Code the studies and compute effect sizes

The final meta-sample includes a total of 37 studies and 349 point estimates, this means almost doubling the number of studies considered by Daniel, Florax, and Rietveld (2009a) and more than trebling the number of point estimates. The date of publication of studies is between 1987 and 2013. The availability of empirical evidence is geographically confined to the United States contributing with 33 studies across 12 different States. The sample also includes studies for Australia, The Netherlands, New Zealand and United Kingdom (see table 1.3 below).

Once we select the studies for the meta-analysis, their main characteristics and results have to be coded. From studies using a standard HPF, generalized in equations (23) and (24), the coefficient of interest is 𝜃̂_𝑖, which represents the relative price differential for floodplain location at different levels of risk.

Although all studies in the meta-sample use a similar variable to control for flood risk, the functional form of the hedonic price function is not the same; therefore some of the observations are not expressed in the same units and adjustments have to be done. The effect size of interest for this meta-analysis is the relative price differential for floodplain location, following the same notation as Daniel, Florax, and Rietveld (2009a), this is referred as 𝑇, with associated standard errors 𝑠_𝑇. Most studies use a semi-loglinear specification as in equation (35) below, where 𝑙𝑛𝑃_𝑖 denotes the natural logarithm of the

selling price of house 𝑖, 𝐹 represents a dummy variable equal to one if the property is located in a floodplain, 𝑍 represents the set of all other house specific characteristics 𝑗 and 𝜀_𝑖 is the house specific error term which is assumed ε_𝑖~N(0, σ2I). In this case, the effect size 𝑇 and the standard errors 𝑠_𝑇 are considered to be the coefficient 𝜃 and the standard error 𝑠𝜃 as recorded from the primary studies.10 Studies by Donnelly (1989), Bialaszewski

and Newsome (1990), Speyrer and Ragas (1991), US Army Corps of Engineers (1998), Harrison, Smersh, and Schwartz (2001) and Shultz and Fridgen (2001) report estimates from linear specifications as in equation (36); in this case 𝑇 = 𝜃 𝑃̅⁄ and 𝑠_𝑇 = 𝑠_𝜃⁄ , where 𝑃̅ 𝑃̅ is the sample mean of the selling price.

𝑙𝑛𝑃_𝑖 = 𝛽₀+ 𝜃𝐹_𝑖+ ∑_𝑗=1𝛽_𝑗𝑍_𝑖𝑗 + 𝜀_𝑖 (35)

𝑃𝑖 = 𝛽0+ 𝜃𝐹𝑖 + ∑𝑗=1𝛽𝑗𝑍𝑖𝑗 + 𝜀𝑖 (36)

𝑃_𝑖𝜆−1

𝜆 = 𝛽0+ 𝜃𝐹𝑖 + ∑𝑗=1𝛽𝑗𝑍𝑖𝑗+ 𝜀𝑖 (37)

Studies by MacDonald, Murdoch, and White (1987), MacDonald et al. (1990), Dei-Tutu and Bin (2002) and Bin (2004) report estimates using a Box-Cox specification as in equation (37); in this case 𝑇 = 𝜃𝑃̂̅1−𝜆̂_{, where 𝑃̂̅ represents the mean estimated selling price}

and 𝜆̂ is the estimated non-linearity parameter. Notice that, in this case, the effect size, 𝑇, is a function of two random parameters, therefore the standard errors, 𝑠_𝑇, cannot easily be computed from the parameters reported in primary studies; following Daniel, Florax, and Rietveld (2009a), these have been approximated using the Delta method, as in equation (38).

10

Notice that, formally, in the case of a dummy variable in a semi-log specification the marginal effect should be adjusted to 𝑒𝜃− 1 (Halvorsen and Palmquist, 1980). However, following Daniel, Florax, and Rietveld (2009a) adjustments are not taken into account given the small magnitude of the coefficients.

