On the convergence of theory and practice in the measurement of

FISIM

Paper prepared by Athol Maritz (Macroeconomics Research Section, ABS)

for the

Economic Measurement Group Workshop

Sydney November 2012

On the convergence of theory and practice in the measurement of

FISIM1

Abstract

The poor performance of FISIM measures during the GFC has renewed debate about the

conceptual basis of FISIM. What exactly do our FISIM measures measure, and do these

square with any reasonable definition of FISIM? What is a reasonable definition of FISIM?

Should it include compensation for risk? Do the current measures include a proper

compensation for risk, or not? What is a proper compensation for risk, and how would we

measure it? Faced with the ongoing conceptual debate, the difficulty in agreeing a

theoretically correct definition of FISIM, and then in developing a good measure of the

concept, the ISWGNA FISIM Taskforce has asked that countries undertake an empirical

study of the performance of alternative FISIM measures. The Taskforce has provided a

number of criteria on which to judge alternative measures.. These criteria naturally reflect

some underlying view of what FISIM is, and how it should behave through periods of market

volatility. How does this square with the conceptual debate? This paper presents the results of

an Australian study of the performance of different measures of FISIM through the GFC, and

draws some tentative conclusions that bear on the conceptual debate, including the potential

value of distinguishing between expected FISIM and realised FISIM and the implications this

might have for the broader issue of how to measure income in the national accounts.

1. Introduction

The FISIM literature centres on five questions of theory:

What is the credit spread, and should it be included in the definition of FISIM

What default risk is taken by the bank, what is the compensation for this default risk,

and should this compensation be included in the definition of bank FISIM

What maturity mismatch risk is taken by the bank, what is the compensation for this

maturity mismatch risk, and should this compensation be included in the definition of

bank FISIM

In finance, risk is compensated by an expected return premium. Actual returns almost

certainly will differ from expected returns. Should the difference between actual and

expected returns be included in the definition of bank FISIM

1 The author works in the Macroeconomics Research Section of the ABS. The views expressed in this paper are

those of the author and do not necessarily reflect the views of the ABS.

How best to decompose nominal FISIM into price and volume components. Closely

related is the question of how to produce a price index for FISIM for inclusion in the

CPI.

The answers to these questions underpin one of the key challenges facing national

statisticians – how to measure the most important component of output and production for

one of the most important industries in a modern economy. The fact that the answers have

proven elusive is cold comfort to practising statisticians who cannot avoid or postpone

measuring the contribution of the financial sector to the national accounts.

This paper presents a view on these questions of theory and considers the consequent

measurement issues. The paper also reports on an empirical study conducted by the ABS into

the performance of alternative FISIM measures (reference rates) through the GFC.

2. Theoretical issues

2.1 Treatment of the credit spread

Much of the early FISIM literature, and some of the later writings, fail to distinguish clearly

between the credit spread inherent in the interest rates charged by banks and the default risk

experienced by banks. A credit spread exists because of the risk that borrowers may default.

But this does not necessarily mean the bank takes default risk. To illustrate the point,

consider the following example:

A bank makes 10 one-period loans of $100 each. The bank knows one loan will default, but

not which one. Assume that the riskless interest rate is 4.5% and that the bank needs a return

of 5% to cover costs. Then the bank will charge each borrower r%, where 900(1+r/100) =

1000(1+5/100). This implies r% = 16.67%.

Then the credit spread is 16.67% – 5% = 11.67%. Yet in this example, the bank takes no

default risk.

To the extent that the theoretical debate has been resolved at all, it is to recognise that the

dollar value of the credit spread – which might be 11.67% times $1000, or times $900

perhaps, or something in between – should not be included in FISIM.

The main issue is how to ensure the credit spread is eliminated from measures of FISIM.

2.2 Default risk

Banks experience default risk when they are uncertain about how many borrowers will in fact

default, and the theory of finance suggests that banks will be compensated by an expected

return premium that is a function of the non-diversifiable component of this default risk.

