# Evaluating the Impact of Floods on Housing Price Using a Spatial Matching Difference-In-Differences (SM-DID) Approach

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Measuring Urban Externalities: The Hedonic Pricing Model (HPM)

**y**

_{it}is a function of the individual (intrinsic and extrinsic) amenities that form a bundle that describes a real estate good (Equation (1)).

**y**= α

**ι**+

**Xβ**+

**ε**

_{T}× 1), that is usually expressed in a logarithmic transformation; the list of independent variables is stacked in a matrix

**X**of dimension (N

_{T}× K), ι is a vector of one, and ε is a vector of errors; both are of dimension (N

_{T}× 1), where N

_{T}is the total sample size (N

_{T}= ∑

_{t}N

_{t}). The vector of parameters

**β**, of dimension (K × 1), captures the implicit price of each amenity, including the intrinsic as well as the extrinsic amenities, while α is a scalar, constant term parameter. As such, the estimation of the price equation is considered to be quite straightforward and allows one to obtain the implicit price related to extrinsic amenities ([33]).

**D**

_{τ}= {0,1}) in a specific location (within treatment and control areas–

**D**

_{s}= {0,1}). The DID estimator adequately makes it possible to isolate the contribution of one specific amenity after a given, assumed exogenous change or shock occurring in the urban space or landscape. By introducing these two additional variables, one obtains the HPM-DID specification (Equation (2)).

**y**= α

**ι**+

**Xβ**+

**D**

_{s}

**δ**

_{s}+

**D**

_{τ}

**δ**

_{τ}+ (

**D**

_{s}◦

**D**

_{τ})

**γ**+

**ε**

**δ**

_{s}is a matrix of coefficients isolating the impact of being inside the spatial delimitation where the change occurs,

**δ**

_{τ}is a matrix identifying the impact related to any temporal modification in the price determination process, and

**γ**is a matrix of coefficients measuring the impact of the change occurring in a spatially delimited zone (treatment) that is identified after the investigated change occurred. The symbol ◦ indicates a term-by-term multiplication of the elements of both matrices (d

_{ijs}× d

_{ijτ}). The validity of the estimation and the vector of parameters of interest

**γ**both depend on the assumption that there exists a common trend (before the treatment) between both groups (treatment and control).

#### 2.2. Creating a DID Estimator Using the Comparable Sales Approach (CSA)

**y**

_{it}= α

**ι**+

**X**

_{it}

**β**+

**D**

_{is}

**δ**

_{s}+

**D**

_{iτ}

**δ**

_{τ}+ (

**D**

_{is}◦

**D**

_{iτ})

**γ**+

**ε**

_{it}+

[

**y**

_{jt−1}− (α

**ι**+

**X**

_{jt-r}

**β**+

**D**

_{js}

**δ**

_{s}+

**D**

_{jτ}

**δ**

_{τ}+ (

**D**

_{js}◦

**D**

_{jτ})

**γ**+

**ε**

_{jt−1})]

**y**

_{it}−

**y**

_{jt-r}= (

**X**

_{it}−

**X**

_{jt-r})

**β**+ (

**D**

_{si}−

**D**

_{sj})

**δ**

_{s}+ (

**D**

_{i}−

**D**

_{jτ})

**δ**

_{τ}+ [(

**D**

_{is}◦

**D**

_{iτ}) − (

**D**

_{js}◦

**D**

_{jτ})]

**γ**+ (

**ε**

_{it}−

**ε**

_{jt-r}).

**X**

_{it}=

**X**

_{jt−1}) greatly simplifies the equation to obtain the final expression of the predicted sale price that is related to the sale price of an identified previous transaction (of house j), as well as to the “change” occurring in their spatiotemporal context (Equation (5)).

**y**

_{it}−

**y**

_{jt-r}= (

**D**

_{si}−

**D**

_{sj})

**δ**

_{s}+ (

**D**

_{iτ}−

**D**

_{jτ})

**δ**

_{τ}+ [(

**D**

_{is}◦

**D**

_{iτ}) − (

**D**

_{js}◦

**D**

_{jτ})]

**γ**+

**ξ**

_{it}

**D**

_{iτ}= 0) and after (

**D**

_{jτ}= 1) a given event (at t = t*), one can obtain the difference between the sale price before (Equation (6)) and after (Equation (7)) the exogenous change.

