1# RECORD a90efa2e2b4a4c7fde54cbffdb07fb2a1d2e8ed72# TITLE: Examining the vintage effect in hedonic pricing using spatially varying coefficients models: a case study of single-family houses in the Canton of Zurich3# YEAR: 2022.0 VENUE: Swiss Journal of Economics and Statistics DOI: 10.1186/s41937-021-00080-24# AUTHORS: Jakob A. Dambon; Stefan S. Fahrländer; Saira Karlen; M. Lehner; Jaron Schlesinger; Fabio Sigrist; Anna Zimmermann5# PAGES: 14 CANDIDATE TABLE PAGES (1-based): [8]6# ABSTRACT: This article examines the spatially varying effect of age on single-family house (SFH) prices. Age has been shown to be a key driver for house depreciation and is usually associated with a negative price effect. In practice, however, there exist deviations from this behavior which are referred to as vintage effects. We estimate a spatially varying coefficients (SVC) model to investigate the spatial structures of vintage effects on SFH pricing. For SFHs in the Canton of Zurich, Switzerland, we find substantial spatial variation in the age effect. In particular, we find a local, strong vintage effect primarily in urban areas compared to pure depreciative age effects in rural locations. Using cross validation, we assess the potential improvement in predictive performance by incorporating spatially varying vintage effects in hedonic models. We find a substantial improvement in out-of-sample predictive performance of SVC models over classical spatial hedonic models.789===== PAGE 1 (score 12, numeric-paren 0, table-words 0, var-words 12) =====1011Dambon et al. 12Swiss Journal of Economics and Statistics (2022) 158:2 13https://doi.org/10.1186/s41937-021-00080-214ORIGINAL ARTICLE15Examining the vintage effect in hedonic 16pricing using spatially varying coefficients 17models: a case study of single‑family houses 18in the Canton of Zurich19Jakob A. Dambon1,2* , Stefan S. Fahrländer3, Saira Karlen3, Manuel Lehner3, Jaron Schlesinger3, 20Fabio Sigrist2 and Anna Zimmermann3 21Abstract 22This article examines the spatially varying effect of age on single-family house (SFH) prices. Age has been shown to be 23a key driver for house depreciation and is usually associated with a negative price effect. In practice, however, there 24exist deviations from this behavior which are referred to as vintage effects. We estimate a spatially varying coefficients 25(SVC) model to investigate the spatial structures of vintage effects on SFH pricing. For SFHs in the Canton of Zurich, 26Switzerland, we find substantial spatial variation in the age effect. In particular, we find a local, strong vintage effect 27primarily in urban areas compared to pure depreciative age effects in rural locations. Using cross validation, we assess 28the potential improvement in predictive performance by incorporating spatially varying vintage effects in hedonic 29models. We find a substantial improvement in out-of-sample predictive performance of SVC models over classical 30spatial hedonic models.31Keywords: Gaussian process, Spatial statistics, Real estate, Mass appraisal32JEL Classification: C31, C53, R31, R3233© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which 34permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the 35original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or 36other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line 37to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory 38regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this 39licence, visit http://creativecommons.org/licenses/by/4.0/.401 Introduction41Hedonic real estate models contain several predictor 42variables, and age is a key explanatory variable. The mar-43ginal effect of the building age on house prices has been 44well-studied. It has been found that the age effect is non-45linear (Clapp & Giaccotto, 1998; Goodman & Thibodeau, 461995). In particular, Case et al. (2004) report a “plausible 47quadratic form” for the building age. This behavior is a 48result of two main features of the age as an independ-49ent variable: (1) In general, older buildings depreciate 50due to deterioration; (2) “however, beyond some point, 51only those houses with the best locations and the highest 52construction quality survive.” (Case et al., 2004, p. 171). 53The quadratic appearance of the age effect has also been 54observed by Fahrländer (2006) and linked to the build-55ing material and architectural style. Studies investigat-56ing this particular type of behavior, i.e., a deviation from 57a pure depreciative effect once a particular age has been 58reached, are referencing to it as a vintage effect (Clapp & 59Giaccotto, 1998; Goodman & Thibodeau, 1995; Rubin, 601993).61Over the last two decades, there emerged a special 62focus on location specific effects due to newly avail-63able modeling methodologies. There are numerous 64publications which show a clear indication of spatially 65varying covariate effects within hedonic pricing mod-66els. For instance, when applying additive mixed regres-67sion models on rents in Vienna (Austria), Brunauer et al. 68Open Access69Swiss Journal of 70Economics and Statistics71*Correspondence: jakob.dambon@gmail.com721 Department of Mathematics, University of Zurich, Winterthurerstrasse 73190, 8057 Zurich, Switzerland74Full list of author information is available at the end of the article757677===== PAGE 8 (score 44, numeric-paren 22, table-words 5, var-words 8) =====7879Page 8 of 1480Dambon et al. Swiss Journal of Economics and Statistics (2022) 158:2 81Again, this ensures a well-behaved numeric optimiza-82tion while remaining interpretable as the ranges ρj now 83act as a scaling factor on the kilometer distances.844 Results854.1 Parameter estimates86We first look at the ML estimates ˆωMLE , which are given 87in Table 3. Here, we find that the mean estimates match 88our expectations. In particular, the vintage-related covar-89iates, i.e., Z.age and Z.age2 , show the following:901. The mean effect for Z.age is negative, as one would 91expect, and statistically significant at the 0.1% level. 