Exactly what the expected return premium may be is a difficult question and well beyond the

topic of this paper, but to continue the example, let’s assume it is 1%. Then the bank’s

required return is 6% rather than 5% and it will charge each borrower 17.78% rather than

16.67%.

There is more debate about whether the bank’s compensation for default risk should be

included in the definition of bank FISIM. Since taking default risk is part of what banks do,

and get paid for, the obvious position to take on this question is that the expected return

premium for default risk should be included in bank loan FISIM.2

Measuring default risk – as defined - and determining the expected return premium for

default risk, is difficult and unlikely to be done in practice. For a measurement perspective,

the best way forward would be to develop measures of loan FISIM that de facto include any

expected return premium, whatever it may be. This should be feasible because quoted loan

rates and reported interest receipts would include the expected return premium. This is

discussed further below.

2.3 Actual versus expected defaults

In general there will be a difference between actual and expected defaults.3 This begs the

question of whether FISIM should be defined in terms of actual or expected defaults.

Consider the way banks actually do business. A customer asks for a five-year fixed rate loan.

The bank quotes a rate that will be determined by the credit quality (probability of default) of

the borrower, the five-year point on the relevant yield curve, and a required return to cover

other costs and risks the bank takes in the normal course of doing business. The bank quotes a

credit spread to the customer that reflects the probability that the customer will default. For a

portfolio of loans with an expected default rate, the bank includes a credit spread that reflects

the expected rate of default on the portfolio.

This suggests that the natural concept of FISIM is based on what the bank expects to earn at

the time the (portfolio of) loan(s) is made. Call this expected FISIM, and distinguish it from

actual FISIM which is determined by what actually comes to pass.

The analogy between FISIM and insurance has already been drawn in the FISIM literature

(see for example Fixler and Zieschang (2010) and Hood (2010)) to support the argument that

charging a credit spread is like self-insurance against borrower default. The further point is

that the Insurance Service Charge is defined in terms of expected rather than actual claims,

with the difference between expected and actual claims accounted for as a current transfer.

Analogously, FISIM should be defined (and measured) in terms of expected rather than

actual defaults, and the difference between actual and expected defaults should be accounted

for as a capital transfer (see Hood (2010) for a discussion of this issue).

2 Though the contrary view and the ongoing debate on this issue as summarised for example in Zieschang

(2012) is acknowledged. 3 At least in a simple one-period example. More generally, one would expect that actual defaults equal expected

defaults on average over time, if not in every period

Expected FISIM is likely to be a relatively well behaved series over time, and actual FISIM

to be more volatile, particularly through periods of economic difficulty. Assuming expected

FISIM is the relevant concept, the main measurement problem here – as it often is in finance

– is that one observes actual rather than expected returns, and the challenge is to use observed

data to estimate expected defaults.

2.4 Loan FISIM and the role of the reference rate

SNA 2008 defines FISIM and recommends measuring FISIM as the difference between a

loan rate and a reference rate multiplied by a balance, and suggests that the reference rate

should reflect the risk and maturity structure of the loan. This appears somewhat at odds with

the simple example given, where the riskless rate is the natural reference rate.

Consider an even simpler example than that used above – where there is no default risk or

any other risk, and the bank raises money at a riskless rate of 4.5% and lends money at 5% to

cover costs. Then FISIM, equal to the loan rate - here 5% - minus a reference rate - here the

riskless rate of 4.5% - times the loan balance - here 10 times $100 - is earned period-by-

period, and the bank ultimately has principal of $1000 repaid.

Now assume one loan will default, and that the bank charges each borrower a rate of 16.67%

to compensate. The bank earns a margin equal to the loan rate of 16.67% minus the reference

rate of 4.5% times the loan balance of $1000 until the loan defaults, and then the same

margin on a loan balance of $900 thereafter. The important point here is that in order to

equate FISIM earnings in the two examples one needs to subtract $100 of principal from

interest earnings in the second example. More generally one would need to subtract expected

defaults, and in particular expected defaults per period (the default rate), each period. This is

the argument in Hood (2010).

