INTERNATIONAL JOURNAL OF MICROSIMULATION (2014) 7(3) 53-79
INTERNATIONAL MICROSIMULATION ASSOCIATION
A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
1
Valentina Michelangeli
Bank of Italy, Financial Stability Directorate,
Via Nazionale, 91, 00184 Roma
Mario Pietrunti
Institute Bank of Italy, Financial Stability Directorate,
Via Nazionale, 91, 00184 Roma
ABSTRACT: We build a microsimulation model to monitor the financial vulnerability of Italian
households. Starting from household-level data from the Survey on Household Income and
Wealth and matching them with macroeconomic forecasts on debt and income, we project the
future path of households’ indebtedness and debt-service ratio. This allows us to assess
households’ vulnerability at a higher frequency and in a more timely manner than by using
household data alone. We find that the share of vulnerable households (defined as those with a
debt-service ratio above 30 per cent and income below the median) over the total population is
projected to be about stable between 2012 and 2014, with a slight decrease in 2015 due to
positive income growth. Their debt is also projected to decrease in those years. Overall, we find
that the dynamics of income growth are the main driver of households’ vulnerability.
KEYWORDS: households’ vulnerability, debt, stress test.
JEL classification: D14, G10.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
1. INTRODUCTION
After the increase in households’ indebtedness in several OECD countries in the period 2000-
2008 (OECD 2010) and the subsequent financial crisis, several central banks began to develop
indicators and models to monitor and evaluate the risks associated with the household sector.
The increasing indebtedness of many households and the consequent weakness of their balance
sheets raised concerns about their resilience to negative shocks, with implications for both
financial stability and economic growth.
To evaluate households’ vulnerability we build on state of the art microsimulation models and we
use data on Italian households available from the Survey on Household Income and Wealth
(SHIW), available up to 2012. Those data provide a comprehensive picture of the household
sector, distinguishing households according to their idiosyncratic characteristics, such as income,
balance sheet, age, education and occupation. However, they are low frequency data and,
moreover, as the survey runs every two years the data become available with about a year’s delay.
Macroeconomic data are instead high frequency and provide more up-to-date information on the
status of the economy from both a real (income) and a financial (interest rates, growth rate in
total debt) point of view.
In this paper we describe a methodology to simulate the evolution of households’ debt that
integrates the microeconomic household data with the macroeconomic data. This exercise allows
us to monitor closely the financial condition of the household sector and hence to evaluate the
impact of possible policy interventions. The methodology is flexible enough to analyse the
evolution of vulnerable households under stress scenarios (e.g. income or interest rate shocks)
and to measure the impact of policy interventions in the household debt market (e.g. suspension
of loan payments) in the short-to-medium run.
The model is explicitly targeted at modelling the vulnerability of Italian households. After a long
period of feeble positive GDP growth, the Italian economy was exposed to the 2007-2009
financial crisis and to the 2011-12 sovereign debt crisis, whose effects are still in place. In such a
scenario, although household debt has been historically low by international standards
2
, the
recent increase in unemployment, along with the weak dynamics of disposable income, affected
the households’ ability to meet their debt obligations. Nonetheless, the adverse consequences
have been partially mitigated by the low interest rates (see Magri and Pico, 2014, for an analysis of
the impact of the crisis on household debt).
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
The vulnerability of indebted households is typically summarized by the debt-service ratio (DSR),
defined as the share of debt payments to income. In line with most studies (IMF, 2011, 2012,
2013; ECB, 2013), we identify as vulnerable those households with a DSR above a given
threshold. These households are considered more likely to be affected by shocks associated with
important changes in interest rates or income. Their sensitivity to shocks is greater when income
is low; hence, in this paper we focus on households with income below the median in the
population. In most of what follows we define as vulnerable those households with a debt-service
ratio above 30 per cent and an income below the median, consistently with previous studies on
the Italian economy (Magri and Pico, 2012). Our flexible framework allows different definitions
of financial vulnerability to be considered, in line with other studies (Bank of Canada, 2012; IMF,
2010): in particular, we also investigate the financial vulnerability of Italian households under a
less stringent debt-service ratio threshold of 40 per cent.
Simulating the evolution of DSR requires information on households’ future income and debt.
Therefore, we first distinguish households according to their income class. For each income class
we estimate the parameters of the income process using historical microeconomic data and we
allow households to have different income realizations. We then require that the income growth
generated by the model be consistent with the growth in nominal income from macroeconomic
projections. Secondly, we impose some structure on the debt evolution by assuming that
indebted households repay their mortgage according to a French amortization schedule, which
implies that the annual repayment is constant until loan termination and the annual interest
expense is calculated on outstanding debt. Annual repayments may be subject to variations for
variable interest rate mortgages only, due to changes in the interest rate. Mortgage debt associated
with new originations is determined starting from microeconomic estimates, which are then
properly readjusted to match the macroeconomic data on total mortgage debt growth. By
combining those projections of income, debt and debt payments we can compute the projected
share of vulnerable households over time. More precisely, since the SHIW at the time of writing
is available up to 2012, we make use of macroeconomic data to simulate the evolution of
indebted households from 2013 to 2015 under different scenarios. In this regard, our model also
fits in the growing literature on nowcasting, as it provides a granular and accurate picture of the
indebtedness of Italian households almost in real-time. A back-testing exercise is performed on
previous SHIW waves and, overall, the model provides a good fit of the data.
