Modeling the Impacts of Vacancy Taxes on the Taiwan Housing Market

Transcription

1 Proceedngs of the Natonal Scence Councl, ROC Part C: Humantes and Socal Scence 00,Vol.,No. Modelng the Impacts of Vacancy Taxes on the Tawan Housng Market Yen-Jong Chen Department of Urban Plannng Natonal Cheng-Kung Unversty Ta-Hsueh Road, Tanan Tawan 700, ROC ABSTRACT Vacant housng exsts when the number of housng unts exceeds the household demand. Theory suggests that an ncrease n owners cost of vacant unts yelds a decrease n the market prce. Owners of vacant unts reduce prces to avod the mpact of the tax. Vacancy rates would then fall. In ths study, we constructed a smultaneous model to estmate the effect of a proposed vacant housng tax on housng prce. The model was constructed based on two condtons: housng market equlbrum and the balance of famly ncome and expendture. Housng market equlbrum s mantaned so that the housng prce can be obtaned, whch s a functon of famly ncome. The balance of famly ncome and expendture s also mantaned so that famly ncome can be derved as a functon of house prce. The unqueness of the soluton s examned accordng to a suffcent condton of the negatve domnant dagonal (NDD), and s emprcally confrmed. Several sources of reported data on the Tawan housng market were collected and manpulated to calbrate coeffcents n the structural model and to estmate the effects. The estmated results ndcate that an ad valorem vacancy tax wth a % tax rate yelds a decrease n the market prce of housng rangng from.6 to 8.8% n selected study areas. Key Words: housng, vacancy rate, vacancy tax, housng prce, famly ncome, smultaneous equatons, Tawan I. Introducton In the housng market, vacances unts exst when the number of housng unts exceeds household demand (Wheaton, 990). Theoretcally, vacant housng s defned as the excess supply n a compettve housng market; hence, the vacancy level s a measure of the number of dwellng unts that do not clear the market (Rabansk, 998). The vacancy rate changes accordng to housng supply

2 Yen-Jong Chen and demand. For nstance, f housng supply ncreases faster than demand, then the vacancy rate ncreases, and vce versa. Accordng to the prce-adjustment mechansm, the equlbrum market prce decreases when the vacancy rate goes over a standard (or optmal) level. The nverse relatonshp between the vacancy rate and equlbrum prce change has been confrmed n many emprcal studes, such as those of Rosen and Smth (983) and Gabrel and Nothaft (988). However, the valdty of ths mechansm has been questoned n some other studes, such as the work by Eubank and Srmans (979). Moreover, durng the 980s, house prces soared n the Unted States despte hgh vacancy rates. Recently, Belsky and Goodman (996) provded an explanaton of ths paradox. Important factors are the ncrease n the natural vacancy rate and a boom n newly bult housng, for whch exstng housng s not a perfect substtute. In Tawan, the housng vacancy rate has been at a hgh level for at least three decades, whch s as long as the government has been observng the housng market. Accordng to the Tawan Census taken n 980 and 990, the reported vacancy rates were 3.% and 3.3%, respectvely. In fact, the number of households n Tawan s larger than the total number of housng unts. The excess demand was 9,89 unts n 990. Ths mples that more housng constructon s stll needed. However, there also exsted 674,37 vacant unts at the same tme, producng a vacancy rate of 3.9%. The estmated number of vacant unts n 994 was 80,000. () Ths ncludes some deterorated unts, some old but usable unts, and some newly constructed unts. The vacancy rate was hgh compared wth the average natural vacancy level of 4.6% n Tawan, whch was estmated by Ln, et al.(994). Ths llustrates a controversal dea that new housng constructon ncreases the number of unused housng unts on the market and does not proportonally ncrease the amount of occuped housng. Ths can be explaned by the fact that there are many famles, especally low-ncome ones, sharng lvng space wth other famles because they are not able to afford the prces of houses on the market. Ths also provdes another explanaton of the phenomena that many young households lke to stay wth ther parents and other famly members nstead of movng out. Even though there has been a contnuously hgh vacancy rate n Tawan, housng prces have ncreased dramatcally snce the early 970s. () The most recent data, reported n 993, shows average annual rates of ncrease of 9% (Table ). Some famles buy houses only for the purpose of nvestment. Wth hghly expected captal gans, user costs for ownng vacant unts are relatvely low. The offcal record shows that the average house prce was 5.5 tmes famly ncome n 990, and that t was more than 7 tmes famly ncome n Tape and 4 tmes famly ncome n Kaohsung. (3) Meanwhle, there are more than 00,000 famles on the watng lst for publc housng (Chang, 995). The ncreasng housng prces have led to an ncrease n the amount of new housng constructon on the supply sde. However, the hgh vacancy rate has not reduced housng prces back to a level that households can reasonably afford. The controversal fact has produced two nterpretatons. The frst one s housng market falure. Specfcally, the prce mechansm has not functoned wth proper responses. The second nterpretaton was provded by Hsueh(990), who suggested that the return on housng nvestment n Tawan has been so hgh snce the 970s that owners of vacant unts have been

