總體政策對房屋價格的穩定效果 - 政大學術集成

全文

(1)國立政治大學社會科學院經濟學系碩士論文. 總體政策對房屋價格的穩定效果政治. 大. Stabilization effects立 of macroeconomic policy on housing prices. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. 王雨讓. i n C Yu-Rang h e n g cWang hi U. 指導教授：黃俞寧. v. 博士. Yu-Ning Hwang. 中華民國 105 年 7 月.

(2) 中文摘要. 本文的研究目的為，在一個含有房屋及房屋相關貸款的動態隨機一般均衡模型的架構中，比較貨幣政策、財政政策以及總體審慎政策對於房屋價格及房屋相關貸款的穩定效果。本文建構一個經濟封閉體系，其中包含三種不同家計單位、商品生產部門、房屋建商、資本生產部門，並且由政府部門制定相關政策；此模型的特色為，不同家計單位中的借貸行為、名目價格僵固性以及透過房屋價格抵押貸款的限制來刻劃金融摩擦。我們考慮了一般緊縮貨幣政策、提高財產稅率以. 政治大貸款對國內生產毛額的比例立，財政政策及總體審慎政策比起緊縮貨幣政策擁有較及緊縮貸款價值比；本文發現，在三種政策中，對於抑制房屋價格以及降低住房. ‧. ‧ 國. 學. 好的效果。. er. io. sit. y. Nat. 關鍵字：動態隨機一般均衡模型、房屋價格、房屋貸款占 GDP 比率、貨幣政策、. n. al. 財政政策、總體審慎政策. Ch. engchi. i n U. v.

(3) Abstract The main purpose in this paper is to compare the effect of monetary policy, fiscal policy and macroprudential policy on housing price and housing related loans using a micro-based dynamic stochastic general equilibrium (DSGE) model with housing and housing related loans. We equip a closed economy model with three types of infinitely-lived households (patient households, impatient households and renters), a goods firm, housing and capital producer and a government sector. The. 政治大 nominal rigidity in goods立 price and financial friction in the form of collateral. model features borrowing and lending between patient and impatient households,. ‧ 國. 學. constraints tied to price of house. We consider the contractionary monetary policy by raising the interest rate, fiscal policy by increasing property tax rate and the. ‧. macroprudential policy through tightening the loan-to-value (LTV) ratio. We find that. sit. y. Nat. among these three policies, in terms of dampening the price of housing and lowering. n. al. outperforms the contractionary monetary policy.. Ch. engchi. er. io. the loan-to-GDP ratio, raising the property tax and lowering the LTV ratio. i n U. v. Keywords: Dynamic stochastic general equilibrium (DSGE) model, housing price, housing relative loan-to-GDP ratio, monetary policy, fiscal policy, macroprudential policy..

(4) Contents 1.. 2.. Introduction ............................................................................................................ 1 1.1. Motivation ...................................................................................................... 1. 1.2. Literature Review........................................................................................... 4. The Model............................................................................................................... 7 2.1 2.1.1. Households ..................................................................................................... 7 Patient households ..................................................................................... 7. 治政 2.1.3 Renter households .................................................................................... 11 大立 2.2 Firm .............................................................................................................. 12 Impatient households ............................................................................... 10. 2.2.1. Production of non-housing goods and services ....................................... 12. 2.2.2. Capital of housing producers ................................................................... 17. ‧ 國. ‧. Central bank policy ...................................................................................... 19. Nat. y. 2.3. 學. 2.1.2. 2.3.2. Monetary policy ....................................................................................... 20. er. al. n. 2.4. sit. Fiscal policy ............................................................................................. 19. io. 2.3.1. i n U. v. Market clearing and equilibrium .................................................................. 21. Ch. engchi. 3.. Calibration ............................................................................................................ 22. 4.. Results .................................................................................................................. 26. 5.. 4.1. Monetary Policy ........................................................................................... 26. 4.2. Fiscal Policy ................................................................................................. 26. 4.3. Macroprudential policy: lowering the LTV ratio on debt ............................ 28. 4.4. The effects of three policies ......................................................................... 29. Conclusion ............................................................................................................ 34. Reference ..................................................................................................................... 35. I.

(5) 1. Introduction 1.1. Motivation. The housing debt from 2000s is significantly elevated and the ratio that housing loans plus construction loans to GDP in Taiwan was over 40% in 2006.1 It is higher than the international identified warning line which is set as 40%. Some people point out that there is some relation between real estate prices and housing loans. This issue has been studied in Gimeno and Martínez-Carrascal (2006). High housing prices can be. 政治大. the key factor that makes houses less affordable to many Taiwanese without. 立. borrowing.. y. al. n. 4,000,000. sit. io. 5,000,000. er. 6,000,000. 3,000,000 2,000,000. 100 90 80. Nat. 7,000,000. ‧ 國. 8,000,000. (%). ‧. 9,000,000. 學. (million,NTD). Ch. engchi. i n U. v. 70 60 50. Residential Loans. 40. loan-to-GDP. 30 20. 1,000,000. 10. 0. 0 2001. 2003. 2005. 2007. 2009. 2011. 2013. 2015. Source: The Central Bank of Taiwan- Finance Monthly Statistical Bulletin (May 2016). Figure 1 Taiwanese residential loans and loan-to-GDP ratio from 2001-2015. The price index of house in Taiwan has risen significantly in the beginning of 2000s, especially in Taipei city. According to the data between 2001 and 2016 1. Based on the data during 2001-2015 in the Central Bank of Taiwan- Finance Monthly Statistical Bulletin (May, 2016). 1.

(6) reported by Sin-yi Research Center for Real Estate,2 as shown in Figure 2, the price index of housing in Taipei maintained a growth trend in past 15 years. Although the price index of house declines slightly during the period of global financial crisis between 2007 and 2008, the price index of house boomed again in the second quarter of 2009.After 2009, the price index of house rebounded and continued to grow. By the end of 2015, the house price index has become almost 3 times its level in 2001. In response to the rising housing prices, the central bank of Taiwan implemented the credit control on mortgages in June 2010 and regulated the amount of loans in. 政治大 in response to this policy. In March 2013, the central bank decided to implement 立 order to dampen the price of houses, but the price of house did not drop significantly. stricter regulations on mortgages and the housing price had significant drop in. ‧ 國. 學. response to the policy. This policy was just suspended in March 2016. Some people. y. sit. n. al. er. io. 300. Nat. 350. ‧. urge that fiscal policy can be more effective than monetary policy.3. 250 200. Ch. engchi. i n U. v. Taipei. 150. Taiwan. 100 50 0. Source: Sin-yi Research Center for Real Estate (2016Q1). Figure 2 Taiwanese House Price Index from 2001Q1-2016Q1 2 3. The data is obtained from the database of Sin-yi Research Center for Real Estate (2016). Press conference References after Meeting of Board of central bank committee (June 2015). 2.

