Chapter 1 Introduction
3.3 Posteriors distribution
25
We can estimate variants of the model by using Bayesian methods. The Bayesian approach provides a framework for making model comparisons and yields posterior adds for each models.
When a prior p(θi)and a sample of data Y, the posterior density of the model parameters θiis the proportional to the likelihood of the data multiplied by the prior p(θi),
) ( ) ( )
( iY L iY p i
pθ ∝ θ θ
the likelihood function can be estimated using the Kalman filter by combining the state-space representation of the model solution with a measurement equation, linking the state vector to the observed data. The model solution will be written as
ε ϑ ϑ ) ε( )
( 1
1 i t i
t V
V =Φ − +Φ
A measurement equation then relates the model variables V to a vector of observables t x . All t observables are measured in percentage deviations from steady state levels. The vector of observables x is composed of log output (t ytob ), annualized log quarterly changes in the consumption(ctob), annualized log quarterly changes in the monetary (mtob）, annualized log quarterly changes in the wages (wtob), annualized log quarterly changes in the CPI(πtob), annualized log quarterly changes in the interest rates (rtob), annualized log quarterly changes in the labors (ntob),
and annualized log quarterly changes in the investments (ktob ). The linear trends of this observables has been removed. The model variables are scaled to be measured in the same units as the observables. The measurement equations relating the model variables to the observables are
26
Posterior draws are obtained using Markov Monte Carlo methods and made from the posterior distribution using the random walk Metropolis Hastings algorithm. After estimating the posterior distribution of the N models, each model is compared how well they fit the observable variables by using Bayes factors. The Bayes factor of model i over model j is
)
3.4 Solving the DSGE model
The log-linearized model of the DSGE model can be solved by Blanchard and Kahn method.
This method is based on the idea of solving linear systems by searching for the stable manifold of the system of nonlinear equations. In all cases the equilibrium conditions describing the models need to be linearized.
The solution of the rational expectations model is unique if the number of unstable eigenvectors of the system is exactly equal to the number of forward-looking variables. The Blanchard and Kahn condition is that the number of eigenvalues in L greater than 1 must be equal to number of forward-looking variables.
The log-linearized model of the DSGE model must be satisfied in Blanchard and Kahn condition. We estimate and solve the DSGE model using Dynare 4.3.0. Dynare is a software platform for handling a wide class of economic models, in particular dynamic stochastic general equilibrium (DSGE) and
27
overlapping generations (OLG) models. The models is estimated and solved by using Dynare.
Dynare is not its own program but is rather basically a collection of Matlab code, so we first must install Matlab and Dynare and create .mod files then run the Dynare code to obtain the solutions.
28
Chapter 4 Experiment result
4.1 Estimated results
We estimate the mode the posterior distribution by maximizing the log posterior function, which combines the priors with the likelihood given by the data and then use the Metropolis-Hastings algorithm to obtain the posterior distribution. Table 4.1 shows the posterior distribution and means for the structural parameters. Table 4.2 shows the theoretical moments. Fig 4.1 and Fig 4.2 shows the prior distribution. Fig 4.3 and Fig 4.4 shows the prior distribution and the posterior distribution.
Fig 4.5 shows the smoothed shock and Fig 4.6 shows estimated output and historical data.
