Spatial spillovers in the pricing of flood risk: Insights …1438999/...Spatial spillovers in the pricing of flood risk: Insights from the housing market Carolin Pommeranz RWTH Aachen

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Spatial spillovers in the pricing of flood risk: Insights from the housing market

Carolin Pommeranz and Bertram Steininger

Working Paper 2020:8

Division of Real Estate Economics and Finance Division of Real Estate Business and Financial Systems

Department of Real Estate and Construction Management School of Architecture and the Built Environment

KTH Royal Institute of Technology

Spatial spillovers in the pricing of flood risk: Insights from the housing market Carolin Pommeranz RWTH Aachen University, School of Business and Economics, Aachen, Germany [email protected] Bertram Steininger Division of Real Estate Economics and Finance Department of Real Estate and Construction Management Royal Institute of Technology Stockholm, Sweden Email: [email protected]

Abstract: In this study, we analyse how, and to what extent, direct and indirect effects (spatial spillovers) matter when estimating price effects for a property located in a flood zone. Unlike the previous literature, we show the importance of indirect effects resulting from a neighbourhood being situated in a flood zone. Additionally, the types of indirect effects (global vs. local) need to be determined theoretically or empirically using an appropriate spatial model comparison approach. Using the Bayesian model comparison for data related to the flood-prone city of Dresden, Germany, we find strong evidence for a spatial Durbin error model which controls for local spillover effects. These indirect price effects amount to -6.5% for houses and -4.8% for condominiums. However, direct effects diminish when controlling for spatial spillovers. Our results are generally robust across different model specifications, urban areas, and risk-adjusted prices that include future insurance costs, thus providing evidence of the importance of addressing indirect effects in the form of local spillovers in the analysis of flood zone effects. Ignoring indirect flood effects when formulating policy can lead to flood management that is inefficient and not cost-effective, as the economic consequences of flood are underestimated. Keywords: spatial econometrics, spatial spillovers, indirect effects, flood hazards, housing market

JEL Classification: R2, C2, G22, Q51, Q54

Acknowledgements: The authors wish to thank Paul Elhorst, Piet Eichholtz, David Ling and the participants of the 2015 INFER Workshop in Aachen, the 2016 European Real Estate Society (ERES) Annual Conference in Regensburg, and the 2016 American Real Estate and Urban Economics Association (AREUEA) International Conference in Alicante for their insightful comments and suggestions on an earlier version of this paper. Finally, we would like to thank the German Insurance Association (GDV), Westfälische Provinzial AG, and Immobilien Scout GmbH for providing us with raw data and comments on an earlier version of this paper.

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1. Introduction

Floods are the most prevalent natural hazard worldwide in terms of fatalities and financial losses; around

one-third of all reported natural catastrophes and implied economic losses result from flooding.

Although the effects of global warming and climate change are leading to a higher frequency and

severity of flood events, floodplains still provide attractive building land for urban and industrial

development, resulting in an increased concentration of values. As a result, higher economic losses occur

from flood damage, which poses a challenge not only for the real estate sector but the economy as a

whole, and also gives rise to the question of how to adequately price flood risk.

Besides the obvious relevance to urban development, flood risk typically reduces property values due

to the potential for structural damage or even the total loss of a property. When estimating flood risk

price discounts, the existing literature already considers spatial spillovers to control for unobserved

spatial correlation resulting from neighbouring properties. However, unobserved spatial dependence in

the dependent and explanatory variables leads to biased and inconsistent estimates of price effects,

whereas an unobserved spatial lag in the error terms results in a loss of efficiency (Anselin & Bera,

1998). Though it controls for spatial dependence, the previous research mostly focuses on the

interpretation of direct effects for theoretical flood zones (FZs) and actual floodplains. Direct effects can

be compared to coefficients from linear models: they stem from a change in the property itself and

mostly result in discounts for locations with an increased risk (Bin, Kruse, & Landry, 2008; Bin &

Landry, 2013; Rambaldi et al, 2013). Conversely, our measurement of flood price effects aims to

underline the relevance of indirect effects, which capture spatial spillovers from the neighbourhood.

FZ status is only directly reflected in property prices when it is evident to buyers and sellers. Information

costs for observing direct flood risk are high for buyers, therefore, they neglect to search for information,

especially when the prevailing risk is of high consequence and low probability (Browne, Knoller, &

Richter, 2015; Bin & Kruse, 2006; Bin & Polasky, 2004). Although some studies suggest that the

acquisition of insurance may serve as an indicator of flood risk, Kunreuther and Pauly (2004) find that

insurance is often not purchased due to the high transaction costs for obtaining information about

prevailing risk, a low expected return from financial efforts and anticipated excessive costs for sufficient

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insurance. Chivers and Flores (2002) confirm that many buyers are unaware of a property’s floodplain

location and flood insurance costs when purchasing a property. Consequently, buyers have less

information about direct flood risk than sellers and may accept price discounts to compensate for risk

that fall far below the potential statistical economic losses. Thus, the question arises whether the

interpretation of direct effects is sufficient for understanding flood price effects under asymmetric

information. In situations where decisions are made under conditions of uncertainty, Tversky and

Kahneman (1974) suggest that individuals use simplified heuristics based on representativeness or

availability, without considering the explicit trade-offs between costs and benefits for different

alternatives. Regarding flood risk, we assume that these heuristics may include the immediate

neighbourhood as an easily observable indicator of FZs. For example, when neighbours are interviewed,

recent flood damage may still be visible on buildings or the media may report on flooding in the local

area. Spatial regressions include these neighbourhood effects as spatially lagged variables (indirect

effects) that need to be interpreted in the context of flooding. Ortega and Taspinar (2018) analyse

changes in the direct effect from damage due to a flood event at the property itself while controlling for

the damage suffered by properties in the same city block. Using a standard regression model with fixed

effects, they find evidence of an impact from damaged neighbouring properties that leads to significantly

reduced direct effects.

If studies include indirect effects, they are mostly inadequate in determining the type of spatial

spillovers. Spatial dependence can induce either local or global spillover effects. Local spillovers relate

to characteristics of the immediate neighbourhood that influence price setting for the property in

question; however, global spillovers also arise from properties that do not belong to the immediate

neighbourhood. LeSage (2014b) states that “most spatial spillovers are local” and postulates that global

spillovers only arise when there are endogenous interaction and feedback effects. Endogenous

interaction induces a sequence of adjustments in (potentially) all properties in the sample, which in turn

causes feedback effects and leads to a new long-run steady-state equilibrium. In the context of

properties, indirect effects are mostly limited to the immediate neighbourhood due to the shared

characteristics of structure and location, such that endogenous interaction and feedback effects are

unlikely to occur. Flood risk is particularly variable at a local level based on topographic and

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development characteristics. Therefore, we assume that local spillovers are predominant in measuring

flood price effects.

In this study, we shed new light on the importance of including indirect effects for FZs when interpreting

flood price effects, and we aim to increase sensitivity in order to select a correct spatial model. Therefore,

we use recent developments in spatial econometrics to control for spillovers and for unobserved spatial

dependence. The type of spatial dependence is assessed by a Bayesian model comparison approach (see,

e.g., LeSage, 2014a), and we find strong evidence for a spatial Durbin error model that controls for local

spillover effects. We apply this model to the flood-prone city of Dresden, Germany, which experienced

severe flooding from the River Elbe in 2002 and 2013. Indirect effects amount to -6.5% for houses and

-4.8% for condominiums, whereas direct effects are not statistically significant. We also compare price

effects with insurance costs to determine whether sellers accept price discounts that correspond to the

economic loss covered by the insurance contract. While compensating buyers for the costs of covering

economic losses in most FZs, sellers anticipate a higher willingness to pay in a high-risk FZ. Finally,

we incorporate the insurance costs in order to obtain risk-adjusted property prices that confirm the

existence of indirect discounts for all FZs.

2. Theoretical Flood Impact on Property Pricing

Flooding is the prevailing natural risk to urban areas in Germany and can result in significant damage.

Many regions have already been subject to severe flood events, therefore, many property sellers and

buyers have already directly experienced the consequences of flooding. Flood experience typically

induces increased risk awareness due to information campaigns or flood protection measures that are

implemented in the aftermath of an event (Browne & Hoyt, 2000; Michel‐Kerjan & Kousky, 2010;

Kriesel & Landry, 2004). In general, the literature identifies significant price discounts directly

following flood events (Bin & Polasky, 2004; Morgan, 2007; Shultz & Fridgen, 2001). Daniel, Florax,

and Rietveld (2007) coclude that price reductions persist after these events if there is a clear official

communication of flood risks; however, without clear communication, price effects typically diminish

as more time passes since the last experienced flood event (Atreya, Ferreira, & Kriesel, 2013; Lamond

& Proverbs, 2006). Bin and Landry (2013) find a continuous decline in price discounts until they

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completely disappear after a period of six years. In addition, spatial spillover effects for flood risk can

vary with the information source, including information effects (theoretical zones) and visualisation

effects (actual floodplains). Merging both effects would overestimate price effects from theoretical

zones (Atreya & Ferreira, 2015). However, regions with an increased risk status have typically

experienced flooding, so price effects are affected positively or negatively and need to be interpreted in

the context of flooding history to gain comparable estimates. We focus on theoretical zones in our main

analysis but also conduct a robustness check and analyse whether properties in the actual floodplains of

the 2002 and 2013 events are still subject to price discounting.

Another bias can stem from a link between FZs and the positive aspects of a waterside location that must

be addressed in empirical models (Bin, Kruse, & Landry, 2008). This is important since despite high

flood risks there is an increased demand for properties close to water due to the benefits associated with

a waterside location (water views, water sports facilities, etc.), resulting in a positive bias in FZ

estimates.

If damage occurs despite flood protection measures, flood insurance functions as a risk transfer

mechanism, especially for economic losses. Thus, the discounted sum of flood insurance premiums can

provide a reasonable basis for comparison for the size of price effects. Atreya, Ferreira, and Kriesel

(2013) report significantly higher flood discounts than expected based on the insurance premiums due

to uninsurable costs (such as inconvenience or psychological costs). Shultz and Fridgen (2001) obtain

similar results and are able to explain only 80% of price discounts as compensation for future insurance

costs. Although Bin and Kruse (2006) find discounts that nearly correspond to discounted insurance

premiums, Harrison, Smersh, and Schwartz (2001) identify a discount of less than the discounted

insurance premiums, which therefore does not reflect overall risk.

In contrast to previous studies, flood insurance in Germany is voluntary and privately offered.1

Voluntary insurance systems can suffer from behavioural bias, resulting in comparably low insurance

take-up rates and a loss in information value when comparing price effects with insurance premiums.

However, compared to the national average take-up rate of 40%, this rate is higher at 46% in Saxony.

Furthermore, Bin, Kruse, and Landry (2008) find price discounts that are equivalent to flood insurance

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costs even when buyers neglect to insure against flooding. This supports the assumption that FZs reflect

risk information and have an impact on property pricing even if insurance is not obtained.

When insurance take-up rates are low, homeowners typically rely on government relief programmes

when facing losses. Government relief is not guaranteed, but the government paid high levels of

compensation after major flooding along the River Elbe in 2002 and 2013. Buyers and sellers may

anticipate this response and rely on future government relief for flood damage, therefore neglecting to

provide or obtain information about flood risk and insurance regarding their property.