(7) There have been some literature discussing the housing prices and the fundamental of Taiwan, such as Lee, Liang and Chou (2008), Chang, Chen, Teng and Yang (2009), Ma and Lin (2009) and Lin (2012). However, they use the empirical analysis lacking of structural model. Chen and Cheng (2012) use the DSGE model to discuss the effects of financial accelerator on housing market and the relationship between external finance premium and housing prices. The purpose of this paper is to capture the effects of monetary policy, fiscal policy and macroprudential policy on house prices. Different from Chen and Cheng. 政治大 emphasize policy analyses and would like to examine which policy may be more 立 (2012), we use the collateral budget constraint similar to that in Iacoviello (2005). We. effective in dampening the housing prices and reducing the loan-to-GDP ratio with a. ‧ 國. 學. DSGE model.. 4. We follow Alpanda and Zubairy (2013) to set up a DSGE model.. ‧. While their model is a real economy, we include money and nominal rigidity and use. sit. y. Nat. Taiwan’s data to calibrate key parameters for Taiwan to examine the effects of. io. er. policies. We consider tightening the loan-to-value ratio (hence force, LTV), increasing property tax on houses and tightened monetary policy. The calibration results show. al. n. v i n Ch that the fiscal policy and macroprudential policy are more effective to prevent the engchi U price of housing from rising and reduce the loan-to-GDP ratio.. The rest of this paper is organized as follows. In Section 1.2, related literatures are reviewed. In Section 2, we describe the model and represent first-order conditions. The calibration will be described in Section 3. The results and conclusion will be described in Section 4 and Section 5, respectively; we also point out some issues for future research in conclusion.. 4. Loan-to-GDP ratio means the ratio that loan of housing to GDP. 3.

(8) 1.2. Literature Review. Recently, a lot of literature mentions that assets play as key elements in business cycles. The price of assets will affect the households’ consumption through the wealth effect and liquidity constraint. At first, Bernanke and Gertler (1989) formalize the “credit view” in a general equilibrium framework. In 1999, Bernanke, Gertler and Gilchrist use the new-Keynesian setup such as stick-price in the dynamic model. Iacoviello (2005) follows their framework to establish a DSGE model to explain the. 政治大 (2005), he chooses housing as the asset and adds two important dimensions to the 立 interaction between asset price and economic activity. In the study of Iacoviello. literature on financial frictions and the macroeconomy, one is that firms and. ‧ 國. 學. households both will be tied by real estate through the collateral constraints; and. ‧. another is, nominal debt for a subset of the households. The reason why adding. sit. y. Nat. nominal debts is that, almost all debt contracts are in nominal terms in low-inflation. io. er. countries. Two types of households are set through the different time preference. Patient households, as the lenders, have higher discount rate; impatient households, as. al. n. v i n C h rate. Iacoviello (2005) the borrowers, have lower discount shows that debt-deflation engchi U. which amplifies the demand shock but stabilizes the supply shock yields an improved. tradeoff in output-inflation variances for the central bank. They also show that monetary policy’s response to asset prices dose not yield significant welfare gains. In Iacoviello and Neri (2010), they use the DSGE model and explicitly model the price and the quantity of. housing market. Also, they use Bayesian methods to. estimate model parameters. To measure the spillovers from the housing market to the macroeconomy, their model captures two main features of housing. On the supply side, they add heterogeneous sectors, non-housing sector producer and housing sector producer respectively. On the other hand, on the demand side, housing enters 4.

(9) households’ utility, and can be used as a collateral for loans. Also, they generate the nominal rigidity and financing frictions in the household sector. Their research matches the observation that both housing prices and housing investment are strongly procyclical and sensitive to monetary shocks. In their conclusion, they find out that the spillovers from the housing market to the macroeconomy are through consumption. Different from the collateral mortgage constraint setting in Iacoviello (2005), Chen and Cheng (2012) modify the model from Bernanke et al. (1999) and Aoki and. 政治大 Following the assumptions in Bernanke and Gertler (1989), the capital and lending 立. Vlieghe (2004) to study the features of housing market in Taiwan and business cycles.. markets are incomplete markets, and the quantity of debts constrained by the net. ‧ 國. 學. worth of entrepreneur. As a result, the financial accelerator can amplify the effect of. ‧. monetary policy on the macroeconomic fluctuations under exogenous shocks, by the. sit. y. Nat. default risk premium which rise due to information asymmetry, and is the important. io. er. transmission mechanism of business cycles. Chen and Cheng (2012) apply the external finance premium (EFP) to housing market. They find that under various. al. n. v i n C h and the EFP ofUhousing are negatively related. exogenous shocks, the price of housing engchi. The financial accelerator highlights the feature that the correlation between the EFP of. housing and housing business cycles is also negative. In Alpanda and Zubairy (2013), they build a closed-economy real model with owner-occupied and rental housing. In their model, similar to Iacoviello (2005), they feature borrowing and lending across heterogeneous household and financial frictions in the form of collateral constraints tied to house prices. They separate the households into three types: patient households (lenders), impatient households (borrowers) and renter households. Note that renter households’ problem is not intertemporal. They consume their disposable income every period. Furthermore, they include a rich set of 5.

