Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
rent analysis beyond conditional expectation – how to estimate the spatial distribution of quoted rents by using geographically weighted regression Anne Seehase, M. Sc., Amt für Statistik, Landeshauptstadt Magdeburg, Germany July 1, 2016 Scorus-Conference 2016 – Lisbon content 1. Motivation 2. Alternative Data Sources 3. Methodology 4. Empirical Application 5. Conclusion Anne Seehase Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 1 / 25 motivation motivation ∙ 57 percent of all households in Germany are living in a rented accommodation (Statistisches Bundesamt, Wiesbaden 2015, effective 2013). ∙ Most areas with a high population density are embossed by tight and dynamically developing rental markets. ∙ It is expected that the increasing number of households caused by the demographic transition and urbanization leads to increasing rents also in cities like Magdeburg, which right now are characterized by quite a relaxed rental market. ∙ Monitoring of the developments at the rental markets are relevant for urban planning and social welfare. Anne Seehase Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 3 / 25 alternative data sources alternative data sources ∙ Traditional data collection to rental analysis focus asset rents: → information of the common (average) level of residental cost over a longer time-period → insufficient conclusions for the market price by re-letting in very dynamic markets ∙ Alternative data sources make it possible to focus actual rent prices by re-letting: → information about the current market situation and development Advantages Disadvantages ∙ In-time-data-collection of actual offers ∙ Easy availability of a high number of rental property offers, e.g. via online platforms or the advertisement section in local newspapers ∙ Easy and cheap data-collection by the dint of ∙ Web-crawling-algorithms ∙ Web-APIs ∙ Database of commercial service providers Anne Seehase ∙ Rental offers prices may differ from the real price by re-letting. ∙ Data are biased by the interest of supplier. ∙ The researcher has no bearing on the characteristics covered in the rental property offer. ∙ Very good housing supplies are likely to be re-hired without a publication on an online platform. Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 5 / 25 methodology 1500 hedonic price regression ∙ Background: The rental price of a property is determined by the individual characteristics of the flat and the characteristics of the surrounding neighborhood. ● 1000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Cold Rent in € ∙ Method of hedonic modeling: Estimation of the prices of the individual characteristic by multiple regression-models ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ●● ●●● ● ● ●● ● ●● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●●● ●● ● ● ●●● ●● ● ● ●● ● ● ● ● ●●● ●● ● ●●●● ●● ● ●● ● ●● ● ● ● ●● ● ● ● ● ● ● ●●● ●● ●● ● ● ● ●● ● ● ● ●●● ● ●● ● ● ● ● ● ● ● ●●●● ●● ● ● ● ●● ● ● ● ● ● ●● ● ● ●● ●● ● ●● ●● ●● ● ●● ●● ● ● ●● ● ● ● ●● ●● ● ●●●● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ● ● ●●● ●● ●●●● ● ● ● ● ● ● ●●●● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●● ●●● ● ●● ●● ●● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ●●● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●● ●● ●●●● ● ●●●● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ● ●● ● ●● ● ● ●● ●●● ● ● ● ● ● ● ●● ●●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ●● ●● ● ●●●● ●●● ● ●● ●● ●● ●● ● ●● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ●● ●● ●● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ●● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ●●●●● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●●●● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ●●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ●● ● ●●● ● ●● ●● ●● ● ● ● ● ● ● ● ●●● ● ●●● ● ●● ● ●● ● ● ●● ● ●●● ● ● ●●●● ● ●●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●●●●● ●● ● ●● ●●● ● ● ●● ●● ● ● ●● ● ● ● ● ● ● ●●●●●● ●● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ∙ It will be possible to estimate the expected price of a hypothetical average flat and to compare this price depending on the location of the flat or the date of the offer. Anne Seehase ● ● ● 0 ∙ Enables the estimation of the conditional expectation by a special constellation of characteristics. 500 ●● 40 60 80 100 120 140 Living area in square meters © Department of Statistics, Landeshauptstadt Magdeburg Data: Empirica−Systeme Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 7 / 25 1500 hedonic price regression ∙ Background: The rental price of a property is determined by the individual characteristics of the flat and the characteristics of the surrounding neighborhood. ● 1000 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● Cold Rent in € ∙ Method of hedonic modeling: Estimation of the prices of the individual characteristic by multiple regression-models ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ●● ●●● ● ● ●● ● ●● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●●● ●● ● ● ●●● ●● ● ● ●● ● ● ● ● ●●● ●● ● ●●●● ●● ● ●● ● ●● ● ● ● ●● ● ● ● ● ● ● ●●● ●● ●● ● ● ● ●● ● ● ● ●●● ● ●● ● ● ● ● ● ● ● ●●●● ●● ● ● ● ●● ● ● ● ● ● ●● ● ● ●● ●● ● ●● ●● ●● ● ●● ●● ● ● ●● ● ● ● ●● ●● ● ●●●● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ● ● ●●● ●● ●●●● ● ● ● ● ● ● ●●●● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●● ●●● ● ●● ●● ●● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ●●● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●● ●● ●●●● ● ●●●● ● ● ● ● ● ● ●● ● ●● ●● ● ● ● ● ● ●● ● ●● ● ● ●● ●●● ● ● ● ● ● ● ●● ●●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ●● ●● ● ●●●● ●●● ● ●● ●● ●● ●● ● ●● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ●● ●● ●● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ●● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ●●●●● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●●●● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ●●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ●● ● ●●● ● ●● ●● ●● ● ● ● ● ● ● ● ●●● ● ●●● ● ●● ● ●● ● ● ●● ● ●●● ● ● ●●●● ● ●●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●●●●● ●● ● ●● ●●● ● ● ●● ●● ● ● ●● ● ● ● ● ● ● ●●●●●● ●● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ●● ●● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ∙ It will be possible to estimate the expected price of a hypothetical average flat and to compare this price depending on the location of the flat or the date of the offer. Anne Seehase ● ● ● 0 ∙ Enables the estimation of the conditional expectation by a special constellation of characteristics. 