3. Study Area and Data

We analyse inland river flooding in the city of Dresden, the capital of the German federal state of

Saxony. We assume that indirect pricing of flood zones especially applies to urban areas where housing

density is high and the immediate neighbourhood may have a high impact when setting prices of

neighbouring properties. Dresden is one of the largest cities in Germany, with 547,172 inhabitants as of

2016,2 and has enjoyed tremendous popularity as an investment opportunity and residential location in

recent years. Demand for owner-occupied homes is high; the value of home purchases amounted to €512

million in 2014, with increases in property prices of 17.6% between 2007 and 2014. However, the city

is exposed to urban flood risk due to its location by the River Elbe and smaller tributaries, especially the

River Weißeritz. Dresden’s topography is almost entirely flat, with a steep slope in the hinterland such

that there is insufficient space for floodwater to be redirected. This basin location, in combination with

the city’s proximity to low mountain ranges that frequently have high levels of precipitation and an

increased risk of snow-melt, results in a consistently high flood risk. Nevertheless, investors and urban

planners see high potential for building land across the city area, resulting in a noticeable upturn in

construction activity even in exposed areas.

Dresden was hit by severe flooding events in 2002 and 2013. The flood event in 2002 was the result of

intense summer rainfall leading to high discharges and record high river water levels followed by high

groundwater levels; it caused total losses of €6 billion in Saxony, €1.3 billion of that within the city of

Dresden. The River Elbe level was 940 cm on 17 August 2002, whereas the average water level is

165 cm and the average flood water level is 481 cm in the city of Dresden.3 The flood event in 2013 was

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again caused by widespread and intense rainfall at a time the soil was already wet due to exceptionally

high rainfall in the preceding month. The River Elbe level was 878 cm on 6 June 2013 – the second

highest level for the city of Dresden. The last time the river surpassed the 7-metre level was 1940/1941,

so city authorities and citizens might not have been fully prepared for such high water levels. After the

flood of 2002, various measures were implemented to improve flood risk management which went into

effect in 2013. The city of Dresden completed 770 different flood prevention and protection measures

by 2010, for example the city centre is now protected by walls, mobile flood protection systems such as

flood protection gates, and the River Weißeritz bed was partially expanded (for more details regarding

our data sample, see Section 3.3). Thus, the mitigation of potential losses from new protection measures

should have theoretically resulted in an adaption of flood price effects.

3.1. Pricing Data and Structural Characteristics

Housing prices and structural characteristics are provided by the private online platform

ImmobilienScout24 and include all property listed using this service during the sample period from 2008

to 2016. A general overview of this dataset is given by Boelmann and Schaffner (2018). The dataset

contains 6,371 valid observations for houses and 12,358 for condominiums. Asking prices are adjusted

for inflation at the level of the first quarter of 2016 using the German Construction Cost Index.4 We

control for duplicates based on geographic coordinates, living area, number of rooms, and age of

properties. For condominiums, we also use floor numbers. The interpretation of asking prices can be

biased when sellers intentionally over- or underestimate achievable prices. Since sellers usually attempt

to achieve a high price in a short offering time and inflated prices may lead to a significant increase in

the offering time, we include the offering time in our models to control for possible distortion. However,

the average asking price per square metre in our dataset amounts to €2,090 compared to an average

transaction price of €1,990,5 thus, we assume that asking prices listed in advertisements are almost equal

to transaction prices in the sale contract. Furthermore, Harrison, Smersh, and Schwartz (2001) state that

even transaction prices underlie bias in terms of flood risk and do not represent intrinsic property value

in cases where a property’s location in a flood zone becomes transparent after the housing contract is

signed. Because of high information costs and a lack of awareness, buyers typically inform themselves

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about insurance coverage and flood zone status after purchasing a property, as they can then focus on

the FZ classification of one specific property.

The dataset includes structural characteristics such as property type, living area, number of rooms, age,

and quality. Table 1 presents the summary statistics of all locations and higher flood risk locations

presented separately for houses and condominiums. The mean values for properties with a higher flood

risk status, however, do not vary significantly from those for all locations. Thus, properties in flood-

prone areas are not substantially different in terms of price and structural characteristics from those

located elsewhere.

>>> Insert Table 1 about here. <<<

3.2. Neighbourhood and Location Attributes

We merge the previous dataset based on geographic coordinates of a property location with

neighbourhood characteristics containing information on the respective sociodemographic and housing

structure at the postcode level. Neighbourhood characteristics are obtained from GfK Geomarketing and

include attributes such as number of households, household size, migration rate, population age, and

number of residential or partly residential buildings. The improvement in the goodness of fit by using

detailed neighbourhood characteristics in a hedonic analysis is also underlined in other studies (see e.g.,

Gibbons, 2004; Hilber, 2005). Additionally, we measure the availability of amenities by calculating the

geodesic distance from the nearest park, the city centre, and the nearest highway, since these amenities

can directly and indirectly affect the valuation of a property (see, e.g., Baranzini & Ramirez, 2005;

Conway et al, 2010). We also include the distance from the nearest body of water and the River Elbe to

account for effects related to water proximity.

3.3. Flood Characteristics

To identify flood risk, we use both theoretical flood zones (FZ) and actual floodplains. We assign

insurance-based FZs to properties at an individual level using the German Insurance Association’s

(GDV) ZÜRS Geo tool. This zoning system for flood, backwater, and heavy rain is a geospatial platform

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with nationwide data for the risk assessment of properties and insurance premium calculation for

insurers. Flood risk is classified into four different FZs based on the recurring flooding interval and other

locational attributes (see Table 2). FZ 1 includes almost no flood risk. In FZ 2 (100-year floodplain) and

3 (100-year to 10-year floodplain), the risk level increases continuously, and FZ 4 represents the highest

risk area (10-year floodplain). FZ 1 includes 87.1% of houses in the dataset with 12.9% located in FZs

2-4. In the condominium sample, 75.4% are located in FZ 1 and 24.6% in FZs 2-4.


We use geographical information from Dresden’s flood events in 2002 and 2013 to identify property

locations in inundated areas.6 Whereas 9.2% of houses and 13.4% of condominiums were located in

inundation areas in 2002, only 2.5% of houses and 2.2% of condominiums were sited in inundation areas

during the event of 2013. Exhibit 1 presents the floodplains of the respective events in Dresden and the

spatial distribution of properties. However, a comparison of properties in our dataset with all existing

properties7 indicates that there is no sample selection bias in terms of flood risk and floodplain location.

>>> Insert Exhibit 1 about here. <<<

4. Empirical Model

With our empirical model, we aim to estimate spatially unbiased price effects caused by a property’s

location in an FZ. Our approach is divided into three steps: first, we determine the type of spatial

spillovers using a Bayesian model comparison technique (see LeSage & Pace, 2009) and calculate price

effects for flood zones based on a spatial Durbin error model (SDEM). Second, we calculate the average

insurance costs to determine the respective implied discount rate in each FZ; the implied discount rate

provides the basis for an assessment of the size of the price effects compared to economic losses. Finally,

we add the individual insurance costs to the original property price from step one in order to generate a

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risk-adjusted property price and then repeat our spatial estimations. Using risk-adjusted prices allows us

to observe whether sellers account for insurance costs when setting their asking prices.

4.1. Spatial Hedonic Regression for Flood Zones

Since neighbouring properties typically share locational, structural and socioeconomic characteristics,

unobserved spatial dependence arises and needs to be addressed in econometric models. There are

methods from spatial econometrics that control for different types of spatial dependence to prevent

biased and/or inconsistent estimates. These include a spatial lag of the dependent variable, the

explanatory variables or the disturbances (Anselin & Bera, 1998). Non-spatial approaches that exclude

spatial spillovers from the model specification result in estimates that suffer from omitted variable bias.

This bias is intensified if the explanatory variables correlate with any omitted spatial effects (LeSage &

Pace, 2009).

To determine the type of spatial dependence in our dataset, we test three spatial models: the spatially

lagged X model (SLX), the spatial Durbin model (SDM), and the spatial Durbin error model (SDEM).

For an excellent overview of these, see LeSage and Pace (2009). The SLX model is very similar to a

standard linear model but also incorporates all explanatory variables (X) as spatially lagged factors.

These local spillovers relate to property characteristics of the immediate neighbourhood that can

influence price setting for a property.

The SDM includes both spatially lagged dependent and independent variables. From a theoretical

perspective, the spatial lag of the dependent variable is added when neighbouring properties serve as a

benchmark for setting the price of an individual property due to uncertainties in neighbourhood

characteristics or when spillovers from value appreciation/depreciation arise within the neighbourhood

(see Osland & Thorsen, 2013). The influence of the average of the explanatory variables from

neighbouring properties is determined using the spatially lagged independent variables. The SDM is an

addition to the spatial autoregressive model (SAR), where only the spatially lagged dependent variable

is added on the right hand side. As pointed out by Kim, Phippa, and Anselin (2003) and Cohen and

Coughlin (2008), the SAR is superior if a structural spatial interaction is present in the market and/or if

the strength of that relationship is of particular interest for the research question. Even if the former may

be present in our data sample – although pricing data of comparable properties are not easy to obtain

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during the buying process in Germany – the latter is not relevant for us here. From a statistical

perspective, the obtainment of consistent coefficients is a major argument in favour of this model,

whereby efficient estimators result from the alternative spatial error model. This type of model should

be used if spatial interactions are not assumed by theory so that the focus is more on correcting for the

influence of spatial autocorrelation. Even if consistency is a very important property of an estimator, we

conclude that the corrections for the influence of spatial autocorrelation is more important for our

research question in that it ensures correct inference, which takes precedence over an ability to quantify

the strength of the interaction between the price of a property and its neighbouring property.

Furthermore, the SDM simplifies to the SAR when the parameters of the spatially lagged independent

variables take on the value of zero, to the SLX when the scalar parameter of the spatially lagged

dependent variables takes on a value of zero, and to a conventional linear regression model when both

parameter vectors are equal to zero.

As our third model, we use the SDEM; it captures spatial dependence in the explanatory variables and

in the error terms. Although we include a large number of hedonic controls, there might still be

unobserved characteristics that vary over space, resulting in spatial correlation of the disturbances. The

SDEM combines the SLX model with an error process that accounts for this residual correlation.

In Section 5.1, we compare all three models using a Bayesian model comparison approach, which shows

that the SDEM best describes our dataset. Thus, we focus on a description of the SDEM in this study.

