0 Lin and Lin NTERNATONAL REAL ESTATE REVEW 999 Vol. No : pp. 0-5 An Estimation of Elasticities of onsumption Demand and nvestment Demand for Owner- Occupied Housing in Taiwan : A Two-Period Model u-ia Lin Department of Economics, National engci University, Taipei, Taiwan, or nccut00@nccu.edu.tw. Sue-Jing Lin Department of nternational Trade, Lung-Hwa nstitute of Tecnology, Taoyuan, Taiwan, or sjlin@mail.it.lit.edu.tw. Buying a ouse usually satisfies ousing consumption demand and ousing investment demand, simultaneously. n order to disentangle te above two types of demand, ouseolds, in tis study, are separated into tree subtenure groups i.e. renters, owners owning one ouse, and owners buying a second or more ouses. Presumably, renting a ouse is for consumption only, wile buying a second ouse is usually for investment purposes. Applying a two-period model and two data sets from DGBAS and from Land Bank of Taiwan, te estimated results are as follows: Firstly, te income elasticity of pure consumption demand for ousing is very close to unity (.043). Secondly, te income elasticity for a pure investment demand is greater tan one (.643). Finally, for a ouseold owning only one ouse, te sares for consumption motive and for investment motive are 6% and 74%, respectively. Keywords onsumption demand, investment demand, elasticity and ousing, Taiwan.
Elasticities of onsumption and nvestment Demand ntroduction A dwelling unit satisfies a basic demand of living and also serves as an investment good. Buying a ouse usually involves bot consumption demand and investment demand. t will be an interesting issue to disentangle te sare for consumption demand and te sare for investment demand. Moreover, it is also wortwile to know te elasticities bot for consumption demand and for investment demand. Recently, some researc as been publised examining consumption demand and investment demand for ousing. For example, Henderson and oannides (983, 986, 987), Fu (99), and Berkovec (989) ave discussed te factors influencing tenure coice. Lin (990, 994) considers tat omebuyers decide tenure coice and ousing demand simultaneously. oannides and Rosental (994) separate consumers into four ousing subtenures: families renting witout owning properties, renting wile owning property oter tan teir ome, own teir ome witout owning oter properties, and own teir ome in addition to oter properties. Furtermore, tey try to set apart consumption demand and investment demand for ousing by applying an order probit model. All of tose papers are interesting for teir own purposes, but tey did not provide good answers for te questions raised above. Tere are two goals for tis paper. Firstly, te elasticities of consumption demand for ousing and investment demand for ousing will be estimated separately, by applying two data sets from te ousing market in Taiwan. Ten, te consumption sare and investment sare will be calculated according to te Engel aggregation condition, as long as te above two types of elasticities are available. For estimation purposes, te ouseolds are divided into tree subtenures in tis paper, according to oannides and Rosental (994), tat is, renters, ouseolds wit only one ouse, and ouseolds wit more tan one ouse. Additionally, te data set for different subtenures are applied to estimate different elasticities. Presumably, tere is no ousing investment for renters. So it is possible to get a pure consumption elasticity from renters' beavior. On te oter and, it is a pure investment purpose for tose ouseolds wo buy teir second or more dwelling units, since one person could not live in two places at te same time. Finally, te data set for ouseolds wit only See Ranney (98), Scwab (98), Henderson and oannides (983), Poterba (984), Weaton (985), Bosc, Morris, and Wyatt (986), Berkovec (989, 997). t is possible tat different members in a same family are staying at two different dwelling units. Here, for simplicity, we classify tem as two ouseolds.
