Long-Run Mild Deflation Under Fiscal Unsustainability in Contemporary Japan

Abstract

Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy” presented a simple framework of disequilibrium analysis, in which strong money demand, induced by near-zero rates, helps to absorb excess supply in goods, labor, and public bond markets. However, the analysis is at most diagnostic without any theoretical rigor or quantitatively precise simulation. In this chapter presents a formal equilibrium model, in which public bond price bubbles are present temporarily or even persistently, but burst with a tiny probability per year. As discussed in Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy”, those bubbles and their bursting in equilibrium analysis are interpretable as excess money demand and its disappearance in disequilibrium analysis. One of the most important implications in this chapter is that the model can yield reasonable predictions concerning the price level and a wide range of public bond yields, not only for the period when the short-term rate was already near zero (from the mid-1990s), but also for the period when it was far above zero (from the mid-1980s to the mid-1990s). For the latter period, the model predicts that the price level switches from mildly inflationary to mildly deflationary, and that the short-term rate declines quickly, but that yield curves remain upward sloping. For the former period, on the other hand, yield curves were gradually flattening at near-zero rates. In terms of future implications, if the bubbles burst, then the price level and rate of interest would jump immediately. As discussed in Chapter “Public Bonds as Money Substitutes at Near-Zero Interest Rates: Disequilibrium Analysis of the Cur-Rent and Future Japanese Economy”, strong commitment to future fiscal reforms by a government would help a one-off price surge to stop at a level several times higher than before. Here, it is assumed that a rare but catastrophic event, such as a large-scale inland earthquake in Tokyo, causes the bubbles to burst, leading to sharp declines in real output in the following years. Given a strong aversion to catastrophic endowment shocks, the model is able to yield even more realistic predictions for the price paths and the shape of yield curves, both of which would prevail before the bubbles burst.

Appendix: Price Behavior During the FS Regime with \({\varvec{d}} > 0\)

Suppose that the economy switches to the FS regime in time $s$. The price level coincides with ${P}_{s+L}^{QT(d=0)}$ when catastrophic shocks disappear completely in time $s+L$. From Eq. (3.11), the following holds between time $s+L-1$ and $s+L$:

$$\frac{{P}_{s+L-1}^{QT}}{{P}_{s+L}^{QT(d=0)}}=\frac{1}{\beta \left(1-d\right)}\left[1-\lambda {\left(\chi +\frac{{M}_{s+L-1}}{{P}_{s+L-1}^{QT}}\right)}^{-\frac{1}{\sigma }}\left(1-d\right)c\right].$$

Taking ${P}_{s+L}^{QT(d=0)}$ and ${M}_{s+L-1}$ as fixed, and marginally increasing $d$ from zero and ${P}_{s+L-1}^{QT}$ from ${P}_{s+L-1}^{QT(d=0)}$, the following total differential is obtainable by a first-order approximation:

$$\eta =\frac{\Delta {P}_{s+L-1}^{QT}}{{P}_{s+L-1}^{QT(d=0)}}/\Delta d={R}_{1,s}^{QT(d=0)}/\left[1+\frac{{R}_{1,s}^{QT(d=0)}-1}{\sigma }\frac{\frac{{M}_{s}}{{P}_{s}^{QT(d=0)}}}{\chi +\frac{{M}_{s}}{{P}_{s}^{QT(d=0)}}}\right]>0,$$

(A.1)

where ${R}_{1,s}^{QT(d=0)}$ and $\frac{{M}_{s}}{{P}_{s}^{QT(d=0)}}/\left[\chi +\frac{{M}_{s}}{{P}_{s}^{QT(d=0)}}\right]$ are constant, given Eqs. (3.14) and (3.15). If:

$$\frac{{M}_{s}}{{P}_{s}^{QT(d=0)}}/\left[\chi +\frac{{M}_{s}}{{P}_{s}^{QT(d=0)}}\right]>\sigma ,$$

(A.2)

then $0<\upeta <1$.

Equation (A.1) is approximated as:

$${P}_{s+L-1}^{QT}=\frac{1}{{\left(1-d\right)}^{\eta }}{P}_{s+L-1}^{QT(d=0)}.$$

Using the same approximation technique leads to:

$${P}_{s+l}^{QT}={\left[\frac{1}{{\left(1-d\right)}^{\eta }}\right]}^{L-l}{P}_{s+l}^{QT(d=0)},$$

(A.3)

for $l=0, 1, 2,\dots , L-1$.

From Eq. (3.9):

$${R}_{1,t}^{QT}=\frac{1}{\beta \left(1-d\right)}\frac{{P}_{t+1}^{QT}}{{P}_{t}^{QT}}.$$

Together with Eq. (A.1), the total differential is derived by a first-order approximation:

$$\frac{\Delta {R}_{1,t}^{QT}}{{R}_{1,t}^{QT(d=0)}}/\Delta d=1-\eta .$$

(A.4)

Thus, if $0<\upeta <1$, then ${R}_{1,t}^{QT}>{R}_{1,t}^{QT\left(d=0\right)}.$