3 Modelng the Impacts of Vacancy Taxes on the Tawan Housng Market nduced to keep unts vacant n expectaton of great captal gans n the future. Wth regard to the market mechansm, the government plays an mportant role n observng and settng up market rules. Some polces are needed to nterfere n the housng market, so that the market mechansm functons properly. In terms of regulatons on housng nvestment, the most frequently dscussed polcy optons are ncreasng owner costs related to vacant unts (Ln, et al., 994) and reducng the rate of return on real estate nvestment (Hsueh, 990). It would be nterestng also s mportant for the Tawan government to estmate the effect of ncreasng nvestors costs connected wth vacant unts, such as the mpact of hypothetcal vacancy taxes on house prces. In ths study, we constructed a model to estmate the prce change caused by levyng taxes on nvestors vacant unts. The model was desgned based on mantanng the housng market equlbrum and a balance of aggregate famly ncome and expendture. The equlbrum house prce s obtaned under the condton of market clearng and s a functon of famly ncome. On the other hand, the condton of balanced famly ncome and expendture must be held at the macro level and yelds famly ncome that s a functon of house prces. We wll explan the structure of the model n detal n Secton, and dscuss the soluton dentfcaton n Secton 3. In Secton 4, we wll descrbe the emprcal data and coeffcent calbraton process, ncludng data manpulaton and calbraton results. In Secton 5, we wll report the results of senstvty analyss of the controllng parameters. In the fnal secton, we wll summarze our fndngs. II. Model Structure As ntroduced n the prevous secton, the model presented n ths paper was constructed wth a smultaneous structure. Two fundamental condtons formed the bass of the model: statc equlbrum n the housng market and a balance of famly ncome and expendtures.. Housng Market Equlbrum For the frst condton, we assume that the prce of housng (denoted by P) can be determned when housng supply (S) equals occuped housng (O) plus vacant unts (V). Ths can be expressed as S P O P V P. () The subscrpt n Eq.() denotes housng market or zone, whch n ths case refers to local (cty or county) government jursdcton. We assume that housng market equlbrum exsts n every zone. We also assume that each zone s ndependent from the others, so that there s no cross housng demand. The housng supply on the left hand sde of Eq.() s set to be a lnear functon of prce (P ) (4) and housng stock n the prevous year (S 0, ): S ( P ) b b P b S ε () 0 0, where b 0, b, and b are coeffcents and ε s, s the stochastc error term for housng supply. The sgn of the coeffcent of housng prce, b, s expected to be postve. On the demand sde, occuped housng s estmated based on a lnear housng demand functon n the form s, O ( P ) a a P a Y ε, (3) 0 d, where Y denotes famly ncome and a 0, a, 3

