Working Papers
CREDIT MARKET REGULATIONS CHANGES AND LABOR MARKET DECISIONS Daniela Del Boca and Annamaria Lusardi
ChilD n. 22/2001 e-mail:
[email protected] Web site: http://www.de.unito.it/CHILD
CREDIT MARKET REGULATIONS CHANGES AND LABOR MARKET DECISIONS
Daniela Del Boca University of Turin and CHILD Annamaria Lusardi Dartmouth College
Abstract
In
this
paper,
we
examine
whether
the
imperfections
in
the
credit market spill over to the labor market. We examine the case of a country that experienced a very high degree of imperfections in the financial markets, but underwent substantial changes in 1992 due to the liberalization brought by the European unification and other institutional changes. Italy is therefore a good laboratory to study the effects of the financial markets on the labor market.
Examining
the period 1989-1993, we find that labor market decisions are influenced by household debt commitments, and, in particular, by constraints in the mortgage market.
JEL Classification: Keywords:
J2, D91, credit constraints, female labor market Participation.
We would like to thank Rob Alessie, Jim Davies, Gary Engelhardt,Luigi Guiso, Tullio Jappelli and especially Christopher Flinn for useful discussions. Cesare Bastianini provided excellent research assistance. We also thank seminar participants at Copenhagen, Tilburg, Uppsala, Dartmouth, New York, Turin and Cornell. This research was supported by CNR.
1
1. Introduction In this paper we examine the interactions between two different markets, and, in particular we examine whether the imperfections in the credit
market spill over to other markets, in particular to the
labor market. We consider the case of a country that experienced a very high degree of imperfections in the mortgage market, but underwent substantial modifications due to the changes in the banking legislation and to the financial liberalization brought by the European unification in 1992.
This provides us with a good
laboratory to study the effects of the financial markets on the labor market. The data we use has the potential in addressing
the
market decisions.
effects
of
to
credit
be
especially
constraints
We utilize two cross-sections from
on
were
1989 and the other in 1993. Between these two several important changes in the mortgage
reduction purchase foreign
labor
the
Italy's Survey of Household Income and Wealth (SHIW); one in
useful
Bank
collected
dates,
market.
in down-payments increased the percentage of
of
there
First, the
the total
price which could be financed through a mortgage. Second, banks
have
consumers'access competition
to
among
available to a
entered
domestic
market
and
have
widen
the mortgage market as well as increased the
domestic banks. These changes have made mortgages
larger
have also shifted
the
the
group of the population than in the past, but burden from the downpayment to the repayment
of the mortgage debt. Between 1989 and
1993,
the
percentage
of
homeowners
with
a mortgage increased markedly, rising from 16 to 28 percent. At the same time, the percentage of wives who work increased from 43 to 48 percent
among
homeowners.
One
objective
of
our
analysis
is
to
determine how much of the increase in the participation rates of
2
these
married women can
utilization
be
attributed
to
the
increase
in
the
of mortgages in the population of homeowners.
The structure of the paper is as follows.
2
contains
a discussion of previous research on this topic. Sections 3
provides
a
mortgage
description of
Section
the characteristics of the
Italian
market.
Section 4 describes
the theoretical framework. Section
reports
a description of the
data,
econometric specification the
of
and
the
Section
models.
6
describes
Section
7
5 the
reports
empirical estimates.
2. Previous Research
Many studies have documented the effects of imperfections in the financial markets on consumption and saving
decisions
(Browning
and Lusardi 1996, Eberly 1994, Garcia, Lusardi and Ng 1997, Zeldes 1989). One of the most important markets for consumer credit is the mortgage market, and there are a
number
of
works
imperfections in this market have effects on decisions
(Engelhardt
1996,
Caplinet
that
show
household
et
al.
1997,
how
saving Fornero
1992).Other studies show that households rely on family transfers to compensate for market imperfections (Guiso and Japelli 1991, 1995; Cigno et al. 1996; Engelhardt and Meyer 1994). The limitations of the mortage market can affect other markets as well, and, in particular, the labor market. Yoshitawa and Ohtake (1989) have analyzed the case of Japan and found a significant effect of housing demand
on
savings
and
labor
supply. Phillips and
Vanderhoff (1991) have used the
Panel
Study
(PSID)
have
studied
from
the
U.S
and
occupation choice on housing demand. Cameron explored
the
relationship
between
early
on
Income Dynamics
and
the
career
Tracy
effect
of
(1997) have
decisions
and
housing purchasing decisions. Fortin
(1995)
has
studied
more
specifically
of mortgage constraints on labor market decisions. Using 3
the data
effect from
the
1986
impact
Canadian of
assets on
Family
liquidity
Expenditures
constraints
in
survey,
the
she
accumulation
incorporates
a
mortgage
based
on earnings. The
households'
mortgage
choices depend significantly on
levels
the
of
(Fortin,
endogeneity
wife's 1996),
of
the
supply function and Lusardi
explore
housing
qualification
constraint
and
of
the
female labor supply more specifically. She has estimated a
labor supply model that
topic
analyzes
the
indicate the
that
existing
labor earnings. In another paper on this
she
has
mortgage found
(1997)
results
also
relationship
used
issue
of
of
weak exogeneity.
Del
Boca
instrumental variable methods to
between
labor supply using cross
the
qualification constraint in the labor
evidence
have
explored
housing
section
data
financing for
decisions
Italy
and
and reports
similar results. Dau
Schmidt
(1992)
has
provided
additional
evidence
impact of debt commitment on labor supply. He has workers
with high consumption commitments have
intertemporal elasticities similar
lines,
than
Aldershof
al.
(1996)
the
found
that
substantially
lower
non-constrained
et
on
workers.
have
Along
examined
the
interrelation between female labor supply and mortgage constraints for the Netherlands. They important
explanatory
also find that mortgage constraint is an
variable
in
the
female
labor
market
participation equation. While
there
is
mounting
evidence
on
the
relationship
between female lavor supply and mortgage debt commitments, it is hard to
know what the relatonship
indicates;
whether
it
stands
for
households preferences or it is the results of liquidity constraints. In our work, we exploit the sharp changes in the financial market in Italy to study in detail the effect of debt on
labor market participation. Both the European unification as well
as changes in have
commitments
the
regulations
governing
the
credit
market
brought substantial modifications in the supply of consumers'
4
loans (especially for exploits assess
the
This
literature
purchases).
