NeOn Methodology.

This section examines whether the central bank should be aggressive when managing the optimal simple quantitative easing rule or not. The aggressiveness is characterised by the presence of a constant called a credit parameter (<) in the optimal simple rule. Hence, a higher credit parameter reflects a situation when the central bank more aggressively injects credit for banks. This type of aggressiveness is also used in the Gertler and Karadi’s (2011) original model.

However, the presence of a credit parameter in the optimal simple rule has one significant consequence, which is that it will inevitably unbind the optimality of the simple quantitative easing rule, as the feedback coefficient in the optimal simple rule will be changed. An inspection of the impact of aggressiveness is carried out in this section by comparing unconditional variances among variables in the loss function for various levels of credit parameters. Specifically, the optimal simple rule used in the simulation is given in equation (4.56) below.

M_! = }O −0.0422 [j_!$%+ 0.3354Ij_!$%+ 5.0009 gi_!$%P (ç. âú)

Accordingly, Table 4.11 provides the simulation of unconditional variances under the chosen optimal simple quantitative easing rule for various levels of credit paramaters.

Table 4-11: Unconditional Variances of The Optimal Simple Rule Under Various Credit Parameter Credit

parameter (>) _? Unconditional variance _{ù → ã}LOSS

@ A _BA _CA_{1 D}A 1 0.0326 2.6927 0.0458 0.1007 0.0955 2.9672 5 0.0272 2.5388 0.0325 0.0849 0.0325 3.1406 10 0.0257 2.4524 0.0264 0.0803 0.7754 3.3602 50 0.0245 2.4618 0.0246 0.0768 0.8208 3.4085 100 0.0243 2.4572 0.0240 0.0763 0.8517 3.4335

Some findings from the simulation above are of note. First, increasing aggressiveness deteriorates policy performance. As shown in Table 4.11, policy performance increases when the credit parameter rises from 1 to 100. At this rate, optimality is no longer binding, and the policy performance is worsening. The credit injection ratio itself mainly contributes to the worsening of policy performance, which means that the loss function penalizes central bank with greater extent when its aggressiveness elevates. That is, this ratio fluctuates considerably as the credit parameter increases. The increasing credit injection reflects the central bank's increased aggressiveness when injecting abundant credit into the economy.

Second, however, although it worsens policy performance, a higher credit injection into the economy stabilises the variables in the loss function. We found that the variance of output, inflation, credit spread, and the nominal interest rate all decline when the credit parameter increases from 1 to 100. For instance, the inflation fluctuation falls from 0.0326 to 0.0243 (25.46%). The fluctuation of output also declines from 2.6927 to 2.4572 (8.73%). Similarly, credit spread and policy rate are also stabilised by 47.59% and 24.23%, respectively. When aggressiveness increases from 1 to 100, the credit injection ratio’s variance soars from 0.0955 to 0.8517 (791.83%), and policy performance deteriorates from 2.9672 to 3.4335 (15.71%). Considering that policy performance deteriorates more quickly than the improvement of variables in the loss function, we argue that over-aggressiveness is detrimental to the economy. Although increased aggressiveness can benefit macroeconomic stabilisation, this benefit is accompanied by worsened policy performance.

The main point from this finding is that aggressiveness can promote inflation and credit stabilisation but at the cost of worsened policy performance. Also, increased credit injection can dampen the fluctuation of output and policy rate. Figure 4.2 illustrates an example of the economic response for two level of central bank’s aggressiveness (} = 10

and } = 100) when a negative five percent capital quality shock enters the economy.

Figure 4.2 illustrates three simulations: the fully optimal commitment rule, the optimal simple quantitative easing rule with a credit parameter of 10, and the optimal simple quantitative easing rule with a credit parameter of 100. Precisely, the optimal simple quantitative easing rule with a credit parameter 10 is defined as

M! = O −0.422 [j!$%+ 3.354Ij!$%+ 50.009 gi!$%P (ç. âf) while the the optimal simple quantitative easing rule with a credit parameter of 100 is defined as

M_! = O −4.22 [j_!$%+ 33.54Ij_!$%+ 500.09 gi_!$%P. (ç. âç)

As shown in the figure, in general, being aggressive causes the central bank to inject more abundant credit into the economy. The central bank injects the highest amount of credit when it is very aggressive with a credit parameter of 100. This injection can moderate the negative impact of the shock on macroeconomic variables.

For instance, in the first period, the variables like capital, inflation, consumption, investment, output, and asset prices are more stable than those under commitment. However, this stabilisation is a consequence of a massive liquidity injection into the economy, which could have brought negative consequences in the future. Recall that the loss function (4.59) contains the credit injection ratio within its structure, which serves as a penalty for an excessive quantitative easing decision: thus, over-aggressiveness inevitably deteriorates policy performance.

In conclusion, this simulation illustrates that over-aggressiveness unbinds optimality in the simple quantitative easing rule. This occurs because the presence of a credit parameter increases the feedback coefficients in the rule, which consequently worsens loss value due to higher credit injection into the economy. However, as demonstrated by the unconditional variance and the example of impulse response function in Figure 4.2, although excessive aggressiveness when combatting a crisis deteriorates policy performance, the decision helps stabilise the fluctuation of economic variables in the loss function and also benefits the macroeconomy in general. That is, output, inflation, credit spread, and policy rate fluctuate less. However, this occurs at the cost of worsened policy performance.