For example, assume that transition rates (

p

ij

) differ by initial status (public,

cooperative, private; renter, owner) and that the transition process is governed by a first 

order Markov Process.

p

p

. . .

p

11

12

1

N

p

p

. . .

p

21

22

2

N

[

N

. . .

N

]

[

N

. . .

N

]

(14)

1

t

Nt

1

t

&

1

Nt

&

1

.

.

.

.

.

.

p

p

. . .

p

N1

N2

NZ

where 

N

 represents the number of households in a given  state  at time 

t 

and

 p

ij

 are

transition probabilities (assumed constant over time from state

 i

  to state 

j).

Observe average mortgage assessment and house value for recent owners (or for

recent owners transitioning from each state) and calculate the weighted average mortgage

amount for households from each originating category.

N

M

j

M p N

i

i1

it

&

1

(15)

i

1

One could disaggregate to other categories (income, household size, or location)

and the model retains its generality.

Data would come primarily from household interview surveys (probability samples)

and, to a lesser extent, from borrower surveys focusing on mortgages for selected

originating categories.

D.

Another alternative explicitly takes account of supply constraints and borrowing

restrictions.  Borrowers are subject to two restrictions on their ability to borrow one based

on housing payments relative to income, the other based on down payment requirements

relative to assets.  The first of these may be stated as:

a

T

r

M

<

ky

(16)

where 

a

T

r

 = loan amortization factor for interest rate = 

r 

for 

N

 periods

e.g., 30 years, 

a

r

= .08/yr = .00734/mo.

M 

= mortgage amount

k

  = maximum mortgage payment to income ratio (e.g., 0.28 0.33 in U.S.  which

should bear some relation to the  normal  ratio in specific countries). Evidence from

I 14