Table 4 shows the empirical results of models (1) and (2). Amongst the results, the fit criteria (
R ) of model (1) is 0.7306, and model (2) can be
2 divided into two sub-models: one is model (I) with no interaction terms, itR is 0.7262, and the other, model (II), has interaction terms, it
2R is 0.755.
2 The three models do not explain much, and almost all variables in the models keep with the claimed expected direction of the third section, and having 1%significant effect (in addition to the variable, “handover or not”, and its interaction term aren’t significant; vacancy or not and its interaction term, their variable is only significant at 10% level), indicating that the adopting variables explains well in models.To be more detailed, in the case of a situation where
"other variables remain unchanged", each variable’s influence on “direction and coefficient” on real estate is as follows:
(1) In terms of control variables in “quality” category, with other items being under equal circumstances: (a) the linear term and quadratic term’s coefficient of the situated floor (X1) and the situated floor square (X2) in model (1) and (2) are separately negative and positive, which means that the situated floor’s impact on total price is a “negative then positive”, non-linear relationship. (b) The total floors’ (X3) coefficient in model (1) and (2) are both “positive,” which means the higher the total of floors in buildings more impacts pricing. (c) The linear term and quadratic term’s coefficient of floor area (X4) and floor area square (X5) in models (1) and (2) are separately positive and negative, and this once again proved floor area’s impact on price as being “positive then negative.” When the floor area increases, so does the price, but any increase to a certain floor area means that its impact on total price gradually becomes more negative because of diminishing marginal utility. (d) Held land area’s (X6) coefficient in models (1) and (2) are “positive,” meaning that the larger the held land area, the higher the total price. (e) About location variables: a new urban variable (X7_L1) in models (1) and (2) are both “positive,” representing the new urban area’s functions and environmental quality of life as being better than in old urban areas, so
location conditions have a positive impact on total price. To the contrary, the suburbs’ variables (X7_L2) in models (1) and (2) are both “negative,”
meaning suburbs, compared to older urban areas, are poorer in location conditions, so the location conditions have a negative impact on total price.
(2) In terms of empirical results of “market mechanism variables (C)”: Under the same "housing quality” circumstances, the model’s (1) coefficient, -0.18871, reaches a “negative effect” at 1% significant level. After calculation of the converting coefficient, we found that a foreclosed house’s average discount rate is higher than the search market by 17.20%15. It proves that the two different “market mechanisms” of pricing certainly are one of the main factors that makes foreclosed housing’s price lower than search market’s price. The same result appears in model (2) (coefficient in interaction terms’ two sub-models are separately -0.18772 and -0.18709, and it reaches “negative effect” at 1% significant level). Therefore, under a different estimate model, foreclosed housing’s average discount rate is more robust than search market’s; it is within about 20%).
(3) In terms of “market risk”: under “housing quality” and “foreclosure or search house of constant sample circumstances:
a. "Handover or not (M1)": though the coefficient, -0.00953, in model (2, I) is “negative”, it does not have a significant impact; coefficient 0.01751 in model (2, II), and its coefficient of interaction term, -0.02578, are no different from 0 at 10% significant level. This study deeply discusses the reasons that may be the result in Taiwan’s foreclosed housing market.
Handover or not cannot completely guarantee that the winning bidder gets complete ownership. Although the house has handovered, the bidder might face the original tenants or occupants who demand the bidder pay relocation costs to leave, or the house’s destruction; ownership risks
15 Semi-logarithmic model takes its virtual independent variables, and its percentage calculation method of the dependent variable Y’s impact is : anti log (β) -1. So the market mechanism variables’ influence rate on price is anti log (-18.78%) -1 = 17.20%.
remain in existence. Therefore, whether handover or not, there is no significant effect on price.
b. “Vacancy or not (M2)”: the coefficient, 0.0562, in model (2, I) (which is significant at a 1% level), has a “positive” impact on price. After the calculation of the converting coefficient, we found that the average impact rate is at 5.78%16, meaning the lower the occupation risk, the higher the prices. In addition, the coefficient in model (2, II) is 0.0493 (t = 2.05, the coefficient is significant at 5% level), and its interaction term is 0.06172 (t
= 1.70, the coefficient is significant under 10% level), so this study believes that the above may be related to the source restriction of
“vacancy” information; setting “intermediary search samples (C = 0)” as
“vacant house (M2 = 0)” causes this error. Because it may mix with samples that are both “foreclosure (C = 1)” and “vacant house” (C * M2 = 0), which cannot be differentiated and estimated, its effect does not reach 1% effect.