4 Yen-Jong Chen and a are coeffcents, whle ε d, s the stochastc error term for housng demand. It can be expected that housng demand wll decrease wth housng prce and ncrease wth famly ncome; hence, the coeffcent of a s expected to be negatve, and that of a s expected to be postve. The second term on the rght hand sde of Eq.() s vacant housng, whch can be splt nto two parts: unts caused by vacancy chans from housng consumpton and unts caused by housng nvestment: V P VN P VI P, (4) where VN (P ) represents housng unts that are temporarly vacant due to famly relocaton, seasonal vacancy, new constructon or deterorated unts that are vacant pendng demolton. Essentally, these knds of vacant unts consttute the naturally vacant housng. In ths paper, we assume that the number of natural vacances s proportonal to the housng stock. Ths can be estmated by VN P ns P, (5) where n s the natural vacancy rate and S (P ) s the housng stock as defned n Eq. (). Removng the naturally vacant unts, the remanng vacant unts composte the vacant nvestment housng, denoted as VI (P ) n Eq.(4). The vacant nvestment housng would be the object that we proposed to mpose a vacancy tax. We specfy the vacant nvestment housng as a lnear functon of housng prce and the vacancy tax (T ). That s, VI ( P ) e P e T ε, (6) v, where e, e and ε v, are coeffcents and the stochastc error term, respectvely. Addtonally, we desgn a hypothetcal ad valorem vacancy tax. (5) That s T P, where s the vacancy tax rate.. The Balance of Famly Income and Expendture We wll now descrbe the second condton, the balance of famly ncome and expendtures. In modern economc research, the budget constrant s mportant n explanng famly consumpton at the mcro level. We extend ths concept to a macro level n every study zone. In partcular, the total amount of famly expendture, ncludng housng consumpton, transportaton cost, taxes, savngs, and so forth n a study zone must be constraned to equal the total amount of famly ncome n that zone. For the purposes of ths study, we dvded famly expendtures and savngs nto three parts: the captal cost of housng consumpton (YH ), the vacancy tax payment (YT ), and all other expendtures plus savngs (YX ). That s, I Y ) YH ( P ) YT ( P, T ) YX ( Y ), (7) ( where I (Y ) denotes the total amount of famly ncome n zone and can be computed by multplyng the average annual famly ncome (Y ) by the number of famles n that zone (F ). The captal cost of housng consumpton n zone, YH (P ), s the annually measured opportunty cost, ncludng the opportunty cost of equty, payments of mortgage nterest, hazard nsurance premums, mantenance costs, property taxes (except for the proposed vacancy tax), and captal gans. To smplfy the model, we assume that ths cost s proportonal to the house prce (see Mlls and Hamlton, 994: 0-06). Hence, the aggregate housng captal cost can be computed by multplyng the house prce by a rato (denoted by r) and the housng stock n 4

5 Modelng the Impacts of Vacancy Taxes on the Tawan Housng Market each zone, as shown n Eq.(8). YH ( P ) S ( P ) rp. (8) Recall that the housng stock s estmated based on the supply functon defned n Eq.(). The aggregate vacancy tax n zone s computed as the vacancy tax per housng unt tmes the amount of vacant nvestment unts n the zone. Snce we have defned the vacancy tax as an ad valorem tax, the equaton can be wrtten as YT ( P,T ) VI ( P ) T P VI ( ) P. (9) The last term on the rght hand sde of Eq.(7) s famly ncome remanng after housng consumpton and the vacancy tax. The remanng ncome can be used for lvng expendtures other than housng, such as transportaton costs or shoppng needs, and the rest, f any, can be saved. The level of lvng expendture s related to famly ncome. The propensty to consume non-housng goods and servces and to save s assumed to vary by zone wth a value of m. Hence, ( - m ) would be the propensty to consume housng, ncludng payment of the vacancy tax, n zone. The total famly expendture other than housng can be computed by YX ( Y ) F Y m, (0) where F and Y denote the total number of famles and the average famly ncome n zone, respectvely. III. Identfcaton of Structural Form Wth the model structure constructed n the prevous secton, we can rearrange the model by substtutng varables nto Eqs. () and (7) that are taken from the others. A fnal structural form can be obtaned as shown n Eqs.(a) and (b), whch can be used for model dentfcaton. P α α Y α S ε, (a) Y β 0 where, α α α β 0 P β ( m ) F a b a 0 0, ( n ) b nb e a p, P β ( m ) F 0 e, b a nb e e ( n ) b b a nb e br eρ eρ e, 3 P S0, ε ( m ) F, β b0 r,, and β 3 br. y, (b) It can be seen from Eqs. (a) and (b) that there are two endogenous varables, housng prce (P ) and famly ncome (Y ), whch are determned smultaneously based on the housng market equlbrum and the balance of famly ncome. The varables of housng stock n the prevous year (S 0, ), the total number of famles (F ), and the rato of housng expendture to famly ncome ( - m ) are exogenous varables, and are assumed to be constant across zones. Moreover, three controllng parameters are ncluded n the composte coeffcents of the s as well as the s. They are the natural vacancy rate (n), the housng captal cost rate (r), and the vacancy tax rate ( ). Dfferent combnatons of controllng parameters yeld dfferent prce effects. We wll dscuss ths n the secton on senstvty analyss. The structural form of the desgned model s obvously non-lnear, as shown n ncome Eq.(b). It s worthwhle to check the unqueness of the soluton of the structural model. Frstly, we can check a necessary condton for the exstence of a soluton. The number of equatons must be more than or equal to the number of, 5