Microsimulation tools have been recently developed in central banks and international
institutions. As a way of example, the IMF usually assesses the vulnerability of the household
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
sector in its Financial Sector Assessment Program missions (see e.g. IMF, 2013). A recent
contribution is Ampudia et al. (2014), where a series of metrics for measuring the financial
fragility of Euro Area households is proposed. The results of our exercise are consistent with the
outcome of that paper. One of the closest papers to ours is Djoudad (2010), which performs a
similar exercise on Canadian data. While building on that paper, we enhance the methodology,
providing further contributions to current modelling of households’ vulnerability in several
respects. First of all, we impose some structure in the evolution of debt for existing mortgages by
having each household paying a loan instalment determined according to a standard amortization
formula and its specific debt characteristics. Hence, we do not empirically estimate a process for
total debt growth of existing mortgages starting from the empirical data. In fact, our approach
does not require any estimation of the process of total debt growth, which could produce
estimates that are not statistically significant when the number of indebted households is
relatively small in the total population. Moreover, for each household we compute its loan
payment in each period using the standard amortization formula. Thus, we do not keep the share
of principal on current credit balance fixed. We believe that keeping that share fixed may have
significant consequences on the evolution of households’ debt in the short-to-medium run as
well.
3
Moreover, as the formula incorporates parameters that are important in the simulation of
stress test scenarios, we believe that our approach is more accurate when computing each
household’s loan payment and, subsequently, total aggregates.
We explicitly model mortgage terminations taking into account microeconomic data on mortgage
duration and starting year of the mortgage available on Italian data. This is a major advantage of
the SHIW compared with other surveys that do not provide such data. It avoids making arbitrary
assumptions on mortgage termination that could lead to biases in debt evolution. Finally, we
present a way of introducing mortgage originations obtained from a pseudo-panel that builds on
historical data, adjusted to match the total amount of debt using macroeconomic forecasts.
As a remark, given our focus on financial stability, we develop a framework for evaluating the
vulnerability of the household sector in the short-to-medium run (below two years). Thus, we
concentrated on carefully simulating the evolution of debt (both the existing stock and new
originations) and income, whose changes in the short-to-medium run could have significant
effects on the stability of the entire system. Instead, we maintain the other socio-economic
household characteristics constant, with the only exception of the household’s age. We believe
that this assumption is reasonable given the time horizon simulated. The model, however, could
be extended rather easily to introduce time variation for demographic characteristics. We leave
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
this extension to further research.
The main results of the model for the Italian economy are as follows. In a baseline scenario, in
which interest rates are not expected to change significantly and income growth is expected to be
positive, the share of vulnerable households with income below the median is projected to be
almost stable over the next few years, with a small decrease in 2015 mainly because of the
expected growth in income. Moreover, the share of total debt held by those households is
expected to decrease progressively and to revert to 2010 levels.
4
In particular, in 2015 the share of
vulnerable households with income below the median level is projected to be 2.7 per cent and
their debt equal to 16 per cent of total debt.
In our stress test simulations a projected zero income growth in 2015 (instead of 2.9 per cent) has
a bigger effect on the share of vulnerable households than an increase of 100 basis points in
interest rates. Indeed, a cut in income growth at a macro level affects all households, while an
increase in interest rates directly affects only those households with an adjustable rate mortgage
or new mortgages.
All in all and under alterative scenarios of stress, the share of vulnerable households is not
projected to change dramatically in the next few years; hence, indebted households do not
represent a source of significant risk for the financial stability of the Italian system. These results
are confirmed when we consider the 40 per cent threshold for DSR.
The paper is organized as follows: Section 2 presents the data, Section 3 gives a description of the
model, Section 4 sets out the results and Section 5 concludes.
2. DATA
2.1. Microeconomic variables
The microeconomic data used in the analysis are taken from the 2002-12 waves of the SHIW.
5
This database was initiated in the 1960s with the goal of collecting data on the incomes and
savings of Italian households. Over time, the database has been expanded and currently it
contains detailed information on households’ individual characteristics (age, education,
employment status of the head of household), consumption, income and balance sheets. A
representative sample of the Italian resident population is interviewed so that the SHIW is able to
offer a comprehensive picture of the current status of the Italian household sector. The SHIW
data have been widely used for economic research on household income, debt and wealth (see
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
for instance Guiso et al., 1996; Magri 2007; Jappelli and Pistaferri, 2000, 2010) as well as in
institutional publications (see Bank of Italy Annual Report for 2013, among others). Moreover,
the Eurosystem Household Finance and Consumption Survey (HFCS), a survey initiated in 2010
and coordinated by the European Central Bank, incorporates the SHIW households’ microdata
for Italy.
In our exercise, we use household data on demographics, income, and debt. In particular, we
distinguish between different types of debt: mortgage debt on the primary residence, mortgage
debt on other real estate, and consumer credit.
