Including banks in macro models (finally!)

A simple model of credit and
banking

Emanuele Campiglio
Giovanni Bernardo

New Economics Foundation
London
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.

The structure of the model
Aggregate macroeconomic framework

Production Demand Employment

Sectoral accounts

Central Non financial
Banks Bank
Gilt sellers Households
firms
Government

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.

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

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
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.
Balance sheet
• Assets are pictured on the
Assets Liabilities
left-hand side of the balance
sheet.
• Liabilities are pictured on the
right-hand side. Asset 1 Liability
• Net worth, calculated as the
difference between assets and
liabilities, is what makes the
balance sheet balanced.
• In every period assets must be Asset 2
equal to liabilities and, as a Net worth
consequence, total changes in
assets must be equal to the Total assets = Total liabilities
total change in liabilities. Total change in assets = Total change in liabilities


Private banks balance sheet
Private banks in our model Private banks Balance sheet
have two assets: Assets Liabilities
• Reserves at the Central
Bank;
• Loans, the amount of Reserves
credit that the rest of the Deposits
economy (in our case just
firms) owes to them.
They have only one liability:
• Deposits: the amount of Loans
money that other agents
have deposited at the Net worth
bank is a debt that banks
have towards them.
. Total assets = Total liabilities


Firms balance sheet
Non financial firms have Balance sheet
two kinds of assets in our Assets Liabilities
model:
• Deposits at banks;
• The stock of physical
Deposits
capital Loans
(buildings, machinery
etc.). The physical capital
then enters the
production function as a
factor of production.
They have just one liability: Capital stock
Net worth
• Loans. That is, the
amount of debt they
have towards banks.
Total assets = Total liabilities

Central Bank balance sheet
The Central Bank has just one
type of asset: Balance sheet
• Gilts, as to say, governments Assets Liabilities
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 Gilts Reserves
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 Total assets = Total liabilities
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.

“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)

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


How the usual story goes
How 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:

1000
900
800
700
600
500
£

Commercial bank money
400 New loans
300
Monetary base
200
100
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
Lending cycles


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.

1400

1200

1000

800
£

Commercial bank money
600 New loans

400 Monetary base

200

0
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
64
67
70
73
76
79
82
85
88
91
94
97
100
Lending cycles


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
• 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.

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


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.
2500 500

450

2000 400

Monetary Base (billion £)
Broad Money (billion £)

350

1500 300

250

1000 200

150

500 100

50

0 0
May-06 Jan-07 Sep-07 May-08 Jan-09 Sep-09 May-10 Jan-11 Sep-11 May-12
Broad money (M4) Monetary Base (M0)

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


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
Profits (Π) Net Desired
Sales
Profits (ΠN) Investments (ID)

Wages Debt Repayment (DR)

• 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:

L D = ID – Π N
• 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)

• You can see the 90%

results of the 80%

survey in the 70%

picture: since 60%
Unable to obtain any finance
2006/07 the 50%
Demand for loans partially
proportion of the 40%
satisfied
demand for loans 30% Demand for loans entirely
satisfied
that has been 20%

entirely satisfied 10%

has dramatically 0%

decreased. 2006/07 2007/08 2010

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

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.
Loans
Credit Creation Debt repayment

Demand for Desired
Loans (Ld) Investments (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.
Change in
Reserves
reserves

Reserve ratio Desired
Stock of deposits
reserves


Firms assets
• First of all, imagine revenues from sales
as a flow entering the stock of deposits Revenues
of the firms.
• Firms then have some expenses (wage External Wages and debt
payments and the repayment of the finance repayment
debt) that flow out of the deposits stock.
• We model investments as a flow entering
a stock of physical capital, which then Deposits
enters the production function. Credit
• Investments are equal to the net profits Creation
plus the credit creation, if any. Credit
creation also enters the stock of deposits
as “external finance”. Investments
• Finally, in a standard way, we assume
that physical capital stock depreciates at Depreciation
a constant rate. Physical
Net Capital
Profits


The aggregate framework
Realized
Aggregate
Expenditure t+1
Planned Aggregate
To the sectoral accounts of
Expenditure t
Inventories t firms, banks and central bank, we
Sales t add an aggregate macro framework
built as pictured here.
Have a look at this presentation for
more details.

Wages t Planned
Consumption t

Planned Net
Profits t
Investments t Credit
Creation t

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
• This is our default scenario: a
180 14 process of growth leading to a
long-run steady-state.
170 12 • Growth is driven by the net
creation of credit (Credit
160
10 Creation less Debt Repayment).
•
Income and Expenditures

The availability of credit created

Net Credit Creation
150
8 by banks allows the planned
140 expenditures to be higher than
6 the current income.
130 • Realized Expenditures, on the
4
other hand, are always equal to
120 Income, and increase following
2
planned expenditures with a lag
110
of one period.
• Net Credit Creation eventually
100 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 converges to zero as debt and its
repayment become larger.
Income Planned Expenditures Realized Expenditures Net Credit Creation
• Income grows until reaching a
plateau.


Deposits and reserves
• The graph pictures the overall
200 60 amount of deposits existing in
180
the economy and the quantity
50 of central bank reserves.
160
• In our model, deposits
140
40
represent broad money while

Central bank Reserves
120 reserves represent the
monetary base.
Deposits

100 30
• Although the curves exhibit
80
similar shapes, it’s not reserves
20
60 driving credit, but rather the
40 opposite: reserves expand to
10
cover the expansion of private
20
banks liabilities (deposits)
0 0 • After creating new loans (and
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
new deposits) banks ask
Deposits Central Bank Reserves
reserves to the central
bank, who satisfies any
demand.

A banks confidence collapse
180 14

170 12

10
160
Income and Expenditures

8

Net Credit Creation
150
6
Income
140
4 Planned Expenditures

130 Net Credit Creation
2

120
0

110 -2

100 -4
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

• 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.


Recession!
• Although the economy 175
eventually reaches the same
170
steady state a decrease in
banks confidence (i.e. a 165
lower proportion of satisfied
demand for loans) causes a 160

prolonged state of recession. 155
• On the right you can see the
trajectories of income 150
(above) and the growth rate 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
(below) for different 8%
durations of the banking 7%
shock. 6%
• The whole area between the 5%
curves and the “default” 4%
curve (orange) represents
3%
loss of income (or growth).
2%
• If the shock is permanent
1%
(light blue), the economy
never goes back to positive 0%

growth and income -1%
converges to a -2%
new, lower, steady state. 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

2 periods 5 periods 15 periods permanent default


An “animal spirits” scenario
9%

7%

5%

3%

1%

-1%

-3%

-5%
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
2 periods 5 periods 15 periods permanent default

• 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.

Quantitative Easing
140

120

100

80

60

40

20

0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

Deposits Reserves

• 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.


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!

emanuele.campiglio@neweconomics.org
www.neweconomics.org

Including banks in macro models (finally!)

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (19)

Recently uploaded

Recently uploaded (20)

Including banks in macro models (finally!)