In this example the reference rate is unambiguously the riskless rate, though the same

measure of FISIM could be achieved by adjusting the reference rate for expected defaults.4

2.5 Deposit FISIM and the role of the reference rate

In the simple examples given above, depositors will demand the riskless interest rate plus any

expected return premium for default risk taken by the bank less a payment for deposit

services. Any expected return premium earned by the bank is “passed through” to the

depositors who ultimately take the risk and get the reward (assuming a bank with no equity).

If the same riskless reference rate is used for calculating deposit FISIM as for calculating

loan FISIM, then the recommended method – reference rate minus deposit rate times

balances – will subtract the expected return premium from deposit FISIM. This would be

4 Essentially to include the credit spread. Where the SNA suggests that the reference rate should reflect risk, this

should be taken to mean the credit spread.

incorrect and the appropriate adjustment would require estimation of the expected return

premium.5

The point here is that the expected return premium should be included in loan FISIM – and

this requires that it not be included in the reference rate used for calculating loan FISIM – but

the expected return premium has nothing to do with deposit FISIM – and therefore should be

included in the reference rate used for calculating deposit FISIM. This implies that the

reference rate for calculating deposit FISIM should be a capital market cost of funds.

2.6 CPI FISIM

Consideration of CPI FISIM highlights a major complication in the theory and measurement

of FISIM - while loans are originated in period 0, the payment of FISIM on these loans takes

place in later periods. This raises the question of what is meant by the price paid by

households for the acquisition of FISIM services in period t for CPI purposes, and what is

meant by the dollars earned by banks for the provision of FISIM services in period t for

national accounts purposes.

One view is that the costs of providing FISIM services on a loan originated in period 0 are all

incurred in period 0, in which case it can be argued that all FISIM earned on the loan should

be allocated to period 0 irrespective of when it is actually paid for. For both national accounts

and CPI purposes FISIM in period t would be calculated only on loans originated in period t,

but FISIM would be measured on a Net Present Value basis.

The alternative view is that the cost of providing FISIM services extends over the life of the

loan, and that FISIM is earned period-by-period over the life of the loan. In this case FISIM

earned in period t by banks, and paid in period t by households would be calculated on all

loans being serviced in period t irrespective of when they were originated.

2.7 Maturity mismatch risk

Banks are exposed to maturity mismatch (or term) risk when they borrow short and lend long.

Banks will be compensated in the form of an expected return premium to the extent that there

is a non-diversifiable component to this risk. The bank will charge a fee to borrowers (and

possibly lenders) to compensate for this risk, and this fee should be considered part of FISIM

for the same reasons that the expected return premium for the non-diversifiable component of

default risk should be included in FISIM.6

5 In reality banks do have equity capital and bank shareholders earn the bulk of the expected return premium.

Depositors only bear a residual risk of default, and the expected return premium demanded by depositors is

likely to be relatively small. The expected return premium could be estimated by the difference between riskless

rates and the bank’s cost of funds in the capital markets.

6 Whether there is a non-diversifiable component, and what the expected return would be if there were, are

difficult questions to answer analytically. Given deep and liquid interest rate derivatives markets it may be that

banks are able to hedge much of their maturity mismatch risk if they want to. However if banks can only partly

The theory here seems relatively uncontroversial.7 The more difficult question is whether the

current and proposed methods for measuring FISIM – more particularly the current and

proposed reference rates – properly include the compensation for maturity mismatch risk.

This question has been front and centre of the debate about the merits of multiple reference

rates.

2.8 Multiple reference rates

Abstract from default risk, and assume that $1000 of short-term deposits funds $1000 of

long-term loans. Loan rates are set by bank management with reference to riskless long-term

interest rates (or perhaps swap rates) and deposit rates with respect to riskless short-term

interest rates. A FISIM margin is added to obtain loan rates, and subtracted to obtain deposit

rates. On this characterisation, it seems clear that expected FISIM on loans and deposits

should be determined by multiple reference rates along a riskless yield curve.