Table 4.1 The posterior distribution of structural parameters of the DSGE model (by Bayesian estimation)
prior mean
post. mean conf. interval Prior distribution
pstdev
γ 0.599 0.6116 0.6114 0.6118 β 0.0020
σ 0.420 0.4125 0.4125 0.4126 β 0.0020
h 0.650 0.6471 0.6471 0.6472 β 0.0020
β 0.990 0.9718 0.9718 0.9718 β 0.0020
ψ 0.148 0.1473 0.1472 0.1473 β 0.0020
δk 0.025 0.0143 0.0143 0.0143 β 0.0020
δ 0.100 0.1021 0.1021 0.1021 β 0.0020
η 0.200 0.2040 0.2040 0.2040 β 0.0020
ηt 0.900 0.8996 0.8995 0.8996 β 0.0020
α 0.410 0.4137 0.4137 0.4138 β 0.0020
θ 0.350 0.3425 0.3425 0.3426 β 0.0020
φ1 0.420 0.4153 0.4153 0.4154 β 0.0020 ξw 0.828 0.8165 0.8164 0.8166 β 0.0020 ξP 0.905 0.9048 0.9048 0.9049 β 0.0020 γr 0.782 0.7843 0.7843 0.7843 β 0.0020 γw 1.700 1.7118 1.7117 1.7119 γ 0.0020 γY 0.289 0.2944 0.2943 0.2944 β 0.0020 ρz 0.410 0.4137 0.4136 0.4138 β 0.0020 ρe 0.410 0.4066 0.4065 0.4065 β 0.0020
29
ρb 0.410 0.4026 0.4025 0.4028 β 0.0020
µw
ρ 0.410 0.4072 0.4071 0.4072 β 0.0020
µP
ρ 0.410 0.4144 0.4144 0.4145 β 0.0020
ρpo 0.410 0.4108 0.4106 0.4109 β 0.0020 ρu 0.410 0.3973 0.3973 0.3973 β 0.0020 ρv 0.410 0.4112 0.4112 0.4112 β 0.0020
ϕ 0.400 0.4049 0.4049 0.4050 β 0.0020
µP 1.200 1.2112 1.2111 1.2113 γ 0.0020
Table 4.2 – Theoretical moments of the DSGE model (HP filter, lambda = 1600)
VARIABLE MEAN STD. DEV. VARIANCE
m
0.0000 5.0717 25.7221
c
0.0000 0.1232 0.0152
m
0.0000 0.0813 0.0066
π
0.0000 0.0075 0.0001
b
0.0000 0.0502 0.0025
q
0.0000 2.5124 6.3122
i
0.0000 0.3198 0.1023
z
0.0000 0.0502 0.0025
k
0.0000 0.0422 0.0018
po
0.0000 0.0502 0.0025
n
0.0000 0.1609 0.0259
VA
0.0000 0.0701 0.0049
y
0.0000 0.0727 0.0053
w
0.0000 0.0672 0.0045
εTFP
0.0000 0.0502 0.0025
µp
0.0000 0.0502 0.0025
µw
0.0000 0.0502 0.0025
ut
0.0000 0.0502 0.0025
v
0.0000 0.0502 0.0025
30
Fig4.1 The prior distributions of the DSGE model (1)
0.580 0.6 0.62
31
Fig 4.2The prior distributions of the DSGE model (2)
0.4 0.42 0.44 0
100 200
rhoz
0.4 0.42 0.44 0
100 200
rhoe
0.4 0.42 0.44 0
100 200
rhob
0.4 0.42 0.44 0
100 200
rhomuw
0.4 0.42 0.44 0
100 200
rhomup
0.4 0.42 0.44 0
100 200
rhopo
0.4 0.42 0.44 0
100 200
rhou
0.4 0.42 0.44 0
100 200
rhov
0.380 0.4 0.42 100
200
phi
32
Fig 4.3The prior distributions and posteriors of the DSGE model (1) (by Bayesian estimation)
0.595 0.6 0.605 0.61 0
0.415 0.42 0.425
0 1 2
x 104 sigma
0.645 0.65 0.655
0
0.985 0.99 0.995
0
0.1420.1440.1460.148 0.15 0.1520.1540 2
4
x 104 pso
0.02 0.025 0.03
0
0.095 0.1 0.105
0
0.995 1 1.005
0 5000 10000 15000
nu
0.195 0.2 0.205
0 1 2 3
x 104 eta
0.895 0.9 0.905
0 1 2
x 104 etat
0.345 0.35 0.355
0 5000 10000
theta
0.405 0.41 0.415
0 5000 10000 15000
alpha
0.415 0.42 0.425
0 1 2 3
x 104 pso1
0.82 0.825 0.83 0
2000 4000
xiw
0.9 0.905 0.91
0
1.695 1.7 1.705 1.71 0
2000 4000
gammaw
0.285 0.29 0.295
0 5000 10000
gammay
33
Fig 4.4The prior distributions and posteriors of the DSGE model(2) (by Bayesian estimation)
0.405 0.41 0.415
0 2000 4000 6000
rhoz
0.405 0.41 0.415
0 2 4
x 104 rhoe
0.405 0.41 0.415
0 2000 4000 6000
rhob
0.405 0.41 0.415
0 5000 10000
rhomuw
0.405 0.41 0.415
0 0.5 1 1.5 2
x 104 rhomup
0.405 0.41 0.415