(10) housing-related tools in the model. Such as property taxes, mortgage interest deduction, property tax deduction and depreciation allowance for rental income. The conclusion is that, they found that housing-related fiscal policies would potentially lead to a large decline in output in Canada. Especially the fiscal policies which are more broad-based would affect the output more, such as taxing imputed rents from owner-occupied housing or eliminating property tax deductions. In Sami Alpanda and Sarah Zubairy (2014), they establish a closed-economy real model with owner-occupied and rental housing. Different from the research in Sami. 政治大 in Iacoviello (2005). In their setting, mortgage loans are amortized over the long time, 立 Alpanda and Sarah Zubairy (2013), they separate the households into just two types as. thus, one can differentiate between the flow and the stock of household debt. They. ‧ 國. 學. consider the effects of monetary policy and fiscal policies to reduce the household. ‧. debt-to-income ratio. The key point to differentiate effects of policies is that the. sit. y. Nat. policies apply to only new lending or to all existing mortgage debt. In their conclusion,. io. er. monetary tightening is able to reduce the stock of mortgage debt, but lead to higher household debt-to-income ratio. The most effective and least costly policy to reduce. al. n. v i n C hin mortgage interest tightening deduction engchi U. household debt are. and regulatory. loan-to-value (LTV) ratio, followed by increasing property tax rate and monetary tightening. In this study, I follow the setting of Sami Alpanda and Sarah Zubairy (2013), and add the nominal rigidities and monetary policy. The main features in the study are that I use the data of Taiwan to calibrate the parameters and modify the model about the tax rule to let the model more fitting Taiwan’s situation. And I want to research that weather the fiscal policies or monetary policy can stabilize the fluctuation of the price of housing and lower the loan-to-GDP ratio.. 6.

(11) 2. The Model We follow Alpanda and Zubairy (2013) to establish a DSGE model with three types of infinitely-lived households: patient households (savers), impatient households (borrowers) and renters. However, they assume the flexible price; we include nominal rigidity to evaluate the effects of monetary policy. As in Iacoviello (2005), the patient households and impatient households own the occupied housing, and the patient households own the rental housing as well. As in Kiyotaki and Moore (1997) and. 政治大. Iacoviello (2005), the impatient households’ borrowing is constrained by the collateral value that their housing provides.. 立. ‧ 國. 學. 2.1 Households. ‧. 2.1.1. Patient households. sit. y. Nat. io. er. We consider an economy populated by patient households that have infinitely-lived and of measure one. The term “patient” captures the assumption that this kind of. al. n. v i n C hthan other households household has higher discount rate as in Iacoviello (2005). The engchi U household sector has housing in their utility function, and maximizes the utility by choosing consumption, cP ,t , own-occupied housing, hP ,t , and labor supply, lP ,t :.   l 1    Et   P t log cP ,   h log hP , 1  l P ,  1  t    . (1). where  P is the time-discount rate and is smaller than one, t is the time index,  h and  l determine the relative importance of housing and labor in the utility function 7.

(12) respectively, and  is the inverse of the elasticity of labor supply. The budget constraint of patient households can be written as below:. 1   c  cP,t  qh,t  hP ,t  1   h  hP,t 1   qh,t  hR ,t  1   h  hR,t 1   qk ,t  kt  1   k  kt 1   bt  bt g  1 1   wP ,t lP ,t  rh ,t hR ,t 1  rk ,t kt 1  1  Rt 1   bt 1  bt 1g   trP ,t   1  1      t t    1 1   k  rk ,t   k  kt 1   b Rt 1  bt 1  bt 1g  1   t  1   t   . (2).  yP  wP ,t lP ,t   rh ,t   h ,t  hR ,t 1    P ,t qh ,t  hP ,t 1  hR ,t 1   profit.. 立. 政治大. ‧ 國. 學. where hP ,t and hR ,t are owner-occupied and rental housing accumulated by patient households, and they also accumulate capital, kt , with the relative prices, qh ,t and. ‧. qk ,t . rh ,t and rk ,t are the rental income they receive from housing and capital, and. y. Nat. io. sit.  h and  k are their corresponding depreciation rates. Patient households lend to. er. g impatient households and government, bt and bt , and receive a predetermined. al. n. v i n C h tax rate on housing, is the property engchi U. interest rate, Rt .  P ,t.  b is the tax rate on. interest income,  k is the tax rate on rental capital income, and labor and rental housing income are taxed at the rate of  yP and  k . Also, patient households receive transfer in a lump-sum fashion from the government, trP ,t . Patient households will maximize their utility subject to the budget constraint. We solve this problem by Lagrange multiplier method and yield the first-order conditions for consumption (3), owner-occupied housing (4), rental housing (5), capital (6), labor supply (7), and debt (8) where P ,t is the Lagrange multiplier of. 8.

(13) patient households, and. t. is the inflation rate which is defined as.  t   Pt  Pt 1  / Pt 1 . Equation (4) represents the marginal cost of acquiring a unit of housing equates to the marginal utility gain from housing services and expected net-of-tax capital gains. Similarly, equation (5) and (6) represents the respective marginal cost of rental housing and capital equates to the expected marginal gain in net-of-tax rental income and capital gains. The optimality condition for labor equates the marginal rate of substitution between labor and consumption to the after-tax wage rate is written as (7). Finally, equation (8) represents the first-order condition for debt. 政治大 expected discount utility gain 立from the net-of-tax interest income.. that equates the marginal utility cost of forgone consumption from saving to the. ‧ 國. 學 ‧. 1  P ,t 1   c   0 cP ,t. (4). er. io. sit. y. Nat.     1   Et  P h   P ,t 1   qh ,t 1 1   h    P ,t 1qh ,t 1    qh ,t   P ,t hP ,t  P ,t     . (3).       Et  P  P ,t 1   qh,t 1 1   h   rh ,t 1   yP  rh ,t 1   h ,t 1    P ,t 1qh ,t 1    qh ,t       P ,t  . (5).       Et  P  P ,t 1   qk ,t 1 1   k   rk ,t 1   k  rk ,t 1   k     qk ,t     P ,t    . (6). l lP,t  P,t wP,t  yP  1. (7). n. al. Ch. engchi. i n U. v.    1    1  Et  P  P ,t 1  1   b  Rt  1     1    t 1  P ,t    . 9. (8).

