Efficiency in the market for cooperative dwellings

Silje Eretveit, Karl Robertsen and Theis Theisen

Department of Economics and Business Administration University of AgderNorway

Introduction• Efficiency in housing markets important

• Efficiency over time: Case and Shiller (1989)

• Efficiency with respect to financial arrangements:

Goodman and Goodman (2007)

Kelley (1998)

Schill et. al (2007)

Hjalmarsson and Hjalmarsson (2009)

Robertsen and Theisen (2011)

•The present paper builds on RT and HH

Norwegian housing cooperatives• 15 % of dwellings in the country are cooperative

• Housing cooperatives non-profit institutions. Special law

• To obtain a co-op one has to buy a share in the cooperative

• A share in the cooperative gives the right to use a specific dwelling

• The shareholder is free to sell his unit on ordinary market conditions

• Housing cooperatives are partly financed by mutual debt

• The mutual debt is paid down through monthly rent

• The interest rate on mutual debt is in Norway lower than on private

debt

•All shareholders are formally responsible for the full mutual debt

The price of a co-op

The price of a dwelling in a housing cooperative consists of two elements:

• An equity price determined through a normal competitive bidding

process

• The mutual debt: Each dwelling carries a share of the debt held

by the cooperative. The living space of the dwelling determines the

share of mutual debt affiliated with the dwelling

We consider two identical dwellings•Dwelling A carries a mutual debt

Mutual debt is paid down through rent.

At time 0, the dwelling is bought at the price

•Dwelling B carries no mutual debt

At time 0, the dwelling is bought at the price

The full purchasing price has to be financed privately

•What is the relationship between , and ?

•How do equity-prices of the two dwellings change over time (Assume zero inflation: Price of dwelling B constant

0M

0AE

0BE

0AE 0

BE 0M

The financial effects for holders of the two dwellings:•Dwelling A

- Lower interest paiments than dwelling B

- „Overprice“ when the dwelling is bought

- Capital loss when the dwelling is sold

•Dwelling B

- Since we abstract form inflation, the price that the

dwelling can be sold for is constant over time

Time

P

T

0AE

0M

tP

tAE

0 0 0AE M

0BE

0

The relationship between equity prices at time 0

0 0 0 0

0

1

T tp M t it

A B T

T p tt

i i dE E M

d i d

Înterest discount effect

The model can be estimated if mutual debt is known(Robertsen and Theisen (2011))

The case when mutual debt is not observed(Hjalmarsson and Hjalmarsson (2009)

t t t ti M i i iR i M a M bA

tt i ii t

M i

R bAM

i a

Rent-function:

gives:

Substitution into equity-relationship, with, :

00 0 0 0

0 0

1 1

T Ttp M t i p M tt ti i

A B T TM i M iT p t T p tt t

i i d i i dR AE E b

i a i ad i d d i d

0t ti iR R

Asumptions (of Hjalmarson and Hjalmarson):

1ti

p Mi i

ia a

Yield the HH-equation;

00 0 1 i iA B

M M

R AE E b

i a i a

Easily estimated IF a is known

We estimate the two regression functions:

0ˆˆHH HH HH HH HH

i R MAINT iP X R A Y Z

00RT RT RT RT RT

i M iP X M Y Z

Dwellings in housing cooperatives (N=1050)

Minimum Maximum Mean St. deviation

Equity price 55 000 3 600 000 1 504 910 451 656

Mutual debt -23 323 2 700 000 279 608 391 443

Rent 975 13 531 3 162 1 455

Size 23 174 71 21

Age 1 65 37 16

Data: All co-op transactions 2009-2010 in Kristiansand municipality

Mutual debt PV annual rent PV maintenance Size Age

Mutual debt 1 0,6163 0,0526 0,1510 -0,7053

PV annual rent 1 0,5728 0,3200 -0,5130

PV maintenance 1 0,3821 -0,0831

Size 1 -0,1981

Age 1

Correlation matrix

(t-values in parentheses)

Conclusions:

•Empirical support for efficient prices in the Robertsen-Theisen model• The efficiency hypothesis is rejected when the Hjalmarsson-Hjalmarsson model is used with their original assumptions.•Problem: The payback-rate for mutual debt must in the HH-model be pegged prior to estimation. The results are very sensitive to the magnitude chosen for this parameter. Also other assumptions in the HH-model are problematic.