Empirical Results
5.1 Non-spatial Modeling and Spatial Heterogene- Heterogene-ity
As touched upon in the methodology section, the OLS model does not allow for proper spatial modeling of the housing market. Nevertheless, the simplified model should always be estimated as to have certain baseline results of the analysis. Moreover, it is assumed, like in the study of Lipán (2016), that once the non-spatial model filters out all housing characteristics, which are modeled via functional form (3.1), the estimate of the non-systematic element of DGP (the residuals) will provide major foundings regarding the unobserved effect of the location. The main contribution, expending the study of Lipán (2016) is the area of the entire Czech Republic, which we analyze, as well as the more enhanced model functional form and the identification of the "grandiose clusters" and the housing submarkets.
As also mentioned in the methodology section, the multiple model approach 4.4 is utilized. We are fully aware that there are certain drawbacks of the multiple model approach. For instance, our approach assumes that real estate markers within each region are not effected by market in other region. This simplifi-cation, however, is very necessary for an empirical analysis as working with the spatial weight matrix WWW, with extensively large n is not computationally manageable and would challenge a lot of non-linear solvers that are essential for spatial model estimation.
When performing any type of empirical analysis, certain assumptions about the used dataset must be established. In the data filtering process, certain limits and thresholds were discussed and established and then the observations were filtered accordingly. This means that our analysis and inferences are exclusively limited to the real estate properties, which are within the set boundaries. For instance, our results do not necessarily hold for the real estates outside the price intervals specified in Table 3.1. However, all of the specified intervals and boundaries were set thoughtfully, and hence our dataset should cover common and slightly divergent types of estates, which are typically present in the entire housing market.
Also, following the steps of Lipán (2016), the following assumptions of the obtained real estate records from the server sreality.cz are determined:
• The real estate server sreality.cz contains real estates that are represen-tative of the true underlying housing market in the Czech Republic.
• All of the listed estates and their specified characteristics (including the address) are true characteristics of all given estates advertised.
• All of the listed prices of all estates are denoting the true market price.
Or, at the very least, are within a reasonable distance of the true market price.
5. Empirical Results 50
The empirical results and coefficient estimates of the model 3.1, estimated via 4.1.1, for each region of the republic, are summarized in the table 5.1. In this models, all of the coefficients are in the percentage effect, see 3.1. Table 5.1 features all of the estimated coefficients as well as all off the relevant information for discussing the key price determinants of the housing markets of flats. For consistency, we also provide various metrics of in-sample model fit, i.e. the log-likelihood function, the Akaike and Bayesian information criteria AIC and BIC respectively) and pseudo coefficient of determination, given as R2pse = corr(y, yˆ)2.
Note that these metrics cannot be compared between the regions (each column of the table) but rather between all models for each particular region.