6
For each type of debt, we observe the
outstanding amount, the initial amount borrowed, the year when the loan was granted, the total
length of the contract, the amount of the annual instalment, the interest rate, and – in case of
mortgage debt – whether it is adjustable rate or fixed rate.
The starting point of our analysis is the cross-section of the most recent wave, namely 2012. In
that year, about 12.4 per cent of the households in our sample had a mortgage debt on a primary
or secondary residence, with an average outstanding debt of about €78,000 and a starting value of
the debt of €115,000. About 50 per cent of first mortgages on the primary residence were fixed
rate mortgages while the rest were mainly variable rate.
7
If we extend the analysis to all kinds of
real estate debt, that proportion remains about the same. About 10 per cent of households had
consumer credit debt.
The database is an unbalanced panel where only half of each wave’s sample is retained in the next
wave of the survey. Therefore, we miss a full historical track of the same households’
characteristics and choices. Following Djoudad (2010) we simulate the income process by
grouping observations according to their income class, while to simulate the new mortgage
originations we construct a pseudo panel referring to other household characteristics.
2.2. Building a pseudo panel
The pseudo panel constructed in this analysis can be considered a new dataset, in which each
observation is the result of grouping together households with the same characteristics.
Specifically, we group households according to the following characteristics of the household
head:
a. Age groups: 18-34 years, 35-44 years, 45-54 years, 55-64 years, 65 and over.
b. Education groups: 1) no education or elementary education, 2) lower secondary
school, 3) upper secondary school, 4) undergraduate or post-graduate study.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
c. Occupation status: 1) not working, 2) working.
We thus obtain 40 groups of households with similar characteristics. This approach allows a
comparison over time to be made of the data for each group of representative households, so
that we can make inferences about the underlying processes of some variables of interest.
2.3. Macroeconomic data
We also gather macroeconomic data that stand as a benchmark for the aggregate dynamics
obtained starting from the microeconomic data in the household survey. The model dynamics for
total income and total debt are corrected by annual adjustment factors, in order to have them in
line with the macroeconomic picture or with its forecasts. The macro data come from three main
sources and are reported in Table 1.
First, we gather data on income growth over years from the national accounts (Contabilità
Nazionale, CN). The variable of interest is income as defined in the CN, which includes imputed
rents. This measure captures the standard of living of households.
8
Nominal income growth was
negative in 2013, while it is projected to be positive and equal to 2.4 per cent and 2.9 per cent
respectively in 2014 and 2015. Those projections indicate expectations of a potential recovery of
the economy, manifested by positive growth.
9
Second, we make use of projections on lending volumes to households for house purchase
developed by the Bank of Italy. This variable represents the volume of loans in banks’ balance
sheets plus an estimate of securitized loans; data for 2014 and 2015 are a projection based on an
internal macro-econometric model. Total debt growth is negative in 2013 and in 2014 and then
positive and slightly below 2 per cent in 2015.
10
Third, we use projections of the three-month Euribor rate obtained from futures contracts.
11
The
data are employed in our model projections of the interest rate, which affect the loan payments
of households holding a variable interest rate mortgage and those associated with new
originations. This choice is a natural one as mortgage rates in Italy are typically tied to the
Euribor rate and so we choose to model those rates equal to the Euribor rate plus a bank spread.
Implicitly, we are assuming that the bank spread remains fixed across simulation periods. This
assumption is typically true for existing contracts, apart from the case of mortgage refinancing.
12
The change in the value of the Euribor rate
13
is negative in 2013 and is then expected to be close
to zero.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Table 1 Macroeconomic aggregates
(Percentages)
2013
2014
2015
Income growth rate at current prices
0.1
2.4
2.9
(national accounts)
Total debt growth
-1.0
-0.3
1.8
(macro model for forecasting debt growth)
Euribor
0.21
0.27
0.32
(3m Euribor and 3m Euribor futures)
Euribor change
-0.65
0.06
0.05
3. THE MODEL
In this section we describe how households’ income and debt evolve over time.
3.1. Income growth dynamics
Households’ income enters in the denominator of the DSR and therefore affects the projected
share of vulnerable households in the economy. We distinguish between disposable income and
disposable income gross of financial charges and net of imputed rents.
14
The first definition of
income is used to classify households according to their living standard and is consistent with the
CN, helping us to match the model statistics with the macro data. The second definition more
closely resembles the actual income available to the household for current expenses and it enters
directly in the computation of DSR. We compute the income growth dynamics following
Djoudad (2010). Specifically, we group households’ income into four classes, j, of equal
frequency.
The process for the disposable income growth for each class j is given by:
),N(~)log()log(
1,,
d
j
d
j
d
tj
d
tj
yy
for j=1,2,3,4 (1)
Starting from household disposable income and dividing it by a factor that reflects its number of
components, we obtain household equalized income. In each period, we compute the thresholds
for each class of equalized income and we assign each household to a specific class.
The process for the growth of households’ disposable income gross of financial charges and net
of imputed rent for each income class j is given by:
),N(~)log()log(
j1,, jtjtj
yy
for j=1,2,3,4. (2)
To estimate the parameters entering in those equations we employ the SHIW data from 2002 to
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
2008 (t=2002,..., 2008). We use this sample period because the Italian economy is expected to
grow in the next few years. Thus, considering a period of positive economic growth such as
2002-08 could help us to better capture expected income dynamics to 2015.