0 1000 2000 3000 4000
rhopo
0.4 0.405 0.41 0.415 0
0.5 1 1.5 2
x 105 rhou
0.405 0.41 0.415
0 2 4
x 104 rhov
0.395 0.4 0.405
0 5000 10000 15000
phi
34
Fig 4.5The smoothed shock of the DSGE model
(iid distribution,mean 0 and standard deviation is variance sigma)
10 20 30 40 50 60 -1
-0.5 0 0.5 1
etaz
10 20 30 40 50 60 -0.05
0 0.05 0.1 0.15
etae
10 20 30 40 50 60 -40
-20 0 20
etab
10 20 30 40 50 60 -5
0 5
etamup
10 20 30 40 50 60 -2
-1 0 1 2
etamuw
10 20 30 40 50 60 -0.2
0 0.2 0.4 0.6
etapo
10 20 30 40 50 60 -0.5
0 0.5 1 1.5
etau
10 20 30 40 50 60 -0.4
-0.2 0 0.2 0.4
etav
35
Fig 4.6The comparison between estimated output and Taiwan’s quarterlyhistorical data
4.2 Estimated Impulse responses of structural shocks 4.2.1 The production factor shock
Figure 4.7 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and value-add production to an preference exogenous shock is to raise production factor by 1 percent. The maximum response of real variables to the shock occord almost immediately. The effect of this preference shock is to raise output by 0.8 percent, value-add production by 0.8 percent and interest rate 0.05percent. The effect of this production factor shock is to fall monery supply by 0.15 percent, wage by 0.01percent , number of labor by 0.1 percent, investnent by by 0.1 percent and inflation 0.02 percent. But monery supply, consumption,wage will reverse to rise after 1 or 2 years. The rising effect of output,
10 20 30 40 50 60
-0.1 -0.05 0 0.05 0.1
y
10 20 30 40 50 60
-0.1 -0.05 0 0.05 0.1
c
10 20 30 40 50 60
-0.04 -0.02 0 0.02 0.04
m
10 20 30 40 50 60
-0.1 -0.05 0 0.05 0.1
w
10 20 30 40 50 60
-0.02 0 0.02 0.04
pi
10 20 30 40 50 60
-1 0 1 2
r
10 20 30 40 50 60
-0.04 -0.02 0 0.02 0.04
n
10 20 30 40 50 60
-0.4 -0.2 0 0.2 0.4
k
36
value-add production and number of labor will be back to base after about 2 years and the other items will be back to base after about a few more years. From aforementioned results, we know the inflation will fall due to technology process and firm’s marginal costs of production. The output and the value-add production will rise immeand the wage will rise after half a year.
4.2.2 The consumer preference shock
Figure 4.8 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and value-add production to an preference exogenous shock is to raise consumer preference by 1 percent. The maximum response of real variables to the shock occord almost immediately. The effect of this preference shock is to raise output by 0.025 percent, value-add production by 0.01 percent, monery supply by 0.3 percent , wage by 0.04percent,investnent by 0.03 percent, inflation by 0.001 percentand interest rate 0.0025percent. The effect of this preference shock is to fall number of labor. But monery supply will reverse to rise after 1 year. The rising effect of output, value-add production and number of labor will be back to base after about 2 years and the other items will be back to base after about a few more years. From aforementioned results, we know the consumer preference will rise consumption and output. And money supply will fall after about 1 year.