However, if one assumes that the difference between long-term rates and short-term rates is a

measure of the expected return premium for maturity mismatch risk, it seems equally clear

that the use of multiple reference rates eliminates this expected return premium. Put another

way, in this simple example (no defaults) FISIM is the margin between long-term interest

receipts and short-term interest payments. Since the use of multiple reference rates eliminates

much of this margin, it can’t be giving a proper measure of FISIM. By contrast, any single

reference rate would give the whole margin.

In terms of reconciling these views, first note that the difference between long and short rates

should not be interpreted as the compensation for taking maturity mismatch risk. A large

literature on the term structure of interest rates recognises that the shape of the yield curve is

largely determined by inflation expectations. Long rates are higher than short rates because

inflation, and therefore short rates, are expected to increase over time. There are times when

short rates are higher than long rates and this is because inflation, and therefore short rates,

are expected to fall over time.

The important point is that term structures are not static or fixed – they are expected to evolve

over time, and the expected evolution of the term structure is implicit in today’s term

structure. One implication is that over time short rates are expected to have an average close

to the relevant long rate. (This is the basis of an interest rate swap transacted with no upfront

payments or receipts. The average floating rate over the life of the swap is expected to be

approximately equal to the fixed rate). Only the difference between the fixed (longer term)

rate and the average of the floating (shorter term) rates – if a difference exists - can therefore

be interpreted as the compensation for term risk.

hedge this risk using interest rate derivatives, and if the residual risk has a non-diversifiable component, banks

will demand an expected return premium to compensate for this risk.

7 Though note that depositors as claimholders of the bank will also demand an expected return premium to

compensate for that part of the risk that they bear. Depositors bear risk to the extent that the bank may default

and fail to repay depositors

The implication is that on average over time the difference between loan rates and a long

term reference rate would be approximately the same as the difference between loan rates and

a short term reference rate. On average over time FISIM would be approximately the same.

However FISIM is likely to be more variable using short term reference rates as those short

term rates move from lower than the long term rate to higher than the long term rate.

In summary, the use of a short term reference rate for long term loans (a single reference rate)

does not serve to ensure that the current difference between long and short rates is captured as

FISIM – because those short term rates are expected to rise in the future. However, neither

should it because the difference between long and short rates is not a measure of FISIM.

The remaining question is whether the use of a long-term reference rate for long-term loans

and a short-term reference rate for short-term deposits (multiple reference rates) eliminates

the expected return premium for maturity mismatch risk, if indeed an expected return

premium does exist.

If there is a non-diversifiable maturity mismatch risk, and if the expected return premium is

implicit in the existing yield curve (so that for example long-term rates are higher than they

would otherwise be), the bank will capture its expected return premium if it prices off this

yield curve. However using (multiple) long-term and short-term reference rates to measure

FISIM will eliminate the premium. If just short rates are used the premium will show up in

loan FISIM; if just long rates are used the premium will show up in deposit FISIM.8

Together with the practical difficulties involved in implementing a multiple reference rate

approach (discussed in section 4.1 below), this supports a single reference rate methodology.

2.9 Summary of the theoretical position

A summary of the theoretical position is:

The credit spread should not be included in FISIM

The expected return premium for default risk should be included in loan FISIM

The expected return premium for maturity mismatch risk should be included in loan

FISIM

Loan FISIM in period t could be defined in terms of loans originating in period t only,

or all loans being serviced in period t irrespective of when they were originated

Riskless rates are the natural reference rates for loan FISIM and cost of funds are the

natural reference rates for deposit FISIM

Multiple reference rates will (erroneously) subtract the expected return premium for

maturity mismatch risk.

8 And in this simple example a weighted average reference rate would distribute the expected return premium

between loan and deposit FISIM. More generally weighted average reference rates have been advocated as a

way of capturing (some of) the benefits of multiple reference rates without eliminating the expected return

premium for maturity mismatch risk.

3. Measurement of FISIM

3.1 Naïve approaches to the measurement of FISIM

The definition of loan FISIM as the product of the margin between the loan rate and the

reference rate and the loan balance seems uncontroversial. The difficulties are all in the

implementation – what loan rates to use, what reference rates and what balances.