15
The mean and
standard deviation for the income processes
d
y
and
y
are reported for each of the four income
classes in Table 2.
Table 2 Estimated mean and standard deviation for the income process
y
d
growth
y growth
µ
d
σ
d
µ
σ
1
st
– 25
th
percentile
0.035
0.034
0.039
0.025
25
th
– 50
th
percentile
0.029
0.023
0.029
0.025
50
th
– 75
th
percentile
0.026
0.026
0.025
0.023
75
th
– 100
th
percentile
0.025
0.024
0.023
0.024
Table 2 shows that the dynamics for the two definitions of income are fairly similar. Means are
positive as we are estimating the parameters considering a period characterized by positive
income growth. The mean growth is smaller for the 75
st
-100
th
percentile and larger for the 1
st
-25
th
percentile, indicating that households in the lowest group are those that are expected to benefit
the most from an economic recovery. As expected and in line with other studies (see, for
instance, Djoudad, 2010), the standard deviation is higher for lower groups and lower for the
upper groups.
In the model each household receives a random income shock in each period. Since shocks differ
among households we generate some heterogeneity in income growth among households that
belong to the same income class. At the same time the simulated distribution of income growth
for each class is in line with the standard deviations per class reported above.
It is known in the literature that the distribution of any given variable resulting from survey data
almost never matches the one based on macro data. In particular, the discrepancy could be driven
by sampling errors, as surveys are random samples from the population and thus their statistics
could present differences from those of the total population. It could also be associated with
measurement errors or there may be some non-response bias in both the survey and the macro
source. Thus, we could find some discrepancy between macroeconomic projections, computed
though rich autoregressive models, and those based on survey data, whose quality and time-series
properties depend on the microdata used.
In our model, in order to obtain an income growth for the entire economy in line with the
macroeconomic data from the CN we introduce an adjustment factor adj
t
for each time period.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Specifically, we select the adjustment factors so that the per period average growth in nominal
disposable income resulting from the model,
d
t
y
equals the growth in the average nominal
income obtained from the macroeconomics projections,
CN
t
y
:
d
t
y
=
CN
t
y
for t=2013,..,2015. (3)
The adjustment factors introduced in the model are reported in Table 3. It is worth to point out
that the adjustment factors are overall fairly small.
Table 3 Adjustment factors for households’ income
2013
2014
2015
Adjustment factor
0.974
0.970
0.971
After incorporating the adjustment factors households’ disposable income used to compare the
model statistics with the macro projection is:
)log()log(
d
tt
d
t
yadiy
for t=2013,...,2015. (4)
Table 4 shows the growth of the average nominal income in the model and in the macro
projections. The dynamics of income growth for the aggregates are the same. Income growth is
positive and increasing between 2013 and 2015, with the largest growth in 2015.
Table 4 Income growth
(Percentages)
2013
2014
2015
National accounts
0.1
2.4
2.9
Model
0.1
2.4
2.9
Even though adjustment factors are computed starting from disposable income, we also apply
them to our estimates of households’ disposable income gross of financial charges and net of
imputed rents. We believe that this choice has no major effects on the results as the two
definitions of income imply similar econometric estimates of the processes. Therefore,
households’ disposable income gross of financial charges and net of imputed rent, which is used
in the computation of DSR, is given by:
)log()log(
ttt
yadiy
for t=2013,...,2015. (5)
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
3.2. Debt growth dynamics
In order to compute the dynamics of the model for periods t+1 onward, we distinguish between
existing debts and new originations.
3.2.1. Existing debts
We distinguish between mortgage debt and consumer debt.
3.2.2. Mortgage debt
We assume that households with an existing mortgage repay their debt following a French
amortization schedule, which is a widespread amortization schedule for mortgages in Italy. Given
that the share of variable interest rate mortgages among indebted households is quite substantial
in Italy, it is crucial to model an amortization schedule that allows for a readjustment of the
payments associated with a change in interest rates. We also assume that there is no refinancing
or prepayment of the mortgage as prepayment or refinancing are not very common in Italy.
16
For
each household i=1,…, N, where N equals the total number of indebted households, and for
each type of debt y the evolution of the outstanding debt is given by:
tiytiytiy
RPMDebtMDebt
,,,,1,,
(6)
where
tiy
RP
,,
is the annual payment of the principal. The scheduled total annual repayment
tiy
R
,,
,
which includes both the payment of the principal and of the interest, follows a standard
amortization schedule based on the formula:
1)1(
)1(
,,
,,
,,,,,,
A
tiy
tiy
A
tiytiytiy
r
r
rMDebtR
(7)
where
tiy
r
,,
is the interest rate on the debt
tiy
MDebt
,,
, A is the residual duration of the contract.
