VERY PRELIMINARY
DO NOT CIRCULATE
1ST DRAFT APRIL 2005
MORTGAGE LENDING AND THE CHOICE BETWEEN FIXED AND
ADJUSTABLE RATE MORTGAGES
Monica Paiella
Bank of Italy, Research Department
Alberto Franco Pozzolo
Università degli Studi del Molise and Ente Luigi Einaudi
Abstract
This paper analyzes the market for mortgage credit in Italy. First it develops
a simple model of mortgage lending where households can choose between a
fixed interest rate mortgage (FRM) and an adjustable interest rate mortgage
(ARM) and the choice is a function of the mortgage interest rate as well as of
household characteristics. Lenders price loans based on their cost of funds plus a
premium that reflects borrower’s riskiness. Then it estimates the model using the
Bank of Italy’s Survey of Household Income and Wealth (SHIW). The results
show that the probability of taking out a mortgage is increasing in household
income and decreasing in its wealth. It is also increasing in the diffusion of bank
branches and decreasing in interest rates. The probability of choosing an ARM
over an FRM depends primarily on price variables, the interest rate spread in
particular. Initial monthly repayments also seem to matter. Borrower
characteristics do not significantly influence the choice. FRM holders’ demand for
mortgage loans exhibit a much higher price elasticity than ARM holders’ demand.
As a consequence, lenders take greater care in evaluating factors that relate
directly to the risk of default when pricing an FRM rather than an ARM, and FRM
holders pay less on average, ceteris paribus.
JEL classification: D10, G1, G21, E4.
Keywords: household mortgage demand, adjustable rate mortgages, fixed rate
mortgages, lender mortgage pricing, endogenous switching regression model.
Contents
1.
2.
3.
4.
Introduction ......................................................................................................................... 3
An Overview of the Mortgage Market in Italy.................................................................... 7
A Simple Model of Mortgage Lending ............................................................................... 9
Data and Empirical Issues ................................................................................................. 11
4.1 Data............................................................................................................................. 11
4.2 Empirical Issues.......................................................................................................... 14
5. Estimation Results ............................................................................................................. 17
5.1 Choosing whether to take out a mortgage or not........................................................ 17
5.2 Choosing between FRMs and ARMs ......................................................................... 19
5.3 Mortgage demand and interest setting........................................................................ 22
6. Concluding Remarks and Policy Implications .................................................................. 25
Appendix ................................................................................................................................ 26
References .............................................................................................................................. 30
2
1. Introduction1
During the past decade there has evolved an extensive literature dealing with the various
aspects of the demand for housing. The reason is that housing is the major asset in the
portfolio of most households; it is a relatively illiquid investment, with an uncertain capital
value and it is generally highly leveraged, which also makes it a potentially important
channel of transmission of monetary policy. Furthermore, houses are both an asset and a
consumption good. The unusual features of housing wealth and its importance to households
have raised a host of questions including the effects of illiquid risky housing on savings and
portfolio choice (see, for example, Flavin and Yamashita (2002), Cocco (2001) and Paiella
(2001)), the effects of housing wealth on consumption (see, for example, Skinner (1996),
Engelhardt (1996) and Guiso et al. (2005)), the effects of taxation and mortgage laws on
tenure and housing financing choices (see, for example, Poterba (2001), Maki (2001) and
Jappelli and Pistaferri (2004)).
This paper focuses on housing finance, whose implications from a policy perspective are
particularly large due to the effects that changes in interest rates may have on house price
stability, on household behavior and on their welfare. Although there are several channels
through which changes in interest rates can affect housing, the household sector is likely to
play a key role in those countries with predominantly adjustable-rate mortgage contracts
since households bear the risk of higher rates directly through their higher mortgage
payments and smaller remaining income. Nevertheless, it must be said that, although a
nominal fixed-rate mortgage is safe in the sense that its nominal payments are fixed, from
the perspective of the borrower it is also risky because its real capital value is highly
sensitive to inflation.
There is substantial cross-country variation in which type of mortgage contract is most
common. In the United States, for example, most mortgage debt is at rates that are fixed for
the entire duration of the contract (although prepayment options are frequent), whereas in the
UK there is very little mortgage debt that is fixed for more than a few years. In Italy, the
1
The views expressed are those of the authors and do not necessarily reflect those of the Bank of Italy.
Address for correspondence: Monica Paiella, Bank of Italy, Research Department, Via Nazionale 91, Roma
00184, Italy, tel. +39.06.4792.2595, fax. +39.06.4792.3723. E-mail addresses: [email protected];
3
market for mortgages is relatively small, but mortgage lending has been growing fast in the
past seven years, with most new contracts exhibiting rates that are linked to external interest
rates, such as the Euribor.
We analyze household mortgage choice in Italy using a demand-supply model. Borrowers
are allowed to choose between adjustable-rate mortgages (ARMs) and fixed-rate mortgages
(FRMs) and their demand for debt is specified as a function of interest rates and individual
characteristics. Lenders are assumed to have a conservative interest rate risk policy and
charge a rate given by the sum of their cost of funds plus a premium that reflects borrower’s
riskiness and any markup that a lender enjoying some form of market power can charge.
We estimate the simultaneous equation model, distinguishing between the market for
FRMs and the market for ARMs. In the estimation we account for the censoring at zero of
the demand for loans due to rejection of the loan application or to its withdrawal if the terms
are not convenient. We also account for simultaneity of choices regarding the size and the
type of loan. This set up allows to assess whether households can gauge accurately their
circumstances in terms of (non-mortgage related) risk exposure and choose either a fixedrate mortgage or an adjustable-rate one as appropriate. It also allows to identify the
determinants of demand (the loan size) and its elasticity to interest rates. The estimation of
the supply equation (which amounts to an equation for the markup over the lender cost of
funds) gives an insight as to lender’s pricing of borrower’s risk factors and allows to
appraise the extent of lender’s market power in the two markets. By comparing the markup
that lenders apply to borrowers we can see whether there are differences in the pricing of
ARMs and FRMs. For the estimation we use the Bank of Italy’s Surveys of Household
Income and Wealth carried out between 1995 and 2002.
Our first finding is that, conditional on holding a mortgage, the ARM vs. FRM choice
does not depend on borrower characteristics. Overall, pricing variables seem to play a
dominant role and the evidence suggests that in choosing the mortgage type borrowers attach
very much weight to the initial level of repayment. Based on this, one cannot rule out that
many consumers fail to take up mortgage contracts that would best suit their needs. This
could be due to either the inability to assess one’s own future circumstances, and/or to the
inability to choose freely an ARM or FRM contract. Given that a mortgage loan is a [email protected].
4
term and complex product, Italian households seem to prefer focussing on the immediate
mortgage costs, ignoring longer-term income and wealth risk. An alternative explanation for
households’ special consideration for the initial level of repayments, which determines
remaining income, is the presence of liquidity constraints on other credit markets, such as
that for consumer loans which is rather underdeveloped in Italy. In this instance, households’
behavior would not be myopic, but fully rational. Miles (2004) finds evidence of similar
behavior among UK consumers.
The choice between ARM and FRM appears to be independent from that of taking out
(asking and obtaining) a mortgage to finance one’s home purchase. The probability of asking
and obtaining a mortgage (which is joint to that of moving and purchasing a new house)
depends crucially on household resources. In particular, it is increasing in borrower’s income
and decreasing in her wealth. This is consistent with the view that, given the collateral,
banks’ willingness to lend depends on income, which proxies for the ability to pay regularly
the installments on the mortgage: the lower the income, the lower the likelihood of being
granted large amounts of credit, no matter how large one’s wealth is (an income-wealth
interaction term would not affect the result). On the other hand, the higher one’s wealth, the
greater the ability of paying off the house at the time of purchase, and therefore the lower the
demand for credit. Finally, bank competition and especially the diffusion of bank branches in
the area (province) of residence increase the likelihood of taking out a mortgage, but are
irrelevant for the type choice.
The estimation of the mortgage demand-supply model indicates that the amounts lent and
the interest rate charges significantly vary across mortgage markets. There is clear indication
that lenders view FRM holders as relatively less risky, which increases FRM holders’
“outside options” and rationalizes the higher price elasticity of their demand for loans with
respect to ARM holders. As a consequence, when pricing an FRM contract lenders take
greater care in evaluating factors that relate directly to the risk of default and, overall, FRM
holders pay less on average, ceteris paribus. ARM holders appear very much concerned
about the relative cost of borrowing only when it comes to choosing the mortgage type. The
elasticity of their demand to what the market expects to be the average rate on their loan is
less than half of that of FRM holders. Such low elasticity might reflect some form of
5
unobservable optimism that leads these agents to believe that they will actually pay less on
their mortgage than the market forecasts.
To the best of our knowledge, this type of structural approach to analyze mortgage
lending and the choice between ARM and FRM has not been attempted before. Most
existing literature on mortgages takes a demand perspective, treats the mortgage type
selection as a purely dichotomous choice problem and ignores price endogeneity concerns,
giving a partial view of the problem. The results that we obtain show that allowing for a
supply side, even as simple as ours, gives the policy maker important insights regarding the
functioning of the market for ARMs and FRMs, disentangling the effects of different
borrowers’ behaviour on the risk that they face themselves from that they put on the lenders.
There is a large academic literature on mortgage choice, both theoretical and empirical.
The studies that our paper is closest in spirit to are Gary-Bobo and Larribeau (2002 and
2003), which explain mortgage interest rates and loan sizes simultaneously. Gary-Bobo and
Larribeau (2002 and 2003) develop a model of mortgage lending with (liquidity constrained)
borrowers maximizing their utility, subject to a budget constraint, and lenders maximizing
their profits, subject to a zero-profit (competitive equilibrium) or to a zero-surplus
(discriminating monopolist) condition. Their French data-based estimates of the risk premia
in the competitive equilibrium indicate the presence of market power, with the estimated risk
premia reflecting interest rate markups imposed on borrowers. Our analysis depart
significantly from Gary-Bobo and Larribeau’s work as we focus on the differences between
lending and borrowing at fixed as opposed to adjustable rates. Hence, we distinguish
between FRM contracts and ARM ones and allow for different equilibria on the two
markets. Our evidence regarding the determinants of the choice of ARMs versus FRMs can
be compared directly to that of Dhillon et al. (1987) and Brueckner and Follain (1988) for
the US, who also find that price variables play key roles in mortgage choice, whereas
individual borrower characteristics have a weak influence. Our evidence regarding the
mortgage type choice also provides a setting to test some of the predictions of Cocco and
Campbell (2004), who study the choice between FRM and ARM contracts within a life-cycle
model with households subject to labor income risk and borrowing constraints.
The rest of the paper is organized as follows. Section 2 provides a thorough picture of the
market for mortgages in Italy, mainly based on the Banks’ supervisory reports to the Bank of
6
Italy. Section 3 introduces the model we intend to use to assess the functioning of the market
for mortgages in Italy. Section 4 presents the data and section 5 the results of the estimation.
Section 6 draws some tentative policy implications and concludes.
2. An Overview of the Mortgage Market in Italy
Despite its rapid growth, the mortgage market in Italy is relatively small, as compared to
that of most other developed countries. As a share of GDP, the stock of mortgages for home
purchases has risen from slightly more than 6 percent in the early nineties to almost 14
percent at the end of 2004 (Figure 1). In a cross country comparison, considering the stock of
all mortgage loans, in 2003 the ratio of Italy residential debt to GDP was about a third of the
EU15 average and less than a fifth of the ratio for the US, as Figure 2 shows. Mortgage
credit is particularly high in the Netherlands, due to the generous tax treatment of mortgage
debt, in Denmark, in the United Kingdom and in Germany. Among the countries considered
in the figure, only Hungary, Latvia and Poland had lower levels than Italy.
The strength of the mortgage (and housing) markets in Europe can partly be explained
by the favorable interest rate conditions. Falling rates have fuelled demand for housing loans
in the euro area and supported the strong increase in house prices in Italy (figure 3) and other
countries. Figure 4 shows the interest rates charged in Italy according to the initial fixation
period of the interest rate. As expected from the shape of the yield curve, rates charged for
variable rate loans and those fixed for up to one year are lower than others; however, even
rates charged for longer terms fixed-rate loans have fallen significantly.
Figure 5 reports the composition of mortgage lending in Italy, by fixation period of the
interest rate. In 2004 over 90 percent of loans were at rates that are variable or fixed for up to
five years. Countries that are in many other respect very similar to Italy – in terms of GDP
per capita, demographic and industrial structure, degree of development of capital markets –
have very different housing finance system. Overall, at one end, there is France, with almost
half of lending at rates that are fixed for 10 years and over; at the other, there are Finland and
Portugal (and the UK), where basically no loans are granted at rates that are fixed for over
five years. In the euro area as a whole, in 2004, 16 percent of all new mortgages were at rates
that are fixed for 10 years or over; the corresponding figure for the US was about 75 percent.
7
Differences across countries arise also in other dimensions of mortgage contracts. The
amortization period differ significantly across countries. When amortization periods are
longer, households have smaller monthly payments for a mortgage of a given size, but are
also more vulnerable to changes in interest rates. According to the IMF (2002) report,
amortization periods are ten to fifteen years in Italy. Similar terms hold in France, Germany
and Spain. Amortization periods are approximately thirty years in the US, Netherlands and
Japan and twenty-five years in the UK and Canada.
In Italy, the average typical debt service ratio (ratio of mortgage and interest payments
over disposable income) amounts to 19 percent, a level similar to that recorded for the US
and France (20 and 18 percent, respectively), higher than that for the UK (13 percent), but
much lower that the levels of Spain, Germany and other EU countries who report ratios
above 30 percent.
As to the average loan to value ratios at origination, in Italy it is capped at 80 percent
unless the mortgage is guaranteed by third parties and the 1970-1995 average of maximum
loan-to-value for new loans to is relatively low, around 58 percent. In the US, UK, Germany
and most other countries it is over 75 percent.2 Borrowers are likely to have easier access to