It is reasonably obvious that quoted loan rates – or indicator rates – include the credit spread

and that their use as loan rates will overstate loan FISIM. The obvious alternative would be to

rely on reported interest received rather than indicator rates. Reported interest received in

period t is divided by the reported balance in period t to give the loan rate in period t. FISIM

would then be written as:

FISIM = [interest received/balance – reference rate] * balance … (1)

or

FISIM = interest received – [reference rate * balance] … (2)

The obvious problem with this approach is that the reported interest in period t divided by the

reported balance in period t in equation (1) merely recreates quoted interest rates that include

the credit spread – an expected default rate should be subtracted.9 Furthermore, if the relevant

concept is expected rather than actual FISIM, then FISIM on loans made in period 0 should

be based on expected rather than actual balances over the life of the loan.10

The same key point can be made with reference to equation (2). Interest received should be

adjusted for the principal amount of expected defaults. This is the point made in section 2.4

and elaborated by Hood (2010).

The important bottom line for measurement purposes is that information on default rates is

required for a proper measurement of FISIM.

3.2 The problem of unexpected changes in reference rates over time

FISIM in period t on a portfolio of loans originated in period 0 should be measured with

respect to the period 0 reference rate (in other words, the second term in equation (2) above

should be the period 0 reference rate times the period 0 balances). However the naïve

implementation of equation (2) relies on the period t reference rate. This is a problem if

reference rates change. Refer again to the simple example of section 2.1. If riskless rates

change from 4.5% in period 0 to 4% at in period t, the naïve approach will inflate FISIM on

9 Note that there would not be the same problem for non-performing loans carried at, and reported at, book

values. 10

Though in the steady state actual defaults and actual balances will equal expected defaults and expected

balances on average over time

loans by the difference – 0.5% times balances. In periods of interest rate volatility this effect

will translate into (spurious) volatility in the FISIM measure.11

Two methods have been suggested for addressing this problem. The first is to use reference

rates that are appropriately-weighted averages of past reference rates. This is difficult to

implement in practice.12

The second is to base the FISIM measure on period t reference rates

and the period t market value of loans (Fixler and Zieschang (2010), p22). The formula is the

following modification of equation (2) above:

FISIM = interest received – [period t reference rate * period t market value of balance]

The second term is an approximation to the period 0 reference rate * period 0 balances (ie

book values).

3.3 Measurement of FISIM in the Australian National Accounts

3.3.1 Compilation of the interest matrix

The first step in the calculation of FISIM in the national accounts is the compilation of an

‘interest matrix’ showing the flow of interest between institutional sectors. For most sectors

the total interest paid and received is available directly from source data such as APRA. For

the most part, however, inter-sectoral flows are not available from source data, though there

are some exceptions such bank housing interest paid. Inter-sectoral interest flows are

modelled using RBA indicator rates together with balances available from the Financial

Accounts. The indicator interest flows are then pro-rated to ensure the aggregate interest flow

is consistent with the control totals reported in the APRA data. In other words, the inter-

sectoral interest flows are benchmarked to the aggregate interest flows.

3.3.2 Calculation of FISIM

Given interest flows and balances it is possible to calculate rates of interest on loans and

deposits. These rates are referred to as “effective” rates to distinguish them from contractual

or indicator rates.

The ABS uses the midpoint between the effective rate on loans and deposits as the reference

rate. FISIM on loans is the effective rate on loans minus the reference rate multiplied by loan

balances. FISIM on deposits is the reference rate minus the effective rate on deposits

multiplied by the balance on deposits.

11

The volatility is spurious because it is a mark-to-market effect that should not be reflected in the measure of

bank output and production. As argued above, the proper measure of bank output and production is an expected

FISIM measure. 12

Though note that using a reference rate equal to the midpoint between loan and deposit rates effectively

achieves this end. See the discussion in section 3.3.

Figure 1 plots nominal FISIM over the past 10 years, including the GFC period, for all

sectors and for the household sector.13

(Loan and deposit FISIM is shown separately in

Appendix 1).

