend the rest (90£). The ratio between the reserves and the amount of deposits is called the reserve ratio (in this case: 10%).

• The 90£ are deposited by the debtor in his bank. This bank, as the first one, will keep the 10% (9£) and lend the rest to the economy (81£). The new debtor will deposit the loan in his bank, that will keep the 10% and lend the rest, and so on, and so on.

• Since every new loan is smaller than the previous, the total amount of cumulative credit will converge to a limit. See below:


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Commercial bank money New loansMonetary base

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The effect of a monetary base expansion

• In a nutshell, the money multiplier theory implies that the central bank is able to control the amount of credit existing in the economy through the monetary base.

• Suppose that at time 50 the monetary base is expanded: broad money will converge to a new, higher, amount.


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Commercial bank money New loansMonetary base

Lending cycles

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The money multiplier theory is wrong

• Our model starts from the assumption that the money multiplier theory is wrong. In other words, we assume that the central bank has very little control on the dynamics of broad money.

• We have good reasons to embrace this approach. For many decades, central banks haven’t even used the supply of narrow money as a policy tool, preferring to focus on the reference interest rate instead.

• But in recent years we’ve had the chance to test the theory at work. Unable to reduce the reference interest rate, already close to zero, both the Bank of England and the US Federal Reserve have started “unconventional” monetary policy measures called “quantitative easing” (QE).

• Basically, Quantitative Easing involves an expansion of the central bank balance sheet. Two simultaneous things take place:

1. The Central Bank buys government or corporate bonds from the secondary market;

2. The Central Bank correspondingly increase the amount of reserves.


Quantitative easing


Source: Bank of England. Figures available at this link.

• You can clearly see the balance sheet expansion in the pictures below:– On the liabilities side (on the right), you can see the expansion of reserves (light blue)– On the assets side you can see the expansion of the amount of gilts purchased by the Bank (violet).

There are called “Other assets” in the legend because the Bank implements the purchase of gilts through its Asset Purchase Facility.

http://www.bankofengland.co.uk/markets/Pages/balancesheet/default.aspx

http://www.bankofengland.co.uk/markets/Pages/apf/default.aspx

Did it work?• According to the standard theory based on the money multiplier, QE should have had

the effect of expanding the amount of broad money. • Did this happen? No.• Below you can see the dynamics of both the monetary base M0 (the two rounds of QE

can be clearly seen) and the broad money M4: the overall amount of credit in the economy didn’t seem to be affected by QE.


May-06 Jan-07 Sep-07 May-08 Jan-09 Sep-09 May-10 Jan-11 Sep-11 May-120

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Broad money (M4) Monetary Base (M0)

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The creation of reserves• We are here following instead another interpretation of the mechanisms

of credit creation, usually referred to as endogenous money theory.

• In un a nutshell, the theory argues that the causation process is the reverse of what the money multiplier theory postulates:– First, banks decide how much credit to create (how many loans to grant),

independently of how many reserves they have.

– Then, they ask for reserves to the Central Bank. Unless the Central Bank doesn’t want to create a credit crunch, it will satisfy any demand by private banks

• This theory seems to be confirmed by the Bank of England operational framework as before the Quantitative Easing:


Bank of England (2012) The Framework for the Bank of England’s Operations in the Sterling Money Markets (the “Red Book”)

"for each reserves maintenance period (..) the Monetary Policy Committee sets the reserves remuneration rate (Bank Rate) and each scheme participant sets a target for the average amount of reserves they will hold, taking into account their own liquidity management needs.” (Bank of England, 2012)

http://www.bankofengland.co.uk/markets/Documents/money/publications/redbookjune2012.pdf

Banks confidence• So, if the central bank doesn’t control the amount of credit existing in the

economy (broad money), how is this determined?

• It’s very hard to say. The most crucial variable seems to be the level of confidence that the banking system has in the ability to repay of debtors and, more generally, in the performance of the economic system:

– If the banking system is confident and euphoric (as in the pre-crisis period), private banks will be willing to expand broad money by granting a high amount of loans.