Our
methodology
temporal variation experienced by this market
potential
market.
housing
spillover from the financial markets to the labor
approach
on
to
the
is
in
natural
the
spirit
of
the
burgeoning
experiment excellently summarized in
Meyer (1995). The innovations of our empirical work are we consider not only mortgage debt, sources (banks debts
other
institutions,
debts and
from
the
on household behavior.
available between
First,
different
family)
for different purposes: and test whether they have
effects
take
and
but
threefold.
and
different
Second, we exploit the information
in our data on the banking
system
to
differentiate
liquidity constraints from households preferences. Third, we
into
account the issue of endogeneity using a simultaneous
equations model.
5
3. The Institutional Setting
In this section
we
consider
some
institutional
that differentiate Italy from other advanced countries.
factors Table 1
summarizes important characteristics of the Italian mortgage market.
TABLE 1
Mortgage/ house value
Duration of mortgage loans
Mortgages/GNP
Countries
Italy
50-60
10
Germany
60-80
12-30
40.0
Great Britain
75-100
25
57.0
France
US
6.0
80
10-20
24.0
80-90
25-30
60.0
Source: European Mortgage Federation
"Annual Report 1993-1994".
The percentage of mortgage loans as a
proportion
of
the
house value is about sixty per cent of the house value, which is much lower than in other developed countries. The ratio of mortgages GNP
is only six per cent in
Italy,
6
which
is
also
a
very
to low
value
in comparison with other selected countries.
An
important
feature
of the mortgage market is the short duration of loans. While
in
the
US the average duration is between 25 and 30 years, in Italy
it
is
Italy
only ten years. The in
mortgage
duration
has
shortened
in
the seventies and remained low during the seventies and
nineties. Another
important
characteristic
of
the
mortgage
market
concerns the costs of transactions, which include the charges real
of
estate agents and taxes. While in Great Britain the cost of
transactions
is about 4.5 percent of the house value, in Germany it
is 12 percent, This
in France 16 percent, and in Italy
higher
homeownership
cost
is
duration:
associated
while
in
18
with
a
Great
Britain
per
relatively the
cent. higher average
duration is 7 years, in Germany it is 28 years and Italy 50 years. While in
countries
loan applications
are
like
the
processed
Canada,
rapidly
credit reference agencies who are able the
US,
to
and
the
UK,
because by specialized provide
information
on
credit record of potential borrowers, in Italy the process is
much slower and more bureaucratic. A recent report of the Bank Italy
shows
of
that part of the high transaction costs is associated
with the
complicated process of repossessing collateral (Generale
and
1995).
Gobbi
It
takes
5.5
years
on
average
for
a
bank
to
repossess the
collateral
(4.5
in North and 6.6 in the South). This
difference is
consistent
with
the empirical evidence indicating a
mortgage
holders in the South than in the
lower percentage of North. In spite of these
imperfections
in
the
mortgage
market,
the proportion of Italian households who are homeowners is higher than
in most other developed countries. The overall home ownership
rate
rose from 46 percent in 1961 to 59 per cent in 1981 and grew to
75 per cent in 1995. market
have
shown
that
Studies which focus on the Italian housing the
high
7
demand
for
homeownership
stemsfrom
the
studies have
of alternative in the rental market1 . Other
lack explained
the high homeownership rate by the bequest
motive, the low cost of Italian
family
and
higher education, the stability of
the
very
In recent years a process
the
low geographic mobility. of
liberalization of
the
financial
market has started (Miles 1992). As we have mentioned above, the year
1992
marked
liberalization circulation
the
beginning
of
of
goods and services across
banks
across
which
is
and
specialized
in
Italy.
Woolwich
conditions
(Casini has
and
enhanced
entrance
of
1995).
pressured a wider
The
example,
mortgages,
a
Abbey
British National
Other foreign banks that have
entered the Italian mortgage markets are
competition
financial
European countries, but
Italian market. For
currently has 12 branches in
and
of
national borders. Several banks, especially
British banks, entered the bank,
period
in Italy and in Europe. Not only did it there free
ti also freed movements of capital foreign
a
Ucb, Paribas, Banque Lazard
resulting increase in banking
domestic
accessibility
banks to
to the
offer
advantageous
mortgage market2.
A comparison across the conditions offered show Woolwich, Abbey and Ucb allow a maximum duration
that
of
20
only years
while Abbey National allows a maximum mortgage as a percentage of the house
value
of
85
per
cent.
Together
with
improved
financing
conditions, the length of time riquired for a mortgage application has been shortened, and transaction costs have decreased. In addition to the effect of foreign competition there was a change in the banking structure induced by the Amato Act of 1990.This Act has changed in particular the housing credit market by allowing commercial banks to provide mortgage loans which were formerly the
1
The rental market has also been heavily regulated creating a shortage of rental homes. Foreign banks were present in Italy before 1992, but their activity in the mortgage market was quite limited. For example, the number of loans provided by foreign banks was only 403 in 1989 versus 8,264 in 1992. See Casini (1995).
2
8
responsibility of specialized credit institutions (Nomisma 1997, Bank of Italy 1995).
As a result of this in
increased
competition
and
these
changes
the banking regulations, the number of mortgages as well as their
average amount have increased. However, their duration have substantially longer period
than of
shifted
10
of the
income has
years
has
duration
not significantly increased in the
work suggests that the burden of the mortgage has indeed
from
payment
The proportion of mortgages a
observation.
Recent
that
changed.
not
the accumulation for the down-payment to the re-
the
mortgage debt. For example, Villosio (1995) shows
incidence
of
first mortgage installments on family
become 52 percent in 1993 (while it was about 27 percent
in 1975). Very similar results are reported in Nomisma (1995) for the period 1988-1993. The impact of the mortgage debt may then induce household
members
to
increase
their labor supply. While it would
seem relevant to analyze the impact on the in
Italy
the
distribution
of
weekly hours
hours
is
of
work,
highly concentrated
around 35 hours for women and 40 for men. Recent research focusing on the charachteristics of labor supply in
Italy, have
hours of
work
shown that there are important constraints in the choice
in Italy
al. 1991, Rettore 1995). there are
profound
countries.
While
part-time
As far as the labor market is concerned,
differences in Italy with respect to
in
employees
(Del Boca Flinn 1985, Colombino et
most is
advanced countries the proportion
between
a
consequence
of
given the scarcity of part-time and rate of Italian women
is
lower
and has not increased in
the
several regulations, and
temporary
than
9
of
20-30 percent of the total work
force, in Italy it is about 5-6 percent recent years. As
other
that
in
jobs, the employment other countries: it
is approximately 33 per cent of the
working
population compared
with an average of 45 percent in other European countries. In spite of the new law that in 1984 which has part-time work, the prevailing arrangement is still Therefore
the
basically a rate
seems
choice
of
working
hours
for
introduced full
Italian
time.
workers
is
binary one: zero or 38 hours a week. The participation to
be
the
relevant
dimension
of
to
study
in
the
empirical analysis.