mortgage credit in those countries where mortgage lenders recover the house quickly after
borrower default. According to Bianco et al. (forthcoming), these foreclosure proceedings
generally run a year or less in most industrialized countries, but can take as long as five years
in Italy. Because these lengthy foreclosure proceedings are costly to lenders, they may
compensate requiring large downpayments or restricting credit in other ways.
From a supply side perspective, over the past 7 years loans to households for home
purchase have risen also as a share of bank total loans, from 8 percent in 1987 to over 15
percent at the end of 2004. In a cross country comparison, in 2004 the ratio of Italy
household residential loans to bank total loans was still about half the EU average, as figure
6 shows. As a share of total loans to households, mortgages amount to slightly more than 50
per cent in Italy, while in the rest of the euro area they average around 70 per cent (figure 7).
In the last six years, the rate of growth of household mortgages has constantly exceeded
that of total bank loans to the non-financial sector, with a particularly strong acceleration in
2
These loan to value ratios are taken from Bianco et al. (forthcoming). The value reported for Italy should
be taken with caution, because it varies somewhat across different studies and reports.
8
the South (figure 8). Overall, in the Center and in the South mortgages account for a larger
share of loans to the non-financial sector than in the North of Italy. They also represent a
relatively larger share for mutual banks (figure 9) and for small and very small banks (figure
10). In terms of market shares, limited company banks prevail, although mutual banks have
increased steadily their share in the last years, mostly at the expenses of cooperative banks
(figure 11). The market share of branches of foreign banks has increased from less than 1 per
cent to almost 3 per cent, with some oscillations due to acquisitions by Italian banks.3
3. A Simple Model of Mortgage Lending
When demanding a loan for home purchase financing, households can choose between
two types of contracts, adjustable rate mortgages (ARM) and fixed rate mortgages (FRM).
Conditional on the type of contract, we assume that the demand for loans is a function of
household characteristics, which determine households’ desired level of housing, and of the
expected cost of the mortgage. We then specify household demand for loans as follows
(omitting the subscript h):
Lmt = Φ m ( x )Wtγ−1 Atσ (P m )
m
m
−ε m
e ut , m = FRM, ARM
(1)
where Lm denotes time t demand for a mortgage of type m of duration T and P m is the unit
cost of borrowing. Φm(x) is a function of observable household characteristics x, W denotes
its wealth and A is the down-payment on the house. um denotes household unobserved
heterogeneity, which includes all those household’s unobservable characteristics that affect
its loan demand. γm, σm, and εm are positive parameters. Since the loan size and type choices
are simultaneous, the regime switching mechanism (ARM versus FRM) cannot be treated as
exogenous. This simultaneity brings into the analysis a self-selectivity problem that needs to
be addressed in the empirical appraisal of the model.
We assume that lenders have a very conservative interest rate risk policy. They sell
bonds or certificates of deposits to finance their loans and match the payments on their debt,
bearing interest rate i, with the timing of the revenues from their mortgage portfolio. We also
3
Data for branches of foreign banks relative to December 2003 and March 2004 reflect the acquisitions of
foreign entities by part of Italian banks.
9
assume that they can fund any demand for mortgage credit at the current rate, i. Hence, the
interest rate on a T-period FRM granted at t to household h is given by:
h
h
rt FRM
= i t ,T + θ tFRM
,
,T
,T
(2)
where it ,T is the interest on a T-period bond issued at time t, and θ t,FRM
T
h
is a mortgage
premium that compensates the borrower for the default risk and captures any additional
markup that a lender endowed with some form of market power can charge.
h
rt FRM
corresponds to the cost of borrowing of FRM holders.
,T
The date τ interest rate on a T-period ARM granted at time t is given by:
h
h
rτ ARM = iτ + θ tARM
,
,T
(3)
h
is the
where iτ is the interest on a 1-period bond issued at time τ, with τ∈[t, T], and θ t,ARM
T
mortgage premium, which is fixed throughout the life of the mortgage. Hence, the annuity
varies because iτ may change at each τ. However, if the pure expectation hypothesis holds
and returns are lognormal and homoskedastic, E t [i t ,T − iτ ] ≈ (1 / 2 )Var[i t ,T − iτ ] , with
Var[it ,T − iτ ] measuring the quantitative importance of the Jensen’s inequality effect in a
lognormal homosckedastic model.4 Hence, per unit borrowed, ARM holders can expect to
pay on average approximately the following:
P ARM ≈ i t ,T + θ tARM
− (1 / 2 )Var (i t ,T − iτ ) .
,T
(4)
Notice that the term in the variance is constant under the assumption that returns are
homoskedastic; hence, it cannot be identified, as it cannot e disentangled from the constant
in the demand equation. The Appendix includes an alternative specification of the costs per
unit borrowed for ARM and FRM holders.
We specify the interest rate premiums, which are set when the loan is granted, as
follows:
θ tm,T = θ 0m + θ 1m ' hh + θ 2m ' b + θ 3m ' (Lh / H h ) + θ 4m (Q hm / Y h ) + v m ,
h
10
m = FRM, ARM
(5)
where hh is a vector of household characteristics that proxy for borrower’s default riskiness;
b is a vector of characteristics of the local credit market, to capture competition in lending.
L/H is the loan-to-(house) value ratio and Q hm / Y h is the debt service (capital + interest) to
income ratio; together they measure the borrower’s “effort ratio” and capture the idea that a
heavy debt burden increases the risk of repayment problems.
Taking logs of (1) and using (3), (4) and (5), we obtain the following econometric
specification, determining the loan size and risk premium simultaneously (omitting again the
subscript h):
log( Lmt ) = ϕ m ( x ) + γ m log(Wt −1 ) + σ m log( At ) − ε m (it ,T + θ tm,T ) + u tm
θ tm,T = θ 0m + θ 1m ' h + θ 2m ' b + θ 3m ' (L / H ) + θ 4m (Q m / Y ) + v m
(6)
(7)
m = FRM, ARM
Equations (6) and (7) define our problem, which is switching model with endogenous
switching, since households choose the mortgage type. Each regime consists in a classical
simultaneous equation system, where the endogenous variables are the requested loan and
θ t,mT , the interest rate premium. Model identification is due to classical parameter and
exclusion restrictions and will be discussed to greater extent later in the paper. um and vm are
well-behaved,
( )= σ
E v hm,t
2
2
vm
classical
disturbances
E (u hm,t ) = 0 ,
with
E (v hm,t ) = 0 ,
( )= σ
E u hm,t
2
2
m
,
and E (u hm,t , v hn,t ) = 0 , ∀ m, n; m = ARM, FRM, n = ARM, FRM.5 After
addressing the selection issue due to the endogeneity of the mortgage type choice, we can
estimate the two regimes separately.
4. Data and Empirical Issues
4.1 Data
We estimate our model using the Bank of Italy’s Survey of household income and
wealth (SHIW). The SHIW is a representative sample of the Italian resident population and
4
See Campbell et al. (1997) for a discussion and a derivation of this result.
5
There is no reason to expect u and v to be correlated, since the former reflects household unobservable
heterogeneity and affects the demand for loans, whereas the latter is a random noise in the equation for the
interest rate premium.
11
provides detailed data on household socio-demographic characteristics, consumption,
income and balance sheet items.
We use data from the surveys run in 1995, 1998, 2000 and 2002, which are broadly
homogeneous as to the sampling methodology, the sample size and the contents of the
information collected. Over the period considered, each survey covers about 8,000
households. For an exhaustive description of the data, of the sampling methods and issues,
see Brandolini and Cannari (1994), D’Alessio (1997), D’Alessio and Faiella (2000, 2002a
and 2002b) and Biancotti et al. (2004).
We exclude those households whose head is less than 20 or more than 70 years old (18
percent of the sample), those who do not own, nor pay cash rent for their home (9 percent of
the sample) and those with non-positive income (1 percent of the sample). Finally, we
exclude about two percent of mortgage holders whose mortgage annual repayments are
completely inconsistent with the loan.6 The sample composition is reported in table 1: 75
percent of households own their home and around 13 percent of homeowners has mortgage.
Quite surprisingly, the share of households with a mortgage is significantly higher in 1995
than in the following years.7 From 1998, it has risen steadily. About half of mortgage holders
has a fixed rate loan. Around 6 percent of homeowners and over 13 percent of mortgage
holders has moved into their home in the two years prior the interview. Among those who
have moved in the two years prior the interview the share of ARMs is around 55 percent.
It must be acknowledge that the share of ARM holders in the SHIW (and also in the data
that we use for the estimation on the model) is substantially lower than that resulting from
the banks’ supervisory reports to the Bank of Italy (figure 5). The discrepancy may be
explained on several grounds. First of all, data in figure 5 refer to new residential mortgages.
Second, the survey under-sampling of the rich might explain the relatively lower share of
ARM holders, since there is some evidence (see table 2) that among mortgage holders those
with higher income and wealth are more likely to hold an ARM. Furthermore, there might be
some classification errors with households in the survey with a loan whose rate is fixed for a
6
For another two percent of mortgage holders we are able to recover the “true” payments or loan based on
other information, such as that coming from other interviews (for the households in the panel).
7
Notice that after 1995, the Bank of Italy changed the criteria for choosing the company running the
interviews. As a consequence the company in charge of the 1998 survey is different from that which run it in
12
few years reporting a FRM. If we re-classify as fixed-rate those mortgages in the reports
whose rates are fixed for over 1 year, there is a tendency for the difference between the
SHIW and banks’ reports to disappear.
Table 2 reports some summary statistics for the whole sample of households, for that of
mortgage holders, and for several sub-samples. With respect to the sample average, the head
of a household with a mortgage is significantly younger, more likely to be a male, to be
married, is more educated, is more likely to have moved away from her province of birth.
Mortgage holders are concentrated in the North and the fraction of mortgage holders living
the North has increased over time (from below 60 percent in 1995 and 1998 to over 65
percent in the following years). One out of four is self-employed. Household net income is
substantially higher and the number of income recipients is also higher. Most of the
differences in terms of real asset wealth come from the fact that 25 percent of the sample
consist of renters, who tend to be less wealthy than homeowners. In terms of financial
wealth, mortgage holders have fewer financial assets and their liabilities are higher. Overall,
some of the differences might be due to age (or cohort) effects.
The third column of the table reports summary statistics for the sample that we use to
estimate equations (6) and (7) that excludes those mortgage holders who are not recent
movers, specifically those who have moved and obtained a loan more than two years before
the date of the survey. This exclusion is necessary because the SHIW does not contain
sufficient information to obtain reliable measures of the downpayment and income
constraints that non-movers faced when they acquired their home and of their characteristics
at the time (for e.g. income and wealth in previous years are not available). This sample is
somewhat different from that analyzed in column 2: recent movers are slightly better
educated, have a lower income, and less net wealth and financial assets; their mortgage
payments (capital plus interest) are higher and their stock of debt is also higher. Most the
differences are likely to be related to cohort effects since the sample of recent movers is
about 5 year younger than the whole sample of mortgage holders.
1995 and in the previous few years. Further changes occurred in 2000. Since 2000, the survey has been run by
the same company.
13
The last two columns of the table distinguish between recent movers with an FRM and
recent movers with an ARM. The head of a household with an ARM is less likely to be a
male, is more educated and is more likely to have moved away from her province of birth.
ARM holders are concentrated in the North and the fraction living the North has increased
over time (from below 65 percent in 1995 and 1998 to around 73 percent in the following
years). They are more likely to be self-employed or employed in the public sector. They are
better off in terms of both household income and net and real wealth, but they have less
financial assets. Interestingly, they do not exhibit significant differences in portfolio
composition. Their liabilities are slightly higher. In terms of loan characteristics, the amount
borrowed by ARM holders is larger and the average loan-to-value ratio is also slightly
higher, at around 42 percent. The average interest rate is comparable. Mortgage payments
over the year are larger on ARMs, but as a share of earnings, they turn out to be lower (12.8
vs. 13.4 percent). These numbers suggests that SHIW households’ mortgages are somewhat
smaller in absolute and relative terms than those in the official bank statistics, but the
pictures are not so different. Some of the ‘absolute’ differences might once again be due to
the under-sampling of the very rich; some of the ‘relative’ differences might arise from
measurement error in income and wealth. The table reports also the average risk premium
charged to mortgage holders, which has been computed as the difference between the
mortgage rate paid by the household in the year of interview and the interest rate of one-year
government bonds – if it is an ARM – or the interest rate of government bonds with a
maturity as close as possible as that of the mortgage – if it is a FRM. The premium charged
to ARM holders amounts to 1.81 percentage points on average, 0.61 points above the
average premium of FRM holders.
4.2 Empirical Issues
Two issues must be addressed when estimating equations (6) and (7). The first concerns
the censoring at zero of the demand for loans. The second relates to the switching nature of
our model and the distinction between ARMs versus FRMs holders, and is related to the
simultaneity of loan size and mortgage type choice.
As to the first issue, in our data the demand for mortgages is zero for several types of
households. It is zero for renters, for the non-movers, for those who have inherited or just
14
haven’t paid for their home, and for those who have purchased their home without needing
financing. Since we focus only on the non-zero observations, we allow for sample selection
by estimating our model using a Heckman correction. In recognition of the jointness of the
moving, tenure and financing decisions, a single Heckman correction term shall account for
the exclusion of all these agents.
Let D be a dummy variable that is equal to 1 if the agent has purchased her home in the
past two years, and has financed it with a mortgage (L>0). D is equal to 0 if she has
purchased her home in the past two years and has paid it in full, or if she has not purchased a
house or moved in the past two years (L=0). More precisely, let D be defined as follows:
α' w ≥ ω
D =1
iff
,
D = 0 otherwise
(8)
where w is a vector of variables capturing the “affordability” of the home purchase from the
point of view of the household, which will be discussed thoroughly in the next section, and
ω is a zero mean error capturing unobservable factors affecting the choice.
In addition to accounting for the left-hand censoring of the loan variable, the estimation
of our model must allow for households’ self-selection into ARM versus FRM contracts.
Since the loan type and size choices are simultaneous, the mortgage choice cannot be treated
as exogenous. In the following we assume that the choice of purchasing a home and
financing it with a mortgage is independent from the mortgage type choice (the validity of
this assumption can and will be tested). This allows us to treat the issue of self-selection
independently from that of censoring. Then, we can account for sample separation using a
simple two-stage method, where in the first-stage we estimate a model for the probability of
choosing an ARM and in the second we estimate the equations of interest augmented by a
Heckman-type correction term.
Let the mortgage type index I be defined as follows:
γ 'z ≥ζ
I =1
iff
,
I = 0 otherwise
(9)
where z is a vector of variables that include both borrower characteristics and prices and
terms of contracts, which will be discussed thoroughly in the next section, and ζ is a zero
mean error capturing unobservable factors affecting the choice.
15
Since α and γ in (8) and (9) are estimable only up to a scale factor, we shall assume
that Var(ω) = Var(ζ) = 1. We also assume that uARM, uFRM (from equation (6)), ω and ζ have
a quadrivariate normal distribution, with mean zero and covariance matrix:
2
σ ARM