Lin and Lin one ouse is used to calculate te sare for consumption demand and te sare for investment demand. A basic two-period model is introduced in Section, were te estimation metod employed in te paper is also discussed. n Section 3, income elasticities for different subtenures in Taiwan are estimated first. Ten consumption sare and investment sare for ouseolds owning only one ouse are computed by using tose estimated elasticities. Section 4 concludes tis study. A Two-Period Model of Housing Demand For simplicity, we assume tat tere are two periods for every ouseold, i.e. t=,. And ouseolds consume te same ouse during teir life. Terefore, tere are two goods in te world, ousing service (H) and te oter composite good (X t ), and teir prices are P and P t, respectively. Te object for a ouseold is to maximize is utility under is budget constraint. For te ouseold in question, is utility function is U ( H, X ) U = U ( H, X ) +, + ρ were U(H, X t ) is te utility function and ρ is te rate of time preference. Suppose initial saving is zero. Ten te renters budget constraint for two periods are as follows: P X + S + RH = Y, P X + RH = Y + ( + r ) S, were R t is te rent of ousing service, r t is te interest rate of saving, S t and Y t represent ouseold savings and income. On te oter and, te owners budget constraints are as follows: m P X + S + r M + ( b P H = Y, ) m P X + r M = Y + ( + r ) S, m were b is te mortgage ratio, M = M = bp H is te mortgage, r t is te interest rate of mortgage at time t. Finally, we assume te ousing value at te end of period is equal to te mortgage. 3 Using te budget constraints of renters or owners, te objective function and budget constraint can be written as : 3 Generally, ousing price is variant but te mortgage is uncanged. For simplicity, we assume tat te ousing value at te end of period is equal to te mortgage.
Elasticities of onsumption and nvestment Demand 3 max U ( H, X ) U = U ( H, X ) +, + ρ s.t. P X P X + + PH = Y, () + r were Y Y = Y + is te ouseold s total income of te previous period. + r For renters, P P R R R = = + ; wile for owners, + r m O m r P = P = b( r + ) P. + r Solving te first order condition, one can get te ousing demand function wic is a function of income, price of ousing service, price of composite commodity in two periods, i.e. H = H Y, P, P, P ). ( For estimation purposes, we assume tat ousing demand is a log-linear form, ten te ousing demand function can be sown as: logh = γ + η logy + ε log P + log P + β logp, () restriction η + ε + + β = 0. 4 were η is te income elasticity, ε is te price elasticity, and β are te cross elasticities. Now, let E be te total expenditure of ousing services, E = PH, ten one can rewrite Equation () as E log Y P P = γ + η log + ( + ε )log + β log, (3) P P P P were P is inflation rate plus, tat is a constant across ouseold. Let P P γ ' = γ + β log, and we can rewrite Equation (3) as P E log P Y P = γ ' + η log + ( + ε ) log. P P n sort, LEH = γ ' + ηly + ( + ε ) LPH, (4) 4 γ η ε β Owing to te log-linear demand function assumption, H = e Y P P P, te demand function is omogeneous of degree zero in Y, P, P, and P, if te consumers ave no money illusion, in oter words, η + ε + + β = 0.
4 Lin and Lin were E LEH = log, Y LY = log, and P LPH = log. After tat, we will use P P P Equation(4) to estimate te income elasticity(η) and te price elasticity(ε). Furtermore, te estimated elasticities can be employed to calculate te sares for consumption demand and investment demand separately for ouseolds wit only one ouse. Assuming tat consumption demand and investment demand are divisible, i.e. H = H + H. 5 Now, by differentiating Equation (), and let dp = dp = dp = dr = 0 and substitute it into te budget constraints, one gets PdX + P dx + P ( dh + dh = dy + r ). (5) Divided by dy on bot sides of Equation (5), we obtain P X Y dx P X Y dx PH Y dh + + Y X dy + r Y X dy Y H dy + = Y H dy PH n fact, tis equation is te Engel aggregation condition, i.e. xη x + xηx + η + η =, (6) + r and η = η + η. (7) n Equation (6) and (7), η and η x are te income elasticities of ousing service and composite commodity, and η and η are te income elasticities of consumption demand and investment demand for ousing. Meanwile, and x are te sares of ousing expenditure and composite commodity expenditure to total expenditure, wile and are te sares of consumption expenditure and investment expenditure to total expenditure. n oter words, P ( H + H ) =, P X + P X ( + r ) x =, PH =, PH =, and Y Y Y Y + x =, (8) + =. (9) Substitute Equation (9) into Equation (7), one obtains η = η + ( ) η = ( η η) + η. (0) Finally, Y dh. 5 See Henderson and oannide (983), oannides and Rosental (994). Virtually, H and H influence eac oter, wic makes tis study muc more complicated. Since it is not te main purpose of tis paper, we neglect tis problem.