𝑠𝑇 = √( 𝜕𝑇 𝜕𝜆) 2 𝜎_𝜆2_{+ (}𝜕𝑇 𝜕𝜃) 2 𝜎_𝜃2_{+ 2 (}𝜕𝑇 𝜕𝜆) ( 𝜕𝑇 𝜕𝜃) 𝑟𝜃𝜆𝜎𝜃𝜎𝜆 (38)

Where 𝜎_𝑖 represents the standard error of parameters 𝜆 and 𝜃, respectively, and 𝑟_𝜃𝜆 is its correlation coefficient. For studies such as MacDonald, Murdoch, and White (1987) and MacDonald et al. (1990) which do not provide an estimate of 𝜎_𝜆, we approximate this using a standard error of 𝜆 2⁄ as in Daniel, Florax, and Rietveld (2009a); this makes 𝜆 significantly different from zero at the 5% significance level. Since an estimate of 𝑟_𝜃𝜆 is generally unavailable, we assume a value of ±0.9 depending on whether (𝜕𝑇 𝜕𝜃⁄ )(𝜕𝑇 𝜕𝜆⁄ ) is positive or negative, respectively, in order to have conservative standard errors.

All studies using a hedonic DID model, generalised in equations (25) and (28), assume a semi-loglinear specification. From these models it is possible to recover estimates for the pre-flood and post-flood relative price differential for floodplain location. In the case of pre-flood estimates 𝑇 = 𝜃, with standard errors 𝑠𝑇 = 𝑠𝜃, as recorded from primary studies.

For post-flood estimates 𝑇 = Θ, as defined in equation (27); therefore, we have to collect information on two coefficients: the pre-flood relative price differential for floodplain location, 𝜃̂𝑖 and the incremental effect due to information conveyed by the flood in known

risky locations, 𝜓̂_𝑖. Since 𝑇 is given by a linear combination of two parameters, the standard errors have to be estimated using the following formula:

𝑠𝑇 = √𝜎𝜃2+ 𝜎𝜓2 + 2𝑟𝜃𝜓𝜎𝜃𝜎𝜓 (39)

Again, 𝜎_𝑖 represents the standard error of parameters 𝜃 and 𝜓, respectively, and 𝑟_𝜃𝜓 is the corresponding correlation coefficient. Since the latter is generally unavailable, a value of 0.9 has been assumed to keep standard errors conservative. We do not include evidence

from repeat-sales models in the analysis, as equation (30) makes clear that from these specifications it is only possible to recover an estimate of 𝜓̂𝑖 and therefore is not possible

to compute the coefficient of interest.

All estimates included in the analysis are based on actual transaction data, i.e. selling price. We exclude 13 estimates by US Army Corps of Engineers (1998) based on appraised values.11 For studies using a spatial lag model only, we collect only the ‘pure’ effect of flood risk location (i.e. the pre-dynamic effect), and spatial spillovers due to prices of nearby properties are not considered; studies dealt with thus include Daniel, Florax, and Rietveld (2007), Bin et al. (2008), Posey and Rogers (2010), Atreya and Ferreira (2012a), Atreya and Ferreira (2012c), Atreya, Ferreira, and Kriesel (2012), Atreya, Ferreira, and Kriesel (2013) and Meldrum (2013).12

The number of observations collected from each primary study varies widely, ranging from studies such as Donnelly (1989), Shilling, Benjamin, and Sirmans (1985), Bialaszewski and Newsome (1990), Dei-Tutu and Bin (2002) and Rambaldi et al. (2012) contributing with one observation each, up to studies such as Atreya, Ferreira, and Kriesel (2013) and Kousky (2010), that contribute with 40 and 46 observations, respectively. Table 1.3 shows a summary of the studies and the effect sizes that were computed.

It is important to note that the mean effect sizes that we report in table 1.3 corresponds to the relative price differential for floodplain location (100, 500-year floodplain or both) and have not been adjusted for different levels of risk. Daniel, Florax, and Rietveld (2009a) standardised the effect sizes (and corresponding standard errors) to account for differences in the level of risk and report them as 𝑇∗ _{= 𝑇 × (1/𝜔 × 100)}−1_{, where 𝑇 represents the}

unstandardised effect size and 𝜔 the recurrence interval of the floodplain, for instance 100

11

These were, however, included in the meta-analysis by Daniel, Florax and Rietveld (2009a).

12

or 500-year. However, such a transformation assumes the relative price differential for floodplain location is linear in risk and applying it to the effect sizes led, in some cases, to unrealistic figures.13 Therefore, we do not standardise the effect sizes prior to the analysis, instead we explore differences arising due to different levels of risk as part of the meta- analysis.