500 ●● 40 60 80 100 120 140 Living area in square meters © Department of Statistics, Landeshauptstadt Magdeburg Data: Empirica−Systeme Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 7 / 25 1500 quantile regression (qr) ∙ The quantile regression enables the analysis of the conditional quantile to the quantile value τ ∈ (0, 1) of a dependent variable in conjunction with a set of explanatory variables (Koenker and Basset (1978)). ● 1000 ● ● ● ● ● Quantile Regression Model for τ ∈ (0, 1) Cold Rent in € ● ● ● =β0 (τ ) + β1 (τ )X1i + . . . + β(p−1) (τ )X(p−1)i + Ui (τ ) T =Xi β(τ ) + Ui (τ ) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ●● ●●● ● ● ●● ● ●● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●●● ●● ● ● ● ●●● ●● ● ● ●● ● ● ● ● ●●● ●● ● ●●●● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ●●● ●● ●● ● ● ● ●● ● ● ● ● ●● ● ●●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ●● ●● ●● ● ●●● ●● ● ●●●● ●● ● ● ● ●● ●● ● ● ●●●● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ● ● ●●● ●● ●●●● ● ● ● ● ● ● ●●●● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●● ●●● ● ●● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●●● ● ● ●● ●● ●● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●● ● ● ● ● ●● ● ●● ● ●● ● ● ● ● ● ●● ● ●● ● ● ●● ●●● ● ● ● ● ● ● ●● ●●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ●●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ●● ●● ● ●●●● ●●● ● ●● ● ● ●●● ●● ● ●● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ●● ●● ●● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ●● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ●●●●● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●●●● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●●● ● ● ●● ● ● ● ● ●●● ● ● ● ● ● ●●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ●● ● ●●● ● ●● ●● ●● ● ● ● ● ● ● ● ●●● ● ●●● ● ●● ● ●● ● ● ●● ● ●●● ● ● ●●●● ● ●●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ● ● ●● ● ●● ●●● ● ● ●●● ●●● ● ● ● ● ● ● ● ● ● ●●●●●● ●● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● 500 Yi ● ● ● ● ● ● ● ● ● ● ● i = 1, . . . , n Assumption: FUi (τ ) (0) = τ ⇒ QY (τ |Xi = xi ) = xTi β(τ ), Ui (τ ) for i = 1, . . . , n are independent. ● Xi = . . .dependent variable (1, X1i , . . . , X(p−1)i ) . . .independent variables (β0 (τ ), . . . , β(p−1) (τ )) . . .parameters depending on τ 0 ● ● Yi 40 60 80 100 120 140 Living area in square meters β(τ ) = Ui (τ ) Anne Seehase © Department of Statistics, Landeshauptstadt Magdeburg Data: Empirica−Systeme . . .perturbation depending on τ Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 8 / 25 1500 quantile regression (qr) ∙ The quantile regression enables the analysis of the conditional quantile to the quantile value τ ∈ (0, 1) of a dependent variable in conjunction with a set of explanatory variables (Koenker and Basset (1978)). ● 1000 ● ● ● ● ● Quantile Regression Model for τ ∈ (0, 1) Cold Rent in € ● ● ● =β0 (τ ) + β1 (τ )X1i + . . . + β(p−1) (τ )X(p−1)i + Ui (τ ) T =Xi β(τ ) + Ui (τ ) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ●● ●●● ● ● ●● ● ●● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●●● ●● ● ● ● ●●● ●● ● ● ●● ● ● ● ● ●●● ●● ● ●●●● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ●●● ●● ●● ● ● ● ●● ● ● ● ● ●● ● ●●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ●● ●● ●● ● ●●● ●● ● ●●●● ●● ● ● ● ●● ●● ● ● ●●●● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ● ● ●●● ●● ●●●● ● ● ● ● ● ● ●●●● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●● ●●● ● ●● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●●● ● ● ●● ●● ●● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●● ● ● ● ● ●● ● ●● ● ●● ● ● ● ● ● ●● ● ●● ● ● ●● ●●● ● ● ● ● ● ● ●● ●●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ●●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ●● ●● ● ●●●● ●●● ● ●● ● ● ●●● ●● ● ●● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ●● ●● ●● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ●● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ●●●●● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●●●● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●●● ● ● ●● ● ● ● ● ●●● ● ● ● ● ● ●●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ●● ● ●●● ● ●● ●● ●● ● ● ● ● ● ● ● ●●● ● ●●● ● ●● ● ●● ● ● ●● ● ●●● ● ● ●●●● ● ●●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ● ● ●● ● ●● ●●● ● ● ●●● ●●● ● ● ● ● ● ● ● ● ● ●●●●●● ●● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● 