Elasticities of onsumption and nvestment Demand 5 and were H η = = H η H η = = H η and η, () η η η, () are te sares of consumption demand and investment demand in ousing for ouseolds owning teir own ouses. Empirical Analysis To get information for tree subtenure groups, two data sets ave been employed in tis paper. n te "Annual Housing Survey" data set from Directorate-General of Budget, Accounting and Statistics (DGBAS), ouseolds in Taiwan could be separated into renters and owners. 6 By pooling tose annual data sets from 988 to 993, tere are,770 and,60 sample points for renters and owners, respectively. n order to separate owner-occupied ouseolds into two groups, i.e. ouseolds wit only one ouse and ouseolds wit more tan one ouse, te "Personal House Loan" data set from te Land Bank of Taiwan from 988 to 99 is applied ere. 7 By examining te data set from 988 to 99, tere are 0 sample points suitable for our purpose to separate owner-occupied ouseolds into te above two groups. Among tose 0 ouseolds, 34 of tem are ouseolds owning only one ouse, te rest 68 are ouseolds buying teir second ouse or more. Te definitions of variables in tis study are as follows: E : Housing expenditure. For owners, total ousing expenditure includes imputed rent and oter expenditure. For renters, ousing expenditure is te yearly rent plus oter expenditure, suc as utility payments. P : Price of ousing units. For owners, P is te purcase price per unit adjusted at te base of investigation year. 8 R : Yearly rent for renters. t 6 n te data set, owners include bot ouseolds wit one ouse and ouseolds wit more tan one ouse. For details of te data set, see S.J. Lin (993). 7 For details of te data set, see ang and Lin (993). 8 For details on te adjustment year, see ang and Lu (99).
6 Lin and Lin P t : Price of composite commodity. P t is computed from consumer price index and consumer price index-ousing. See Table A. in te appendix for details. Y t : Houseolds' yearly income Basic statistics for te above variables of DGBAS and Land Bank are sown in Table and Table. n Table, one may see tat renters' ousing expenditure and te floor space are muc lower tan tat of owners (79,953 vs. 09,79; 79.4 vs. 3.70), wic is consistent to our expectation. On te oter and, renters' income is also lower tan owners' (46,67 vs. 494,5). n Table, te average income, te ousing expenditure, and te floor space for owners wit one ouse only are lower tan owners wit more tan one ouse (774,4 vs.,00,46; 84,038 vs. 0,48; 5.6 vs. 38.98). Table. Basic Statistics: DGBAS Renters Unit: NT dollar Total Owners Housing Expenditure 79,953 09,79 Houseold ncome 46,67 494,5 Rent / Housing Price 49,94 3,033,397 Floor Space (m ) 79.4 3.70 Number of Observations,770,60 Sources: "Annual Housing Survey" from DGBAS of Taiwan. Table. Basic Statistics: Land Bank Total Owners Owners wit One House Only Unit: NT dollar Owners wit Second or More Housing Housing Expenditure 9,37 84,038 0,48 Houseold ncome 85,735 774,4,00,46 Housing Price 4,506,547 4,08,50 5,43,89 Floor Space (m ) 9.6 5.6 38.98 Number of Observations 0 34 68 Sources: "Personal House Loan" from te Land Bank of Taiwan. omparing te two data sets, we find tat te average income for owners of DGBAS is lower tan tat of Land Bank (494,5 vs. 85,753). Te ousing value as a similar situation for renters and owners. Te basic statistics ave