– If, instead, the banking system is frightened and worried about the stability of the economy system, banks just won’t lend, irrespective of the amount of reserves that the central bank creates. This situation resembles the current one, where banks are rationing credit even after the massive injections of reserves by central banks during QE.


Let’s now go back to the model and see how we tried to include banks confidence in it.

Profits and desired investments


Net Profits (ΠN)

DesiredInvestments (ID)

Debt Repayment (DR)

Profits (Π)

Wages

Sales

• First of all, suppose the revenues coming from selling the output are distributed between wages and profits.

• A part of firms profits is used to repay (a portion of) the previously accumulated debt. We here suppose for simplicity that no interests are paid on the loans.

• Firms end up with a certain amount of Net Profits.• Then, firms decide how many investments they would like to make. Trying to

estimate the determinants of desired investments is tricky business, and many different investment functions have been proposed in economic theory.

• But however they’re determined, the desired investments will be equal, higher or lower than the firms net profits.

Desired investments• In other words, Desired investments will be equal to a proportion

(which we call η) of Net Profits:ID = ηΠN• Suppose η = 1: firms will invest the whole and exact amount of net

profits (ID = ΠN).

• Suppose η < 1: we are now in the case where firms want to invest less than their net profits (ID < ΠN). Firms will therefore accumulate liquidity

(in our model, bank deposits).

• Finally, suppose η > 1: firms will want to invest more than their net profits. That is, their planned expenditures are higher than their current income (ID > ΠN).


Demand for loans

• In the last case (η > 1), firms will seek for credit from the only agents in modern economies capable of financing the gap between planned expenditure and income: banks.

• Demand for Loans (LD) is then defined as the difference between Desired Investments and Net Profits:LD = ID – ΠN

• That is, the whole amount of net profits are invested; if firms then want to invest more than that, they will try to finance the rest through debt.


Credit creation

• At this point, banks have to decide whether to:– Reject the demand;

– Satisfy a proportion of demand;

– Satisfy the entire demand of loans.

• We model this by assuming that banks satisfy a proportion β of the demand for loans. Credit Creation (CC) is therefore defined as:

CC= β*LD• Basically, β represents the banks “approval rate”. We take this as a proxy

for banks confidence:– When banks are confident β will be higher (a higher proportion of loans demand

will be satisfied);

– When banks are not confident, β will be lower (a lower proportion of demand will be satisfied)


Banks confidence• Unfortunately, there exists almost no data regarding banks approval rate. We don’t know

how much is the demand for loans, nor how much banks satisfy this demand. • The only data comes from a survey conducted by BIS (the UK Department for Business,

Innovation and Skills) on small and medium enterprises (SMEs)


Just a word on the methodology we’re using now..

2006/07 2007/08 20100%

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Unable to obtain any financeDemand for loans partially satis-fiedDemand for loans entirely satis-fied

• You can see the results of the survey in the picture: since 2006/07 the proportion of the demand for loans that has been entirely satisfied has dramatically decreased.

http://www.bis.gov.uk/assets/biscore/enterprise/docs/b/11-p74-bis-small-business-survey-2010

A word on system dynamics

• The model is built employing system dynamics, a methodology used to study the behaviour of complex systems and based on the explicit representation of feedback loops. Its basic units are:– Stocks and Flows (basically, differential equations)– Connectors (parameters or simultaneous equations)

See this simple example where Population is a stock, new born and deaths are flows affecting the level of the stock, and the rest of variables are exogenous parameters or defined by simultaneous equations.


The stock of debt• Loans (debt) are modelled as a stock.• The two flows affecting it are:– Credit creation (new loans granted by banks to firms)– Debt repayment• Credit creation is calculated as presented in the previous slides: it’s equal to a

fraction β of the demand for loans coming from private firms, which in its turn will depend on how much firms desire to invest.

