The House Producer

For the lump-sum transfer, we set it as a convex function of ¹

1

2.3 The House Producer

The house producer uses a linear production technology. The investment for house production can be written as

       

H

_t

 I

_t^h

  (1

_h

) H

_t1

       ^.      (11) The representative house producer wants to maximize his profit in period t, the profit maximization problem is as following

      ₁

 is a convex function that represents the adjustment cost function of producing a new house. From the first-order condition, we can get the house supply of the representative house producer.

      ^'

There are many firms lying in the interval [0, 1]. We set the representative firm according to Calvo price setting. The likelihood for the firm to keep its price is θ.

The representative consumption goods producer uses a Cobb-Douglas Production technology. The firm uses fixed capital and labor for its production. The production

‧

function of the representative firm can be written as following:

1

t t t

Y  A K L

^{ }

(14) The goal of the firm is to maximize its profit.

     



^,



^*

 

The first order condition yields the optimal price setting,

       

By log-linearization, we can obtain the Philip’s curve

      t  

E

t t ₁

⁽¹



⁾⁽¹



⁾ mc ^

t

u

t

First, we set a traditional Taylors rule, which is used in Chen and Cheng (2012)

     

R 

_tⁿ



 _



_t



_{Y t}

Y   v 

_t

       ^..      (19)

where

v

^t

follows an AR(1) process        

4

The firm decides its labor demand according to cost minimization subject to its production function.

 

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Then, we add the house price gap into the output gap as the following:

R

_tⁿ 

  

_ _t+ _{y t}

Y

 



_{q t}

q

_¹

v

_t

       

..

      (20)

Lastly, we set the parameters for output gap and house price gap equals to zero. The interest rate is targeted only according to inflation gap.

2.6 Exogenous Variables

There are four exogenous variables in this model. They are inflation rate shock, productivity shock, interest rate shock and preference shock. These shocks all follow AR (1) process. They can be written as following:

     

u 

_t



_{u t}

u 

_1



^u

       .      (21)

A 

_t



_A

A 

_t1



_t^A

.

. (22)

     

v 

_t



_{v t}

v 

_1



_t^v

       

..

 .      (23)



j

_t 



_{j t}

j

_1



_t^j

. . (24)

where

0 

   _{u, A}

,

_v

,

_j

 1

.

2.7 Market Clearing and Equilibrium

All the markets in our model have to be cleared. They include, labor market, house market, funds market and commodity market. The market clearing condition for the commodity market can be written as:

     

Y

_t

 C

_t

 I

_t^h       

.      (25)

Using the above equations and those mentioned in the previous sections, we can solve

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the steady state equilibrium for the model.

3. Calibration

3.1 Parameters Setting

We follow Chen and Cheng (2012) for most of the parameters settings. The parameter settings are shown in Table 1.

We set the discount factor in household ,β equals to be 0.99, and the elasticity of labor supply to be 3 as the setting in Aoki (2005). In our work, the elasticity of demand for different variety of goods is chosen to be 6 as the traditional setting, and the price stickiness chosen to be 0.75 so that the representative retailer is likely to change its price every four periods. Also here the depreciation rate of house is fixed to be 0.005 and the difference between marginal borrowing rate and real interest rate to be 0.015 according to the setting in Chen and Cheng (2012) . Furthermore, we set the steady state of leverage ratio (the ratio between house owner net wealth and house expenditure) to be 0.7, and the elasticity of house price with respect to investment house ratio to be 0.32 as the setting in Chen and Cheng (2012). In addition, we choose the parameter for house preference to be 0.5.

For the parameters of auto-correlation of exogenous variables, we follow the settings in Chen and Cheng (2012), and the parameter for monetary policy shock in our work is set to be 0.32. We also fix the parameters of technology shock and house demand shock to be 0.85 and 0.09, respectively. For the interest rate rule, we first follow the setting in Chen and Cheng (2012) and set the parameters of inflation gap and output gap to 1.2 and 0.13.

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Table 1

Calibration Parameters

Note: In our calibration, we have tried different values ofα

q

and the results are similar. In here, we just show the result with the value 0.05.

3.2 Calibration Results

In our calibration, we will compare the effect of a 1% inflation shock (cost-push), technology shock and interest rate shock under different interest rate rule.