Following the method used by Pace and LeSage (2004), the estimation of the SDEM is based on

maximum likelihood with Monte Carlo approximate log-determinants8 and is specified as follows:

ln(𝑃𝑃𝑖𝑖𝑖𝑖) = 𝛼𝛼 + 𝛽𝛽(𝐹𝐹𝐹𝐹𝑖𝑖 + 𝑋𝑋𝑖𝑖𝑖𝑖 + 𝑄𝑄𝑖𝑖𝑖𝑖) + 𝛾𝛾𝑾𝑾(𝐹𝐹𝐹𝐹𝑖𝑖 + 𝑋𝑋𝑖𝑖𝑖𝑖 + 𝑄𝑄𝑖𝑖𝑖𝑖) + 𝜇𝜇𝑖𝑖𝑖𝑖

𝜇𝜇𝑖𝑖𝑖𝑖 = 𝜆𝜆𝑾𝑾𝜇𝜇𝑖𝑖𝑖𝑖 + 𝜀𝜀𝑖𝑖𝑖𝑖 ,

[1]

where 𝑃𝑃𝑖𝑖𝑖𝑖 is the asking price for property 𝑖𝑖 at time 𝑡𝑡, 𝐹𝐹𝐹𝐹𝑖𝑖 is a dummy vector indicating whether property 𝑖𝑖

is located in a specific flood zone (FZ 2-4), 𝑋𝑋𝑖𝑖𝑖𝑖 is a matrix of explanatory variables including structural,

neighbourhood, and locational attributes, 𝑄𝑄𝑖𝑖𝑖𝑖 represents quarterly time-fixed effects, 𝑊𝑊 is a spatial

weight matrix, 𝜆𝜆 indicates the spatial autocorrelation in the error terms, and 𝜀𝜀𝑖𝑖𝑖𝑖 is an independent and

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identically distributed random error term. Regarding the transformation of the dependent variable, we

use the log-linear (semi-log) equation form, which is consistent with Rosen (1974) and is preferred over

a linear functional form. For the explanatory variables, we use quadratic transformations for structural

variables, such as number of rooms and age, thus addressing the declining price effects with an

increasing characteristic expression. Locational variables measuring the distance from different

amenities are log-transformed in order to capture price effects that decline with distance. Quarterly time-

fixed effects control for time variations and seasonal effects in price levels. The adjustment of W captures

the geographical area that may share unobserved characteristics. We use a standardised, inverse

distance-based spatial weight matrix that identifies properties with their ‘four nearest neighbours’ as a

neighbourhood cluster.9 The beta coefficients of the SDEM are interpreted as direct effects stemming

from a change in the property characteristics averaged over all properties. Thus, the direct effect is the

effect of a change in an explanatory variable of property 𝑖𝑖 on the dependent variable of property 𝑖𝑖. The

gamma coefficients from spatially lagged variables are interpreted as indirect effects (LeSage & Pace,

2009). The indirect effects measure how a change in an explanatory variable of property 𝑗𝑗 affects the

dependent variable of property 𝑖𝑖. They should capture all spillover effects from the set of explanatory

variables. For example, this effect determines the impact of all neighbouring properties being located in

a flood zone on the price of an individual property, again averaged over all properties. The total effects

measure the sum of both the direct and the indirect effects.

4.2. Calculation of Insurance Costs

Insurance costs can provide insights into whether price effects for flood zones are adapted to potential

economic losses. Thus, we calculate theoretical insurance costs according to the following equation:

𝑃𝑃𝑃𝑃𝑖𝑖 = 𝐼𝐼𝐼𝐼𝑖𝑖𝑟𝑟

= (𝑅𝑅𝑅𝑅𝑖𝑖∗𝐼𝐼𝐼𝐼𝑖𝑖∗𝐿𝐿𝐼𝐼𝑖𝑖)𝑟𝑟

, [2]

where 𝑃𝑃𝑃𝑃𝑖𝑖 is the present value of insurance costs, 𝐼𝐼𝑃𝑃𝑖𝑖 is the individual insurance premium at the property

level and 𝑟𝑟 is the average real estate return. More precisely, we determine the 𝐼𝐼𝑃𝑃𝑖𝑖s by applying a

calculation scheme provided by the German Insurance Association. This scheme is based on a three-

step procedure: the specification of the rebuilding value (𝑅𝑅𝑃𝑃𝑖𝑖), the index-linked adjustment factor (𝐼𝐼𝐹𝐹𝑖𝑖),

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and the loss factor (𝐿𝐿𝐹𝐹𝑖𝑖). First, we calculate the 𝑅𝑅𝑃𝑃𝑖𝑖 that covers costs for rebuilding in the case of

complete destruction and accounts for various housing attributes (e.g., building type, living area, and

quality).10 This value can significantly differ from the current market value and ensures the prevention

of underinsurance in the case of value appreciation over time. Second, we adapt the 𝑅𝑅𝑃𝑃𝑖𝑖 to the offering

year by using an index-linked adjustment factor (𝐼𝐼𝐹𝐹𝑖𝑖). This factor is provided annually by the German

Insurance Association based on economic indicators such as the construction price index and the wage

index for the construction sector. Third, we measure an individual loss factor (𝐿𝐿𝐹𝐹𝑖𝑖) as a function of the

flood zone and the 𝑅𝑅𝑃𝑃𝑖𝑖. This factor covers marketing and selling expenses, administrative costs, and the

profit margin of insurance companies. The insurance premiums for properties located in FZ 4 are not

part of this standard calculation scheme and are based on an individual assessment. Thus, we use an

extrapolation of the FZ 1 to FZ 3 calculation scheme for the determination of theoretical premiums in

FZ 4. For the average real estate return (𝑟𝑟), we set 5% as the sum of the risk-free interest rate of 3%

(average of 10-year German government bonds over the last 20 years) plus a risk premium of 2% for

properties in Dresden. Finally, we compare price discounts for flood zones with the annual insurance

costs and determine the average implied discount rate. The implied discount rate – the required rate

equal to the present value of future insurance costs and the price effect – provides the basis for an

assessment of the size of price effects compared to economic losses. Whereas the implied discount rate

is lower than the average real estate return (𝑟𝑟), sellers compensate potential buyers at an amount equal

to more than the costs of insurance coverage. Higher implied discount rates imply that sellers are able

to apply price discounts that are lower than the costs of insurance coverage.

4.3. Spatial Hedonic Regression Including Insurance Costs

We extend our approach and add the present value of individual insurance costs (𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖), based on a

discount rate of 5%, to the original property price (𝑃𝑃𝑖𝑖𝑖𝑖) in order to simulate a risk-adjusted property price

and then repeat our spatial regressions. Using risk-adjusted prices as the dependent variable allows us

to observe whether sellers account for insurance costs when setting their asking prices.11 Note that these

risk-adjusted prices only arise when buyers decide in favour of flood insurance; therefore, we adjust the

present value of insurance costs to the prevailing insurance take-up rate of 45%. Lastly, we modify the

model according to the following equation:

15

ln(𝑃𝑃𝑖𝑖𝑖𝑖 + 𝑃𝑃𝑃𝑃𝑖𝑖𝑖𝑖) = 𝛼𝛼 + 𝛽𝛽(𝐹𝐹𝐹𝐹𝑖𝑖 + 𝑋𝑋𝑖𝑖𝑖𝑖 + 𝑄𝑄𝑖𝑖𝑖𝑖) + 𝛾𝛾𝑾𝑾(𝐹𝐹𝐹𝐹𝑖𝑖 + 𝑋𝑋𝑖𝑖𝑖𝑖 + 𝑄𝑄𝑖𝑖𝑖𝑖) + 𝜇𝜇𝑖𝑖𝑖𝑖

𝜇𝜇𝑖𝑖𝑖𝑖 = 𝜆𝜆𝑾𝑾𝜇𝜇𝑖𝑖𝑖𝑖 + 𝜀𝜀𝑖𝑖𝑖𝑖 ,

[3]

where the model specifications and variable descriptions equal those of Equation [1]. Adding the

insurance costs to the dependent variable, we assume that there would be no cost compensation left for

FZs if sellers were to determine their price discounts on the basis of economic losses. Further transaction

costs that a buyer may incur during the purchasing process (e.g., tax or brokerage fee) are not conditional

to flood risk and consequently are not relevant to this model.

5. Results

To verify the importance of indirect price effects of a location in different FZs, we divide our empirical

analysis into three steps. First, we run spatial regressions on the natural logarithm of property prices to

measure direct and indirect price effects for FZs. Second, we determine the average insurance costs in

each FZ in order to calculate the respective implied discount rate. Third, we add the individual insurance

costs to the original property price in step one in order to gain a risk-adjusted property price and then

repeat our spatial regressions.

5.1. Spatial Hedonic Regressions

Before estimating flood price effects, we need to determine whether there are structural differences in

the results between houses and condominiums; we therefore run a Chow test to determine whether we

will need to separate our sample for houses and condominiums (Chow, 1960). The resulting test statistics

indicate a clear argument for a separation (F = 25.56, p-value < 0.0001). Therefore, we run two separate

regressions for these two property types. In line with LeSage and Pace (2009), we also determine the

appropriate spatial model (SLX, SDM or SDEM; see Section 4.1) and the best specification of the spatial

weights matrix using a Bayesian model comparison approach. The log-marginal likelihood and the

posterior model probability suggest that SDEM is the most appropriate model as it best describes our

dataset (see Panel A in Table 3). For the spatial weight matrix, we choose the ‘four nearest neighbours’

16

specification, which determines the four nearest properties (immediate neighbourhood), as the source of

indirect effects (see Panel B in Table 3). For a variation of the spatial weight matrix, see Appendix A.1.


According to the Chow test, we split our sample into houses and condominiums, and according to the

Bayesian model comparison (Table 3), we proceed with an SDEM with a spatial weights matrix of four

nearest neighbours. Combining the house and condominium subsamples with three different model

specifications (separated zones, water amenities, and combined zones), the coefficients of six different

regressions are shown in Table 4. The general existence of spatial correlation in all regression models

is confirmed by the statistics of likelihood ratio tests and Wald tests on the joint significance of spatial

parameters (significant at the 1% level). Our estimation approach fully captures the existing spatial

correlation, as indicated by the statistically insignificant and low values of Moran’s I for the residuals.

For the calculation of these, we use the classical approach based on Moran (1950) for the serial

independence of residuals. An alternative test could be the adjustment of Anselin and Kelejian (1997)

encountering regression specifications with instrumental variables or spatially lagged dependent

variables. Even if the latter case applies to one of our model specifications (SDM), we adhere to the

classical approach since we use for our main analyses SDEM without spatially lagged dependent

variables. In addition, the authors point out that their adjusted Moran’s I test is the only acceptable in

the presence of spatially lagged dependent variables. Even so, we think that this adjustment is a valuable

contribution to models with lagged dependent variables.

While assessing the impact of flood risk, we mainly discuss the direct and indirect coefficients for

flooding variables (FZs and Spatial Lag FZs). Other estimated coefficients for the structural,

neighbourhood, and distance variables (see Equation [1]) are not the main focus of this study, but are

mostly statistically significant, have the usual signs, and are robust across model specifications.


17

First, we discuss the model specification of ‘separated zones’, which, besides the three FZ dummies

(FZ 2-4), includes all hedonic variables and time-fixed effects. The price effects are economically

meaningful; for example, a property price increase of 1% has an economic impact of €3,355 for houses

and €1,912 for condominiums. Direct effects for houses indicate that, compared to the low-risk reference

category FZ 1, prices are reduced by -1.2% in FZ 2, increased by 2.5% in FZ 3, and again reduced by -

0.5% in FZ 4. All of these spatially non-lagged FZ coefficients, however, are statistically insignificant

at any conventional level. This indicates that there is no price discount for the increased flood-risk status

stemming from the property itself and thus sellers do not directly compensate buyers for a property’s

location in an FZ. Conversely, indirect effects show statistically significant price effects; prices are

reduced by -5.2% in FZ 2, by -6% in FZ 3, and by -26.6% in FZ 4. Thus, only indirect effects from the

neighbourhood cause discounts for an FZ. This is the case when buyers are only able to inform

themselves about housing quality in indirect ways.

