1# RECORD ba26780937630bfce76ea1bcc89a7777faa87ed02# TITLE: Earthquake Risk Embedded in Property Prices: Evidence From Five Japanese Cities3# YEAR: 2018.0 VENUE: Journal of the American Statistical Association DOI: 10.1080/01621459.2021.19285124# AUTHORS: Masako Ikefuji; R. Laeven; J. Magnus; Y. Yue5# PAGES: 13 CANDIDATE TABLE PAGES (1-based): [7, 9, 11]6# ABSTRACT: Abstract We analyze the impact of short-run (90 days) and long-run (30 years) earthquake risk on real estate transaction prices in five Japanese cities (Tokyo, Osaka, Nagoya, Fukuoka, and Sapporo), using quarterly data over the period 2006–2015. We exploit a rich panel dataset (331,343 observations) with property characteristics, ward attractiveness information, macroeconomic variables, and long-run seismic hazard data, supplemented with short-run earthquake probabilities generated from a seismic excitation model using historical earthquake occurrences. We design a hedonic property price model that allows for subjective probability weighting, employ a multivariate error components structure, and develop associated maximum likelihood estimation and variance computation procedures. Our approach enables us to identify the total compensation for earthquake risk embedded in property prices, to decompose this into pieces stemming from short-run and long-run risk, and to distinguish between objective and subjectively weighted (“distorted”) earthquake probabilities. We find that objective long-run earthquake probabilities have a statistically significant negative impact on property prices, whereas short-run earthquake probabilities become statistically significant only when we allow them to be distorted. The total compensation for earthquake risk amounts to an average –2.0% of log property prices, slightly more than the annual income of a middle-income Japanese household. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.789===== PAGE 1 (score 3, numeric-paren 0, table-words 0, var-words 3) =====1011Full Terms & Conditions of access and use can be found at12https://www.tandfonline.com/action/journalInformation?journalCode=uasa2013Journal of the American Statistical Association14ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/uasa2015Earthquake Risk Embedded in Property Prices:16Evidence From Five Japanese Cities17Masako Ikefuji, Roger J. A. Laeven, Jan R. Magnus & Yuan Yue18To cite this article: Masako Ikefuji, Roger J. A. Laeven, Jan R. Magnus & Yuan Yue (2021):19Earthquake Risk Embedded in Property Prices: Evidence From Five Japanese Cities, Journal of the20American Statistical Association, DOI: 10.1080/01621459.2021.192851221To link to this article: https://doi.org/10.1080/01621459.2021.192851222© 2021 The Author(s). Published with23license by Taylor & Francis Group, LLC.24View supplementary material 25Published online: 23 Jul 2021.26Submit your article to this journal 27Article views: 56628View related articles 29View Crossmark data303132===== PAGE 7 (score 29, numeric-paren 0, table-words 4, var-words 14) =====3334635M. IKEFUJI ET AL.36the Koji-Chika dataset published by the Ministry of Land,37Infrastructure, Transport, and Tourism (MLIT). The Koji-38Chika dataset provides fictional sales prices (as produced by39“experts”) and they are only available at annual intervals,40which we consider to be too long for our purpose. We use41a different dataset, which provides self-reported transaction42prices at three-months intervals. This dataset, also provided43by the MLIT, is known as the “real estate transaction-price44information;” see https://www.land.mlit.go.jp/webland_english/45servlet/MainServlet. The information in this dataset is based46on the results of a questionnaire survey of persons involved47in real estate transactions conducted by MLIT, compiled and48published quarterly. We thus know the transaction price and49the transaction date (quarter), and also in which district the50property lies and the name of the nearest station. In addition,51many property characteristics are provided, of which we shall52only consider: total area in square meters, total floor area in53square meters, distance to nearest station measured in walking54minutes, age of the building (if applicable), building structure55with varying degrees of earthquake resistance (reinforced56concrete, steel, or wood), purpose of city planning in the urban57control area, maximum building coverage ratio (BCR), and58maximum floor area ratio (FAR). Furthermore, as there were59major changes in the regulations on earthquake-resistance60building standards in 1981 and 2000, our regression design61also features built-1981–2000 and built-after-2000 dummies.62Different types may have different regressors. For example, the63equation for land only does not have “building structure” or64“building age” as a regressor; and the equation for condos does65not use “building structure” as a regressor.66Economic indicators. Property prices are affected by general67economic conditions. To incorporate possible effects of these68economic conditions, we have selected two national macroeco-69nomic indicators: GDP and CPI.70Long-run earthquake risk. We consider two