• Debt repayment is simply modelled as a proportion of the stock of loans representing the debt repayment time. Suppose every new loan has to be repaid over 10 years: in each period a 1/10 of the stock of debt flows out because repaid.

LoansCredit Creation Debt repayment

Demand for Loans (Ld)

DesiredInvestments (Id)


The stock of reserves• The other asset in banks balance sheet, apart from Loans, is the stock of

central bank reserves.• We assume that the central bank passively responds to the desires of

private banks: whatever the demanded quantity of reserves, the central bank will just create/reduce them accordingly.

• Simultaneously, the central bank balances its accounts by buying/selling gilts from/to the secondary market, which we assume unlimited.

• Desired reserves will be equal to a proportion of the stock of deposits (which, remember, are a liability for banks). This proportion is called the Reserve Ratio.


ReservesChange in reserves

Desired reserves

Stock of depositsReserve ratio

Firms assets


Physical Capital

Investments

Deposits

Revenues

External finance

Wages and debt repayment

Credit Creation

Net Profits

Depreciation

• First of all, imagine revenues from sales as a flow entering the stock of deposits of the firms.

• Firms then have some expenses (wage payments and the repayment of the debt) that flow out of the deposits stock.

• We model investments as a flow entering a stock of physical capital, which then enters the production function.

• Investments are equal to the net profits plus the credit creation, if any. Credit creation also enters the stock of deposits as “external finance”.

• Finally, in a standard way, we assume that physical capital stock depreciates at a constant rate.

The aggregate framework


Wages t

Profits t

Planned Consumption t

Planned Investments t

Planned Aggregate Expenditure t

Net Credit

Creation t

Sales t

To the sectoral accounts of firms, banks and central bank, we add an aggregate macro framework built as pictured here. Have a look at this presentation for more details.

Realized Aggregate

Expenditure t+1


Inventories t

http://www.neweconomics.org/blog/2012/07/25/reconciling-krugman-and-keen-using-nefs-model

A snapshot of the model


This is how the model looks like on the software we use, STELLA.

Default scenario

• For the first run, we set the following initial values:• Initial Realized Expenditure: 100• Initial level of debt = 0• Infinite inventories (we are here focusing on the demand side of the economy

and rule out the case of supply bottlenecks: all demand can be satisfied)• Initial level of deposits = 100• Initial level of physical capital = 300

• And the following parameters values:• Investment propensity (η) = 1.4• Banks confidence (β) = 1• Reserve ratio = 0.1 (=10%) • Debt repayment time (r) = 5• Alpha (α) = 0.7


Income, expenditure and credit


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• This is our default scenario: a process of growth leading to a long-run steady-state.

• Growth is driven by the net creation of credit (Credit Creation less Debt Repayment).

• The availability of credit created by banks allows the planned expenditures to be higher than the current income.

• Realized Expenditures, on the other hand, are always equal to Income, and increase following planned expenditures with a lag of one period.

• Net Credit Creation eventually converges to zero as debt and its repayment become larger.

• Income grows until reaching a plateau.

Deposits and reserves


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• The graph pictures the overall amount of deposits existing in the economy and the quantity of central bank reserves.

• In our model, deposits represent broad money while reserves represent the monetary base.

• Although the curves exhibit similar shapes, it’s not reserves driving credit, but rather the opposite: reserves expand to cover the expansion of private banks liabilities (deposits)

• After creating new loans (and new deposits) banks ask reserves to the central bank, who satisfies any demand.

A banks confidence collapse

• We here model the case of a shock in banks confidence: at time 15, we impose a shock to the parameter β, which drops from 1 to 0.8 for 10 periods. This means that banks won’t satisfy the entire demand for loans anymore, but just 80% of it.

• The shock leads to a drop in Net Credit Creation that becomes negative: the amount that firms pay to repay the debt is now higher than the amount of new loans granted by banks.

