特徵價格法之參數與半參數電腦輔助大量估價(CAMA)模型之研究─臺北地區法拍屋住宅市場之實證分析
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(2) 86 住宅學報. 1. Introduction In recent years, many countries have developed Computer Assisted Mass Assessment systems (CAMA) to be a tool for tax-assessment. The systems generally build valuation models, which apply the hedonic price parametric and nonparametric models. Several literature discuss the function forms for hedonic price parametric models, for example, Ridker & Henning(1967) estimated the effects of housing price by the degree of air pollution, Stull(1975), Li & Brown(1980), Thibodeau(1989), Clapp, Giaccotto & Tirtiroglu(1991) made a price index by using the hedonic price model. In recent years, several studies have proposed the semi-parametric model. Additionally, the parametric model such as the hedonic price model is too restrictive in the problem for identifying function forms and estimating the parameters. It is important to seek for the fitting function forms. Otherwise, the wrong function forms will bring incorrect results. However, the nonparametric regression model and semi-parametric model can improve these drawbacks. There are several literature reviews for semi-parametric model function forms. These include references from researchers such as Pace(1995), Anglin & Genca(1996), Gencay & Yang(1996), Thorsnes(1998), Pavlov(2000), Clapp(2004) and Bin(2004) which proposed that the methods of semi-parametric estimators should combine the merits of parametric and nonparametric estimation. The semiparametric models might have the function of linear, convex, or concave of curvilinear. And the semi-parametric models might need a few structures which have complicated estimation processes to produce a fitted model. In our study we did a comparison between the semi-parametric and the parametric modelling to find the relation of the attributes of court auction residences in the Taipei Metropolitan Area from period of 2001 to 2003. In addition, we also adopted the GIS system with spatial factors in the level of final bid price on the court auction residences. The remainder of this paper contains three sections. The first section discusses the literature reviews. The empirical evidence is reported in the second section and the final section concludes this study.. 2. Literature Reviews and Methodology This is divided into three subsections. We first review the literature. In the second subsection, we show how the auction market works. In the concluding subsection, we establish the model frameworks.. 2.1 Literature Reviews There are several literature reviews for semi-parametric model function forms, for example, Pace (1995) showed that the OLS parametric estimators can attain well-specified models in efficiency. Meanwhile, the nonparametric estimators greatly reduce specification error, but at the cost of efficiency. However, the semi-parametric method can act as a compromise between them and obtain better estimators. Anglin & Gencay (1996) and Gencay & Yang (1996) recommended a.
(3) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 87. Box-Cox model in the specification of hedonic price models. However, the above parametric model involves implicit restrictions and they can be reduced by using a semi-parametric model. Thorsnes (1998) found out that the semi-parametric estimators combined the benefits of the parametric and nonparametric estimations. The semi-parametric models permitted the function to be linear, convex, or concave of curvilinear and sought for the best fitted model. Pavlov (2000) discussed that the nonparametric models can consider the important value of spatial variation. This had been previously ignored in hedonic pricing models. Clapp (2004) derived the local regression model with a semiparametric approach to estimate a location value surface. They found that the semi-parametric approach can more accurately provide estimates as compared to the parametric approach. Bin (2004) extended the approach of Hastie & Tibshirani (1990) using the additive semi-parametric models with GIS and found it can be useful for measurement and prediction of housing sales prices. We show literature reviews of the semi-parametric approach as in Table 2-1.. 2.2 How the Auction Market Works In the literature review (see Table 2-2), we find that the auction market works on different rules of sales, and in most of the markets the sales rules follow the English auction-open called bid format, which is found in Australia, the U.S.A, and New Zealand. In Taiwan, we generally follow the sales. rules of the first-price sealed bid on the auction market. Some of auctions have open called bids in the private sales market (such as the [silver] and [diamond] auction markets in Taiwan), which occupy 2% market share of the total auction market. The Taiwan court auctions are viewed as a way to dispose of distressed properties. Most of the properties in court auctions are related to debtor-creditor, amount due of mortgage or nonperforming loans (NPL) ---mortgage foreclosures, and tax foreclosures. The creditor declares a court auction by the law of enforcing performance in court. The buyers bring secret bids to the auction site inside the court room before the fixed period of date. This is followed by the executing judge openly announcing the highest winning bid. The Taiwan court auction methods are more similar to the first-sealed bid auction where the buyer has claim to the object auctioned by making the highest bid. During the process, buyers do not know the other bids, are not aware of the number of bidders and the bid-prices of other bidders. If in the event when a successful bidder defaults, the court shall call a secondary auction. In the event of an unsuccessful-bid (if it is not a closed auction, or in the case where no bidders reach the base price); the court might have a second, third and subsequent auctions. The bid-times may be a one-shot, two, three or up to eight or more, etc. in order to win the bid and the court can close the auction. Each additional auction will reduce the base price by approximately 20%. The average auction bid times (counts) is three to four times. The winning bidder would pay the full strike-price within seven days of the date notification. Sometimes, the court auction is not efficient in time spent to deal with the properties.. 2.3 Establishment of the Model Frameworks The semi-parametric price function model is adjusted by the hedonic price function to the semi-.