measures of71earthquake risk: short-run risk (i.e., seismic excitation; see72Section 2.1) and long-run risk. Long-run earthquake risk is73defined as the probability of an earthquake exceeding certain74intensity thresholds in the next 30 years in a given area, provided75by the Japan Seismic Hazard Information Station (JSHIS). We76select the threshold intensities “5-lower” (medium risk) and77“6-lower” (high risk) in our analysis. The JSHIS probabilities78are provided in various mesh sizes, varying from one square79km to 250 square meters. For each district, we identify its80center and then define the risk of that district as the JSHIS risk81associated with the smallest available mesh in which this center82lies. Although the JSHIS exceedance probabilities are updated83every one or two years, we take the average of the JSHIS risk data84over all available years, thus obtaining a time-invariant measure85of long-run risk for each district, not influenced by short-86term deviations. Clearly, new events happening or new insights87within this time window may have impacted the modeling of88JSHIS, and lead to different predictions. However, the variation89in the long-term earthquake probabilities provided by JSHIS90is mostly modest. These probabilities are included as objective91measures of long-run earthquake risk in our regression design,92at the district level. Choosing a district of relative safety may93be viewed as a form of self-insurance. Therefore, provided94this information, which is publicly available, is known among95Table 2. Seismic hazard probabilities per city, averaged over districts and time96(2005–2014).97City98Mean99Min10025%10150%10275%103max104sd105Exceeding intensity level “5 lower”106Tokyo1071.001080.991090.991101.001111.001121.001130.00114Osaka1150.931160.901170.921180.941190.951200.971210.02122Nagoya1230.961240.911250.941260.971270.981280.981290.02130Fukuoka1310.391320.061330.301340.421350.481360.561370.12138Sapporo1390.331400.051410.211420.331430.441440.511450.12146Exceeding intensity level “6 lower”147Tokyo1480.351490.161500.221510.281520.491530.591540.13155Osaka1560.371570.221580.301590.391600.441610.521620.09163Nagoya1640.561650.211660.411670.611680.671690.771700.14171Fukuoka1720.031730.001740.021750.031760.031770.051780.01179Sapporo1800.011810.001820.011830.011840.021850.031860.01187consumers, we would expect higher property prices in relatively188safe areas all else being equal.189If the intensity is “5 lower,” then according to the Japan190Meteorological Agency, many people will be frightened and feel191the need to hold on to something. Hanging objects (such as192lamps) will swing violently, books may fall from bookshelves,193and unstable furniture may topple over. Windows may break,194electricity poles may move, and roads may sustain damage.195There may be cracks in the walls of wooden properties. If the196intensity is “6 lower,” then the effects will be more severe. It will197be difficult to remain standing, unsecured furniture will move198and topple over, and cracks in walls, crossbeams, and pillars will199appear not only in wooden properties but also in properties built200from reinforced concrete.201Summary statistics are shown in Table 2. It is clear from202Table 2 that Tokyo, Nagoya, and Osaka are high-risk cities203with respect to “small” earthquakes. In fact, it is almost certain204that an earthquake will occur in Tokyo with an intensity more205severe than “5 lower” within the next 30 years. Regarding the206occurrence of “severe” earthquakes (“6 lower”), Nagoya is more207exposed than Tokyo and Osaka, and much more exposed than208Fukuoka and Sapporo. The variation in probabilities of severe209earthquakes in Tokyo, Osaka, and Nagoya is also much larger210than in the other two cities. Fukuoka and Sapporo are not211likely to have severe earthquakes, but there is still considerable212probability (and variation) of smaller earthquakes. This suggests213that it is important to use both thresholds, 5-lower and 6-lower,214in characterizing the distribution of long-run earthquake risk215for our purpose. This also guarantees sufficient variation of216long-run probabilities in the hedonic price model discussed in217Section 4.2184. The Model219The dependent variable is log-property price, and we denote the220hth observation of type k in district i during quarter t as y(h,k)221it222.223The most common method of modeling the property market224is hedonic pricing, pioneered by Rosen (1974) who argued that225an item’s total price can be thought of as the sum of the price226of each of its homogeneous characteristics, so that the effect of227each characteristic on the price can be determined by regressing228(log)price on these characteristics. We shall follow the hedonic229approach. In our case, the (log)price is determined by charac-230teristics of the property itself (size, age, etc.), the surrounding231232233===== PAGE 8 (score 8, numeric-paren 0, table-words 3, var-words 2) =====234235JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION2367237environment (location, crime rate, schools, etc.), earthquake238risk factors, and macroeconomic influences.239The