(14) 2.1.2. Impatient households. Not only the patient household, the economy is also populated by impatient households that have infinitely-lived and of measure one. They have the same utility function as patient households except that their time-discount rate is less than patient households (  I   P ) that means they discount the future more heavily than the patient ones. The impatient households maximum the utility by choosing consumption,. cI ,t , housing, hI ,t , and labor supply, lI ,t :. 政治大. 立 E   log c . t . I.  . I ,.  lI , 1   h log hI , 1  l  1  . (9). 學 ‧. ‧ 國. t.  t. The budget constraint of impatient households is following：. 1 1   t . n. er. io. al. sit. y. Nat. 1   c  cI ,t  qh,t hI ,t  1   h  hI ,t 1   1  Rt 1  bt 1. i n U. v.  1   wI ,t lI ,t  bt  trI ,t   yI  wI ,t lI ,t  Rt 1bt 1   q h 1   t   P,t h,t I ,t 1 . Ch. engchi. (10). where hI ,t is owner-occupied by impatient households, and they can’t accumulate capital and rental housing. Impatient households as a borrower, they borrow bt from patient households for consumption or housing and pay the interest rate, Rt .  yI is the income tax for inpatient households and they receive transfer in a lump-sum fashion from the government, trI ,t . As borrowers, impatient households face a borrowing constraint： 10.

(15) Bt  t qh ,t hI ,t Pt. (11). where t is the loan-to-value ratio that can be collateralized for borrowing. Impatient households will maximize their utility subject to the budget constraint and borrowing constraint. We solve the problem by Lagrange multiplier method and yield the first-order conditions for consumption (12), owner-occupied housing (13), labor supply (14), and borrowing (15) where I ,t is the Lagrange multiplier of impatient households and t is the Lagrange multiplier on the borrowing constraint.. 1  I ,t 1   c   0 cI ,t. (12). 學. ‧ 國. 立. 政治大. y.  I ,t 1   1 1  1   yI  Rt  t 1b       I ,t  1   t 1    . n. er. io. 1  t   Et  I . 2.1.3. (14). sit. Nat. l lI ,t  I ,t wI ,t  yI  1. al. (13). ‧.  1  Et  I h  I ,t 1  qh ,t 1 1   h    P ,t 1qh ,t 1    I ,t qh ,t  t I ,tt qh ,t  0  hI ,t . Ch. engchi. i n U. v. (15). Renter households. The economy is also populated by renter households that are infinitely-lived and of measure one. They have the same utility function as impatient households, however, the difference between impatient households and renter households is that renter households’ problems is not intertemporal as in Alpanda and Zubairy (2013). The impatient households maximize the utility by choosing consumption, cR ,t , housing,. hR ,t , and labor supply, lR ,t : 11.

(16) . Et   I.  t. t .   lR , 1   log cR ,   h log hR , 1  l  1    . (16). The budget constraint of renter households is shown below:. 1   c  cR,t  rh,t hR,t 1  1   yR  wR,t lR,t  trR,t. (17). where  yR is the income tax for renter households who receive transfer in a. 政治大. lump-sum fashion from the government, trR ,t . Renter households can’t accumulate. 立. capital and occupied-housing. We solve the problem by Lagrange multiplier method. ‧ 國. 學. for maximizing their utility and yield the first-order conditions for consumption (18),. n. al. 1  R ,t 1   c   0 cR ,t. Ch. e n gc h i. er. io. sit. y. Nat. renter households.. ‧. renter housing (19), and labor supply (20) where R ,t is the Lagrange multiplier of. i n U. v. (18). 1   Et  I rh ,t 1  Et  I h  R ,t 1hR ,t  . (19). l lR,t  R,t wR,t  yR  1. (20). 2.2 Firm 2.2.1. Production of non-housing goods and services. Producers,. each. of. whom. is. indexed 12. by. j ,. use. a. Cobb-Douglas.

(17) constant-return-to-scale technology that uses capital and three types of labor as inputs to produce a non-housing goods,. yt  j  for consumption, investment and. government expenditure (21). Consumption uses the CES technology (22). Investment and government uses the CES technology as consumption.. 1.     yt  j   zt ut  j  kt 1  j  lP ,t  j  P lI ,t  j  I lR ,t  j  R   . (21).  y ,t /  y ,t 1.  y ,t 1 / y ,t   1 ct    ct  j  dj   0 . (22). 政治大. 立. ‧ 國. 學. where  is the share of capital in production, ut denotes the utilization rate of capital, and  P ,  I ,  R are the share of patient households, impatient households. ‧. and renter households respectively. zt denotes the aggregate productivity shock. al. er. io. sit. y. Nat. which follows an AR(1) process:. v. n. log zt  1   z  log z   z log zt 1   z ,t. Ch. engchi. i n U. (23). where  z is the shock parameter of the productivity shock persistence and  z ,t is the stochastic shock of productivity. The firm j minimizes the total cost subject to the production function by choosing the quantity of output and input which include three types of labor demand (24)-(26), capital (27) and utilization rate of capital (28):. WP ,t Pt.  t (1   ) P. 13. yt ( j ) l P ,t ( j ). (24).

(18) WI ,t.  t (1   ) I. yt ( j ) l I ,t ( j ). (25).  t (1   ) R. yt ( j ) l R ,t ( j ). (26). Pt. WR ,t Pt. t. yt ( j )   rk ,t  u ut ( j )1  1 kt 1 ( j ) 1 . (27). yt ( j )   u ut ( j ) kt 1 ( j ) ut ( j ). (28). t. .  P (1 ).  I (1 ).  WI ,t      I Pt .  R (1 ).  WR,t      R Pt . (29). al. er. io. sit. Nat. 1 1  rk ,t (1   )   u 1 1  WP ,t  mct   u  P  (1   )1   zt     P t. ‧. ‧ 國. 學. as shown in (29):. y. where t. 政治大 is the Lagrange立 multiplier of the firm which is equal to the marginal cost. n.  u is the level in the cost specification of utilization and  denotes the inverse of. Ch. engchi. i n U. v. the elasticity of the utilization rate to the rental rate of capital. The type of the firm is monopolistically competition; they produce heterogeneous goods and aggregate them into a homogeneous good using the CES aggregate production function as in Iacoviello (2005). In order to motivate price stickiness, we assume that firms have implicit cost when they adjust the nominal price as in Bernanke et al. (1999). Each firm sells yt ( j ) at the price Pt  j  . Aggregate output index and price index are given by (30)-(31):. 14.