Table5.1:OLSModel OLSModel DependentVariable:LogofPrice (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) Meters0.012∗∗∗0.011∗∗∗0.008∗∗∗0.010∗∗∗0.005∗∗∗0.006∗∗∗0.008∗∗∗0.010∗∗∗0.004∗∗∗0.008∗∗∗0.007∗∗∗0.008∗∗∗0.008∗∗∗0.010∗∗∗ (0.001)(0.0004)(0.0005)(0.0001)(0.0004)(0.001)(0.001)(0.0004)(0.0003)(0.001)(0.0003)(0.0002)(0.001)(0.0004) Room−0.0020.0010.002∗∗−0.001∗∗∗0.006∗∗∗0.002−0.004∗∗∗0.009∗∗∗0.004∗∗−0.005∗∗∗0.007∗∗∗0.003∗∗0.0020.001 (0.002)(0.001)(0.001)(0.0004)(0.001)(0.001)(0.001)(0.002)(0.002)(0.001)(0.002)(0.001)(0.001)(0.003) Floor−0.017∗∗∗0.024∗∗∗0.027∗∗∗0.0010.018∗∗0.029∗∗∗−0.0040.0040.023∗∗0.044∗∗∗0.041∗∗∗0.0070.035∗∗∗0.001 (0.005)(0.008)(0.007)(0.002)(0.007)(0.011)(0.008)(0.003)(0.009)(0.008)(0.005)(0.005)(0.010)(0.005) FloorZero−0.049∗0.0030.009−0.088∗∗∗0.041−0.069−0.046−0.052∗∗−0.089∗∗−0.0140.064∗∗0.011−0.066∗−0.078∗∗∗ (0.030)(0.036)(0.031)(0.014)(0.039)(0.047)(0.038)(0.025)(0.039)(0.040)(0.026)(0.020)(0.037)(0.028) FloorTop0.048∗−0.142∗∗∗−0.045∗−0.0180.008−0.147∗∗∗0.033−0.076∗∗∗−0.210∗∗∗−0.126∗∗∗−0.124∗∗∗−0.016−0.098∗∗∗−0.072∗∗∗ (0.027)(0.031)(0.027)(0.013)(0.031)(0.042)(0.040)(0.023)(0.035)(0.035)(0.022)(0.017)(0.034)(0.025) Buildingtype:Concrete−0.079∗∗∗−0.361∗∗∗0.058∗−0.240∗∗∗−0.090∗∗∗−0.083∗−0.130∗∗∗−0.082∗∗∗−0.108∗∗∗−0.073∗∗−0.028−0.057∗∗∗−0.001−0.017 (0.024)(0.029)(0.030)(0.013)(0.031)(0.046)(0.036)(0.021)(0.038)(0.037)(0.028)(0.021)(0.036)(0.028) Condition:Verygood0.176∗∗∗0.223∗∗∗0.146∗∗∗0.026∗∗0.121∗∗∗0.136∗∗∗0.060∗0.122∗∗∗0.147∗∗∗0.170∗∗∗0.072∗∗∗0.081∗∗∗0.117∗∗∗0.119∗∗∗ (0.021)(0.027)(0.027)(0.012)(0.030)(0.039)(0.033)(0.020)(0.034)(0.033)(0.024)(0.019)(0.031)(0.026) Condition:Afterreconstruction0.199∗∗∗0.254∗∗∗0.160∗∗∗0.077∗∗∗0.156∗∗∗0.0730.178∗∗∗0.247∗∗∗0.243∗∗∗0.130∗∗∗0.186∗∗∗0.0090.189∗∗∗0.200∗∗∗ (0.027)(0.035)(0.036)(0.015)(0.043)(0.055)(0.043)(0.026)(0.045)(0.043)(0.028)(0.024)(0.042)(0.034) Private0.287∗∗∗0.379∗∗∗0.308∗∗∗0.224∗∗∗0.087∗∗∗0.200∗∗∗0.180∗∗∗0.270∗∗∗0.193∗∗∗0.242∗∗∗0.072∗0.084∗∗∗0.107∗∗0.094∗∗ (0.020)(0.088)(0.058)(0.015)(0.033)(0.053)(0.038)(0.018)(0.041)(0.049)(0.037)(0.027)(0.044)(0.043) Kitchenette0.070∗∗∗0.109∗∗∗0.245∗∗∗0.0050.120∗∗∗0.292∗∗∗0.070∗∗0.178∗∗∗0.171∗∗∗0.096∗∗∗0.201∗∗∗0.116∗∗∗0.094∗∗∗0.003 (0.026)(0.030)(0.029)(0.011)(0.030)(0.037)(0.032)(0.022)(0.039)(0.031)(0.024)(0.017)(0.034)(0.029) Balcony/Terrace0.064∗∗0.221∗∗∗0.158∗∗∗0.038∗∗∗0.107∗∗∗0.156∗∗∗0.102∗∗∗0.096∗∗∗0.0350.067∗∗0.104∗∗∗0.108∗∗∗0.133∗∗∗0.129∗∗∗ (0.025)(0.027)(0.027)(0.010)(0.026)(0.035)(0.034)(0.018)(0.030)(0.032)(0.019)(0.016)(0.027)(0.022) Garage−0.077∗0.077∗∗−0.025−0.0020.0170.0700.133∗∗∗0.161∗∗∗0.037−0.085∗0.122∗∗∗0.068∗∗∗0.0030.040 (0.041)(0.035)(0.031)(0.011)(0.039)(0.050)(0.039)(0.032)(0.042)(0.046)(0.024)(0.019)(0.039)(0.034) Concrete×NewEstate0.1470.833∗∗0.175∗0.278−0.419∗∗∗0.417−0.200−0.781∗∗0.219−0.109 (0.248)(0.411)(0.092)(0.362)(0.144)(0.254)(0.332)(0.333)(0.173)(0.252) Brick×NewEstate0.951∗∗∗0.347∗∗∗0.182∗∗∗−0.034∗∗0.360∗∗∗0.272∗∗∗0.389∗∗∗0.255∗∗∗0.376∗∗∗0.075−0.0080.114∗∗∗0.137∗∗∗0.403∗∗∗ (0.113)(0.051)(0.037)(0.014)(0.050)(0.058)(0.054)(0.044)(0.051)(0.051)(0.029)(0.022)(0.042)(0.038) Constant12.961∗∗∗13.166∗∗∗13.609∗∗∗14.822∗∗∗14.182∗∗∗14.008∗∗∗14.097∗∗∗13.422∗∗∗14.142∗∗∗13.865∗∗∗14.322∗∗∗14.290∗∗∗13.874∗∗∗13.981∗∗∗ (0.048)(0.099)(0.073)(0.023)(0.056)(0.080)(0.067)(0.038)(0.059)(0.073)(0.049)(0.039)(0.067)(0.060) Log−like-1183.748-664.822-221.842-172.185-337.512-432.358-281.238-767.66-364.792-175.31-434.086-366.498-59.477-14.71 AIC2399.4951361.643473.684376.37707.024894.717594.4751567.319759.584382.619900.172764.996148.95461.421 BIC2489.7911444.179544.915474.089783.411963.343667.8981656.845830.15452.755984.284853.198211.467133.489 R2 pse.0.3850.6430.4230.7190.3830.3540.5190.5220.4360.3520.4620.4880.4780.662 Observations2,0871,2858533,3198757177271,9898165921,4181,831477668 Note:∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
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Empirical Results 5.1 Non-spatial Modeling and Spatial Heterogeneity
As is seen, the coefficients on the variable Meters have (expected) positive and significant magnitude. This is the case for every single region. The variables Room and Floor and its derived values do not seem significant nor have high magnitudes. On the other hand, interestingly enough, the Floor zero is neg-atively perceived in the case of the capital city, and also in the Zlin region, which much lower certainty, however. Secondly, we can see that the factors of Building condition, Building type and theType of ownership are determined with quite a strong effect on the price of an estate. These effects are (mostly) very strong among all fourteen regions. This provides support for our certainty that building types and conditions are also key price determinants.
