Time on Market and Demand for Real Estate (Characteristics)

Daniel Sager, Meta-Sys AG, Zurich

European Real Estate Society 20th Annual ConferenceVienna, AustriaJuly 3-6, 2013

1

Demand for real estate is difficult to measure.

Vacancy rates are one-sided, there is only limited potential to measure excess demand.

Time on market can help.

What is this Study about?

I. Theoretical model

II. The natural rate of TOM

III. Empirical model

IV. Results

V. Conclusion

Literature

Table of Contents

I. Theoretical modelMoving (Wheaton (1990))

𝑀 𝑡1=(1−𝑐1→ 2 )𝑀 𝑡 −1

1 +𝑚1𝑆𝑡 −11 +𝑐2→ 1𝑆𝑡 −1

2(1)

where

households of type 1 in houses of type 1 (“matched”)households of type 2 in houses of type 1 searching in market 2

(“searching”)rate of type 2 households becoming type 1matching rate of households searching in market 1 (Poisson)

𝑆𝑡1=𝑐2→1𝑀𝑡 −1

2 +(1−𝑚1−𝑐1→ 2)𝑆𝑡− 11 (2)

Matching households in market 1

Searching households in market 1

I. Theoretical modelStock flow (Poterba (1984))

(3)

where   aggregate demand for houses of type 1) average demand per household for houses of type 1

rent for houses of type 1other variables affecting demandthe quality index of house type 1

price of house type 1marginal cost of production of new houses (convex!)new houses of type 1

𝑃 𝑡1=𝑐 (𝐼 𝑡1 ) (4)

(effective) demand

production of new houses

𝐻𝑡𝑑 ,1= (𝑀 𝑡

1+𝑆𝑡2) h1 (𝑅𝑡

1 , 𝑋𝑡 ,𝑄1 )

I. Theoretical modelStock flow (Poterba (1984))

(5)

(6)

𝐻𝑡1= (1−𝛿 ) 𝐻𝑡+1

1 +𝐼 𝑡1

where   stock of houses of type 1

rate of depreciation

𝑃 𝑡+1−1 𝑃 𝑡

1+𝑅𝑡1=𝑐 𝑃 𝑡

1

where (gross) capitalization rate

Evolution of the stock of houses

Capital market equilibrium

I. Theoretical modelSome specials

«notional» demand

𝑅𝑡1=(1+𝜉 )𝑅𝑡 −1

𝑝𝑐 , 1

where   measure of product market power

market clearing rent under perfect competition

where  vacancy rate

𝑣𝑡=𝐻𝑡

1−𝐻𝑡𝑑 , 1

𝐻𝑡1

𝐻𝑡𝑑 ,1 ,𝑛𝑜𝑡𝑖𝑜𝑛𝑎𝑙=(𝑀 𝑡

1+𝑆𝑡1 )h (𝑅𝑡

1, 𝑋 𝑡 ,𝑄1 )

Myopic rent setting with product market power

Vacancies

(7)

(8)

I. Theoretical modelSome specials

Capital market equilibrium including vacancies

Adaptive expectations

𝑃 𝑡+1−𝑒 ,1 𝑃 𝑡

1+𝑅𝑡1(1−𝑣𝑡)=𝑐 𝑃 𝑡

1

𝑃 𝑡+1𝑒 ,1=𝜗 𝑃 𝑡

1+(1−𝜗)𝑃𝑡𝑒, 1

where  rate of adaptation of expectations

(8)

(9)

I. Theoretical modelTime on market

𝑜𝑡1=

𝑚1𝑆𝑡1h1(.)

𝐻𝑡1−𝐻𝑡

𝑑 ,1+𝑚2𝑆𝑡2h2( .)