37
Fig 4.7 Impulse response to a 1%production factor shock
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; va: added value production) 10 20 30 40
-1 0 1
y
10 20 30 40 -0.1
0 0.1
c
10 20 30 40 -5
0 5
m
10 20 30 40 -0.05
0 0.05
w
10 20 30 40 -0.05
0 0.05
pi
10 20 30 40 -0.05
0 0.05
r
10 20 30 40 -0.2
0 0.2
n
10 20 30 40 -0.2
0 0.2
k
10 20 30 40 -1
0 1
va
38
Fig 4.8 Impulse response to a 1%consumer preferences shock
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; va: added value production)
4.2.3 The price adjustment cost shock
Figure 4.9 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and value-add production to an preference exogenous shock is to raiseprice adjustment cost by 1 percent. The effect of this preference shock is to fall output by 0.015 percent, value-add production by 0.015 percent, monery supply by 0.1 percent ,and number of labor by 0.04 percent. The effect of this preference
10 20 30 40 -0.05
0 0.05
y
10 20 30 40 -0.2
0 0.2
c
10 20 30 40 -0.5
0 0.5
m
10 20 30 40 -0.05
0 0.05
w
10 20 30 40 -5
0
5x 10-3 pi
10 20 30 40 -5
0
5x 10-3 r
10 20 30 40 -0.02
0 0.02
n
10 20 30 40 -0.05
0 0.05
k
10 20 30 40 -0.05
0 0.05
va
39
shock is to rise wage by 0.04 percent , inflation by 0.02 percent and inflation by 0.015 percent. All effects will be back to base after about several years. From aforementioned results, we know the price adjustment cost shock will rise inflation and fall consumption. And money supply will fall after about 1 year.
Fig 4.9Impulse response to a 1% price adjustment cost shock
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; va: added value production)
4.2.4 The wage adjustment cost shock
Figure 4.10 presents the estimated response of output, aggregate consumption, money supply, the 10 20 30 40
-0.02 0 0.02
y
10 20 30 40 -5
0
5x 10-3 c
10 20 30 40 -0.2
0 0.2
m
10 20 30 40 -0.05
0 0.05
w
10 20 30 40 -5
0
5x 10-3 pi
10 20 30 40 -2
0
2x 10-3 r
10 20 30 40 -0.05
0 0.05
n
10 20 30 40 -5
0
5x 10-3 k
10 20 30 40 -0.02
0 0.02
va
40
nomial wage, inflation, interest rate, number of labor, investment, and value-add production to an preference exogenous shock is to raise wage adjustment cost by 1 percent. The effect of this preference shock is to raise output by 0.025 percent, value-add production by 0.025 percent, monery supply by 1 percent , wage by 0.04 percent,andinvestnent by 0.03 percent. The effect of this preference shock is to fall number of labor, interest rateby 0.01percent and inflation by 0.015 percent. All effects will be back to base after about several years. From aforementioned results, we know thewage adjustment cost shock will rise consumption, inflation and output. And money supply will fall after about 1 year.
Fig 4.10Impulse response to a 1% wage adjustment cost shock
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; va: added value production) 10 20 30 40
-0.05 0 0.05
y
10 20 30 40 -0.05
0 0.05
c
10 20 30 40 -2
0 2
m
10 20 30 40 -0.05
0 0.05
w
10 20 30 40 -0.02
0 0.02
pi
10 20 30 40 -0.02
0 0.02
r
10 20 30 40 -0.02
0 0.02
n
10 20 30 40 -0.05
0 0.05
k
10 20 30 40 -0.05
0 0.05
va
41
4.2.5 The oil price shock
Figure 4.11 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and value-add production to an preference exogenous shock is to raiseoil price by 5 percent. The effect of this preference shock is to raise consumption by 0.015 percent, value-add production by 0.03 percent, monery supply by 0.8 percent , wage by 0.01 percent, inflation by 0.0015 percent, number of labor by 0.025 percent, andinvestment by 0.03 percent. The effect of this preference shock is to fall output by 0.15 percent, and interest rateby 0.015 percent. All effects will be back to base after about 1 or 2 years. From aforementioned results, we know theoil price shock will rise inflation andmoney supply. And output will fall due oil price shock.