(4) 88 住宅學報. Table 2-1. Related Literature Reviews for the Function Forms of the Semi-Parametric Price Model. Authors Bin (2004). Model Semi-parametric regression, Hedonic price function. Study area Data Pitt County of North 2,595 observations, Carolina form July, Single-family 2000 to June, 2002 residential homes sold. Clapp (2004). Local regression model (LRM) Location value surface Local regression model. Massachusetts from 5,713 observations, January, 1990 to Sales prices and April, 1999 dates Fairfax County of Washington, D.C. from 1972Q1 to 1991Q2. 49,511 sales data. Semi-parametric multi-dimensional K-nearest-neighbor smoothing Semi-parametric model. Los Angeles County from April 1 and September 30, in 1997 Portland, Oregon, metropolitan area from 1980 to 1987. 3,000 observations, real estate transaction data. Gencay& Yang (1996) Anglin & Gencay (1996). Semi-parametric model. Windsor in 1990. 955 residential houses sold. Semi-parametric model, Box-Cox model. Windsor and Essex 546 residential County from July to houses sold September, in 1987. Pace (1995). Semi-parametric model. Memphis, January in 379 single family 1987 dwellings sold. Clapp (2004). Pavlov (2000) Thorsnes & McMillen (1998). 158 undeveloped parcels. Variables Price, square footage, number of bed/ bath rooms, age of house, other attributes, geographic locations including Tar River, major roads, streets, business centers, streams and creeks Price, square footage, building age, bathrooms, lot size, latitude and longitude Price, rooms, beds baths, half bath, fireplaces, age, land area, geographic locations, latitude and longitude and dummy Sales price, size of living rooms, bedrooms, bathrooms, X, Y coordinates Sale price, size of the undeveloped parcels, size of the developed land, distance from Portland CBD or freeway or arterial street 26 variables of which 19 are dummy Price, Driveway, Recreation room, Finished basement, gas heating, central air, garage, neighborhood dummy variable, lot size, number of bedrooms/ full bathrooms/ stories Price, age, other area, kitchen area, and lot area.
(5) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 89. Author. Table 2-2. Literature Review of the Auction Markets Comparisons Auction System. Real Estate Market Type. Real Estate Type. Lusht(1996). English AuctionOpen Called Bid. Normal Asset, Residential House. Dotzour, Moorhead& Winkler(1998) Mayer(1998). English AuctionOpen Called Bid. Australia, The Auction Market Attains Half of the Market Share in the Real Estate Market New Zealand, The Auction Market Attains Lower Market share U.S.A. The Auction Market Attains Lower Market Share. Marcus(2001). English AuctionOpen Called Bid English AuctionOpen Called Bid The First-Price Sealed Bid. Quan(2002) Lin, Tsai& Chang(1997). English AuctionOpen Called Bid. U.S.A. The Auction Market Attains Lower Market Share U.S.A Taiwan. Evaluation Method Hedonic Price Theory. Residential House. Hedonic Price Theory. Normal and NPL Asset Mixed, Residential House NPL by HUD Residential House Residential Vacancy Land NPL. Repeated Sale Method Hedonic Price Theory Hedonic Price Theory Hedonic Price Theory. parametric regressions model. The smoothing methods based on Hastie & Tibshirani (1990) are as follows: 1. Bin Smoothers, 2. Running-Mean and Running-Line Smoothers, 3. Kernel Smoother, 4. Regression Splines, 5. Cubic Smoothing Splines, 6. Locally-Weighted Running-Line Smoothers. The more applied smoothing methods are Kernel Smoother, Cubic Smoothing Splines and LocallyWeighted Running-Line Smoothers; but the most applied method based on the Cubic Smoothing Splines. This study estimate a hedonic price function using the Cubic Smoothing Splines additive semi-parametric models, the model is written as: y=α＋. βiXi＋. fi(Zj) ................................................................................................................ (1). fi(Zj) is the portion of Semi-parametric, where where βiXi is the portion of parametric, 2 V(lnP∣X,Z)=σ , an unknown parameter. Note that the usual linear function of Z is replaced with the sum of unspecified functions. The functions fj(Zj) that appear in Eq. (1) are estimated using the iterative procedure known as the back-fitting estimator, which reduces multivariate regression to continuous simple regressions. We follow Bin’s (2004) detail to estimate the approaches as follows: (1) backfitting / iteration approach The backfitting procedure starts with setting initial values for the unknown functions mj(Zj) for j=1-6 and then defines the partial residual of j th attribute for the v th iteration as: ............................................................... (2).