(19)  y ,t /  y ,t 1.  y ,t 1 / y ,t   1 yt    yt  j  dj   0 . . (30). 1/ 1 y ,t. 1 y ,t  1  Pt    Pt  j  dj   0 . . (31). So, each firm faces the individual demand curve:.  P  j  yt  j    t   Pt .  y ,t. yt. (32). 政治大. 立. ‧ 國. 學. where yt and Pt are the aggregate output and price respectively. Time-varying elasticity of substitution between the differentiated goods is  y ,t .  P,t   y ,t /  y ,t  1. ‧. which follows an AR(1) process:. sit. y. Nat. n. al. er. io. log  P,t  1  P  log  P  P log  P,t 1   P,t. Ch. engchi. i n U. v. (33). where  P is the markup in the steady-state. Firms can choose the sale price Pt  j  taking Pt and the demand function as given in each period. Furthermore, the price can only be changed with the probability 1  d  , and remains same as last period with the probability d . Each firm solves the optimal prices given by:.   P ( j)  MaxEt  d  t ,t  yt ( j )  t  mct    0  Pt  . 15. (34).

(20) where t ,t    P  cP,t / cP,t   is the patient household’s relevant discount factor. Introducing (32) and t ,t    P  cP,t / cP,t   into (34) gives:. . MaxEt   d  P. .  0. .  y ,t  P ( j ) 1 y ,t  Pt  j   t yt   mct       Pt    Pt  . cP ,t cP ,t . (35). By symmetry, all optimizing firms make the same decision. Letting Pt denote the reset nominal price and the frim index is dropped. Hence, the first-order condition of firms is:. 政治大. Et   d  P   0. .  y ,t. P  yt  t    Pt . cP ,t. cP ,t .   P  Ptt  t   Pt . 學. . ‧ 國. 立.   y ,t     mc 0  t      1   y , t   . (36). ‧. Nat. er. io. sit. y. where Ptt   Pt / Pt  is the relative price of firms that optimize and the general price level. In Calvo’s setup, as a fraction d of prices remain the same as the previous. n. al. i n period, the aggregate price levelC can be written as follows: hengchi U 1 y ,t. Pt. 1 y ,t. Dividing through by Pt.  d  Pt 1 . 1 y ,t.  1  d  Pt. 1 y ,t. v. (37). and rearranging, we can yield the relative price of. optimizers as a function of the inflation rate:. 1  d 1   t Ptt  t   1  d  16.  . 1.  y ,t 1 1 y ,t.   . (38).

(21) Combining (36) and (37) yields a forward-looking Phillips curve.. 2.2.2. Capital and housing producers. To make sure that capital and housing have a single price across agents, we. assume that the accumulations of them are undertaken by perfectly competitive market such as Bernanke et al. (1999). First, following the setting in Alpanda and Zubairy (2013), the capital producers purchase the undepreciated part of the installed capital from patient households at a price qk ,t , and then, they make new capital. 政治大 investment goods from the final goods producers at a relative price of 1 to produce the 立 capital stock. The capital stock will be carried to the next period. The production is. ‧ 國. 學. subject to adjustment costs when it changes in investment. The law of motion of. n. Ch. engchi. 2.   ik ,t  . sit. io. al.  ik ,t   1    ik ,t 1 . er. Nat.   kt  1   k  kt 1  1  ik 2  . y. ‧. capital is:. i n U. (39). v. where  ik is the parameter of the investment adjustment cost of capital. The installed capital stock that capital producer produce will be sold back to the patient households at the price qk ,t . Therefore, the capital producer will maximum their profit subject to the law of motion of capital:. . Et  P t  t. P, [q k  q 1   k  k 1  ik , ] P,t k ,  k ,. 17. (40).

(22) . Max Et  ik ,t.  t.  t P. P, P,t. 2          q 1    k  1   ik  ik ,t  1  i   q 1    k  i  k t 1 k ,t k , k  1 k ,  k ,    2  ik ,t 1         . (41). where the discount rate of patient households is used for discounting future payoff. For optimization, we can obtain the first-order condition of capital which yields an investment demand:.   i  i  qk ,t 1   ik  k ,t  1 k ,t  ik i    k ,t 1  ik ,t 1 2 .  ik ,t   1    ik ,t 1 . 立. 2. 2      ik ,t 1  ik ,t 1   P ,t 1    P Et   1  1   ik qk ,t 1   i   ik ,t   P ,t  k ,t      . (42). 政治大. ‧ (43). n. al. er. io. sit. Nat. 2    i   , h t ht  1   h  ht 1  1  ih   1  ih ,t 2  ih,t 1     . y. subject to adjustment costs when the investment is made:. 學. ‧ 國. Similar to capital producer, we also can get the law of motion of housing that is. where  ih is the parameter C of hthe investment. engchi. iv n adjustment U. cost of housing and. ht  hP,t  hI ,t  hR ,t . The housing stock that housing producer produced will be sold. back to the patient households at the price qh ,t . Therefore, the housing producer will maximize their profit subject to the law of motion of housing:. . Et  P t  t. P , [q h  q 1   h  h 1  ih, ] P,t h,  h,. 18. (44).

(23) . Max Et  ik ,t.  t.  t P. P, P,t. 2          q 1    h  1   ih  ih,t  1  i   q 1    h  i  h t 1 h ,t h , h  1 h ,  h,    2  ih,t 1         . (45). where using the discount rate of patient households to discount. To find the optimization, we can get the first-order condition of housing and yield an investment demand：. 2 2      ih,t  ih,t  ih  ih,t    ih,t 1  ih,t 1   P ,t 1  1 qh,t 1   ih   1    1    P Et   1   ih qh,t 1  i i  i   2  ih,t 1   ih,t   P ,t  h ,t 1 h ,t 1 h ,t         . 立. 政治大. ‧ 國. 學. 2.3 Central bank policy 2.3.1. (46). Fiscal policy. ‧. n. al. trP ,t   P yt . Ch. trR ,t   R yt . where  is the level parameter and. b. i n U. v. b. Bt 1g Pt 1. b. Bt 1g Pt 1. (48). b. Bt 1g Pt 1. (49). engchi. trI ,t   I yt . er. io. sit. y. Nat. The fiscal authority makes the aggregate transfer to households：. (47). is the parameter that determines the response. of transfers to government debt. The total tax revenue of the government comes from the tax of consumption, labor income, rental housing income, capital income, interest 19.

