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 consumption of about 1% and a 1% increase in wage adjustment leads to raise in consumption of about 0.025%. A 1% increase in price adjustment leads to fall in output of about 0.02% . And a5%
increase in the real price of oil leads to fall in output of about 0.2% and an increase in inflation of about 0.001%.
Second, the contractionary effect of the oil shock is due mainly to the endogenous tightening of
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the production conductions. By the forecasting of the DSGE model, the oil tax will affect the consumer preference, and weaken the effects of production factor, wage adjustment and capital utilization. Production, consumption and the amount of oil consumptionwill also be reduced and CPI inflation will be raised. There are two types of oil tax rules discussed in this paper:one is that the amount of oil tax is proportion tooil price and another is that the amount of oil tax is proportion tothe amount of oil consumption. However, the effects of two types are not obviously different.
Third, the numerical results show that interest rate and output raise at the same time. But a 1%
increase in interest rate adjustment cost leads to fall in output of about 0.25% .
The main contribution of this paper is that we simulate how the exogenous shocks would affect macroeconomic by using the estimated DSGE model. And the numerical results show that the variables are not substantially affected by the presence of nominal rigidities. This paper also aims to explore the complications of the effects between these exogenous shocks. The suggestions of this paper are followings. First, the oil tax would reduce oil consumption and impact economic growth.
Second, the effects of different types of oil tax are not obviously different.
In the future work, we must provide a more accurate DSGE macroeconomic model to explain the relations of this economic variables and the mechanisms of changes of this economic variables. The model must include the domestic and foreign economic facts. We can also use the DSGE model to find the optimal oil tax to reduce oil consumptions, but the impacts of oil taxi to economic growth is minimal.
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Reference
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Appendix A－ － －Log-linear Model of DSGE model －
Household
Momentary equation：
t
Investment equation：
})
Technology of the intermediate firm：
gt
the demand curves for labor and oil by minimizing cost
t Wage equation：
ˆ ))
Inflation equation :
ˆ )
60
Taylor’s rule of Central Bank’s monetary policy :
t price adjustment cost shock :
wage adjustment cost shock : wageoil price shock :
interest rate adjustment cost shock : capital utillzation shock :
where and x are the values of the exogenous shocks in steady state.
isdistributed (iid) series with mean 0 and standard deviation is variance σz.
z
61
Appendix B－ － － －Dynare Code
var m c r pi b q i z k po n va y w epsilontepmuptmuwut v;