district i determines the city c(i), which takes values2401, . . . , 5 depending on the city in which district i is situated.241Also, the time variable t determines in which quarter q(t) the242transaction took place, taking values 1, . . . , 4 depending on243whether t refers to the first, second, third, or fourth quarter.244The number of observations varies per district, type and quarter,245and this affects the precision. We let H(k)246it247denote the number248of observations on each type k = 1, 2, 3 in district i during249quarter t. We model the difference between cities by a shift αc(i)250in the intercept term, but we assume that all other parameters251are the same between cities. The difference between cities is thus252completely captured by αc(i).253Our model can now be written as254y(h,k)255it256= α(k)2570258+ αc(i) + γq(t) + x(k)259i·260′β1 + x(k)261·t262′β2263+x(h,k)264it265′β3 + rit(ψ)′β4 + u(h,k)266it267,268(3)269where xi· denotes a variable that is constant over time, but varies270over districts (attractiveness variables), x·t denotes a variable271that is constant over districts, but varies over time (economic272indicators), xit denotes a variable that varies over districts and273over time (property characteristics), and rit denotes the risk data274(same for each type k) given by the (distorted) short- and long-275run earthquake probabilities. The reference dummies are the276city dummy for Tokyo and the quarter dummy for Q4; these are277set to zero.278The property price is log-linear in the (distorted) short-279run and long-run earthquake probabilities, instead of in280the logarithm of these earthquake probabilities. This is due281to two main reasons: statistical performance and economic282motivation. Indeed, in our analysis, the model specification283without a log-transformation of earthquake probabilities turns284out to statistically significantly outperform a specification with285log-transformed probabilities. Economically, a specification286with log-prices and probabilities (the latter without log-287transformation) occurs naturally in a simple (rank-dependent)288expected utility model (Von Neumann and Morgenstern 1944;289Quiggin 1982) with the canonical log-utility function. This290utility function is a special case of interest in the constant relative291risk aversion family of utility functions, by far the most widely292applied family of utility functions in economics and decision293sciences (Wakker 2008). Indeed, the certainty equivalent loss,294that is, the compensation for risk, in this canonical risk model295is log-linear in (distorted) probabilities.296Although the model appears to be linear in the parameters297this is not completely the case, because the risk variable rit is298a nonlinear function of one or more ψ’s which appear in the299probability weighting function w(p) discussed in Section 2. This300complicates the estimation, and we shall discuss this issue in the301next section. To obtain a (balanced) panel we average over h, and302obtain303¯y(k)304it305= α(k)3060307+ αc(i) + γq(t) + x(k)308i·309′β1 + x(k)310·t311′β2312+¯x(k)313it314′β3 + rit(ψ)′β4 + ¯u(k)315it ,316(4)317where we average over H(k)318it319items, which thus depends on how320many properties of type k there are in a given district. Next, we321combine the three types of property into one 3 × 1 vector:322¯yit = α0+(αc(i)+γq(t)) ı+X∗323i·β1+X∗324·tβ2+X∗325itβ3+ırit(ψ)′β4+¯uit,326(5)327where ı = (1, 1, 1)′, which we write more succinctly as328¯yit = ¯Xitβ + ¯uit329(i = 1, . . . , N; t = 1, . . . , T),330(6)331where ¯yit is a p × 1 vector of random observations, explained by332regressors ¯Xit = ¯Xit(ψ), an unknown parameter vector β, and333random errors ¯uit (p × 1). In our case p = 3.3345. Estimation Method335We wish to estimate the parameters and their precisions of336the model thus described. This is essentially, apart from the337nonlinearity caused by ψ, a linear mixed model with a large338variance matrix. Such models arise in many contexts (genomics:339Lippert et al. 2011; Heckerman et al. 2016; spatial statistics:340Dutta and Mondal 2015, 2016), and various estimation pro-341cedures have been developed; see also Demidenko (2013). In342our setup, we will employ a (multivariate) error components343structure, since this has a natural interpretation in our context.344For our purpose, we need not only the estimate of ψ, which345could conceivably be obtained via profile-likelihood, but also346its (asymptotic) estimated variance. This means that we need347a comprehensive approach to our estimation problem, which348provides all estimated variances jointly, as follows.3349The errors are assumed to follow a p-variate three-error350components structure,351¯uit = ζi + ηt + ϵit,352(7)353a sum of three independent components each of which is iid354with zero means and variances355var(ζi) = 356ζ,357var(ηt) = 358η,359and360var(ϵit) = 361ϵ,362(8)363where 364ζ and 365η are positive semidefinite, and 366ϵ is positive367definite, all of order p × p. Multivariate two-error components368were first employed by Chamberlain and Griliches (1975) using369maximum likelihood techniques. Multivariate