ERES 2015 | Main Sessions06-25-2015

A Hedonical Spatial Office Rent IndexAn Application for Madrid Market

Ramiro J. RodríguezA presentation for

ERES 2015 - Regular Sessions | Istanbul, Turkey

The opinions and analyses are the responsibility of the authors and, therefore, do not necessarily coincide with those of BNP Paribas Real Estate

ERES 2015 | Main Sessions06-25-2015

Motivation for the research

1. Explaining office letting rents dynamics with an econometric approach

1. An alternative to [weighted] average rents to describe rents evolution

2. Study the impacts of hedonic characteristics

2. Implementing spatial models for the office market

3. Performance comparison between ‘classical’ hedonic models and spatial hedonical models

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Main findings

• Significant evidence on spatial feedback• Spatial models have higher explanatory capacity

than classical hedonical estimations• Non-time variant unseen characteristics captured

via Spatial endogenous-variable-lag model• Business district, age, technical building quality are

the main determinants of prices• Spatial rent index indicates a lower rent in Madrid in

the crisis period than shown by average rents– Sample composition issues corrected– Surface biases corrected

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Performance comparison (€/sqm/month)

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hedonical rent Average rent Geo-hedonical rent Weighted average rent

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On estimation methods • Average rents present skewness towards

– Large transactions– More transacted area

• Hedonical models: Not affected by deal sizes yielding more realistic estimated rents

• Spatial approach: – Fits the idea of non-observed interdependence of

price levels among neighbours in real estate transactions

– Uses the full power of the database, in opposition to pseudo-panels

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Market stylized facts

• Relatively small Madrid’s market, averaging 500,000 sqm of gross absorption each year with around 120 letting transactions

• Spanish crisis deeply affecting office market– Office space take-up more than halved– Prime rents plummeted 40%– Average rents decreasing around 30%– Strong implementation incentives for new contracts

• Demand seems to be recovering in 2015

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Market stylized facts – Prime rents

Central London

Central Paris

600

700

800

900

1,000

1,100

1,200

1,300

1,400

1,500

1,600

1,700

1,603

750

High Point (Since 2007)

Q4 2014

Q4 2013

Low Point (Since 2007)

€/m²/year

Milan Frankfurt Munich Madrid Hamburg Berlin Brussels200

250

300

350

400

450

500

550

600

480

456

414

318 300

276 265

High Point (Since 2007)Q4 2014Q4 2013Low Point (Since 2007)

€/m²/year

Source: BNPPRE

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Reference literature

• Marginal effects• Rent index• Externalities

Hedonic estimations

• Controlling underlying property characteristics

• Marginal effectsPanel data

• Controlling unseen location feedback

• Lagged, error and Durbin models

• Panel data and pseudo panels

Spatial econometrics

• Kain and Quigley (1970)• Straszheim (1974)• Clapp (1980)• Torto and Wheaton (1994)• Malle (2009)

• Quigley (1995)• Gao and Wang (2007)• Hansen (2009) • Osland (2013)

• Cliff and Ord (1973, 1981)• Anselin (1988, 1996)• Kapoor, Kelejian and Prucha (2004)• LeSage (2005)• Rambaldi and Prasada (2011)

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Variables and data

DDBB with most of the hedonic variables identified the literature review

o Transaction list provided by BNP Paribas Real Estate (3,600 obs)o Matched with information from the Spanish Land Registry (Cadastre)

o Structure: Half year data

o Start date: 2003:1

o End date: 2014:1

o Rent deflated by the implicit GDP deflator (2010=100)

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Variable definition• Endogenous: Real office rent per square meter

(rrent)* Headline rent from new contracts list

• Regressors:

Business districts*(CBD, Centre, Decentralized, Outskirts left out in regressions)

Building characteristics**(Age, Stately, Exclusive, Stories, Quality index, distance to metro entrance)

Lease contract***(Corporate tenant Dummy variable as commitment proxy )

Time dummies***(H1 2003 left out in regressions)

• Spatial instrument Geographic coordinates**

(X_coord Y_coord)

Source:* BNPPRE** Cadastre*** Calculated

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Office zones

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Market intensityOffice transactions Q1-Q4 2014

Transaction density under 100 mts.

2 4 6 80 10

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Spatial hedonical model (1)Benchmark model (OLS)

(1)

Spatial lag model

(2)

scalar parameter indicating spatial dependence intensity

matrix of average distance among transactions• Row standardized inverse distance matrix of transactions inside 10 km• Diagonal set to zero• Distances calculated with Euclidean formula

Model selection using GETS methodology

Constant s indicate stable technology in 2003-2014

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Spatial hedonical model (2)

Spatial marginal effects

(3)

(4)

Spatial out-of-the sample estimated rent

(5)

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Regression analysis (OLS)

Number of observations: 3,912R-Squared: 0.62Root MSE: 0.22

Estimator p-value Estimator p-value Estimator p-value

cons 2.7595 0.0000

cbd 0.5658 0.0000 H12004 -0.1050 0.0000 H12010 -0.1870 0.0000

centre 0.3753 0.0000 H22004 -0.1194 0.0000 H22010 -0.2464 0.0000

dec 0.1690 0.0000 H12005 -0.1276 0.0000 H12011 -0.2510 0.0000

age -0.0012 0.0000 H22005 -0.0937 0.0000 H22011 -0.3063 0.0000

floors 0.0021 0.0000 H12006 -0.0671 0.0000 H12012 -0.3384 0.0000

exclusive 0.0752 0.0000 H22006 -0.0586 0.0010 H22012 -0.4091 0.0000

qual_adj -0.0500 0.0000 H12008 0.0622 0.0010 H12013 -0.4364 0.0000

metro_distance -0.00001 0.0000 H12009 -0.0893 0.0000 H22013 -0.4427 0.0000

corporate 0.0939 0.0000 H22009 -0.1482 0.0000 H12014 -0.4713 0.0000

(1)

