The widely used approach to evaluating the macroeconomic effects of unconventional monetary policy is the ‘plug-in’ approach, which uses estimates of the impact of unconventional policy measures on asset prices to plug them into standard macroeconomic models. For example, Chung et al. (2012) use the estimate reported in Gagnon et al. (2011) – namely that the Federal Reserve’s asset purchases in 2009 lowered the yield on ten-year Treasury and high-grade corporate bonds – to implement simulation exercises employing well-established macroeconomic models such as the FRB/US model. Because this plug-in approach needs to rely on the estimates of separate studies on the reaction of financial markets, possible biases and uncertainty regarding the estimates, if exist, may lead to unreliable simulation results of the macroeconomic model (see, e.g., Hamilton and Wu 2012). In addition, the unconventional monetary policy shocks estimated from separate studies are not necessarily consistent with the macroeconomic models based on the conventional monetary transmission mechanism.

# A latent threshold approach

Our recent research (Kimura and Nakajima 2013) employs a data-driven approach using structural vector autoregression with identifying restrictions on the simultaneous relations among variables. Some existing studies based on vector autoregression models impose the sign restriction that a compression in the long-term yield spread leads to an increase in inflation and output growth within a quarter of the impact to identify unconventional monetary policy shock with the interest-rate zero lower bound (see, for example, Baumeister and Benati 2010). However, such a restriction may not always be plausible when taking the lag structures in monetary-policy transmission mechanisms into consideration.

We propose a new framework to identify conventional and unconventional monetary policy shocks in the presence of the zero lower bound in a time-varying parameter vector autoregression model. One limitation of the standard time-varying parameter vector autoregression model is that the identifying restriction is fixed over time, which makes it impossible to precisely describe the regime change between the conventional and unconventional policies. To overcome this difficulty, we exploit the latent threshold model developed by Nakajima and West (2013). This approach models time-varying parameters that are shrunk to zero in some periods by setting the latent thresholds. Here, we apply and extend the latent threshold model approach to the simultaneous relations among variables in order to identify monetary-policy shocks and to take account of the zero lower bound in conventional and unconventional policy regimes.

# Interest-rate rule and bank-reserve rule

In order to identify conventional and unconventional monetary policy shocks, the following simple but fundamental model is considered for each of the regimes. In the conventional policy regime, the central bank sets the short-term interest rate as its policy instrument in response to macroeconomic shocks associated with inflation and the output gap. Deviation from this interest-rate rule is regarded as a conventional monetary policy shock.

In the unconventional policy regime, in contrast, the central bank expands its balance sheet under the zero lower bound. Although unconventional policies can be classified into ‘quantitative easing’ and ‘credit easing’, depending on whether the central bank focuses on the liability side or the asset side of its balance sheet, a key aspect here is that the implementation of unconventional policy in both the quantitative easing and the credit easing is associated with an increase in bank reserves. In the unconventional policy regime of our model, the central bank controls bank reserves in response to macroeconomic shocks. A deviation from this bank reserve rule is defined as an unconventional monetary policy shock.

We introduce the extended latent threshold model structure in the time-varying parameters of simultaneous relations among variables to embed the identifying restrictions for the interest-rate rule in the conventional policy regime and the bank reserve rule in the unconventional regime.

# Japan’s unconventional monetary policy

We apply our estimation framework to Japan’s economy. The analysis uses quarterly data from 1981 to 2012 on the CPI inflation rate, the output gap, the overnight call rate, the outstanding balance of current accounts held at the Bank of Japan, and the yield on ten-year Japanese government bonds. We define the unconventional policy regime as the periods from 2001/Q1 to 2006/Q1 (labelled as UC1), and from 2010/Q1 to the end of the observation period (labelled as UC2), and the conventional policy regime as other periods, when the overnight call rate is the main operating target. Regarding UC1, the Bank of Japan introduced the quantitative easing policy in March 2001, changing its main operating target for money-market operations from the overnight call rate to the outstanding balance of current accounts held at the Bank of Japan. Regarding UC2, the Bank of Japan introduced a new funds-supplying operation in December 2009 in order to encourage a further decline in longer-term interest rates in the money market through provision of ample longer-term funds at an extremely low interest rate. Then, in October 2010, the Bank of Japan introduced its policy of ‘comprehensive monetary easing’ to further enhance monetary easing by purchasing various financial assets such as Japanese government bonds, treasury discount bills, commercial paper, corporate bonds, exchange traded funds, and Japanese Real Estate Investment Trusts.