4.2.6 The capital utillzation shock
Figure 4.12 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and value-add production to an preference exogenous shock is to raise capital utillzationby 1 percent. The effect of this preference shock is to fallconsumption by 0.1 percent, money supply by 5 percent, and investment by 0.2 percent. The effect of this preference shock is to rise wage by 0.3 percent, inflation by 0.04 percent, interest rate by 0.1 percent, wage by 0.01 percent, number of labor by 3 percent, andoutput by 1 percent. Output and number of labor will be back to baseabout 1 or 2 years, other iterms will be back to base about more years From aforementioned results, we know thecapital utillzation shock will rise output due to the raise of number of labor.
42
Fig 4.11Impulse response to a 5% oil price shock
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; va: added value production) 10 20 30 40
-0.2 0 0.2
y
10 20 30 40 -0.02
0 0.02
c
10 20 30 40 -1
0 1
m
10 20 30 40 -0.02
0 0.02
w
10 20 30 40 -2
0
2x 10-3 pi
10 20 30 40 -0.02
0 0.02
r
10 20 30 40 -0.05
0 0.05
n
10 20 30 40 -0.05
0 0.05
k
10 20 30 40 -0.05
0 0.05
va
43
Fig 4.12Impulse response to a 1% capital utilization shock
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; va: added value production)
4.2.7 The interest rate adjustment cost shock
Figure 4.13 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and value-add production to an preference exogenous shock is to raise interest rate adjustment costby 0.5 percent. The effect of this nterest rate adjustment cost is to fallconsumption by 0.5 percent, money supply by 25 percent, wage by 0.3 percent ,investment by 0.25 percent, inflation by 0.2 percent. The effect of this interest rate
10 20 30 40 -2
0 2
y
10 20 30 40 -0.2
0 0.2
c
10 20 30 40 -10
0 10
m
10 20 30 40 -0.5
0 0.5
w
10 20 30 40 -0.05
0 0.05
pi
10 20 30 40 -0.1
0 0.1
r
10 20 30 40 -5
0 5
n
10 20 30 40 -0.5
0 0.5
k
10 20 30 40 -1
0 1
va
44
adjustment cost is to rise interest rate by 0.5 percent, and number of labor by 0.15 percent. All effects will be back to base after about 1 or 2 years. From aforementioned results, we know theinterest rate adjustment cost shock will fall output and added-value goods.
Fig 4.13Impulse response to a 1% interest rate adjustment costshock
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; va: added value production) 10 20 30 40
-0.5 0 0.5
y
10 20 30 40 -1
0 1
c
10 20 30 40 -50
0 50
m
10 20 30 40 -0.5
0 0.5
w
10 20 30 40 -0.1
0 0.1
pi
10 20 30 40 -1
0 1
r
10 20 30 40 -0.2
0 0.2
n
10 20 30 40 -0.5
0 0.5
k
10 20 30 40 -0.5
0 0.5
va
45
Chapter 5 Discussion about Oil Tax
5.1 Oil tax and the DSGE model
In this chapter, we will discuss the influence of oil tax on the DSGE model. There are two cases discussed in this chapter: one is that the amount of oil tax is proportion to oil price, the other is that the amount of oil tax is proportion to the amount of oil consumption. The two model’s posterior distributions are estimated by maximizing the log posterior function, which combines the priors with the likelihood given by the data and then use the Metropolis-Hastings algorithm to obtain the posterior distribution. Table 5.1 shows the posterior distribution and means for the structural parameters. Then the estimated impulse responses of structural shocks will be shown in section 5.2 and section 5.3.
