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Nonmarket allocation and the willingness to pay in regulated housing markets

Jos N van Ommeren and Arno J van der Vlist

Department of Economics Department of Economic Geography VU University University of Groningenj.n.van.ommeren@vu.nl a.j.van.der.vlist@rug.nl

ERES – July 4, 2013

Regulated housing in Global cities

Households cannot reveal

their true willingness to pay

Literature on regulated housing markets

› Random housing allocation -> misallocation (Glaeser and Luttmer, 2003)

› Rent control in private regulated housing -> limited housing supply (Olsen and Barton, 1983; Gyourko and Linneman, 1989)

This paper

› Methodology that exploit the queueing time to estimate the households’ marginal willingness to pay (MWP)

› Present and compare results for households’ MWP for regulated housing vis-a-vis private housing in Amsterdam Metropolitan Housing Market

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Model outline

Housing market

•Number of households N0

•Private market vs. regulated market

•Regulated housing is preferred over private

•Households in queue stay in private market

•v= v (X,r) with market value X and rent r

•

•Number of regulated housing N1 < N0

v > v0

v

vdvNN1

Model - households

T

tt dtevevV

)(0

0

Households’ lifetime utility V

Private market Regulated market

Model – households’ optimal queueing time

T

tt dtevevV

)(0

0

Maximizing lifetime utility V with respect to queueing time

Maxτ(v)gives

0])([

1/

0

e

ee

vvv

T

τ(v)

Model – housing market

Steady state Housing market

• nv/τ(v) households receive a house offer

• Nv/[T-τ(v)] households leave the housing market

• Excess demand equals queue:

• In steady state: nv/τ(v) = Nv/[T-τ(v)]

•

∂nv/∂v = ∂nv/∂τ(v) * ∂τ(v)/ ∂v > 0

( )

( )v

v

N vn

T v

v

v NNn 10

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0])([

1/

0

e

ee

vvv

T

∂nv/∂v = ∂nv/∂τ(v) * ∂τ(v)/ ∂v > 0

Model –towards an empirical model

/ log /.

/ log /

v X X

v r r

From households’ maximization we have

From the steady state housing market condition we have

It follows that

Empirical model

rX logloglog

log / log.

log / logx

X rMWP

r X

τ(v) Queuing time

X property tax appraisal value

r regulated rent

-+

Data

Data

Estimation results

Robustness analysis

› Eligible vs noneligible households (low- high income)

› Tobit analysis for Censoring duration

Estimation results

Conclusion

› Queueing time can be exploited to estimate the MWP for housing in regulated markets

› Queuing time varies with market value + and rent –

› MWP for regulated housing is close to the annual capitalization rate for private housing [4.7-6.2]

› Households pay about (2/3) of MWP so that inefficient housing consumption is most likely