σ A, F
2
σ FRM
σ A,ω
σ F ,ω
1
σ A,ζ 

σ F ,ζ 
0 

1 
.
(10)
Finally, ω and ζ are assumed to be independent from the vm of the markup equation in (7).
The model can then be estimated in stages as follows. First we obtain an estimate of α
using the probit with observations D and compute the Heckman correction term for the
censoring of the loan demand. Also, we obtain an estimate of γ using the probit with
observations I and compute the corrections for the self-selection into a specific regime.
Equations (6) then become:
log( LtARM ) = ϕ ARM ( x ) + γ
ARM
log(Wt −1 ) + σ
ARM
)+
log( At ) − ε ARM (i t ,T + θ tARM
,T
− σ A,ω λ (αˆ ' w) − σ A,ζ λ ARM (γˆ ' z ) + ξ tARM ,
for
I =1
)+
log( LFRM
) = ϕ FRM ( x ) + γ FRM log(Wt −1 ) + σ FRM log( At ) − ε FRM (i t ,T + θ tFRM
t
,T
− σ F ,ω λ (αˆ ' w) + σ F ,ζ λ FRM (γˆ ' z ) + ξ tFRM ,
where λ (•) =
for
I =0
;
(11.1)
,
(11.2)
φ (•)
φ ( •)
φ (•)
, λ ARM (•) =
, λFRM (•) =
, with φ and Φ denoting the
Φ ( •)
1 − Φ ( •)
Φ (•)
marginal and cumulative distributions of the standard normal, respectively, and the ξARM and
ξFRM are the new residuals with zero conditional means. These corrections will also be
applied to equations (7) defining the risk premium.
Next, we estimate equations (11.1) and (7), appropriately corrected, for m = ARM and
(11.2) and (7), appropriately corrected, for m = FRM. We estimate the two systems
separately, which affects the efficiency, but not the consistency of our results.
16
5. Estimation Results
5.1 Choosing whether to take out a mortgage or not
When they decide to move and purchase a new home, households may take out a
mortgage. The probability of moving and purchasing a new home depends on a set of
“affordability” constraints and on household observable and unobservable preference
parameters. The affordability constraints consist in a wealth constraint, which determines
one’s ability to afford the outright purchase of one’s home or the required down-payment,
and in an income constraint, which determines one’s ability to meet the scheduled mortgage
payments. The wealth and income constraints depend on household’s net wealth and income,
on the terms of the mortgage contract, on the desired level of housing – hence, on the
household socio-economic status and demographic characteristics and on the user cost of
housing –, and on the desired level of non-housing consumption. Notice that these
affordability constraints can result in liquidity constraints that would prevent home
ownership.
Table 3 reports the results of the estimation of the probit for the probability that the
household has purchased its home in the twenty-four months prior the interview and has
taken out a mortgage, i.e. has asked and obtained a loan to finance its home purchase.
Interpreting the coefficients of regressors8 is not straightforward as most variables affect
both demand and supply and the signs of the effects might be different and cancel out. The
probability of interest is decreasing in the household head’s age, which is consistent with the
life cycle hypothesis that the demand for credit is relatively higher for young consumers,
whose earnings profiles are upward sloping. This effects seems to prevail over the supply
side adverse selection considerations suggesting that the debts ceilings are likely to be lower
for young consumers than for the rest of the population. Schooling, occupation and the
gender dummy are all insignificantly different from zero. The probability of a mortgage is to
a little extent higher among those who have moved from their place of birth. This most likely
reflects a greater demand for loans due to lower financial support from parents/relatives
when buying a home away from the place of birth, where parents might still be living. The
8
Variables are exactly defined in the note to the table.
17
probability is lower among those living in small municipalities, possibly as a result of wider
intra-household informal credit in small towns. It is higher for married couples, to whom
banks are relatively more inclined to lend, especially when first-time buyers. It is lower the
larger the household size, which probably reflects greater reluctance/problems to move. It is
lower in the Center and in the South, which is consistent with both lower supply, due for
example to greater aggregate risk or contract enforcement problems, and with lower demand,
due for example to preference heterogeneity and wider intra-household informal credit.
Overall, these results are consistent with those of Magri (2004).
The probability of borrowing/being granted a loan is increasing in income, but is
decreasing in the number of income recipients. It is convex in (beginning of period) net
wealth, but the minimum is achieved at the 99th percentile of the distribution. This is
consistent with the view that, given the collateral, banks’ willingness to lend depends on
income, which proxies for the ability to pay regularly the installments on the mortgage: the
lower the income, the lower the likelihood of being granted large amounts of credit, no
matter how large one’s wealth is (an income-wealth interaction term would not affect the
result). On the other hand, the higher one’s wealth, the greater the ability of paying off the
house at the time of purchase, and therefore the lower the demand for credit. Ceteris paribus,
the probability of borrowing/being granted a loan tends to be increasing in the cost of
owning relative to renting (measured as ratio of median province-wide house value of
owners to median province-wide rent for renters), which is consistent with both a greater
demand for and a greater supply of funds where houses are relatively overpriced. It is
decreasing in the cost of housing relative to that of non-durable consumption, which could
result from a substitution effect.
Price considerations do seem to matter, as the probability of holding a mortgage is
significantly decreasing in interest rates: a one percentage point increase in the average
interest rate charged on mortgages (lagged one period) decreases the probability by four
percentage points. Also the term spread of 10-year government bonds on 1-year bills is
significant as a ratio of income, which captures household’s ability to endure future rate
changes: the higher the term spread relative to income the lower the likelihood of borrowing.
Finally, as expected, the probability of asking and obtaining a mortgage is increasing in the
18
number of bank branches and also in the degree of bank competition on the local market for
loans, although the latter coefficient is hardly significant.
5.2 Choosing between FRMs and ARMs
When choosing the mortgage type, households choose between different types of risk. A
nominal FRM is a risky contract because its capital value is highly sensitive to inflation. On
the other hand, the risk of an ARM comes from the short-term variability in the real
payments that are required each period. As a consequence, the mortgage instrument choice
must account for individual aversion to the risk of rising interest rates, borrower expected
mobility and current level of savings. If a household knows that it is likely to move in the
near future or if it is currently liquidity constrained, the most appropriate contract would be
the one with the lowest current interest rate. Numerous proxies have been used to capture the
choice determinants that are household specific. For mobility, proxies include age (the older,
the less mobile), marital status (married couples are less mobile), whether the household has
moved from another area (movers are more mobile) and income and wealth (the wealthier
are more mobile). Households with greater affordability problems are those who live in high
house price areas and with low wealth. The difference between the cost of FRMs and ARMs
measures the ability of ARMs to address affordability problems and proxies for the price
advantage of ARMs for more mobile homebuyers. Notice that the difference is not driven
only by the yield spread between long-term and short-term bond yields, but also by any
difference in the pricing of the default risk on the markets for the two contracts. Finally, in
addition to all these (observable) factors, the choice between FRM and ARM is likely to
depend on individual (unobservable) expectations regarding the relationship between future
short-term rates and observed yield spreads: for example, “optimistic” borrowers might
expect future short-term rates to be lower than the spread-based forecast and, on this ground,
choose an ARM contract.
Table 4 reports the results of the estimation of the probit for the probability that the
household has chosen an ARM. The probit is estimated on the sample of households who
have purchased their home in the twenty-four months prior the interview and have taken out
a mortgage, i.e. have asked and obtained a loan to finance their home purchase. Once again,
19
interpreting the coefficients is not straightforward as the observed outcome is the result of
demand and supply factors and many regressors affect both.
Overall, individual borrower characteristics have little influence on the mortgage choice,
which is in line with the evidence of Dhillon et al. (1987) for the United States. Notable
exception are education, with the more educated more likely to choose an ARM, the area of
residence, with a lower share of ARM holders in the South, and the dummy for small
municipality, whose sign is also negative. The positive relationship between education and
ARM holding can be rationalized on two grounds. First of all, higher schooling attainments
generally corresponds to higher financial awareness (see Guiso and Jappelli …) and ARMs
tend to be more complex that FRMs. Second, the more educated tend to have steeper income
profile and, given the inability to borrow against future income, are more likely to be
liquidity constrained. The negative relationship between ARM holding and the South
dummy could reflect a greater aversion towards income and consumption risk among those
living in the South (see Guiso and Paiella, 2001). In addition to this, there is a tendency for
the probability of holding an ARM as opposed to an FRM to be concave in age, peaking
around 40 and to be higher among households with male head. Instead, it tends to be lower
among married couples, whose mobility tends to be lower. Finally, it is unrelated to
employment, income- and wealth-related characteristics.
In contrast, price variables are significant and have a quantitatively important effect. The
probability of holding an ARM increases by 6 percentage points (12 percent of its sample
mean) if the interest rate differential with respect to FRMs rises by 1 percentage point,
ceteris paribus. The term spread has the expected negative sign, consistent with conventional
wisdom suggesting that if households expect interest rates to rise in the future, they may
favor FRM as they involve a lower degree of rate volatility. However, the coefficient is
scarcely significant. Similarly, the coefficient on the average rate charges on ARMs, which
proxies for the overall loan affordability, is not significant. Hence, assuming that the
expected net present value of the two types of loans is the same, all this provides evidence
that household choices are strongly affected by the initial size of the payment. This is
consistent with the fact that the coefficient on the (instrumented) mortgage payment ratio,
which we include in the regression in column (4) is negative we find a negative relationship
20
between this regressor and the probability of taking out an ARM.9 The implication seems to
be that the size of the initial payment crucially affects household choice, and the probability
of an ARM is higher, the lower its initial payment with respect to the initial payment of
FRM. This is similar to Miles (2003)’s findings that a great many UK households attach
enormous weight to the level of initial monthly repayments, which tend to be lower on
ARMs.
The probit includes also some dummies for the bank where the household holds the
account it uses the most. Over 40 percent of the households in the sample that we use in the
estimation name as its “main” bank one of the banks we include. We cannot consider all the
banks that households name because there is no mortgage type variability. Furthermore,
these dummies are very noisy because we set them to zero not only when the household does
not hold an account at the bank being considered, but also when it does not respond. The
noise induced by this procedure might be a source of attenuation bias which explains the low
level of significance of these variables. Nevertheless, taken together, a likelihood test of the
hypothesis that the combined effect of these variables is zero can be rejected, implicitly
suggesting a role for supply side determinants of the choice between ARMs and FRMs. The
overall evidence presented is robust to the exclusion of these dummies (third column).
In the last column of the table, we run the probit controlling for sample selection, in
order to verify whether the sub-sample of households who have moved in the twenty-four
months prior the interview and has taken out a mortgage, that we use for the estimation, is
“selected”. Our estimates appear robust to the inclusion of a Heckman correction term based
on the regression of table 3, which focuses on the probability that the household has
purchased its home twenty-four months prior the interview and has taken out a mortgage (i.e.
has asked and obtained a loan to finance its home purchase). In fact, the additional regressor
does not affect the coefficients of the other variables in any significant way and a likelihood
ratio test of independent equations does not reject the null (chi-square test statistic of 0.00, 1
degree of freedom, p-value 0.9900). Hence, we can safely consider the mortgage type choice
independent from that of moving and borrowing.
9
The regression is available upon request.
21