6 Yen-Jong Chen endogenous varables. Ths condton s obvously satsfed. Secondly, we can check a suffcent condton for unqueness. The soluton s unque f the transpose of the Jacoban matrx has the negatve domnant dagonal (NDD) property (Anas, 98: 03-05). The Jacoban can be obtaned by takng the second dervatves of smultaneous equatons wth respect to every endogenous varable. In our case, t s a two dmensonal square matrx. Unfortunately, we are unable to dentfy that the soluton s unque snce one of the dagonal elements n the transpose of the Jacoban matrx has an ambguous sgn. (6) Ths rases a queston about the stablty of the model. However, the NDD property s a suffcent but not a necessary condton. It s stll possble to draw conclusons from emprcal results. (7) It should be noted that dentfcaton based on emprcal results can be made only when the data and the calbraton approaches were carefully examned. In other words, lackng n drect proof from the systematc dervaton, our approach to dentfcaton s lmted. A theoretcal model can be re-derved or modfed based on more dealstc assumpton(s) so that dentfcaton can be made. However, nterpretaton could be more lmted. An alternatve approach s to adopt econometrc calbraton to examne and test the hypothess, so that the results wll be statstcally acceptable and more explanatory of the real stuaton. IV. Coeffcent Calbraton and Effect Measurement The coeffcents n the structural model are calbrated usng cross sectonal data for 99, derved from several sources. The study zones are defned based on cty or county boundares. There are a total of 3 zones (8). Our frst problem n ths step s the lack of perfect data. There s no sngle data source that provdes the prce of housng together wth famly ncome, whch are both endogenous varables n our model. Housng prces can be found n the Tawan Housng Status Survey n 993. The prces were recorded accordng to each household s recollecton of the orgnal purchase prce. Hence, the prces need to be nflated (or deflated) to obtan 99 values. (9) Then, the average prce per png can be computed for every zone. The famly ncome can be obtaned from the Survey Report of Famly Income and Expendture (FIE) n 99. Other data for exogenous varables, ncludng the number of famles (F ), the average rato of housng expendture to famly ncome ( - m ), and housng stock n the prevous year (S 0, ), can be collected from the Annual Statstcal Report of Housng Informaton n 99, FIE n 99, and the Tawan Census Survey of Housng and Populaton n 990, respectvely. The varables and data sources are lsted n Table. The second problem that needs attenton s the absence of any emprcal data relevant to the possble mpacts of vacancy taxes n Tawan. Because we are unable to create any proxy data for a vacancy tax, we have desgned the model so that the ad valorem vacancy tax rate ( ) s ncluded n the composte coeffcents n the structural model. The composte coeffcents can be calbrated systematcally and then followed up wth senstvty analyss by settng the vacancy tax rate n a range from low to hgh. The coeffcents n the structural model were calbrated by means of a 3-stage-least-squares (3SLS) procedure that s provded n the SAS computer applcaton package. The calbraton results are shown n Table 3. As can be seen from ths table, only three varables are sgnfcant. They are the constant term and the famly ncome varable n the housng prce equaton, and the composte 6