(24) income and property as following:. taxt   c ct   yP. WP ,t Pt. WI ,t. lP ,t   yI. Pt. lI ,t   yR. WR ,t Pt. lR ,t   yP  rh ,t   h ,t  hR ,t 1   k  rk ,t   k  kt 1.  1 1  1  b Rt 1  bt 1  bt 1g   P ,t qh,t  hP ,t 1  hR ,t 1  hI ,t 1     yI Rt 1bt 1 (1   t )  (1   t )  (1   t ). (50). The accumulation of government debts follows the law of motion as follows:. 政治大. Bt g B g  1  Rt 1  t 1  gt  trP ,t  trI ,t  trR ,t  taxt Pt Pt. 學. ‧ 國. 立. (51). where g t is the government expenditure which follows an AR(1) process:. (52). Nat. er. io. sit. y. ‧. log gt  1   g  log g   g log gt 1   g ,t. where  g is the shock parameter of government expenditure persistence, g is the. n. al. Ch. engchi. i n U. v. government expenditure level in steady state and  g ,t denotes the fiscal policy shock.. 2.3.2. Monetary policy. The central bank uses the Taylor rule to target the nominal interest as in Alpanda and Zubairy (2013):.  1   t    log yt    Rt   Rt 1  1     R   log  1    y y  R,t  20. (53).

(25) where  is the policy parameter of persistence of Taylor rule,   is the policy parameter of the inflation of Taylor rule,  y is the policy parameter of the output of Taylor rule and  R ,t denotes the monetary policy shock.. 2.4 Market clearing and equilibrium Including labor market, housing market, funds market and commodity market, all of the markets in the model should be cleared. The market clearing condition for. 政治大 and housing market is given 立by (54)-(57):. 學. ct  it  gt  yt. io. n. al. ht  hP,t  hI ,t  hR ,t. Ch. engchi U. sit. Nat. it  ik ,t  ih,t. y. t. er. ct  cP, t  c, I  t c, R. (54). ‧. ‧ 國. non-housing goods market, total non-housing consumption market, total investment. v ni. (55) (56) (57). Using the equations above and those mentioned in the previous sections, we can solve the steady state of this model.. 21.

(26) 3. Calibration We follow Alpanda and Zubairy (2013) for most of the parameters settings. We calibrate the parameters to make the steady-state value of key variables in the model match the data from DGBAS (Directorate General of Budget, Accounting and Statistics) of Taiwan. The specification of parameters is shown in Table 1. It is required that  P   I to ensure impatient households have greater motivation to borrow. Therefore, the subjective discount factor of patient and impatient households,  P and  I , are set to 0.9916 and 0.9852, respectively, as in. 政治大 Alpanda and Zubairy (2013). The inverse labor supply elasticity is set to 1, following 立. Alpanda and Zubairy (2013). The loan-to-value ratio in the steady state is set to 0.9 in. ‧ 國. 學. the baseline case. Furthermore, the disutility of labor,  l , is calibrated to 0.6, to. ‧. generate the labor supply of patient households to be equal to one at the steady state. y. Nat. without loss of generality. And the utility level for housing,  h , is calibrate to 0.7 in. io. sit. the steady state to generate the total housing value to be around 5.6 times the GDP5.. al. er. The parameters of the level and elasticity in the utilization cost,  and  u , are. n. v i n C h is equal to 1 atUthe steady state. The adjustment calibrated to ensure that the utilization engchi. costs of investment,  ik and  ih , are set to 8 and 30, following Alpanda and Zubairy (2013). Following the setting of parameters in Iacoviello (2004), the depreciation rate of housing and capital,  h and  k , are set to 0.005 and 0.015 respectively, and the capital share in production,  , is set to 0.3. Because we do not have data for wages of patient, impatient and renter households separately, we borrow data of the share of buying houses without debts,. 5. Based on the data from Directorate General of Budget, Accounting and Statistics, Executive Yuan, R.O.C.-Population and Housing Census in Taiwan and Fujian area (2000). 22.

(27) with debts and rent houses that Lin and Chen (2005) present to calibrate the wage share of patient households, impatient households and renter households,  P ,  I and  R , to be 0.64, 0.26 and 0.10 respectively. The parameters of transfers to households are calibrated to ensure that the transfers to the three types of households are zero in the steady state. To preserve determinacy of the model while ensuring that government debt doesn’t play a major role in determining the dynamics of the model, the response parameter of transfers to the government bonds,. b. , is 0.005 as in. Alpanda and Zubairy (2013). The tax rates of consumption and interest income,  c and  b , are specified as. 政治大 5%, based on the tax’s law of Taiwan. Also, Taiwan has implemented a progressive tax 立 system for individual income taxes, thus we set the labor income tax of three different. ‧ 國. 學. types of households,  yP ,  yI and  yR , to be 0.25, 0.25 and 0.05 respectively. The tax. ‧. rate of capital income is captured using the taxation of capital gains on securities and. sit. y. Nat. is set as 15%. Finally, the tax rate of property is set to 1.2% in the baseline case, based. n. al. er. io. on the tax’s law of Taiwan.. Ch. engchi. 23. i n U. v.

(28) Table 1 Calibration parameters. Parameter. Description. Value. P. Discount factor-Patient household. 0.9916. I. Discount factor-Impatient household. 0.9852. d. Probability of remain pricing. 0.75. . Inverse labor supply elasticity. 1. . Utilization cost elasticity. 5. l. Level for labor in utility. 0.6. h. Level for housing in utility. 0.7. y. Elasticity of substitution between different goods. 5. ‧ 國. Capital share in production. Labor share in production-Patient household. ‧. P. 學. . 立. 政治大. 0.3 0.64. Labor share in production-Renter household. h. Housing depreciation rate. k. Capital depreciation rate. u. Utilization cost level. 0.025.  ih. Housing investment adj. cost. 30.  ik. Capital investment adj. cost. 8. P. Transfer share-Patient household. 0.002. I. Transfer share-Impatient household. 0.002. R. Transfer share-Renter household. 0.002. Response of transfer to gov. bonds. 0.005. n. Ch. engchi. 24. 0.10. er. io. b. al. y. R. 0.26. sit. Labor share in production-Impatient household. Nat. I. i n U. v. 0.005 0.015.