5.3 Mortgage demand and interest setting
Table 5 shows the results of the 3SLS estimation of the quantity and price equations: the
first two columns refer to the market for ARMs, the last two refer to FRMs. The left-handside variable of the quantity equation is the log of the initial size of the loan. The left-handsize of the price equation if the markup over the cost of funds charged by lenders, computed
as the difference between the mortgage rate paid by the household over the year and the
interest rate of one-year government bonds – if it is an ARM – or the interest rate of
government bond with a maturity as close as possible as that of the mortgage – if it is a
FRM.
The identification is due to classic parameter and exclusion restrictions, based on the
following considerations. Household income enters linearly in the demand for credit, with
those with higher incomes expected to prefer larger houses and to demand larger loans. The
income level matters also for mortgage pricing, i.e. for the determination of the default risk,
but only indirectly as a benchmark to appraise the affordability of the payments. Similarly,
the market interest rate plays a direct role in the demand equation, as it crucially determines
the cost of funds, and an indirect one in the price equation as a determinant of the
affordability of payments.10 The house dimension affects demand directly and price
indirectly, at the denominator of the loan-to-value variable, to appraise the margin over the
collateral for the lender. Initial wealth has been excluded from the price equation because
mortgages are collateralized and the liquid component, which is what may matter for the
ability to repay, is not observable. Initial (pre-loan) wealth may affect the demand for loans
trough two channels. On the one hand, a large stock of initial resources may reduce the funds
needed to purchase one’s home; on the other, initial wealth may proxy for the borrowers
economic status and be positively related to the level of “desired” housing and to the demand
for credit to purchase a relatively larger house. Finally, we have excluded from the demand
equation the number of income recipients, which may be positively related to household
income stability, and the number of bank branches per inhabitant and the Herfindahl index of
10
We use as market interest rate that on the government bond issued in the year when the household takes
out the mortgage, with a maturity as close as possible to that of the loan (the same that we use in order to
calculate, as a difference, the mark-up). Such rate is a proxy of the cost of funding a FRM of similar maturity
and of the average cost of funds that ARM lenders can expect to pay based on market information over the life
of the contract.
22
bank concentration on the loan market within the province of residence, which proxy for the
degree of competition in mortgage loan contracts. We have also excluded a dummy that
takes on value one if the loan is “subsidized”, which affects demand only via the overall rate
charged by the lender. We do not include mortgage duration because of its collinearity with
the cost of funds measure. Instead we use a dummy11 which is equal to one if the mortgage
duration is greater than the median duration, which is 15 years.
We have estimated the model with and without dummies for the year of interview, which
are highly collinear with such variables as the market interest rate and the provincial price
per square meter of residential housing. We control for censoring and sample selection in
both equations of the system.
Based on a comparison of column 1 and 3 of the table, the market for ARMs appears to
be quite different from that for FRMs. The size of the loan that FRM holders demand
depends exclusively on the cost of the loan and a test of the hypothesis that the coefficient of
the market interest rate is equal to that of the markup does not reject the null (chi-square test
statistic of 0.20, 1 degree of freedom, p-value 0.6579). The market interest rate elasticity
implicit in the coefficient estimate is -0.8712, which implies that a one percent increase in
interest rates decreases loan size by 0.87 percent. A one percentage point increase in interest
rates (corresponding to a 13 percent rise in average rates) would reduce the loan size by 11
percent. The elasticity to the interest markup is lower, around -0.2.
ARM holders demand seems much less elastic to the cost of credit and appears to be
much more sensitive to house prices and individual housing “requirements”. The elasticity to
market interest rates is around -0.35 and the loan size does not seem to be affected by
markup changes. These differences affect mortgage pricing across the two markets: an ARM
holder is likely to pay more for a loan than an FRM holder, ceteris paribus.
11
The mortgage duration could in principle be treated as endogenous. However, this would have increased
the complexity of the model and the equation determining it would be very difficult to determine. Moreover,
the empirical distribution of the duration is very much concentrated at 5, 10, 15 and 20 years. Therefore we
have chisen to consider the duration as an exogenous variable.
12
The elasticity
d log L d log L
d log L
=
can be computed by noticing that:
i . The first term on the
d log i
di
d log i
right-hand-side is the coefficient of the return on long-term bonds in the demand equation; i is set equal to its
mean, which is 7.67 percent.
23
The price equation estimates are also consistent with the hypothesis of significant
differences in the pricing of the risk of default across markets. The FRM default risk
premium is significantly increasing in the level of the loan-to-value ratio – hence the
premium for the risk of default is higher when the loan-to-value is high. The coefficient on
the dummy for long maturity is negative, which implies that, based on affordability
considerations, lenders consider less risky a borrower who repays her loan over a longer
period. The mortgage payment-to-income ratio is not significant, which implies that banks
do not consider this as a major source of risk, at least in the case of FRM holders. Those with
a subsidized mortgage pay 1.9 percentage points less, on average. The premium for the risk
of default is decreasing in the number of income recipients, which proxies for greater income
stability, and it is increasing in the price per square meter of housing, which captures the risk
of an overvaluation of the collateral. The variables proxing for bank competition are not
significant.
The premium for the risk of default on ARM is increasing in the loan-to-value ratio – and
the coefficient is slightly larger – and also in the payment-to-income ratio. The duration
dummy and the dummy for subsidized loan have a negative coefficient. All the other
variables are insignificant and overall the predictive power of the equation is low.
The coefficient on the Heckman correction to account for the censoring at zero of the
demand for loans is never significant, suggesting that the size of the loan is independent
from the choice of getting one and lenders do not view those who ask for a loan as a
relatively riskier subset of the population. The correction accounting for self-selection into a
mortgage market is significant only in the price equation for FRM with a negative sign,
which suggests that default risk premium charged to FRM holders is lower than the average
premium based on observable characteristics only. In other words, the negative coefficient
indicates that those who chose a FRM are on average less risky than the average potential
FRM borrower. This is consistent with the hypothesis that lenders value relatively more
FRM borrowers, which enhances their market power. Hence, the higher price elasticity. All
this makes lenders price FRM loans with greater care, accounting explicitly for observable
factors that relate directly to the risk of default. This is consistent with the overall worse
performance of our model when predicting the premium on ARMs, as opposed to that on
FRMs.
24
6. Concluding Remarks and Policy Implications
The stock of mortgages for home purchases in Italy has risen significantly in the last
fifteen years. Based on the recent trend and on international comparisons, it can be expected
to rise further in the coming years. Understanding the functioning of this market is therefore
of increasing importance, because of the potential effects that interest rates swings – and in
particular rises from the actual historically low levels – can have on the investment and
consumption choices of the growing number of indebted households. The evidence presented
in this paper, although preliminary, has provided a basis to answer some of the most
important questions that are still open.
A first issue is that of the determinants of the rapid surge in house related lending in
Italy in the last decade. Based on the results of the empirical analysis, both demand and
supply factors seem to have mattered. Among the demand factors, the reduction in the
interest rates seems indeed to have favoured an increase of the number of households
holding a mortgage – although the size of this effect is not as significant as it might have
been expected. Among the supply factors, the positive correlation between the number of
bank branches in a province and the probability that its inhabitants hold a mortgage points to
the increase in bank competition as one of the possible explanations for the increase in house
financing. Further evidence consistent with this interpretation comes from the estimation of
the model for the demand and supply of mortgages, showing a negative dependence of the
financing requirement on the interest rate level (and, for FRMs, on the level of the mark-up
charged by banks) and a negative dependence of the mark-up on measures of local bank
competition. Taken together, these results suggest that the reduction in interest rates and the
increase in competition have determined an increase in both the number of household
financed and, to a larger extent, in the average mortgage size.
A second important question that the results of the empirical analysis help answering is
on the characteristics of households holding ARMs, and therefore facing a higher risk of
suffering a reduction in disposable income in case of an increase in interest rates. Contrary to
the indications of the theoretical literature, household characteristics proxying for its risk
aversion, exposure to other risks and for the degree of inflation indexation of its major
income sources seem to have very low explanatory power on the choice between ARM and
FRM. Indeed, only the average interest rate on FRMs seem to have a positive and significant
25
effect on the probability that households choose ARMs. This suggests that ARM holders are
mainly interested in the initial per-period payment that they face than in the overall cost of
the mortgage, without a careful evaluation of the risk faced in the event of a rise of the
reference interest rates. The estimates of the mortgage demand equations provide some
further, although indirect, evidence in favour of this hypothesis. Indeed, they show that the
elasticity of the amount demanded with respect to the interest rate is much lower for ARMs
than for FRMs, and that the elasticity with respect to the mark-up is not even significantly
different from zero in the case of ARMs. A possible rationale for these results is that ARM
holders are only interested in finding the mortgage with lowest possible per-period payment,
and they condition the choice on the amount to demand only on individual housing
“requirements”, such as the size of the house and its price.
Banks seem to be aware of the different types of risk posed by ARM and FRM holders.
While a higher ratio of the value of the loan to that of the house increases the mark-up
charged by banks, the share of household income devoted to per period mortgage payments
has a significant effect only in the case of ARM holders (that, if previous interpretation is
correct, are relatively more likely to face this type of risk). Instead, the potential loss on the
value if the collateral, as proxied by the average price of houses, only affects the mark-up on
FRMs.
Overall, the evidence presented in the paper suggests that some attention should be paid
on the negative effects that an increase in interest rates might have on ARM holders, whose
choices seem to have been dictated more by somewhat myopic considerations on the relative
cost of the loan than by a careful analysis of the available financing options. On the side of
banks, there seems to be no evidence of excessive risk taking.
Appendix
In this appendix we derive an alternative approximation of the per-period payment on
the mortgage. Let the average expected per-period payment on the mortgage be defined as:
( )
t +T
~
P m = T −1 ∑ E t Pτ m , m = FRM, ARM, where t denotes the date when the mortgage (of
τ =t
~
duration T) is granted and Pτ m is the random payment in period τ,τ∈[t,T]. For a household
that at time t borrows for T years and chooses an FRM, per euro borrowed, the self-
26
~
amortising annuity is constant over time, with Pτ FRM = P FRM , and the expected per-period
payment is given by:
P
FRM
=P
FRM
=
)
1 − (1 / 1 + rt FRM
,T
)
1 − (1 / 1 + rt FRM
,T
T
,
(A1)
where rt FRM
is the per-period interest rate, which can vary across households, but from the
,T
point of view of the borrower is fixed over time.
With ARMs, things are slightly more complicated. Let’s consider a household that at
time t borrows for T years and chooses an ARM. The amount that it will pay back at any
period τ > t can be computed by equating (addendum by addendum) the stream of payments
on the ARM to that on a loan of duration T granted at t at fixed rate, that pays back a
constant annuity A(t,T) and exhibits no default (borrower) risk. Hence, at t, the household
expected per-period payment is the following:
τ

