1

Estimating the Impact of Floods on House Prices: An Application to the 2005 Carlisle Flood

Paper presented at ERES 2009 Stockholm

Gwilym Pryce, Yu Chen, Danny MackayUniversity of Glasgow

Structure of Presentation

1. Introduction

2. Theoretical framework

3. Proposed econometric model

4. Background to 2005 Carlisle Flood

5. Data

6. Estimation

7. Future work

1. Introduction: the project

Downscaled Climate Change & Flood Risk Estimates

EWESEM Model

(Based on impact of

past floods)

Simulate Socio-Economic

Impacts for Case Study Area

Digimap terrain, SWERVE 2008

Stakeholder Engagement

(PP2)

+

Web Interface

(WISP)

From SWERVE

Introduction

• Aims of this paper: – To estimate the impacts of historical flood events

on house prices– To capture spatial spill-over effects of floods

• Why house prices?– If heterogeneities in the type of dwelling can be

controlled for, • variation in house price across space offers a way

of placing a monetary value on the variation in the desirability (and hence quality of life) of a location,

• and of the willingness to pay for avoiding flood risk.

– house price is potentially a powerful measure of the impact on wellbeing of extreme weather

2. Economic Theory

• Q1/ Why should house prices change at all in the event of a flood?– If markets are efficient, prices should already be

fully risk adjusted.– Areas with higher perceived flood risk will have

lower house prices, all else equal.– Yet, previous studies do indeed find:

• Temporary fall in house prices after a flood

• Followed by a gradual bounce back

• A1/ The most plausible explanation is market amnesia– Market prices drift away from the risk adjusted

level the longer the time lapse since last flood.– People actively cover up evidence of flood risk– Framing & herd behaviour (Zeckhauser 1996):

• tendency to underestimate risks that appear distant or global, or which others seem to accept without concern

• JARring Actions: Jeopardize Assets that are Remote (Zeckhauser 2006)

• Q2/ Why do house prices bounce back?• A2/ This is what you’d expect if the amnesia

hypothesis is valid– Flood event is a reminder of the true risk– The more frequent the reminder, the less prices

will diverge from the risk adjusted price• So prices will not fall so much, and the bounce back

effect will be correspondingly smaller.

– Crucially, house prices observed in the aftermath of the flood reveal the true risk adjusted house price.

• Whether floods are frequent or rare in an area, the price observed in the aftermath of a flood should be a good estimate of the risk adjusted price.

• This is important, because climate change will lead to more frequent flooding, and so prices in areas worst affected will eventually converge to their risk adjusted price as floods become more frequent.

• This allows us to estimate future house price impacts of flood risk.

3. Proposed econometric model

ln(pricei) = f(Si , Z, CBD, Green, Dep, year),where,

pricei = selling price of dwelling iSi exp(ӨDijHi)

= distance decay flood event variable captures the spill-over effect

Dij = distance from dwelling i to nearest flooded postcode unit j

Hi = elevationZ = vector of dwelling characteristicsCBD = distance to central business districtGreen = distance to woodland Dep = index of deprivation year = year dwelling sold

• Distance decay methods

• Explicit spatial econometrics models

4. Background to Carlisle 2005 Floods

• Located in northwest England, capital of Cumbria

• A long historical record of flooding. – Over 50 flood events occurred from 1800 to 1979, with

severe flooding every 11.4 years and major floods every 42.7 years

• January 2005: 15% of average annual rain fell in 36 hrs, once in 150 years

• Flood Defences were overwhelmed by the extreme flows. – 1,925 properties were flooded up to two metres. – 3 people died – Over 3000 people were made homeless for up to 12

months– Infrastructure was destroyed– An estimate of losses exceeded 450 million pounds

Source: EA 2005

5. Data

• Housing transaction data – House prices, property attributes– Nationwide building society 2006-07

• Location and accessibility measures– Elevation, distance to CBD, woodland. – Ordinance Survey

• Neighbourhood variable– Index of multiple deprivation

• Flood: – Flood outline overlayed with postcode boundaries in

GIS

• Distance between each postcode and its nearest flooded postcode

6. Estimation: functional form

• We incorporated distance to the nearest flooded postcode and height above sea level into the functional form of the flood variable:

Si = exp(ӨDijHi)

• A Maximum likelikood grid search procedure on the following model,

LnP = a0 + a1Bathroom + a2Bedroom + a3lnfloorsize + a4Centralheating + a5Newproperty + a6bungalow + a7lnCBD +a8lnwoodland +a9 imd + a10Si + a11year2007