As discussed in Section 1, we assume that high information costs, or even constraints, hinder potential

homeowners from obtaining information about a property’s individual FZ status and insurance coverage

before signing a contract. Instead, the neighbourhood serves as an indicator of flood hazard, for example,

if recent flood damage to buildings is still visible or the media report on flooding in the local area. Sellers

then adjust their asking prices to flood-related neighbourhood effects. The data for condominiums

confirm these results: direct effects are again statistically insignificant and indirect effects indicate

statistically significant price discounts of -5.6% in FZ 2 and -5.1% in FZ 3. However, the indirect price

discount of -13.2% is statistically insignificant in FZ 4. This insignificant coefficient could be a result

of the small sample size in this zone. For condominiums, the whole owner community proportionally

shares financial losses regarding the building’s structure. Basements, as well as common low-lying

spaces, are smaller in relation to houses, so price discounts for FZs are generally smaller.

Furthermore, separating price effects for flood risk location and proximity to water amenities captures

a potential positive bias in FZ effects. Controlling for a positive link between water amenities and other

water-related factors, we include an interaction term for the land elevation of a property and its distance

from the River Elbe in a second model specification (‘water amenities’) in Table 4. While property

prices are assumed to decrease with increasing distance from the Elbe, this effect is mitigated by

18

controlling for increased land elevation, which is in turn positively linked to a water view. Even in this

model specification, indirect effects result in discounts of -5.6% in FZ 2, -7% in FZ 3, and -26.6% in

FZ 4. All lagged coefficients are significantly different from zero at a level of 5%. For condominiums,

spatially lagged coefficients show statistically significant discounts of -5.4% in FZ 2, -4.7% in FZ 3,

and -13.4% in FZ 4. Whereas coefficients in FZ 2 and FZ 3 are statistically significant at a respective

level of 1% and 5%, the price effect for FZ 4 is again insignificant. We also use likelihood ratio tests to

compare both model specifications and find that the model on ‘water amenities’ is preferred for houses

(p-value = 0.0027) and for condominiums (p-value = 0.0144) compared to the ‘separated zones’ model.

A comparison of direct and indirect price effects for both housing types based on this model specification

is presented in Exhibit 2. Overall, price effects are again less negative in the condominium segment.

Furthermore, the coefficient for FZ 2 is slightly lower compared to FZ 3 within the condominium

segment. Thus, FZ status is considered less essential when setting prices for condominiums compared

to houses, and only flood-related neighbourhood effects result in statistically significant discounts in

both property segments. Results for both model specifications (‘separated zones’ and ‘water amenities’)

are comparable, such that a reduction in price effects does not occur after controlling for water view.

For a table with all coefficients from the ‘water amenities’ model, see Table A2-1 in Appendix A.2.

>>> Insert Exhibit 2 about here. <<<

In the third model specification in Table 4, FZs are combined to measure an aggregated price effect for

a general floodplain location (‘combined zones’). Since our previous risk classification is more detailed

than in the recent literature, this model specification allows our results to be compared with other studies.

Moreover, this literature mostly does not distinguish between direct and indirect flooding effects. For

houses, an FZ location results in an indirect effect of -6.5%; for condominiums, the indirect discount is

-4.8%. Both effects are statistically significant at a level of 1%.

Taken together, indirect effects are almost in line with the findings from other studies (5-10%) obtained

without a differentiation of direct and indirect effects (Bin & Landry, 2013; Bin & Polasky, 2004; Bin

Bin, Kruse, & Landry, 2008). With our results, we are able to show that the indirect effect, and therefore

19

the immediate neighbourhood, is the driver of the price discount for FZ location and that this discount

is robust to controlling for water amenities. From a theoretical perspective, buyers use the immediate

neighbourhood as a heuristic for flood risk and assume that it is representative of the flood risk at the

property they are considering buying. Furthermore, the information costs for assessing flood risk based

on neighbouring properties may be lower due to visible structural damage, topographic characteristics,

or headlines in local media and the information is therefore more readily available to buyers.

5.2. Calculation of Insurance Costs and Implied Discount Rate

We also analyse whether flood price discounts are equal to economic losses, which can be approximated

by insurance costs. Thus, we calculate the implied discount rate as the rate that equals the present value

of future insurance costs and the flood price effect. Comparing these implied discount rates with the

average real estate return of 5% (see also Bin, Kruse, & Landry, 2008), we assume that lower implied

discount rates imply that sellers overcompensate potential buyers for direct insurance costs and vice

versa.

First, we compute individual insurance premiums for the 25th, 50th, and 75th percentile of the asking price

distribution in each FZ. By doing so, we favour the actual distribution of prices for an artificial property

with median values for all characteristics. To determine the implied discount rate, we use the

predominant type of insurance contract in Germany, which includes a deductible of €1,000. In the next

step, we match the present value of these premiums with estimated price effects that are equal to the

total effect.12 Our approach for FZ 4 is slightly different. Since the number of observations in FZ 4 is

small, we only estimate the implied discount rate for the median price. Furthermore, the insurance

premium calculation is based on an extrapolation of the official premium calculation scheme since

flooding is not classified as a random event in FZ 4 and the premium calculation is therefore subject to

an individual assessment. Table 5 shows price effects, annual insurance premiums, and the implied

discount rates.

For houses, the average implied discount rates amount to 8.7% in FZ 2, 25.6% in FZ 3, and 4.9% in

FZ 4. These discount rates are almost stable across the price quartiles within each FZ. Implied discount

rates for condominiums are 4.6%, 15.0%, and 4.3%. For the combined FZ, we find an implied discount

rate of 18.4% for flood risk for houses and 5.5% for condominiums. Therefore, the benchmark of 5%

20

almost corresponds to our estimates for condominiums in FZ 2 (4.6%) and for both property types in

FZ 4 (4.9% or 4.3%). Equal rates indicate that sellers compensate buyers in an FZ for the costs to cover

economic losses. The discount rates for houses in FZ 2 (8.7%) and for both property types in FZ 3

(25.6% or 15.0%) are higher, indicating that sellers anticipate a higher willingness to pay among

potential homeowners in these FZs. We are not able to find implied discount rates lower than the average

real estate return that would have indicated that sellers accept discounts which are higher than statistical

economic losses.


5.3. Spatial Hedonic Regression with Insurance Costs

Since flood insurance covers potential economic losses, homeowners could voluntarily decide in favour

of acquiring such a protection. Assuming a perfect market, sellers adjust property prices and compensate

buyers for future insurance costs. Thus, we sum asking prices and the present value of insurance

premiums in order to generate risk-adjusted property prices, and we include these as a new dependent

variable in our previous regression Equation [3]. Using risk-adjusted prices allows us to observe whether

sellers account for insurance costs when setting their asking prices – this is a novel approach in our

research. The results are presented in Table 6.

The model specifications with ‘separated zones’ and ‘water amenities’ show almost equal results for

direct and indirect effects in comparison to the approach without insurance costs (Table 4). The results

indicate positive direct effects for houses, e.g., in the ‘water amenities’ model, of around 12% in FZ 3

and FZ 4, which are statistically significant at a level of 1% and 10%, respectively. The positive and

statistically significant effects imply that sellers assume a willingness to pay for an FZ location that is

higher than potential economic losses, for example, due to other beneficial location amenities. Thus,

sellers do not compensate buyers for insurance costs. Indirect effects of all FZs are not affected by

controlling for insurance costs. This is reasonable, as insurance coverage is independent from the

neighbourhood since it only covers economic losses at the property itself. Flood damage to neighbouring

properties can still have a negative price effect. For condominiums, we also find a positive direct effect

21

of 5.8% in FZ 3, which is statistically significant at the 1% level. Indirect effects are again robust while

controlling for insurance costs. Results for the ‘combined zones’ model indicate positive direct effects

for houses (8.3%) and condominiums (1.6%). Both price effects are statistically significant at a

respective level of 1% and 10% and indicate that sellers may assume that the willingness to pay is higher

than the potential economic losses expressed by the capitalised insurance premiums. Indirect effects

remain unchanged.


Taken together, previous results indicate that local spillovers indicated by indirect price effects from the

immediate neighbourhood contribute to lower property prices, whereas direct effects for the flood zone

location of the property itself mostly diminish when controlling for spatial dependence. These effects

are also robust to an analysis with risk-adjusted prices that includes future insurance costs to cover

economic loss, providing further evidence of the importance of indirect effects in the analysis of flood

zone effects.

6. Conclusion

In this study, we analyse direct and indirect price effects for the flood zone location of properties. Since

the interpretation of indirect effects varies with the type of spatial spillovers (global vs. local), and

theoretical considerations do not explicitly point towards one of these spillover types, we use the

Bayesian model comparison approach to choose the appropriate model (see LeSage, 2014a). We only

find evidence for local spillover effects that stem from the immediate neighbourhood in our estimation

and therefore calculate an SDEM corresponding to the statement by LeSage (2014b) that most spillovers

are local. The detailed discussion of indirect effects, the use of the Bayesian model comparison, and the

SDEM are unique to our research in comparison to previous flooding research.

Our main results are as follows: Direct effects from the FZ location of the property diminish when

controlling for spatial dependence. However, in line with our theoretical considerations, we find strong

evidence for indirect price effects. Price effects are generally lower for condominiums compared to

22

houses. These results are mostly robust to flood zone effects measured from risk-adjusted prices that

include future insurance costs to cover economic loss. Within various robustness analyses, where we

compare a neighbouring city with a similar flood risk, a neighbouring city without high flood risk, and

the entire river basin, we find that the relevance of indirect effects from flood zone or floodplain location

persists. Thus, our results provide evidence of the importance of addressing indirect effects in the

analysis of flood zone effects.

Since waterside locations are attractive to property buyers, flood-prone areas are increasingly used for

urban development. Consequently, the sum of insured losses has also increased in recent decades. Due

to the observed relevance of flood price effects for individual sellers and buyers, as well as for the

economy as a whole, incorporating indirect effects resulting from the immediate neighbourhood in

policy interventions is very important and can substantially contribute to an adequate calculation of the

economic consequences of flooding. This in turn can stimulate policy formulation for effective flood

risk management and cost-efficient, correctly assessed protection measures, such as dikes, retention

areas and the renaturation of former building land.

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26

Exhibits

Exhibit 1: Inundated Properties during the Flooding Events in 2002 and 2013

Notes: This exhibit shows affected properties in Dresden during the flooding events in 2002 (left) and 2013 (right). The first row presents properties of our dataset and the second row the general building development in inundation areas obtained by OpenStreetMap.

27

Exhibit 2: Direct and Indirect Price Effects for Flood Zone Location

Panel A: House

Panel B: Condominium

Notes: This exhibit presents direct and indirect price effects for flood zone location of the ‘water amenities’ model in Table 4 for houses (Panel A) and condominiums (Panel B). While direct effects resulting from the property itself are low and statistically insignificant, indirect effects capturing the influence of the neighbourhood determine discounts for flood zones. Note that the indirect effect for FZ 4 in the condominium panel is also statistically insignificant.