92This can be interpreted in the sense that on average 93the value of a single-family home typically decreases 94with age.952. The quadratic effect for Z.age2 shows a relatively 96small, positive mean effect, which is statistically sig-97nificant at the 10% level. A larger quadratic mean age 98effect would correspond to an emphasized vintage 99effect.100All other mean effects have plausible signs, too. 101Namely, all other coefficients of continuous covariates 102are positive and statistically significant at reference levels. 103As for the categorical covariates, we observe some tem-104poral price volatility for the transaction year and quarter, 105a premium for stand-alone, detached SFHs compared to 106other SFHs for the type of SFH and a premium for houses 107with enhanced energy efficiency for the energy standard.108The estimates for ranges of the Gaussian processes 109show that the range for the intercept and Z.age are con-110siderably larger than the one for Z.age2 . This will be 111expressed in larger spatial structures for the SVCs mod-112eling the intercept and the linear age effect compared 113to the SVC modeling the quadratic age effect. The small 114range of Z.age2 on the other hand indicates that the SVCs 115corresponding to the quadratic age effect will behave 116much more selective in their deviations from the mean. 117Finally, we analyze the estimated variances of the spatially 118varying coefficients. The intercept’s variance is the largest 119and highly statistically significant. As for the linear and 120quadratic age effects, the range of the coefficients’ values 121is smaller, see Table 3 and Fig. 5.1224.2 Visualization and interpretation of SVCs123In Fig. 5 we visualize fitted and predicted SVCs. Specifi-124cally, the figure shows the estimated SVCs for the obser-125vation locations the model has been trained on as well 126as for the spatial predictions for all other cell’s centroid 127where we did not have any observations. The quality of 128these coincides with the previous parameter estimates’ 129interpretations from Sect. 4.1 and real estate experts’ 130knowledge.131Table 3 Mean and covariance estimates ˆωMLE of the SVC model (5)132The corresponding estimates’ standard errors are given in parenthesis. In most cases, the standard errors can be approximated and computed by the Hessian from the 133numeric optimization. For the mean and the variance estimates, we use a two-sided Z- and a Wald-test to test whether ˆµj = 0 and ˆσ 2134j > 0 , respectively. This is only 135possible if the standard error is available.136Significance levels: ‘.’ p < 0.1; ‘*’ p < 0.05; ‘**’ p < 0.01; ‘***’ p < 0.001; ‘n.s.’ not statistically significant, ‘n.a.’ not available137Covariates138Mean ˆµj139Sign. level140Range ˆρj141Variance ˆσ 2142j and ˆτ 2143Sign. level144Intercept1459.1555 (0.1571)146***14713.5511 (4.1157)1480.0413 (0.0116)149***150Z.age151− 0.1495 (0.0254)152***15318.9370 (41.6414)1540.0009 (n.a.)155n.a156Z.age21570.0114 (0.0062)158 .1591.7153 (0.8673)1600.0003 (0.0003)161n.s162log (volume)1630.5132 (0.0222)164***165log (plotsize)1660.1720 (0.0129)167***168renov1690.0274 (0.0059)170***171standard1720.0911 (0.0082)173***174micro1750.0385 (0.0075)176***177yearquarter201841780.0040 (0.0160)179n.s180yearquarter201911810.0235 (0.0137)182 .183yearquarter201921840.0327 (0.0135)185*186yearquarter201931870.0357 (0.0135)188**189yearquarter201941900.0279 (0.0149)191 .192SFHtype 2193− 0.0062 (0.0120)194n.s195SFHtype3196− 0.0274 (0.0165)197 .198energy21990.0119 (0.0281)200n.s201Error term2020.0242 (0.0010)203204205===== PAGE 9 (score 5, numeric-paren 0, table-words 0, var-words 5) =====206207Page 9 of 14208Dambon et al. Swiss Journal of Economics and Statistics (2022) 158:2 209 210For the intercept’s SVC, c.f. Fig. 5a, which also can be 211interpreted as a mean price level, we can see that the 212highest values are achieved close to the city of Zurich and 213Lake Zurich, with a local peak in the city of Winterthur. 214As expected, the lowest values can be found towards 215the northern and eastern borders of ZH, which are rural 216areas.217A similar pattern as for the intercepts’ SVC can 218be observed for the Z.age SVC, c.f. Fig. 5b. In 219absolute values, the linear age effect is smallest in the city 220of Zurich and in the area surrounding Lake Zurich, while 221it increases towards the northern and eastern regions 222of the Canton of Zurich. This indicates that the depre-223ciation of SFH prices by age is higher in rural areas. For 224the Z.age2 SVC, c.f. Fig. 5c, small scale deviations from 225the mean effect can be observed around Lake Zurich 226and the city of Winterthur. This hints at the presence of 227a vintage effect in the metropolitan areas of Zurich and 228Fig. 5 Estimated and spatially predicted SVCs of model (5). Note that the coefficients’ value spans are according to their variance estimates σ 2229j , i.e., 230descending from (a) to (c)231