4.2
Welfare Analyses

The welfare examinations are conducted by applying a second-order approximation to the system, and are computed with the software package, Dynare. The optimized policies are obtained by choosing the policy parameters αH, α^H_p , α^H_mcand α^H_e for the monetary growth rate rule and αR, α^R_p, α^R_mc and α^R_e for the interest rate rule which lead to the highest level of γ^a.¹⁹

4.2.1 The benchmark model: optimized money growth rate rule

In this section, we first examine the benchmark optimal money growth rate rule under the four types of real shocks which occur all together. The results are listed in Ta-ble 4. The optimized monetary aggregate policy can be characterized by∆h^{OP T}_t = 0.9[−2∆p_t− 0.2mc_t− 2∆e_t] + 0.1∆h_t−1+ ε^H_t . This policy suggests that much at-tention is directed at stabilizing the inflation and exchange rate depreciation rates, but with not much effort being made to stabilize the output gap. This policy generates volatilities for the macroeconomic variables such as those for the GDP and the infla-tion rate of 7.3% and 0.1%, while leading to greater fluctuainfla-tions in exports and the terms of trade with standard deviations of 15.4% and 4.4%, respectively. As shown, this policy will incur a welfare gain of 0.57% of the steady state consumption.

Table 4 also reports the macroeconomic performance under each individual shock aided by the implementation of the optimized money growth rate rule. The results show that the shock to the foreign interest rate is the main factor that drives significant fluctuations in the exports and terms of trade, accounting for 98% of the fluctuation in output, 100% of the fluctuation in the price inflation and 95% of the fluctuation in the exchange rate. However, if home productivity, export or international price shocks occur, this policy can successfully assist in the stabilization of the economy.

19We conduct grid search to obtain the optimized policy parameters. For stabilization purposes, the policy parameters of the monetary aggregate rule should be negative, while those of the interest rate rule should be positive. The search ranges for the monetary growth rate rule under real shocks are from 0 to 0.9 forα_H with step size 0.1, and from−2 to 0 for α^H_p, α^H_mcandα^H_e with step size 0.2. The search ranges for the interest rate rule are from 0 to 0.9 forα_R, from 0 to 2 forα^Rp, α^Rmc, andα^Re with the step sizes same as above. These ranges are chosen arbitrarily, but the welfare gains under the parameters outside the range are lower, or can be negligible if there are any. This method can also be seen in Bergin et al. (2007).

Table 4^ Optimal Monetary Growth Rate Rule: Benchmark Model (under Real Shocks)

Optimized monetary growth rate rule:∆h^{OP T}_t = 0.9[−2∆pt− 0.2mct− 2∆et] + 0.1∆h_t−1+ ε^H_t . Money growth rate rule:∆h^{OP T}_t

Shock ε^A, ε^R∗, ε^ex, ε^P∗ ε^A ε^R∗ ε^ex ε^P∗ Welfare (as the percentage of the steady state consumption)

γ^a 0.5702 −0.0028 0.0058 0.0000 −0.0047

Standard deviations (in the percentage deviation from the steady state)

Y 7.30 1.45 7.19 0.06 0.73

C 8.90 1.01 8.86 0.03 0.10

n 11.30 0.64 11.23 0.09 1.14

EX 15.40 1.50 15.23 0.16 2.00

IM 8.40 1.03 8.38 0.02 0.09

∆p 0.10 0.05 0.51 0.00 0.02

∆p^d 0.37 0.06 0.36 0.00 0.05

∆e 1.20 0.04 1.14 0.01 0.06

TOT 4.40 0.27 4.36 0.02 0.19

q 8.30 1.12 8.20 0.03 0.09

R^IB 0.89 0.06 0.89 0.01 0.02

R^L 0.89 0.06 0.88 0.00 0.02

R^T 0.88 0.05 0.88 0.00 0.02

EFP 0.03 0.00 0.03 0.00 0.00

Means (in the percentage deviation from the steady state)

Y −0.7314 −0.0014 −0.7314 −0.0014 −0.0014

C 0.4453 −0.0047 0.4453 −0.0047 −0.0047

n −1.1473 0.0027 −1.1473 0.0027 −0.0073

EX −0.9245 −0.0045 −0.9045 −0.0045 −0.0145

IM 0.4856 −0.0044 0.4856 −0.0044 0.0056

Note: TOT denotes the terms of trade, measured by eP^d/P^m, EX denotes the export and IM denotes the import.