three-error com-370ponents were first considered by Avery (1977) who derived371a feasible Aitken estimator, which is however not maximum372likelihood and turns out to be asymptotically inefficient. Balt-373agi (1980) derived an alternative estimator, also not maximum374likelihood, which is asymptotically efficient. Magnus (1982)375discussed the estimation and testing of the multivariate two-376and three-error components models in a maximum likelihood377context.378Our error structure implies that379E(¯uit ¯u′380js) =381⎧382⎪⎪⎪⎨383⎪⎪⎪⎩384385ζ + 386η + 387ϵ388if i = j and t = s,389390ζ391if i = j and t ̸= s,392393η394if i ̸= j and t = s,3950396if i ̸= j and t ̸= s.397(9)3983The multivariate error components regression R package mvecr that we399have developed for this article is available from the article’s github page.400401402===== PAGE 9 (score 31, numeric-paren 0, table-words 6, var-words 10) =====4034048405M. IKEFUJI ET AL.406Let407Y =408⎛409⎜⎜⎜⎝410¯y11 ¯y12 . . . ¯y1T411¯y21 ¯y22 . . . ¯y2T412...413...414...415¯yN1 ¯yN2 . . . ¯yNT416⎞417⎟⎟⎟⎠,418U =419⎛420⎜⎜⎜⎝421¯u11 ¯u12 . . . ¯u1T422¯u21 ¯u22 . . . ¯u2T423...424...425...426¯uN1 ¯uN2 . . . ¯uNT427⎞428⎟⎟⎟⎠,429(10)430and431¯X(t) =432⎛433⎜⎜⎜⎝434¯X1t435¯X2t436...437¯XNt438⎞439⎟⎟⎟⎠,440X =441⎛442⎜⎜⎜⎝443¯X(1)444¯X(2)445...446¯X(T)447⎞448⎟⎟⎟⎠.449(11)450Then, we can write Equation (6) in stacked form as451y = Xβ + u,452(12)453where y = vecY and u = vecU. We shall assume that y is454normally distributed with mean μ = Xβ and variance (θ) =455var(u), so that β refers to the mean parameters and θ to the456variance parameters.457Maximum likelihood estimation for the model in Equation458(12), via optimization of the corresponding loglikelihood under459normality, and associated variance computation pose several460nontrivial challenges. One complication lies in the fact that461the nonrandom matrix X depends on a parameter (vector) as462well, so that X = X(ψ). Another complication is the high463dimensionality of the variance matrix = (θ). Appendix A464(supplementary material) provides our detailed treatment of465how to overcome these and related challenges.466Although the variance matrix = var(u) is of a very large467dimension, the error components structure allows us to write it468in a convenient form, allowing simple expressions for its inverse469and determinant, and also for quadratic forms like v′ −1v and470X′ −1X. The relevant formulas are provided in Appendix A471(supplementary material).472In a nutshell, estimation of the parameters then proceeds as473follows. For given ψ, we maximize the concentrated likelihood474with respect to the variance parameters θ, where using the475explicit expression for the gradient will speed up the optimiza-476tion. Performing a grid search on ψ we obtain the maximum477likelihood estimates ˆθ and ˆψ. Next, we find ˆβ and finally the esti-478mated variances of ˆβ and ˆψ; see the development in Appendix A479(supplementary material), in particular (A.7)–(A.12).4806. Estimation Results481Our primary interest is in earthquake risk and its impact on482property prices. More specifically, we wish to answer three ques-483tions: (i) do objective long-run earthquake probabilities have an484effect on property prices, (ii) do objective short-run earthquake485probabilities have an effect on property prices, in addition to the486effect of long-run probabilities, and (iii) do potentially distorted487short-run earthquake probabilities have an effect on property488prices, in addition to the effect of long-run probabilities?489Table 3. Estimation results under various risk assumptions.490Variable491LR492LR and493Base494only495objective SR496model497Intercepts498Land & building4993.75925004.55935014.3812502Land only5033.59495044.39405054.2155506Condo5073.10255083.90245093.7244510City Dummies511Osaka512−0.2273513−0.2625514−0.2615515Nagoya516−0.3801517−0.4100518−0.4139519Fukuoka520−0.8770521−0.9133522−0.9108523Sapporo524−1.2050525−1.2458526−1.2388527Ward528Immigrants5296.72455306.72245316.7218532Attractiveness533Crime534−0.0437535−0.0436536−0.0436537Unemployment538−4.3360539−4.3395540−4.3399541Executives5423.34265433.34475443.3464545Economic546log(GDP)5470.56065480.52205490.5229550indicators551log(CPI)5521.53475531.46875541.5030555Property556Area (m2)5570.00255580.00255590.0025560Characteristics561Floor area (m2)5620.00065630.00065640.0006565Distance to nearest station566−0.0145567−0.0145568−0.0145569Age570−0.0121571−0.0121572−0.0121573Built 1981–20005740.16745750.16585760.1652577Built after 20005780.41365790.41265800.4123581Structure: reinf. concrete5820.43485830.43445840.4343585Structure: steel5860.18675870.18675880.1867589Structure: wood590−0.1264591−0.1266592−0.1266593Urban control594−0.8972595−0.8967596−0.8967597max BCR598−0.0019599−0.0019600−0.0019601max FAR6020.00046030.00046040.0004605Risk606Long run 45–55607−0.1433608−0.1427609−0.1427610Long run 55+611−0.5037612−0.5039613−0.5041614Short run615–616−0.0915‡617−0.0514618ˆψ619–620–6213.74†622