(6) 90 住宅學報. Where v=1,2… and , and denote the estimated coefficients and estimated function. For the initial values, is defined as the (n×1) vector of zeros. In each end of the iteration the six unknown functions are updated. Iterations are continuous until the sum of squared residuals is changed (the equation as below), which is smaller than a pre-specified measure of tolerance between iterations.. In the iteration, the functions to be estimated are updated via the local polynomial regression that has the partial residual r j as the dependent variable and the attribute Z j as the independent variable for j=1-k. The local polynomial estimator of p-degree for. is defined as:. ................................................................................................ (3) where e1 is a (p+1)×1 vector having the value one in the first entry and zero elsewhere. .............................................................................................. (4). Wtj is an n-dimensional diagonal matrix with elements given by (1/hj)K((Ztj-Zsj)/hj) for s=1,2,...,n, K is the chosen kernel function, and hj is a suitably chosen bandwidth.. (2) plug-in approach Opsomer & Ruppert (1998) proposed an updating plug-in bandwidth selection method, in which a crucial aspect of any non-parametric estimation procedure is the selection of the bandwidths that underlie the calculation of . The basic principle behind this plug-in method is the direct estimation of function form by the optimal bandwidths. The bandwidths hj are chosen to minimize the conditional mean average squared error (MASE): MASE. ................................................ (5). Finally, an estimates covariance matrix for each , and. is obtained by. R jR' j where. =Rjlnp. Then, the lower and upper bounds. on the estimates regressions are constructed by using ±2 times the square root of the diagonal of RjR'j.. After the model be established, the best fitted model will selected by the criteria of RMSE, MAPE, AS-Ratio mean, variance and Hit Ratio which are shown as follows: (1) Root Mean Squared Errors, RMSE.
(7) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 91. ei=yi－ The smaller RMSE is the better result is. (2) Mean Absolute Percentage Errors, MAPE=. *100% (yt≠0) ei=yi－ ;. MAPE not over 5%~15% were better.. (3) Assessment Ratio, AS Ratio, AS Ratio= /y AS Ratio indicates the fair assessment, with a value closer to 1 as being better. The variance of the AS Ratio not over 15%~25% was better. (4) Hit Ratio. HitRatio= *100%; n: the number of hit the range, N: sample size Hitting Range=y－y(α)≤ ≤y＋y(α) where Y represents the actual value, α are the significant levels : 5%, 10%, 20%, If the forecast value falls in the hitting range defined 1, otherwise defined 0. Adding up the ‘1’ the sum ratio to the total sample defines the Hit Ratio. The higher r=atio defines the small gap between the actual value and the forecast value.. 3. The Empirical Analyses We include five topics in this section. In the first topic we show the empirical study data and their statistics. In the second subsection, we show the important factors affecting the auction housing prices in Taiwan. In the third topic we established the empirical model of the Semi-parametric function forms. In part four we show the predicted results of the semi-parametric modeling. And finally we did a valuation comparison between the semi-parametric and the parametric modeling.. 3.1 Data and Descriptive Statistics There are up to three or four types of auction markets. Occupying the majority of the auction market share is the court auction market and the others are the [gold], [silver], and [diamond] auction markets. The latter only have a 2% market share in the Taiwan real estate market. Most of them deal with the unsuccessful-bid court auction objects which are originally sourced from the NPL bank. The auctioneers, not the court auction, can be the Taiwan Financial Asset Service Corp., entrusted by the Taipei District Court, the bank itself, or the auction agent, entrusted by the Bank. The 16 nationwide courts have executed 17,000 auction property cases in 1992. However this decade has dramatically risen to 306,495 cases (see Figure 3-1). Table3-1-row (9) indicates the court auction change from 1.00% in 1992 to 13.75% in 2003 on the real estate market share in most cases. The successful-bid property cases amount changed from 182 (NT$ a hundred million) in 1992 to 1,872 (NT$ a hundred million) in 2003 and reached a new high in 2004 to around 3000 (NT$ a hundred million). We found in Table 3-1, that the total court auction property cases for the city of Taipei are as follows. 16% of the Taiwan count auction market share have cases which reached 47,189 in 2002 and.
(8) 92 住宅學報. Figure 3-1. 1992-2003 Comparison between the Taiwan Area Court Auction Property Cases and Successful-Bid (Bidden) Property Cases. Table 3-1. 1992-2003 Taiwan Area Court Auction Property Cases Statistic Data (1) Year 1992. 1993. 1994. 1995. 1996. 1997. (2) Transaction Property Cases (a) for Taxation Goals. 1998. 1999. 2000. 2001. 2002. 2003. 312,796 371,720 464,480 491,884 508,748 466,568 385,969 385,074 321,165 259,494 320,285 349,789 (3) Court Auction Property Cases (b) 17,000 24,000 32,000 45,000 66,779 80,388 101,633 151,658 192,009 247,131 297,651 306,495 (5) Successful-Bid Property Cases (c) 3,059. 4,167. 5,831. 7,608 12,250 14,678 15,367 19,810 19,583 22,800 36,661 48,096. 182. 270. 419. 534. 698. 920. 838. 915. 951. 820. 1,357. 1,872. 595. 648. 719. 702. 570. 627. 545. 462. 486. 360. 370. 389. (6) Successful-Bid Property Cases Amount (NT$ Hundred Million). (7) Successful-Bid Property Cases Average Amount Per Case (NT$ Ten Thousand ) (8) Successful Bidding Rate (c)/(b). 18.00% 17.40% 18.20% 16.90% 18.30% 18.30% 15.10% 13.10% 10.50% 9.20% 12.32% 15.69%. (9) Percentage of (c)/(a) 1.00%. 1.10% 1.30% 1.50% 2.40% 3.10% 4.00% 5.10% 6.10% 8.80% 11.45% 13.75%.