Figure 1 Nominal FISIM for all sectors and for households

For both households and all sectors, FISIM rose steadily over the period, but accelerated at

the onset of the subprime crisis in mid-2007 for household FISIM, and from the onset of the

GFC in mid-2008 for total FISIM. In both cases FISIM rose over 50% between March 07 and

March 09. In a midpoint methodology for FISIM, the only factors that influence time series

variability of FISIM are changing margins between loan and deposit rates and changing

balances. The charts in Appendix 2 show that margins rose about 15% from Sep 08 to March

09, with the bulk of the rise in nominal FISIM due to an increase in balances.

3.3.3 Assessment of the ABS methodology

The ABS methodology is a naïve approach in that it fails to subtract expected defaults from

reported interest received and it uses reported balances for period t rather than original

balances from period 0. It therefore fails to remove the credit spread.

However the use of midpoints as the reference rate largely mitigates the spurious volatility

due to unexpected changes in interest rates (see section 3.2). This is because midpoints are

(by definition) based on reported loan and deposit rates that in themselves are weighted

averages of past loan and deposit rates. The lower volatility of FISIM based on midpoints is

evident in empirical analyses such as that reported below comparing the performance of

different reference rates through the GFC. These consistently show that FISIM based on

midpoints is less volatile than FISIM based on exogenous reference rates.

13

The household sector here includes owner-occupied housing

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Nominal FISIM ($m)

All Sectors Households

3.3.4 Price and volume decomposition

The ABS calculates a Laspeyres Chain Volume Measure (CVM) for FISIM in two steps.

Nominal balances are first deflated by the IPD for Domestic Final Demand to remove the

impact of prices on balances. The Laspeyres CVM for FISIM then employs margins as prices

and deflated balances as quantities.

Figure 2 plots nominal and volume FISIM over the past 10 years, including the GFC period.14

Figure 2 Nominal and volume measures of FISIM for all sectors

3.4 Measurement of FISIM in the Australian CPI

The ABS also compiles a price index for FISIM that was included in the CPI until the recent

16th

series review of the CPI, when it was removed from the headline measure on the basis of

concerns about its impact on the CPI through the GFC.15

The conceptual approach to compiling the price index for FISIM in the CPI is similar to that

used in the national accounts, and the CPI price index for FISIM therefore suffers the same

14 The quarter-by-quarter volatility in volume FISIM evident in this chart is due to the fact that nominal FISIM

is first calculated on an annual basis and a quarterly current price series is obtained by diving annual FISIM by

4. However the CVM is calculated on a quarterly basis. This introduces a (spurious) volatility into the quarterly

volume measures.

15 However note also that the price index for FISIM continues to be included in an analytical series. The ABS

plans to include FISIM in the CPI once measurement concerns have been addressed.

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Total FISIM for All Sectors

Nominal ($m) Volume

limitations as the national accounts measure of FISIM. The main difference is in the data

sources employed. While the national accounts compiles interest flows and balances in

aggregate for each institutional sector, the CPI collects interest flows and current balances by

product from a sample of banks.16

Figure 3 plots the CPI price index for FISIM. The chart also includes the IPDs for FISIM

from the national accounts.

Figure 3 The CPI price index and national accounts IPDs for household FISIM

The CPI measure rose and fell sharply through the GFC. This is consistent with the rise and

fall in the margin between loan rates and deposit rates reported in section 3.3.2. Interestingly,

the IPDs for FISIM from the national accounts show markedly different behaviour – they rise

but do not fall. This may be due to scope differences – the CPI measure only covers

household FISIM, though it does include FISIM paid by owner-occupied households.

Nevertheless, the difference raises some concern about the current methodology for

generating volume measures of FISIM in the national accounts and illustrates the importance

of better integrating the measures of FISIM used in the CPI and the national accounts.

4. Empirical tests of different reference rates

In response to the ongoing international debate about the proper measurement of FISIM, the

Inter-secretariat Working Group on National Accounts (ISWGNA) FISIM Task Force

16

There are also minor differences in the detail – for example, the CPI calculates a separate reference rate for

each bank.