4.2.2^ The alternative interest rate rule under real shocks

If the central bank implements the interest rate rule instead, the welfare-maximizing rule is R^{IB,OP T}_t = 0.1[0.0029 + 1.4∆pt+ 2mct+ 0.0∆et] + 0.9R_t−1^{IB,OP T} + ε^R_t. The associated moments of the endogenous variables are listed in Table 5. In contrast to

Table 5^ Optimal Interest Rate Rule: Benchmark Model (under Real Shocks)

Optimized interest rate rule:R^{IB,OP T}_t =0.1[0.0029+1.4∆pt+2mct+0.0∆et]+0.9R^{IB,OP T}_t−1 +ε^R_t. Interest rate rule: R^{IB,OP T}

Shock ε^A, ε^R∗, ε^ex, ε^P∗ ε^A ε^R∗ ε^ex ε^P∗ Welfare (as the percentage of the steady state consumption)

γ^a 0.5142 −0.0021 0.0052 0.0000 0.0000

Standard deviations (in the percentage deviation from the steady state)

Y 7.93 1.73 7.73 0.02 0.38

C 8.89 1.07 8.83 0.01 0.10

n 12.11 0.58 12.08 0.03 0.59

EX 15.02 1.59 15.04 0.13 1.57

IM 8.36 1.05 8.29 0.01 0.09

∆p 0.56 0.05 0.55 0.00 0.05

∆p^d 0.36 0.05 0.35 0.01 0.07

∆e 1.18 0.12 1.16 0.01 0.16

TOT 4.90 0.45 4.87 0.03 0.27

q 8.19 1.00 8.12 0.01 0.10

R^IB 0.89 0.07 0.88 0.00 0.08

R^L 0.89 0.07 0.88 0.00 0.08

R^T 0.88 0.06 0.88 0.01 0.08

EFP 0.03 0.00 0.03 0.00 0.00

Means (in the percentage deviation from the steady state)

Y −0.7614 −0.0014 −0.7614 −0.0014 −0.0014

C 0.4553 −0.0047 0.4553 −0.0047 0.0053

n −1.1973 0.0027 −1.1873 0.0027 −0.0073

EX −0.7845 0.0055 −0.7845 −0.0045 −0.0045

IM 0.5256 −0.0044 0.5256 −0.0044 0.0056

Note: Refer to Table 4.

the optimized monetary aggregate rule, the optimized interest rate rule is characterized by attaching higher weights to the lagged interest rate and output gap than to the CPI inflation or exchange rate depreciation. The welfare under the interest rate rule can be

0.056% lower each quarter than under the monetary aggregate rule.²⁰This shows that it will not improve welfare to switch from the monetary aggregate rule to the interest rate rule.

The reason for the welfare superiority of the monetary aggregate rule is that the monetary aggregate rule does a better job of stabilizing the economy. Without explicit effort in removing the output fluctuations, the optimized monetary aggregate rule can generate lower volatilities in output and the CPI inflation which are 7.30% and 0.1%, respectively, under the monetary aggregate rule, relative to 7.93% and 0.56% under the interest rate rule. It is because of the liquidity effect that the monetary aggregate gen-erates. The high-powered money, which is the reserve money of the banking system, is directly relevant to the deposit which supports the consumption and thereby the output in the economy. The implementation of the money growth rate rule with the inflation targeting requires good control of the growth rate of the high-powered money which in turn reduces not only the fluctuations in the inflation rate, but also the output. With the direct liquidity services that the monetary aggregate can supply, the control of the monetary growth rate moderates both real and nominal fluctuations. This is consistent with the monetarists’ view on the monetary policy which advocates controlling the monetary aggregate to stabilize the economy while leaving the interest rate to fluctuate more widely.²¹

4.2.3^ Financial shocks

The inclusion of a frictional banking sector allows us to examine optimal policy re-sponses to shocks that originate from the credit market. These shocks resemble the causes of the subprime crisis which were mainly the domestic credit market disrup-tion. The credit market failure is also one of the factors that exacerbated the economic downturns during the East Asian financial crisis in 1997. The financial shocks that impacted the effectiveness of collateral and efficiency of monitoring efforts for credit checks can well characterize the shocks that are normally factors causing the credit market to deteriorate. In this section we thus emphasize the optimal policy reaction to the credit market failure of these types.