28

Tables

Table 1: Descriptive Statistics

Panel A: House Panel B: Condominium all (FZ 1-4) FZ 2-4 all (FZ 1-4) FZ 2-4

Price (€) 335,501.4 333,956.1 191,185.2 198,600.1 Insurance Costs (€/year) 687.66 3,118.87 203.82 594 Time on Market (months) 1.75 1.85 4.91 4.87 Structural Characteristics

Living Area (m2) 157.61 157.17 86.39 92.24 Number of Rooms 5.32 5.39 2.97 3.03 Floor 2.90 2.93 Age (years) 23.99 25.37 44.08 44.25

Structural Quality (%)

Luxury 2.09 2.07 2.62 3.42 Good 35.58 36.95 35.58 37.39 Normal 61.03 60.49 61.60 59.06 Simple 1.30 0.49 0.19 0.13

Neighbourhood Characteristics

Household Size 1.90 1.86 1.79 1.78 Number of Households 8,867.61 10,163.19 12,329.36 13,331.53 Immigration Rate (%) 2.58 2.79 4.13 3.71 Residential Buildings 2,243.51 2,226.41 1,881.87 1,918.83 Residential/Commercial Buildings 75.29 79.27 93.89 91.59 Population Age (%)

<18 years 15.94 15.76 15.15 15.13 18-29 years 14.34 14.82 19.68 16.99 30-49 years 27.63 28.16 28.12 27.64 49-65 years 20.03 18.74 16.06 16.49 >65 years 22.05 22.52 20.99 23.75

Locational Characteristics (meters) Distance from the City Centre 6,878.46 6,503.96 4,146.82 4,501.48 Distance from Nearest Park 671.66 564.41 323.55 262.17 Distance from Nearest Motorway 3,458.71 3,433.96 3,927.85 4,439.59 Distance from Nearest Water Body 408.48 539.98 3,927.85 628.06 Distance from the River Elbe 2,789.32 1,100.81 1,369.10 1,020.26

Inundated Properties (%)

Flood Event 2002 9.17 13.36 Flood Event 2013 2.48 2.23

Flood Zones (%)

FZ 1 87.13 75.39 FZ 2 4.76 15.84 FZ 3 7.33 8.62 FZ 4 0.78 0.15

N 6,371 820 12,358 3,041 Notes: This table provides the mean values for houses (Panel A) and condominiums (Panel B). Statistics are given for the overall sample and for increased flood zone (FZ 2-4) status, respectively. Information on floor is only available for condominiums.

29

Table 2: Flood Zone Classification

Flood Zones Flood Risk Description FZ 1 Low risk No flooding FZ 2 Moderate risk Statistical probability of flooding at least once in 100 years FZ 3 High risk Statistical probability of flooding once in 10-100 years FZ 4 Extremely high risk Statistical probability of flooding at least once in 10 years

Note: This table presents the four flood zones defined by the German Insurance Association (GDV). These flood zones (FZ) are also implemented in the geographical information system ZÜRS Geo, which is used for flood zone identification in this study.

30

Table 3: Log-marginal Likelihood Values and Posterior Model Probability

Panel A: Bayesian Model Comparison Model Log-marginal Likelihood Value Posterior Model Probability Spatially Lagged X (SLX) -4575.8 0.00 Spatial Durbin Model (SDM) -3984.6 0.00 Spatial Durbin Error Model (SDEM) -3972.9 1.00

Panel B: Bayesian Model Comparison with Spatial Weights Matrix

Number of Neighbours SLX SDM SDEM 3 0.00 0.00 0.00 4 0.00 0.00 0.82 5 0.00 0.00 0.18 6 0.00 0.00 0.00

Notes: This table presents the Bayesian model comparison approach for the house sample. The results for the condominium sample is shown in Table A2-2 in Appendix A.2. Panel A includes the log-marginal likelihood values and the posterior model probabilities. Panel B extends this approach and shows the model probabilities for a variation in the number of neighbours in the spatial weight matrix. For comparability reasons, we focus on the model and the spatial weight matrix specification chosen for the house sample.

31

Table 4: Price Effects for Flood Zone Location

Separated Zones Water Amenities Combined Zones House Condominium House Condominium House Condominium

Direct Effects

FZ 2 -0.012 [0.024]

-0.014 [0.010] -0.012

[0.024] -0.017 [0.010]

FZ 3 0.025 [0.023]

0.015 [0.018] 0.021

[0.023] 0.012

[0.018]

FZ 4 -0.005 [0.070]

-0.038 [0.079] -0.022

[0.070] -0.034 [0.079]

FZ 2-4 0.006 [0.018]

-0.009 [0.010]

Indirect Effects

Spatial Lag FZ 2 -0.052* [0.028]

-0.056*** [0.013] -0.056**

[0.028] -0.054***

[0.013]

Spatial Lag FZ 3 -0.060** [0.028]

-0.051** [0.021] -0.070**

[0.028] -0.047** [0.021]

Spatial Lag FZ 4 -0.266** [0.117]

-0.132 [0.117] -0.266**

[0.117] -0.134 [0.117]

Spatial Lag FZ 2-4 -0.065*** [0.021]

-0.048*** [0.011]

Time-Fixed Effects Yes Yes Yes Yes Yes Yes Structure Yes Yes Yes Yes Yes Yes Location Yes Yes Yes Yes Yes Yes Neighbourhood Yes Yes Yes Yes Yes Yes Water No No Yes Yes Yes Yes N 6,371 12,358 6,371 12,358 6,371 12,358 λ 0.259*** 0.425*** 0.260*** 0.424*** 0.258*** 0.425*** Log Likelihood -1599.0 -170.5 -1594.5 -167.5 -1597.0 -170.2 Likelihood Ratio Test 278.9*** 1496*** 280.9*** 1491.3*** 280.0*** 1495.6*** Wald Test 303.0*** 1840.6*** 301.1*** 1834.2*** 304.1*** 1786.4*** Residuals Moran’s I -0.031 -0.086 -0.032 -0.085 -0.031 -0.086

Notes: This table presents results of the SDEM. The first model shows results for the specification with separated flood zones (separated zones), the second with an additional interaction term for the land elevation of the property and the distance from the River Elbe (water amenities), and the third for a combined flood zone including FZ 2-4 (combined zones). Results are presented separately for houses and condominiums. We also indicate whether we control for time-fixed effects, structure, location, neighbourhood, and water characteristics. The model parameters (N (observations), λ (spatial correlation), etc.) are shown in the last rows. The dependent variable is the natural logarithm of asking prices (€). Standard errors are presented in brackets. * p<0.10, ** p<0.05, *** p<0.01

32

Table 5: Comparison between Price Effects and Insurance Costs

Flood Zones IQR Average Price

Average Price Effect

Annual Insurance

Costs

Present Value Insurance

(3%)

Implied Discount

Rate

Average Implied

Discount Rate Q1 241,560 16,426 1,534 51,133 9.3% 8.7%

(Condo: 4.6%) FZ 2 Q2 304,825 20,728 1,829 60,967 8.8% Q3 412,668 28,061 2,315 77,167 8.2% Q1 238,235 11,674 3,191 106,367 27.3% 25.6%

(Condo: 15%) FZ 3 Q2 307,059 15,046 3,655 121,833 24.3% Q3 378,670 18,176 4,582 152,733 25.2%

FZ 4 Q2 300,485 86,540 4,240 141,333 4.9% 4.9% (Condo: 4.3%)

Floodplain FZ 2-4

Q1 236,208 13,464 2,711 90,367 20.1% 18.4% (Condo: 5.5%) Q2 301,895 17,208 3,384 112,800 19.7%

Q3 396,285 22,588 3,466 115,533 15.3% Notes: This table presents the comparison of price effects with insurance premiums for houses (the implied discount rate for condominiums is given in parentheses). The average price effect is based on the ‘water amenities’ model in Table 4 and accounts for the total effect (direct + indirect effect). Prices, price effects, insurance costs, and values are given in €. To take the generally skewed pricing distribution of properties into account, we show the results for all three quartiles of the interquartile range (IQR). The breakpoints are: 25th percentile (Q1), median (Q2), and 75th percentile (Q3). Because of the small data sample of FZ 4, we focus on the median (Q2). Insurance premiums for FZ 4 are based on a theoretical calculation scheme. In practice, determination of insurance premiums is subject to an individual assessment.

33

Table 6: Price Effects for Flood Zone Location with Insurance Costs

Separated Zones Water Amenities Combined Zones House Condominium House Condominium House Condominium

Direct Effects

FZ 2 0.033 [0.023]

0.005 [0.010] 0.033

[0.023] 0.002

[0.010]

FZ 3 0.126*** [0.022]

0.060*** [0.017] 0.121***

[0.022] 0.058*** [0.017]

FZ 4 0.137** [0.068]

0.030 [0.078] 0.120*

[0.068] 0.034

[0.078]

FZ 2-4 0.083*** [0.018]

0.016* [0.009]

Indirect Effects

Spatial Lag FZ 2 -0.056** [0.027]

-0.055*** [0.012] -0.060**

[0.027] -0.054***

[0.012]

Spatial Lag FZ 3 -0.060** [0.027]

-0.049** [0.020] -0.070**

[0.027] -0.044** [0.020]

Spatial Lag FZ 4 -0.275** [0.114]

-0.115 [0.115] -0.274**

[0.114] -0.116 [0.115]

Spatial Lag FZ 2-4 -0.060*** [0.021]

-0.042*** [0.011]

Time-Fixed Effects Yes Yes Yes Yes Yes Yes Structure Yes Yes Yes Yes Yes Yes Location Yes Yes Yes Yes Yes Yes Neighbourhood Yes Yes Yes Yes Yes Yes Water No No Yes Yes Yes Yes N 6,371 12,358 6,371 12,358 6,371 12,358 λ 0.261*** 0.426*** 0.261*** 0.425*** 0.261*** 0.427*** Log Likelihood -1443.0 19.1 -1438.9 22.6 -1445.9 15.8 Likelihood Ratio Test 284.3*** 1508.4*** 285.4*** 1504.3*** 288.7*** 1520.8*** Wald Test 308.2*** 1842.8*** 338.1*** 1362.1*** 317.2*** 1881.9*** Residuals Moran’s I -0.032 -0.085 -0.032 -0.085 -0.032 -0.085

Notes: This table presents results of the SDEM with insurance costs. The first model shows results for the specification with separated flood zones (separated zones), the second with an additional interaction term for the land elevation of the property and the distance from the River Elbe (water amenities), and the third for a combined flood zone including FZ 2-4 (combined zones). Results are presented separately for houses and condominiums. We also indicate whether we control for time-fixed effects, structure, location, neighbourhood, and water characteristics. The model parameters (N (observations), λ (spatial correlation), etc.) are shown in the last rows. The dependent variable is the natural logarithm of asking prices plus the annual insurance costs (€). Standard errors are presented in brackets. * p<0.10, ** p<0.05, *** p<0.01

34

Appendix 1 – Robustness Analyses

We also analyse whether the relevance of indirect price effects for flood zone location varies with the

specific characteristics of our model specification, observation time and study area. Thus, we run three

robustness analyses. First, we alternate the spatial weight matrix to test the robustness of flood price

effects across these variations. Second, we use our previous dataset for the flood-prone city of Dresden

but swap theoretical FZ for actual floodplains. We also test for a variation in these floodplain price

effects over time. Third, we analyse theoretical FZs in the neighbouring cities of Magdeburg and Leipzig

and finally in the whole Elbe area.

A.1. Variation of Spatial Weight Matrix

In this step, we test the sensitivity of our results regarding a variation in the spatial weights matrix. We

start with an OLS regression as the base model. Then we use an inverse distance ‘five nearest

neighbours’ setting, which has the second highest model probability in the Bayesian model comparison

(see Panel B of Table 3). Additionally, we use an inverse distance band specification, including

properties within a threshold of 100 m as a cluster.13 The new calculated FZ effects are mostly robust to

all variations (see Table A1-1). In general, indirect effects naturally decrease when the threshold of the

matrix, and thus the number of affected properties, is lower. For the distance-based approach, there are

properties left with zero neighbours, resulting in mostly decreased indirect effects. The significant

coefficients of direct effects from the OLS model disappear while controlling for spatial correlation.

