As of May 2012, under the initiative of the Ministry of Finance (MOF), the Noda administration is attempting to force significant hikes in the consumption tax rate from the current 5% to 8% and then 10%, referring to economic crises overseas that are totally different from the situation in Japan, as well as even taking advantage of the great disaster in Japan, trumpeting “the reform for consolidating social security and taxes,” stating that, “without a tax increase, Japan would go fiscally bankrupt like Greece,” and that, “restoration from the great earthquake disaster requires tax hikes.” Economists under the influence of MOF and the Bank of Japan (BOJ) are following this movement. If the consumption tax were raised under the current deflation-led recession, however, this economic slump would be deteriorated further, leading to a higher ratio of outstanding government bonds to GDP (roughly equivalent to the national income). The true solution for the issue of accumulated Japanese government bonds is not to increase the consumption tax, but to overcome deflation. Below, I will summarize its theoretical and empirical reasons.
(1) Mathematical law of accumulated government bonds
Though it is exceptional to show a mathematical formula in an article like this, we need to mention the following fundamental equation—to be precise, an approximate formula—expressing the mathematical law of accumulated government bonds in order to explain the paradoxical nature of the issue of accumulated Japanese government bonds (see Asada  for details):
Δd = (G/Y) – (T/Y) – (ΔH/pY) + (r – π – g)d (1)
where G = real government spending; Y = real GDP; T = real taxation value; p = the price level; pY = nominal GDP; H = the nominal balance of high-powered money issued by the central bank; B = nominal net outstanding government bonds (this represents net debts to the private sector net of government bonds held by governmental agencies or the central bank as well as government-held assets, unlike the term Gross Government Bonds Outstanding used by the MOF for their tax hike campaign); d = (B/pY) = the ratio of outstanding government bonds (the ratio of nominal net outstanding government bonds to nominal GDP); r = the nominal interest rate for long-term government bonds; π = Δp/p = the price increase rate or the inflation rate; g = ΔY/Y = real GDP growth; gN = g + π = nominal GDP growth; and Δ is a symbol representing a change (for example, Δd represents a change in d per unit of time). Equation (1) is derived from the government constraint for Integrated Government incorporating the central bank, which expresses that government spending including interest payment for government bonds (pG + rB) is financed through either taxation (pT), newly issued government bonds underwritten by the private sector (ΔB), or high-powered money newly issued by the central bank (ΔH).
In Equation (1), if the value of d’s coefficient (r – π – g) is negative, the increase in d induces a lower Δd to prevent an accumulated increase in d, which is called the stabilization effect. If the value of this coefficient is positive, by contrast, the increase in d generates a higher Δd to drive an accumulated increase in d, which reveals its destabilization effect. Therefore, the following inequality called the Domar condition:
Nominal interest rate for long-term government bonds = r < g + π = gN = nominal GDP growth (2)
is a stabilization factor preventing the accumulation of government bonds, and the reversed inequality represents a destabilization factor.
(2) Explanation for the paradox of accumulated Japanese government bonds based on mathematical law
The Japanese economy in the last 20 years is characterized by several facts as follows (see Asada  and the article by Takaaki Mitsuhashi and Yoichi Takahashi in the Da Capo Special Edition ). For 20 years since the BOJ intentionally broke the economic bubble by the extreme credit crunch from 1989 to 1992, including the period during the subprime shock and after the great earthquake disaster, the BOJ has continued to restrain the nominal money stock increase to approximately a fifth of that during the bubble economy in the 1980s, and the government has continued to rapidly reduce nominal public investment. In addition, the consumption tax rate was raised from 3% to 5% on the initiative of the MOF under the Hashimoto administration in 1997. As a result, the nominal GDP has totally stopped increasing since 1997. Nominal GDP—which amounted to 520 trillion yen in 1997—declined by as much as 40 trillion yen in 13 years to 480 trillion yen in 2010 immediately before the great earthquake disaster. The total tax revenue dropped by no less than 15 trillion yen from the amount before the consumption tax increase. During this period, the Japanese economy has fallen into a deflation-led recession, where the price continued to fall steadily by around 1% annually, and the ratio of nominal outstanding government bonds to nominal GDP surged. In other words, Japan in the past 20 years has experienced an apparently paradoxical outcome that the tax increase with the cut in governmental public spending and money tightening by the BOJ led to increase, rather than decrease, in the ratio of outstanding government bonds (a supplement to avoid misunderstanding: this mechanism is not related to the declining birthrate and the aging population, and government bonds are not liabilities but assets from the perspective of the private sector).
The paradox of accumulated Japanese government bonds pointed out above can be explained theoretically by using Equation (1). While the decline in G and the increase in the consumption tax rate were supposed to have the effect of restraining Δd in this fundamental equation, Δd was actually boosted by the drop in Y, induced by the same factors and the decrease in the average tax rate T/Y caused by the plunge in the income tax and corporate tax revenue due to the economic downturn, as well as the decrease in ΔH caused by BOJ’s passive monetary policy. Furthermore, this resulted in the deeper deflationary recession, during which r, π, and g also dropped in tandem. While r has also maintained positive 1 to 2% per annum since 2000, gN = g + π even became negative occasionally. After 2000, when gN dipped below annual positive 2%, the Domar condition (2) that had been met until then was no longer satisfied. Since then, d started to rise rapidly.
If the Domar condition is to be met again, the deflation-led recession must be overcome by maintaining the inflation rate at about positive 2% per annum and the nominal GDP growth at about positive 4% (merely comparable with the average in OECD countries in the past 10 years) through an inflation targeting policy and a policy mix of aggressive fiscal and monetary policies based on the agreement between the government and BOJ, including the 20-trillion-yen-level fund underwritten by the BOJ for restoration from the great earthquake disaster. The consumption tax hike under the deflationary recession would further shrink GDP and facilitate Japan dropping out of the club of economically developed nations. As can be said about the issue of nuclear power plants, even when a wrong policy brings about disastrous outcomes, none of the advocators and followers of such policy are ever willing to take responsibility in this country, Japan.
 Toichiro Asada, “Macro Dynamics of Accumulated Government Bonds and Fiscal and Monetary Policy: On the Inappropriate Policy Mix [Kokusai Ruiseki to Zaisei Kin’yu Seisaku no Makuro Dogaku: Futekisetsu na Porisi Mikkusu ni tsuite],” in Kazunori Watanabe ed., Finance and Income Distribution [Kin’yu to Shotoku Bunpai], Nihon Keizai Hyoronsha, December 2011.
 Da Capo Special Edition, Why Is the Consumption Tax Hike Wrong? [Shohizei Zozei wa Naze Dame nanoka?], Magazinehouse, May 2012.
Professor, Faculty of Economics, Chuo University
Areas of Specialization: Macro-Economics, especially Macro-Economic Dynamics
Current position: Professor on the Faculty of Economics, Chuo University
Born in Aichi Prefecture in 1954. Graduated from the School of Political Science and Economics, Waseda University in 1977. Completed the Doctoral Program at the Graduate School of Economics, Hitotsubashi University in 1982. Holds a PhD in economics (Chuo University). After serving as Associate Professor on the Faculty of Economics, Komazawa University and the Faculty of Economics, Chuo University, he assumed his current position in 1994. Current research themes include economic changes based on methods in macro-economic dynamics, as well as research in macro-economic policy. His major written works include the Macro-Dynamics of Growth and Cycles (Nihon Keizai Hyoronsha, 1997, single authorship) and Monetary Macro-Dynamics (Routledge, London, 2010, co-written).