We calibrate welfare-maximizing monetary policies under financial shocks which

20Lucas (1987) estimates that the costs of business cycle fluctuations are 0.04% of annual consumption, which is concluded to be trivial. With a two-country DSGE model, Bergin et al. (2007) find that the welfare gain from the optimized interest rate rule is 0.04% relative to the fixed exchange rate, which is considered to be small.

21See King and Lin (2005).

Table 6^ Optimal Policy Rules under Financial Shocks(ε^K, ε^m)

Optimized monetary growth rate rule:∆h^FIN_t = [−2∆pt− 2mct− 2∆et] + 0.0∆h^FIN_t−1 + ε^H_t . Optimized interest rate rule:R^IB,FIN_t = [0.0029 + 1.4∆pt+ 0.2mct+ 2∆et] + 0.0R^IB,FIN_t−1 + ε^R_t.

(A) (B) (C) (D)

∆h^FIN R^IB,FIN ∆h^{OP T} R^{IB,OP T}

Welfare (as the percentage of the steady state consumption)

γ^a −0.0642 0.0000 −0.0654 −0.0592

Standard deviations (in the percentage deviation from the steady state)

Y 0.41 0.97 0.41 0.47

C 0.75 0.83 0.76 0.79

n 0.64 1.52 0.64 0.74

EX 0.23 1.00 0.34 0.15

IM 0.39 0.66 0.41 0.44

∆p 0.01 0.03 0.03 0.02

∆p^d 0.00 0.02 0.01 0.01

∆e 0.01 0.02 0.04 0.02

TOT 0.08 0.87 0.13 0.15

q 0.85 0.13 0.82 0.76

R^IB 0.17 0.18 0.18 0.16

R^L 0.12 0.13 0.13 0.11

R^T 0.02 0.02 0.03 0.01

EFP 0.05 0.05 0.05 0.05

Means (in the percentage deviation from the steady state)

M −0.0314 −0.1214 −0.0314 −0.0414

C −0.0747 −0.0747 −0.0747 −0.0747

n −0.0573 −0.1873 −0.0573 −0.0673

EX −0.0145 −0.1255 −0.0145 −0.0045

IM −0.0344 −0.0644 −0.0344 −0.0344

Note: Column (A) and (B) list the results with the implementation the welfare-optimizing pol-icy reactions to the financial shocks. Column (C) and (D) list the results under the financial shocks with the implementation of the optimized policies for real shocks.

are ρ_K = 0.9, ρ_m = 0.99 and σ_K = σ_m = 3%. The results are listed in columns (A) and (B) in Table 6. Under adverse financial distress, all macroeconomic variables such

as the output, consumption and employment decline. Due to shocks to the financial system, it is required that more collateral be accumulated, which results in greater amounts of bonds and leads to larger fluctuations in the home bond rate. This will in turn give rise to the exchange rate volatility which will translate into the volatility of exports.

Therefore, the required optimal policy responses to the financial shocks are dif-ferent from those to the real shocks, particularly the interest rate rule. The optimized money growth rate rule ∆h^FIN_t = [−2∆p_t− 2mc_t− 2∆e_t] + 0.0∆h^FIN_t−1 + ε^H_t is slightly less persistent, but places greater emphasis on output fluctuations than the de-sirable policy under real shocks. This policy shows that, while there is an adverse financial shock, the central bank which uses the money growth rate rule should raise the money growth rate in accordance with the GDP recession resulting from a shock.

The expansionary monetary policy will help dampen the decline as well as stabilize the economy. On the other hand, the optimized interest rate rule can be stated as:

R^IB,FIN_t = [0.0029 + 1.4∆pt+ 0.2mct+ 2∆et] + 0.0R^IB,FIN_t−1 + ε^R_t. By reinforcing its role in the stabilization of the inflation and exchange rates, the interest rate rule can also assist in economic stabilization, but less well than the monetary aggregate rule.

In contrast to the real shocks, however, the interest rate rule generates a higher welfare level than the money growth rate rule. The interest rate rule leads to greater economic contraction than the monetary aggregate rule and thus causes a sharper de-cline in employment. The welfare gain from the dede-cline in the labor supplied domi-nates the welfare loss from the reduction in consumption and thus makes the interest rate welfare dominating. This policy, however, may not be desirable.