The annual payment for interest
tiy
RI
,,
is given by:
tiytiytiy
MDebtrRI
,,,,,,
(8)
So that the principal repayment could be obtained as:
tiytiytiy
RIRRP
,,,,,,
(9)
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
3.2.3. Consumer debt
In the baseline scenario, we assume that the annual payment
tiy
RI
,,
for consumer debt
tiy
CDebt
,,
remains constant in the periods of the simulation. We are implicitly imposing a French
amortization schedule with fixed interest rate for consumer debt, which points to fixed payments
over time for the household. As our simulation involves only a few periods and given that the
largest percentage of consumer debt involved payments based on a fixed interest rate in the past,
we believe that this assumption cannot significantly affect the main results.
3.2.4. Total annual payments and total debt
Given that households are allowed to take different types of debt, total outstanding debt is
written as:
)(
,,,,,, tiy
y
tiytiy
CDebtMD ebtDebt
(10)
The annual payment is given by the sum of the annual payments on mortgage debt and consumer
credit:
y
tiyti
RR
,,,
. (11)
3.3. New mortgage originations
New originations bring about a change in the total number and in the average characteristics of
indebted households, inducing a composition effect that affects the share of vulnerable
households in the economy.
To evaluate the debt dynamics associated with new mortgage originations we use the panel
component of the SHIW, including the last three waves (2008, 2010, 2012). We focus on this
period because we noted a non-trivial structural change in the characteristics of the new
originations relative to a pre-crisis period, with an associated reduction of their weight in total
households’ indebtedness.
17
Thus, considering only the last few years allows us to better model
the expected dynamics of debt originations in the near future.
A new mortgage origination occurs when a household has a mortgage debt equal to zero at time
t-1 and a positive mortgage debt at time t (
,0
1,,
tiy
MDebt
0
,,
tiy
MDebt
). Using the pseudo
panel household groups we compute the percentage of new originations in each of those groups.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
For each group k, the number of new originations at time t,
tk,
, equals the number of
originations for the same group in the previous period
1, tk
:
18
1,,
tktk
. (12)
Based on the SHIW historical data, we assume that 50 per cent of the originations have a variable
mortgage rate while the rest have a fixed mortgage rate. To each household with a new
origination we assign a debt amount equal to the mean debt at origination for households
belonging to the same group who had an origination between 2010 and 2012. We then readjust
the amount of debt associated with new originations to match the macro data. Table 5 shows the
total debt growth deriving from the Bank of Italy projections and that generated by the model.
Table 5 Total debt growth
(Percentages)
2013
2014
2015
Macro
-1.0
-0.3
1.8
Model with originations
-1.0
-0.3
1.8
Model without originations
-5.1
-5.7
-6.1
3.4. Mortgage terminations
The reduction in total debt in the model without originations is driven by mortgage terminations.
Some households exit from the pool of indebted households, causing a change in the
composition of the pool itself. We assume that mortgage prepayment is not allowed so
households exit from the mortgage market only after they have completely extinguished their
debt. By introducing mortgage terminations we are then able to capture another important
feature of the mortgage market. We introduce this aspect benefiting both from the Italian
household data, where the duration of the mortgage is explicitly given, and from our model
structure, which allows us to follow the evolution of debt for each household.
3.5. Vulnerable households
Households’ vulnerability is measured referring to the DSR, defined as the share of loan
payments to income. A household is defined as vulnerable if it has a debt-service ratio greater
than a threshold that we set at 30 per cent:
3.0
,
,
,
ti
ti
ti
y
R
DSR
. (13)
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
To evaluate households’ vulnerability in the initial year we make use of micro data from the 2012
wave of the SHIW. The sample is composed of 8151 households. For each household we
compute the debt-service ratio starting from their statement of annual loan payments and
income.
In the following periods household income evolves following the process described above and
the annual mortgage payments are obtained under the assumption of a French amortization
schedule. We are then able to compute a debt-service ratio for each household in each simulation
period.
4. RESULTS
In this section, we present the model results for a backtesting exercise, for the baseline scenario,
for an extended baseline scenario with the possibility of a temporary suspension of the mortgage
payments and for two scenarios of stress (100 basis point increase in the Euribor rate and zero
income growth in 2015). We generate a series of 50 realizations of the shock to each household
income in any simulation year and for each scenario considered. We then derive the median
estimate and a confidence interval for each of the variables of interest. In the figures, the lines
connect the median estimates for different years.
4.1. Backtesting
To test the forecasting performance of our model we perform a backtest on previous waves of
the SHIW (2008 and 2010). The main results of those simulations are reported in Figure 1 and
Figure 2. In particular, we show the percentage of all vulnerable households and of those with
income below the median over total households.
In the following figures red diamonds are historical SHIW data. The values for 2009 and 2011
have been interpolated by cubic splines. The solid blue lines are projections of the median value
of the share of vulnerable households across 50 simulations, while the dashed lines represent the
10
th
and 90
th
percentiles.
19
On average, we are able to replicate quite well the percentage of vulnerable households in 2010
and 2012 starting from the 2008 and 2010 waves. The differences between the model results and
the data are due to two main factors. First, the SHIW data are an unbalanced panel, in which only
half of the sample is maintained in the next wave. As the composition of households can change
there could be differences in the total share of vulnerable households and in their characteristics.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Second, there is some measurement error as is common in any household survey.