500 Yi ● ● ● ● ● ● ● ● ● ● ● i = 1, . . . , n Assumption: FUi (τ ) (0) = τ ⇒ QY (τ |Xi = xi ) = xTi β(τ ), Ui (τ ) for i = 1, . . . , n are independent. ● ● ● Xi = . . .dependent variable (1, X1i , . . . , X(p−1)i ) . . .independent variables (β0 (τ ), . . . , β(p−1) (τ )) . . .parameters depending on τ conditional exspectation conditional quantile 0 Yi 40 60 80 100 120 140 Living area in square meters β(τ ) = Ui (τ ) Anne Seehase © Department of Statistics, Landeshauptstadt Magdeburg Data: Empirica−Systeme . . .perturbation depending on τ Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 8 / 25 1500 quantile regression (qr) ∙ The quantile regression enables the analysis of the conditional quantile to the quantile value τ ∈ (0, 1) of a dependent variable in conjunction with a set of explanatory variables (Koenker and Basset (1978)). ● 1000 ● ● ● ● ● Quantile Regression Model for τ ∈ (0, 1) Cold Rent in € ● ● ● =β0 (τ ) + β1 (τ )X1i + . . . + β(p−1) (τ )X(p−1)i + Ui (τ ) T =Xi β(τ ) + Ui (τ ) ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ●●● ● ● ● ● ●● ●●● ● ● ●● ● ●● ● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●●● ●● ● ● ● ●●● ●● ● ● ●● ● ● ● ● ●●● ●● ● ●●●● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ●●● ●● ●● ● ● ● ●● ● ● ● ● ●● ● ●●● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●● ●● ●● ●● ● ●●● ●● ● ●●●● ●● ● ● ● ●● ●● ● ● ●●●● ● ● ● ● ● ● ● ● ●● ●● ● ●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ● ● ●●● ●● ●●●● ● ● ● ● ● ● ●●●● ● ● ● ●● ● ● ● ● ●● ●● ● ● ●● ●●● ● ●● ●● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ●●● ● ● ●● ●● ●● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●●● ●●● ● ● ● ● ●● ● ●● ● ●● ● ● ● ● ● ●● ● ●● ● ● ●● ●●● ● ● ● ● ● ● ●● ●●● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ●●● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ●● ●● ● ●●●● ●●● ● ●● ● ● ●●● ●● ● ●● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●●● ● ● ● ●● ●● ●● ● ● ● ●● ●● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ●● ● ●● ● ● ● ● ●● ● ● ● ●● ● ● ●●●●● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ●●●● ●● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●●● ● ● ●● ● ● ● ● ●●● ● ● ● ● ● ●●● ●● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ●● ● ●●● ● ●● ●● ●● ● ● ● ● ● ● ● ●●● ● ●●● ● ●● ● ●● ● ● ●● ● ●●● ● ● ●●●● ● ●●● ● ●● ● ●● ● ● ●● ● ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ● ● ●● ● ●● ●●● ● ● ●●● ●●● ● ● ● ● ● ● ● ● ● ●●●●●● ●● ● ●●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ● ● ● ●● 500 Yi ● ● ● ● ● ● ● ● ● ● ● i = 1, . . . , n Assumption: FUi (τ ) (0) = τ ⇒ QY (τ |Xi = xi ) = xTi β(τ ), Ui (τ ) for i = 1, . . . , n are independent. ● ● ● Xi = . . .dependent variable (1, X1i , . . . , X(p−1)i ) . . .independent variables (β0 (τ ), . . . , β(p−1) (τ )) . . .parameters depending on τ conditional exspectation conditional quantile 0 Yi 40 60 80 100 120 140 Living area in square meters β(τ ) = Ui (τ ) Anne Seehase © Department of Statistics, Landeshauptstadt Magdeburg Data: Empirica−Systeme . . .perturbation depending on τ Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 8 / 25 principal of the geographically weighted regression ∙ Toblers first law of geographic: “Everything is related to everything else, but near things are more related than distant things.” (Tobler (1970)) ∙ The principal of the geographically weighted regression (GWR) is based on the ideas of Fotheringham et al. (2002). The geografical weighted extension of QR-Modell is based on the description from Chen et al. (2014) and McMillen (2013). ∙ The basic idea of the geographical weighting is a local estimation of the model at special target-points which are denoted by their geographical position si = (lati , loni ). Model of the Geografically Weighted Quantile Regression (GWQR) Yi = XTi β(τ ; si ) + Ui (τ ; si ), i = 1, . . . , n Assumption: FUi (τ ;si ) (0) = τ ⇒ QY (τ ; si |Xi = xi ) = xTi β(τ ; si ), Ui (τ ; si ) is independent. Yi . . . dependent variable Xi = (1, X1i , . . . , X(p−1)i ) . . . independent variables Ui (τ, si ) . . . perturbation depending on τ β(τ ; si ) = (β0 (τ, si ), . . . , β(p−1) (τ ; si )) . . . parameters depending on τ Anne Seehase at location si Rent Analysis by Using Geographically Weighted Quantile Regression at location si July 1, 2016 9 / 25 principal of the geographically weighted regression Basic Principle Anne Seehase ∙ Nearby observations will be integrated with a higher weight. d ∙ The weights are denoted by a kernel function K( hi0 )|i=1,...,n of the scaled distance di0 of the observation i to the target-point by the bandwidth h. ∙ Fixed kernel weighting routine ∙ Adaptive kernel weighting routine Gaussian Kernel Function 1.0 Tri−Cube−Kernel Function ●● ● 0.35 0.8 ● ● −1 0 1 0.25 kernal weight −2 ● ● 0.05 ●● ● ● 0.15 0.6 0.4 0.2 0.0 h0 B1 kernal weight ● E0 d10 ● 2 scaled distance Rent Analysis by Using Geographically Weighted Quantile Regression ●● ● −2 −1 0 ● 1 ● 2 scaled distance July 1, 2016 10 / 25 empirical application empirical application Data ∙ Rental offers from the empirica systema AG database ∙ Published between January 1, 2012 and the March 31, 2016 ∙ Subset of the row data by ∙ geocoded offers with a location precision fewer than 10 meters ∙ accommodations with a living area of 30 to 250 squares meters ∙ 18442 offers are included into the research Methodical Specification Anne Seehase ∙ Semi-log model; dependent variable: log of price per square meter ∙ First step: Estimation a global global OLS-model and global QR-models by the quantile values τ ∈ {0.1, 0.25, 0.5, 0.75, 0.9} ∙ Seccond step: Estimation the local GWR-models and GWQR-models by the quantile values τ ∈ {0.1, 0.25, 0.5, 0.75, 0.9} ∙ Spatial weighting by a gaussian kernel-function and an adaptive bandwith ∙ target-points: location of each observation ∙ mapping: target points are the center points of a grid over the town area which covered with buildings (adaptive bandwidth have to be under 1 km) Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 12 / 25 semi-log qr/gwqr-model for τ = 0.5 GWQR τ = 0.5 mean min 1st quantile median 3rd quantile Intercept 1.69 1.55 1.66 1.68 1.72 log(living area) -0.03 -0.07 -0.03 -0.02 -0.02 elevator 0.02 -0.05 -0.00 0.01 0.04 balcony/terrace 0.03 -0.02 0.02 0.03 0.04 parking 0.06 0.02 0.05 0.06 0.08 kitchen 0.04 -0.01 0.03 0.04 0.05 social housing -0.04 -0.10 -0.04 -0.04 -0.03 good condition -0.00 -0.03 -0.00 0.00 0.01 bad condition -0.08 -0.17 -0.11 -0.08 -0.05 time 0.02 0.01 0.02 0.02 0.02 GWR Intercept 1.63 1.49 1.58 1.61 1.65 log(living area) -0.01 -0.07 -0.02 -0.01 -0.00 elevator 0.04 -0.01 0.02 0.03 0.06 balcony/terrace 0.03 -0.01 0.01 0.03 0.04 parking 0.06 0.03 0.05 0.06 0.07 kitchen 0.05 0.01 0.04 0.05 0.06 social housing -0.06 -0.11 -0.07 -0.06 -0.05 good condition 0.01 -0.02 0.01 0.01 0.01 bad condition -0.07 -0.14 -0.1 -0.07 -0.05 time 0.02 0.02 0.02 0.02 0.02 Significance levels [0,001]’***’;(0.001,0.01]’**’;(0.01;0.05]’*’;(0.5,0.1]’°’,(0.1,1]’ ’ Anne Seehase Rent Analysis by Using Geographically Weighted Quantile Regression max 1.91 0.004 0.11 0.05 0.11 0.07 -0.00 0.01 0.02 0.03 1.90 0.02 0.11 0.06 0.11 0.08 -0.01 0.02 0.03 0.03 QR Std. 1.658 -0.02 0.01 0.02 0.07 0.05 -0.03 0.00 -0.10 0.02 OLS 1.67 -0.00 0.03 0.02 0.06 0.06 -0.05 0.01 -0.08 -0.02 July 1, 2016 Sign. *** *** * *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 13 / 25 spatial heterogeneity of the time effect (magdeburg) Anne Seehase tau=0.1 tau=0.9 no evaluation 0.0111 to 0.0131 0.0131 to 0.0152 0.0152 to 0.0172 0.0172 to 0.0192 0.0192 to 0.0213 0.0213 to 0.0233 0.0233 to 0.0253 0.0253 to 0.0274 0.0274 to 0.0294 0.0294 to 0.0314 0.0314 to 0.0335 0.0335 to 0.0355 0.0355 to 0.0375 0.0375 to 0.0396 0.0396 to 0.0416 © Amt für Statistik, Landeshauptstadt Magdeburg Data: Empirica−Systeme Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 14 / 25 prediction of the cold rent per square meter (in €) Anne Seehase GWQR−model (tau=0.1) GWQR−model (tau=0.9) no evaluation 3.82 to 4 4 to 4.18 4.18 to 4.36 4.36 to 4.54 4.54 to 4.72 4.72 to 4.9 4.9 to 5.08 5.08 to 5.26 5.26 to 5.44 5.44 to 5.62 5.62 to 5.8 5.8 to 5.98 5.98 to 6.16 6.16 to 6.34 6.34 to 6.52 Flat characteristics: 61.8 square meters, balcony, good condition effective July 1,2012 © Amt für Statistik, Landeshauptstadt Magdeburg Data: Empirica−Systeme Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 15 / 25 prediction of the cold rent per square meter (in €) Anne Seehase GWQR−model (tau=0.1) GWQR−model (tau=0.9) no evaluation 3.82 to 4 4 to 4.18 4.18 to 4.36 4.36 to 4.54 4.54 to 4.72 4.72 to 4.9 4.9 to 5.08 5.08 to 5.26 5.26 to 5.44 5.44 to 5.62 5.62 to 5.8 5.8 to 5.98 5.98 to 6.16 6.16 to 6.34 6.34 to 6.52 Flat characteristics: 61.8 square meters, balcony, good condition effective July 1,2015 © Amt für Statistik, Landeshauptstadt Magdeburg Data: Empirica−Systeme Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 16 / 25 prediction of the cold rent per square meter (in €) Anne Seehase GWQR−model (tau=0.5) GWR−model no evaluation 3.82 to 4 4 to 4.18 4.18 to 4.36 4.36 to 4.54 4.54 to 4.72 4.72 to 4.9 4.9 to 5.08 5.08 to 5.26 5.26 to 5.44 5.44 to 5.62 5.62 to 5.8 5.8 to 5.98 5.98 to 6.16 6.16 to 6.34 6.34 to 6.52 Flat characteristics: 61.8 square meters, balcony, good condition effective July 1,2012 © Amt für Statistik, Landeshauptstadt Magdeburg Data: Empirica−Systeme Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 17 / 25 prediction of the cold rent per square meter (in €) Anne Seehase GWQR−model (tau=0.5) GWR−model no evaluation 3.82 to 4 4 to 4.18 4.18 to 4.36 4.36 to 4.54 4.54 to 4.72 4.72 to 4.9 4.9 to 5.08 5.08 to 5.26 5.26 to 5.44 5.44 to 5.62 5.62 to 5.8 5.8 to 5.98 5.98 to 6.16 6.16 to 6.34 6.34 to 6.52 Flat characteristics: 61.8 square meters, balcony, good condition effective July 1,2015 © Amt für Statistik, Landeshauptstadt Magdeburg Data: Empirica−Systeme Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 18 / 25 prediction of the cold rent per square meter (in €) ● ● ● ● conditional median 2012 conditional median 2015 conditional mean 2012 conditional mean 2015 Milchweg 2012 Milchweg 2015 Hasselbachplatzviertel 