Parameter Description Value

β Discount rate of household’s utility 0.99

 Elasticity of labor supply 3



h House depreciation rate 0.005



Capital Share in production 0.33



Price stickiness 0.75



H Elasticity of house price with respect to investment house ratio

0.32

  

Elasticity of demand of different variety of goods 6

j

Parameters for House Preference 0.5

N

qH

Steady state value for leverage ratio 0.7



F

 

Elasticity of transfer with respect to leverage Ratio 3 s Steady State value for external finance premium 1.015

Auto-correlation parameters



u Auto-correlation of Inflation Shock 0.5



A Auto-correlation of Technology Shock 0.9



v Auto-correlation of Interest Rate Shock 0.32

 j Auto-correlation of Housing Preference Shock 0.85

Interest Rate Parameters



 Parameter for Inflation gap 1.2



Y Parameter for Output gap 0.13

 q Parameter for House Price Gap 0.05

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3.2.1 Calibration under Taylors Rule

We first assume the authority set the interest rate under traditional Taylors Rule, as shown in (19). The results are shown as Figure 3 to Figure 6.A positive inflationary shock will cause the representative firm to decrease its output and lead to a decrease in labor demand and wage. With lower income, the representative household will decrease its consumption and house renting demand. This will decrease the house rental price and house owner’s house demand. The house price will decrease and the house investment will decrease as a result.

A positive technology shock will lead to an increase in output. The household’s income will increase as a result. With more income, the representative’s house renting demand and consumption will increase. The rental price will increase and the house owner‘s demand on houses will increase as well. Consequently, the house price will increase, followed by an increase in house producer’s investment.

A positive shock to interest rate will increase the opportunity cost of borrowing funds.

This will make buying houses more difficult for the representative house owner.

Therefore, the house demand of representative household and the house price will decrease. Lower house price will lower the house producer’s incentive on investment and cause a decrease in house investment. Also, an increase in interest rate will cause the representative household to save more money in period t and decrease his consumption. The decrease in consumption and house investment will cause a decrease in output and lead to a decrease in labor demand and real wage rate.

An increase on household’s preference for houses will lead to higher demand on house renting for household. The house rental price will increase and cause the house price to rise consequently. Higher house price will lead to higher investment on houses. Also, since the representative household spends more on houses, there will be

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less consumption. In order to seek for more budgets on buying houses, consumer will increase its labor and lead to an increase on output along with the increased investment.

Figure 3 An Inflationary Shock under Taylor’s Rule

5 10 15 20

-5 0

5x 10^-3 Consumption

5 10 15 20

-2 0

2x 10^-3 House Price

5 10 15 20

-0.01 -0.005

0 Output

5 10 15 20

-5 0

5x 10^-3 Rental Price

5 10 15 20

-0.01 -0.005

0 Investment

5 10 15 20

-5 0

5x 10^-3 Real Interest Rate

‧

Figure 4 A Technology Shock under Taylor’s Rule

Figure 5 A Monetary Shock under Taylor’s Rule

5 10 15 20

0x 10^-3 Real Interest Rate

5 10 15 20

‧

Figure 6 A Household’s Preference Shock under Taylor’s Rule

3.2.2 Calibration under Taylor’s Rule with House Price Gap Targeting

We now use an interest rate policy with house price gap added. The calibration results are shown in Figure 7 to Figure 10. When interest rate is set according to output growth, inflation gap and house price gap, the impulse response to house price of a inflation shock, technology shock and interest rate shock does not change significantly. For other macroeconomic variables such as output gap and consumption, the change rate is similar with the one under Taylor’s Rule. Though the house price growth decrease a little in the preference shock, the decline is not significant as well.

Therefore, adding house price gap into Taylor’s rule interest rate setting do not help in stabilizing house price significantly.

5 10 15 20

1x 10^-3 Real Interest Rate

‧

Figure 7 An Inflationary Shock under Taylor’s Rule with House Price Gap Targeting

Figure 8 A Technology Shock under Taylor’s Rule with House Price Gap Targeting

5 10 15 20

-5 0

5x 10^-3 Consumption

5 10 15 20

5x 10^-3 Real Interest Rate

5 10 15 20

0x 10^-3 Real Interest Rate

‧

Figure 9 A Monetary Shock under Taylor’s Rule with House Price Gap Targeting

Figure 10 A Preference Shock under Taylor’s Rule with House Price Gap Targeting

5 10 15 20

2x 10^-3 Real Interest Rate

‧

3.2.3 Calibration under Interest Rate Rule with Inflation Targeting

Then, we set the monetary authority use an inflation targeting interest rule. The impulse response results of the three shocks are shown in Figure 11 to Figure 14. In the absence of output gap in interest rate rule, the effect on the economy is stronger.

With a cost push shock (inflationary shock), the house price will decline more because the real interest rate rises when the decline of output is not taken into account in interest rate policy setting. The representative household will have more incentive in saving rather than consumption in period t with higher interest rate. Therefore, consumption will decline more compared to the one with Taylor’s Rule interest rate policy setting. The house price growth caused by an advance in technology is larger because the opportunity cost for house-owner is lower. For the monetary shock, there will be less fluctuation in house price and other macroeconomic variables as well.

Without output gap in interest rate policy setting, house price will be less stable.