(1 + r jARM ) 1 − (1 1 + it ,T )  ∏Tj=1 (1 + r jARM )
∏
~ ARM
j =1

Et P
= E t  A(t , T )
τ
 ,
 = 1 − (1 1 + i )T E t  (1 + i )T
(
1 + i t ,T )

t ,T
t ,T




(
)
(A2)
where it ,T is the interest on a T-period bond issued at time t. rjARM is the interest rate on the
ARM, which the borrows has to pay in period j.
The estimation is less simple than it seems due to the severe non-linearity in variables.
We proceed by approximating the expected per-period payment on the mortgage as follows.
For FRMs, let:
log(P
FRM
) = log1 − 1FRM
 1 + rt ,T

1
≈
 1 + r FRM
t ,T

 

1
 − log1 − 

  1 + r FRM
t ,T

 
T




T





−T
−1
1
 −
)
)
= (1 + rt FRM
− (1 + rt FRM
,
,
T
T
FRM

1 + rt ,T

= 1 yields:
Expanding linearly around 1 + rt FRM
,T
log(P FRM ) ≈ 1 − 1 + ( −T + 1) rt FRM
,T
= (1 − T ) rt FRM
,T
.
= (1 − T )(i t ,T + θ tFRM
)
,T
27
.
For ARMs, things are more complicated. Let x be a log-normally distributed and
homoskedastic random variable. Then, it follows that:
1
log E t (x ) = E t log( x ) + σ x2 ,
2
~
where σx denotes the standard deviation of x. Assuming that Pτ ARM is conditionally
lognormally distributed and homoskedastic, and using the above relationship twice (over the
individual expectations and over the time average, we can approximate the expected perperiod payment on the mortgage log E t (P ARM ) as:
log(P
ARM
 ∏τ (1 + rτARM )
) = log( A(t, T )) + T ∑ E t log j =1 τ  + 12 σ P2
(1 + it ,T ) 
τ =t

