Literature Review

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related literature. The model will be described in Section 2, with first order condition and monetary policy. In Section 3, we show the results of calibration and compare the results of different monetary policies. Finally in Section 4, we make the conclusion according to our calibration and point out some issues for future research.

1.2 Literature Review

Let us review a little bit on literatures related to this work. We start with literature on capital investment with external finance premium using DSGE model, and then, move on to those with housing market and borrowing constraint. Lastly, we will look at literatures about effect of monetary policies on asset pricing and how it is associated with Taiwanese housing market.

Before we look at how monetary policies or related financial conditions affect the housing market, we shall have a look on how financial properties such as financial accelerator and credit market imperfection influence investment and the price of capital. A classical literature for this issue is Bernanke, Gertler and Gilchrist (1999), which set up a DSGE model with entrepreneur who invests capital for production input and seeking capital gain. The entrepreneur borrows fund from a financial sector, which bear the risk that the debt could not be realized. Therefore, the financial sector decides its loan rate according to the default risk. The entrepreneur chooses its optimal capital investment based on the price of capital, loan rate given by the financial sector and the depreciation rate. Furthermore, a government sector decides the fiscal and monetary policy. Bernanke, Gertler and Gilchrist (1999) discusses the effect of exogenous shock on macroeconomic variables with and without financial accelerator. Output and investment change more with financial accelerator when there is an exogenous shock. In the cases with investment delays, financial accelerator will exacerbate the exogenous effect on investment and output as well.

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Next, we take a look at some literatures that discuss the housing market with a DSGE model. In Chen and Cheng (2012), the authors suggest that there are two types of households, a representative house-owner and a consumer who rents houses from the house-owner. Consumer can spare his income in consumption, house-renting or money-holding. For the individual house-owner, he borrows funds from financial sectors for house-investing. Chen and Cheng (2012) assumes the existence of default risk on the individual house-owner. According the risk, the financial sector sets its house loan rate which is higher than the saving rate. This difference is the external financial premium. In the production sector, Chen and Chang (2012) sets a house production firm with linear production technology, an intermediate-good firm with house and labor as input, and a retailer that uses Calvo pricing. Lastly, there is a central bank which implements its monetary policy according to Taylor’s rule. Chen and Chang (2012) discusses the relation of fluctuations of external financial premium and macroeconomic variables in response to various shocks. From the calibration in Chen and Chang (2012), the effect of exogenous shocks on external premium and house price turn out to be in opposite ways. For instance, a decrease in wealth would increase the external financial premium because the default risk of house-owners increases while the house price decrease owing to a negative income effect on demand for houses. Chen and Chang (2012) concludes that a decrease in house price caused by exogenous shocks will increase the default risk owing to a decrease in return, therefore push the external financial premium to increase. The rise in external financial risk premium will increase the investment cost for houses, therefore discourage the housing investment and lowers the house price. Furthermore, the financial accelerator will strengthen the effect of exogenous shocks.

Similar discussion about financial accelerator in housing market can also be found in Aoki (2002), in which there are two types of consumers, representative house

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owner, house producer and final goods producer. The major difference is that the consumer who follows permanent income hypothesis decides its consumption in period t and certain ratio of consumption will goes to house renting, while the rest will be consumption on other goods. Also, houses are only bought by the representative house owner and are not used in production. In addition to the effect of financial accelerator, Aoki (2002) also discuss the effect of the elasticity of transfer with respect to leverage ratio on macroeconomic variables. Higher elasticity of transfer will decrease the growth in house price and house investment in response to interest rate shock but the effect on consumption will be larger.

Iacoviello (2005) uses the housing market to discuss the effect of collateral constraint to the macroeconomic variables with nominal debt contracts and collateral constraints. In Iacoviello (2005)’s model, there are patient and impatient households along with entrepreneurs and policy maker. The entrepreneurs use houses as production input and households gain utility from buying houses. From the calibration, a positive house-price shock without collateral effect will lower the consumption and when the collateral effect increases, the effect for consumption will become positive.

In the later part, Iacoviello (2005) discusses whether central banks should response to housing price by examining the effect of change of correlation between asset price and interest rate. A small increase of the correlation between interest rate and house price does not change the fluctuation of output and inflation rate. This suggests that a monetary policy responding to housing price does little on stabilizing the economy.

