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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



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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