4. Theoretical Framework
The
theoretical
scheme
which
is
guiding
our
empirical
estimation is a simple intertemporal model of
consumption
and
leisure
constraint.
The
household
in
the
is
presence
assumed
of
a
borrowing
to maximize an additive separable utility
function: 1)
max E
N
τ =t
1
(1 + β )τ −t
[U (Cτ ) + V (Lτ )]
subject to the following constraints:
2)
Aτ = (1 + r ) Aτ −1 + M τ + wτ (T − Lτ ) − pτ Cτ
3)
Aτ ≥ φ 0
4)
T − Lτ ≥ 0
τ =t,...,N-1
At-1 given and AN = 0
10
where: •
C is consumption
•
L is leisure
•
M is other (non- capital) income
•
A is non-human wealth
•
p is the price of consumption
•
w indicates wage
•
r is the interest rate which is assumed to be fixed
•
β is the rate of time preference
•
N indicates the terminal period
The
maximization
negative
labor
constraint. In borrowing
is
supply
subject
not
only
constraint,
to
but
a
also
budget
and
to
borrowing
a
non-
this specification we capture the fact that household go beyond a certain limit ( φ 0 ). It is well known
cannot
that in the presence of a binding borrowing constraint,
contrained
households
will
consume less than unconstrained ones. It is
to
that
constrained households will also work more than
show
easy
unconstrained ones. One
can
envision
cases
where
the
borrowing
constraint
exacerbates the effect on the labor supply. For example, if borrowing is the
earning related, i.e. it depends on current labor income, then effect
strong
(see
discussion families
of constraints
of who
Alessie, this have
on
Melemberg type
debts
labor
supply
and
Weber
are
wives
in
quite for
a
more likely to be close to the likely to modify labor supply.
Given that the male labour supply is not observe
1988,
be
of constraint). One can claim that
binding limit and are therefore more
should
can
families
11
with
very flexible in Italy, we debt commitments to work
more
in
order
to
increase
family
earnings
and
thus
making
the
constraint less binding. In the empirical work, we model the labor market participation of women not only as a function of variables that can proxy for wages and household resources, but also as a function of variables proxying for
the
burden
of
the
the
mortgage
debt.
Since
information on the residual amount of mortgage debt, dummies that
for the
consumer
family
and
households have It
is
not
credit
markets
are
so
that
we
imperfect
have
rely
Italy, network
debts
with their family.
difficult
to
differentiate
the
market participation. For example, it
could
effect may be
of
influence the
case
who participate in the labor market and enjoy a high
level of labor supply are the ones who choose to have debts. In work
we
on
friends.We therefore also insert a dummy for whether
quite
wives
in
only from banks but also from their
borrowing constraints from other reasons why debt labor
only
the existence of a mortgage and for other debts. Given
households borrow of
we
exploit
Amato Act of
our
the variation in the mortgage markets after the
1990 and the financial liberalization of 1992 (which
led to changes in the
banking system and the supply of credit), to
pin down the effects of borrowing constraints on female labor market participation. The decision to participate in the labor market and to a mortgage are not necessarily contemporaneous.
It
can
obtain
well
that women enter the labor market before obtaining a mortgage to
due
the need of accumulating assets for the downpayment. Additionaly,
they may continue working afterwards due to acquired labor experience. the
be
Rather than
using
the
actual
outcome,
we
market model
decision to participate in the labor market and to take out a
mortgage as a latent variables model. We therefore reason in terms of propensities
instead of actual choices.
12
One attractive way to visualize the [short-run] effect the change in financial market regulations and
wives'
participation
rates
is
have
through
on
mortgage
the
latent
that usage
variable
simultaneous equation model first formulated by Heckman (1978).
In
this
to
structure
participate
in
[home-owning] values
of
observed;
we
think
the
family
of
the
propensity
for
the
wife
labor market and the propensity for to
the
latent
instead
only
hold
a mortgage as latent variables.
variables themselves are an
the
not
The
directly
indicator variable is observed if the
value of each exceeds a certain
threshold which is particular to the
variable considered. In order to identify on variables proxing for
the the
direction credit
of
causality,
system
and
the mortgage market across different periods of
the
time.
we
rely
changes We
think
the changes in mortgage regulations as effectively serving
in of
to
lower
the threshold which maps the propensity to have a mortgage
into
actually holding one.
If our hypothesis is correct, changes
mortgage market will shift the intercept term only
in
the
in
the
mortgage
equation without altering any other characteristic of the structural model.
5. The Data
The
data
are
from
the
Bank
of
Italy's
Survey
of
Income and Wealth (SHIW) in 1989 and 1993. We have selected
Household married
couples, in the age range of 21 to 59 for men and 21 to 55 for women, in
order
retiring.
to exclude individuals who are in
school
or
who
are
Other selection criteria are described in Table A.1 in
Appendix 1. We
first
note
that
a
substantial
share
of
households,
approximately 20 per cent, did not buy their house, but received ti as gift or bequest. Not only do many Italian Households rely on these
13
trasfers, but they also receive loans from the rest of the family. Our data show that there are three sources of debts. Households borrow not only from banks, credit institutions or firms, but also from the network of the extended family. While fewer households use this
informal
channel
of
credit,
the
amount
borrowed
is
irrelevant. The conditional mean and median of family loans are million While
and
9 million liras
(approximately
$9,000
and
not 14.5
$5600).
households report owing other debts, their total amount is
much lower than family debts. The conditional mean and median of other debts are for
many
7.2
and
households
information only
on
5 millions liras. The most relevant debt
is
the mortgage debt. The survey provides residual mortgage debt3 . The conditional
the
mean and median of mortgage
debt
are respectively 35.1 million and
25 million of liras4 respectively. Simple comparisons across years which
households
rapidly
have
accessed
the
show
that the
mortgage
market
degree has
to
changed
in the 4-year period. The mortgage rate among homeowners
increased
from 16 percent in 1989 to 28 percent in 1993, an increase
of 12 percentage points5. The female labor market participation rate had a more
modest increase over the period: it went from 43.7
percent in
1989
proportion
of
increased.