log L623−68.5624−15.8625–626Before we answer these questions and comment on our esti-627mates in Table 3, we explain our econometric modeling strategy.628This strategy is based on two ingredients. First, we aim for par-629simony. We want the smallest model that captures the essence630of our story. This means that sometimes regressors have been631deleted from our model even when the associated parameters632are “significant.” Significance does not imply importance, and633importance is what interests us. Second, we make a distinction634between focus and auxiliary regressors. The focus regressors are635the effects that we are interested in or are part of the minimum636set that would make up a credible model, while the auxiliary637regressors are only in the model because they improve the638estimation of the focus parameters.639Since we have many observations, most estimates are likely to640be significant at the usual 1.96 level. We provide more informa-641tion about the results by strengthening the significance require-642ment on the t-values. Thus, a ‡ will indicate that |t| ≤1.96,643which we interpret as not significant, while † indicates signifi-644cance with 1.96 < |t| ≤4.00. Estimates without superscript are645therefore significant with |t| > 4.00. The choice of 4.00 is some-646what arbitrary and chosen a posteriori in order to provide more647information about the precision of our estimates, in particular648our parameter estimates pertaining to the risk variables. (All649t-values test the null hypothesis that the parameter of interest650equals zero, except the t-value of ˆψ which tests the null that651ψ = 1.)652Ideally, one would like to combine the concepts of model653selection and estimation into one procedure. This is called654655656===== PAGE 10 (score 32, numeric-paren 0, table-words 10, var-words 11) =====657658JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION6599660“model averaging.” Also, one would like to combine the concepts661of significance and importance into one procedure, and the662so-called “fence method” provides the required flexibility by663allowing the criterion of optimality for the selection within664the fence to incorporate scientific, economical, political, and665even legal concerns, in addition to statistical ones (Jiang et al.6662008; Jiang and Nguyen 2015). Both issues are, however, not667fully developed yet and their application is beyond us in this668nonstandard regression model.669Now consider the first question. The results are presented in670Table 3 under the heading “LR only” and we see that all estimates671are significant (i.e., appear without superscript), that is, their t-672value (in absolute terms) exceeds 4.00. Regarding the long-run673risk effects, we remark that long run 45–55 (medium risk) indi-674cates the JSHIS probability that an earthquake occurs in the next67530 years of higher intensity than 5-lower and lower intensity676than 6-lower; and that long run 55+ (high risk) indicates the677JSHIS probability that in the next 30 years an earthquake occurs678of intensity 6-lower or higher. Both medium risk and high risk679appear to have a significant negative impact on property prices.680The higher risk level has a more severe impact, which is intu-681itively reasonable. Hence, long-run risk matters. This answers682the first question.683Next, we consider the second question: given that long-run684risk plays a role, do objective short-run probabilities also have685an effect on property prices? The results are presented in the686next column of Table 3 under the heading “LR and objective SR”.687Apparently they do not: the effect of the risk variable short run,688while negative as we would expect, is not significantly different689from zero.690Finally, we consider the third question: given that long-run691risk plays a role, do potentially distorted short-run probabil-692ities also have an effect on property prices? The results are693displayed in the final column of Table 3 under the heading “Base694model”. Apparently they do: after distortion, short-run probabil-695ities have a significant negative effect on property prices.696The difference between objective and distorted short-run697risk is that short-run probabilities are now allowed to be698distorted using a probability weighting function, in this case699the one-parameter weighting function (2) proposed by Prelec700(1998), which yields the highest likelihood. The parameter ψ in701the Prelec function is estimated to be 3.74 and is significantly702different from unity, since the absolute value of its t-value lies703between 1.96 and 4.00; in fact |t| = 2.91.704As shown in Figure 3, the estimated probability weighting705function has an S-shaped pattern where small probabilities are706underweighted and large probabilities are overweighted, which707is in contrast to the inverse S-shaped probability weighting708function often found in experiments. This contrast may be709explained by the fact that with a positive background intensity710of earthquakes, temporary deviations of short-run earthquake711probabilities caused by seismic excitation are not evaluated (and712overweighted) with respect to a reference probability of zero713but with respect to a positive reference probability level. This714applies in particular to Tokyo where the 90-day probability