**y**

_{i(Dτ=1)}−

**y**

_{j(Dτ=1)}) = (

**D**

_{si}−

**D**

_{sj})

**δ**

_{s}+ (

**D**

_{iτ}−

**D**

_{jτ})

**δ**

_{τ}+ (

**D**

_{s}◦

**D**

_{τ})

**γ**

**y**

_{i(Dτ=0)}−

**y**

_{j(Dτ=0)}) = (

**D**

_{si}−

**D**

_{sj})

**δ**

_{s}+ (

**D**

_{iτ}−

**D**

_{jτ})

**δ**

_{τ}

**D**

_{iτ}=

**D**

_{jτ}, which simplifies both equations.

**y**

_{i(Dτ=1)}−

**y**

_{j(Dτ=1)}) − (

**y**

_{i(Dτ=0)}−

**y**

_{j(Dτ=0)}) = (

**D**

_{s}◦

**D**

_{τ})

**γ**

**D**

_{si}−

**D**

_{sj})

**δ**

_{s}in Equations (6) and (7) is canceled out because both transactions are spatially close, having similar spatial characteristics.

## 3. Identifying Counterfactuals

**X**). This score is calculated by regressing the probability that a given unit i faces an exogenous event (the “treated” status) and is represented by (D

_{s}= {0,1}), given its own characteristics (stocked in a vector

**X**) (Equation (9)).

**D**= 1) = f (

_{s}**X**

_{it}

**θ**)

**θ**is the vector of coefficients associated with the matrix of characteristics of all goods

**X**

_{it}, while f(.) is a general function. Usually, this approach is based on a logit model. As such, it is assumed that the f(.) takes the following form (Equation (10)):

**X**

_{it}

**θ**) = exp(

**X**

_{it}

**θ**)/[1 + exp(

**X**

_{it}

**θ**)].

**X**

_{it}) = exp(

**X**

_{it}

**θ**

**)/[**1 + exp(

**X**

_{it}

**θ**)].

_{τ}= {0,1}).

**X**

_{it}), makes it possible to find and identify neighbors, or counterfactuals, for each observation depending on their status. The neighbor is defined by the difference,

**d**(

**i**), between the propensity score for an observation i and that of observation j and necessitating a variation of the goods’ status (as being either treatment or control) (Equation (12)).

**d(i)**= min|| p(

**X**

_{it}|

**D**

_{si}) − p(

**X**

_{jt}|

**D**

_{sj}) || ≤ c

_{si}≠ d

_{sj}) identifies the nearest neighbors and helps to calculate the “counterfactual” for both status (Average Treatment Effect-ATE) or for the treated cases (Average Treatment on Treated-ATT). The difference between the observations can be limited to a certain threshold value, c, to ensure a better comparison. After having identified the distance between the observations that are of different status, it is possible to calculate the effect of the treatment (being subjected or not to a given extrinsic amenity).

_{0}: (

**y**

_{i}(

**D**

_{τ}= 0) −

**y**

_{j}(

**D**

_{τ}= 0)) = 0; and H

_{0}: (

**y**

_{h}(

**D**

_{τ}= 1) −

**y**

_{g}(

**D**

_{τ}= 1) = 0)) and with the alternative that the differences are different from 0. Another approach, which happens to be more robust, consists of making a falsification test based on a random permutation of the status ([46,47]). This approach allows one to estimate and construct a distribution of the “potential” impact based on the assumption that the treatment is randomly assigned. Repeating this exercise several times returns a distribution of the “random impact”, which should be centered around 0. After calculating and charting the distribution of the fictive effect, it is possible to compare it with the rank of the value obtained from the real differences (based on real and actual status) to obtain a pseudo-significance ([48]). This approach appears to be more robust than that of traditional statistics since it is based on a non-parametric method. These simulation and pseudo-significance approaches are well used in spatial analysis, since the exact distribution of the statistics is hard to establish ([49]).

## 4. Data

## 5. Results

**D**= 1-or no-

_{s}**D**= 0-), i.e., receiving the treatment. This model has no particular meaning. It helps to identify the houses that have similar characteristics, as shown in the propensity score, based on the prediction of the probability of facing a flood event. It is not necessary to restrict the used variables to the “classical” amenities typically used in housing price models. It could also include other variables, such as the X and Y geographical coordinates. The addition of these variables helps to identify similar goods having similar locations and takes explicitly into account the spatial dimension.