Most studies follow the definition of flood zones by the US Federal Emergency Management Agency (FEMA) under the National Flood Insurance Program (NFIP) and analyse the implicit price of flood risk for areas defined as Special Flood Hazard Area (SFHA). SFHAs are areas regarded to have a 1% probability (or higher) of being flooded in any single year, also known as 100-year floodplains; these areas are subdivided in Flood Zones with categories V and A, the former usually correspond to first-row, beach-front properties with additional hazards due to storm-induced velocity wave action, and the latter usually describes zones subject to rising waters. Other studies also consider areas of moderate flood hazard which are classified as zones B or X by the FEMA and are designated between the limits of the 100-year floodplain and the 0.2% annual probability of flooding, also known as 500-year floodplain. Studies by US Army Corps of Engineers (1998), Bin, Kruse, and Landry (2008) and Bin and Landry (2013) include regressions where a dummy variable is use to indicate floodplain location in either 100-year or 500- year floodplain without proper distinction; these estimates have been excluded from the final meta-sample. Estimates by US Army Corps of Engineers (1998) corresponding to 10, 25, and 50-year floodplain have been considered within the 100-year floodplain, as this is the highest flood hazard area considered by the FEMA. Estimates by Bartosova et al. (1999) for 200, 300 and 400-year floodplain have been classified as being within the 500- year floodplain. For estimates outside the US similar flood zones are distinguished.

13 _{For instance, Atreya and Ferreira (2012a) reports the effect size which represents the highest price discount for location}

in a 500-year floodplain of -0.34. Applying the standardisation procedure proposed by Daniel, Florax and Rietveld (2009a) would imply 𝑇∗= −0.34 × (1 500⁄ × 100)−1= −1.7, i.e. an estimated discount of 170% of the price of the house for being located in a 100-year floodplain, which results implausible.

Table 1.3. Summary of studies included in the meta-sample

ID Authors Year Country1 Location Flood risk

(floodplain) No. Obs.

Effect size (T)

Mean S.D. Min. Max.

1 MacDonald, Murdoch and Whitea 1987 US Louisiana 100 2 -0.077 0.014 -0.086 -0.067

2 Skantz and Stricklanda 1987 US Texas 100 8 -0.025 0.019 -0.056 -0.012

3 Donnellya 1989 US Wisconsin 100 1 -0.121 - - -

4 Shilling, Sirmans and Benjamina 1989 US Louisiana 100 1 -0.076 - - -

5 Bialszewski and Newsomea 1990 US Alabama 100 1 0.000 - - -

6 MacDonald et al.a 1990 US Louisiana 100 2 -0.100 0.024 -0.117 -0.083

7 Speyrer and Ragasa 1991 US Louisiana 100 4 -0.098 0.073 -0.204 -0.042

8 US Army Corps of Engineersa 1998 US Texas 100 14 -0.029 0.083 -0.268 0.080

9 Bartosova et al.a 1999 US Wisconsin 100 and 500 7 -0.016 0.074 -0.078 0.144 10 Harrison, Smersh and Schwartza 2001 US Florida 100 4 -0.025 0.013 -0.041 -0.014 11 Shultz and Fridgena 2001 US ND and MI 2 100 and 500 4 -0.032 0.073 -0.102 0.031

12 Troy 2001 US California 100 20 0.024 0.022 -0.017 0.061

13 Dei-Tutu and Bina 2002 US North Carolina 100 1 -0.062 - - -

14 Bin 2004 US North Carolina 100 4 -0.062 0.015 -0.076 -0.044

15 Bin and Polaskya 2004 US North Carolina 100 3 -0.060 0.023 -0.084 -0.038

16 Troy and Romma 2004 US California 100 2 -0.011 0.030 -0.032 0.009

17 Hallstrom and Smitha 2005 US Florida 100 8 0.066 0.118 -0.113 0.173

18 Bin and Krusea 2006 US North Carolina 100 and 500 9 0.107 0.235 -0.103 0.610 19 Lamond and Proverbs 2006 UK North Yorkshire 100 2 -0.175 0.005 -0.178 -0.171 20 Daniel, Florax and Rietveld 2007 NL Meuse River 100 15 -0.026 0.042 -0.064 0.066