Table 5.1 posterior distribution and means for the structural parameters.
prior mean
Mode
(the amount of oil tax is proportion to oil
price)
Mode
(the amount of oil tax is proportion to the amount of oil)
Prior distribution
pstdev
γ 0.599 0.5992 0.5992 β 0.0020
σ 0.420 0.4171 0.4187 β 0.0020
h 0.650 0.6550 0.6523 β 0.0020
β 0.990 0.9830 0.9833 β 0.0020
ψ 0.148 0.1480 0.1480 β 0.0020
δk 0.025 0.0145 0.0345 β 0.0020
δ 0.100 0.1032 0.0897 β 0.0020
η 0.200 0.2000 0.2000 β 0.0020
ηt 0.900 0.9000 0.9003 β 0.0020
α 0.410 0.4147 0.4124 β 0.0020
θ 0.350 0.3499 0.3498 β 0.0020
φ1 0.420 0.4195 0.4198 β 0.0020
ξw 0.828 0.8251 0.8277 β 0.0020
ξP 0.905 0.9019 0.9032 β 0.0020
γr 0.782 0.7842 0.7811 β 0.0020
46
γw 1.700 1.700 1.6999 γ 0.0020
γY 0.289 0.2887 0.2893 β 0.0020
ρz 0.410 0.4100 0.4100 β 0.0020
ρe 0.410 0.4099 0.4073 β 0.0020
ρb 0.410 0.3984 0.4072 β 0.0020
µw
ρ 0.410 0.4101 0.4101 β 0.0020
µP
ρ 0.410 0.4111 0.4100 β 0.0020
ρpo 0.410 0.4100 0.4237 β 0.0020
ρu 0.410 0.4105 0.4121 β 0.0020
ρv 0.410 0.4088 0.4089 β 0.0020
ϕ 0.400 0.4000 0.4000 β 0.0020
µP 1.200 1.1985 1.2049 γ 0.0020
5.2 Impulse responses of structural shocks -the amount of oil tax is proportion to oil price
5.2.1 The production factor shock
Figure 5.1 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and oil consumption to an preference exogenous shock is to raise production factor by 1 percent in the DSGE model including oil tax. With comparison to the DSGE model without oil tax, it is obvious that the upraised amptitudes of output is smaller. The aforesaid fact shows the oil tax will affect the production’s increasing.
5.2.2 The consumer preference shock
Figure 5.2 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and value-add production to an preference exogenous shock is to raise consumer preferences by 1 percent in the DSGE model
47
including oil tax. With comparison to the DSGE model without oil tax, it obvious that the upraised amptitudes of output and consumption are smaller, and the unemployment rate is rising. The aforesaid fact shows the oil tax will affect the consumer preference.
Fig 5.1Impulse response to a 1% production factor shock (oil tax is considered) (y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; og: oil consumption)
5.2.3 The price adjustment cost shock
Figure 5.3 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and oil consumption to an
10 20 30 40 -0.05
0 0.05
y
10 20 30 40 -5
0
5x 10-3 c
10 20 30 40 -0.2
0 0.2
m
10 20 30 40 -2
0
2x 10-3 w
10 20 30 40 -2
0
2x 10-3 pi
10 20 30 40 -5
0
5x 10-3 r
10 20 30 40 -0.01
0 0.01
n
10 20 30 40 -0.01
0 0.01
k
10 20 30 40 -0.05
0 0.05
og
48
preference exogenous shock is to raise price adjustment cost by 1 percent in the DSGE model including oil tax. With comparison to the DSGE model without oil tax, the upraised amptitudes of output is smaller and the unemployment rate is rising. The aforesaid fact shows the oil tax let the positive effects of price adjustment are obvious.
Fig 5.2Impulse response to a 1% consumer preferences shock(oil tax is considered) (y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; og: oil consumption)
5.2.4 The wage adjustment cost shock
Figure 5.4 presents the estimated response of output, aggregate consumption, money supply, the 10 20 30 40
-2 0
2x 10-3 y
10 20 30 40 -0.01
0 0.01
c
10 20 30 40 -0.05
0 0.05
m
10 20 30 40 -5
0
5x 10-3 w
10 20 30 40 -2
0
2x 10-4 pi
10 20 30 40 -2
0
2x 10-4 r
10 20 30 40 -1
0
1x 10-3 n
10 20 30 40 -2
0
2x 10-3 k
10 20 30 40 -2
0
2x 10-3 og
49
nomial wage, inflation, interest rate, number of labor, investment, and oil consumption to an preference exogenous shock is to raise wage adjustment cost by 1 percent in the DSGE model including oil tax. With comparison to the DSGE model without oil tax, the upraised amptitudes of consumption and wage are smaller and the inflation is rising. The aforesaid fact shows the oil tax reduces the effects of wage adjustment .
