Online Appendix“Inﬂation, Business Cycle, and Monetary Policy: The Role ofInﬂationary Pressure” by Masahiko Shibamoto
A.1

Information content of ﬁnancial and macroeconomic variables for future
inﬂation

We present empirical evidence on the information content of ﬁnancial and macroeconomic variables for inﬂation dynamics. Speciﬁcally, we examine inﬂation predictability using the following
predictive regression model:

πt+h =K ∑4∑hδk,jyk,t−j +k=1 j=04∑hδπ,jπt−j + µh + eπt+h ,(1)j=0where eπt+h is a zero-mean forecast error for h-quarter-ahead inﬂation. We estimate the regression (1) by ordinary least squares (OLS). As candidate variables, we consider ﬁve macroeconomic
variables: real gross domestic product (GDP) (gdp), shadow policy rate (sr), 10-year treasury
yield (lr), dividend/stock price (dy), and eﬀective exchange rate (er). To statistically examine
the signiﬁcant information content of candidate ﬁnancial and macroeconomic variables for inﬂation dynamics, we estimate the marginal impact of each predictor at quarter t on the inﬂationh for each k = gdp, sr, lr, dy, and er. We also compute White (1980)
rate h-quarter-ahead, δk,0

heteroskedasticity-robust F statistics for the test under the null hypothesis that the coeﬃcientson the zero-to-four-quarter lags of yk,t for each k = gdp, sr, lr, dy, and er are all equal to zero.
Table A1 shows the results.

A.2

Empirical results for the UCSV model

In this subsection, we conﬁrm the time-series property of the trend inﬂation in Japan. Then,
we compare the trend inﬂation with the time series of inﬂation dynamics due to inﬂationarypressure shocks to verify that inﬂationary pressure shocks identiﬁed as shocks that capture
medium-term inﬂation variations encapsulate stochastic changes in low-frequency movementsof trend inﬂation.
We follow the methodology proposed by Stock and Watson (2007) to measure the trend of
CPI inﬂation. They specify inﬂation πt as the sum of the stochastic trend component st and1

Table A1: Predictive content of ﬁnancial and macroeconomic variables for future inﬂation
Dependent variable
Predictor
Real GDP(100 × log)

δgdp,0F-stat

Shadow policy rate(%)δsr,0F-stat

10-year treasury yield(%)

δlr,0F-stat

Dividend/stock price(log)

δdy,0F-statEﬀective exchange rate
(100 × log)

δer,0F-stat

R2
Sample end

πt+1

πt+4

0.18∗
(0.08)
2.78[0.02]
0.54∗∗(0.18)
2.68[0.02]
0.04(0.24)
1.85[0.11]-0.59(1.12)
0.57[0.73]-0.040∗(0.017)1.78[0.12]-0.04(0.11)
2.41[0.04]
0.06(0.26)
1.82[0.11]
0.58∗∗(0.21)
3.48[0.01]-2.48∗(0.99)
1.80[0.12]-0.043∗(0.021)1.43[0.22]

0.64
2018Q30.46
2017Q4

Notes: We run predictive regression model (1) for each h-quarter-ahead inﬂation described in the upper header on
the ﬁnancial and macroeconomic variables. The zero-to-four-quarter lags of consumer price index (CPI) inﬂationand the constant are included as control variables in the regression model. δk,0 for k = gdp, sr, lr, dy, and er report
the point estimates for the coeﬃcient on the predictor at quarter t described in the left header. The numbers
in parentheses are White (1980) heteroskedasticity-robust standard errors for least squares.

∗∗and ∗ indicate

statistical signiﬁcance at the 1% and 5% levels, respectively. F-stat reports White (1980) heteroskedasticity-robust
F -statistics testing the restriction that coeﬃcients on the zero-to-four-quarter lags of the predictor described in
the left header are all equal to zero. The numbers in brackets are the p-values of the test. The sample spansfrom the ﬁrst quarter of 1983 through the quarter depending on the regression described in the last row.