We also conduct experiments where the central bank retains optimized rules pro-posed above in the benchmark case with real shocks, without recognizing a deterio-rating credit environment. The results reported in column (C) show that the preceding optimized monetary aggregate rule can cause greater economic fluctuations and result in a large welfare loss. The results in column (D), however, show that the preceding optimized interest rate rule can perform a better job in stabilization, but leads to a higher welfare loss by exacerbating the economic downturn.

4.2.4^ The current monetary aggregate rule of the central bank

Based on the optimized monetary policies obtained above, it would be helpful and interesting to use this framework to assess the welfare implications of current monetary policy, estimated from the small open economy DSGE model of Teo (2009). The

Table 7^ The Estimated Monetary Aggregate Rule (under Real Shocks)

∆h^Est_t = 0.319[−1.116∆pt− 0.0mct− 0.403∆et] + 0.681∆h^Est_t−1+ ε^H_t .

Estimated MA policy:∆h^Est_t

Shock ε^A, ε^R∗, ε^ex, ε^P∗ ε^A ε^R∗ ε^ex ε^P∗ ε^K, ε^m Welfare (in the percentage deviation from the steady state)

γ^a −1.3193 −0.0186 −1.2916 0.0000 −0.0095 −0.0714

Standard deviations (in the percentage deviation from the steady state)

Y 14.27 1.17 14.19 0.06 0.89 0.61

C 8.52 0.90 8.47 0.01 0.10 0.71

n 22.26 1.41 22.18 0.10 1.40 0.96

EX 20.44 1.75 20.24 0.17 2.19 0.94

IM 8.05 0.88 8.00 0.01 0.09 0.32

∆p 1.89 0.14 1.88 0.00 0.04 0.10

∆p^d 0.68 0.09 0.67 0.00 0.05 0.04

∆e 3.13 0.11 3.12 0.00 0.03 0.14

TOT 7.57 0.22 7.57 0.02 0.13 0.31

q 8.77 0.81 8.73 0.01 0.07 1.09

R^IB 0.86 0.07 0.85 0.00 0.03 0.21

R^L 0.85 0.07 0.85 0.00 0.03 0.16

R^T 0.84 0.07 0.84 0.00 0.03 0.08

EFP 0.03 0.00 0.03 0.00 0.00 0.05

Means (in the percentage deviation from the steady state)

Y −1.0513 −0.0014 −1.0514 −0.0014 −0.0014 −0.0314

C −0.0847 −0.0047 −0.0747 −0.0047 −0.0047 −0.0747

n −1.6373 0.0027 −1.6373 0.0027 −0.0073 −0.0473

EX −2.9645 −0.0245 −2.9145 −0.0045 −0.0245 −0.0245

IM 0.7656 −0.0044 0.7656 −0.0044 0.0056 −0.0245

estimated monetary policy can be stated as∆h^Est_t = 0.319[−1.116∆pt+ 0.0mct− 0.403∆et] + 0.681∆h^Est_t−1 + ε^H_t , which is more persistent than the optimized policy, but follows by stabilizing the CPI inflation and exchange rates in a similar fashion.

Table 7 reports the results. As shown, this policy leads to higher macroeconomic fluctuations in most of the variables such as output, CPI inflation and exchange rate.

This policy also lowers the mean levels of output, consumption and employment which consequently results in a significant welfare loss of 1.89% of the steady state consump-tion, relative to the implementation of the optimized policy. Under financial shocks, this policy leads to higher variations in output, inflation as well as exchange rates, and results in lower welfare than that under the optimized rule.

This study may suggest that, while the monetary aggregate policy rule that Tai-wan’s central bank conducts is in line with the welfare-optimizing monetary policy rule, it may be welfare improving by alleviating some of the need to smooth the mon-etary growth rate and by strengthening its efforts in stabilizing the inflation and ex-change rate fluctuations.

5.
S ENSITIVITY ANALYS ES

In this paper, we consider some variations of the benchmark model to check for the robustness of the results obtained above in which the monetary aggregate rule is opti-mal.

在文檔中 Optimal Monetary Policy for Taiwan: A Dynamic Stochastic General Equilibrium Framework (頁 21-28)