(4) In terms of “market competition (M3)”: under the same “housing quality”,
“foreclosure or search house”, and “market risk,” the coefficient in model (2, I) is -0.15991 (which is significant at 1% level); the coefficient in model (2, II) is -0.16002 (t = -13.56, the coefficient is significant at a 1% remarkable effect); and its coefficient of interaction term is -0.15975 (t = -19.44, the coefficient is significant at 1% level). So, the three coefficients do not differentiate much. We found, after calculation of converting coefficient, that when there is only one bidder, the foreclosed housing price discount was 15.99%17; when there are two bidders, the discount reduces to 7.995%; if there are five bidders, the discount is only 3.198%. It reveals the lower degree of market competition; the larger seriousness of the discount situation;
16 Same as note 17’s calculation logics, anti log (5.62%)-1=5.78%
17 Take the average of three coefficients, 15.99%, as an example. This study takes a composite of bidder numbers as a measure of the degree of competition. When there is one bidder, the variable is 1/1, and their impacts on price is 1 × (-- 15.99%) = 15.99%. When there are two bidders, the variable is 1/2, and their impacts on price is 1/2 × (15.99%) = 7.995%. So, when the number of bidder changes, its impacts on price can be calculated by these methods.
and the higher the degree of market competition, foreclosed house’s price would increase because of bidding, so a low degree of competition could easily lead to a foreclosed house deviated from real market prices. Figure 3’s first half part is based on Quan (1994) and Mayer’s (1998) “theory”
relationship diagram of market price undercutting and the number of bidders;
the second half part is in accordance with the empirical results of this study charted “empirical” relationship diagram of price undercutting and the number of bidders. Both of the diagrams match perfectly, which means, with an increasing number of bidders, the market price difference will show a diminishing marginal slope on a nonlinear curve, approximating to market price. The effect in terms of this study’s samples, when there are less than six bidders, along with an increasing number of bidders, the shrinking of the foreclosed discount rate grows, but when it is more than six bidders, the shrinking effect of the foreclosed discount is slightly lowered. So, here it is shown that there is an interesting phenomenon: when there are over twenty bidders, foreclosed houses are at the state of a slight discount, which does not, as foreign documents show, that auction may also be subject to the premium phenomenon. This study has discussed the possible reasons in the introduction section: foreclosure, in quality of invisible product, still reflects the pattern of financing (such as how to pay off all prices in such a short time, and even shorter loan time), safety transactions (such as handover or not), and other risks, so discount reflects risk premium in these sections.
Overall, the three empirical models show: the coefficient of the “housing quality” variable does not change a lot because of the extension of market mechanism variable, which causes excessive fluctuation. Its coefficient is only differentiated before the third decimal point. According to Quan’s (1994) view, most of a market mechanism’s impacts on pricing in a model (1) can be explained by model’s and (2) extended by variables, such as handover or not, vacant house or not, and the degree of market competition. Furthermore, “the degree of competition variables” is significant in the mode of the two sub-models and a variety of robust testing models; therefore, it explains most of the market mechanism variables’ impacts on price.
Discount rate Bidder number
-18%
-16%
-14%
-12%
-10%
-8%
-6%
-4%
-2%
0%
1 6 11 16 21 26
Figure 3 Relationships between Market Price Undercutting and Number of Bidders
Note: (1) The first half is based on Quan (1994) and Mayer’s (1998) “theory” relationship diagram of market price undercutting and the number of bidders; (2) The second half is in accordance with the empirical results of this study, charted as “empirical”
relationship diagram of price undercutting and the number of bidders.
Foreclosed house price
Search Market Price (market equilibrium price)
Higher bidder number
Large
discount Smaller discount