of715an earthquake exceeding the magnitude threshold of 5.5 never716drops below 35% in the period that we analyze.717In summary: long-run risk matters, objective short-run risk718does not, but distorted short-run risk does. In addition, all719Figure 3. Estimated probability weighting of short-run probabilities, Prelec proba-720bility weighting function, ˆψ = 3.74.721nonrisk parameter estimates in the second and third columns722are similar to the ones in the first column and all are significant723(with a t-value larger than 4.00 in absolute value).724We briefly comment on these other (nonrisk) parameters in725the base model:726Intercept and city dummies. Tokyo, of course, is the most727expensive city to buy property. If we set the property price level728of Tokyo at 1.00, then the average property price levels of the729other cities are 0.77 in Osaka, 0.66 in Nagoya, 0.40 in Fukuoka,730and 0.29 in Sapporo. (Recall that we do not regress price but731log-price on these dummies.) Also, if we set the price of land732and building at 1.00, then the average price of the other types of733property are 0.85 for land only and 0.52 for condos.734Ward attractiveness. As discussed in Section 3, we selected 11735characteristics for each ward, divided into 6 categories. Only736four of these 11 characteristics appear in our base model:737percentage of immigrants (representing population); number738of criminal offenses (representing safety); and unemployment739ratio and percentage of executives (representing employment).740Executives make a ward more attractive, while crime and741unemployment make it less attractive. Immigrants too make742a ward more attractive, which makes sense if we realize that743the word “immigrant” refers to somebody moving into the744ward from another municipality, usually within Japan. Hence,745the more people move in from other areas in Japan, the more746attractive the ward apparently is.747Economic indicators. Property prices are affected by general748economic conditions, and two indicators appear in Table 3 and749in our base model: log(GDP) and log(CPI), both of which have a750positive effect on property prices. The inclusion of log(CPI) has751the additional advantage that if we wish to explain real (rather752than nominal) property prices, then all results remain the same753except that the effect of log(CPI) is now 0.503 rather than 1.503.754Hence, CPI has a positive effect not only on nominal but also755on real property prices.756Property characteristics. A large (floor) area and proximity757to the nearest station contribute positively to the price. New758759760===== PAGE 11 (score 17, numeric-paren 0, table-words 3, var-words 8) =====76176210763M. IKEFUJI ET AL.764buildings are preferred to old ones, where we have included two765dummies because major changes occurred in the regulations on766earthquake-resistance standards in both 1981 and 2000. As a767result, buyers prefer a house built between 1981 and 2000 over768a house built before 1981, and they like a house built after 2000769even better. Regarding the structure, wood is not desirable, steel770is desirable, but reinforced concrete is preferred. Urban control771signifies restrictions on development possibilities, and this has772a negative effect on prices.773For all three property types, the designated maximum BCR774and the maximum FAR are provided. These ratios are legally775allowed maxima, different for each piece of land. The BCR is776the percentage of the building area to the site area; the FAR is777the percentage of the total floor area to the site area. We use778both ratios in our regression and find a negative effect of BCR779and a positive effect of FAR. Shimizu and Nishimura (2006)780and Nakagawa, Saito, and Yamaga (2009) used only FAR and781found mixed effects and a positive effect, respectively. Hidano,782Hoshino, and Sugiura (2015) used both ratios (as we do) and783found a negative effect of BCR and a mixed effect of FAR.784Quarterly effects. Estate agents sometimes tell customers that785some months are better to buy or sell than others. Our results786(in quarters, not months) are ambiguous, which is why we787have omitted the quarter dummies from our regression. We788return to this issue in our sensitivity analysis, see Appendix B789(supplementary material).790Error components. We estimated the coefficients using the mul-791tivariate three-error components structure, as described in Sec-792tion 5. It turns out that793tr(794ϵ) = 0.406 > tr(795ζ) = 0.129 ≫tr(796η) = 0.002,797and as a result we set 798η = 0, so that we end up with a two-error799components structure. The effect of this is negligible and will800be discussed further in our sensitivity analysis in Appendix B801(supplementary material).802Appendix C (supplementary material) provides a detailed803analysis of the corresponding impact of each of the explanatory804variables component on the (log) property prices, and the805premia for earthquake risk embedded in property prices. We806find in particular that the joint impact of long-run and distorted807short-run earthquake risk amounts to an average −2.0% of808log property prices, which