However, the simple OLS model (λ = 0) is rejected due to a high and statistically significant Moran’s I

statistic for OLS residuals and significantly positive λ in all other spatial specifications. For all spatial

model specifications, Moran’s I statistics are insignificant and approximately equal to zero, indicating

that these models almost completely account for the existing spatial correlation.

>>> Insert Table A1-1 about here. <<<

35

A.2. Event Studies

The major flooding that Dresden experienced in 2002 and 2013 resulted in significant losses. Thus, we

analyse price effects for the location in inundated areas and use dummy variables for both flood events,

which are equal to the affected area in 2002 (inundated during the ‘flood 2002’ = 1, zero otherwise) and

in 2013 (inundated during the ‘flood 2013’ = 1, zero otherwise). On average, we expect negative direct

and indirect price effects for a location in a floodplain due to flood damage at the property or in the

neighbourhood. However, these negative effects can be offset due to other beneficial location

characteristics, reconstruction measures after the flood events, or simply by buyers and sellers being

unaware of the flood risk. Results for the dummy variables are presented in Table A1-2. The ‘flood

2002’ model indicates statistically insignificant price effects apart from a positive indirect effect of 4.2%

for condominiums, which can stem from a desirable neighbourhood location that offsets the floodplain

status of these properties. Furthermore, the period between the ‘flood 2002’ and our observation time is

rather long, therefore prior floodplain status may not be available to buyers, resulting in insignificant or

positive price effects. The location in inundated areas from ‘flood 2013’ results in a direct effect of 8.9%

for houses, which is significant at a level of 5%. A positive price effect of houses in inundated areas in

2013 that outweighs negative effects after the flood may be due to either an attractive location or a better

building structure after reconstruction due to flooding. The indirect effect for houses within the

inundation area is statistically significant at the 10% level and indicates a price discount of -9.1%. This

is reasonable in cases where flood damage to neighbouring properties is visible and reduces the prices

of property nearby. The direct and indirect effects for condominiums, however, are statistically

insignificant, indicating that for condominiums, location in a prior floodplain has no remaining price

impact. Thus, while interpreting price effects from floodplains, sources of potential biases need to be

taken into account in order to understand the pricing of actual flood risk.


The following analysis is based on either actual floodplains (‘memory 2013’) or theoretical flood zones

(‘memory zones’). To analyse whether flood price effects change over time, for instance due to changing

36

flood awareness based on the memory effects of buyers and sellers (see Section 2), we implement a

spatial ‘difference in differences’ (DND) model. The DND is a quasi-experimental approach and enables

us to determine the observed changes in prices of a treatment group – properties in the inundation area

or in FZ 2-4 – against prices of a control group – properties outside of the inundation area or in FZ 1 –

due to an exogenous event, here ‘flood 2013’ (for a general discussion, see Greenstone & Gayer, 2009;

Parmeter & Pope, 2013). Changing price effects are measured by an interaction term that incorporates

both a binary variable for the inundation area (or the theoretical insurance-based flood zone) and a time

variable counting the months after the flood event occurred in June 2013.

The results are presented in Table A1-3. For the ‘memory 2013’ model, we find a positive and

statistically significant direct effect for houses (15.8%) and find a negative coefficient for the interaction

term of -0.4%. This indicates that the positive price effect stems from a generally beneficial location

associated with the inundation area before the 2013 event occurred. After the event, the locational price

effect is reduced due to experienced loss. For condominiums, indirect effects are statistically significant

and suggest that prices are reduced by -15% from the location of the neighbourhood in inundation areas

before the 2013 event occurred. Indirect effects also show a price increase of 0.8% per month after the

event, which could be a result of reconstruction in the neighbourhood. Thus, prices for condominiums

are generally not affected by being located in a floodplain. However, when controlling for the

development of price effects after the 2013 event, condominiums are more sensitive to impacts of

neighbouring properties compared to houses. This is supported by the dense neighbourhood structure of

condominiums, where a neighbouring property might be located in the same building, thus

reconstruction measures have a stronger impact on prices for condominiums.


For the ‘zone 2013’ model, we observe a statistically significant direct effect of -14.9% in FZ 4 and an

indirect effect in FZ 4 of -34.8% for houses before the 2013 event, which is further reduced by -0.8%

per month after the event. For condominiums, there is a statistically significant direct price effect in

FZ 2 of -2.7% before the event. Furthermore, spatially lagged coefficients indicate that there are

37

statistically significant price reductions of -9.7%, -10%, and -39.3% in the respective FZs resulting from

the neighbourhood. However, these indirect price effects were increased by 0.3% and 0.4% per month

in FZ 2 and FZ 3 after the event occurred, which confirms the results from the ‘memory 2013’ model

for condominiums. Thus, indirect price effects for flood zone status of condominiums are changed due

to the 2013 flood event, whereas there is only an adjustment of price effects in FZ 4 for houses. Summing

up, price effects from theoretical flood zones and actual floodplains vary widely, so our separated

analysis is reasonable in order to gain unbiased comparisons of flood price effects. This is also in line

with Atreya and Ferreira (2015).

A.3. Spatial Variations in Flood Risk

We also extend our study to the neighbouring cities of Magdeburg and Leipzig as a spatial test for

robustness, comparing price effects from the different locations. We test whether the high relevance of

indirect effects is a special case in Dresden and whether these indirect effects depend on specific urban

characteristics. Spatially robust indirect effects, however, would provide further evidence for their

importance in the context of flood risk. Magdeburg was affected by flooding events in 2002 and 2013

also and is, like Dresden, directly located on the River Elbe. Although Magdeburg is located downstream

and the warning time is typically longer, the amount of floodwater is not reduced as it cannot expand

into open spaces due to protection measures in upstream cities. Whereas the floodplain in Dresden in

2013 was significantly smaller than in 2002, the amount of floodwater in Magdeburg was significantly

higher in 2013. Conversely, Leipzig is located further away from the River Elbe and only indirectly

experienced flooding during the events of 2002 and 2013. However, in regional economic importance

and population size Leipzig almost equals Dresden, thus providing a comparative basis between mostly

theoretical FZs (Leipzig) and a mixture of theoretical FZs and flood experience (Dresden). This allows

us to analyse whether the risk awareness of sellers and buyers varies with the type of risk information

available across the same region.

The results are presented in Table A1-4. In Magdeburg, property prices are reduced by -21.4% in FZ 3

for houses and increased by 11.8% in FZ 4 for condominiums. Indirect effects only indicate a price

reduction of -14.3% in FZ 3 for houses. Since most of the properties in our dataset for Magdeburg are

located outside inundation areas and have not experienced structural damage, we find insignificant or

38

even positive price effects. However, average flood damage in Magdeburg was high, so our sample may

exhibit a selection bias. In general, a sample selection bias occurs if the dataset is non-randomly

collected and therefore is not representative of the whole population. Contrarily, it would be at least

representative of a specific period: sellers do not offer properties in these locations in the aftermath of a

flood event, as they may assume reduced selling opportunities. A comparison of our dataset with all

existing properties in Magdeburg indicates that properties in floodplains are underrepresented, perhaps

resulting in positive biased price effects.14 Condominiums in FZ 4 of our dataset may not have

experienced flooding, resulting in a positive price adjustment. In Leipzig, we find direct price effects of

12.9% in FZ 3 for houses and 6.6% in FZ 2 for condominiums. Indirect effects indicate price increases

of 30.6% in FZ 2 and 30.3% in FZ 3 for houses. For condominiums, indirect effects amount to -6.6% in

FZ 2 and -53.4% in FZ 4. Although the indirect effects for condominiums almost correspond to our

findings in Dresden, the positive direct and indirect effects for houses indicate a different pricing of FZs.

Since Leipzig is not located on the River Elbe, we control for positive amenities correlated with

waterside location by including an interaction term between the land elevation and the distance from the

nearest body of water. For houses, there may be other positive amenities correlated with FZs, resulting

in positive direct and indirect price effects.

Finally, we analyse direct and indirect flood price effects in the whole ‘Elbe area’ to incorporate all

locational differences in study areas along the river and estimate average price effects for the whole

river basin. We include in our estimation properties within a distance corridor from the River Elbe of

about 10 km to each side of the river and find that for houses, direct effects indicate a statistically

significant price reduction of -4.0% in FZ 2 and significant indirect effects of -2.4% and -15.3% in FZ

2 and FZ 4, respectively.15 For condominiums, we find statistically significant direct effects of -2.0% in

FZ 2 and -12.5% in FZ 4. Indirect effects are only statistically significant for FZ 2 and amount to -3.8%.

These results indicate that there is no substantial variation in flood price effects from those of the city

of Dresden. However, direct effects of flood zone location have a slightly higher relevance when

analysing the whole river basin. In areas that are more rural, housing density is less high, so effects from

the neighbourhood become less important, perhaps resulting in a higher relevance of direct effects.

39

Taken together, the size and importance of indirect effects vary with the specific characteristics of the

study area including flood experience (Leipzig) and urban structures (Elbe area). In Leipzig, four out of

six indirect effects become statistically significant and are partly positive. For the Elbe area, we find

three statistically significant indirect effects that almost correspond to those in Dresden. The results for

Magdeburg must be interpreted carefully, since significantly fewer properties are situated on

floodplains. Overall, the spatial variations provide further evidence that indirect effects are generally

important in analysing flood price effects, but they need to be interpreted in the context of the specific

study area.


40

Appendix 1 – Exhibits and Tables

Exhibit A1-1: Inundated Properties during the Flooding Events in 2002 and 2013 Panel A: Magdeburg

Panel B: Leipzig

Notes: This exhibit shows affected properties during the flooding events in 2002 (left) and 2013 (right). Panel A presents maps for the city area of Magdeburg and Panel B of Leipzig. Whereas Magdeburg was directly affected due to its close proximity to the River Elbe, Leipzig was spared from significant losses from flooding. For Magdeburg, the first row of maps presents properties in our dataset, whereas the second row shows the general building development in floodplains obtained by OpenStreetMap. For Leipzig, only properties of our dataset are presented, since there are only small floodplains.