Offers (Poisson)

(10)

moving in

moving outvacancy

Time on Market

𝑡𝑜𝑚𝑡=1

𝑜𝑡1 (11)

I. Theoretical modelTime on market: steady state comparative statics

𝑡𝑜𝑚𝑡=1𝑜𝑡1=

𝐻 𝑡1−𝐻𝑡

𝑑 ,1( .,𝑐1→2 ,𝑐2→1)+𝑚2𝑆𝑡2(𝑐1→2 ,𝑐2→1)h

2 ( . )𝑚1𝑆𝑡

1(𝑐1→2,𝑐2→1)h1( .) (12)

𝛿𝑡𝑜𝑚𝑡

𝛿𝑐1→2>0

𝛿𝑡𝑜𝑚𝑡

𝛿𝑐2→1<0

𝛿𝑡𝑜𝑚𝑡

𝛿𝑐𝑥→ 𝑦

≤0𝑐1→2=𝑐2→ 1

𝛿𝑡𝑜𝑚𝑡

𝛿𝜉>0

I. Theoretical modelTime on market and vacancy: dynamics after demand shock

II. The natural rate of TOM

𝑡𝑜𝑚∗=𝑏 ′ 𝑧𝑎

�̇�=𝑏′ 𝑧−𝑎∗𝑡𝑜𝑚

�̇�=𝑔 (𝑡𝑜𝑚∗ (𝑧 )− 𝑡𝑜𝑚)

depends for example on

(13)

(14)

(15)

AdScan Database: All Swiss online advertisments (real estate) since 2004Time on market <- time advertised

divide Switzerland in 25 market regions:

11 «large» agglomerations7 regions with smaller agglomerations7 rural areas

III. Empirical modelData

Estimate price growthHedonic regression with exogeneous variables («market segment»): price level at zip, rooms, market region, new/renovated vs other, house or apartmentEstimate value of base portfolio for consecutive periods for market regions

III. Empirical modelEstimations

N = 1’103’391F( 9,1103381) = 5275.58

Dependent variable: Logarithm of time on market

robust regression

Estimate equilibrium TOMCoefficient Standard Error t

price growth -7.011 0.06312 -111.1

Number of Rooms2 -0.105 0.00435 -24.23 0.115 0.00406 28.44 0.295 0.00422 69.95 0.352 0.00556 63.36-9 0.524 0.00766 68.4

Popuation density -0.024 0.00029 -82.0Agglomeration -0.058 0.00347 -16.8House (not Apartment) -0.180 0.00529 -34.0Constant 10.392 0.06398 162.4

III. Empirical modelDemand indicator

Calculate deviation from equilibrium TOM for each real estate object

derive aggregate descriptive statics for market region, housing types ...

or

III. Empirical modelEstimate demand of characteristics for the city of Zurich in 2012

Odds Ratio Standard Error z P(z)

house / apartment 1.453 0.606856 0.89 0.37elevator 1.212 0.128142 1.81 0.07fireplace 0.726 0.123187 -1.89 0.06

balconylarge 1.247 0.132014 2.08 0.04small 1.103 0.323384 0.33 0.74

viewlake 1.432 0.175137 2.94 0.00other 0.821 0.165480 -0.98 0.33

private landlord 1.336 0.151986 2.55 0.01wheelchair 1.079 0.279157 0.29 0.77

apartment type two storey 1.220 0.329900 0.73 0.46attic 0.939 0.265409 -0.22 0.82

other variables ... ... ... ...

N = 2’818CHI2 = 434.05

dependent variable: 1 tom housing unit < tom*0 tom housing unit > tom*

Logistic regression

IV. ResultsDemand: Federal Office of Housing: Indicator of housing market scarcity

median Dtomfor 108 market regions, classified according to 10 classes representing all market situations over the last 10 years.

IV. ResultsDemand of characteristics: Probability of being scarce in the city of Zurich

IV. ResultsDemand of characteristics: Probability of being scarce and change over time

V. Conclusions

Time on market can serve as a demand indicator, when price setting does not immediately clear the market.

It can even serve as an indicator for demand of characteristics.

Even at low vacancy, time on market shows increasing (notional) demand.

Equilibrium time on market has to be carefully described (otherwise erroneous conclusions may arise).

The extension to owner-occupied housing should be straightforward.

Potential for standardized international market analysis.

Analysis of behaviour under different market mechanisms (search efficiency etc.).

Literature

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