(9) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 93. the dollar amount was 32.00% of the market share which amounted to 438.2 (NT$ hundred million).. 3.2 Important Factors Affecting Auction Housing Prices in Taiwan From review of the literature, one discovers that most housing price studies did not include the values that cannot be quantitative (such as timing, location, type, which includes those so-called “quality” variances). Also, are those attributes (such as area, age of the housing, etc.) included in most foreign countries literature really important factors, which affect the auction housing price? Are they as sensible as conceived? The present research will make a review on these model frameworks with certain examples, in order to establish a more suitable model framework as the foundation for an empirical study. In an attributes analysis of the auction housing price, one should begin from the angle of a user. and draw in the following factors (see Table 3-2 and Table 3-3): First, consider the auction attributes, such as bid times auction date, total reserved price (base price), land reserved price, successfulbid total price, handing in over term by term; next finding house internal/ external attribute such as dwelling, building unit characters/neighborhood. The most important auction market factors were price, which include reservation price, bid price, and the winning-bid price. Indeed, the auction price factors need to be studied. Whether the handing is over term by term or not, the process will affect the winning-bid price. The higher price they will chose the handing over term by term. The more bid-times the lower the reservation bid price as well the winning-bid price. The more the number of bidders, the higher the winning-bid price, but this can not obtained (unobserved in the databank of this study) variable. The dwelling unit factor refers to the interior condition of a dwelling unit. Generally, one can begin with the proportion of the public facilities, stayed-floor, floor-area, location, management fee, bathroom and toilette, and the number of rooms. As there are different standards for public facilities, locations, and management fees, bathrooms and toilettes, and the number of rooms are all dependents of the dwelling unit’s total floor-area. One can simplify these factors to floor-area and stayed-floor. The building block factor refers to the appearance of the entire building above the construction site, i.e. the “type of building”. One can examine this factor from the utilization, age of the building and the number of floors. The neighborhood factor is often connected to the location of the building, which can be divided into a major and minor neighborhood. A major neighborhood refers to the administration district in which a building is located. As the feature of the administration district is different from that of the distance from the CBD, living standards, and the standards of the neighborhood, each has its individual development. For example, the six districts that were only included in the Taipei municipality since 1976 have been developing as residential areas, while the old districts are used as commercial areas. Near neighborhood refers to the convenience of the building to the neighboring public facilities. For example, the price of a building located beside the main road will be higher than one that is located in an alley. Other factors including corner area, and the distance from bus stations, parks, and markets, which are also important attributes relating to accessibility. In Table 3-4 we found the court auction data from 2001Q1-2003Q4, the total are 3,016 cases. We.
(10) 94 住宅學報. Attribute Categories. Table 3-2. The Court Auction Housing Variable Attributes Attribute Contents. Measurement terms. Variables Coding number. Specific Performance Case ID S5 Number The Coding of Auction Court S2. Bid-times before auction close SSNO1 Auction Attribute Auction Characters. Housing Unit Characters. Auction Date. S29D. Land Area. SIZE2. In-Floor Level. FLOOR SB : SB1=1, first floor O.W.=0 SB2=1, high rising Buildings O.W.=0 SB3=1, apartments O.W.=0 STRUC : SC1=1, RC, SRC etc. O.W.= 0 SC2=1, Brick, Iron, Wooden, Soil etc. O.W.=0 AGE. Total Reserved Price Land Reserved Price Successful-bid Total Price. STP STPP SLP Pro=1, Handing in Handing in Over term by term Pro=0, Not Handing in Over Building Area HSIZE Total Floor Levels. Building Type. House Internal Attribute Building Unit Characters. Building Construction Structure Age. Address of Building. Other Attribute. Dummy. Quarterly Season Location. TOTFLOR. ADDR_T Q1=1, 1st season O.W.=0 Q2=1, 2nd season O.W.=0 Q3=1, 3rd Season O.W.=0 Q4=1, 4th season O.W.=0 LA=1, land high price areas O.W.=0. House External Macro Economy GDP, Salary GDP, Salary Attribute Indication Note: Location variable defined by the official land present value lot media price, the district lies on the higher lot media price are referred to as the high price area in Taipei city. LA=1, there are half of the 12 districts located in high price areas such as Chung-Chen, Chung-Shen, Shung-Sha Tan-An, SinYi and Sin-Lin district..