41

Table A1-1: Variation of the Spatial Weights Matrix

OLS (none) k-nearest Neighbour

(knn = 5) Distance Band (threshold = 100m)

House Condominium House Condominium House Condominium Direct Effects

FZ 2 -0.071*** [0.020]

-0.069*** [0.008] -0.007

[0.024] -0.017 [0.010] -0.047**

[0.023] -0.027** [0.010]

FZ 3 -0.037** [0.018]

-0.031*** [0.010]

0.027 [0.023]

0.011 [0.018]

0.000 [0.022]

-0.032* [0.016]

FZ 4 -0.133*** [0.049]

-0.110* [0.057] -0.017

[0.070] -0.026 [0.078] -0.094*

[0.055] -0.062 [0.070]

Indirect Effects

Spatial Lag FZ 2 -0.063**

[0.029] -0.053***

[0.013] -0.034 [0.030]

-0.067*** [0.014]

Spatial Lag FZ 3 -0.083***

[0.029] -0.051** [0.022] -0.055*

[0.030] -0.002 [0.021]

Spatial Lag FZ 4 -0.292**

[0.128] -0.129 [0.126] -0.074

[0.110] -0.168 [0.108]

Time-Fixed Effects Yes Yes Yes Yes Yes Yes Structure Yes Yes Yes Yes Yes Yes Location Yes Yes Yes Yes Yes Yes Neighbourhood Yes Yes Yes Yes Yes Yes Water Yes Yes Yes Yes Yes Yes N 6,371 12,358 6,371 12,358 6,371 12,358 λ 0.277*** 0.450*** 0.227*** 0.440*** Log Likelihood -1581.2 -144.4 -1658.8 -281.8 Likelihood Ratio Test 287.0*** 1544.2*** 206.3*** 1111.4*** Wald Test 313.2*** 2310.3*** 216.9*** 1302.6*** Residuals Moran’s I 0.186*** 0.284*** -0.031 -0.086 -0.027 -0.083

Notes: This table presents results of the spatial weight matrix variations. The OLS specification does not control for spatial autocorrelation. Other matrix specifications include a k-nearest neighbour (knn = 5) and a distance band approach (100 m). Results and controls for time-fixed effects, structure, location, neighbourhood, and water characteristics for houses are presented. The model parameters (N (observations), λ (spatial correlation), etc.) are shown in the last rows. The dependent variable is the natural logarithm of asking prices (€). Robust standard errors are presented in brackets. * p<0.10, ** p<0.05, *** p<0.01

42

Table A1-2: Event Studies

Flood 2002 Flood 2013 House Condominium House Condominium

Direct Effects

Flood Event 2002 -0.002 [0.024]

0.015 [0.019]

Flood Event 2013 0.089** [0.041]

-0.021 [0.029]

Indirect Effects

Spatial Lag Flood Event 2002 -0.038 [0.029]

0.042** [0.021]

Spatial Lag Flood Event 2013 -0.091* [0.051]

0.019 [0.035]

Time-Fixed Effects Yes Yes Yes Yes Structure Yes Yes Yes Yes Location Yes Yes Yes Yes Neighbourhood Yes Yes Yes Yes Water Yes Yes Yes Yes N 6,371 12,358 6,371 12,358 λ 0.260*** 0.426*** 0.262*** 0.428*** Log Likelihood -1601.0 -178.7 -1599.6 -184.4 Likelihood Ratio Test 286.8*** 1518.4*** 290.3*** 1520.6*** Wald Test 226.2*** 1918.9*** 308.4*** 1887.0*** Residuals Moran’s I -0.032 -0.086 -0.032 -0.086

Notes: This table presents results of the SDEM, including variables for the flood events 2002 and 2013. Results are presented separately for houses and condominiums. We also indicate whether we control for time-fixed effects, structure, location, neighbourhood, and water characteristics. The model parameters (N (observations), λ (spatial correlation), etc.) are shown in the last rows. The dependent variable is the natural logarithm of asking prices (€). Standard errors are presented in brackets. * p<0.10, ** p<0.05, *** p<0.01

43

Table A1-3: Event Studies (Difference in Differences)

Memory 2013 Memory Zones House Condominium House Condominium

Direct Effects

Flood Event 2013 0.158*** [0.054]

-0.021 [0.035]

FZ 2 -0.021 [0.028]

-0.027** [0.012]

FZ 3 0.019 [0.027]

-0.007 [0.020]

FZ 4 -0.149* [0.089]

0.040 [0.118]

Months after June 2013 0.006*** [0.000]

0.006*** [0.000] 0.006***

[0.000] 0.006*** [0.000]

Flood Event 2013 × Months after June 2013 -0.004* [0.002]

0.001 [0.001]

FZ 2 × Months after June 2013 0.000 [0.001]

0.000 [0.000]

FZ 3 × Months after June 2013 -0.001 [0.001]

0.000 [0.001]

FZ 4 × Months after June 2013 0.008* [0.005]

-0.001 [0.005]

Indirect Effects

Spatial Lag Flood Event 2013 -0.087 [0.072]

-0.150*** [0.046]

Spatial Lag FZ 2 -0.044 [0.032]

-0.097*** [0.016]

Spatial Lag FZ 3 -0.015 [0.037]

-0.100*** [0.024]

Spatial Lag FZ 4 -0.348** [0.150]

-0.393** [0.184]

Spatial Lag Months after June 2013 -0.001* [0.000]

0.000 [0.000] -0.001

[0.000] -0.001** [0.000]

Spatial Lag Flood Event 2013 × Months after June 2013 0.001 [0.003]

0.008*** [0.001]

Spatial Lag FZ 2 × Months after June 2013 0.001 [0.002]

0.003*** [0.001]

Spatial Lag FZ 3 × Months after June 2013 -0.002 [0.002]

0.004*** [0.001]

Spatial Lag FZ 4 × Months after June 2013 -0.348** [0.015]

0.013 [0.008]

Time-Fixed Effects No No No No Structure Yes Yes Yes Yes Location Yes Yes Yes Yes Neighbourhood Yes Yes Yes Yes Water Yes Yes Yes Yes N 6,371 12,358 6,371 12,358 λ 0.280*** 0.429*** 0.280*** 0.424*** Log Likelihood -1849.5 -542.7 -1848.0 -517.4 Likelihood Ratio Test 367.0*** 1579.0*** 359.8*** 1530.9*** Wald Test 315.5*** 1881.9*** 391.4*** 1928.2*** Residuals Moran’s I -0.038 -0.096 -0.038 -0.093

Notes: This table presents results of the SDEM for the changing price effects after the flood 2013. Changing price effects are measured for the inundated area during the flood 2013 (Memory 2013) and for the flood zones (Memory Zones). Results are presented separately for houses and condominiums. We also indicate whether we control for time-fixed effects, structure, location, neighbourhood, and water characteristics. The model parameters (N (observations), λ (spatial correlation), etc.) are shown in the last rows. The flooding event in 2013 took place on June 6-10. Including the interaction term between the number of months after the event and a dummy variable indicating if a property was affected by the event, we observe time dependent changes in prices for properties that were inundated and subject to a loss. * p<0.10, ** p<0.05, *** p<0.01

44

Table A1-4: Spatial Studies

Magdeburg Leipzig Elbe Area House Condominium House Condominium House Condominium

Direct Effects

FZ 2 0.001 [0.062]

0.065 [0.050] 0.048

[0.039] 0.066** [0.028]

-0.040*** [0.012]

-0.020* [0.011]

FZ 3 -0.214** [0.105]

-0.044 [0.078] 0.129**

[0.051] 0.026

[0.029] -0.021

[0.015] -0.005 [0.016]

FZ 4 -0.033 [0.061]

0.118* [0.068] 0.065

[0.076] 0.002

[0.141] -0.032

[0.025] -0.125***

[0.035]

Indirect Effects

Spatial Lag FZ 2 0.005 [0.067]

-0.053 [0.056] 0.306***

[0.053] -0.066** [0.031]

-0.024* [0.014]

-0.038*** [0.013]

Spatial Lag FZ 3 -0.143** [0.186]

-0.107 [0.105] 0.303***

[0.072] -0.023 [0.034]

-0.018 [0.018]

-0.001 [0.019]

Spatial Lag FZ 4 0.092 [0.111]

-0.045 [0.096] -0.516

[0.360] -0.534***

[0.170] -0.153***

[0.044] -0.010 [0.048]

Time-Fixed Effects Yes Yes Yes Yes Yes Yes Structure Yes Yes Yes Yes Yes Yes Location Yes Yes Yes Yes No No Neighbourhood Yes Yes Yes Yes Yes Yes Water Yes Yes Yes Yes Yes Yes N 2,234 1,546 5,543 10,950 37,863 16,314 λ 0.187*** 0.233*** 0.254*** 0.342*** 0.356*** 0.502*** Log Likelihood -576.1 -271.7 -1526.4 -3189.7 -19405.5 -2997.5 Likelihood Ratio Test 37.1*** 39.1*** 220.5*** 864.4*** 4042.4*** 3422.5*** Wald Test 39.0*** 43.3*** 128.4*** 999.1*** 4711.9*** 4632.5*** Residuals Moran’s I -0.010 -0.016 -0.024 -0.061 -0.048 -0.103

Notes: This table presents results of the SDEM for the city of Magdeburg, the city of Leipzig, and the Elbe Area. Results are presented separately for houses and condominiums. We also indicate whether we control for time-fixed effects, structure, location, neighbourhood, and water characteristics. The model parameters (N (observations), λ (spatial correlation), etc.) are shown in the last rows. * p<0.10, ** p<0.05, *** p<0.01

45

Appendix 2 – Further Tables

Table A2-1: Price Effects for Flood Zone Location (All Variables)

Water Amenities House Condominium

Direct Effects

FZ 2 -0.012 [0.024]

-0.017 [0.010]

FZ 3 0.021 [0.023]

0.012 [0.018]

FZ 4 -0.022 [0.070]

-0.034 [0.079]

Log(Time on Market) 0.009*** [0.008]

-0.004 [0 .003]

Log(Living Area) 0.776*** [0.018]

1.005*** [0.012]

Number of Rooms 0.038*** [0.011]

0.145*** [0.009]

Number of Rooms_SQ -0.002*** [0.001]

-0.013*** [0.001]

Age 0.001 [0.001]

-0.013*** [0.000]

Age_SQ 0.000*** [0.000]

0.000*** [0.000]

Quality Luxury 0.361*** [0.029]

0.305*** [0.015]

Quality Good 0.147*** [0.009]

0.152*** [0.005]

Quality Simple -0.098*** [0.036]

-0.238*** [0.052]

Household Size 0.518*** [0.147]

0.010 [0.159]

Number of Households 0.000*** [0.000]

0.000** [0.000]

Immigration Rate 0.008 [0.014]

0.012 [0.010]

Residential Buildings 0.000* [0.000]

0.000*** [0.000]

Residential/Commercial Buildings 0.000 [0.000]

0.001*** [0.000]

Population Age <18 years 1.870* [1.045]

0.350 [0.831]

Population Age 18-29 years -1.075** [0.422]

-1.192*** [0.283]

Population Age 30-49 years -1.223** [0.529]

-0.643* [0.355]

Population Age 49-65 years -0.893* [0.519]

-0.251 [0.471]

Log(Distance City Centre) -0.219* [0.133]

-0.158** [0.066]

Log(Distance Park) -0.024** [0.010]

-0.018*** [0.006]

Log(Distance Highway) 0.041 [0.025]

0.119*** [0.034]

Log(Distance Water Body) 0.002 [0.009]

0.022** [0.010]

Log(Distance River Elbe) -0.006 [0.021]

-0.019 [0.024]

Height × Log(Distance River Elbe) 0.000* [0.000]

0.000*** [0.000]

see next page

46

Table A2-1 continued

Indirect Effects

Spatial Lag FZ 2 -0.056** [0.028]

-0.054*** [0.013]

Spatial Lag FZ 3 -0.070** [0.028]

-0.047** [0.021]

Spatial Lag FZ 4 -0.266** [0.117]

-0.134 [0.117]

Spatial Lag Log(Time on Market) -0.005 [0.016]

-0.006 [0.005]

Spatial Lag Log(Living Area) 0.085*** [0.028]

0.007 [0.021]

Spatial Lag Number of Rooms -0.031* [0.018]

0.027* [0.016]

Spatial Lag Number of Rooms_SQ 0.002 [0.001]

-0.002 [0.002]