0 10 20 30 40mean of ll

D_H_p09

D_H_p08

D_H_p07

D_H_p06

D_H_p055

D_H_p05

D_H_p045

D_H_p04

D_H_p035

D_H_p03

D_H_p025

D_H_p02

D_H_p015

D_H_p01

D_H_p005

D_H_p001

D_H_p0009

D_H_p0008

D_H_p0007

D_H_p0006

D_H_p0005

D_H_p0004

D_H_p0003

D_H_p0002

D_H_p0001

D_H_1p1

D_H_1p0

0 1 2 3 4mean of t_abs

D_H_p09

D_H_p08

D_H_p07

D_H_p06

D_H_p055

D_H_p05

D_H_p045

D_H_p04

D_H_p035

D_H_p03

D_H_p025

D_H_p02

D_H_p015

D_H_p01

D_H_p005

D_H_p001

D_H_p0009

D_H_p0008

D_H_p0007

D_H_p0006

D_H_p0005

D_H_p0004

D_H_p0003

D_H_p0002

D_H_p0001

D_H_1p1

D_H_1p0

Log likelihood values for different values of Ө

T-values (based on White’s Standard Errors) for different values of Ө

It reveals that the most appropriate value for Ө to be -0.005.

6. Estimation: spatial econometrics

• Spatial Auto-Regressive Model SAR: – y = ρWy + Xβ + e– Correction for house price in place i depending on the weighted

average of house prices nearby

• Spatial Error Model SEM:– y = Xβ + u; u = λWu + e– To adjust errors caused by omitted variables which vary

spatially

• General Spatial Model GSM:– y = ρWy + Xβ + u; u = λWu + e– Both a spatially lag variable and a spatially weighted error term

• Estimation methods:– Maximum Likelihood: typically used but with problems, e.g.

assuming normality– Generalised Moment Method as an alternative

A spatial weight matrix

• A square matrix measuring closeness in space

• Spatial contiguity matrix dij =1/0– where 1 denotes locations sharing the same boundary– only allow contiguous neighbours to affect each other

• K nearest neighbours: – where 1 denotes locations being one of the k nearest neighbours

• Defining a neighbour using a distance threshold

• Ways of calculating distance:– straight line distance– great circle distance– travel time– economic distance – trade costs, market access

• Row standardised

Selecting a spatial weight matrix

330 340 350 360 370 380 390

1

5

9

13

17

21

25

29

K n

eare

st n

eig

hb

ou

rs

Log-likelihood

Log-likelihood of SEM models

0 100 200 300 400 500 600 700

0

100

200

300

400

500

600

700

nz = 11981

Plot of W21 (783*783)

SEM model using a spatial weight matrix with 21 nearest neighbours has the highest log-likelihood.

Contiguity

List of models using spatial weight matrix with 21 nearest neighbours

Variable OLS SAR_ML SEM_ML GSM_ML SEM_GMM

constant 10.278587*** 10.262238*** 9.504726*** 9.380543*** 9.606181***

bathroom 0.107283*** 0.107987*** 0.065869*** 0.061220*** 0.068351***

bedroom 0.055401*** 0.056796*** 0.070982*** 0.072790*** 0.070008***

lnfloorsize 0.593950*** 0.586525*** 0.573139*** 0.569168*** 0.575033***

centralheating 0.098258** 0.099148** 0.124554*** 0.126222*** 0.123285***

newproperty 0.194032*** 0.197093*** 0.195552*** 0.194077*** 0.194811***

bungalow 0.250270*** 0.246316*** 0.249200*** 0.248236*** 0.249605***

lnCBD -0.083740*** -0.082627*** -0.032512** -0.025310* -0.039321*

lnwoodland -0.061884*** -0.060543*** -0.032726** -0.026478 -0.036334**

imd -0.014007*** -0.014018*** -0.011483*** -0.011129*** -0.011690***

flood -0.310461*** -0.307233*** -0.151275** -0.126336** -0.172821**

year2007 0.067920*** 0.068077*** 0.085071*** 0.087032*** 0.084149***

rho 0.002657 -0.016973

lamdba 0.883962*** 1.123361*** 0.796783***

Rbar-squared 0.724700 0.724900 0.782200 0.786200 0.772400

log-likelihood 311.112610 385.526510 384.383000

N 783 783 783 783 783

Normality of error term in SEM was rejected. SEM_GMM is more appropriate.

OLS: Ordinary Least Squares

SAR: Spatial Autoregressive Model

SEM: Spatial Error Model

GSM: General Spatial Model

ML: Maximum Likelihood

GMM: Generalised Moments Method

7. Future work

• Estimate the location value impact of the flood: PA t-1 - PA t

– Predict the CQP surface before the flood– Subtract the CQP surface after the flood

• Do the CIs overlap?

– How will size of impact vary across space?

• Simulate house price impact of a hypothetical flood event due to climate change

Thank you!