translates in monetary terms into809a marginal effect of around −7 million Japanese yen per810property—slightly more than the average annual income of a811middle-income Japanese household in the period 2006/Q2 to8122015/Q3 we analyze. The impacts of long-run and distorted813short-run earthquake risk are nearly the same for all property814types but differ substantially among cities. Furthermore, the815earthquake risk variables stand almost on equal footing with816ward characteristics in explaining dispersion in property prices.8177. An Extension818In our base model, we use objective long-run probabilities and819distorted short-run probabilities based on the Prelec probability820weighting function. This raises various questions. First, one821could argue that we should allow long-run probabilities to be822distorted too; and second, we could experiment with different823probability weighting functions.824In Table 4, we experiment with an alternative functional825form for the short-run risk variable, namely the weighting func-826tion (1) introduced by Tversky and Kahneman (1992). In par-827ticular, in column 2 (Dist. SR, TK) we replace the Prelec func-828tion applied to the short-run earthquake probabilities with the829Tversky-Kahneman probability weighting function. The estima-830tion results are similar to the base model, but somewhat less pre-831cise, and the loglikelihood decreases. The Tversky-Kahneman832probability weighting function is found to be S-shaped, just like833the Prelec function, confirming the robustness of this finding.834Next, we also allow long-run risk to be distorted using both835the Prelec and the Tversky-Kahneman weighting functions. The836model contains two related time-invariant long-run probabili-837ties and we quite naturally assume that these two probabilities838share the same weighting function with the same parameter γ .839(In particular, distorted long run 45–55 is computed as distorted840long run 45+ minus distorted long run 55+, consistent with841Choquet integration.) In columns 3 and 4 of Table 4 we allow842both long-run risk and short-run risk to be distorted.843The model with the higher likelihood is the one with an844inverse S-shaped Tversky-Kahneman weighting function for845Table 4. Sensitivity and extension—probability weighting functions.846Base847Dist. SR848Dist. LR849Dist. LR850TK851Prelec852TK853Area (m2)8540.00258550.00258560.00258570.0025858Floor area (m2)8590.00068600.00068610.00068620.0006863Distance to nearest station864−0.0145865−0.0145866−0.0143867−0.0143868Age869−0.0121870−0.0121871−0.0121872−0.0121873Long run 45–55874−0.1427875−0.1427876−0.8644877−0.4856878Long run 55+879−0.5041880−0.5039881−1.3838882−1.5028883Short run884−0.0514885−0.0733‡886−0.0517887−0.0518888ˆψ8893.74†8901.40‡8913.78†8923.77†893ˆγ894–895–8960.178970.32898
log L899–900−14.6901152.8902167.6903Figure 4. Implied probability weighting functions of long-run and short-run earth-904quake risk.905906907===== PAGE 12 (score 9, numeric-paren 0, table-words 0, var-words 9) =====908909JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION91011911long-run risk and an S-shaped Prelec weighting function for912short-run risk, as shown in Figure 4. We note that the Prelec913function for long-run risk, although yielding a lower loglikeli-914hood than the Tversky-Kahneman weighting function, is also915found to be inverse S-shaped, which is again reassuring for916the robustness of our results. Thus, in an extension of our917base model that allows for distortion of time-invariant long-918run earthquake probabilities we find evidence of a conven-919tional inverse S-shaped probability weighting function for long-920run earthquake probabilities. This means that when purchasing921property in Japan, people tend to overweight small long-run922probabilities and underweight large long-run probabilities.9238. Conclusion924We have studied the impact of earthquake risk on Japanese925property prices using a rich panel dataset. We have not only926allowed for time-invariant long-run earthquake probabilities to927impact property prices, but we have also analyzed the impact928of short-run earthquake probabilities generated from a seismic929excitation model. We have designed a hedonic property prices930model that accommodates probability weighting, employing a931multivariate error components structure, and have developed932the associated maximum likelihood and variance computation933procedures. We have shown that long-run earthquake proba-934bilities negatively impact property prices and increasingly so at935higher risk levels. We have also shown that short-run earthquake936probabilities have a negative impact on property prices, and that937this effect becomes statistically significant only after we allow for938probability weighting.939The probability weighting function associated with short-940run earthquake probabilities is found to be S-shaped. That941stands in contrast to the familiar inverse S-shaped probability942weighting functions predominantly found in experiments. The943shape we find may be explained by the fact that in our setting944there is a nonnegligible positive background