(11) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 95. Table 3-3. Spatial Factors Description. Variables / Dummy variables Contents SDIST/ SCDIST The Distance from Small Regional Parks/ of a Circle Radius Within 500 Meters, SCDIST=1, O.W. SCDIST=0 BDIST/ BCDIST The Distance from Big Regional Parks /of a Circle Radius Within 500 Meters, BCDIST=1, O.W. BCDIST=0 STDIST/ SCTDIST The Distance from Stations of the Mass Rapid Transit System/ of a Circle Radius Within 500 meters, SCTDIST=1, O.W. SCTDIST=0 S_101DIST/ S_101CDIST The Distance from the Taipei 101 high-rise building or the Shin-Kuang department store in the main Taipei Train Station (Whichever Place is Closer). / of a Circle Radius Within 500 meters (Whichever Place is Closer), S_101CDIS=1, O.W. S_101CDIS=0 Note: We try two data-format types for spatial factors, one is continuous-format distance type, and the other is dummy-format distance type.. Table 3-4. The Empirical Study In/Out Sample Data on the Taipei City Court Auction Houses /Adjusted by Outlier Checking Year 2001 2002 2003. Added spatial factors 2001 2002 2003. In Sample Data. Out Sample Data. Outliers for Adjusting. 1,019. 110. 71. 584. 65. 34. 1,111. 127. 577. 65. 33. 114. 59. 1,008 998. 108. 65. 71. use 90% in-sample data for regression analysis, the 10% out-sample for post forecast. Outliers have been adjusted for the data by Lin (1996) empirical results which shown the DFFITS outlier removal better method. The final data we use in study show as Table 6. After adding spatial factors, the data is also shown in Table 6.. 3.3 Semi-parametric/ Parametric Function Forms Based on the data, we have a limit on the possible data factors. The selected-factors are listed in Table 3-2 and Table 3-3. There are auction variables, house variables, and others. This study chooses two models for each comparison. In the semi-parametric-model the first model is used as a benchmark model, the second model is chosen between the generalized additive model and the spline model to smooth the estimate. In the parametric-model the first model is used as a benchmark model, the second model is chosen by add- or drop-variables in model selection. The empirical model, a benchmark model, is shown as follows:.
(12) 96 住宅學報. log(HPi)=β0＋β1(snoi)＋β2(hsi)＋β3(agi)＋β4(tfi)＋s1(proi)＋s2(lai)＋s3(fi)＋s4(sb1i)＋s5(sb2i)＋ s6(sc1i)＋εi ................................................................................................................................ (6) where β0 is intercept, β1～β4 are coefficient of parametric, S1～S6 are coefficient only in the semi-parametric model (or β5～β11 in the parametric model), and εi is error term, we have εi～N(0,σ).. 3.4 The predicted results of the semi-parametric/ parametric modeling The parametric-models were chosen by three criteria (smaller then one t-value variable drop, max AdjR2, and min Root MSE). And the semi-parametric-models were chosen by two rules, the rules are the smaller backfitting times and the smaller deviance of the final estimate. The indicators found that for the better models, the criteria are exhibited in Table 3-5. Table 3-6 and Table 3-7 show the better semi- parametric /parametric-models results from the years 2001 to 2003. We found important factors such as handing over term by term, the bid times, total reservation price, house total size and age all have significance in the winning-bid price model. The positive contributing factors included the handing over term by term (PRO), total reservation price (STP) and house total size (HSIZE). The negative contributing factors are shown as bid times (SSNO1) and age (AGE). The others were vague in the direction for the winning-bid price. In addition, we added the spatial factors which adopted the GIS system and the distance with the significant landmarks. The signs include the Taipei 101 high-rise building, small and big regional Park, the rapid transit system and Sin-Kua department store in the main Train station. Table 3-5. The Parametric / Semi-Parametric-model- Chosen Criteria The Parametric-model-chosen criteria---Adj R2 Year. Model 1 Model 2. 2001. 0.9360. Model 2. 0.9170. 0.1197. 0.1348. 2001. 2002. 2003. -. 5. 0.1140. The Semi-Parametric-models chosen criteria---Backfitting Year. Model 1 Model 2. 6. 0.9253. Model 2. 1.8796 -. 0.9173. 0.1162. 5. The Semi-Parametric-models chosen criteria---Deviance of the Final Estimate Model 1. 2003. 0.9235. The Parametric-model-chosen criteria---Root MSE Model 1. 2002. 10.6644 5.4389. 0.1340. 5 5. 6.2806 6.2293.