_{s}^{2}of 0.4787, and is globally significant (χ

^{2}= 120.19; p = 0.0000). It also has a good specification, with a non-significant Hosmer & Lemeshow ([45]) statistic (p = 0.6171). The logit model has five (5) individual variables that appear to be statistically related to the location of the houses (Table 4).

_{s}= {0,1}) and on the times when the transactions were recorded (D

_{τ}= {0,1}).

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Correction Statement

## References

- Verhoef, E.T.; Nijkamp, P. Externalities in the Urban Economy; Tinbergen Institute Discussion Paper No. 2003-078/3; Tinbergen Institute: Amsterdam, The Netherlands, 2003. [Google Scholar]
- Rosen, S. Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition. J. Political Econ.
**1974**, 82, 34–55. [Google Scholar] [CrossRef] - Gibbons, S.; Machin, S. Valuing School Quality, Better Transport, and Lower Crime: Evidence from House Prices. Oxf. Rev. Econ. Policy
**2008**, 24, 99–119. [Google Scholar] [CrossRef] - Dubé, J.; Thériault, M.; Des Rosiers, F. Commuter Rail Accessibility and House Values: The Case of the Montréal South Shore, Canada, 1992–2009. Transp. Res. Part A
**2013**, 54, 49–66. [Google Scholar] [CrossRef] - Dubé, J.; Des Rosiers, F.; Thériault, M.; Dib, P. Economic Impact of a Supply Change in Mass Transit in Urban Areas: A Canadian Example. Transp. Res. Part A
**2011**, 45, 46–62. [Google Scholar] [CrossRef] - Dubé, J.; Legros, D.; Thériault, M.; Des Rosiers, F. A Spatial Difference-in-Differences Estimator to Evaluate the Effect of Change in Public Mass Transit Systems on House Prices. Transp. Res. Part B
**2014**, 64, 24–40. [Google Scholar] [CrossRef] - Kolak, M.; Anselin, L. A Spatial Perspective on the Econometrics of Program Evaluation. Int. Reg. Res. Rev.
**2019**, 43, 128–153. [Google Scholar] [CrossRef] - Dubé, J.; Legros, D.; Thériault, M.; Des Rosiers, F. Measuring and Interpreting Urban Externalities in Real-Estate Data: A Spatiotemporal Difference-in-Differences (STDID) Estimator. Buildings
**2017**, 7, 51. [Google Scholar] [CrossRef] - Antonakis, J.; Bendahan, S.; Jacquart, P.; Lalive, R. On Making Causal Claims: A Review and Recommendations. Leadersh. Q.
**2010**, 21, 1086–1120. [Google Scholar] [CrossRef] - Kuminoff, N.V.; Pope, J.C. Do “Capitalization Effects” for Public Goods Reveal the Public’s Willingness to Pay? Int. Econ. Rev.
**2014**, 55, 1227–1250. [Google Scholar] [CrossRef] - Yousfi, S.; Dubé, J.; Legros, D.; Thanos, S. Mass Appraisal without Statistical Estimation: A Simplified Comparable Sales Approach based on Spatiotemporal Matrix. Ann. Reg. Sci.
**2020**, 64, 349–365. [Google Scholar] [CrossRef] - Sandink, D.; Kovacs, P.; Oulahen, G.; McGillivray, G. Making Flood Insurable for Canadian Homeowners; Discussion Paper; Institute for Catastrophic Loss Reduction and Swiss Reinsurance Company Ltd.: Toronto, ON, Canada, 2010. [Google Scholar]
- Jakob, M.; Church, M. The Trouble with Floods. Can. Water Resour. J.
**2010**, 36, 287–292. [Google Scholar] [CrossRef] - Franco, S.F.; Macdonald, J.L. Living on the Edge: How Does Your House Price Respond to Urban Hazard Risk? Available online: https://economics.ucr.edu/wp-content/uploads/2019/10/Franco-paper-for-11-2-18-seminar.pdf (accessed on 6 June 2020).
- Rajapaksa, D.; Wilson, C.; Managi, S.; Hoang, V.; Lee, B. Flood Risk Information, Actual Floods and Property Values: A Quasi-Experimental Analysis. Econ. Rec.