Our
to
mortgages data
mortgage debt. If we in
1988
million.
and
considered
the remaining mortgage
in
1993.
also
Not
the
only
amount
did
the
borrowed
reports information only on the residual the households who bought the house
their
households
that
percent
increase, but
set
1989,
For the
other factors
48.9
debt
indicate
remaining mortgage debt is 30.65
who
bought
is
58.29
a
the house in 1992 or 1993 million liras.
lessening
the mortgage market. For example, the 3
of
average
There are
the constraints in age
of home buyers
The question related to the mortgage debt includes also mortgage debt for house restoration. The ratio of debt to residual household income (total income minus wives’ income) has a mean of 1.47 and a median of 0.67. If we restrict to the households who bought the house (and have a mortgage) in the last two years, the mean and median are 3.18 and 1.66 respectively. 5 The proportion of homeowning went from 62.2 to 67.4. 4
14
went from 35.7 in 1989 to 34.3 in 1993. pattern of homeownership across age younger from
households
liberalization.
households in
are
1989
the
The
groups
ones
rate
We have
of
and
examined the
found
the
benefitting
the
most
homeownership
among
those
who are below 30 years of age went from
to
that
18.6
percent
43.6 percent in 1993.
Table 2a and 2b report some additional descriptive statistics of
husbands'
and
wives'
characteristics
by
different
situations for 1989 and 1993 . The critical point that that,
financing
emerges
among homeowners, the participation rate of women is very
different is 43.7
across housing financing modes: women's participation rate and
48.9 percent (in 1989 and 1993 respectively) among the
homeowners Among the homeowners who inherited the house or it
is
as
a
gift,
received
the participation rate is much lower, it is 41.1
per cent in 1989 and 42.7 percent in 1993. Participation is also much lower
among
In
renters.
households
which
financed
their
home
purchase
with
a
mortgage, the labor participation rate of wives is much higher than in the other groups: 57 and 58.9 percent. Families who have mortgage
debt
younger North
and and
are also those where both husband and wife
have
to
a are
higher education, are more likely to live in the
work
more hours. We also note that households with a
mortgage are more likely to have other debts. As mentioned before, of households who
borrowed
increased substantially. mortgage
between 1989 and 1993, from
the
One can see
the
financial
that
the
percentage market
changes
in
has the
market have affected the most recent buyers. The proportion
of new homeowners (bought their house in the last two years with a mortgage)
went
from 44.8 in 1989 to 61.1 percent in 1993.
In our empirical work, we focus female
participation
in
the
labor
15
on
the
market.
probability We
consider
of as
exogenous determinants of the wife's probability of the
working
and
mortgage debt the following sets of variables:
1. Personal characteristics. We include in this set the wife's age, the wife's schooling, the husband's schooling, the number of children between 0 and 6 years
of age,
the
household's
income
(residual
income
after
the
wife's earnings, expressed in 1993 million liras) and the
region of residence (a dummy variable equal to 1 if they live in the North).
2. Family economic contributions. As we have mentioned before, the family also has a role in trying to compensate for the limited borrowing opportunities of Italian mortgage market. did
the
We note that in our sample many homeowners
not directly buy the house but rather received it as a gift or a
bequest.
Another
important
variable
relatives.
We
the
contribution
is
the debts
both
of
family contributions in the empirical work.
types
with
describing
family
account
for
3. Other debts. The survey provides information on other household debt (debts on
cars,
installment
payments
on
household
appliances
etc.).
consider those debts as well in the empirical work. They allow to that
examine whether the effect of the mortgage is different of
indicators
other types of debt. Additionally, they could serve of
We us
from as
the attitude towards debt.
4. The credit system. The survey reports data on the respondent's relationship with
16
banks
and
markets. a
on
variables
For example,
that
households
measure
are
access
asked
credit
appropriate
for
households post
cards
do
have
The
use
of
they
using,
these
have
and
how
variables
is
a checking account (but have, for example,
saving
households have
hold.
credit
the Italian case, where a relevant fraction of
not
office
they
to
whether
checking account, how many banks they have been
many
a
other
a
account)
credit
card.
identifying different types different degrees
of
and
a
very
small
fraction
of
These variables can be useful for
of
borrowers and also for picking up
asymmetric
information that could affect bank
lending. It is important for our purpose that we have
indicators
the changes occurring in the financial market between 1989 1993.
of and
We have used a variable indicating whether the house was
purchased
after
1992
to
capture
the
effects
of
the
financial
liberalization.
6. Econometric Specification Our empirical work focuses on the effect of debt commitments on labor market activities of married women between
1989
and whether this effect is different from that of
and
other
1993 debts.
Several problems arise in analyzing the relationship between debt commitments and female labor market participation. One problem that
the
second
two events are likely to be non-contemporaneous.
problem
indicator
is that
of
the
liquidity
mortgage contraints,
can but
be
not
also
a
is The
only
an
proxy
for
preferences. In this section we discuss the models we have estimated which are based and
on
latent
participation
interpretation when
a
some
or
variable
decisions.
specification It
is
of
the
well-known
of the linear regression-type models is
mortgage that
the
problematic
all dependent variables are binary, as is the case
17
here.
Latent
which
to
variable models provide a
framework
within
the relationships between
discrete
random
interpret
useful
variables,
at
the
present
the
linear
in
cost
of introducing some restrictions not
estimation case particularly in the context
of simultaneous equation systems]. One
of
the
mortgage
dummy
whether
it
market
rather
in
to
the
the
labor
market
the
nature
participation
only how the propensity to
propensity
of
equation
the is
have
a
mortgage
to participate, but also how the propensity
affects
model we propose allows have
interpreting
than preferences toward work. It is then important to
participate
We
of
is indeed proxying for constraints in the financial
investigate not affects
problems
the propensity to have a mortgage.
for
estimated
The
non-recursiveness.
two
special
cases
of
the
type
of
simultaneous equation model involving latent variables proposed by Heckman(1978). The general structure is: y1*i = x1i β1 + δ 1 y 2*i + η1 y 2i + ε 1i 13)
y 2*i = x2i β 2 + δ 2 y1*i + η 2 y1i + ε 2i æ é0ù é 1 æε ö where çç 1i ÷÷ ≈ N çç ê ú , ê è ε 2i ø è ë0 ë ρ and
ρùö , ∀i ; 1
ì1 if y ki > 0 y ki = í . 0 if y ki ≤ 0
y1i takes the value 1 if the wife in household i was participating in the labor market at the time of the interview and assumes the value 0 otherwise; y2i
takes the value 1 if household i currently has a
mortgage on the house; X1i and X2i are vectors of exogenous variables in
the
participation
error term vector.
