Building a realistic
banking system within a
stock-flow coherent
model
Marc Lavoie
University of Ottawa
(based on work with Wynne
Godley)
Work in progress
Part of a manuscript written with W.G.:
 Monetary economics: an integrated
approach to credit, money, income,
production and wealth
 One block among several other blocks:

 production
firms block
 households block
 government sector block
 central bank sector block
Two PK banking models



The basic model
Based on Godley CJE
1999 article
Operational



The more realistic
model
Adds several realistic
features to the
standard CJE model
Operational, but still
fragile
PK vs Neoclassical banks

PK banks

Bank loans are key
Banks accept all
deposits
Banks provide all
credit-worthy loans
Banks set deposit
rates which are
endogenous
loan rates are
marked-up over
deposit rates





Neoclassical
banks

Asset allocators
Make asset and
liability choices
Banks have supply
functions of deposits
and loans
Deposit and loan
rates clear deposit
and loan markets



The buffer principle
All sectors need a buffer that
provides an adjustment factor
Firms: inventories and bank loans
 Households: holdings of money
deposits
 Government: bills issued
 Central bank: residual purchaser of bills
or advances made to private banks
 Banks: bills held or advances obtained
from central bank

The balance sheet of Model INSOUT (Basic banks)
Hhholds Firms
Inventories
Govt
Central
bank
Banks
+IN
HPM
+Hh
Checking
deposits

+IN
H
+Hb
0
+M1h
M1
0
Time
deposits
+M2h
M2
0
Bills
+Bh
B
+Bb
0
Bonds
+BLh.pbL
BL.pBL
+Bcb
0
L
Loans
+L
0
Balance
V
0
+GD
0
0
IN

0
0
0
0
0
0
The banks balance sheet
constraint
Bbd = M1s + M2s - Ls - Hbd
 Banks provide money deposits and loans
on demand, and they must hold bank
reserves Hbd ;
 All elements of the banks’ balance sheet
are predetermined, except for Treasury
bills Bbd.
 Hidden equation of system: Hbs = Hbd
Reserves are supplied on demand

The determination of interest
rates




The Treasury bill rate is set exogenously by the
central bank (or by Taylor rule)
The bond rate is also set exogenously, or it can
be made endogenous
The deposit rate is set by banks, based on a
reaction function that depends on the liquidity
preference of banks
The lending rate is set by banks, with a markup
on the deposit rate.
The banking liquidity ratio





Banks compute a Banking liquidity ratio (BLR)
BLR = T.Bills/Deposits
This is the converse of Eichner’s 1986 degree
of liquidity pressure (loans/deposits)
The BLR must be within a certain range
(bottom, top) in the medium run
The BLR range is a reflection of bank liquidity
preference
Liquidity mechanism
When banks have an insufficient amount
of bills relative to their liquidity preference,
they increase interest rates on deposits,
and induce households to trade their
Treasury bills for bank deposits; this allows
banks to recover a proper bills to deposits
ratio.
 When banks have a liquidity preference for
bills, they raise the (bottom, top)
thresholds

Determination of deposit
rates






Deposit rates rise as long as BLR < bottom
Deposit rates diminish as long as BLR > top
Under the following two conditions:
There is a ceiling to deposit rates: they
cannot be any higher than bill rates
There is a floor to loan rates: they cannot be
any lower than bill rates
When these conditions are not met, the BLR
convention is inadequate system-wide
What happens when the bank
liquidity ratio is inadequate systemwide ?


In the overdraft system: banks pay little attention
to their relative holdings of T.Bills; the
conventionnal target BLR will be modified or
ignored.
In the asset-based system (anglo-saxon world),
where bank liquidity ratios are important, there
must be an escape market: this market is the
commercial paper market; firms issue CP when
loan rates are too high, and they retire CP when
loan rates are low.
More realistic PK bank







Banks issue equity
Banks have retained earnings and net worth
Banks make loans to consumers
The loan markup over deposit rates is
endogenous
Banks face a BIS-imposed capital adequacy
ratio (CAR)
Banks may take advances from central bank
Banks have labour costs
Two possible balance sheets of banks
Standard accounting
Macro-economic
accounting
Assets
Liabilities Assets
Liabilities
Bb
M1
Bb
M1
L
M2
L
M2
Hb
Ab
Hb
Ab
OFb
eb.peb
Total assets = Total Assets - Liabilities =
Liabilities
Vb
Table 11.1: The balance sheet of Model COMP
Households
Firms
Govt
Central
bank
Banks

Inventories
+IN
IN
Fixed
capital
+K
K
HPM
+Hh
Demand
deposits
Time
deposits
H
+Hb
0
+M1h

M1
0
+M2h

M2
0
+A

Ab
0
+Bcb
+Bb
0
Advances
Bills
+Bh

B
Bonds
+BLh.pbL

BL.pBL
Commercial
paper
+CPh

CP
0
Equities of
firms
+ef.pef

ef.pef
0
Equities of
banks
+eb.peb
0

L
Loans

eb.peb
0
+L
0
Balance

Vh

Vf

Vg
0

Vb
(IN+K)

0
0
0
0
0
0
The determination of the own
funds of banks
= OFb-1 + FUb + )ebs.peb - NPL
 OF = own funds
 FU = retained earnings
 )ebs = new issues of bank shares
 NPL = non-performing loans
(bankrupcies)
 OFb
Realistic banks target profits

Banks need to make a definite amount of
profits, first to cover the dividends payments
which their household shareholders view as
desirable, and secondly to augment their own
funds in line with the BIS rules on capital
adequacy ratios. These two requirements,
given the interest rates administered by the
central bank, determine the spread between
the rate of interest on loans and the rate of
interest on deposits.
Targets of banks
FbT = FUbT + FDbT
 FDbT = rdb.OFb-1 or rdb.ebs-1 .pebe-1
 CAR = OFb / Ls
 CARM = minimum capital adequacy ratio
 CART = target capital adequacy ratio
 OFbT = CART.Ls-1
 If CARM < CAR-1 < CART
 FUbT = [(OFbT - (OFb-1 + )ebs.pebe-1)]
 If CAR-1 > CART,  = 0
 If CAR-1 < CARM ,  =1

Determination of loan rates
Fb = rl.Ls-1 + rb-1.Bbd-1 - rm.M2s-1 - ra-1.Abd-1 - WBb
realized profits of banks;

rl = rm + >

the rate of interest on loans
 The endogenous markup > is obtained by
equalizing the realized profits to the target
amount of bank profits ; all else equal, low
realized CARs require higher markups.
 The deposit rate is determined as in the basic
model, on the basis of banks’ liquidity
preference

Loans and deposits
The relationship between loans and
deposits, through the balance sheet
constraint of banks, is given by the
compulsory reserve ratio (res), the actual
bank liquidity ratio (blr) and the actual
capital adequacy ratio (car):
 L/M = (1 - res - blr)/(1 - car)
 Only by fluke would that ratio be 1.

Problems with the realistic banks




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It is much more difficult to find a reference steady
state;
Falling loans may actually lead to rising loan markups
on deposit rates, due to the shrinking profit base that
absorbs fixed costs;
Loans to consumers create instabilities as well,
because these loans are only partially absorbed by
household deposits;
Financial assets held by firms may be a partial
solution, but this creates problems with regards to the
determination of prices
Commercial paper issued by firms help to stabilize
interest rates.
Three experiments with the
complete model (CP)
Raise (again) compulsory reserve
requirements
 Introduce random demand shocks
 Raise the target stock of fixed capital
