プリンストン大のマーカス・ブルナーメイヤー(Markus K. Brunnermeier)とユリ・サニコフ(Yuliy Sannikov)のコンビ*1が、もう一人のプリンストン大の研究者Sebastian A. Merkelと共に、表題の件を分析したNBER論文「The Fiscal Theory of Price Level with a Bubble」を上げているungated版)。

Different monetary theories emphasize different roles of money and different equilibrium equations to determine the price level. The Fiscal Theory of the Price Level (FTPL) stresses the role of money as a store of value and argues that the real value of all outstanding government debt, i.e., the nominal debt level divided by the price level, is given by the discounted stream of future primary government surpluses. Primary surpluses are the difference between government revenue and expenditures excluding interest payments. Absent government default, an increase in primary deficits leads to an increase in the price level, i.e., inflation, by devaluing outstanding debt.
Critics of the FTPL often point to Japan. Even though Japan has mostly run primary deficits since the 1960s (see Figure 1) and with no primary surpluses in sight, the price level has not risen much. Indeed, inflation levels are depressed even though the government and central banks leave no stone unturned to boost inflation closer to 2%.
In this paper, we revisit the key FTPL equation and argue that including the typically ignored bubble term allows us to reconcile the FTPL with Japan's experience. Indeed, we show that the transversality condition is often insufficient to rule out a bubble on the aggregate economy, refuting the usual justification to simply dismiss the bubble term. While the FTPL literature puts a lot of emphasis on distinguishing between monetary and fiscal dominance, the bubble term cannot be ignored under any policy regime.

導入部では続けてバブル項の出現条件に付いて説明している。バブル項はr ≤ gの時に生じ、そこでの安全利子率rは、リスクプレミアム込みの民間の金利(>g)よりは低くなる、との由。

A bubble term emerges whenever the real rate paid on government debt is persistently below the growth rate of the economy, i.e., whenever r ≤ g. It is well known that this can be the case in overlapping generations models (Samuelson 1958), models of perpetual youth (Blanchard 1985), and incomplete market models a la Bewley (1980). In this paper we provide another simple example based on Brunnermeier and Sannikov (2016a,b) in which the r ≤ g outcome arises naturally and agents can invest in both physical capital and government bonds. Physical capital is subject to uninsurable idiosyncratic return risk. Hence, the expected return on capital exceeds the growth rate g since agents require a risk premium. Government bonds are the safe asset in the economy and allow agents to indirectly share part of their idiosyncratic risk. High idiosyncratic risk makes the government bond more attractive and depresses r below g.
バブル項は、政務債務の実質金利が恒常的に経済の成長率を下回る時、即ち r ≤ gの時に常に現れる。世代重複モデル(サミュエルソン、1958*2)、不老モデル(ブランシャール、1985*3)、およびビューリー流の不完全市場モデル(1980*4)でそうしたことが成立し得ることは良く知られている。本稿で我々は、ブルナーメイヤーとサニコフ(2016a,b*5)に基づく、r ≤ gの結果が自然に生じるとともに経済主体が物的資本と国債の両方に投資できる別の単純な例を提示する。物的資本には保険が掛けられない固有の収益リスクがある。従って、経済主体がリスクプレミアムを要求することから、資本の期待リターンは成長率gを上回る。国債は経済において安全資産であり、経済主体はそれによって各自固有のリスクの一部を間接的に分散することができる。高い固有リスクは国債をより魅力的なものとし、rをg以下に抑える。


By "printing" bonds at a faster rate, the government imposes an inflation tax that reduces the return on the bonds further. Since government bonds are a bubble, the government in a sense "mines a bubble" to generate seigniorage revenue. The resulting seigniorage revenue can be used to finance government expenditures without ever having to raise extra taxes.
For example, if the primary surpluses are always negative, then their discounted stream is also negative, and only the positive value of the bubble can ensure a positive price level. The size of the bubble, and hence the price level, is determined by wealth effects and goods market clearing. A larger bubble raises agents' wealth and hence their demand for output. To ensure goods market clearing, the bubble has to take on a certain size, which together with the FTPL equation determines the price level.
The price level is uniquely determined if the fiscal authority backs the bubble to rule out equilibria that lead to hyperinflation. Such fiscal backing is only required off-equilibrium.



  1. 民間の保有している政府債務を予想外の形で減価することによるシニョリッジ
    • 定常的な収益源にはなり得ない。GDPの5%を超える可能性は1%以下。
  2. 流動性サービスを提供しているマネーストックの形での債務によるシニョリッジ
    • 先進国では重要な収益源にはなり得ない。フローでGDPの0.36%、現在価値では20%程度で、最大でも30%。
  3. これまで追究されてこなかった、今回の論文で焦点を当てたシニョリッジ
    • 将来の税で支払う必要なく政府債務を増加させていくポンツィスキーム。
    • 予想外のインフレによる希薄化と違い、民間が完全に予想する形でバブル価値を薄めていくことが可能。
    • マネーストックに加えて政府債務の増加が収益源となるため、マネーストックだけの増加によるシニョリッジよりは大きい。