80

90

100

110

120

130

140

Deposit and loan facilities (CPI) IPD

requested that member countries conduct an empirical analysis of the performance of

different approaches to the measurement of FISIM through the GFC.

4.1 Australian results

The following analysis compares FISIM based on the (endogenous) midpoint methodology

and a series of exogenous reference rates: the short term interbank rate, the 5-year

government bond rate, a weighted-average rate and maturity-matched (multiple) reference

rates. The analysis focuses on bank FISIM for the household sector.17

The measurement of FISIM using a single reference rate is relatively straightforward. The use

of multiple reference rates is complicated by the limited availability of interest flows and

balances split by maturity. The Australian data do provide balances by product for the

household sector, which enables an approximate split between long-term and short-term

balances. For example, transaction deposit accounts are readily classified as short term and it

is possible to make reasonable assumptions about the split of long-term (>1 year) and short-

term (<1 year) term deposits.

Interest flow data is more problematic because there is no product detail for interest flows

that would enable a direct measurement of interest flows on long-term products versus short

term-products. The ABS has used an approximate method based on indictor rates reported on

the RBA bulletin. Given the long-term and short-term balances, total interest flows are

calculated based on the indicator rates. These flows are then benchmarked to control totals

for total interest reported.18

Figure 4 shows the different reference rates, together with the effective loan and deposit rates

for households.

17 The main results are presented for the household sector a) to facilitate comparison with the CPI analysis in

section 4.3, b) because data on maturity is much better for the household sector, and c) because the

results/conclusions are similar for the household sector alone and all sectors.

18 Essentially, the calculated long-term and short-term effective rates are proportional to long-term

and short-term indicator rates.

Figure 4 Alternative reference rates and effective loan and deposit rates for households

The time profile of alternative reference rates is similar until mid-2007. All rates rise in the

period leading up to the GFC and then fall sharply. However, the fall in exogenous rates is

more exaggerated than the fall in loan and deposit rates, and the midpoint.

Figure 5 shows FISIM calculated using the different reference rates. (Appendix 3 shows the

results for loan FISIM and deposit FISIM separately).

Figure 5 Household FISIM for different reference rates

0

2

4

6

8

10

12

Alternative reference rates and effective rates - households (%)

RR - 5 year Gov Bond Deposit

Loans RR - interbank lending rate

midpoint Weighted avg RR

0

2000

4000

6000

8000

10000

12000

14000

Total FISIM - Households ($m)

Midpoint interbank lending rate 5 yr Gov Bond rate

Maturity matched Avg RR

FISIM calculated using exogenous reference rates is notably more volatile during the GFC

than FISIM calculated using the midpoint reference rate. The additional volatility is due to

the varying ‘distance’ of the exogenous rates from the effective loan and deposit rates (see

figure 4).19

As discussed in section 3.2, this distance varies because exogenous rates are

current (period t) rates while the effective rates on loans and deposits are weighted averages

of past (period 0) rates.

FISIM calculated using exogenous reference rates is also notably higher during the GFC than

FISIM calculated using the midpoint (for the reasons noted in footnote 14). Given that theory

points towards exogenous reference rates this suggests that the midpoint methodology has

understated FISIM during and after the GFC.

Another feature of the Australian results is that all reference rates – including multiple

reference rates – give approximately the same measures of FISIM in the period prior to the

GFC. The reasons are evident from figure 4 – there was very little difference between long

and short rates for much of the period considered.

For households, total FISIM under the maturity matched approach is almost indistinguishable

from FISIM using the interbank rate – even through the GFC – because 80% of loans and

70% of deposits are short-term.

4.2 European results

The Eurostat report “Results on the FISIM tests on maturity and default risk” presents the

results of an empirical study by European countries of different approaches to measuring

FISIM. The study focused on different approaches to the treatment of maturity and default

risk in the calculation of FISIM.