2the transitory component ηtT in the unobserved components with stochastic volatility (UCSV)
model as follows;

πt = st + ηtT , where ηtT = σT,t ζT,t ,(2)st = st−1 + ηtS , where ηtS = σS,t ζS,t ,(3)22log(σT,t) = log(σT,t−1) + νT,t ,(4)22log(σS,t) = log(σS,t−1) + νS,t ,(5)′′where ζt = (ζT,t , ζS,t ) ∼ i.i.d.N (0, I2 ), νt = (νT,t , νS,t ) ∼ i.i.d.N (0, 0.04I2 ). We apply theUCSV model to the CPI inﬂation and compute the estimates of the posterior distribution forparameters σS,t , σT,t and stochastic trend st using the Markov Chain Monte Carlo (MCMC)
algorithm.
Figure A1 plots the smoothed estimates of σS,t and σT,t from the UCSV model. In estimating
the UCSV model, we use the longer sample from the second quarter of 1970. We set a vague
prior for the initial condition and lower bounds of 0.0085(=sample variance of changes in CPI
inﬂation×0.002) on the variances of permanent and transitory innovations in implementing theMCMC method.
The UCSV model captures the time-series evolution of the permanent and transitory sourcesof ﬂuctuations in Japan’s CPI inﬂation since the 1980s. The estimates in Figure A1 show
signiﬁcant movements in the standard deviations of permanent and transitory innovations overtime. In particular, we can see that the volatility of permanent innovation σS,t was high inthe early 1980s but gradually moderated through the mid-2000s. In contrast, the volatility oftransitory innovations σT,t slightly changed from the early 1980s to the mid-2000s, but a surge
in volatility can be observed in the second half of 2000.
Figure A2 plots the ﬁtted values of CPI inﬂation from the vector autoregressive (VAR)
model due to identiﬁed inﬂationary pressure shocks and the trend inﬂation. We measure thetrend inﬂation as the smoothed estimates of the stochastic trend of the actual CPI inﬂation
using the UCSV model.
By comparing the actual CPI inﬂation with the extracted inﬂation trend, we can visuallyconﬁrm the two distinctive properties of the inﬂationary pressure shocks in inﬂation dynamics.
First, inﬂation dynamics due to the identiﬁed inﬂationary pressure shocks are eliminated from3

Figure A1: Estimates of the standard deviations of the permanent and transitory innovationsof the CPI inﬂation using the UCSV model
Notes: The ﬁgure shows the 17%, 50%, and 83% quantiles of the posterior distributions of the standard deviationsof the permanent and transitory innovations of the CPI inﬂation from the ﬁrst quarter of 1983 to the fourth quarterof 2018.

variations owing to the transitory component. Reﬂecting the estimated evolution of volatilitiesof the transitory and permanent components, as shown in Figure A2, we can see that thestochastic trend dominated inﬂation dynamics until the mid-2000s; however, the deviation fromthe trend was more signiﬁcant in the latter part of the period. This tendency holds within thedynamics due to inﬂationary pressure shocks.
Second, inﬂation dynamics due to identiﬁed inﬂationary pressure shocks are broadly in linewith the stochastic changes in the inﬂation trend. As shown in Figure A2, the estimatedstochastic trend captures the low-frequency movements in actual inﬂation. These timings ofstochastic changes in the trend are broadly consistent with those of inﬂation dynamics thatcan be explained by the inﬂationary pressure shocks identiﬁed by the VAR model. This result
suggests that inﬂationary pressure shocks capture the driving forces of stochastic changes in thetrend underlying inﬂation dynamics.

4Figure A2: Comparison of inﬂation dynamics due to inﬂationary pressures and the trend inﬂation
Notes: The sample period spans from the ﬁrst quarter of 1983 to the fourth quarter of 2018. The blue bold line
indicates the series explained by the inﬂationary pressure shocks using the VAR model. We set the lag lengthto ﬁve quarters in the reduced-form VAR estimation. Trend inﬂation is measured as the 17%, 50%, and 83%
quantiles of the posterior distributions of the smoothed estimates of the stochastic trend of the CPI inﬂation
using the UCSV model.

A.3

Robustness check and sensitivity analysis

In this subsection, we re-estimate the model under several alternative settings to examine therobustness and sensitivity of our empirical ﬁndings.