(29) c. Consumption tax rates. 0.05. b. Interest income tax rate. 0.05. k. Capital income tax rate. 0.15.  yP. Labor income tax rate-Patient household. 0.25.  yI. Labor income tax rate-Impatient household. 0.25.  yR. Labor income tax rate-Renter household. 0.05. Shock parameter-persistence. . Persistence of Taylor rule. z. Persistence of productivity shock. g. Persistence of government expenditure shock Persistence of property tax shock Persistence of LTV shock. sit. io. n. al. 0.9999. 0.6802 0.8795. er. Persistence of housing preference shock. y. Persistence of markup shock. Taylor rule parameters. 0.9021. 0.9999. Nat. h. 0.5. ‧. P. ‧ 國. . 政治大. 學. . 立. 0.7239. Ch. . Parameter for inflation. y. Parameter for output. engchi. 25. i n U. v. 5 0.

(30) 4. Results 4.1 Monetary Policy We first consider that the central bank conducts contractionary monetary policy in the attempt to reduce housing prices. Figure 3 outlines the impulse response functions of key macroeconomic variables under a 1% increase in the interest rate. First, impatient households reduce their borrowing by about 1% when they face higher interest rate and lower their demand for housing and consumption. The decline in the demand for. 政治大. housing leads to a fall in housing price, and leads to a fall in home equity of. 立. borrowers.. ‧ 國. 學. Second, faced with lower discounted value of future returns due to higher interest rate, patient households reduce their consumption and the investment purchase of. ‧. house and capital. This will lead to a fall in the capital price. Although the fall of. sit. y. Nat. housing prices may make patient households increase their own-occupied housing, the. al. er. io. overall decline in demand leads to a fall in production and wages and leads to a. n. reduction in the aggregate output, yt , and inflation,  t . In particular, the inflation. Ch. engchi. i n U. v. rate falls about 4%. Therefore, rental households reduce their consumption and demand for rental housing increase cause the decline in interest rate of housing. Finally, the decline in debts is stronger than the decline in the overall output; thus, the loan-to GDP ratio falls about 0.35% and the decline in the demand for housing leads to a fall in housing price about 0.014%.. 4.2 Fiscal Policy In this section, we investigate how exogenous and near-permanent changes in raising the property tax rate would affect housing price, household’s debt and other 26.

(31) macroeconomic variables. We will evaluate which policy is more effective to reduce the price of housing and lowers the loan-to GDP ratio. We let the property tax rate follows AR(1) process as:.  P,t  1    P   P,t 1   ,t. (58). Figure 4 plots the impulse response functions under an increase in the property tax rate. We assume that the property tax rate is raised from 1.2% to 1.56% annually, a. 政治大 holding house is increased, 立and the lower housing demand leads to a fall in the. 0.36 percentage point increase annually. The housing demand falls because the cost of. ‧ 國. 學. nominal house prices.. For impatient households, the increased cost of holding housing leads to a decline. ‧. in their demand for housing. The fall in nominal housing price and lowered housing. sit. y. Nat. demand means lower home equity of borrowers, and thus, impatient households. n. al. er. io. reduce their borrowing and consumption.. i n U. v. For patient households, they increase their consumption and reduce the capital. Ch. engchi. purchase, so the price of capital falls.6 Because of the decline in saving, the real interest rate rises upon impact. The decline in saving leads to the decline in the supply of credit and tightens the borrowers’ constraint. For renter households, the demand for rental housing increases because of the decrease in the interest rate of housing. Therefore, renter households increase their consumption because they have lower cost of rental housing. Overall, the increase in the property tax rate results in lower aggregate output and debt. However, the decline in debt is stronger than the decline in overall output, and. 6. Cause non-residential investment declines along with residential investment in the short-run. 27.

(32) thus, the loan-to GDP ratio falls about 2%.. 4.3. Macroprudential policy: lowering the LTV ratio on debt. The control on the LTV ratio has been considered as one of the primary macroprudential policies. In this section, we investigate how exogenous and near-permanent changes in lowering the LTV ratio would affect housing price, household’s debt and other macroeconomic variables. We let regulatory LTV follows AR(1) process as:. 立. 政治大   1          t. .  t 1. (59).  ,t. ‧ 國. 學. Figure 5 plots the impulse response functions under a negative shock to the LTV. ‧. ratio. We lower the LTV ratio from 0.9 to 0.7, a 20% decrease. In this case, the direct. sit. y. Nat. effect of lowering the LTV ratio is on the impatient households’ (borrowers) borrowing. n. al. er. io. constraint. Due to the lower amount of their borrowing, impatient household reduces. i n U. v. their consumption and demand for housing. The decline in the housing demand leads. Ch. engchi. to the decline in housing price and overall housing investment. For renter households, the lowering LTV ratio leads to a fall in the interest rate of housing, thus they increase their demand for rental housing. Given the substitutability between housing and consumption, renters decrease their consumption about 3%. For patient households, lowering the LTV ratio also decreases the inflation rate, which prompts the central bank to reduce the interest rate, Rt . The lowered interest rate will make patient households increase their consumption and lower their saving. But the decline of renter households’ consumption is stronger in the beginning, which leads to the initial decline in the aggregate consumption. The decline in housing price 28.

(33) incentivizes patient households to increase their holding of housing. Lowering the LTV ratio results in lower debts. The decline in debt is stronger than the increase in the overall output and thus the loan-to GDP ratio falls about 5%.. 4.4 The effects of three policies Figure 6 shows the effects of the three policies on the output, households’ debt, households’ debt-to-GDP ratio and housing prices for a 5 year horizon. In the aggregate output, tightened monetary policy leads to a fall in the aggregate output. But. 政治大. raising the property tax and lowering the LTV ratio lead to a rise in the aggregate. 立. output.. ‧ 國. 學. As for the households’ debt, tightened monetary policy causes a 1% fall in households’ debt, smaller than its decline under rest of the two policies. Furthermore,. ‧. tightening the LTV ratio has greater impact on households’ debts than raising the. y. Nat. n. al. er. io. sector.. sit. property tax rate due to the fact that it is a targeted policy instrument for the housing. i n U. v. As for the households’ loan-to-GDP ratio, tightened monetary policy shock leads. Ch. engchi. to a stronger decline in debts than in the overall output. Therefore, the loan-to-GDP ratio falls about 0.35%. Other two policies also result in the decline in the loan-to-GDP ratio. Finally, regarding the housing price, increasing the property tax rate has the most significant effect among all three. Note that, although tightening the LTV ratio increases housing price by only 0.003%, it still has a negative effect on housing price after 2 periods and it has a much more persistent effect than tightening monetary policy in suppressing housing price.. 29.