For maturities, countries compared the time series of "implied" loan and deposit rates with

the time series of two possible reference rates: an interbank rate and a weighted average of

long-term and short-term rates, with the weights proportional to balances. Overall, the

weighted average reference rate performed slightly better with respect to reducing the

volatility and incidence of negative measured FISIM. However the results differed from

country to country and were largely inclusive. A limited number of countries were also able

to test a multiple reference rate approach – for the rest suitable data were not available – but

again the results were largely inconclusive.

19 Note that if loan and deposit balances were the same, total FISIM would be the same for all reference rates,

and the only impact of different reference rates would be the split between deposit and loan FISIM. The

reference rate affects total FISIM only if loan and deposit balances are different, which is generally the case. In

the normal case where loan balances are greater than deposit balances, a reference rate closer to the effective

rates on deposits and further from the effective rate on loans will result in higher FISIM.

Countries also attempted to correct for "expected losses on loans going into default" by

accessing data on write-offs and provisions for bad and doubtful debts. However Eurostat

reports that the results were “inconclusive” due to the limited availability of suitable data.

4.3 Comparison of national accounts results with CPI results

A similar study of alternative reference rates has been conducted by the ABS for CPI FISIM

(Barosevic, Conn and Cullen (2010)). For completeness, the key chart from this report is

reproduced in figure 6 below. In this chart, the cost of funds reference rate is a weighted

average of retail deposit rates, short-term wholesale (money-market) funding rates and long-

term wholesale (AA-rated corporate bond market) funding rates.

Figure 6 The CPI price index for FISIM under three different reference rate models

Consistent with the previous analysis, the use of a midpoint reference rate produces a

substantially less volatile price index for FISIM than the use of exogenous rates.20

20

There is a slight difference in the CPI FISIM index curves in figure 6 and figure 3. This is due changes in the

data used to calculate the index.

References

Fixler, D.J. and Zieschang, K.D. (2010), Deconstructing FISIM: Should Financial Risk

Affect GDP? Paper prepared for the 31st General Conference of the International Association

for Research in Income and Wealth

Hood, K.K. (2010), Computing Nominal Bank Services: Accounting for Default, Paper

prepared for the 31st General Conference of the International Association for Research in

Income and Wealth

Zieschang, K.D.(2012), FISIM Accounting, IMF Working Paper

Appendix 1 Loan and Deposit FISIM

Figure 1.1 Nominal Loan FISIM for households and all sectors

Figure 1.2 Nominal Deposit FISIM for households and all sectors

0

2000

4000

6000

8000

10000

12000

Loan FISIM ($m)

All Sectors Households

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Deposit FISIM ($m)

All Sectors Households

Appendix 2 FISIM margins and balances

Figure 2.1 Effective loan and deposit rates and the margin between the two - households

Figure 2.2 Loan and deposit balances - households

0

2

4

6

8

10

12

Inte

rest

rat

e (

% p

.a.)

Effective loan and deposit rates and the margin between the two - households

r(D) r(L) difference

0

200000

400000

600000

800000

1000000

1200000

1400000

Balance for loans and deposits ($m) - Households

Loan Deposit

Figure 2.3 Effective loan and deposit rates and the margin between the two – all sectors

Figure 2.2 Loan and deposit balances – all sectors

0

1

2

3

4

5

6

7

8

9

10

Inte

rest

rat

e (

% p

.a.)

Effective loan and deposit rates and the margin between the two - all sectors

loan deposit Difference

0

200000

400000

600000

800000

1000000

1200000

1400000

1600000

1800000

Balance for loans and deposits ($m) - all sectors

Loan deposit

Appendix 3 Loan and deposit FISIM for households using alternative reference rates

Figure 3.1 Loan FISIM – households – using alternative reference rates

Figure 3.2 Deposit FISIM – households – using alternative reference rates

0

2000

4000

6000

8000

10000

12000

14000

Loan FISIM - Households ($m)

Midpoint interbank lending rate 5 yr Gov Bond rate

Maturity matched Avg RR

-500

0

500

1000

1500

2000

2500

3000

3500

Deposit FISIM - Households ($m)

Midpoint interbank lending rate 5 yr Gov Bond rate

Maturity matched Avg RR