2012 Hasselbachplatzviertel 2015 Fliedergrund 2012 Fliedergrund 2015 0.6 0.4 0.2 0.0 density 0.8 1.0 ● Milchweg Hasselbachplatzviertel Fliedergrund Anne Seehase ● 3 4 ● ●● 5 ● ● 6 Price per square meter 7 8 © Amt für Statistik, Landeshauptstadt Magdeburg Data: Empirica−Systeme Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 19 / 25 conclusion conclusion Anne Seehase ∙ Geocoded online-data are a substantial data-source for the analysis of rental data. ∙ Enables a lot of analysis in detail; high potential for geostatistical analysis ∙ Data-restriction has to be kept in mind. ∙ Quantile regression allows a detailled view at the conditional distribution of the variable of interest. ∙ Main advantages: rubustness aigainst outlier ∙ Disadvantages: local estimation could lead to quantile-crossing ∙ The extension of the geographical weighting allows to consider the location of interest. ∙ Time trends could be analyzed considering the geographical position. ∙ Indicator for the development in special districts (social segmentation or heterogenity). ∙ GWQR-Model based on local estimation. ∙ computationally intensive ∙ difficults in modell-selection Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 21 / 25 Anne Seehase Thank you for your attention! Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 22 / 25 references Anne Seehase ∙ Chen, Vivian Y.; Deng, Wen-Shuenn; Yang, Tse-Chuan; Matthews, Stephan: Geographically Weighted Quantile Regression (GWQR): An Application to U.S. Mortality Data. In: Geographical Analysis 44(2) 2012, pp. 134-150 ∙ Fotheringham, A. Stewart ; Brunsdon, Chris ; Charlton, Martin: Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley 2002 ∙ Koenker, Roger: Quantile regression, Cambridge university press 2005 ∙ Koenker, Roger; Basset Jr., Gilbert: Regression quantiles. In: Econometrica: journal of the Econometric Society, 1978, pp. 33-50 ∙ McMillen, Daniel P.: Quantile regression for spatial data. Berlin, Springer, 2013 ∙ Tobler, Waldo R.: A Computer Movie Simulating Urban Growth in the Detroit Region. In: Economic Geography, Vol. 46,1999, pp. 234-240 Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 23 / 25 quantile regression (qr) Anne Seehase ∙ In case of empirical analysis, the unknown parameter β(τ ) has to be estimated. ∙ Solution of the minimization problem: n ∑ T β̂(τ ) = arg min Rτ (β) = arg min ρτ (yi − xi β) β∈Rp β∈Rp ∙ The loos-function ρτ is defined by: ρτ (u) = (u)(τ − I(u < 0)) = { τ ·u u·u i=1 , , for for u≤0 u<0 0.2 0.4 loos 0.6 0.8 1.0 ∙ Rτ (β) is not differentiable. → The minimization-problem has to be solved by methods of linear programming. 0.0 quadratic loos tau=0.5 tau=0.75 tau=0.25 −1.0 −0.5 0.0 0.5 1.0 u Rent Analysis by Using Geographically Weighted Quantile Regression July 1, 2016 24 / 25 principal of the geographically weighted regression Basic Principle ∙ Nearby observations will be integrated with a higher weight. d ∙ The weights are denoted by a kernel function K( hi0 )|i=1,...,n of the scaled distance di0 of the observation i to the target-point by the bandwidth h. ∙ Fixed kernel weighting routine ∙ Adaptive kernel weighting routine Gaussian Kernel Function 1.0 Tri−Cube−Kernel Function ●● ● 0.35 0.8 ● ● −1 0 1 0.25 kernal weight −2 ● ● 0.05 ●● ● ● 0.15 0.6 0.4 0.2 0.0 h0 B1 kernal weight ● E0 d10 ● 2 ●● ● −2 scaled distance −1 0 ● 1 ● 2 scaled distance Minimization Problem Anne Seehase β̂(τ ; s0 ) = arg min β∈Rp n ∑ T (ρτ (yi − xi β(s0 )) · K( i=1 Rent Analysis by Using Geographically Weighted Quantile Regression di0 )) h July 1, 2016 25 / 25