(34) 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. Figure 3 Impulse responses to a 1% innovation in the Taylor rule.. 30.

(35) 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. Figure 4 Impulse responses to a 0.36 % persistent increase in the property tax rate.. 31.

(36) 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. Figure 5 Impulse responses to a 20 % persistent decline in the regulatory LTV on loans.. 32.

(37) 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. Note: contractionary monetary policy (red line), fiscal policy (blue line) and macroprudential policy (black line).. Figure 6 Comparing the effects of the three policies on household’s loan-to-GDP ratio.. 33.

(38) 5. Conclusion In this paper, we examine the effects of tightening monetary policy, raising the property tax and lowering the LTV ratio on housing price and loan-to-GDP ratio with a dynamic stochastic general equilibrium (DSGE) model. In this study, we follow Alpanda and Zubairy (2013) to set up housing and capital producer, three types of infinitely-lived households (patient households, impatient households and renters), a goods firm and a government sector. Different from the model of Alpanda and. 政治大 include the nominal rigidity立 in price and monetary policy in the model.. Zubairy (2013), we modify the tax system to let this model fit Taiwan’s situation, and. ‧ 國. 學. We calibrate the parameters to let the steady-state values of this model to match the long-term situation in Taiwan. We find out that, the monetary policy has smaller. ‧. effect in suppressing the price of housing and lowering the loan-to-GDP ratio.. sit. y. Nat. Furthermore, tightening the LTV ratio has greater impact on households’ loan-to-GDP. n. al. er. io. ratio and price of housing than increasing the property tax rate.. i n U. v. We conclude this paper by pointing out some related issues for future research.. Ch. engchi. First, we can consider different debts including long-term mortgages and flow household debts. Also, we can consider an alternative central bank’s monetary policy which responds to the change in price of housing. Furthermore, we can consider more fiscal policies that can affect housing price in their effects on stabilizing housing prices.. 34.

(39) Reference Alpanda, S., and S. Zubairy (2013), “Housing and Tax Policy,” Bank of Canada Working Paper No.2013-33. Alpanda, S., and S. Zubairy (2014), “Addressing Household Indebtedness: Monetary, Fiscal or Macroprudential Policy?” Bank of Canada Working Paper No.2014-58. Aoki, K., J. Proudman, and G. Vlieghe (2004), “House Prices, Consumption, and Monetary Policy: A Financial Accelerator Approach,” Journal of Financial Intermediation, 13(4), 414–435.. 治政 Bernanke, B. and M. Gertler (1989), “Agency Costs, 大 Net Worth, and Business 立 Review, 79(1), 14–31. Fluctuations,” American Economic ‧ 國. 學. ‧. Bernanke, B., M. Gertler, and S. Gilchrist (1999), “The Financial Accelerator in a Quantitative Business Cycle Framework,” in J. B. Taylor and M. Woodford (eds), Handbook of Macroeconomics, 1341–1393, Amsterdam; Oxford: Elsevier.. Nat. sit. y. Calvo, Guillermo (1983), “Staggered Prices in a Utility-Maximizing Framework,”. io. n. al. er. Journal of Monetary Economics, 12, pp. 383-398.. i n U. v. Central Bank of Taiwan (2014), Press conference References after Meeting of Board of central bank committee, Retrieved from the website of Central Bank of Taiwan.. Ch. engchi. Chang, C.-O., M.-C. Chen, H.-J. Teng, and C.-Y. Yang (2009), “Is There a Housing Bubble in Taipei? Housing Price vs. Rent and Housing Price vs. Income,” Journal of Housing Studies, 18(2), 1–22. Chen, N.-K. and H.-L. Cheng (2012), “External Finance Premium, Taiwan's Housing Market and Business Fluctuations,” Academia Economic Papers, Institute of Economics, Academia Sinica, 40(3), 307-341. Directorate General of Budget, Accounting and Statistics, Executive Yuan, R.O.C. (2000), “Population and Housing Census in Taiwan and Fujian area,” Retrieved from the website of Directorate General of Budget, Accounting and Statistics, Executive Yuan, R.O.C.. 35.

(40) Gimeno, R. and C. Martinez-Carrascal (2006), “The interaction between house prices and loans for house purchase. The Spanish case,” Banco de Espana Documentos de Trabajo, No. 0605. Iacoviello, M. (2005), “House Prices, Borrowing Constraint, and Monetary Policy in the Business Cycle,” American Economic Review, 95(3), 739–764. Iacoviello, M. and S. Neri (2010), “Housing Market Spillovers: Evidence from an Estimated DSGE Model,” American Economic Journal: Macroeconomics, 2(2), 125– 164. Lee, C.-C., C.-M. Liang, and H.-J. Chou (2008), “Identifying Taiwan’s Real Estate Cycle Turning Points: Application of the Two-Variate Markov-Switching Autoregressive Model,” Journal of Taiwan Land Research, 11(2), 155–177.. 立. 政治大. ‧. ‧ 國. 學. Lin,C.-C. and C.-L. Chen (2005), “Tenure Choice, Mortgage Payment, and Household Composition of Generation: An Application of Nested Logit Model,” Journal of Housing Studies, 14(1), 1–20.. sit. y. Nat. Lin, T.-Y. (2012), “Monetary Policy and the House Price,” (NSC100-2400-H-004-198) Ministry of Science and Technology, Taiwan: Taipei City.. al. er. io. Ma, Y.-C. and C.-C. Lin (2009), “Reconfirmation of the Turning Points of Real Estate. n. Cycle Indicators in the Taiwan Real Estate Market: An Application of Markov-Switching Vector Auto-Regression Models,” Journal of Housing Studies, 18(1), 23–37.. Ch. engchi. 36. i n U. v.

(41)