(13) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 97. Table 3-6. Estimate of the Better Fitted Parametric Model (Taking into Consideration the Auction Price Modeling) Model A Variables. Expected Sign. Intercept ssno1 stp. pro. hsize size2 Sb1 Sb2 age sc1. totflor floor. floor2 la. gdp Adj R2. － ＋ ＋ ＋ ＋ ＋ ＋ － ＋ ＋ － ＋ ＋ ＋. Note: * P-value significance level 10% ** P-value significance level 5%. 2001. Taipei City 2002. 2003. 4.9214**. 5.4498**. 4.9115**. 0.0017**. 0.0018**. 0.0018**. 0.0032**. 0.0033**. -0.0132** 0.0217*. 0.0016** 0.0268 0.0189. 0.0012** 0.0165. -0.0005. -0.0026**. 0.0018. -0.0030**. 0.015. -0.0093 0.0009. 0.0255** 0.0001 0.936. 0.004. 0.0020** 0.0022** 0.0317** 0.0252** 0.0677* -0.001. 0.0346**. 0.0462**. 0.9253. 0.9173. -0.0001*. 0.0001*. The Table 3-8 and Table 3-9 show the results of the better models with additional factors of spatial from the year 2001 to 2003. We found that the important factors are similar to the results of Table 3-6 and Table 3-7 adding up the distance from the small regional Park. The distance from the small regional Park show a positive contribution on the winning-bid price model. The best fitted model was selected by the criteria of RMSE, MAPE, AS-Ratio mean, variance and Hit Ratio. The 10% out-sample forecast model final results are shown in Table 3-10. The RMSE, MAPE criteria show the out-sample forecast model results are consistence, the Semi-Parametric Models(with or without the Spatial Factors for Auction Price Modeling; Model D & Model B) come out the smaller RMSE, MAPE. AS Ratio AVG criteria indicate the Parametric Models (Model A & C) are over-valuation price. However, both models show the variance of the AS Ratio are not over 15%~25%. Finally, The higher Hit Ratio of Model B & D defines the small gap between the actual value and the forecast value in the Semi-Parametric Models. We also set up the search market model by the data from the transaction sales cases from the official transaction sales data banks (see Table 3-11). We found the factors which contributed to the search market price were given by house size (hsize / Builarea), the road width (Road_w) and location (la). The less contributing factors to the search market price were found as house type (Type), house.
(14) 98 住宅學報. Table 3-7. Estimate of the Better Fitted Semi-Parametric Model (Taking into Consideration the Auction Price Modeling) Model B Variables. Intercept SSNO1 PRO SB1 SB2 AGE SC1 LA TOTFLOOR FLOOR Linear(SSNO1) Linear(STP) Linear(HSIZE) DF Spline(SSNO1) Spline(STP) Spline(HSIZE). Expected Sign. 2001 5.1840**. + + + + + + + +. 0.0144** 0.0182** 0.0030 -0.0012** -0.0028 0.0036 0.0007 0.0006 0.0059 0.0019** 0.0015**. + +. 3.9361** 13.2287** 3.1676**. Note: * P-value significance level 10% ** P-value significance level 5%. Taipei City 2002 5.1826** 0.0098**. 2003 5.1849**. 0.0098 0.0183** -0.0012**. 0.0182** 0.0097. 0.0187 -0.0012**. 0.0136**. 0.0019** 0.0021**. 0.0050* 0.0019** 0.0015**. 18.5082** 2.7846**. 3.0000** 19.2286** 2.9352**. age and house stay-floor. In addition, the auction housing characters put in the deepest contributes in housing modeling. Especially the reservation bid price have the extensive effect on auction price. Some of spatial factors did put significant effects on the pricing auction market such as the distance factors from park (SDIST/ BDIST) and the Taipei 101 high-rise building areas (S_101CDIS). The rapid transit system may not be significant in this study, it is a surprise result. We suggest checking the modeling or the GIS system measurement on the distance for further research in the spatial factors side.. 3.5 Comparison between the Semi-parametric and Parametric Modeling We evaluate the housing price respectively by year and by type. In this study we applied the semi-parametric and parametric modeling results. After that, we derived the standard housing price based on 2001 housing characters (see Table 3-12). The empirical results using parametric modeling for measurement and prediction might bring a big-gap (say max 73%) between the search market and the auction market, and using the semiparametric approach might bring the price into a small-gap (about 25% to 30%). Similar results were discovered by adding spatial factors, in which both semi-parametric and parametric modeling might result in a small-gap (about 22% to 30%). Overall, the semi-parametric modeling with or without.
(15) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 99. Table 3-8. Estimate of the Better Fitted Parametric Model (with the Spatial Factors for Auction Price Modeling) Model C Variables Intercept SSNO1 STP. PRO. HSIZE SIZE2 SB1 SB2. AGE SC1. TOTFLOR FLOOR Floor2 LA. GDP Q1. SDIST. BDIST. STDIST. S_101DIS. _MODEL_. _P_. 2001. 2002. 2003. PARMS. PARMS. PARMS. -0.0122*. -0.0001. 0.0071. 4.9071** 0.0017** 0.0244** 0.0034** 0.0014** 0.0283 0.0188. 5.4767** 0.0018** 0.002. 0.0034** 0.0011** 0.015. 0.0273**. -0.0008. -0.0021**. 0.0013. -0.0042**. 0.0142. -0.0099. 0.0009*. 0.0319** 0.0001*. 0.0553. -0.0018 0.0002. 0.035**. -0.0001**. 4.883** 0.0019** 0.002. 0.0022** 0.0015** 0.0286. 0.0373** 0.0004** 0.0478. -0.0015** -0.0059 0.0003. 0.047**. 0.0001**. -0.0001*. -0.0001** 0 0 19. m1. -0.0001** 0 0 0 19. 0.0121. 0.0169* 0.0135. m1. 0.0375** 19. _EDF_. 525. 918. 920. N-P-1. 525. 918. 920. N-1. _RMSE_ _RSQ_. Adj-RSQ. 543 0.1131. 0.9393 0.9372. Note: * P-value significance level 10% ** P-value significance level 5%. 936 0.1198. 0.9253 0.9239. m3. 938 0.1346 0.9256 0.9241.