Elasticities of onsumption and nvestment Demand 7 confirmed our expectation tat renters ave lower income and live in lessexpensive ousing units, wile owners live in better places. 9 Applying te ordinary least-squares metod (OLS) in Equation (4), te ousing expenditure functions for renters and owners are estimated. Te estimation results are sown in Table 3. Almost all te estimated coefficients in Table 3 are significant wit rigt signs for bot equations. Additionally, bot R s are also satisfied in te two equations. Table 3. Te Expenditure Function of Rental Housing and Owner-Occupied Housing Renters Owners ntercept -.304** -5.033** (30.56) (43.7) LY.043**.55** (64.9) (34.7) LPH 0.0006 0.03** (0.36) (5.07) R 0.938 0.994 F-value 8930.050** 0590.33** Number of Observations 770 60 Notes: () Dependent variable is LEH, i.e. log of real ousing expenditure. () LY and LPH represent log of real income and log of real ousing price, respectively. (3) ** indicates tat te coefficient is significantly under 95% significance level and te absolute t-value is in te parentesis. One interesting result in Table 3 is tat renters' income elasticity is almost equal one (η =.043), wile it is greater tan unit (η A =.55) for all owners. Te result sows tat ousing is a normal good for a pure consumption demand, since renters' demand could represent a pure consumption demand. On te oter and, ousing is a luxury good for ome owners. Since tere are bot consumption and investment motives for owning a ouse, it is easy to 9 A problem one may see in Table and Table is tat te average income for renters and for total owners are lower tan tat for owners wit one ouse only and owners wit more tan one ouse. Te average ousing price as similar problem. Tis problem is caused by different data set. n "Annual Housing Survey" data set, because of restrictions te data is pooled from 988 to 993. On te oter and, te observation period in "Personal Housing Loan" is from 988 to 99. Wat is interesting is tat ousing price/income ratio is similar for bot data sets, tey are 6.4, 5.8, 5.44, and 5.04 for total owners of DGBAS data set, total owners of Land Bank data set, owners wit one ouse only, and owners wit more tan one ouse, respectively.
8 Lin and Lin sow tat te income elasticity of investment demand for ousing sould be greater tan one. Now, te "Personal House Loan" data set is applied ere specifically to estimate te income elasticity of investment demand for ousing. Te data set is also divided into two subtenure groups, ouseolds wit only one ouse and ouseolds wit a second ouse or more. Again, by applying OLS metod te estimation results are sown in Table 4. All coefficients in Table 4 are significant at 95% significance level wit rigt signs for bot subtenture groups. Additionally, R s are also quite ig. Table 4. Te Expenditure Function of Owning One House and Owning a Second or More Houses All Owners Owners wit One House Only OwnersBuying Second or More Houses ntercept -0.076 0.789-0.7949 (0.) (0.8) (0.34) LY 0.930** 0.8945** 0.9379** (.88) (5.03) (5.60) LPH -0.50** -0.448** -0.0534 (.8) (.93) (0.74) R 0.7050 0.673 0.7934 F-value 4.46**.95** 3.55** Number of Observations 0 33 68 Notes: () Dependent variable is LEH, i.e. log of real ousing expenditure. () LY and LPH represent log of real income and log of real ousing price, respectively. (3) ** indicates tat te coefficient is significantly under 95% significance level and te absolute t-value is in te parentesis. Wen a ouseold buys a second or more ouses, is buying beavior could be classified as a pure investment motive since e does not enjoy any ousing consumption tere. 0 On te oter and, wen a ouseold owns only one ouse, e enjoys bot consumption demand and investment 0 n fact, owning a second ouse may not be a pure investment motive. For example, some families own teir second ouses for recreation purposes. For tis case, we may get an over estimation of investment motivation. However, generally speaking, te demand for second ouses as recreation purposes is quite low in Taiwan. Terefore, we believe tat te situation of upward bias for estimating investment motive in Taiwan is not as serious as in oter countries.