The main downside of estimated models thus far is the fact that the spatial nature of the housing data is not modeled. The first indicator of this phe-nomenon, as can be expected, is supported by the absence of homoscedasticity within the residuals of all models. The Breusch-Pagan (Wooldridge 2010) test results, for each region, can be observed in the table 5.2.
Table 5.2: Breuch-Pegan and Jaque-Berra Tests for OLS models.
Region Name B-P test B-P p-value J-B test J-B p-value
Aussig 124.100 0.000 61.720 0.000
Carlsbad 39.720 0.000 109.100 0.000
Pilsner 56.290 0.000 598.000 0.000
Capital city Prague 275.800 0.000 4,993.000 0.000 South Bohemian 122.000 0.000 399.000 0.000
Hradec Králové 55.900 0.000 74.040 0.000
Liberec 55.750 0.000 500.600 0.000
Moravian-Silesian 430.400 0.000 8,433.000 0.000
Olomouc 212.100 0.000 554.200 0.000
Pardubice 63.820 0.000 189.700 0.000
South Moravian 169.700 0.000 75.390 0.000 Central Bohemian 202.800 0.000 2,605.000 0.000
Vysocina 34.280 0.000 376.200 0.000
Zlín 35.310 0.000 284.000 0.000
The null hypothesis of homoscedasticity is rejected and thus Heteroscedasticity is assumed. To account for assumed Heteroscedasticity, the bootstrap stan-dard errors were obtained. Then, moving toward the spatial frameworks, The Moran’s Tests and the Moran’s scatterplot are conducted in order to explore the spatial dependence within the flat real estate market.
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The results of the Moran’s I tests are presented in the table 5.3. It clearly evidences a presence of an extensively strong spatial dependence within the housing market.
From the methodological point of view, this supports the validity of utilizing the spatial methodology in the empirical analysis. Moreover, the empirical results until now shall be taken with great awareness as clearly, the non-spatial methodology is neglecting essential patterns within the data.
Table 5.3: Moran I test for all Regions (Flat Estates)
Region Name Moran I-statistic Expectation Variance p-value
Aussig 0.547 -0.0004 0.00005 0.000
Carlsbad 0.596 -0.001 0.0001 0.000
Pilsner 0.343 -0.001 0.0001 0.000
Capital city Prague 0.348 -0.0003 0.00003 0.000
South Bohemian 0.426 -0.001 0.0001 0.000
Hradec Králové 0.484 -0.001 0.0001 0.000
Liberec 0.527 -0.001 0.0001 0.000
Moravian-Silesian 0.535 -0.0005 0.0001 0.000
Olomouc 0.543 -0.001 0.0001 0.000
Pardubice 0.421 -0.001 0.0002 0.000
South Moravian 0.437 -0.001 0.0001 0.000
Central Bohemian 0.386 -0.0005 0.0001 0.000
Vysocina 0.372 -0.002 0.0002 0.000
Zlín 0.388 -0.001 0.0001 0.000
Each individual Moran’s scatterplots are presented in the figure 5.1 and also evidence a strong positive relationship and presence of strong spatial auto-correlation. This can be concluded by the significant and positive slope of all regression lines. In the next section, the results of spatial frameworks are discussed.
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Empirical Results 5.1 Non-spatial Modeling and Spatial Heterogeneity
Vysocina Zlín
Pilsner South Bohemian South Moravian
Moravian-Silesian Olomouc Pardubice
Central Bohemian Hradec Králové Liberec
Aussig Capital city Prague Carlsbad
13 14 15 13 14 15 16
Figure 5.1: Moran’s Scatter Plots of Each Region
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