Fig 5.3Impulse response to a 1%price adjustment cost shock (oil tax is considered) (y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; og: oil consumption) 10 20 30 40
-1 0
1x 10-3 y
10 20 30 40 -5
0
5x 10-4 c
10 20 30 40 -0.01
0 0.01
m
10 20 30 40 -2
0
2x 10-3 w
10 20 30 40 -2
0
2x 10-4 pi
10 20 30 40 -2
0
2x 10-4 r
10 20 30 40 -2
0
2x 10-3 n
10 20 30 40 -2
0
2x 10-4 k
10 20 30 40 -5
0
5x 10-4 og
50
5.2.5 The oil price shock
Figure 5.5 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and oil consumption to an preference exogenous shock is to raise oil price by 5 percent in the DSGE model including oil tax.
With comparison to the DSGE model without oil tax, the upraised amptitudes of consumption and output are smaller. The aforesaid fact shows the oil tax will reduce the consumption and production.
Fig 5.4Impulse response to a 1%wage adjustment cost shock (oil tax is considered) (y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; og: oil consumption) 10 20 30 40
-2 0
2x 10-3 y
10 20 30 40 -5
0
5x 10-3 c
10 20 30 40 -0.1
0 0.1
m
10 20 30 40 -5
0
5x 10-3 w
10 20 30 40 -1
0
1x 10-3 pi
10 20 30 40 -1
0
1x 10-3 r
10 20 30 40 -1
0
1x 10-3 n
10 20 30 40 -2
0
2x 10-3 k
10 20 30 40 -2
0
2x 10-3 og
51
5.2.6 The capital utillzation shock
Figure 5.6 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and oil consumption to an exogenous shock is to raise oil price by 5 percent in the DSGE model including oil tax. With comparison to the DSGE model without oil tax, the upraised amptitude of wage is smaller . The aforesaid fact shows the oil tax will affect the impcat of capital utilization.
Fig 5.5Impulse response to a 5%oil price shock (oil tax is considered)
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; og: oil consumption) 10 20 30 40
-2 0
2x 10-3 y
10 20 30 40 -2
0
2x 10-4 c
10 20 30 40 -0.01
0 0.01
m
10 20 30 40 -2
0
2x 10-4 w
10 20 30 40 -2
0
2x 10-5 pi
10 20 30 40 -2
0
2x 10-4 r
10 20 30 40 -5
0
5x 10-4 n
10 20 30 40 -5
0
5x 10-4 k
10 20 30 40 -0.05
0 0.05
og
52
5.2.7 The interest rate adjustment cost shock
Figure 5.6 presents the estimated response of output, aggregate consumption, money supply, the nomial wage, inflation, interest rate, number of labor, investment, and oil consumption to an preference exogenous shock is to raise capital utilization by 1 percent in the DSGE model including oil tax. With comparison to the DSGE model without oil tax, the upraised amptitude of output and the decreasing amptitudes of consumption are smaller. The aforesaid fact shows the oil tax will affect the impcat of interest rate adjustment cost.