# Policy response

Figure 1 and Figure 2 show the estimation results of simultaneous response of policy variables to macroeconomic shocks. Figure 1 shows a marked shrinkage in the simultaneous responses of short-term interest rates to inflation and the output gap as short-term interest rates approached zero in the 1990s. This shrinkage is induced by the latent threshold model, indicating that the zero lower bound constraint has been relevant since the early 2000s. Figure 2 shows the dynamics of the simultaneous responses of bank reserves to inflation and the output gap. These parameters are estimated to be around zero in the conventional policy regime, but are substantially negative in the unconventional policy regime, implying that the Bank of Japan increases bank reserves in response to negative inflation and output gap shocks.

**Figure 1**.

**Figure 2**.

Another important result is the simultaneous response of long-term interest rates to a bank reserve shock, which is plotted in Figure 3. The parameter is clearly negative during the unconventional policy regime, which implies that increasing bank reserves lowers long-term interest rates, consistent with the portfolio rebalancing effect and/or signalling effect of unconventional policy. Furthermore, the trajectory shows that a bank reserve shock has a larger impact on long-term interest rates in UC2 than UC1, which possibly reflects differences in the way bank reserves were expanded. In the quantitative easing policy during UC1, the Bank of Japan aimed to expand the liability side of its balance sheet by mainly increasing the outright purchase of long-term Japanese government bonds as well as conducting the short-term funds-supplying operations. In UC2, in contrast, the Bank of Japan has purchased various financial assets, including riskier market products, which may have resulted in a larger impact of the expansion of bank reserves on financial markets.

**Figure 3**.

# Impulse response of macroeconomy

Figure 4 and Figure 5 display the impulse responses of inflation and the output gap to identified monetary-policy shocks. Trajectories show the responses two years after the policy shock in the case of inflation and one year after in the case of the output gap. For the conventional monetary policy regime, Figure 4 suggests that the impact of a short-term interest rate shock on inflation and the output gap was relevant in the 1980s, but that it gradually declined after the burst of the bubble economy at the beginning of the 1990s.^{1}

**Figure 4**.

**Figure 5**.

For the unconventional monetary policy regime, the impact of a bank reserve shock on inflation and the output gap is positive but very uncertain, as shown in Figure 5. Although the impact of a bank reserve shock on the financial market is relevant in the unconventional policy regime (as shown in Figure 3), the transmission effect from the financial market on the real economy involve considerable uncertainty, which leads to the wide credible intervals for the impact of unconventional policy actions on inflation and the output gap.^{2}

# Concluding remarks

In April 2013, the Bank of Japan introduced a new regime of monetary easing called ‘quantitative and qualitative monetary easing’, doubling not only the monetary base and the amount outstanding of Japanese government bonds held by the Bank of Japan in two years but also its average remaining maturity of Japanese government bond purchases. Measuring effects of such unconventional policy actions on the economy using our estimation framework, after more data periods are available, is of particular interest, which remains as a future work. It is also interesting to apply our estimation approach to the case of unconventional monetary policy of other central banks such as Federal Reserve and Bank of England.

# References

Baumeister, C, and L Benati (2010), “Unconventional Monetary Policy and the Great Recession -- Estimating the Impact of a Compression in the Yield Spread at the Zero Lower Bound”, Working Paper Series, No. 1258, European Central Bank.

Chung, H, J P Laforte, D Reifschneider, and J C Williams (2012), “Have We Underestimated the Likelihood and Severity of Zero Lower Bound Events?”, *Journal of Money, Credit and Banking*, 44(s1), 47-82.

Gagnon, J E, M Raskin, J Remache, and B Sack (2011), “The Financial Market Effects of the Federal Reserve’s Large-Scale Asset Purchases”, *International Journal of Central Banking*, 7(1), 3-43.

Hamilton, J D, and J C Wu (2012), “The Effectiveness of Alternative Monetary Policy Tools in a Zero Lower Bound Environment”, *Journal of Money, Credit and Banking*, 44(s1), 3-46.

Kimura, T, and J Nakajima (2013), “Identifying Conventional and Unconventional Monetary Policy Shocks: A Latent Threshold Approach”, Bank of Japan Working Paper Series, No 13-E-7.

Nakajima, J, and M West (2013), “Bayesian Analysis of Latent Threshold Dynamic Models”, *Journal of Business and Economic Statistics*, 31(2), 151-164.

1 The interest-rate elasticity of private expenditures may have declined when the Japanese economy was struggling with the deleveraging problem following the burst of the bubble.

2 Although we omit the estimation result, the volatilities of identified structural shocks of inflation and the output gap become large in the second half of the 2000s due to the impact of the fluctuation in global commodity prices on inflation and due to the impact of the global financial crisis on output gap. In principle, the TVP-VAR is a multivariate regression model; that is, larger volatility in the residuals generally yields larger uncertainty in the regression coefficients. This leads to the greater uncertainty in the impulse response analysis shown in Figure 5.