Elasticities of onsumption and nvestment Demand 9 demand. Terefore, te income elasticity for a ouseold wo buys is second or more ouses ( η ) sould be iger tan tat for a ouseold owning one ouse only ( η ), since te former represents a pure investment demand wic intuitively contains a iger income elasticity. n Table 4, te empirical results confirm tis statement, since η (0.9379) is larger tanη (0.8945). However, comparing Table 4 wit Table 3, one may find tat te income elasticity for all owners in Table 4 is muc smaller tan tat of Table 3 (0.930 vs..55). n order to compare tree subtenure groups at a same base, i.e. renters, owners wit only one ouse, and owners wit more tan one ouse, te income elasticities for te latter two are adjusted according to te income elasticity in Table 3. After te adjustment, te income elasticity for owners wit more tan one ouse ( η ) is.643, wile it is.057 for owners wit one ouse only ( η ). Te income elasticities for tree subtenure groups are summarized in Table 5. Housing is an necessity wen it serves as pure consumption good, since renters' income elasticity ( η ) is almost equal one (.043). On te oter and, it is a luxury good wen a dwelling unit serves as an investment good, since ouseolds' income elasticity for pure investment purpose ( η ) is greater tan unit (.643). Furtermore, te order of income elasticities for different A subtenure groups in Table 4 is η < η < η < η. 3 We cart te estimated results in Figure. H as a flat slope comparing to H since consumption demand sould ave a smaller income elasticity. n te meantime, H as a positive intercept (a) sowing tat a minimum amount of ousing consumption is necessary even for a ouseold wit zero income. Tere is one reason to explain wy te estimated coefficients in Table 4 are underestimated. One as to note tat te data set employed in Table 4 comes from Land Bank of Taiwan. Wen people file teir income data to apply for an equity loan, tey tend to inflate teir income so tat tey may ave a iger cance of getting teir application approved. So te estimated income elasticity could be underestimated since income as been inflated tere. Te adjustment for η is:.55/0.930=η /0.9379, so te adjusted η =.643. For η,.55/0.930=η /0.8945, so η =.057. 3 One as to note tat η A sould ave a larger elasticity tan η, since te former contains total owners wile te latter is for owners wit one ouse only.
0 Lin and Lin Moreover, it is intuitive to assume tat bot types of demand are normal and so tat tey are positive correlated wit income (Y). For simplicity, we assume tat ouseolds wit income less tan Y will rent teir ouses,
Elasticities of onsumption and nvestment Demand Table 5. ncome Elasticities of Housing Demand for Different Subtenure Groups Subtenure Groups ncome Elasticity Renters (pure consumption demand) η =.043 Owners wit one ouse only (bot for consumption and investment) Owners buying second or more ouses (pure investment demand) Total Owners(bot for consumption and investment) η =.057 η =.643 η A =.55 Figure. ncome Elasticities of Housing Expenditure Housing Expenditure H, H, H a 0 Y Y H=H +H H η ( η A =.654) =.508 =.997 η H ( =.043) Y ncome Notes:. Assume ouseolds wit income less tan Y are renters; ouseolds wit only one ouse ave income between Y and Y ; and ouseolds aving income greater tany are tose wo own more tan one ouse.. η : income elasticity for renters (pure consumption motive), η : income elasticity for owners wit only one ouse, η A : income elasticity for total owners, η : income elasticity for owners buying second or more ouses (pure investment motive). wile a ouseold wit an income between Y and Y will own only one ouse. For ouseolds wit income iger tan Y, tey will own more tan one ouse. n conclusion, te estimation procedure is sown in Figure. Firstly, a data set wit renters only is applied to estimate income elasticity (η ) standing for