Figure 1 Percentage of vulnerable households in the population
Figure 2 Percentage of vulnerable households with income below the median
4.2. Baseline scenario
Figure 3 reports the distribution of the debt-service ratio among indebted households in the
initial year 2012 and in 2015. The share of indebted households with DSR above 30 per cent is
about constant in the two periods.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Figure 3 DSR Distribution
Note: the figure represents the empirical probability density function (pdf) of indebted households according to their DSR.
Figure 4 shows the evolution of the fraction of vulnerable households in the total population in
the baseline scenario. That share is expected to decrease between 2012 and 2015, moving to
about 4.4 per cent. As reported in Table 7, the confidence interval for this value is rather narrow
as 80 per cent of the observations are comprised within 4.3 and 4.5 per cent. In 2013, the
reduction in the share of vulnerable households is driven by the decrease in the interest rate as
households with variable interest rate mortgages pay lower instalments. To a minor extent that
reduction is also associated with negative credit growth. In 2014 and in 2015 positive income
growth drives the low share of vulnerable households, which decreases slightly relative to 2013.
In particular, in 2015 the expected increase in income growth is even larger than in 2014, but at
the same time the increase in total debt growth in the economy generates an increase in indebted
households, inducing a composition effect. However, in line with the supply conditions observed
in recent years, it can be argued that new loans are mostly given to non-vulnerable households
20
and, as a result, in 2015 new originations can only explain about 0.4 percentage points of the
increase in the share of vulnerable households.
21
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Figure 4 Percentage of vulnerable households in the population
Note: results are based on 50 simulations of the model. The solid line represents median results; the dashed lines are results at both the
10th and the 90th percentiles. Data for 2009 and 2011 are interpolated via cubic splines.
In Figure 5, we focus on the percentage of vulnerable households with income below the median.
That percentage is about stable between 2012 and 2013 with a slight decrease of 0.2 percentage
points in 2015
22
, falling in the range of 2.7-2.9 per cent (see Table 8): the decrease is almost
completely driven by positive income growth. Those numbers suggest that also among
households with income below the median there are no major risks for financial stability.
Figure 5 Percentage of vulnerable households with income below the median in total households
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Figure 6 presents the percentage of total debt held by vulnerable households, distinguishing
between those belonging to the lower (below the median) and the upper (above the median)
groups of equalized income. Those percentages decrease between 2012 and 2015. The share of
total debt held by vulnerable households with income below the median moves from 20 per cent
to 16 per cent, in line with the estimates for 2010. Similar to 2010, the increase in income growth
reduces the percentage of vulnerable households; at the same time, the increase in the total debt
growth in 2015 is mainly directed towards households with a low level of vulnerability, so that the
share of total debt held by vulnerable households does not increase significantly regardless of a
positive growth of total debt in the economy.
Figure 6 Percentage of debt held by all vulnerable households
(above and below the median income)
In Table 6 we report the characteristics of all vulnerable households. Some trends are evident.
Vulnerable households belong mainly to the 35-to-54 age group, have secondary education and
are in work.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Table 6 Percentage of vulnerable households by age, education and occupation
(Mean values)
2012
2013
2014
2015
Total
population
(2012)
Age
<35
16.8
14.2
12.9
10.7
9.5
35-44
33.5
31.1
29.3
28.9
20.2
45-54
28.4
32.7
35.0
35.7
21.3
55-64
9.4
9.6
11.0
12.2
16.2
>65
11.9
11.9
11.3
12.1
32.8
Education
No education or primary education
6.2
6.3
6.3
6.1
23.3
Lower secondary education
39.7
38.4
38.3
36.0
35.8
Upper secondary education
39.7
40.7
41.2
45.3
27.8
Undergraduate or post-graduate
14.5
14.8
14.4
13.6
13.1
Occupation
Not working
16.0
15.7
15.1
14.4
41.0
Working
84.0
84.2
84.4
85.4
59.0
4.3. Extended baseline scenario and stress test scenarios
In this section we present an extended baseline scenario and two stress test scenarios. Figure 7
shows how the percentage of all vulnerable households changes in each scenario. Table 7 reports
both the median estimates and ranges. Detailed tables with results are reported in the online
Appendix.
In the extended baseline scenario we consider the baseline changes in income, interest rate, and
total debt (Table 1), but we also include the possibility of obtaining a temporary suspension of
mortgage payments for a specific period of time. This option was widely used in the period 2009-
12, even with bilateral agreements with banks. The cure rate was quite high: more than 60 per
cent of households that obtained suspensions started to repay the mortgage (Bartiloro, Carpinelli,
Finaldi Russo and Pastorelli, 2012). We assume that this option is still available until 2015. We
modelled it following the data from the 2012 SHIW wave, according to which, between 2009 and
2012, 22 per cent of households with a mortgage belonging to the first income class and 9 per
cent of those in the second income class obtained a suspension of mortgage payments over the
period. Under this scenario, the percentage of vulnerable households with income below the
median drops to 2.6 per cent in 2015, hence it is on average 0.1 percentage points lower than in
the baseline scenario.