7 Modelng the Impacts of Vacancy Taxes on the Tawan Housng Market P S0, varable of n the famly ncome ( m ) F equaton. From the housng prce equaton, t can be seen that housng prce s sgnfcantly affected by famly ncome. When famly ncome ncreases, prce also ncreases. The estmated coeffcent s Ths mples a $ ncrease of ncome results n a margnal ncrease of $0.388 n housng prce, keepng other factors constant. Another mportant coeffcent n the structural model s that of the composte varable of P n the famly ncome ( m ) F equaton. The sgn of can be used to dentfy the unqueness of the soluton, whch remans unresolved due to the NDD property dentfed n the prevous secton. As can be seen n Table 3, the estmated value of s.454. The negatve sgn mples that the soluton of the structural model could be unque gven our emprcal data. However, we are stll not confdent about the result because the estmated coeffcent s not statstcally sgnfcant. The effect of the ad valorem vacancy tax rate on the prce of housng can be derved from Eq.(a): P e P. () ρ ( b a nb e e ) By substtutng from the formulas for, and 3, t can be seen that ( n ) β 3 ( b a nb e e ), and rα e ( β br eρ ). Hence, Eq.() can ρ be replaced by: P ρ rα ( β br eρ ) P. (3) ρ ( n ) β 3 In Eq.(3),, and 3 are estmated emprcally whle r, n and are controllng parameters. The parameter of b s defned as n Eq.() by takng the frst dervatve of housng stock wth respect to housng prce. That s, b measures the margnal ncrease of housng stock when house prces ncrease by one unt. Smlarly, the parameter e can be defned as n Eq.(6) and s the margnal ncrease n vacant nvestment unts of housng wth respect to a unt ncrease n house prce. By assumng that the prce elastcty of housng supply ( s ) and the prce elastcty of vacant nvestment housng ( VI ) are both unty, the parameters b and e can be obtaned by S P P solvng η s ( ) b and P S S VI P η VI ( ) P VI P e VI V. Senstvty Analyss, respectvely. The effect of the ad valorem vacancy tax rate on house prces s related to the estmated coeffcents and the controllng parameters. There are three controllng parameters: the natural vacancy rate, the housng captal cost rate, and the vacancy tax rate. As can be seen from Eq.(3), dfferent combnatons of controllng parameters result n dfferent effects on house prces. The effects can be explored through senstvty analyss. We frstly fxed the ad valorem vacancy tax rate at % of housng prce and examned ts effect on prces by varyng the natural vacancy rate as well as the housng captal cost rate. We focused on Tape Cty, the largest cty n Tawan. A surveyed market prce of NT$5,400 per png was used as the equlbrum pont (0). Table 4 shows the computatonal results. When the rate of housng captal cost s fxed at 5% of housng prce () and the natural vacancy rate vares from 3% to 0%, the housng unt prce per png decreases n a range 7