−1
 1
≈ 
 1 + i t ,T
T
t +T

 1
 −

1 + i
t ,T


≈ (1 − T )i t ,T
t +T

τ
1
 + T −1 ∑ E t ∑ (rτARM − i t ,T ) + σ P2 .
j =1

2
τ =t

t +T
τ
1
+ T −1 ∑ E t ∑ j =1 (rτ ARM − i t ,T ) + σ P2
2
τ =t
~
where σp denotes the standard deviation of Pτ ARM . The term
τ
∑ (rτ
j =1
ARM
− i t ,T ) is a yield
spread, i.e. the difference between the yield on a one-period bond (rolling return) and the
yield on an T-period bond, a measure of the shape of the term structure up to τ. For
lognormal and homoskedastic interest rates, its expectation measures the quantitative
importance of the Jensen’s inequality effect in a lognormal homosckedastic model. As an
approximation, when the variance terms are small, we can equate the expected log returns
).13 Hence:
on bonds of all maturities, which implies E t ∑ j =1 (r jARM − i t ,T ) = E t (τθ tARM
,T
τ
13
This assumption is acceptable even in our framework, where the choice of interest depends on the
expected term premium. In fact, within a standard framework of a multiperid investment with a T-period bond
and a rolling security, with log and homoskedastic return: E t rτ − i t ,T = −0.5Var rτ − i t ,T . Under stationarity
(
and
Et
homoskedasticity,
∑ (r
τ
j =1
j
E t (τ ) = T −1
)
(
we
can
extend
)
)
all
(
this
)
to
our
equation:
− it ,T = Et − τ 0.5Var ( rj − it ,T ) = −0.5Var ( rj − it ,T ) Et (τ ) . Since in Italy, T is relatively small and
T
∑ k = 0.5 * (T + 1) ,
k =1
we get Et
τ
∑ (r
j =1
j
)
− it ,T ≈ − 0.52 (T + 1)Var ( rj − it ,T ) , which is presumably
small.
28
t +T
1
−1
log(P ARM ) ≈ (1 − T )i t ,T + θ tARM
τ + σ P2
T
∑
,T
2
τ =t
.
T + 1 ARM 1 2
= (1 − T )i t ,T +
θ t ,T + σ P
2
2
Notice that the unconditional variance of the log annuity σ P2 ends up in the regression
constant and cannot be identified.
29
Figures and Tables
Figure 1
Outstanding residential mortgages as a share of GDP in Italy
(percentage values)
15
14
13
12
11
10
9
8
7
6
5
Source: Banca d’Italia, Financial accounts, and ISTAT. Mortgage data refer to the whole
household sector (including producer households) and to all mortgages.
20
05
20
04
20
03
20
02
20
01
20
00
19
99
19
98
19
97
19
96
19
95
19
94
19
93
19
92
19
91
19
90
19
89
19
88
4
Figure 2
Outstanding residential mortgages as a share of GDP, selected countries
(percentage values; December 2003)
110
100
90
80
70
60
50
40
30
20
10
Source: European mortgage federation.
33
Ita
ly
Hu
ng
ar
y
La
tv
ia
Po
la
nd
Sp
ai
n
Fi
nl
an
d
Lu
xe
m
bu
rg
Be
lg
iu
m
Fr
an
ce
G
re
ec
e
Ne
th
er
la
n
De d
nm
Un
ar
k
ite
d
St
Un
at
ite
es
d
Ki
ng
do
m
G
er
m
an
y
Po
rtu
ga
l
Eu
S
w
ro
e
pe
de
an
n
Un
iio
n
15
Ire
la
nd
0
Figure 3
Interest rates on household mortgages, house prices
and loans for home purchase in Italy
(percentage values and index numbers, 1995 = 100)
15
240
12
180
9
120
6
60
3
0
0
I1
98
5
I1
98
6
I1
98
7
I1
98
8
I1
98
9
I1
99
0
I1
99
1
I1
99
2
I1
99
3
I1
99
4
I1
99
5
I1
99
6
I1
99
7
I1
99
8
I1
99
9
I2
00
0
I2
00
1
I2
00
2
I2
00
3
I2
00
4
300
House prices
Loans for house purchase
Real interest rates on residential loans (right hand scale)
Source: Banca d’Italia and Informatore mobiliare. Loans for home purchases are deflated using
the index of house prices and normalized to 1995 = 100.
34
Figure 4
Interest rates on bank loans to households for home purchase in Italy
according to the initial fixation period of the interest rate
(percentage values)
6.0
5.5
5.0
4.5
4.0
3.5
Ja
n03
Fe
b03
M
ar
-0
3
Ap
r-0
3
M
ay
-0
3
Ju
n03
Ju
l-0
3
Au
g03
Se
p03
Oc
t-0
3
No
v03
De
c03
Ja
n04
Fe
b04
M
ar
-0
4
Ap
r-0
4
M
ay
-0
4
Ju
n04
Ju
l-0
4
Au
g04
Se
p04
Oc
t-0
4
No
v04
De
c04
3.0
Average
up to 1 year
between 1 and 5 years
Source: Banca d’Italia
35
between 5 and 10 years
over 10 years
Figure 5
New residential mortages in the Euro area by type of interest rate
(percentage values)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Ire
lan
d
Gr
ee
ce
Lu
xe
m
bu
rg
Po
rtu
ga
l
Fixed rate for no less than five years
Fi
nla
nd
Be
lgi
um
Au
str
ia
Ne
he
rla
nd
Eu
ro
ar
ea
Sp
ain
Fr
an
ce
Ge
rm
an
y
Ita
ly
0
Fixed rate for more than one year and less than five years
Adjustable rate or fixed rate for less than one year
Source: Banca d’Italia and ECB. Data refer to new residential mortgages granted between January
1 and October 31, 2004.
36
Figure 6
Bank loans to households for home purchase in the euro area
as a share of total bank loans
(percentage values)
45
40
35
30
25
20
15
10
Se
p
De -97
c
M -97
ar
Ju -98
n
Se -98
pDe 98
c
M -98
ar
Ju -99
n
Se -99
p
De -99
c
M -99
ar
Ju -00
n
Se -00
p
De -00
c
M -00
ar
Ju -01
n
Se -01
p
De -01
c
M -01
ar
Ju -02
n
Se -02
p
De -02
c
M -02
ar
Ju -03
n
Se -03
p
De -03
c
M -03
ar
Ju -04
n
Se -04
p04
5
France
Germany
Italy
Netherland
Source: Banca d’Italia and ECB.
37
Euro area
Euro area
Figure 7
Bank loans to households for home purchase in the euro area
as a share of bank loans to households
(percentage values)
90
85
80
75
70
65
60
55
50
45
40
35
Se
p
De -97
c
M -97
ar
Ju -98
n
Se -98
p
De -98
c
M -98
ar
Ju -99
n
Se -99
p
De -99
c
M -99
ar
Ju -00
n
Se -00
p
De -00
c
M -00
ar
Ju -01
n
Se -01
pDe 01
c
M -01
ar
Ju -02
n
Se -02
p
De -02
c
M -02
ar
Ju -03
n
Se -03
p
De -03
c
M -03
ar
Ju -04
n
Se -04
p
De -04
c04
30
France
Germany
Italy
Netherland
Source: Banca d’Italia and ECB.
38
Spain
Euro area
Ju
n9
Se 8
p9
De 8
c-9
Ma 8
r-9
Ju 9
n9
Se 9
p9
De 9
c-9
Ma 9
r-0
Ju 0
n0
Se 0
p0
De 0
c-0
Ma 0
r-0
Ju 1
n0
Se 1
p0
De 1
c0
M 1
ar
-0
Ju 2
n0
Se 2
p0
De 2
c0
M 2
ar
-0
Ju 3
n0
Se 3
p0
De 3
c-0
M 3
ar
-0
Ju 4
n0
Se 4
p0
De 4
c-0
4
Figure 8
Outstanding mortgages as a share of total bank loans by area
(percentage values)
28
24
20
16
12
8
North-West
North-East
Center
Source: Banca d’Italia.
39
South
Islands
Italy
Figure 9
Outstanding mortgages as a share of total bank loans by bank type
(percentage values)
27
24
21
18
15
12
9
6
3
Ju
n9
Se 8
p9
De 8
c-9
Ma 8
r-9
Ju 9
n9
Se 9
p9
De 9
c-9
Ma 9
r-0
Ju 0
n0
Se 0
p0
De 0
c-0
Ma 0
r-0
Ju 1
n0
Se 1
p0
De 1
c0
M 1
ar
-0
Ju 2
n0
Se 2
p0
De 2
c0
M 2
ar
-0
Ju 3
n0
Se 3
p0
De 3
c-0
M 3
ar
-0
Ju 4
n0
Se 4
p0
De 4
c-0
4
0
Limited company banks
Branches of foreign banks
Source: Banca d’Italia.
40
Cooperative banks
Mutual banks
Ju
n9
Se 8
p9
De 8
c9
M 8
ar
-9
Ju 9
n9
Se 9
p9
De 9
c9
M 9
ar
-0
Ju 0
n0
Se 0
p0
De 0
c0
M 0
ar
-0
Ju 1
n0
Se 1
p0
De 1
c0
M 1
ar
-0
Ju 2
n0
Se 2
p0
De 2
c0
M 2
ar
-0
Ju 3
n0
Se 3
p0
De 3
c0
M 3
ar
-0
Ju 4
n0
Se 4
p0
De 4
c04
Figure 10
Outstanding mortgages as a share of total bank loans by bank size
(percentage values)
20
18
16
14
12
10
8
Largest
Large
Medium
Source: Banca d’Italia.
41
Small
Very small
Figure 11
Market share of mortgages to households by bank type
(percentage values)
84
12
82
10
80
8
78
6
76
4
74
2
72
0
70
Ju
n9
Se 8
p9
De 8
c9
M 8
ar
-9
Ju 9
n9
Se 9
p9
De 9
c9
M 9
ar
-0
Ju 0
n0
Se 0
p0
De 0
c0
M 0
ar
-0
Ju 1
n0
Se 1
p0
De 1
c0
M 1
ar
-0
Ju 2
n0
Se 2
p0
De 2
c0
M 2
ar
-0
Ju 3
n0
Se 3
p0
De 3
c0
M 3
ar
-0
Ju 4
n0
Se 4
p0
De 4
c04
14
Branches of foreign banks
Cooperative banks
Source: Banca d’Italia.
42
Mutual banks
Limited company banks (right hand scale)
Table 1
Sample Composition
Share of:
1995
1998
2000
2002
Homeowners
0.735
0.741
0.760
0.763
Homeowners with home-related debt
0.214
0.140
0.150
0.165
Homeowners with home-mortgage
0.168
0.100
0.112
0.128
Mortgage holders with FRM
0.547
0.457
0.445
0.501
Mortgage holders with ARM
0.453
0.543
0.555
0.499
Moved in last 2 years with mortgage
0.122
0.124
0.188
0.108
of which: with ARM
0.536
0.517
0.578
0.515
Number of observations
5,450
5,669
5,944
6,183
NOTE: Sample weights are used. FRM holders include those reporting a zerointerest mortgage (1.1 percent of the sample).
43
Table 2
Summary statistics
All households refers to the entire sample of the data set. Recent movers refers to those households who have
purchased their home in the two years prior the interview. ‘With FRM’ and ‘With ARM’ refer to the sub-samples of
recent movers with fixed rate mortgage and ajustable rate mortgage, respectively. Values are weighted means, unless
specified otherwise. All monetary variables are evaluated at euros of year 2000. Shares are also weighted. (a)
indicates that the mean is based on positive observations only.
Recent Movers
All
households
Mortgage
holders
With
mortgage
With FRM
With ARM
Share of home owners
0.750
1
1
1
1
Share of mortgage holders
0.096
1
1
1
1
Share of FRM
0.048
0.496
0.459
1
0
Age
50
44
40
40
39
Share of males
0.726
0.797
0.786
0.809
0.765
Share of married hh
0.740
0.861
0.876
0.874
0.875
Hh size
3.006
3.277
3.075
3.060
3.075
Share with up to elementary
0.305
0.125
0.105
0.139
0.071
Share with up to middle
0.303
0.300
0.299
0.323
0.276
Share with high school diploma
0.304
0.438
0.422
0.371
0.468
Share with university degree
0.088
0.137
0.175
0.167
0.184
Share of movers from province of birth
0.258
0.359
0.364
0.309
0.414
Share living in the North
0.486
0.624