**2016**, 92, 52–67. [Google Scholar] [CrossRef] - Rajapaksa, D.; Wilson, C.; Hoang, V.; Lee, B.; Managi, S. Who Responds more to Environmental Amenities and Dis-amenities? Land Use Policy
**2017**, 62, 151–158. [Google Scholar] [CrossRef] - Rajapaksa, D.; Zhu, M.; Lee, B.; Hoang, V.; Wilson, C.; Managi, S. The Impact of Flood Dynamics on Property Values. Land Use Policy.
**2017**, 69, 317–325. [Google Scholar] [CrossRef] - Bin, O.; Landry, C. Changes in Implicit Flood Risk Premiums: Empirical Evidence from the Housing Market. J. Environ. Econ. Manag.
**2013**, 65, 361–376. [Google Scholar] [CrossRef] - Bin, O.; Landry, C. Flood Hazards, Insurance Rate, and Amenities: Evidence from the Coastal Housing Market. J. Risk Insur.
**2008**, 75, 63–82. [Google Scholar] [CrossRef] - West, T.L. Flood Mitigation and Response: Comparing the Great Midwest Floods of 1993 and 2008. Master’s Thesis, Naval Postgraduate School, Monterey, CA, USA, 2010. [Google Scholar]
- Montz, B.E. The Effects of Flooding on Residential Property Values in Three New Zealand Communities. J. Disaster Stud. Manag.
**1992**, 16, 283–298. [Google Scholar] [CrossRef] [PubMed] - Eleuterio, J. Flood Risk Analysis: Impact of Uncertainty in Hazard Modelling Vulnerability Assessments on Damage Estimations. Ph.D. Thesis, University of Strasbourg, Strasbourg, France, 2012. [Google Scholar]
- Square One Insurance Services, Canadian Flood Maps: Is your Home in a Flood Zone. 2020. Available online: https://www.squareoneinsurance.com/resource-centres/home-personal-safety/canadian-flood-maps (accessed on 6 June 2020).
- Chruch, R.L.; Cova, T.J. Mapping Evacuation Risk on Transportation Network using a Spatial Optimization Model. Transp. Res. Part C
**2000**, 8, 321–336. [Google Scholar] - Beltrán, A.; Maddison, D.; Elliott, R.J.R. Is Flood Risk Capitalized into Property Values? Ecol. Econ.
**2017**, 146, 668–685. [Google Scholar] [CrossRef] - Beltrán, A.; Maddison, D.; Elliott, R.J.R. The Impact of Flood on Property Price: A Repeat-Sales Approach. J. Environ. Econ. Manag.
**2019**, 95, 62–86. [Google Scholar] [CrossRef] - Atreya, A.; Ferreira, S. Seeing is Beleiving? Evidence from Property Prices in Inundated Areas. Risk Anal.
**2015**, 35, 828–848. [Google Scholar] [CrossRef] [PubMed] - Atreya, A.; Ferreira, S.; Kriesel, W. Forgetting the Flood? An Analysis of the Flood Risk Discount over Time. Land Econ.
**2013**, 146, 668–685. [Google Scholar] [CrossRef] - Bin, O.; Kruse, B. Real Estate Market Response to Coastal Flood Hazards. Nat. Hazards Rev.
**2006**, 7, 137–144. [Google Scholar] [CrossRef] - Landry, C.; Hindsley, P.; Bin, O.; Kruse, J.B.; Whitehead, J.C.; Wilson, K. Weathering the Storm: Measuring Household Willingness-to-Pay for Risk-Reduction in Post-Katrina New Orleans. Mar. Resour. Econ.
**2013**, 28, 991–1013. [Google Scholar] - Bin, O.; Polasky, S. Effects of Flood Hazards on Property Values: Evidence before and after Hurricane Floyd. Land Econ.