8 Yen-Jong Chen from NT$3,600 to NT$5,800. The percentage change ranges from 6.03 to 7.0%. The prce changes are not bg. On the other hand, the housng unt prce per png decreases n a range from NT$500 to NT$7,900 when the captal cost rate vares from % to 7% of prce whle the natural vacancy rate s kept at 5%. The percentage change s n a range 0. to.38%, whch s much broader than the effect of changng the natural vacancy rate. Secondly, we fxed the natural vacancy rate at 5% of housng stock and the captal cost rate at 5% of prce. The change n housng prces caused by dfferent vacancy tax rates was computed, and the results are shown n Table 5. The prce change per png vares from -NT$4,00 at a % vacancy tax rate to NT$,000 at a 0% rate. The margnal prce change dfference s nonlnear and decreasng whle the tax rate ncreases. In other words, the margnal effect of the ad valorem vacancy tax on house prces s larger when the tax rate s low and smaller when the tax rate s hgh. We now turn to a comparson across ctes n Tawan. We selected 8 out of 3 areas n our study. The selected areas ncluded densely populated ctes, such as Tape Cty and Tachung Cty, where house prces are hgh. Some of them were rural areas, such as Pngtung and Tatung countes. All of the selected zones are lsted on the frst column of Table 6 along wth the estmated natural vacancy rate and average housng unt prce n columns two and three. We set the rate of housng captal cost at 5% and set the vacancy tax rate at %, whch yelds dfferent amounts of vacancy tax n dfferent areas. As shown n Table 6, the prce change per png n the selected zones s NT$5,00 n Tape Cty, NT$7,400 n Tachung Cty and only NT$,00 n Tatung County. The percentage prce change vares wthn a range from.55% n Tatung County to 8.80% n Tachung County. The percentage prce change per unt s smaller where unt prces are cheaper. VI. Conclusons In ths study, we have constructed a smultaneous model to estmate house prce changes due to a hypothetcal vacancy tax. The model was constructed based on two condtons: the housng market equlbrum and the balance of famly ncome and expendtures. Housng market equlbrum s assumed so that the prce can be obtaned, whch s a functon of famly ncome. The balance of famly ncome and expendture s mantaned so that famly ncome can be derved as a functon of house prce. We constructed the structural form of the model and have examned the unqueness of the soluton. Mathematcally, the NDD property of the Jacoban matrx of our model ndcates an ambguous concluson. However, the unque soluton s confrmed by the emprcal results when the sgns of the coeffcents were calbrated. The model ncludes an ad valorem vacancy tax. House prce changes due to the vacancy tax rate can be derved from the model and computed emprcally. The emprcal results show that the market house prce decreases when the vacancy tax s mposed. The effect on prces depends on the level of house prces, the natural vacancy rate, the rate of housng captal cost and the vacancy tax rate. Hence the effect s dfferent across dfferent areas. Estmated results for Tape Cty show that, the housng unt prce per png decreases n a range from NT$3,600 to NT$5,800 wth a % vacancy tax rate, the housng captal cost s 5% of house prce, and the natural 8

9 Modelng the Impacts of Vacancy Taxes on the Tawan Housng Market vacancy rate vares from 3% to 0%. On the other hand, the housng unt prce per png decreases n a range from NT$500 to NT$7,900 when the housng captal cost rate changes from % to 7% of housng prce, whle the natural vacancy rate stays at 5%. Moreover, the prce change per png vares from NT$4,00 to NT$,000 when the vacancy tax rate changes from % to 0%, gven a natural vacancy rate of 5% and a captal cost rate at 5% of housng prce. It s concluded that house prces are more senstve to the housng captal cost rate and less senstve to the natural vacancy rate. We also fnd that the margnal effect of the ad valorem vacancy tax on house prces decreases when the tax rate ncreases. Comparng selected areas, we estmate that the housng prce change per png ranges from NT$,00 to NT$5,00. The percentage prce change vares wthn a range of.55 to 8.80%. We also observe that the prce change per unt s smaller when the unt prce s Lower. Even though we have demonstrated that an ad valorem vacancy tax has a sgnfcant effect n house prces, there has been debate about the techncal problems nvolved n mplementng such a tax. In partcular, there are ssues concernng the dentfcaton of vacant nvestment unts and also regardng the specfc means of mposng the tax. Currently, a goal of the Tawan government s housng polces s to make owner-occuped housng more affordable by subsdzng the mortgage nterest rate, ncreasng the maxmum amount of mortgage loans elgble for subsdy, and relaxng the requrement that only lower-ncome households are elgble for subsdes. These subsdes apply to new dwellngs and are not restrcted to the frst-tme home buyers or to prncpal dwellngs; therefore, they may actually encourage hgh vacancy rates. However, house prces are stll beyond the reach of many households. () In ths study, we have llustrated that a vacancy tax sgnfcantly affects the owner s cost of vacant nvestment housng and reduces house prces. In constructng the prototype model n ths study, we made many assumptons. From the emprcal pont of vew, some of the assumptons could be strongly challenged: the exstence of housng market equlbrum, the lnearty of the functon form, and ndependence of housng submarkets from each other, for nstance. Even though the model used n ths study was constructed based on a smplfed structure, the model dentfcaton of unque soluton was stll not clear. For further studes, more studes desgned to examne ths nteracton are needed so the ndependence assumpton can be removed. Further work s also needed to properly evaluate the benefts of vacancy taxes as aganst the costs of mposton. In addton, alternatve polces need to be consdered more carefully. Specfcally, an operatonal defnton of the so-called vacant unt s needed so that tax polces can be desgned. Acknowledgment Ths paper s a part of research project funded by the Natonal Scence Councl, R.O.C. (NSC H006-00). The author thanks Professor Steven C. Bourassa of the Department of Urban and Publc Affars, the Unversty of Lousvlle, for revewng ths paper. Thanks are also due to Mr. Cha-Yuan Yeh for computer work. The comments and constructve crtcsms of the anonymous referees are hghly apprecated. 9