Lin and Lin pure ousing consumption demand, tat is, for ouseolds wit income less tan Y. Secondly, a data set wit only ouseolds wo buy teir second ouse, tat is for tose ouseolds wit income iger tan Y, is employed to estimate te income elasticity (η ) for pure investment demand. Tirdly, a data set wit ouseolds wo own only one ouse, i.e. for tose income between Y and Y, is used to estimate teir gross income elasticity (η ). 4 Finally, a data set wit ouseolds aving one or more tan one ouse (i.e. total owners) will also be applied ere to estimate teir gross income elasticity (η A ). 5 After getting te estimated income elasticities, it is not difficult to compute te sares of consumption demand and of investment demand for ouseolds wit only one ouse. According to Equation () and (), te sares of consumption demand and investment demand for ousing are computed as follow, = H η η.057.643 = = = 0.68, H η η.043.643 and H η η = = = = 0.68 = 0.737. H η η Tat is, for ouseolds owning one ouse, te sare of consumption demand for ousing is about 6.8%, and te sare of investment demand for ousing is about 73.7%. 6 n oter words, most of omebuyers in Taiwan consider investment factors more important tan consumption factors wen tey purcase teir ouses. onclusion 4 Since η is a linear combination of η and η, according to Equation (6) and (7), η sould be somewere between η and η. 5 η A sould be greater tan η intuitively, since it also contains ouseolds wo own more tan one ouse. 6 One may argue tat te estimated proportion for investment demand for ousing is iger tan one s intuition. Tere are two reasons to explain our results: Firstly, some ouseolds may own teir second ouses for recreation purposes, not for investment purposes. Terefore, wen we assume tat investment is te only purpose for owning a second ouse, we may get an upward biased result. Secondly, tere may exist a lock-in effect for buying a ouse mainly because te moving cost is very ig. Terefore, wen a ouseold buys a ouse e/se may consider buying a ouse larger tan is/er optional size because e/se may need a larger space in te future (for is/er cildren to use, for example). We appreciated a referee's comment on tis viewpoint.
Elasticities of onsumption and nvestment Demand 3 Buying a ouse is usually to satisfy ousing consumption demand and ousing investment demand simultaneously. n order to disentangle te above two types of demand, ouseolds are separated into tree subtenure groups in tis study, i.e. renters, owners owning one ouse, and owners buying a second or more ouses. Presumably, renting a ouse is for consumption only, wile buying a second ouse could represent a pure investment demand since it serves almost no consumption purposes. For ouseolds owning only one of te ouse could be purcase for bot consumption and investment purposes. Applying two data sets from Land Bank of Taiwan and DGBAS, te estimated results are as follows: Firstly, ousing is a necessity in Taiwan for a pure consumption motive wit a income elasticity near one (.043). Secondly, te income elasticity for a pure investment demand is greater tan one (.643), wic sows tat a dwelling unit is a luxury good wen it serves as an investment good. Finally, for a ouseold owning one ouse only, te sares for consumption motive and for investment motive are 6% and 74%, respectively.
4 Lin and Lin Appendix Table A.. Te Price of omposite ommodity ( P t ) Year P (a) P-HOUS (b) Weigt ( w ) (c) (d) P t 979 60.04 58.70 86.88* 60.58 980 7.45 70.37 84.78* 7.88 98 83. 79.89 84.78* 84.4 98 85.58 8.04 84.78* 86.99 983 86.75 83.64 66.88 87.88 984 86.7 84.38 66.88 87.57 985 86.58 84.70 66.88 87.6 986 87.9 84.58 66.88 88.4 987 87.64 85.0 66.88 88.60 988 88.77 85.60 75.58 89.98 989 9.68 89.40 75.58 93.93 990 96.5 94.54 75.58 97.6 99 00.00 00.00 75.58 00.00 99 04.46 05.5 96.64 04.7 Source : ndices of onsumer Price in ommodity-price Statistics Montly in Taiwan Area of te Republic of ina, ed. by Directorate-General of Budget, Accounting and Statistics, Executive Yuan. Notes : (a) onsumer Price ndex---general ndex. (b) onsumer Price ndex---housing, including rents; maintenance and repairs wic contain materials, maintenance and repair services; ouseold appliances and equipment wic contain fabric decoration, furniture, electric appliances and kitcen utensils; ouseold keeping services, water supply, electricity and gas wic contain gas, water, electricity and public services. (c) Te tousandt sare of te ousing expenditure in total expenditure. * is substituted by te indices of Urban onsumer Price in Taiwan Area for lack of te ndices of onsumer Price in Taiwan Area. (d) ( a) ( b) * w Pt =, wic is computed by te autors. w
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