23
We also consider two alternative scenarios of stress for the financial conditions of indebted
households. First, we consider an increase of 100 basis points in the Euribor rate in 2015 (from
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
0.3% to 1.3%). That increase affects both the loan payments associated with existing variable
interest rate mortgages and new mortgage originations.
24
Relative to the baseline scenario, the
share of all vulnerable households increases by about 0.2 percentage points and their debt
increases by about 2 percentage points.
Second, we consider an adverse scenario in which income growth is equal to zero in 2015. The
shock affects all households. Relative to the baseline scenario the share of all vulnerable
households is about 0.3 percentage points higher and their debt about 2 percentage points higher.
Figure 7 Percentage of vulnerable households under alternative scenarios
Figure 8 gives the results for vulnerable households belonging to the first two income classes,
namely those with income below the median. The mechanisms described above apply and the
share of vulnerable households tends to increase slightly following a rise in the Euribor rate or a
decrease in nominal income growth.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Figure 8 Percentage of vulnerable households with income below the median under alternative
scenarios
Table 7 and Table 8 report the central estimates and ranges for the baseline case, the extended
baseline with suspension of the payments, and the two stress test scenarios that underlie Figure 7
and Figure 8.
Table 7 Percentage of vulnerable households under alternative scenarios
2012
2013
2014
2015
Baseline
Suspension of
payments
Interest rate
shock
Income shock
Central estimate
4.8
4.6
4.4
4.4
4.3
4.6
4.7
10
th
-90
th
percentiles
--
4.5-4.7
4.3-4.6
4.3-4.5
4.2-4.5
4.5-4.7
4.6-4.8
Table 8 Percentage of vulnerable households with income below the median under alternative
scenarios
2012
2013
2014
2015
Baseline
Suspension of
payments
Interest rate
shock
Income shock
Central estimate
2.9
2.9
2.8
2.7
2.6
2.9
3.0
10
th
-90
th
percentiles
--
2.9-3.0
2.6-2.9
2.7-2.9
2.6-2.8
2.7-3.0
2.9-3.1
Figure 9 shows how the share of total debt held by vulnerable households with income below the
median evolves over time in the baseline scenario and in the alternative scenarios described
above. In the baseline scenario, the debt held by those vulnerable households tends to decrease
from about 20 per cent in 2012 to about 16 per cent in 2015, a level similar to the one recorded
in 2010. The reduction is smaller if shocks to income or interest rate occur.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
Figure 9 Percentage of total debt held by vulnerable households with income below the median
4.4. Alternative definition of vulnerability: DSR above 40 per cent
Some central banks and policy institutions (Bank of Canada, FSR 2012; ECB, 2013) define a
household as vulnerable if its DSR is equal or above 40 per cent. We implemented the same
approach and re-computed the percentage of vulnerable households according to the new, less
stringent definition. As shown in Figure 10 the share of vulnerable households now equals 2.3
per cent in 2012 and it is projected to decrease slightly over time, to 2.1 per cent in 2015. As
mentioned before, the reduction is mostly driven by the positive income growth.
Figure 10 Percentage of vulnerable households with DSR above 40%
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
5. CONCLUSIONS
This paper presents a framework to study how the vulnerability of Italian households evolves
over time. Starting from the SHIW microeconomic data and incorporating some macroeconomic
projections on income growth, total debt growth and interest rates, we built a model that
captures the evolution of households’ debt and vulnerability over time. The micro-founded
model delivers aggregate variables that are in line with projected macroeconomic statistics and is
therefore suitable for simulating stress scenarios to evaluate households’ resilience to negative
shocks, such as income or interest rate shocks. The model is also well suited to study the effects
of stress scenarios, alternative policy measures or the effects associated with the suspension of
loan payments driven by banks’ decisions.
We found that the percentage of vulnerable households with equalized income below the median
is projected to be almost stable between 2012 and 2015, being in the order of 2.7 per cent in
2015. Similarly, the share of total debt held by those vulnerable households decreases
progressively to 16 per cent in 2015, a value similar to the one in 2010. When simulating
scenarios of stress, zero income growth has a larger effect on the share of vulnerable households
than a 100 basis point increase in interest rates.
Future research aims to improve the current model. First of all, we could include a probability of
becoming unemployed. Households facing spells of unemployment of different severity and
duration may become vulnerable and so could raise the percentage of vulnerable households.
Other important factors of vulnerability which can be simulated starting from our microdata
could be incorporated. For instance, changes in household composition due to birth of a child or
divorce may affect the income committed to debt repayment and thus the ability to service the
debt. Second, we could try to incorporate other sources of macroeconomic data when modelling
new mortgage originations. Third, we could study other indicators of households’ vulnerability
and accordingly evaluate their evolution over time. Fourth, we could improve our modelling
approach for consumer credit debt.
Finally, one related question that could be addressed in some future work is whether the
dynamics of the mortgage debt has any impact on the outcome indicators at the micro-level. In
particular, it would be worth analysing how the mortgage debt affects some groups of households
that are especially prone to the risk of unemployment and poverty in Italy, e.g. young people
households.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
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le misure di sostegno a imprese e famiglie’, Bank of Italy Occasional Papers (Questioni di economia e
finanza) 111.