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Regression analysis (Spatial)

Existence of Spatial feedback checked with Moran’s I test:

H0: No spatial autorcorrelation

Fitted model: (1)

Evidence of geographic proximity dependence

Test Statistic df p-value----------------------------------------------------------------------------------Spatial error:Moran's I 60.996 1 0.000Lagrange multiplier 2683.75 1 0.000Robust Lagrange multiplier 1929.98 1 0.000 Spatial lag:Lagrange multiplier 873.308 1 0.000Robust Lagrange multiplier 119.536 1 0.000----------------------------------------------------------------------------------

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Regression analysis (Spatial)

Number of observations: 3,912Variance ratio: 0.665

Estimator p-value Estimator p-value Estimator p-value

cons 0.4134 0.0000 H22003 -0.0307 0.1070 H12010 -0.2077 0.0000

rho 0.8863 0.0000 H12004 -0.1326 0.0000 H22010 -0.2625 0.0000

cbd 0.2751 0.0000 H22004 -0.1551 0.0000 H12011 -0.2667 0.0000

centre 0.1243 0.0000 H12005 -0.1564 0.0000 H22011 -0.3291 0.0000

dec 0.0268 0.0330 H22005 -0.1217 0.0000 H12012 -0.3662 0.0000

age -0.0017 0.0000 H12006 -0.0916 0.0000 H22012 -0.4259 0.0000

stately 0.0273 0.0400 H22006 -0.0803 0.0000 H12013 -0.4661 0.0000

floors 0.0026 0.0000 H12007 -0.0474 0.0050 H22013 -0.4681 0.0000

exclusive 0.0804 0.0000 H12008 0.0448 0.0110 H12014 -0.4846 0.0000

qual_adj -0.0464 0.0000 H12009 -0.1090 0.0000

corporate 0.0877 0.0000 H22009 -0.1688 0.0000

(2)

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Stability test

04-18-2015

cbd

centre

dec

age

stately

qual_adj

corporate

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

2008 2009 2010 2011 2012 2013-H12014

cbd centre dec age stately qual_adj corporate

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Marginal effects comparisonSpatial marginal effects

(3)

(4)rho NA 0.8863

cons 2.7595 0.4134

cbd 0.5658 0.2751

centre 0.3753 0.2751

dec 0.1690 0.0268

age -0.0012 -0.0017

floors 0.0021 0.0026

exclusive 0.0752 0.0804

qual_adj -0.0500 -0.0464

metro_distance -0.00001 NA

corporate 0.0939 0.0877

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Fernandez & Montero (Geostatistical Air Pollution index in Spatial Hedonical Models: The case of Madrid - 2012) define is a nxn matrix:

“[of] spatial spillovers or effects of the independent variables on the dependent variable”

“The sum across the i-th row of represents the total impact on the individual observation yi resulting from changing the r-th explanatory variable by the same amount across all n observations”

∑ 𝑟𝑜𝑤 (𝑖 )∨¿𝛿𝑟

𝛿𝐶𝐵𝐷=2,41¿

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Residuals normality (non parametric test)

Parametric tests on residuals yield non-normal residuals distributionsIssues on sample size

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The prototype office

cbd centre dec x_coord y_coord age (years) stately floors exclusive qual_adj metro_distance corporate lrrent

1 0 0 441666.68 4476074.24 41 1 12.9 1 2.7 183 1 ?

0 1 0 442425.28 4477113.92 34 1 7.3 1 2.6 186 1 ?

0 0 1 446734.16 4475984.32 16 1 6.6 1 3.2 562 1 ?

0 0 0 450738.92 4477704.32 19 1 2.4 1 2.9 1,540 1 ?

1. Definition of the archetype office

Average characteristics by zone

Age, floors, metro distance, quality index, geographic coordinates

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Hedonical rent estimation

1. Definition of the archetype office

2. Imputation in DDBB with replacement

One hedonic office for each zone, each period (no rent datum)

3. Recalculation of weight matrix

4. Estimation of r_hat with (5)

Recovery of imputed hedonical office

5. Average of estimated rent for each zone

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Rent estimation (€/sqm/month)

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Geo-hedonical rent

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Rent estimation (€/sqm/month)

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hedonical rent

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Performance comparison (€/sqm/month)

Flight to quality

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Hedonical rent Average rent Geo-hedonical rentWeighted average rent

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Rent index

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hedonical rent Average rent Weighted average rent Geo-hedonical rent

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Conclusions

1. Explanatory capacity improves with Spatial models

2. Estimation with spatial component yields normal residuals

3. Estimated rent index corrects:

1. Sample composition effects

2. Deal size issues

4. Classical hedonic techniques issues such as unobservable characteristics are corrected

5. Side products such as semi-elasiticities are valuable for market insights

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Q&A

Suggestions are much appreciated!

Thank you

?06-25-2015