(16) 100 住宅學報. Table 3-9. Estimate of the Better Fitted Semi-Parametric Model (with the Spatial Factors for Auction Price Modeling) Model D Variables. Expected Sign. 2001. Intercept. +. 5.1748 **. PRO. +. 0.0138 **. SB2. +. 0.0018. SSNO1 SB1. -. +. AGE. -. SC1. +. TOTFLOOR. +. LA. FLOOR. + -. SCDIST. +. STCDIST. +. BCDIST. S_101CDIS. Linear(SSNO1) Linear(STP). Linear(HSIZE) DF. Spline(SSNO1) Spline(STP). Spline(HSIZE). Note: * P-value significance level 10% ** P-value significance level 5%. + + -. + + -. + +. 0.0198 ** -0.0014 ** -0.0060 0.0070 0.0008 0.0008. Taipei City 2002. 5.1778 ** 0.0090 ** 0.0114. 0.0182 **. -0.0012 ** 0.0201. -0.0010 **. 0.0112 **. 0.0102 **. 0.0048. 0.0114 *. 0.0081 -0.0011. 0.0068 *. 0.0019 ** 0.0016 ** 3.7202 **. 13.0747 ** 3.1429 **. 0.0019 ** 0.0022 **. 18.4071 ** 3.0054 **. 2003. 5.1255 ** 0.0178 ** 0.0216 ** 0.0142 *. 0.0154 **. 0.0097 0.0095. 0.0187 ** 0.0066 ** 0.0020 ** 0.0015 ** 3.0000 **. 20.0417 ** 2.6782 **. spatial factors is better than parametric modeling. We can more accurately predict housing prices using the semi-parametric approach.. 4. Conclusion According to the above analyses, the summary of conclusions of our study is as follows:. 4.1 Interpreting Statistical Results In both markets, the auction and search market share common factors such as the house price. The auction-factors include handing over term, the bid times, and the total reservation price. The.
(17) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 101. Table 3-10. The Out-Sample Criteria for the Estimate of the Better Fitted Model (with/without the Spatial Factors for Auction Price Modeling) YEAR. 2001. Root MSE (RMSE). 2002. 2003. Model A (in TABLE 3-6). 120.35. 156.01. 135.34. Model C (in TABLE 3-8). 109.77. 146.30. 184.28. Model B (in TABLE 3-7). 41.03. Model D (in TABLE 3-9). 134.08. 51.97. MAPE. 54.10. 74.43. 56.88. Model A (in TABLE 3-6). 10.87%. 12.52%. 13.27%. Model C (in TABLE 3-8). 10.62%. 12.24%. 14.89%. Model A (in TABLE 3-6). 1.0086. 1.0226. 1.0271. Model C (in TABLE 3-8). 1.0003. 1.1636. 1.0484. Model B (in TABLE 3-7). 4.62%. Model D (in TABLE 3-9). 7.79%. 5.68%. AS Ratio AVG. Model B (in TABLE 3-7). 9.66%. 0.9476. Model D (in TABLE 3-9). 9.77%. 0.9756. 0.9984. AS Ratio cv (%). 7.17%. 0.9555. 1.0011. 1.0035. Model A (in TABLE 3-6). 14.37%. 16.88%. 16.70%. Model C (in TABLE 3-8). 13.98%. 14.32%. 17.25%. Model B (in TABLE 3-7). 23.03%. Model D (in TABLE 3-9). Hit Ratio. 15.94%. 7.01%. 5%. 10%. 24.24%. 11.90%. 20%. 5%. 10%. 12.32% 20%. 5%. 10%. 20%. Model A (in TABLE 3-6) 25.00% 42.00% 89.00% 28.00% 51.00% 86.00% 24.00% 52.00% 77.00%. Model B (in TABLE 3-7) 56.92% 87.69% 95.38% 31.82% 80.00% 98.18% 33.07% 64.57% 92.91% Model C (in TABLE 3-8) 25.00% 45.00% 91.00% 26.00% 50.00% 88.00% 24.00% 50.00% 75.00% Model D(in TABLE 3-9) 53.85% 84.62% 99.00% 22.73% 42.73% 78.18% 25.20% 53.54% 81.89%. house character-factors are house total size and age; the more contribute to the search market price factors are given by house size, the road width and location. In additions, some of the spatial factors did put a significant effect on pricing the auction market such as distance from small regional Parks. Location and house size are the important variables in every submarket as expected. The influence of the stayed-floor at the same time should not be ignored in each market. If one considers location to be the horizontal accessibility (to the CBD) indicator, stayed-floor to be the vertical.