• This means that for 10 periods the planned expenditures are lower than current income. More specifically, planned investments are lower than current firms profits.

• Finally, when the shock is over and β goes back to its original value, the economy bounces and converges to its previous steady state. Emanuele Campiglio – Giovanni Bernardo – New Economics Foundation

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Recession!


• Although the economy eventually reaches the same steady state a decrease in banks confidence (i.e. a lower proportion of satisfied demand for loans) causes a prolonged state of recession.

• On the right you can see the trajectories of income (above) and the growth rate (below) for different durations of the banking shock.

• The whole area between the curves and the “default” curve (orange) represents loss of income (or growth).

• If the shock is permanent (light blue), the economy never goes back to positive growth and income converges to a new, lower, steady state.

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An “animal spirits” scenario


• We now model the case of a shock in firms propensity to invest (η), which at time 15 jumps from 1.4 to 1.8. This is very similar to Keynes “animal spirits”.

• In the picture above you can see the dynamics of the growth rate for different durations of the shock. There is an initial positive reaction of growth rates, which then fall down once the shock is over. The longer the duration of the shock the harsher the recession when the shock fades out.

• In other words, a negative shock in the propensity to invest (a decrease in η from 1.8 to 1.4) will bring about negative growth rates.

• The only case in which the negative shock is avoided is when the increase in η is permanent.

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Quantitative Easing


• Finally, we model the case of an exogenous increase in the stock of central bank reserves: as you can see from the graph above, this has no effect whatsoever on the dynamics of broad money.

• This result is not surprising given our theoretical framework. Still, the simulation above appears to be remarkably similar to the graph shown earlier, derived from real data! (slide 17)

• The only variables capable of affecting broad money in our model are the demand for loans by non financial firms (derived from their investment desires) and the confidence level of banks, which represents the willingness of the banking system to satisfy the demand for loans.

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Some conclusions (1)• The model presented here is characterized by a range of limiting assumptions and

simplifications:– Some of the crucial parameters are treated as exogenous: in particular, the propensity

to invest (η) and banks confidence (β) would deserve a more detailed study in order to make them endogenous. For example, they both could be defined as some functions of the profit rate, or the economy’s growth rate, or the ratio of debt to GDP. Testing different functional forms will be part of the next step of research.

– The supply side of the economy is absent. This is an assumption made for this presentation: the wider nef model does have a representation of the process of production with production of factors (capital and labour) gradually adjusting to demand.

– No interests are paid on debt.– No price dynamics is modelled.– etc.

• Still, we believe the model presented here is capable of grasping some unexplored features of how modern economies work, and in particular the role of debt in influencing aggregate demand.


Some conclusions (2)• We presented a simplified version of nef macroeconomic model, composed of a macro “core

unit” and a set of sectoral accounts that represent the agents populating the economy.

• We offered an original tractation of the banking system and its interactions with the “real” economy. We explicitly modelled the crucial role that banks play in the creation of credit by operating a distinction between planned expenditures and current income.

• We showed that a strong connection exists between the process of credit creation and the growth experienced by the economy: a confident banking system, willing to grant credit to firms for productive investments, is a necessary prerequisite for the economy to prosper.

• We argued that modelling the monetary dynamics of the economy as driven by the decisions of the private banking system - rather than the central bank – offers a more realistic representation of the economic system. We showed some evidences supporting our conclusion, discussing the recent measures of “Quantitative Easing”.

• We built the model using system dynamics methodology, which allows us to run simulations of dynamic scenarios. We also employed a double-entry bookkeeping technique to model the agents of the economy (non financial firms, banks and the central bank) and ensure consistency.

• Finally, we presented some numerical simulations to show how our model reacts to shocks. The level of confidence of the banking system and the propensity to invest of entrepreneurs appear to be two crucial variables in determining the dynamic of the system.


Thank you!

[email protected]

Including banks in macro models (finally!)

Education

frb model

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