The
and
mortgage
data
equations,
available
18
to
respectively.
estimate
The
(13) consist
of a random sample of
observations
{y1i , y 2i , x1i , x2i }1N=i
on
known6 that such information is not sufficient to structural parameters restrictions on
which
the
logical consistency
appear
model [these
are are
in
(13).
required typically
"coherency conditions"] and then to secure
A
.It is well-
identify all the number
first
of to
referred
ensure to
identification
as
in
the
classical sense. We consider two specific cases (model 1 and 2) of the general model: Model 1:
δ1 = δ 2 = 0 η2 = 0 ρ =0 y1*i = x1i β1 + η1 y 2i + ε 1i
1)
y 2*i = x 2i β 2 + ε 2i Because the error terms are assumed to be uncorrelated [ ρ = 0 ], there is no simultaneity in this specification of the model.
Having
a mortgage is assumed to affect the latent variable interpreted the propensity to participate
in
market participation is assumed not have
a mortgage.
estimation of
the
the
labor
market,
to
affect
the
but
first
equation
alone
provides
labor
propensity
Since the error terms are uncorrelated,
as
to
probit
consistent
and
efficient estimates of η1 and β1 under the model assumptions. Model 2:
η1 = η 2 = 0 y1*i = x1i β1 + δ 1 y 2*i + ε 1i
2)
y 2*i = x 2i β 2 + δ 2 y1*i + ε 2i This corresponds to
the
classic
6
See Heckman (1978)
19
linear
simultaneous
equation
model except for the fact that system are all latent. those
which
are
required
condition a
must
be
the
dependent
more
the
variables
for identification.
are
the
In the
are
In
imposed
addition,
for
the
model
a to
probabilistic structure, namely 1 − δ 1δ 2 > 0 . This
condition is not imposed in at
restrictions
satisfied ["coherency"]
well-defined
checked
in
matrix, exclusion restrictions are required.
specifications estimated, many
be
variables
in particular, in the absence of restrictions on the
covariance
than
dependent
Identification conditions are identical to
in the model for
observable;
the
model
maximum likelihood
the estimation of the model but is
estimates
estimator
to verify the unconstrained
satisfies
it. The ln likelihood
function for this model is reported in Appendix 2.
7. Empirical Results We estimate the probability on
personal
characteristics
of
(wife's
wife's age,
working
age
conditional
squared,
number
of
children less than six years of age, region of residence, wife's and husband's
schooling)
situation
of
1)
variables
describing
the
financial
the household (income, family debts, other debts).
In Table 3 (Model
and
for
and the
4,
entire
we report the estimates of the probit sample
of
homeowners
including
and
excluding homeowners who received their house as a gift or bequest for the sample 1989 and 1993 separately. We use two different indicators for mortgage debt. The a dummy variable indicating whether the household debt (in column I and III),
and
the
has
second
a
first is mortgage
indicates
the
mortgage amount still owed (column II and IV). The
estimates
husband
is
household always
indicate
always
positive
income (residual
negative
that
the
and income
schooling
very
of
significant,
after
wives'
and significant. As expected, age
20
the
wife
while earnings) of
the
and the is wife
is
positive
children
while
younger
age squared is negative, and the number of
than
probability of wives
six
in
working.
the
Living
household
decreases
the
in the North significantly
increases the probability of working. We now consider the effects of the most
important
variables
in our model. Both the dummy indicating that the household mortgage debt and the variable debt
indicating
the
remaining
has
mortgage
are positive and significant. Even after controlling
for
many
variables that affect participation, we still find that having a mortgage
has
an
consistent
effect
with
on
the
wives'
results
participation. of
other
This
studies
finding
(Fortin
is
1995,
Aldershof et. al. 1996). Having received a house as a gift or bequest [thus, a
these
negative We
households
effect
have
on
also
never faced
a
financing
decision],
has
female participation.
included
a
variable
indicating
whether
the
household has other debt (car, appliances). We include this variable as a
dummy and
whether We
as
the
remaining
amount
owed,
to
examine
mortgage commitment is different than other types of debt.
find
that
the
estimates
of
other
types
of
debt
are
not
statistically significant. We
have
also
introduced
into
different indicators for family debt): a
the
debt
(as
equation for
the
dummy indicating whether the family has
relatives,
and
a
two mortgage
debt
with
the amount owed. The most interesting finding is
that the effect of family debt is substantially different in 1989 and 1993. While in 1989 it significant,
in
is greater in
1993
the
different from zero. This seems rely
much
more
on
the
magnitude
coefficient
coefficients
specification
are
statistically
not
statistically
to indicate that households tend to
financial market after 1992.
We then estimate a probit on the The
is
and
reported
we introduce also a
21
pooled
in year
sample
Table dummy.
5. The
1989-1993. In year
this dummy
captures
the
interest
rates,
periods.
effect
of macroeconomic conditions such as changes in
and
All
the slow down of the economy between the two
estimates
of the variables related to personal
characteristics are very similar 1989 sample. The
estimates
household
to
seem
be
to the estimates of the 1993 and
related
a
to financial
little
context, while the dummy
for
the
statistically
of
the
more significant in a temporal
significantly different from zero. is positive and
position
year
The
is positive but not
coefficient of the mortgage
different
from
zero, while the
coefficients related to other debts are not significant
and family
debt has a negative sign. Table 6 and 7 report the estimates of the latent model in 1989 and 1993.
variable
The latent variable specification [Model
shows evidence of simultaneity.
The
correlation
between
2] the
structural disturbances is estimated to be approximately -.816 ( with a
standard error of .358) and -.811. (with a standard error of
.081).
We
note
simultaneity,
there
The propensity of the
mortgage
that, is
the
while
there
is
wife
propensity,
but
the
estimated from zero.
in
error
Conversely,
mortgage
in
propensity
1993. on
for
to work has a positive direct effect on
.302 with a .150 standard error .117
evidence
no strong evidence of non recursiveness.
marginally significantly different
of
some
the
wife
coefficient
is
only
The coefficients are
1989 and .206 with a standard the effect of
participation
the
is positive and
very significant statistically in both years (.804 with a standard error of .118 in 1989 and
.781
with
a
standard
error
of .083 in
1993). The
empirical
results
of
this
model
confirm
the
different
effects of family debt between the two years: the coefficient is negative in
1989.
Engelhardt
and significant in the wife's participation equation only This result is consistent with other recent research. and
Meyer
(1994)
show
22
that
transfer
recipients
have
lower than
savings,
but
still purchase their home significantly earlier
non-recipients.
Guiso and Jappelli (1995), using 1991 Bank of
Italy data,reported liquidity
that
the family
constraints
transfers shorten the
in
housing
transfers
help
purchases.
The
intervivos
saving time by one to two years and allow
households to purchase considerably larger al (1995) found
overcome
that,
during
the
homes. Finally, Haurin et
year
of
home purchase, about
14 percent of households receive gifts, three times as much than the years prior to ownership. We then now look at the variables that are used as of the access to the credit credit access (such as many
banks
positive
they
effect
comparison
market.