Figure 11 An Inflationary Shock under Inflation Rate Targeting

5 10 15 20

5x 10^-3 Real Interest Rate

‧

Figure 12 A Technology Shock under Inflation Rate Targeting

Figure 13 A Monetary Shock under Inflation Rate Targeting

5 10 15 20

0x 10^-3 Real Interest Rate

5 10 15 20

‧

Figure 14 A Preference Shock under Inflation Rate Targeting

We then change our interest rate rule into a more aggressive one as discussed in Bernanke and Getler (2000) by increasing the parameter for inflation target into 2.

The impulse response results are shown as in Figure 15 to Figure 18. The effect of an inflationary shock on house price will be more severe because there will be larger interest rate growth. For the monetary shock, with a more aggressive interest rate rule setting, the impulse shock on house price and other macroeconomic variables will be less strong. Therefore, whether an aggressive monetary policy works better in house price stabilization compared to an accommodating one (when the parameter for inflation gap is 1.2) is ambiguous.

5 10 15 20

1x 10^-3 Real Interest Rate

‧

Figure 15 An Inflationary Shock under Aggressive Inflation Rate Targeting

Figure 16 A Technology Shock under Aggressive Inflation Rate Targeting

5 10 15 20

0x 10^-3 Real Interest Rate

‧

Figure 17 A Monetary Shock under Aggressive Inflation Rate Targeting

Figure 18 A Preference Shock under Aggressive Inflation Rate Targeting

5 10 15 20

1x 10^-3 Real Interest Rate

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4. Conclusion

In this paper, we compare the effect of various shocks on house price under different monetary policies by using the dynamic stochastic general equilibrium model (DSGE). In our model, we set up a house producer, a representative house owner, a representative household who rent houses from the house owner, a goods firm and a monetary authority (so-called “Central Bank”). We compute the steady state and linearize the model. We calibrate the impulse response of the macroeconomic variables with various shocks under a traditional Taylor’s Rule, an interest rate policy with house price gap added in traditional Taylor’s Rule and an inflation targeting interest rate rule. Then, we calibrate an aggressive inflation targeting interest rate rule and compare with the accommodating one. We find out that adding house price gap into traditional Taylor’s Rule does not work better in house price stabilization compared to traditional Taylor’s Rule. Also, through our calibration, we find out the importance of traditional Taylor’s Rule in stabilization of house price and other macroeconomic variables. When the interest rate rule policy can react to an economy’s output growth, the economy’s boom and bust will be eased off and there will be less fluctuation in the housing market.

We conclude this paper by pointing out some related issues for future research.

First, we can discuss the effect of different loan borrowing rate (the ratio that an individual is allowed to borrow for the house purchase) on house demand and house price. Also, we have discussed an economy in absence of fiscal policies. We can add some fiscal policies such as implementing a tax on return on buying houses.

Furthermore, we can compare the effect of monetary policies and fiscal policies on house price stabilizing.

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Reference

Aoki, K., J. Proudman, and G. Vlieghe (2002), “House Prices, Consumption, and Monetary Policy: A Financial Accelerator Approach”, Bank of England Working

Paper, 169-190.

Bernanke, B. and M. Getler (1999), “Monetary Policy and Asset Price Volatility”,

Economic Review, 4, 17-51.

Bernanke, B., M. Getler, and S. Gilchrist (1999), “The Financial Accelerator in a Quantitative Business Cycle Framework”, Handbook of Macroeconomics, 1, 1341-1393.

Central Bank of China (Taiwan) (2013), Meeting of Board of Central Bank Committee (News Announcement No 130), Retrieved from http://www.cbc.gov.tw/

ct.asp?xItem=44416&ctNode=302&mp=1.

Central Bank of China (Taiwan) (2014), The International Perspective on House

Price, Interest Rate and Cautious Policies, Retrieved from http://www.cbc.gov.tw/

public/Attachment/422416342071.pdf.

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”, Economic Thesis, Institute of Economics,

Academic Sinica, 40(3), 307–341.

SinYi Research Center for Real Estate (2014), Taiwanese House Price Index (Data file). Retrieved from the website of National ChengChi University College of Commerce: https://www.ncscre.nccu.edu.tw/webroot/xponent/exponent_

1314260174.docx.

Iacoviello, M. (2005), “House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle”, American Economic Review, 95(3), 739-764.

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Lin, T. Y. (2012), “Monetary Policy and the House Price” (No. 100-2410-H-004-198), Ministry of Science and Technology, Taiwan: Taipei City, Retrieved from http://nccur.lib.nccu.edu.tw/bitstream/140.119/52370/1/100-2410-H-004-198.pdf.

Taiwanese Economic Journal (2014), Taiwanese House Price to Income Ratio (Database). Retrieved from Taiwanese Economic Journal Database.

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Appendix Linearization

(A) Household

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_t

t t t

mc



w

  

L Y

 

.

(A13) (E) Market Clearing

+

h h

t t t

C I

Y C I

Y Y

 

 

. (A14)

The monetary policies and exogenous shocks are as listed in Section 2.6 and Section 2.7.

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