**2004**, 80, 490–500. [Google Scholar] [CrossRef] - Kousky, C. Learning from Extreme Events: Risk Perceptions After the Flood. Land Econ.
**2010**, 86, 395–422. [Google Scholar] [CrossRef] - Boyle, K.; Kiel, A. A Survey of House Price Hedonic Studies of the Impact of Environmental Externalities. J. Real Estate Lit.
**2001**, 9, 117–144. [Google Scholar] - Ratcliffe, R. Valuation for Real Estate Decisions; Democrat Press: Washington, DC, USA, 1972. [Google Scholar]
- Colwell, P.F.; Cannaday, R.E.; Wu, C. The Analytical Foundations of Adjustment Grid Methods. Real Estate Econ.
**1983**, 11, 11–29. [Google Scholar] [CrossRef] - Pace, R.K.; Giley, O.W. Generalizing the OLS and Grid Estimators. Real Estate Econ.
**1998**, 26, 331–347. [Google Scholar] [CrossRef] - Des Rosiers, F.; Dubé, J.; Thériault, M. Hedonic Price Modelling: Measuring Urban Externalities in Québec. In Modelling Urban Dynamics: Mobility, Accessibility and Real Estate Value; Thériault, M., Des Rosiers, F., Eds.; ISTE-Wiley: London, UK, 2011; pp. 255–283. [Google Scholar]
- Cavailhès, J. Le prix des atttributs du logement. Écon. Stat.
**2005**, 381–382, 91–123. [Google Scholar] - Huang, Z.; Chen, R.; Xu, D.; Zhou, W. Spatial and Hedonic Analysis of Housing Prices in Shanghai. Habitat Int.
**2017**, 67, 69–78. [Google Scholar] [CrossRef] - Rodgers, T. Property-to-property Comparison. Apprais. J.
**1994**, 62, 64–67. [Google Scholar] - Sheppard, S. Hedonic Analysis of Housing Markets. In Handbook of Regional and Urban Economics; Cheshire, P.C., Mills, E.S., Eds.; Elsevier: Amsterdam, The Netherlands, 1997; Volume 3, pp. 1595–1635. [Google Scholar]
- French, N.; Gabrielli, L. The Uncertainty of Valuation. J. Prop. Investig. Financ.
**2004**, 22, 484–500. [Google Scholar] [CrossRef] - Rubin, D.B. Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies. J. Educ. Psychol.
**1974**, 66, 688–701. [Google Scholar] [CrossRef] - Rosenbaum, P.R.; Rubin, D.B. The Central Role of the Propensity Score in Observational Studies for Causal Effects. Biometrika
**1983**, 70, 41–55. [Google Scholar] [CrossRef] - Hosmer, D.W.; Lemeshow, S. A Goodness-of-fit Test for Multiple Logistic Regression Model. Commun. Stat.
**1980**, 9, 1043–1069. [Google Scholar] [CrossRef] - Heβ, S. Randomization Inference with Stata: A Guide and Software. Stata J.
**2017**, 17, 630–651. [Google Scholar] - Edgington, E.S. Randomization Tests, 2nd ed.; Marcel Dekker: New York, NY, USA, 1987. [Google Scholar]
- Onghena, P. Randomization and the Randomization Test: Two Sides of the Same Coin. In Randomization, Masking, and Allocation Concealment; Berger, V., Ed.; Chapman & Hall/CRC Press: Boca Raton, FL, USA, 2018; pp. 331–347. [Google Scholar]
- Anselin, L. Local Indicators of Spatial Association—LISA. Geogr. Anal.
**1995**, 27, 93–115. [Google Scholar] [CrossRef] - AbdelHalim, M. Estimating Flood Impact on Residential Values (Housing Price): The Case of Laval (Canada). 1995–2007. Master’s Thesis, Université Laval, Québec, QC, Canada, 2020. [Google Scholar]
- Hidano, N.; Hoshino, T.; Sugiura, A. The Effect of Seismic Hazard Risk Information and Property Prices: Evidence from a Spatial Regression Discontinuity Design. Reg. Sci. Urban Econ.
**2015**, 55, 113–122. [Google Scholar] [CrossRef]

