# RECORD a90efa2e2b4a4c7fde54cbffdb07fb2a1d2e8ed7 # TITLE: Examining the vintage effect in hedonic pricing using spatially varying coefficients models: a case study of single-family houses in the Canton of Zurich # YEAR: 2022.0 VENUE: Swiss Journal of Economics and Statistics DOI: 10.1186/s41937-021-00080-2 # AUTHORS: Jakob A. Dambon; Stefan S. Fahrländer; Saira Karlen; M. Lehner; Jaron Schlesinger; Fabio Sigrist; Anna Zimmermann # PAGES: 14 CANDIDATE TABLE PAGES (1-based): [8] # 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. ===== PAGE 1 (score 12, numeric-paren 0, table-words 0, var-words 12) ===== Dambon et al. Swiss Journal of Economics and Statistics (2022) 158:2 https://doi.org/10.1186/s41937-021-00080-2 ORIGINAL ARTICLE Examining the vintage effect in hedonic pricing using spatially varying coefficients models: a case study of single‑family houses in the Canton of Zurich Jakob A. Dambon1,2*  , Stefan S. Fahrländer3, Saira Karlen3, Manuel Lehner3, Jaron Schlesinger3, Fabio Sigrist2   and Anna Zimmermann3  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. Keywords:  Gaussian process, Spatial statistics, Real estate, Mass appraisal JEL Classification:  C31, C53, R31, R32 © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/. 1  Introduction Hedonic real estate models contain several predictor variables, and age is a key explanatory variable. The mar- ginal effect of the building age on house prices has been well-studied. It has been found that the age effect is non- linear (Clapp & Giaccotto, 1998; Goodman & Thibodeau, 1995). In particular, Case et al. (2004) report a “plausible quadratic form” for the building age. This behavior is a result of two main features of the age as an independ- ent variable: (1) In general, older buildings depreciate due to deterioration; (2) “however, beyond some point, only those houses with the best locations and the highest construction quality survive.” (Case et al., 2004, p. 171). The quadratic appearance of the age effect has also been observed by Fahrländer (2006) and linked to the build- ing material and architectural style. Studies investigat- ing this particular type of behavior, i.e., a deviation from a pure depreciative effect once a particular age has been reached, are referencing to it as a vintage effect (Clapp & Giaccotto, 1998; Goodman & Thibodeau, 1995; Rubin, 1993). Over the last two decades, there emerged a special focus on location specific effects due to newly avail- able modeling methodologies. There are numerous publications which show a clear indication of spatially varying covariate effects within hedonic pricing mod- els. For instance, when applying additive mixed regres- sion models on rents in Vienna (Austria), Brunauer et al. Open Access Swiss Journal of Economics and Statistics *Correspondence: jakob.dambon@gmail.com 1 Department of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland Full list of author information is available at the end of the article ===== PAGE 8 (score 44, numeric-paren 22, table-words 5, var-words 8) ===== Page 8 of 14 Dambon et al. Swiss Journal of Economics and Statistics (2022) 158:2 Again, this ensures a well-behaved numeric optimiza- tion while remaining interpretable as the ranges ρj now act as a scaling factor on the kilometer distances. 4  Results 4.1  Parameter estimates We first look at the ML estimates ˆωMLE , which are given in Table 3. Here, we find that the mean estimates match our expectations. In particular, the vintage-related covar- iates, i.e., Z.age and Z.age2 , show the following: 1. The mean effect for Z.age is negative, as one would expect, and statistically significant at the 0.1% level. This can be interpreted in the sense that on average the value of a single-family home typically decreases with age. 2. The quadratic effect for Z.age2 shows a relatively small, positive mean effect, which is statistically sig- nificant at the 10% level. A larger quadratic mean age effect would correspond to an emphasized vintage effect. All other mean effects have plausible signs, too. Namely, all other coefficients of continuous