10 Yen-Jong Chen Notes () Estmated by the Councl for Economc Plannng and Development, ROC. () We attempt to defne housng prce n a manner that s consstent wth the concept of housng servces (see Olsen, 969). Assumng that housng servces vary closely wth floor area, prces are measured per png, whch s the unt most frequently used n measurng housng lot sze, as well as floor area, n Tawan. One png equals about 3.3 square meters. (3) The actual market prce to ncome rato (PIR) s known much hgher than that gven n the offcal report and s ncreasng. (4) Wthout loss of generalty, the functon forms are specfed as lnear for housng supply, housng demand and housng nvestment as well. (5) There are other possble alternatve vacancy taxes, such as a lump sum tax, a specfc tax, a revenue tax, and so on. Dfferent specfcatons of the vacancy tax n Eq.(6) could result n dfferent forms of the structural model and, hence, dfferent solutons to the model. Here, we focus on what seems the most lkely form of vacancy tax. (6) From Eq.(b), we have Y P β ( m ) F. The sgn depends on β, whch s a composte coeffcent wth an ambguous sgn by defnton. However, β s one of the coeffcents of Eq. (b) and can be calbrated emprcally to estmate the sgn. (7) As explaned n footnote 6. (8) Here, we tentatvely defne housng submarkets based on admnstraton boundares because of our data lmtatons. Consderng the fact that housng nvestment s not lmted by spatal boundares, the assumpton of ndependence between zones n the theoretcal model would be emprcally volated. Hence, more emprcal evdence s needed to re-defne housng submarkets. (9) In the absence of any better deflator, we use the Consumer Prce Index. Ideally, one would use ndexes of housng prces per png. (0) The surveyed market prce s also used n model calbraton. () The annual user s cost (emprcally the proxy of the annual housng rent) s 3.% of the housng prce on average (Ln, 99) and 0% for the emprcally hgh value n Tawan. () Ownershp rates n Tawan are hgh, but stable. Accordng to the 990 census, the ownershp rate was 78.5%. Accordng to a 995 survey, t was 80.7%. References Anas, A. (98). Resdental Locaton Markets and Urban Transportaton: Economc Theory, Econometrcs, and Polcy Analyss wth Dscrete Choce Models. New York, NY: Academc Press. Belsky, E., & Goodman, J. (996). Explanng the vacancy rate-rent paradox 0