Fig 5.6Impulse response to a 1% capital utilization shock (oil tax is considered) (y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; og: oil consumption) 10 20 30 40
-0.1 0 0.1
y
10 20 30 40 -0.01
0 0.01
c
10 20 30 40 -0.5
0 0.5
m
10 20 30 40 -0.02
0 0.02
w
10 20 30 40 -5
0
5x 10-3 pi
10 20 30 40 -5
0
5x 10-3 r
10 20 30 40 -0.2
0 0.2
n
10 20 30 40 -0.02
0 0.02
k
10 20 30 40 -0.1
0 0.1
og
53
Fig 5.7Impulse response to a 1% interest rate adjustment costs hock (oil tax is considered) (y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; og: oil consumption)
5.3 Impulse responses of structural shocks -the amount of oil tax is proportion to the amount of oil consumption
In this section, the amount of oil tax of the DSGE model is proportion to to the amount of oil consumption, With comparison to the the cases in section 5.2, the estimatined impulses are not obviously different. Figure 5.8 presents the estimated response of output, aggregate consumption,
10 20 30 40 -0.05
0 0.05
y
10 20 30 40 -0.1
0 0.1
c
10 20 30 40 -5
0 5
m
10 20 30 40 -0.05
0 0.05
w
10 20 30 40 -0.01
0 0.01
pi
10 20 30 40 -0.1
0 0.1
r
10 20 30 40 -0.02
0 0.02
n
10 20 30 40 -0.05
0 0.05
k
10 20 30 40 -0.05
0 0.05
og
54
money supply, the nomial wage, inflation, interest rate, number of labor, investment, and oil consumption to an preference exogenous shock is to raise oil consumption by 5 percent. production factor shock is to fall monery supply by 0.15 percent, wage by 0.01percent , number of labor by 0.1 percent, investnent by by 0.1 percent and inflation 0.02 percent. But monery supply, consumption,wage will reverse to rise after 1 or 2
Fig 5.8Impulse response to a 5%oil price shock (oil tax is considered)
(y: Output; c: Consumption; m: Monetary; w:Wage; pi: Inflation; r: Interest rate;
n: Labor; K: Investment; og: oil consumption) 10 20 30 40
-2 0
2x 10-3 y
10 20 30 40 -2
0
2x 10-4 c
10 20 30 40 -0.01
0 0.01
m
10 20 30 40 -2
0
2x 10-4 w
10 20 30 40 -2
0
2x 10-5 pi
10 20 30 40 -2
0
2x 10-4 r
10 20 30 40 -1
0
1x 10-3 n
10 20 30 40 -1
0
1x 10-3 k
10 20 30 40 -0.02
0 0.02
og
55
Chapter 6 Conclusion
In this paper, we present an estimated a New Keynesian DSGE model for the Taiwanese economy.
This paper has estimated a DSGE model of Taiwan developed originally by Christiano et al ( 2005), Ireland (1997) and Peersman et al (2012).The basic building blocks of the model are standard in the literature. There are three consumption goods: non-energy output, petrol and utilities; consumers choose how much of each of these goods to consume in order to maximize their utility in their overall wealth. Oil is used as an input to production and a part of households’ consumption in this paper. There is a flexible elasticity of substitution between oil and other types of consumption goods in the consumption bundle. We also simulate the oil tax shock on macroeconomic. The results of the present paper are based on a Bayesian estimated model and support the view that inflation and interest rate move in opposite directions after an oil price shock. The simulated results also support the view that the oil tax will make the data worsen.
The main results of this paper are followings. First, the production factor shock, consumer preference shock, wage adjustment cost shock will immediately raise output, the value-add production consumption. The capital utilization shock will raise output due to the raise of number of labor. The price adjustment cost shock, oil price shock will raise inflation and fall consumption. The interest rate adjustment cost shock will fall output and added-value goods. A 1% increase in production factor leads to raise in output of about 1% and a 1% increase in consumer preference leads to raise in output of about 0.025%. A 1% increase in consumer preference leads to raise in
The main results of this paper are followings. First, the production factor shock, consumer preference shock, wage adjustment cost shock will immediately raise output, the value-add production consumption. The capital utilization shock will raise output due to the raise of number of labor. The price adjustment cost shock, oil price shock will raise inflation and fall consumption. The interest rate adjustment cost shock will fall output and added-value goods. A 1% increase in production factor leads to raise in output of about 1% and a 1% increase in consumer preference leads to raise in output of about 0.025%. A 1% increase in consumer preference leads to raise in