covariates are positive and statistically significant at reference levels. As for the categorical covariates, we observe some tem- poral price volatility for the transaction year and quarter, a premium for stand-alone, detached SFHs compared to other SFHs for the type of SFH and a premium for houses with enhanced energy efficiency for the energy standard. The estimates for ranges of the Gaussian processes show that the range for the intercept and Z.age are con- siderably larger than the one for Z.age2 . This will be expressed in larger spatial structures for the SVCs mod- eling the intercept and the linear age effect compared to the SVC modeling the quadratic age effect. The small range of Z.age2 on the other hand indicates that the SVCs corresponding to the quadratic age effect will behave much more selective in their deviations from the mean. Finally, we analyze the estimated variances of the spatially varying coefficients. The intercept’s variance is the largest and highly statistically significant. As for the linear and quadratic age effects, the range of the coefficients’ values is smaller, see Table 3 and Fig. 5. 4.2  Visualization and interpretation of SVCs In Fig. 5 we visualize fitted and predicted SVCs. Specifi- cally, the figure shows the estimated SVCs for the obser- vation locations the model has been trained on as well as for the spatial predictions for all other cell’s centroid where we did not have any observations. The quality of these coincides with the previous parameter estimates’ interpretations from Sect.  4.1 and real estate experts’ knowledge. Table 3  Mean and covariance estimates ˆωMLE of the SVC model (5) The corresponding estimates’ standard errors are given in parenthesis. In most cases, the standard errors can be approximated and computed by the Hessian from the numeric 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 2 j > 0 , respectively. This is only possible if the standard error is available. Significance levels: ‘.’ p < 0.1; ‘*’ p < 0.05; ‘**’ p < 0.01; ‘***’ p < 0.001; ‘n.s.’ not statistically significant, ‘n.a.’ not available Covariates Mean ˆµj Sign. level Range ˆρj Variance ˆσ 2 j and ˆτ 2 Sign. level Intercept 9.1555 (0.1571) *** 13.5511 (4.1157) 0.0413 (0.0116) *** Z.age − 0.1495 (0.0254) *** 18.9370 (41.6414) 0.0009 (n.a.) n.a Z.age2 0.0114 (0.0062)  . 1.7153 (0.8673) 0.0003 (0.0003) n.s log (volume) 0.5132 (0.0222) *** log (plotsize) 0.1720 (0.0129) *** renov 0.0274 (0.0059) *** standard 0.0911 (0.0082) *** micro 0.0385 (0.0075) *** yearquarter20184 0.0040 (0.0160) n.s yearquarter20191 0.0235 (0.0137)  . yearquarter20192 0.0327 (0.0135) * yearquarter20193 0.0357 (0.0135) ** yearquarter20194 0.0279 (0.0149)  . SFHtype 2 − 0.0062 (0.0120) n.s SFHtype3 − 0.0274 (0.0165)  . energy2 0.0119 (0.0281) n.s Error term 0.0242 (0.0010) ===== PAGE 9 (score 5, numeric-paren 0, table-words 0, var-words 5) ===== Page 9 of 14 Dambon et al. Swiss Journal of Economics and Statistics (2022) 158:2 For the intercept’s SVC, c.f. Fig. 5a, which also can be interpreted as a mean price level, we can see that the highest values are achieved close to the city of Zurich and Lake Zurich, with a local peak in the city of Winterthur. As expected, the lowest values can be found towards the northern and eastern borders of ZH, which are rural areas. A similar pattern as for the intercepts’ SVC can be observed for the Z.age SVC, c.f. Fig.  5b. In absolute values, the linear age effect is smallest in the city of Zurich and in the area surrounding Lake Zurich, while it increases towards the northern and eastern regions of the Canton of Zurich. This indicates that the depre- ciation of SFH prices by age is higher in rural areas. For the Z.age2 SVC, c.f. Fig. 5c, small scale deviations from the mean effect can be observed around Lake Zurich and the city of Winterthur. This hints at the presence of a vintage effect in the metropolitan areas of Zurich and Fig. 5  Estimated and spatially predicted SVCs of model (5). Note that the coefficients’ value spans are according to their variance estimates σ 2 j  , i.e., descending from (a) to (c)