Spatial Lag Age 0.004*** [0.001]

-0.001** [0.000]

Spatial Lag Age_SQ 0.000*** [0.000]

0.000*** [0.000]

Spatial Lag Quality Luxury 0.125*** [0.046]

0.114*** [0.025]

Spatial Lag Quality Good 0.067*** [0.015]

0.019** [0.008]

Spatial Lag Quality Simple 0.113*** [0.054]

0.118 [0.119]

Spatial Lag Household Size -0.477*** [0.168]

0.687*** [0.177]

Spatial Lag Number of Households 0.000*** [0.000]

0.000*** [0.000]

Spatial Lag Immigration Rate 0.079*** [0.016]

-0.025** [0.011]

Spatial Lag Residential Buildings 0.000 [0.000]

0.000 [0.000]

Spatial Lag Residential/Commercial Buildings 0.001** [0.000]

0.001** [0.000]

Spatial Lag Population Age <18 years 1.351 [1.162]

-1.351 [0.961]

Spatial Lag Population Age 18-29 years -2.004*** [0.461]

-0.590** [0.297]

Spatial Lag Population Age 30-49 years -0.565 [0.567]

-1.204*** [0.377]

Spatial Lag Population Age 49-65 years -0.625 [0.561]

-4.531*** [0.577]

Spatial Lag Log(Distance City Centre) 0.142 [0.136]

0.101 [0.064]

Spatial Lag Log(Distance Park) 0.004 [0.011]

0.021*** [0.007]

Spatial Lag Log(Distance Highway) -0.009 [0.027]

-0.117*** [0.035]

Spatial Lag Log(Distance Water Body) 0.001 [0.011]

-0.029*** [0.011]

Spatial Lag Log(Distance River Elbe) -0.018 [0.023]

-0.022 [0.025]

Spatial Lag Height × Log(Distance River Elbe) 0.000** [0.000]

0.000** [0.000]

Time-Fixed Effects Yes Yes N 6,371 12,358 λ 0.260*** 0.424*** Log Likelihood -1594.5 -167.5 Likelihood Ratio Test 280.9*** 1491.3*** Wald Test 301.1*** 1834.2*** Residuals Moran’s I -0.032 -0.085

Notes: This table presents all coefficients from the ‘water amenities’ model stated in Table 4. The dependent variable is the natural logarithm of asking prices (€). Standard errors are presented in brackets. * p<0.10, ** p<0.05, *** p<0.01

47

Table A2-2: Log-marginal Likelihood Values and Posterior Model Probability (Condominium)

Panel A: Bayesian Model Comparison Model Log-marginal Likelihood Value Posterior Model Probability Spatially Lagged X (SLX) -6119.0 0 Spatial Durbin Model (SDM) -3460.7 1 Spatial Durbin Error Model (SDEM) -3482.0 0

Panel B: Bayesian Model Comparison with Spatial Weights Matrix

Number of Neighbours SLX SDM SDEM 3 0 0 0 4 0 1 0 5 0 0 0 6 0 0 0

Notes: This table presents the Bayesian model comparison approach for the condominium sample. Panel A includes the log-marginal likelihood values and the posterior model probabilities. Panel B extends this approach and shows the model probabilities for a variation in the number of neighbours in the spatial weight matrix.

48

Table A2-3: Variation of the Spatial Weight Matrix

OLS k-nearest Neighbour Distance Band none knn = 3 knn = 5 threshold = 100m threshold = 800m

Panel A: House Direct Effects

FZ 2 -0.071*** [0.020] -0.025

[0.024] -0.007 [0.024] -0.047**

[0.023] -0.007 [0.024]

FZ 3 -0.037** [0.018]

0.018 [0.023]

0.027 [0.023] 0.000

[0.022] -0.010 [0.021]

FZ 4 -0.133*** [0.049] 0.000

[0.071] -0.017 [0.070] -0.094*

[0.055] -0.086 [0.064]

Indirect Effects

Spatial Lag FZ 2 -0.049* [0.027]

-0.063** [0.029] -0.034

[0.030] -0.115** [0.053]

Spatial Lag FZ 3 -0.071*** [0.027]

-0.083*** [0.029] -0.055*

[0.030] -0.099** [0.048]

Spatial Lag FZ 4 -0.247** [0.104]

-0.292** [0.128] -0.074

[0.110] -0.001 [0.176]

Time-Fixed Effects Yes Yes Yes Yes Yes Structure Yes Yes Yes Yes Yes Location Yes Yes Yes Yes Yes Neighbourhood Yes Yes Yes Yes Yes Water Yes Yes Yes Yes Yes N 6,371 6,371 6,371 6,371 6,371 λ 0.236*** 0.277*** 0.227*** 0.441*** Log Likelihood -1602.1 -1581.2 -1658.8 -1548.8 Likelihood Ratio Test 267.3*** 287.0*** 206.3*** 191.0*** Wald Test 288.9*** 313.2*** 216.9*** 349.3*** Residuals Moran’s I 0.186*** -0.033 -0.031 -0.027 -0.014

Panel B: Condominium

Direct Effects

FZ 2 -0.069*** [0.008]

-0.010 [0.010]

-0.017 [0.010]

-0.027** [0.010]

-0.029*** [0.010]

FZ 3 -0.031*** [0.010]

0.035* [0.018]

0.011 [0.018]

-0.032* [0.016]

-0.009 [0.016]

FZ 4 -0.110* [0.057]

-0.026 [0.081]

-0.026 [0.078]

-0.062 [0.070]

-0.089 [0.067]

Indirect Effects

Spatial Lag FZ 2 -0.051*** [0.012]

-0.053*** [0.013]

-0.067*** [0.014]

-0.113*** [0.033]

Spatial Lag FZ 3 -0.066*** [0.020]

-0.051** [0.022]

-0.002 [0.021]

-0.039 [0.042]

Spatial Lag FZ 4 -0.047 [0.108]

-0.129 [0.126]

-0.168 [0.108]

0.223 [0.221]

Time-Fixed Effects Yes Yes Yes Yes Yes Structure Yes Yes Yes Yes Yes Location Yes Yes Yes Yes Yes Neighbourhood Yes Yes Yes Yes Yes Water Yes Yes Yes Yes Yes N 12,358 12,358 12,358 12,358 12,358 λ 0.382*** 0.450*** 0.440*** 0.746*** Log Likelihood -239.79 -144.4 -281.8 -209.6 Likelihood Ratio Test 1377.3*** 1544.2*** 1111.4*** 911.7*** Wald Test 1632.6*** 2310.3*** 1302.6*** 1902.2*** Residuals Moran’s I 0.284*** -0.087 -0.086 -0.083 -0.017

Notes: This table presents results of the spatial weight matrix variations. The OLS specification does not control for spatial autocorrelation. Other matrix specifications include a k-nearest neighbour (knn = 3 or 5) and a distance band approach (100m or 800m). Results and controls for time-fixed effects, structure, location, neighbourhood, and water characteristics for houses are presented. The model parameters (N (observations), λ (spatial correlation), etc.) are shown in the last rows. The dependent variable is the natural logarithm of asking prices (€). Robust standard errors are presented in brackets. * p<0.10, ** p<0.05, *** p<0.01

49

Table A2-4: Comparison between Price Effects and Insurance Costs (Condominium)

Flood Zones IQR Average Price

Average Price Effect

Annual Insurance

Costs

Present Value Insurance

(3%)

Implied Discount

Rate

Average Implied

Discount Rate Q1 82,350 5,847 351 11,700 6.0% FZ 2 Q2 150,432 10,681 473 15,767 4.4% 4.6% Q3 259,865 18,450 651 21,700 3.5% Q1 99,000 3,465 691 23,033 19.9% FZ 3 Q2 180,025 6,301 845 28,167 13.4% 15.0% Q3 295,217 10,333 1,223 40,767 11.8% FZ 4 Q2 136,495 22,931 994 33,133 4.3% 4.3%

Floodplain FZ 2-4

Q1 93,111 5,494 390 13,000 7.1% Q2 163,046 9,620 505 16,833 5.2% 5.5% Q3 279,537 16,492 681 22,700 4.1%

Notes: This table presents the comparison of price effects with insurance premiums. The average price effect is based on the ‘water amenities’ model in Table 4 and accounts for the total effect (direct + indirect effect). Prices, price effects, insurance costs, and values are given in €. To take the generally skewed pricing distribution of properties into account, we show the results for all three quartiles of the interquartile range (IQR). The breakpoints are: 25th percentile (Q1), median (Q2), and 75th percentile (Q3). Because of the small data sample of FZ 4, we focus on the median (Q2). Insurance premiums for FZ 4 are based on a theoretical calculation scheme. In practice, determination of insurance premiums is subject to an individual assessment.

50

Summary

In this study, we analyse direct and indirect price effects from flooding for the flood-prone city of

Dresden (Germany) by using a spatial Durbin error model which controls for local spillover effects. We

shed new light on the importance of including indirect effects for flood zones when interpreting flood

price effects. These indirect price effects amount to -6.5% for houses and -4.8% for condominiums in

our observation period from 2008 to 2016; the direct effects diminish when controlling for spatial

spillovers. Our results are generally robust across different model specifications, urban areas, and risk-

adjusted prices that include future insurance costs. We conclude that indirect effects in the form of local

spillovers are important in the analysis of flood zone effects since otherwise the economic consequences

of flooding may be underestimated and flood management policies may be inefficient and not cost-

effective.

51

Endnotes

1 Flood insurance is acquired in a bundle with insurance against other natural disasters including risks from earthquake, land

subsidence, landslide, snow pressure, and avalanches. According to the German Insurance Association, the determining

factor for the insurance premium calculation is the prevailing risk source. We follow this market approach and completely

assign insurance premiums to flood risk, since all other natural hazards have no statistical relevance in our study area.

2 German Federal Statistical Office (2017).

3 See https://www.umwelt.sachsen.de/umwelt/infosysteme/hwims/portal/web/wasserstand-pegel-501060 for the water levels.

4 The construction cost index is obtained from the German Federal Statistical Office. This index is preferred over the consumer

price index, since it only measures the price trend in construction costs of properties depending on labour and material costs

(including equipment, energy, operating, and building supplies).

5 Annual housing market report by the city of Dresden (2015). However, those data do not include housing attributes and are

not suitable for our analysis.

6 German Federal Office of Cartography and Geodesy (BKG) and German Federal Office of Hydrology (BfG).

7 OpenStreetMap (2017).

8 We use the 3.2.2 (64-bit) version of R for calculating our spatial regressions.

9 We use the k-nearest neighbour approach to account for underlying spatial correlation between observations. A robustness

check for the variation of the spatial weights matrix is provided in Table A1-1.

10 As this is the market standard, the rebuilding value is calculated for the year 1914. In 1914, the German currency was on a

gold standard and exceptional increases in property prices were inhibited.

11 For endogeneity reasons, we refrain from including insurance costs as an explanatory variable.

12 The total effect is defined as the direct effect + indirect effect (LeSage & Pace, 2009).

13 100 meters (m) is the average distance between all houses and half of the average distance between condominiums.

14 A comparison of properties in our dataset with all existing properties from OpenStreetMap is provided in Exhibit A1-1.

15 We note that we do not control for locational characteristics in the ‘Elbe area’ model.

https://www.umwelt.sachsen.de/umwelt/infosysteme/hwims/portal/web/wasserstand-pegel-501060

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