Diﬀerent truncation horizon in the identiﬁcation problem
Figures A3 and A4 report the estimated impulse response functions to an inﬂationary pressureshock identiﬁed, under which we set the horizon in the identiﬁcation problem at h = 4 andh = 40, respectively.

Using alternative price indexes as the measure of inﬂation
Figures A5 and A6 report the estimated impulse response functions to an inﬂationary pressureshock in the VAR model where we use the quarterly CPI for all items (Headline CPI) andCPI for all items excluding fresh food and energy (CPIxFE), respectively, in constructing themeasure of inﬂation.
5Figure A3: Estimated responses to an inﬂationary pressure shock: Truncation horizon h = 4Notes: The solid line with circles represents the point estimates of the impulse responses to one standard deviation
inﬂationary pressure shock. The shaded areas denote one-standard-error bands, calculated using 1000 bootstrap
samples. We set the lag length to ﬁve quarters in the reduced-form VAR estimation. Estimation samples spanfrom the ﬁrst quarter of 1983 to the fourth quarter of 2018.

Using GDP gap as the measure of real output
Figure A7 report the estimated impulse response functions to an inﬂationary pressure shockin the VAR model, where we use the GDP gap retrieved from the Cabinet Oﬃce (%) as themeasure of real output.

Subsample analysis using data through the fourth quarter of 2007
Figure A8 shows the estimated impulse response functions to an inﬂationary pressure shockusing a subsample from the ﬁrst quarter of 1983 to the fourth quarter of 2007.

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Figure A4: Estimated responses to an inﬂationary pressure shock: Truncation horizon h = 40
Notes: The solid line with circles represents the point estimates of the impulse responses to one standard deviation
inﬂationary pressure shock. The shaded areas denote one-standard-error bands, calculated using 1000 bootstrap
samples. We set the lag length to ﬁve quarters in the reduced-form VAR estimation. Estimation samples spanfrom the ﬁrst quarter of 1983 to the fourth quarter of 2018.

References
Stock, James H., and Mark W. Watson. 2007. “Why Has Inﬂation Become Harder toForecast?” Journal of Money, Credit and Banking 39 (1): 3–34.
White, Halbert. 1980. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a
Direct Test for Heteroskedasticity.” Econometrica 48 (4): 817–838.

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Figure A5: Estimated responses to an inﬂationary pressure shock: Headline CPI inﬂation
Notes: The solid line with circles represents the point estimates of the impulse responses to one standard deviation
inﬂationary pressure shock. The shaded areas denote one-standard-error bands, calculated using 1000 bootstrap
samples. We set the lag length to ﬁve quarters in the reduced-form VAR estimation. Estimation samples spanfrom the ﬁrst quarter of 1983 to the fourth quarter of 2018.

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Figure A6: Estimated responses to an inﬂationary pressure shock: CPIxFE inﬂation
Notes: The solid line with circles represents the point estimates of the impulse responses to one standard deviation
inﬂationary pressure shock. The shaded areas denote one-standard-error bands, calculated using 1000 bootstrap
samples. We set the lag length to ﬁve quarters in the reduced-form VAR estimation. Estimation samples spanfrom the ﬁrst quarter of 1983 to the fourth quarter of 2018.

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Figure A7: Estimated responses to an inﬂationary pressure shock: GDP gap
Notes: The solid line with circles represents the point estimates of the impulse responses to one standard deviation
inﬂationary pressure shock. The shaded areas denote one-standard-error bands, calculated using 1000 bootstrap
samples. We set the lag length to ﬁve quarters in the reduced-form VAR estimation. Estimation samples spanfrom the ﬁrst quarter of 1983 to the fourth quarter of 2018.

10Figure A8: Estimated responses to an inﬂationary pressure shock: Subsample 1983:I–2007:IVNotes: The solid line with circles represents the point estimates of the impulse responses to one standard deviation
inﬂationary pressure shock. The shaded areas denote one-standard-error bands, calculated using 1000 bootstrap
samples. We set the lag length to ﬁve quarters in the reduced-form VAR estimation. Estimation samples spanfrom the ﬁrst quarter of 1983 to the fourth quarter of 2007.

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