varexoetazetaeetabetamupetamuwetapoetauetav;
parameters gamma sigma h beta psodeltak delta nu eta etat theta alpha pso1
xiwxipgammargammawgammayrhozrhoerhobrhomuwrhomuprhoporhourhov phi psi mup;
gamma=0.5992;
sigma=0.42;
h=0.65;
beta=0.99;
pso=0.148;
deltak=0.025;
delta=0.1;
phi=0.4;
psi=0.5;
nu=1;
eta=0.2;
etat=0.9;
theta=0.35;
alpha=0.41;
pso1=0.42;
xiw=0.8284;
xip=0.9053;
mup=1.2;
gammar=0.7822;
gammaw=1.7;
gammay=0.289;
rhoz=0.41;
rhoe=0.41;
rhob=0.41;
rhomuw=0.41;
rhomup=0.41;
rhopo=0.41;
rhou=0.41;
rhov=0.41;
model(linear);
62
(-1/gamma)*m+(1/(sigma*(1-h)))*(c-h*c(-1))=(beta/(1-beta))*r;
c=(1/(1+h))*c(+1)+(h/(1+h))*c(-1)+(sigma*(1-h)/(1+h))*(-r+pi(+1)-(b(+1)-b)) ;
i=(beta/(1+beta))*i(+1)+(1/(1+beta))*pso*q+(1/(1+beta))*(beta*z(+1)-z) +(1/(1+beta))*i(-1);
k(+1)=(1-deltak)*k+deltak*i;
w=(1/(1+beta))*(pi(-1)+w(-1))-pi+(beta/(1+beta))*(w(+1)+pi(+1))-((1-beta*xiw)*(1-xiw)/((1+beta)
*xiw))*(w-muw-((-(w-(ut/0.27))+(1+0.27)*k)/pso1)-(1/(sigma*(1-h))*(c-h*c(-1))));
pi=(1/(1+beta))*pi(-1)+(beta/(1+beta))*pi(+1)+((1-beta*xip)*(1-xip)/((1+beta)*xip))*(-epsilontep+
alpha*(ut/0.27)+(1-alpha)*w-mupt);
n=-(w-(ut/0.27))+(1+0.27)*k;
va=epsilontep+theta*n+(1-theta)*k;
y=etat*va+(1-etat)*(-alpha*(po-((1-theta)*(ut/0.27)+theta*w-epsilontep))+va);
y=(mup*(1-beta*(1-delta))-alpha*beta*delta)/(mup*(1-beta*(1-delta)))*c+(alpha*beta*delta)/(mup
*(1-beta*(1-delta)))*i;
r=(1-gammar)*(gammaw*pi+gammay*y)+gammar*r(-1)+v;
z=rhoz*z(-1)+etaz;
epsilontep=rhoe*epsilontep(-1)+etae;
b=rhob*b(-1)+etab;
mupt=rhomup*mupt(-1)+etamup;
muw=rhomuw*muw(-1)+etamuw;
po=rhopo*po(-1)+etapo;
ut=rhou*ut(-1)+etau;
v=rhov*v(-1)+etav;
end;
initval;
m=0;
c=0;
r=0;
pi=0;
b=0;
q=0;
i=0;
z=0;
k=0;
po=0;
va=0;
n=0;
y=0;
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w=0;
v=0;
epsilontep=0;
mupt=0;
muw=0;
end;
shocks;
varetaz; stderr 0.05;
varetae; stderr 0.05;
varetab; stderr 0.05;
varetamup; stderr 0.05;
varetamuw; stderr 0.05;
varetapo; stderr 0.05;
varetau; stderr 0.05;
varetav; stderr 0.05;
end;
steady;
check;
stoch_simul(hp_filter = 1600, order = 1, irf = 40);
varobs y c m w pi r n k;
estimated_params;
gamma, beta_pdf, 0.5992, 0.002;
sigma, beta_pdf, 0.42, 0.002;
h, beta_pdf, 0.65, 0.002;
beta, beta_pdf, 0.99, 0.002;
pso, beta_pdf, 0.148 , 0.002;
deltak, beta_pdf, 0.025, 0.002;
delta, beta_pdf, 0.1, 0.002;
nu, gamma_pdf, 1, 0.002;
eta, beta_pdf, 0.2 , 0.002;
etat, beta_pdf, 0.9, 0.002;
theta, beta_pdf, 0.35, 0.002;
alpha, beta_pdf, 0.41, 0.002;
pso1, beta_pdf, 0.42, 0.002;
xiw, beta_pdf, 0.8284, 0.002;
xip, beta_pdf, 0.9053, 0.002;
64
gammar, beta_pdf, 0.7822, 0.002;
gammaw, gamma_pdf, 1.7, 0.002;
gammay, beta_pdf, 0.289, 0.002;
rhoz, beta_pdf, 0.41, 0.002;
rhoe, beta_pdf, 0.41, 0.002;
rhob, beta_pdf, 0.41, 0.002;
rhomuw, beta_pdf, 0.41, 0.002;
rhomup, beta_pdf, 0.41, 0.002;
rhopo, beta_pdf, 0.41, 0.002;
rhou, beta_pdf, 0.41, 0.002;
rhov, beta_pdf, 0.41, 0.002;
phi, beta_pdf, 0.4, 0.002;
psi, beta_pdf, 0.5, 0.002;
mup, gamma_pdf, 1.2, 0.002;
end;
estimation(datafile=test5,mode_compute=6)