(18) 102 住宅學報. Table 3-11. Estimate of the Better Fitted Model (Taking into Consideration the House-Search Market Price Modeling) Variables. Expected Sign. Intercept. ROADW. +. LA. +. TOTFLOOR. +. ZON. +. TYP. -. Linear(ROADW). +. Linear(AGE). -. Linear(BUILAREA) Linear(FLOOR). + -. Note: * P-value significance level 10% ** defined P-value significance level 5%. Taipei City. 2001. 2002. 5.4429 **. 5.4844 **. 5.4392 **. 0.1979 **. 0.1995 **. -0.1091 **. -0.0411 **. 0.0085 **. 0.0087 **. 0.0012 *. 0.0032 **. 0.0059. 0.1991 **. -0.0242. -0.0659 ** 0.0086 **. -0.0025 ** -0.0127 **. 2003. -0.0253. -0.0030 ** -0.0114 **. 0.0213. 0.0020 **. -0.0044 ** -0.0055 **. Table 3-12. Court Auction Residential Housing Prices 2001-2003 (in Nominal Prices) Data. Year. 2001. 2002. 2003. Existing House Market Price (EHMP) (a). Parametric model. 553.11. 566.86. 557.51. Semi-parametric model. 565.04. 565.38. 563.6. Auction House Successful-bid Price (AHFBP) (b). Parametric model. 421.30. 327.94. 478.14. Semi-parametric model. 431.28. 445.94. 448.17. Parametric model. 433.62. 450.52. 456.96. Semi-parametric model. 433.99. 450.48. 455.26. 31.29%. 72.85%. 16.60%. 31.01%. 26.78%. 25.76%. 27.56%. 25.82%. 22.00%. 30.20%. 25.51%. 23.80%. Auction House Successful-bid Price Added Spatial factor (AHFBP/Spatial) (b) Discount ratio(/Premium) Non Added Spatial factor. Added Spatial factor. (a-b)/b% Parametric model – AHFBP vs. EHMP Semi-parametric model – AHFBP vs. EHMP Parametric model – AHFBP/ Spatial vs. EHMP Semi-parametric model – AHFBP/ Spatial vs. EHMP.
(19) A Comparison between the Semi-parametric and Parametric CAMA Modeling of... 103. accessibility (to the first floor) indicator, house size (Floor-area) or land size to be the profitability of space, one will realize that the space size of a city is the most influential factor of the real estate price. In general, the greater the floor-area we have, the higher the total price. The coefficients of typecategory of each submarket model can reflect the quantitative change from the standard values, which can be applied to real estate price estimation.. 4.2 The Results of Forecast Comparison The RMSE, MAPE criteria show the out-sample forecast model results are consistence, the Semi-Parametric Models(with or without the Spatial Factors for Auction Price Modeling) come out the smaller RMSE, MAPE. AS Ratio AVG criteria indicate the Parametric Models (Model A & C) have over-valuation price. However, both models show the variance of the AS Ratio are not over 15%~25%. Finally, The higher Hit Ratio of Semi-Parametric Models define the small gap between the actual value and the forecast value. By means of parametric modelling of measurement and prediction might bring a big-gap between the search market and auction market. The use of semi-parametric modelling might bring the smallgap about 25% to 30%. Similar results exposed by adding spatial factors, both semi-parametric and parametric modelling might bring the small-gap to about 22% to 30%. Overall, the semi-parametric modeling with or without spatial factors is better than parametric modeling. We can more accurately predict housing prices in the semi-parametric approach..
(20) 104 住宅學報. References Anglin, P. M. & R. Gencay 1996 “Semi-parametric Estimation of Hedonic Price Function,” Journal of Applied Econometrics. 11:633-648. Bin, O. 2004 “A Prediction Comparison of Housing Sales Price by Parametric Versus Semi-parametric Regressions,” Journal of Housing Economics. 13:68-84. Clapp, J. M. 2004 “A Semi-parametric Method for Estimating Local House Price Indices,” Real Estate Economics. 32(1):127-160. Clapp, J. M. 2004 “A Semi-parametric Method for Valuing Residential Locations: Application to Automated Valuation,” The Journal of Real Estate Finance and Economics. 27(3):303-320. Clapp, J. M., C. Giaccotto and D. Tiroglu 1991 “Housing Price Indices: Based on All Transactions Compared to Repeat Subsamples,” AREUEA Journal. 19(3):270-285. Dotzour, M. G., E. Moorhead & D. T. Winkler 1998 “The Impact of Auctions on Residential Sales Prices in New Zealand,” The Journal of Real Estate Research. 16(1):57-71.. Gencay, R. & X. Yang 1996 “A Forecast Comparison of Residential Housing Prices by Parametric versus Semiparametric Conditional Mean Estimators,” Economics Letters. 52:129-135. Hastie T. & Tibshirani R. 1990 Genernalized Additive Models. New York: Chapman & Hall. Li, M. M. & H. J. Brown 1980 “Micro Neighborhood Externalities and Hedonic Housing Prices,” Land Economics. 56(2):125-141.. Lin, V. C. C. 1996 “The Robust Study on Rental Housing Modeling - The Outlier Analysis,” Journal of Housing Studies. 4(1):51-72 (in Chinese with English Abstract).. Lin, V. C.C., F.T. Tsai & C.O. Chang 1997 “The Study of Price Factors on the Auction Hosing Market in Taipei City,” Conference of Chinese Society of Housing Studies, Taipei, Taiwan, R.O.C. (in Chinese). Lusht, K. M. 1996 “A Comparison of Prices Brought by English Auctions and Private Negotiations,” Real Estate Economics. 24(4):12-130. Marcus, A..
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