21 Morgan 2007 US Florida 100 3 0.254 0.080 0.165 0.321

22 Bin et al.a 2008 US North Carolina 100 2 -0.139 0.037 -0.165 -0.113

23 Bin, Kruse and Landrya 2008 US North Carolina 100 and 500 6 -0.054 0.028 -0.078 -0.010

24 Popea 2008 US North Carolina 100 and 500 22 -0.002 0.025 -0.045 0.038

25 Daniel, Florax and Rietveld 2009 NL Meuse River 100 4 -0.049 0.041 -0.086 0.005

26 Kousky 2010 US Missouri 100 and 500 46 -0.024 0.017 -0.073 0.008

27 Samarasinghe and Sharp 2010 NZ Auckland 100 4 -0.040 0.025 -0.064 -0.014

28 Posey and Rogers 2010 US Missouri 100 2 -0.082 0.023 -0.098 -0.066

29 Atreya and Ferreira 2011 US Georgia 100 and 500 6 -0.134 0.143 -0.375 0.042

30 Rambaldi et al. 2012 AU Queensland 100 1 -0.013 - - -

31 Atreya and Ferreira 2012c US Georgia 100 20 -0.187 0.245 -0.722 0.127

32 Atreya and Ferreira 2012a US Georgia 100 and 500 18 -0.174 0.195 -0.677 0.102 33 Atreya, Ferreira and Kriesel 2012 US Georgia 100 and 500 22 -0.084 0.163 -0.382 0.100 34 Atreya, Ferreira and Kriesel 2013 US Georgia 100 and 500 40 -0.164 0.226 -0.753 0.087 35 Bin and Landry 2013 US North Carolina 100 and 500 18 -0.093 0.101 -0.423 0.041

36 Meldrum 2013 US Colorado 100 21 -0.038 0.040 -0.096 0.010

37 Turnbull, Zahirovic and Mothorpe 2013 US Louisiana 100 and 500 10 -0.006 0.016 -0.023 0.014

Overall 349 -0.059 0.147 -0.753 0.610

Notes: 1 AU = Australia, NL = The Netherlands, NZ = New Zealand, UK = United Kingdom, US = United States. 2 ND = North Dakota, MI = Minnesota.

a _{Studies included in the previous meta-analysis by Daniel, Florax and Rietveld (2009a).}

There is general agreement in that prices of properties in a flood prone area are lower than those of equivalent houses outside; a total of 33 studies, out of 37, estimate a mean negative price effect of flood risk location on property prices. Evidence suggests that properties located in a floodplain are discounted, on average, by 5.9%; however, there is great within-study and between-study variability as highlighted by the columns reporting

the standard deviation (SD) of the effect sizes, as well as their minimum (Min.) and maximum (Max) values. Estimates range from a price discount of 75% suggested by Atreya, Ferreira, and Kriesel (2013), to a price premium of 61% by Bin and Kruse (2006). Figure 1.3 shows the 349 effect sizes included in the meta-sample. Given the broad heterogeneity in results, it is difficult to conclude to what extent (if any) flood risk location is capitalised in property prices. Nonetheless, it is important to remember that the effect sizes represent different levels of risk, and that other characteristics of the study and the location of interest are not accounted for. The following sections explore the wide heterogeneity in results.

Figure 1.3. Meta-sample: Relative price differential for floodplain location

Source: Own elaboration based on results from primary studies.

Finally, although all studies included in the meta-sample by Daniel, Florax, and Rietveld (2009a) are represented in our meta-analysis, the number of point estimates collected from each study is not always the same; some of the differences require special mention. As noted earlier, 13 point estimates by US Army Corps of Engineers (1998) based on appraised values are not included. This meta-analysis includes three additional estimates by Bin and Kruse (2006) associated with locations within a 100-year floodplain with additional vulnerability to wave action, one of the flood zone subdivisions within SFHAs

as specified by the US FEMA.14 For those studies using a Box-Cox specification the effect sizes have been computed based on the estimated sales prices at the average values of the characteristics of the properties in the sample of the studies; as a result the final meta- sample only includes two estimates by MacDonald, Murdoch, and White (1987) and MacDonald et al. (1990) and only one from Dei-Tutu and Bin (2002).15