All
variables
indicators related
to
whether they have a checking account, how
use,
how
many
credit
cards
they
on the probability of having a
hold)
have
mortgage.
a
The
between
the coefficients of these variables in the two
years show that the
effect of all three is much larger in 1993 and
is also more significant. Table 8 reports the sample 1989-1993. In
empirical
this
model
results
we
have
also
variable indicating whether the household bought 1992. from
The coefficient
the
aggregate
of
and
a
mortgages.
pooled
introduced the
house
significantly
purchasing using
the
house
the after
different
after
Consistent
1992 with
evidence reflecting institutional changes, homeowners were
is
in
to have a mortgage in 1993 than in 1989. The year
fact
very
However, the year dummy
wives
that
probability
much more likely
market
positive
zero. This suggests
increases
dummy
is
for
participation in
this
is
significant
the
mortgage
equation.
not significant in the wife's labor
equation.
population
in
Thus the participation rate of
seems
to
1993 not only through a secular trend but such as the increased percentage
of
pressure of the mortgage.
23
have increased from 1989 to also due to other factors,
homeowning households under the
In Table 9 we report likelihood ratio statistics used to test the time-invariance of the relationships specified in the the first test the null hypothesis of no the alternative
change
is
model.
tested
In
against
that all parameters changed between 1989 and 1993.
In the second test, the null
hypothesis
is
that
only
the
constant
terms changed across the two periods. The results show that
we
reject the hypothesis that nothing changed between the two
can
years. The accounted
second test indicates that the change for
components evident
of the temporal variability
from
the
results
be
solely
by shifts in intercepts, although these are important in
the
model.
It
appears
the comparison of the coefficients of the 1989 and
1993 equation that are
cannot
the relationships that have changed more markedly
onesassociated
show
that
changed between
the
we
with
the
credit
market
variables.
cannot reject the hypothesis that something
two
years, but it also show that the changes
in the constant are a very important component of
the
changes.
We have used the coefficients of the simultaneous equation
model to
compute the elasticities of wives' participation to changes in 7
mortgage
.We
consider
The
the
effect
on
wives'
labor
the
market
participation behavior in response to shifts in the constant terms in the mortgage equation.
We interpret these shifts
as
resulting
from changes in the institutional setting in which agents operate. We are interested in a) the cross-elasticity, which is defined as the percentage change in the probability of agent i
participating
in
the labor market (or analogously having a mortgage) associated with a perturbation of the constant term, divided by the percentage change in
the
constant
term
of
the
mortgage
equation,
b)
the
"derived" elasticity which is defined as the ratio of the percentage change
in the probability of labor market participation induced by
the shift
7
in the constant term of the mortgage equation divided by
See Appendix 3 for details on the computation of the elasticities.
24
the
percentage change
in
the
mortgage
shift. All the elasticities
are
evaluated
induced
by
at
sample
the
The "derived" elasticity is .589. This indicates
this
same
means.
that
there
is some responsiveness in labor market participation to
changes
the
though
it
give
predictions
structure
of
quantitatively
the
mortgage
large.
market,
However,
it
even does
consistent with the empirical evidence over the sample
is
in not
period.
Over the period from 1989 to 1993, in fact, mortgage usage among
homeowners
participation
increased
from
16
to
28
percent,
while
of wives in the homebuyers sample increased from 45.4
to 50.4 percent. Using the elasticities mentioned above we predict, for
this
rate
of
growth
in
mortgage
usage,
an
increase
in
participation from 45.4 to 52 percent, which is close to the observed growth rate some
over
credibility
the to
period 1989-1993. This would seem to
our
lend
model estimates and our conceptualization
of the policy experiment. Our
model
suggests
that
part
of
the
increase
in
labor participation could be attributed to the wider access to the mortgage market. Given that the burden of the mortgage from the
shifted
the accumulation for the down-payment to the re-payment
of
mortgage debt, we can expect to see more women participate to
the labor
market as the access to mortgages
many
particular young) families
own
has
(in a
home.
application interaction
A to
wider
and
desire
to
natural extension of this study is certainly
an
panel
between
becomes
fulfill
their
data which would allow us to study the
debt
comitments
choices in a dynamic context.
25
decisions
and
labor
market
8. Conclusions In this paper we have estimated models in which the labor market
participation
of
wives
depends
not
characteristics, wages and income, but also
on
only the
on
personal
household
debt
commitment. We analyze the effect that the change in financial market regulations has on mortgage usage and using a changes in
pooled the
wives'
participation
rates
data set (1989-1993). Our results indicate
that
mortgage markets were among the reasons that explain
the increase in the
labor market participation
homeowners
1989-93 period.
over
the
of
wives
among
Our analysis shows tha there are important sillover effects from the financial markets to the labor markets and that the financial liberalization now in progress can be expected to have a significant impact on female labor participation.
26
TABLE 2a Participation Rates of Husbands and Wives across Financing Modes 1993 All
Homeowners
Buyers
Buyers with Gift Renters Mortgage and Bequest
Husband age
42.9
43.7
44.0
42.2
42.6
41.2
Wife age
39.4
40.1
40.3
39.0
39.1
38.0
Husband 96.6 Participation
97.6
98.2
99.0
95.1
94.3
Wife 43.8 Participation
48.9
50.4
58.9
42.7
33.4
Husband 40.1 hours of work
40.6
40.8
41.6
39.5
39.2
Wife's hours of work
14.7
16.2
16.8
19.8
13.5
11.6
North
39.6
38.4
39.9
39.9
31.9
42.2
Husband Schooling
9.6
9.9
9.8
10.6
10.0
9.0
Wife Schooling
9.3
9.5
9.5
10.3
9.5
8.7
Number of Children
1.7
1.7
1.6
1.6
1.7
1.7
Number of children 0-6
.37
.34
.31
.35
.46
.44
25.6
27.0
27.8
30.0
23.9
22.7
Husband's Income
27
All
Homeowners
Buyers
Buyers with Gift Renters Mortgage and Bequest
Wife's Income
8.4
9.6
10.0
12.0
7.8
5.8
% Family Debts
5.2
4.9
5.7
6.6
3.4
5.6
16.7
12.7
13.3
17.5
10.2
25.0
(2712)
(1828)
(1477)
(513)
(351)
% Other Debts
28
(884)
TABLE 2b Participation Rates of Husbands and Wives across Financing Modes 1989 All
Homeowners
Buyers
Buyers Gift and with Mortgage Bequest
Renters
Husband age
42.5
44.0
44.6
41.5
41.7
40.1
Wife age
39.0
40.3
40.9
38.3
38.1
36.8
Husband 98.3 Participation
98.7
99.0
99.6
97.9
97.5
Wife 41.5 Participation
43.7
45.4
57.0
41.1
37.0
Husband hours 41.4 of work
41.6
41.7
41.4
41.0
41.2
Wife's hours of work
15.5
16.5
17.0
20.8
15.3
13.7
North
38.6
37.2
38.6
40.9
32.1
41.0
Husband Schooling
9.5
9.6
9.5
10.6
9.7
9.3
Wife Schooling
9.0
9.1
9.1
10.3
9.2
8.9
Number of Children
1.7
1.7
1.7
1.7
1.7
1.6
Number of children 0-6
.36
.32
.29
.39
.43
22.5
23.3
23.8
25.4
21.1
21.2
Wife's Income
7.0
7.5
7.8
10.1
6.8
6.0
% Family debts
3.8
3.1
3.3
7.5
2.5
4.9
% Other debts
9.9
7.9
8.0
11.6
7.6
13.1
(3562)
(2219)
(1750)
(293)
(469)
Husband's Income
29
.43
(1343)
TABLE 3 Probability of wife working (Model 1) Sample 1989
I Specification
Variable
Estimate
Constant
II Specification
s.e
Estimate
s.e
-2.010
.804
-2.090
.805
.338
.403
.389
.403
Wife's age sq.