Djoudad R (2010) ‘The Bank of Canada’s analytic framework for assessing the vulnerability of
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Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, 13(1), 133-153.
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dall’indagine sui loro bilanci’, Bank of Italy Occasional Papers (Questioni di economia e finanza) 241.
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1
Financial Stability Directorate, Bank of Italy. We thank Paolo Angelini, Antonio Di Cesare,
Giorgio Gobbi, Silvia Magri, Matteo Piazza, Luigi Federico Signorini the editor and two
anonymous referees for their useful comments. The analysis and conclusions expressed herein
are those of the authors and should not be attributed to the Bank of Italy.
2
It currently stands at around 63 per cent of disposable income. See Bank of Italy (2014).
3
This is particularly true for the highest income groups. A back test exercise keeping the share
of principal on current balance fixed is reported in the online Appendix.
4
This result follows, to a minor extent, from our assumption that lending standards will remain
somewhat tight in the next few years compared with the levels observed before the financial
crisis.
5
For a general description of the survey, see
http://www.bancaditalia.it/statistiche/tematiche/indagini-famiglie-imprese/bilanci-
famiglie/index.html?com.dotmarketing.htmlpage.language=1
6
The data allow us to differentiate between first mortgage, second mortgage and third
mortgage on the primary residence and on other real estate.
7
Studies based on data provided by financial intermediaries indicate a higher fraction of
households with variable rate mortgages (see Felici et al., 2012). We also tested our model
assuming 70 per cent of mortgages with variable rate (see the online Appendix); the results are
overall confirmed.
8
As explained below, in the computation of the DSR we use the disposable income gross of
financial charges and net of imputed rent, which better captures the monetary income
available to the household for consumption or as a buffer against unexpected shocks. In the
model we keep track of both definitions of income to be able both to match the
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
macroeconomic aggregates and to compute correctly the DSR. The equalized income,
computed starting from the disposable income and using the OECD equivalence scale, is used
to group households into four income classes.
9
The model has been used to evaluate the evolution of households’ vulnerability in accordance
with the economic slowdown registered as November 2014. We used a baseline scenario in
which both nominal income and lending to households begin to rise again only in 2015 and
interest rates remain almost unchanged. For an overview of the simulation results see Financial
Stability Report No. 2, November 2014, Bank of Italy.
10
Those projections on total debt growth were developed in April 2014.
11
Euribor is short for Euro Interbank Offered Rate. It is defined as “the rate at which Euro
interbank term deposits are offered by one prime bank to another prime bank within the
EMU zone” (http://www.emmi-benchmarks.eu/euribor-org/about-euribor.html).
12
An alternative assumption for new originations, relying on projections of interest rates on
loans for house purchase developed at Bank of Italy, has been tested. The results of the
simulation exercise (available upon request) do not differ significantly from the ones presented
here.
13
Data on the Euribor rate refer to March in each year.
14
The value of imputed rents is provided by each household in the survey. The related questions
are: “Imagine you wanted to let your house/flat, what monthly rent do you or the household
think could be charged? Do not include condominium charges, heating or other expenses.”
and “If you wanted to let the property, what annual rental could the household obtain? total
amount in the year.”
15
Alternatively, to estimate the mean and standard deviation of the income process we could
have used the SHIW data from 2008 to 2012. This sample captures the slowdown of the
Italian economy and therefore would be adequate if the recession were to continue. As shown
in the online Appendix, the estimated income means associated with the period 2008-12 are
negative, but the mean growth is less negative for the 75st-100th percentile and more negative
for the 1st-25th percentile, indicating that households in the lowest group are those that suffer
the most. In periods of expansion and in periods of recession income movements for the
lowest income group are stronger and therefore it is important to take them properly into
account. We also present a sensitivity test using as income parameters those estimated using
the 2008-12 sample period and we find that the share of vulnerable households is projected to
be slightly higher than in the baseline scenario.
16
The share of households renegotiating a mortgage contract was about 2 per cent in 2012,
while the share of those refinancing it was below 3 per cent (Source: Regional Lending
Banking Survey).
17
See e.g. Financial Stability Report No. 6, November 2013, Bank of Italy.
18
In the code we set
2,,
5.0
tktk
in the first period as the survey is biannual.
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MICHELANGELI, PIETRUNTI A Microsimulation Model to evaluate Italian Households’ Financial Vulnerability
19
A further backtesting exercise is reported in the online Appendix. In that exercise we also
present the results for the assumption of an amortization schedule in which the share of
principal on current credit balance is kept fixed, as in Djoudad (2010).
20
This result is confirmed by the case with no originations reported in the online Appendix,
where the dynamics for the share of vulnerable households in the population is very similar to
the case with originations. This result suggests that changes in interest rates or in income are
the primary driving forces of households’ vulnerability.
21
This result is obtained comparing the baseline scenario with the scenario without originations.
22
This result is based on a comparison of the median values obtained across simulations in
different years.
23
This result and the following comparisons with the baseline scenario are based on the
difference between median values obtained across simulations under alternative economic
scenarios.
24
We assume that the interest rate change has no effect on consumer debt.