0.647
0.557
0.726
Share living in the Center
0.191
0.188
0.171
0.221
0.133
Share living in the South and Islands
0.323
0.187
0.182
0.221
0.141
Share of self-employed
0.161
0.251
0.236
0.230
0.248
Share of public employed
0.196
0.239
0.236
0.211
0.251
Share of unemployed
Total net income
No. income recipients
Total expenditure
0.036
0.013
0.022
0.048
0.000
30,209
36,941
32,922
30,947
34,963
1.776
1.874
1.739
1.724
1.758
22,014
27,279
27,159
25,368
28,805
Net wealth (mean value)
201,000
220,000
165,000
161,000
170,000
Real assets
179,000
230,000
206,000
199,000
214,000
Home value (mean)
137,000
165,000
165,000
166,000
165,000
Real assets net of home
66,126
65,394
41,247
33,200
48,054
Financial assets
26,656
22,139
16,736
19,487
14,758
Bank and post accounts
12,408
9,871
8,031
8,250
7,955
Government bonds and bills
4,802
3,684
2,971
4,585
1,688
Other financial assets
9,446
8,584
5,733
6,653
5,115
Total liabilities
4,717
31,992
57,785
56,923
58,688
Share of hhs with home-related debt
0.134
1
1
1
1
29,276
31,043
57,579
56,360
58,791
Share of hhs with durable-related debt
0.123
0.172
0.141
0.121
0.161
Durable-related debt (a)
6,162
6,937
5,284
6,621
4,436
Home-related debt (a)
44
Table 2 continued
Recent Movers
All
households
Mortgage
holders
With
mortgage
With FRM
With ARM
Share of hhs with other bank debt
0.009
0.011
0.021
0.014
0.028
Other bank debt (a)
8,760
5,163
4,131
2,126
5,000
Share of hhs with loans from friends
0.026
0.042
0.088
0.104
0.077
Loans from friends and relatives (a)
8,790
10,070
10,879
11,604
10,048
Initial loan
-
41,277
58,452
57,863
59,106
Mortgage duration
-
14
13
13
14
Interest rate (mean, %)
-
-
-
7.142
7.151
Interest rate (st. dev., %)
-
-
-
3.919
3.520
Interest rate (median, %)
-
-
-
6.000
6.000
Mortgage payments over the year
-
5,076
6,117
5,888
6,369
Mortg. payments to earnings (mean)
-
0.111
0.133
0.134
0.128
Mortg. payments to earnings (st. dev.)
-
0.104
0.123
0.130
0.120
Mortg. payments to earnings (median)
-
0. 089
0. 110
0.110
0.109
Loan to value (mean)
-
0.297
0.412
0.402
0.418
Loan to value (st. dev.)
-
0.215
0.243
0.253
0.235
Loan to value (median)
-
0.250
0.375
0.364
0.381
Default risk premium
-
-
-
1.200
1.809
23,246
2,386
323
152
163
Number of observations
45
Table 3
Probability of holding a mortgage
The dependent variable takes the value of one if the household has been granted a mortgage in
the year of interview or in the previous year, zero otherwise. The mortgage interest rate is the
average rate over ARM and FRM. It is gross (1+r), lagged one year and has been deflated using
the consumer price index. The term spread is computed as difference between the return on tenand one-year government bonds. It is in percentage points. Household income does not include
income from financial wealth. Net wealth is beginning of period and has been computed by
subtracting household savings from end-of-period wealth. Cost of owning to renting is the ratio
of median value of housing of owners to median value of housing of renters in the province of
residence. Cost of housing to non-durables is the ratio of rent for renters or imputed rent for
owners to non-durable expenditure. The herfindahl is an index of bank concentration of the
credit market. Standard errors in parentheses. * significant at 10 per cent level; ** significant at 5
per cent level; *** significant at 1 per cent level.
Coefficient
(std.error)
Variables
Average mortgage interest rate
-2.951
(1.798)
0.118
(0.104)
-0.063
(0.020)
-0.735
(1.999)
-2.842
(2.240)
0.011
(0.063)
0.019
(0.055)
0.073
(0.054)
-0.153
(0.052)
0.317
(0.081)
-0.067
(0.027)
0.063
(0.061)
0.034
(0.066)
0.099
(0.170)
1.153
(0.510)
-0.480
(0.310)
-0.126
(0.043)
-0.057
(0.015)
2.80e-04
(9.25e-05)
0.064
(0.053)
0.377
(0.121)
0.456
(0.232)
-0.318
(0.430)
-0.180
(0.075)
-0.360
(0.130)
0.150
(1.901)
Term spread (10 yrs)
Term spread / Income
Age/100
Age/100 squared
Gender (Male=1)
High education attainment
Moved from province of birth
Town <40.000 inhabit.
Married
Household size
Public sector employee
Self-employed
Unemployed
Household income (100,000 euros)
Household income (100,000 euros) squared
Number of income recipients in household
Net wealth (100,000 euros)
Net wealth (100,000 euros) squared
Cost of owning to renting
Cost of housing to non-durables
Bank branches per inhabitant
Herfindahl index
Living in the Center
Living in the South
Constant
46
Sign.
*
***
***
***
**
**
***
***
***
***
**
**
***
Marginal
effect
(std.error)
-0.043
(0.026)
0.002
(0.001)
-0.001***
(0.000)
-0.011
(0.029)
-0.041
(0.031)
0.000
(0.001)
0.000
(0.001)
0.001
(0.001)
-0.002
(0.001)
0.004
(0.001)
-0.001
(0.000)
0.001
(0.001)
0.001
(0.001)
0.002
(0.003)
0.017
(0.008)
-0.007
(0.005)
-0.002
(0.001)
-0.001
(0.000)
4.05e-06
(1.39e-06)
0.001
(0.001)
0.005
(0.002)
0.007
(0.003)
-0.005
(0.006)
-0.002
(0.001)
-0.005
(0.002)
Sign.
*
***
***
***
**
**
***
***
***
***
**
**
***
23076
Observations
Pseudo R2
23,076
0.13
47
Table 4
Probability of holding an ARM (FIXXX)
The dependent variable takes the value of one if the household has taken out an ARM in the year of interview or in the
previous year, of zero if it has taken out an FRM. The average rates on ARMs and FRMs have been computed as
macro area (North, Center and South of the country) averages in each year. The term spread is computed as difference
between the return on thirty- and one-year government bonds. The mortgage payment to income ratio has been
instrumented using housing characteristics (size, location, type…), dummies for sector of occupation and non-durable
consumption, as a proxy of permanent income. The R-squared of the first stage regression is around 0.50. Mortgage
subsidy is a dummy that takes on value one if the mortgage is subsidized by the borrower’s employer, by the
government, …. Maturity ratio is the ratio between the average duration of ARMs and the average duration on FRMs.
The averages are computed as macro area averages per year. The payment ratio is the ratio of mortgage payment in the
year to household total income. High education attainment denotes a household head who has obtained at least a high
school diploma. The Mills ratio controls for the exclusion of those who have not moved in the 24 months prior the
interview and have not borrowed to purchase a new home. The coefficient reported is a correlation estimate. Time
dummies have been included. Standard errors in parentheses. * significant at 10 per cent level; ** significant at 5 per
cent level; *** significant at 1 per cent level.
Basic regression
(1)
Average rate on ARMs
Average FRM-ARM rate
differential
Fitted mortgage payment to
income ratio
Term spread (10 yrs)
Mortgage subsidy
Age/100
Age/100 squared
Gender (Male=1)
High education attainment
Moved from province of birth
Town <40.000 inhabit.
Married
Household size
Self-employed
Household income (100.000
euro)
No. of income recipients
Net wealth (100,000 euros)
Living in the Center
Living in the South
Coeff.
(std.error)
Marginal
effect
(std.error)
0.075
(0.063)
0.148
(0.066)
0.030
(0.025)
0.059
(0.026)
-0.491
(0.343)
-0.231
(0.160)
9.597
(7.635)
-11.888
(8.856)
0.284
(0.207)
0.321
(0.177)
0.165
(0.169)
-0.300
(0.164)
-0.349
(0.300)
0.015
(0.092)
-0.005
(0.207)
0.533
(0.601)
-0.069
(0.139)
-0.032
(0.041)
-0.410
(0.227)
-1.292
(0.328)
-0.196
(0.137)
-0.092
(0.063)
3.824
(3.042)
-4.736
(3.529)
0.113
(0.082)
0.128
(0.070)
0.066
(0.067)
-0.119
(0.065)
-0.136
(0.113)
0.006
(0.037)
-0.002
(0.083)
0.212
(0.240)
-0.027
(0.055)
-0.013
(0.016)
-0.162
(0.088)
-0.462
(0.092)
Initial mortgage
payment to
income ratio
(3)
No bank
dummies
(2)
Sig.
**
*
*
*
***
48
Marginal
effect
(std.error)
0.027
(0.025)
0.050
(0.026)
-0.210
(0.135)
-0.098
(0.062)
3.732
(2.997)
-4.568
(3.484)
0.098
(0.080)
0.122
(0.069)
0.063
(0.066)
-0.104
(0.063)
-0.123
(0.111)
0.003
(0.036)
-0.003
(0.082)
0.263
(0.238)
-0.029
(0.055)
-0.014
(0.016)
-0.151
(0.085)
-0.413
(0.095)
Sig.
**
*
*
*
***
Heckman
correction
(4)
Coeff.
(std.error)
Sig.
-0.075
(0.063)
0.148 **
(0.066)
-0.491
(0.343)
-0.231
(0.161)
9.585
(7.699)
-11.833
(9.900)
0.284
(0.207)
0.321
*
(0.187)
0.165
(0.175)
-0.298
*
(0.202)
-0.353
(0.434)
0.016
(0.107)
-0.005
(0.209)
0.522
(1.111)
-0.068
(0.151)
-0.031
(0.074)
-0.409
*
(0.247)
-1.290
***
(0.369)
Table 4 continued
Basic regression
(1)
Bank 1
Bank 2
Bank 3
Bank 4
Coeff.
(std.error)
Marginal
effect
(std.error)
-0.322
(0.635)
0.916
(0.802)
0.649
(0.609)
-1.306
(0.782)
-0.127
(0.245)
0.315
(0.204)
0.239
(0.193)
-0.419
(0.148)
Initial mortgage
payment to
income ratio
(3)
No bank
dummies
(2)
Sig.
Marginal
effect
(std.error)
Sig.
Coeff.
(std.error)
-0.321
(0.638)
0.915
(0.809)
0.650
(0.611)
-1.305
(0.785)
-0.012
(0.993)
-0.058
(1.907)
***
Mills ratio (rho)
Constant
Observations
-1.312
(1.632)
309
(0.13)
309
(0.11)
49
Heckman
correction
(4)
309
(0.12)
309
Sig.
Table 5