-.042
.050
-.048
.050
Children 0-6
-.104
.067
-.100
.068
North
.439
.067
.439
.067
Wife's Schooling
.157
.013
.142
.011
Husband's Schooling
.141
.011
.011
.011
-.289
.097
-.300
.098
.202
.088 .005
.002
Wife's age
Income Mortgage (dummy) Mortgage (amount) Family Debts Other Debts
SAMPLE log likelihood
-.386
.188
-.028
.013
.169
.112
.005
.007
1750
1750
-1032.5402
-1028.7779
30
TABLE 4 Probability of wife working (Model 1) Sample 1993
I Specification
Variable
Estimate
Constant
-4.253
Wife's age
Estimate
s.e
.915
-4.281
.919
1.377
.462
1.405
.464
Wife's age sq.
-.173
.058
-.176
.058
Children
-.276
.075
-.293
.075
North
.538
.075
.538
.075
Wife's Schooling
.153
.013
.153
.013
Husband's Schooling
.024
.012
.025
.013
-.660
.172
-.631
.175
.189
.078 .003
.001
Income Mortgage (dummy)
s.e
II Specification
Mortgage (amount) Family Debts Other Debts
SAMPLE log likelihood
-.001
.160
-.010
.007
.068
.105
.017
.012
1750
1750
-818.245
-814.269
31
TABLE 5 Probability of wife working (Model 1) Pooled sample 1989-1993
I Specification Variable
Estimate
Constant
-2.979
.600
-3.029
.602
Wife's age
.787
.308
.821
.302
Wife's age sq.
-.098
Children 0-6
s.e
II Specification
.037
Estimate
s.e
-.103
.037
-.170
.049
-.175
.050
North
.472
.049
.470
.049
Wife's Schooling
.146
.008
.147
.008
Husband's Schooling
.001
.008
.001
.008
-.369
.084
-.363
.084
.192
.057 .004
.001
Income Mortgage (dummy) Mortgage amount Family Debts
-.166
.120
-.001
.005
Other Debts
.118
.076
.009
.006
Year 1993
.019
.049
.034
.048
SAMPLE
log likelihood
3227
-1860.8886
3227
-1856.5156
32
TABLE 6 Simultaneous Equation model with latent variables Sample 1989 Estimates Std. err. Wife's Participation Equation Constant
-1.564
1.147
Wife's age/10 Wife's age sq. N. Children 0-6 North Wife's Schooling Income/100 Family Debts Other Debts
-1.038 .157 - .049 .202 .617 -.151 -.099 .095
.519 .068 .039 .107 .253 .157 .042 .067
.804
.118
-3.297
.936
Wife's Age/10 Wife's Age sq. North Income/100 Husband's Schooling Bank More banks Credit card Work propensity
1.514 -.223 -.014 -.439 -.009 .151 .168 .075 .305
.039 .062 .081 .142 .055 .094 .081 .052 .160
ρ
-.816
.358
Mortgage propensity Mortgage Equation Constant
SAMPLE
1750
log likelihood
- 1766.660
33
TABLE 7 Simultaneous Equation model with latent variables. (Model 2) Sample 1993 Estimates
Std. err.
Wife's Participation Equation Constant
-2.660
1.039
Wife's age/10 Wife's age square N. Children 0-6 North Wife's Schooling Income/100 Family Debts Other Debts Mortgage propensity
-1.007 -.111 -.159 .378 .837 -.131 .051 .031 .781
.494 .062 .046 .049 .069 .092 .092 .059 .083
.860
.920
Wife's Age/10
-.259
.462
Wife'age square North Income/100 Wife's Schooling Bank More banks Credit cards Work propensity
.015 -.131 -.575 .170 .335 .223 .220 .207
.058 .079 .186 .089 .121 .071 .077 .117
ρ
-.811
.081
Mortgage Equation Constant
SAMPLE
1477
log likelihood
1715.166
34
TABLE 8 Simultaneous Equation model with latent variables. (Model 2) Pooled sample 1989-1993 Specification I Estimates
Std. err.
Specification II Estimates
St. err.