Next, we will look at some literatures discussing the effect of monetary policy on asset price. Bernanke and Gertler (1999) discusses the effect of monetary policies on macroeconomic variables with asset bubble shock and inflation shock. The authors follow most of the setting in their paper of 1999. They compare the impulse response on interest rate in response to expected interest rate, current interest rate and interest

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rate in respond to the market price of assets as well as inflation rate. Also, they compared the effect of different parameter settings. Their major conclusion is that a monetary policy that responds to asset price is not necessary or desirable for price stabilizing. Also, an aggressive interest rate rule with inflation gap will decrease the variability of asset price and output gap.

Central Bank of China (Taiwan) points out that low interest rates do not necessarily lead to higher house price in a report published in February, 2014. CBC (2014) uses some empirical facts from IMF to show that many countries such as British has a high interest rate but the growth rate in house price is larger than United State, which implements a lower interest rate. Also from some empirical facts, the effect of interest rates on house price is not significant. Therefore, increasing interest rate is not an effective policy on lowering the house price. The CBC claims other non-interest rate policies such as lowering funds lending rate is more desirable.

2. Model

We consider a closed economy with the representative household, house-owner, house producer, good firm and monetary authority. In our model, the representative household rent houses from the representative house-owner. The flow of funds is shown as Figure 2.

2.1 Household without houses

The household maximizes his lifetime utility by allocating his income to consumption of goods, house renting from house-owner and money holding. Also, he has to decide the amount of labor supply. His lifetime utility function can be written as follows:

‧

where

C denotes the representative household’s consumption in period t,

_t

H

_t denotes the house that the representative household rents from house owner in period t, and 

j   is the parameter for household’s preference on houses.

_t

The budget constraint for household in period t is: dt-1

       

C

_t

 x H

_t^h _t

 d

_t

 R d

_{t1 t1}

 w L

_{t t}

 F

_t^h (2)

where

x

_t^h is the house rental price in period t,

d

_t1 the deposit in period t-1,

F

_t^h

the lump-sum transfer from house-owner, and

R

_t1  the real interest rate.

Solving the optimization problem we yield the following:

       

From (3), in steady state we can get the relationship of interest rate and inflation:

1

R

^



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Figure 2 Flow of funds

2.2 House owner

The house owner makes his decision on the amount of houses he buys. In period t, he uses the net wealth and borrows funds from the financial sector to buy houses.

The amount of money he borrows from the financial sector at the end of period t can be written as:

b

_t1

q H

_{t t1}

N

_t1 (6)

where

q denotes the real house price in period t,

_t

H

_t1 the amount of houses he

buys at the end of period t, and

N

_t1 the wealth that the individual house owner has at the end of period t. The individual house owner rents the houses to the individual household at period t+1.

The return of buying houses includes rent revenue from the representative households and the net gain of house price:

Transfer Ren

Consumption Expenditure

Wage Borrowing

Financial Intermediarie

Saving

Household House Producer

House owner

Expenditure on Houses

Goods Producer

‧

During the house purchasing in period t, the representative house owner also faces a borrowing cost. For a house owner seeking to maximize his profit in the house purchase, his optimal house purchase decision will be made at where marginal cost for borrowing will equal the expected return he can receive through house borrowing.

Therefore,

R

_t^h_1  also equals the marginal borrowing cost or the interest rate that the house owner faces for his borrowing decision.

We follow the setting in Bernanke, Gertler and Gilchrist (1999).That is, there exists difference between the marginal cost of borrowing and real interest rate. We define

s as the external finance premium (EFP), which equals the expected ratio of

_t return on buying houses between real interest rate at period t+1.       

However, we assume the absence of financial accelerator in this model. In other words, the external risk premium will not be affected by the ratio between net wealth and expenditure on houses in period t+1.³

     

The representative house owner’s earns his income from the revenue of endowment labor, return on house buying. He also has to pay the loans and transfer payment to the household. Therefore, the wealth of representative house owner in period t+1 can be written as:

     

N

_t1

 R q H

_t^h _{t1 t}

 sR b

_{t t}

 F

_t^h      (9)        

3

In Chen and Chang (2012), the external risk premium equals

¹

1

accelerator. Here, we discuss an economy where the external finance premium will not change

according to the leverage ratio of the house owner. Therefore, we set



to zero.

‧

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

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

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