**Figure 1.**Schematic Representation of a Spatial Matching Difference-in-Differences (SM-DID) Estimator.

**Figure 3.**Permutation Test Results. Note: Red Line → Estimation with matching; Histogram → Estimation with falsification. Each sub-figure use different number of nearest neighbours (1 to 4).

Variable Name | Source | Mean | s.d. |
---|---|---|---|

Age (in years) | GMREB | 19.833 | 16.840 |

Lot size (in m^{2}) | GMREB | 5430.186 | 2495.990 |

Garage (Yes/No) | GMREB | 0.369 | 0.484 |

Basement (Yes/No) | GMREB | 0.353 | 0.479 |

Excavated pool (Yes/No) | GMREB | 0.052 | 0.222 |

Bungalow (Yes/No) | GMREB | 0.556 | 0.498 |

Multi-storey House (Yes//No) | GMREB | 0.067 | 0.251 |

Cottage (Yes/No) | GMREB | 0.377 | 0.486 |

Semi-detached house (Yes/No) | GMREB | 0.171 | 0.377 |

Being inside 0–20 years flooding zone (Yes/No) | Données Quebec | 0.175 | 0.380 |

X coordinates (in meters-NAD83) | GMREB | 277,713 | 783.344 |

Y coordinates (in meters-NAD83) | GMREB | 5,047,705 | 671.178 |

_{T}= 252 observations; s.d. → Standard deviation.

Flood Event | |||
---|---|---|---|

Treatment | Before (D_{τ} = 0) | After (D_{τ} = 1) | Total |

Outside the zone (D_{s} = 0) | 67 | 135 | 202 |

Inside the zone (D_{s} = 1) | 19 | 31 | 50 |

Total | 86 | 166 | 252 |

**Table 3.**Descriptive Statistics for Houses Inside and Outside (

**D**

_{s}) the Flood Zone, Before and After (

**D**

_{τ}) the Treatment.

Main Statistics | |||
---|---|---|---|

Final Sale Price (in $) | N | Mean | s.d. |

All Transactions | 252 | 85,938 | |

Outside the zone (D_{s} = 0) | 202 | 88,544 | 1873 |

Before (D_{τ} = 0) | 67 | 81,825 | 2837 |

After (D_{τ} = 1) | 135 | 91,878 | 2379 |

Inside the zone (D_{s} = 1) | 50 | 75,411 | 4496 |

Before (D_{τ} = 0) | 19 | 73,021 | 7468 |

After (D_{τ} = 1) | 31 | 76,876 | 5706 |

Variables | Coefficient | Sign |
---|---|---|

Age (in years) | −0.0057 | |

Lot size (in m^{2}) | 0.0002 | |

Garage (Yes/No) | −1.1927 | ** |

Basement (Yes/No) | 0.5856 | |

Excavated pool (Yes/No) | 0.1517 | |

Bungalow (Yes/No) | Reference | |

House with many storeys (Yes//No) | −2.4311 | ** |

Cottage (Yes/No) | −1.3012 | ** |

Town house: Semi-detached house (Yes/No) | −0.3114 | |

Within a restrained flooding zone (Yes/No) | 3.5358 | *** |

X coordinates (in meters-NAD83) | −0.0046 | *** |

Y coordinates (in meters-NAD83) | 0.0044 | *** |

Constant | −20,825.51 | *** |

Pseudo-R^{2} | 0.4787 | |

χ^{2}-stat | 120.19 | *** |

Hosmer-Lemeshow stat | 6.27 |

_{T}= 252; Legend: *** p < 0.01; ** p < 0.05.

ZIS Zone | ||||
---|---|---|---|---|

# of NN | Before | After | DID | Sign |

1 | 1,373,895 | −1,756,850 | 3,130,745 | *** |

2 | 1,614,360 | −179,040 | 1,793,400 | *** |

3 | 2,236,182 | −27,450 | 2,263,632 | *** |

4 | 1,455,233 | −859,761 | 2,314,994 | *** |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dubé, J.; AbdelHalim, M.; Devaux, N.
Evaluating the Impact of Floods on Housing Price Using a Spatial Matching Difference-In-Differences (SM-DID) Approach. *Sustainability* **2021**, *13*, 804.
https://doi.org/10.3390/su13020804

**AMA Style**

Dubé J, AbdelHalim M, Devaux N.
Evaluating the Impact of Floods on Housing Price Using a Spatial Matching Difference-In-Differences (SM-DID) Approach. *Sustainability*. 2021; 13(2):804.
https://doi.org/10.3390/su13020804

**Chicago/Turabian Style**

Dubé, Jean, Maha AbdelHalim, and Nicolas Devaux.
2021. "Evaluating the Impact of Floods on Housing Price Using a Spatial Matching Difference-In-Differences (SM-DID) Approach" *Sustainability* 13, no. 2: 804.
https://doi.org/10.3390/su13020804