Wife's Participation Equation Constant
-.586
.745
-.887
.718
Wife's age Wife's age sq. N. Children 0-6 North Wife's Schooling Income/100 Family Debts Other Debts Year 1993 Mortgage propensity
.071 .008 -.091 .308 .766 .049 -.044 .079 -.375 .729
.036 .045 .035 .049 .169 .110 .072 .045 .167 .076
.156 -.004 -.111 .339 .887 -.009 -.057 .094 -.331 .681
.337 .043 .039 .061 .140 .104 .083 .052 .165 .074
-1.920
.655
-2.017
.664
Wife's Age/10 .519 Wife's Age sq. -.089 North -.089 Income/100 -.486 Wife's Schooling .068 Bank .247 More banks .205 Credit Cards .129 Year 1993 .543 Bought the house after 1992 Work propensity .264
.329 .042 .061 .112 .053 .079 .054 .045 .052 .089
.643 -.102 -.085 -.509 .088 .290 .229 .151 .511 .428 .214
.331 .042 .057 .112 .066 .084 .053 .048 .052 .106 .078
ρ
.079
-.747
.085
Mortgage Equation Constant
-.817
SAMPLE
log likelihood
3227
-3501.585
-3489.549 35
TABLE 9 TESTS STATISTICS
1.L1 = - 1766.660
- 1715.166
= - 3481.826
(21 restrictions)
all parameters changed 2.L2 = -3501.585 (19 restrictions)
only constants changed
3.L3 = -3563.286 (21 restrictions)
nothing changed,
TEST 1 all parameters changed between 1989 and 1993 (vs nothing changed) HO : (3) HA : (1) 2[ L1 –L3 ] = 162.92 TEST 2 the HO : (2) HA : (1)
prob. under the null 5.9e-024
constant terms changed (vs everything changed)
2[ L1 –L2 ] = 39.518
prob. under the null .004
36
APPENDIX 1
Sample Selection criteria In this Appendix we report a list of the selection rules in our sample
TABLE A.1 SAMPLE SELECTION Selection criteria
Selection criteria 1.Only married couples 2.Only families in which neither the wife nor the husband own a business 3.Only families with wives in the age bracket 20-55 and husbands 20-59. 4.Only families in which neither the husbands or wives have zero incomes or are retired and report non-zero income if they work 5.Only families which either rent or own 6.Only families with no missing values in mortgages, year of house purchasing 7.Only families whose residual income (total - wife's labor earnings) is non-negative or zero. 8.Only homeowners
37
APPENDIX 2 The log-likelihood function for Model 2 is: L(ϑ 2 ) =
å ln
~ −m 1i
~ −m 2i
i∈S00
+
å ln
~ −m 1i
i∈S 01
+
å ln
~ −m 1i
å ln
~ −m 1i
i∈S10
+
i∈S11
where:
f (u , v; ρ~ ) ∂u ∂v
~ −m 2i
~ −m 2i
~ −m 2i
f (u , v; ρ~ ) ∂u ∂v f (u , v; ρ~ ) ∂u ∂v f (u , v; ρ~ ) ∂u ∂v
~ = X 1i β1 + δ 1 X 2i β 2 m 1i τ1 ~ = δ 2 X 1i β1 + X 2i β 2 m 2i τ2
(
τ 1 = 1 + δ 12 + 2δ 1 ρ
(
)
1 2
τ 2 = 1 + δ 2 + 2δ 2 ρ 2
)
1 2
δ + δ 2 + ρ (1 + δ 1δ 2 ) ρ~ = 1 τ 1τ 2 ϑ2 = (β1′β 2′ δ 1δ 2 ρ )′ All ln likelihoods were maximized using the MAXLIK procedure in GAUSS;
numerical procedures were used to compute the gradient vector
and the Hessian. No unusual problems were encountered in the process of estimating these functions, in part probably due to the relatively
38
large
sample
size.In
addition,
to
avoid
possible
problems
we
parameterized the correlation coefficient as ρ = tanh( α ), where
α∈R
and tanh denotes the hyperbolic tangent function.
We then
estimated α directly instead of ρ . The maximum likelihood estimate of
ρ
is then tanh( αˆ
), where αˆ
denotes the m.l.e. of α .
standard error of ρˆ was obtained using the delta method.
39
The
APPENDIX 3
This appendix contains to
compute
the
a
elasticities
description
reported
in
of
the
Section
method
used
from
the
6
structural latent variable model of mortgages and participation. consider the effect on behavior in
the
[in the these in
two equations, β 11
which The
shifts
in
the
constant
terms
[in the participation equation] and β 21
mortgage equation]. shifts
of
We
As discussed in the text, we
interpret
as resulting from changes in the institutional setting
agents operate. elasticities
were
computed
for
the
nonrecursive
latent variable model without "structural shift," or Model
2.
The
reduced form of this model is:
A.1)
y1*i = (1 − δ 1δ 2 )−1 ( X 1i β1 + δ 1 X 2i β 2 ) + v1i y 2*i = (1 − δ 1δ 2 )−1 ( X 2i β 2 + δ 2 X 1i β1 ) + v2i
where:
v1i ≡ (1 − δ 1δ 2 )−1 (ε 1i + δ 1ε 2i ) v2i ≡ (1 − δ 1δ 2 )−1 (δ 2 ε 1i + ε 2i )
Define:
a1i ≡ (1 − δ 1δ 2 )−1 ( X 1i β1 + δ 1 X 2i β 2 ) a 2i ≡ (1 − δ 1δ 2 )−1 ( X 2i β 2 + δ 2 X 1i β1 )
Then the probability of agent i participating in the labor market is:
(
P(d1i = 1 X 1i , X 2i ) = Φ a1i σ v1
)
,
and the probability of agent i having a mortgage is:
40
(
P(d 2i = 1 X 1i , X 2i ) = Φ a 2i σ v2 where σ v j
)
,
is the standard deviation of the reduced-form disturbance
in equation j. Say that an institutional change lowered the barrier to having a mortgage - we model such an event as decreasing the constant in
the
second
perturbed
by
structural some
latent
λ
amount
,
variable then
equation.
we
can
define
If
term
β 21
the
is two
elasticities:
ζ 2, 2
A.2)
[Φ({a (λ ) =
ζ 1, 2 (λ ) =
[Φ({a
1i
} ) (
) ]
+ (1 − δ 1δ 2 ) λ σ v2 Φ a 2i σ v2 − 1 −1
2i
} ) (
[λ β ]
) ]
+ (1 − δ 1δ 2 ) δ 1λ σ v1 Φ a1i σ v1 − 1 −1
1 2
[λ β ] 1 2
The first elasticity in (a.2) is defined as the percentage change in the probability of agent i having a mortgage associated with a perturbation of the constant term to β 21 + λ divided by the percentage change in the constant term.
The "cross-elasticity"
ζ 1, 2 (λ )
is
defined as the ratio of the percentage change in the probability of labor market participation induced by the shift in
β 21
divided by
the percentage change in β 21 . Analogous elasticities are defined when the constant term in first structural equation is perturbed by some amount λ . These are given by: A.3)
ζ 1,1 (λ ) =
[Φ({a
1i
} ) (
) ]
+ (1 − δ 1δ 2 ) λ σ v1 Φ a1i σ v1 − 1 −1
41
[λ β ] 1 1
ζ 2 ,1 (λ ) =
where
ζ 1,1 (λ )
[Φ ({a
is
} ) Φ (a
+ (1 − δ 1δ 2 ) δ 2 λ σ v 2 −1
2i
the
percentage
2i
]
σ v )− 1
change
2
of
[λ
β 11
the
] participation
probability induced by a perturbation of λ in the coefficient β 11 in the structural participation equation. ζ 2,1 (λ ) is the elasticity of the mortgage rate defined with respect to the same perturbation.
42
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