Demand and supply estimation
The dependent variable in the demand equation is the log of the initial size of the loan. The dependent variable
in the supply is the default risk premium. It is computed as the difference between the mortgage rate paid by
the household over the year and the interest rate of one-year government bonds if it is an ARM, or the interest
rate of government bond with a maturity as close as possible as that of the mortgage if it is a FRM. The return
on long-term bonds is the interest rate of government bond with a maturity as close as possible as that of the
mortgage. High education attainment denotes a household head who has obtained at least a high school
diploma. Per-square meter price is the average provincial price of residential housing. House dimension is in
square meters. Mortgage subsidy is a dummy that takes on value one if the mortgage is subsidized by the
borrower’s employer, by the government, …. The Mills ratios controls for the exclusion of those who have not
moved in the 24 months prior the interview and have not borrowed to purchase a new home and for the
exclusions of those who have chosen a different type of mortgage. Standard errors in parentheses. * significant
at 10 per cent level; ** significant at 5 per cent level; *** significant at 1 per cent level.
ARM
Coeff.
(std.error)
Sig.
FRM
Coeff.
(std.error)
Sig
.
Coeff.
(std.error)
Sig.
(time
dummies)
Coeff.
(std.error)
Sig.
(time
dummies)
Demand equation
Return on long-term bonds
Default risk premium
Dummy for maturity>15 yrs
Age/100
High education attainment
Per-square meter price
House dimension
Household income
Household wealth
Living in the South
Mills ratio for L>0
Mills ratio for mortgage type
Constant
Time dummies
No. of obs
Chi2
p-value
-0.446 **
(0.024)
0.019 *
(0.052)
0.082
(0.155)
-1.009
(0.937)
-0.005
(0.012)
1.43e-04 **
(6.85e-05)
0.003 ***
(0.001)
0.064 **
(0.039)
0.000
(0.003)
0.288 **
(0.170)
0.043
(0.286)
-0.079
(0.199)
10.562 ***
(0.559)
NO
148
57.40
0.0000
-0.070
(0.072)
0.010
(0.049)
0.081
(0.149)
-1.375
(0.989)
0.051
(0.118)
1.28e-04
(6.70e-05)
0.003
(0.001)
0.093
(0.043)
-0.002
(0.003)
0.204
(0.166)
0.203
(0.313)
0.007
(0.207)
10.723
(0.962)
YES
**
***
148
51.42
0.0000
-0.114 **
(0.047)
-1.137 *
(0.082)
0.324
(0.258)
0.894
(2.326)
0.073
(0.198)
0.000
(0.000)
-0.001
(0.002)
0.047
(0.100)
0.005
(0.005)
-0.336
(0.248)
-0.323
(0.618)
-0.059
(0.387)
11.936 ***
(1.100)
NO
148
31.37
0.0017
0.048
(0.131)
-0.109
(0.082)
0.316
(0.251)
1.484
(2.404)
0.099
(0.195)
0.000
(0.000)
-0.002
(0.002)
0.052
(0.103)
0.006
(0.005)
-0.271
(0.253)
-0.599
(0.637)
-0.483
(0.383)
10.510
(1.812)
YES
***
148
37.04
66.68
Supply equation
Loan-to-value
Mortgage payment-to-income
Dummy for maturity>15 yrs
Dummy for subsidized loan
Age/100
High education attainment
6.658
(2.173)
2.399
(1.354)
-1.783
(0.707)
-1.451
(0.443)
8.750
(4.266)
0.430
(0.590)
***
*
**
***
**
3.875
(2.065)
2.622
(1.314)
-1.610
(0.621)
-1.658
(0.397)
7.113
(3.757)
0.075
(0.513)
50
*
**
***
***
*
5.671
(3.047)
-2.021
(1.746)
-2.334
(0.988)
-1.937
(0.610)
10.908
(6.544)
0.277
(0.655)
*
**
***
*
-0.846
(3.201)
-0.211
(1.673)
-1.196
(0.889)
-1.684
(0.521)
6.202
(5.815)
0.310
(0.560)
***
Table 5 continued
ARM
Coeff.
(std.error)
Sig.
FRM
Coeff.
(std.error)
Sig
.
Coeff.
(std.error)
Sig.
(time
dummies)
No. of income recipients
Time dummies
-0.517
(0.379)
0.000
(0.000)
2.822
(1.775)
6.435
(4.544)
-0.807
(1.028)
-0.626
(1.018)
0.106
(0.959)
-4.971
(2.796)
NO
No. of obs
Chi2
p-value
122
30.72
0.0037
Per-square meter price
Branches per inhabitants
Herfindahl for loans
Living in the South
Mills ratio for L>0
Mills ratio for ARM
Constant
*
-0.526
(0.361)
0.000
(0.000)
1.316
(1.877)
7.158
(4.416)
-0.701
(0.940)
-0.905
(0.922)
0.036
(0.870)
-2.758
(2.684)
YES
122
52.25
0.0000
51
Coeff.
(std.error)
Sig.
(time
dummies)
*
-1.339
(0.554)
0.001
(0.001)
-0.744
(2.403)
-3.774
(4.704)
0.052
(1.075)
0.545
(1.461)
-2.885
(1.404)
-2.097
(3.925)
NO
122
41.20
0.0001
**
**
**
-0.959
(0.493)
0.001
(0.001)
-3.255
(2.253)
-3.124
(4.000)
-0.271
(0.944)
0.345
(1.303)
-1.113
(1.325)
1.301
(3.617)
YES
122
66.68
0.0000
**
References
Bianco, M., Jappelli, T. and M. Pagano, 2005, Courts and Banks: Effects of Judicial
Enforcement on Credit Markets, Journal of Money, Credit and Banking, forthcoming.
Brandolini, A. and L. Cannari, 1994, “Methodological Appendix: The Bank of Italy’s
Survey of Household Income and Wealth”, in: Ando, A., L. Guiso and I. Visco, eds,
Saving and the Accumulation of Wealth: Essays on Italian Household and Government
Saving Behavior, Cambridge University Press, Cambridge, U.K., 369-386.
Brueckner, J. and J. Follain, 1988, The Rise and Fall of the ARM: An Econometric Analysis
of Mortgage Choice, The Review of Economics and Statistics, 70, 93-102.
Campbell, J., Lo, A. and C MacKinley, 1997, The Econometrics of Financial Markets,
Princeton University Press, Princeton, NJ.
Campbell, J. and J. Cocco, 2003, Household Risk Management and Optimal Mortgage
Choice, Quarterly Journal of Economics, 118, 1449-1494.
Cocco, J. 2001, Portfolio Choice in the Presence of Housing, London Business School
unpublished manuscript.
D'Alessio, Giovanni, 1997, I Bilanci delle Famiglie Italiane nell’Anno 1995, Supplementi al
Bollettino Statistico (nuova serie), Banca d'Italia, 1997, No. 14, Marzo.
D'Alessio, G. and I. Faiella, 2000, “Italian Households Budgets in 1998”, Supplements to the
Statistical Bulletin (new series), Bank of Italy, No. 22.
D'Alessio, G. and I. Faiella, 2002a, “Italian Households Budgets in 2000”, Supplements to
the Statistical Bulletin (new series), Bank of Italy, No. 6.
D'Alessio, G. and I. Faiella, 2002b, “Non-Response Behavior in the Bank of Italy’s Survey
of Household Income and Wealth”, Banca d’Italia, Temi di discussione, No. 462.
D'Alessio, G., I. Faiella and A. Neri, 2004, “Italian Households Budgets in 2002”,
Supplements to the Statistical Bulletin (new series), Bank of Italy, No. 12.
Dhillon, U., Shilling, J. and C. Sirmans, 1987, Choosing between Fixed and Adjustable Rate
Mortgage, Journal of Money, Credit and Banking, 19, No. 1.
European Central Bank, 2003, Structural Factors in the EU Housing Markets, Report of the
Task Force on Housing of the Monetary Policy Committee of the European System of
Central Banks.
European Mortgage Federation, 2004, Hypostat 2003 – European Housing Finance Review,
A Publication of the European Mortgage Federation.
Engelhardt, G., 1996, House Prices and Home Owner Saving Behavior, Regional Science
and Urban Economics, 26, 313-336.
Flavin, M. and T. Yamashita, 2002, Owner-Occupied Housing and the Composition of the
Household Portfolio, American Economic Review, 92, 345-362.
30
Gary-Bobo, R. and S. Larribeau, 2002, A structural Econometric Model of Price
Discrimination in the Mortgage Lending Industry, CEPR Discussion Paper No. 3302.
Gary-Bobo, R. and S. Larribeau, 2003, The Bank’s Market Power and the Interest-Rate
Elasticity of Demand for Housing: An Econometric Study of Discrimination on French
Mortgage Data, CEPR Discussion Paper No. 3745.
Guiso, L. and M. Paiella, 2001, Risk Aversion, Wealth and Background Risk, CEPR DP No.
2728.
Guiso, L., Paiella, M. and I. Visco, 2004, Do Capital gains Affect Consumption? Estimates
of Wealth Effects from Italian Households’ Behavior, in Klein, L., ed: Long-Run
Growth and Short-Run Stabilization: Essays in Memory of Albert Ando 1929-2002,
forthcoming.
International Monetary Fund, 2002, Turbulence in Asset Markets: The Role of Micro
Policies, Report of the Contact Group on Asset Prices, available at:
http://www.imf.org/external/np/g10/turbul.htm
Jappelli, T. and L. Pistaferri, 2004, Incentives to Borrow and the Demand for Mortgage
Debt: An Analysis of Tax Reform, CEPR Discussion Paper No. 3903.
Magri, S. 2002, Italian Households’ Debt: Determinants of Demand and Supply, Bank of
Italy, Discussion Paper No. 454.
Maki, D., 2001, Household Debt and the Tax Reform of 1986, American Economic Review
91, 305-19.
Miles, David, 2003, The UK Mortgage Market: Taking a Longer Term View Interim report.
Miles, David, 2004, The UK Mortgage Market: Taking a Longer Term View Final report
and recommendations.
Paiella, M., 2001, Demand for Housing, Saving Behavior and Wealth Allocation, Bank of
Italy, unpublished manuscript.
Pence, K. And B. Bucks, 2005, Housing and Institution, paper prepared for the LWS
conference on: Construction and Usage of Comparable Microdata on Household
Wealth, Perugia, Italy.
Poterba, J., 2001, Taxation and Portfolio Structure: Issues and Implications, in Guiso, L.,
Haliassoss, M. and T. Jappelli eds: Household Portfolios, Cambridge, MA: MIT Press.
Skinner, J., 1996, Is Housing Wealth a Sideshow?, in Wise, D., ed: Advances in Economics
of Aging, NBER Project Report, Chicago, IL: The University of Chicago Press, 242271.
31