arrival rate of945earthquakes. People may therefore tend to evaluate earthquake946probabilities, and overweight their temporary deviations under947seismic excitation, not with respect to zero but with respect948to a positive reference probability level. This remarkable find-949ing calls for the development of reference-dependent models950for probabilities to augment the large literature on reference-951dependent models for changes in wealth levels.952Our objective short-run earthquake probabilities are based953on a purely temporal ETAS model. Within the spatial windows954used for estimation of the ETAS model, it is assumed that955the earthquake intensity functions, and people’s perception of956seismic risk, are homogeneous (see also our Data Documenta-957tion). A refinement that accounts for spatial variation would be958desirable, but is subject to statistical and computational compli-959cations. Addressing the potential limitations inherent in using960a purely temporal ETAS model in this context is an interesting961and challenging problem for future research.962Acknowledgments963We are very grateful to the editor, associate editor and three referees for964thoughtful comments and suggestions that have significantly improved the965article. Earlier versions of this article were presented at Keio University966in Tokyo, the Technische Universität Wien, the Universities of Oxford,967Madrid and Fudan, and at the 2018 Econometric Society Australasian968Meeting in Auckland and the 2018 China Meeting of the Econometric969Society in Shanghai. We thank the participants and in particular Yoshitsugu970Kanemoto for helpful comments.971Funding972This research was supported in part by the Japan Society for the Promotion973of Science (JSPS) under grant 16K03565 (Ikefuji) and the Netherlands974Organization for Scientific Research (NWO) under grant VIDI (Laeven).975Supplementary Material976This article comes with three supplementary files. First, the Appendix977which contains various technical results, a discussion of the robustness of978our estimation results, an analysis of the influence of each component to979the total property prices and the implied premia for earthquake risk, a brief980literature review, and an auxiliary figure. Second, the Data Documentation,981which contains a detailed description of the data, and is available from982https://bit.ly/3qHcTQ3. And third, the cleaned and compiled datasets and983all codes to implement the procedures developed in this article, including984our multivariate error components regression R package mvecr, available985from https://github.com/yy112/earthquake-risk.986References987Abdellaoui, M. (2000), “Parameter-Free Elicitation of Utility and Probabil-988ity Weighting Functions,” Management Science, 46, 1497–1512. [4]989Aït-Sahalia, Y., Laeven, R. J. A., and Pelizzon, L. (2014), “Mutual Excitation990in Eurozone Sovereign CDS,” Journal of Econometrics, 183, 151–167. [2]991Aït-Sahalia, Y., Cacho-Diaz, J. A., and Laeven, R. J. A. (2015), “Modeling992Financial Contagion Using Mutually Exciting Jump Processes,” Journal993of Financial Economics, 117, 585–606. [2]994Avery, R. B. (1977), “Error Components and Seemingly Unrelated Regres-995sions,” Econometrica, 45, 199–209. [7]996Baltagi, B. H. (1980), “On Seemingly Unrelated Regressions with Error997Components,” Econometrica, 48, 1547–1551. [2,7]998Baltagi, B. H. (2008), Econometric Analysis of Panel Data, New York: Wiley.999[2]1000Beron, K. J., Murdoch, J. C., Thayer, M. A., and Vijverberg, W. P. M. (1997),1001“An Analysis of the Housing Market Before and After the 1989 Loma1002Prieta Earthquake,” Land Economics, 73, 101–113. [2]1003Bin, O., and Landry, C. E. (2013), “Changes in Implicit Flood Risk Premi-1004ums: Empirical Evidence From the Housing Market,” Journal of Environ-1005mental Economics and Management, 65, 361–376. [2]1006Bin, O., and Polasky, S. (2004), “Effects of Flood Hazards on Property1007Values: Evidence Before and After Hurricane Floyd,” Land Economics,100880, 490–500. [2]1009Boswijk, H. P., Laeven, R. J. A., and Lalu, A. (2016), “Asset Returns with1010Self-Exciting Jumps: Option Pricing and Estimation with a Continuum1011of Moments,” Mimeo, University of Amsterdam. [2]1012Brookshire, D. S., Thayer, M. A., Tschirhart, J., and Schulze, W. D. (1985),1013“A Test of the Expected Utility Model: Evidence From Earthquake Risks,”1014Journal of Political Economy, 93, 369–389. [2]1015Chamberlain, G., and Griliches, Z. (1975), “Unobservables with a Variance-1016Components Structure: Ability, Schooling, and the Economic Success of1017Brothers,” International Economic Review, 16, 422–449. [7]1018Daniel, V. E., Florax, R. J. G. M., and Rietveld, P. (2009), “Flooding Risk and1019Housing Values: An Economic Assessment of Environmental Hazard,”1020Ecological Economics, 69, 355–365. [2]1021Demidenko, E. (2013), Mixed Models: Theory and Application with R (2nd1022ed.), New York: Wiley. [7]1023Dutta, S., and Mondal, D. (2015), “An h-Likelihood Method for Spatial1024Mixed Linear Models Based on Intrinsic Auto-Regressions,” Journal of1025the Royal Statistical Society, Series B, 77, 699–726. [7]1026