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 Alpanda and Zubairy (2013). The inverse labor supply elasticity is set to 1, following Alpanda and Zubairy (2013). The loan-to-value ratio in the steady state is set to 0.9 in 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 without loss of generality. And the utility level for housing, h, is calibrate to 0.7 in the steady state to generate the total housing value to be around 5.6 times the GDP5.
The parameters of the level and elasticity in the utilization cost, and u, are calibrated to ensure that the utilization is equal to 1 at the steady state. The adjustment 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).
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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 5%, based on the tax’s law of Taiwan. Also, Taiwan has implemented a progressive tax system for individual income taxes, thus we set the labor income tax of three different types of households, yP, yIand 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 is set as 15%. Finally, the tax rate of property is set to 1.2% in the baseline case, based on the tax’s law of Taiwan.
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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
Capital share in production 0.3
P Labor share in production-Patient household 0.64
I Labor share in production-Impatient household 0.26
R Labor share in production-Renter household 0.10
h Housing depreciation rate 0.005
k Capital depreciation rate 0.015
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
b Response of transfer to gov. bonds 0.005
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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 0.7239
z Persistence of productivity shock 0.5
g Persistence of government expenditure shock 0.9021
Persistence of property tax shock 0.9999
Persistence of LTV shock 0.9999
P Persistence of markup shock 0.6802
h Persistence of housing preference shock 0.8795 Taylor rule parameters
Parameter for inflation 5
y Parameter for output 0
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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 housing leads to a fall in housing price, and leads to a fall in home equity of borrowers.
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 housing prices may make patient households increase their own-occupied housing, the overall decline in demand leads to a fall in production and wages and leads to a reduction in the aggregate output, yt, and inflation, t. In particular, the inflation 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