11 Modelng the Impacts of Vacancy Taxes on the Tawan Housng Market of the 980s, Journal of Real Estate Research, (3), Chang, C. (995). Studes on the Watng Lst of Tawan Publc Housng and Vacant Housng Problem (n Chnese), Tape, Tawan: Chnese Socety of Housng Studes. Gabrel, S. & Nothaft, F. (988). Rental housng markets and the natural vacancy rate, Journal of the Amercan Real Estate and Urban Economcs Assocaton, 6(4), Hsueh, L. (990). Factors of housng prce apprecaton n Tape Cty, Conference of Tawan Bankng and Prcng Problems (n Chnese), Tape, Tawan: Insttute of Economcs, Academa Snca. Ln, C., Chang, C. & Peng, G. (994). An equlbrum analyss on housng vacancy rate and prce adjustment n Tawan area, Conference Proceedng of Economc Research (n Chnese), Tape, Tawan: Natonal Scence Councl. Mlls, E. & Hamlton, B. (994). Urban Economcs(5 th ed.). New York, NY: Harper Collns College Publshers. Olsen, E. (969). A compettve theory of the housng market, Amercan Economc Revew, 59, 6-6. Rabansk, J. (998). Vacancy rate, n: W. van Vlet (Eds) The Encyclopeda of Housng, (p. 6). Thousand Oaks, Calforna: Sage Publcatons. Rosen, K. & Smth, L. (983). The prce-adjustment process for rental housng and the natural vacancy rate, Amercan Economc Revew, 73(4), Svtandes, P. (997). The rent adjustment process and the structural vacancy rate n the commercal real estate market, Journal of Real Estate Research, 3(), Voth, R. & Crone, T. (988). Natonal vacancy rates and the persstence of shocks n U.S. offce market, Journal of the Amercan Real Estate and Urban Economcs Assocaton, 6(4), Wheaton, W. (990). Vacancy, search, and prces n a housng market matchng model, Journal of Poltcal Economy, 98(6), Wheaton, W. & Torto, R. (988). Vacancy rates and the future of offce rents, Journal of the Amercan Real Estate and Urban Economcs Assocaton, 6(4), Table. Average Prce of Housng and Annual Rate of Increase Perod Prce per household (NT$,000) Change from prevous perod Prce per png (NT$,000) Change from prevous perod (%) (%) , , , ,

12 Modelng the Impacts of Vacancy Taxes on the Tawan Housng Market Average, Source: Report of the Housng Status Survey n Tawan Area (993). Table. Varables and Data Sources Varable Descrpton Data Sources Endogenous * P Average unt prce per png (n unts of NT$0,000) Deflated from the Tawan Housng Status Survey Y Average famly ncome (n unts of NT$0,000) Survey Report of Famly Income and Expendture (99) Exogenous F Number of famles (n unts of 0,000) ( m ) Average rato of housng expendture to famly ncome S 0,I Housng stock n the prevous year (n unts of 0,000) Annual Statstcal Report of Housng Informaton (99) Survey Report of Famly Income and Expendture (99) Tawan Census Survey of Housng and Populaton (990) Notes: The subscrpt refers to the study zones (3 ctes and countes). One png equals about 3.3 square meters. 3

13 Yen-Jong Chen Table 3. Estmated Coeffcents n the Structural Form of the Model Varable Coeffcent t-score Prce equaton Constant * Y * S 0,I Income equaton P ( m ) F P ( m ) F PS t, * ( m ) F Note: * Desgnates sgnfcance at the 5% level. Table 4. Senstvty of Prce to Changes n the Natural Vacancy and Captal Cost Rates, Tape Cty Natural vacancy rate (%) Annual captal cost rate (%) Prce change (NT$,000/png) Percentage (%) Note: Assumes a % ad valorem vacancy tax rate and that housng prce before tax s NT$5,400 per png. 4

14 Modelng the Impacts of Vacancy Taxes on the Tawan Housng Market Table 5. Senstvty of Prce to Changes n the ad Valorem Vacancy Tax Rate, Tape Cty Vacancy tax rate (%) Prce change (NT$,000/png) Percentage (%) Note: Assumes a natural vacancy rate of 5%, an annual captal cost rate of 5%, and a before tax housng prce of NT$5,400 per png. 5

15 Yen-Jong Chen Table 6. Effects of a % of ad Valorem Vacancy Tax, by Zone Zone Natural vacancy rate Housng prce before Vacancy tax per png Prce change (NT$,000 Percentage (%) (%)* tax (NT$,000 /png) (NT$,000) /png) Tape Cty Tachung Cty Taoyuan County Tachung County Changhua County Pngtung County Hualen County Tatung County Note: * Values are derved from Lng, Chang and Peng (994). 6