By Elias Oikarinen

Turun kauppakorkeakoulu Turku School of Economics

ERES Conference15-18 June, 2011, Eindhoven

The Adjustment of Housing Prices Towards the Housing Market No-Arbitrage Relation

By

Elias Oikarinen


Background

• Housing market no-arbitrage relation gives the asset market equilibrium for housing prices

• In practice, long-lasting deviations from the no-arbitrage relation have been perceived in a number of countries

• The adjustment process towards the no-arbitrage relation is a central question regarding the dynamics and predictability of housing markets

of importance to households, construction companies, investors and to economic policy makers

• Nevertheless, empirical research on the adjustment towards the no-arbitrage relation is limited


Aim of the Study

• To examine empirically the adjustment towards the no-arbitrage relation in the Helsinki Metropolitan Area (HMA) and in the rest of Finland

• To investigate the role of liquidity constraints in the adjustment process

• To estimate the impact of a user cost shock on the free-market housing prices, rents and supply

• To examine whether the dynamics notably differ between the regions


Housing market four-quadrant model (1)

ASSET MARKET: Rent (€/m2) PROPERTY MARKET:Valuation Rent determination

P=R/u

D = S

Price (€/m2) Stock (m2)

S = C/dP=F(C)

ASSET MARKET: Construction (m2) PROPERTY MARKET:Construction Stock adjustment


Asset market equilibrium – the no-arbitrage relation

E(u) = after-tax opportunity cost of capital (%) + depreciation/maintenance (%) – expected appreciation (%)

In the Finnish case, where the imputed rent is not taxed:

• Because of the notable frictions in the housing market, substantial and long-lasting deviations from the asset market equilibrium relation may emerge and the price adjustment towards the relation may be highly sluggish

Ut = Rt – TtitPt – TttPt

E(Ut) = Rt where E(Ut)= Pt E(ut)


Rent (€/m2)


Construction (m2)

User cost change in the four-quadrant model


• The adjustment dynamics and magnitudes after a user cost shock are of particular interest: via asset price level the shock affects supply, rental price level and the equilibrium price/rent-ratio

• The theory leaves the adjustment speeds and magnitudes open

To get information on the actual adjustment process, rigorous empirical analysis is needed

• Liquidity constraints may influence the adjustment speed

• Adjustment dynamics may differ between regions


Closer look at the impact of a user cost shock

Rent (€/m2)


Construction (m2)

(e1S)

e1S

e1L

e0


Adjustment paths of the equilibrium price level and the actual price level

Price

time

e1S

e1L

e0

t=0 t=1


Drt = Rt –1Y + 2S

Dst = St –1P + 2CC

Econometric Model

• System of three error-correction models:

Where

(R = 0.72*Y – 2.4*S / 0.67*Y – 2.9*S)

(S = 0.23*P – 0.06*CC / 0.31*P – 0.03*CC)

Exact lag structure and variables not know a priori

Dt = ueqt / (Rt / Pt) -1, where ueq = (Rt – TtitPt – TttPt) / Pt

pt = p – pDpt-1 + ∑piθt-i + pt

rt = r – rDrt-1 + ∑rirt-i + ∑riφt-i + rt

st = s – sDst-i + ∑sist-i + ∑siΩt-i + st


Potential Complication

• Comparability between the housing price and rental price series - different dwellings

• Privately finance flat market price data and square meter prices are used: diminishes the heterogeneity problem

• User cost measurement

• Expected appreciation

• Risk premium

• Liquidity constraints

• Other data complications• E.g. measurement of liquidity constraints


Empirical Findings

• Asset prices appear to adjust towards the no-arbitrage relation significantly but slowly

• No evidence of asymmetric adjustment or liquidity constraints affecting the adjustment speed

• Housing price growth and supply changes are highly predictable

• Also the adjustment speeds of R and S towards the long-term equilbirium relations are low (but significant)

• Adjustment slower in HMA

• Rental price response greater in the rest of Finland


Asset price does most of the adjustment in HMA

The estimated impact of a 10% increase in u on asset price level, rental price level and on housing stock, HMA

-1,60%

-1,40%

-1,20%

-1,00%

-0,80%

-0,60%

-0,40%

-0,20%

0,00%

-0,10-0,09-0,08-0,07-0,06-0,05-0,04-0,03-0,02-0,010,000,010,020,030,040,05

0 10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

Quarters from the shock

price

rent

stock


Outside HMA prices adjust less and rents more

The estimated impact of a 10% increase in u on asset price level, rental price level and on housing stock, rest of Finland

-1,80%

-1,60%

-1,40%

-1,20%

-1,00%

-0,80%

-0,60%

-0,40%

-0,20%

0,00%

-0,10

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,100 10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

Quarters from the shock

price

rent

stock


Concluding Remarks

• Theory does not give the adjustment speeds or magnitudes

• Housing prices adjust significantly but slowly towards the asset market equilbirium condition

• It appears that asset prices do the major part of the adjustment after a user cost shock in a highly supply restricted area (HMA)

• The role of rental price adjustment is notably greater in less supply restricted regions (other parts of Finland)

• The impact of changes in the tax code are more complicated: need for further research


Asset market disequilibrium (€/m2, annual level) together with real housing price and rental price indices, HMA

1988 1991 1994 1997 2000 2003 2006 20094.4

4.6

4.8

5.0

5.2

5.4

-12.5

-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5

10.0

Real rental price index

Real housing price index

Disequilibrium (right scale)


Computation of the user cost

• Maintenance costs from Statistics Finland

• A prediction model for expected appreciation• Prediction for nominal price growth based on an ECM (predictors:

one period lagged values of nominal housing appreciation, nominal aggregate income and of the deviation from a long-run relation between housing prices and aggregate income)

• Constant risk premium at 2% (following Himmelberg et al. 2007)

• Risk-free cost of capital is the average after-tax mortgage rate

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By Elias Oikarinen

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