What is the Upper Limit on the Public Debt?

Faculty Fellow, RIETI

Facing a looming hike in the consumption tax, people are starting to worry about the impact it will have on the economy. While the higher tax rate will improve the nation's fiscal position to some extent, its effect will be rather small compared to the massive public debt. This article discusses the relationship between the consumption tax and the size of the public debt that can be supported by the tax.

Generally speaking, it has been regarded that for any kind of tax, if the tax rate is raised too high, tax revenue will decline. Arthur Laffer, president of Laffer Associates, claimed in 1974 that the relationship between tax rates and tax revenues is illustrated by the so-called Laffer Curve as shown in the figure below.

Figure: Laffer CurvesFigure: Laffer Curves

Taking the labor income tax as an example, raising the tax rate will yield higher tax revenue, as long as the rate is still relatively low. However, if the tax rate is raised too high, workers will realize it is ridiculous to work, since such a large part of their pay goes to taxes. They will stop working, and income will decline. As the taxation base grows smaller, tax revenue will fall, even with further tax rate increases. The shape of the Laffer Curve is an inverse U, in other words. Harm to the real economy caused, for example, by raising the tax rate and demotivating workers is known as a "tax distortion."

If this is correct, then there must be an upper limit on the tax revenue which governments can collect, no matter what constitute their taxation policies. Therefore, there must also be an upper limit on the size of the public debt that tax revenue can support. And it is generally accepted that there is a limit on tax revenue, since that revenue obviously must be no larger than the size of the economy itself.

Research conducted in recent years, however, suggests that these assumptions may not hold true as far as the consumption tax is concerned.

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Mathias Trabandt of the European Central Bank and University of Chicago Professor Harold Uhlig estimated the Laffer Curve for the United States and the European Union (EU) countries as it applied to their labor income taxes, capital income taxes, and consumption taxes in a paper they wrote in 2011. In 2013, using this paper as his basis, Senshu University Associate Professor Kengo Nutahara estimated the Laffer Curve for Japan for the project conducted by the Canon Institute for Global Studies.

He calculated it using the data estimated in research conducted in 2011 by Daito Bunka University Associate Professor Hiroshi Gunji and Hosei University Professor Kenji Miyazaki. Nutahara argued that to maximize tax revenue, Japan should raise taxes on labor income and lower them on capital income (equivalent to corporate taxes).

Trabandt and Uhlig as well as Nutahara had discovered that their respective Laffer Curves on consumption taxes are upward. In other words, the amount of tax revenue yielded by the consumption tax will continue to rise if we raise the consumption tax (see Figure). In their models, if the consumption tax is continued to be raised, revenue from that tax will continue to increase toward some fixed number, namely, consumption tax revenue may continue to grow, but it has an upper limit.

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If we slightly change our assumptions, however, the results are vastly different. Trabandt and Uhlig assume that the supply of capital stock such as production equipment fluctuates and decreases at times. According to my calculations, if we assume that "economic activity requires factors of production that have a fixed supply, such as land," then we can make tax revenue grow indefinitely by raising the consumption tax rate.

Why is it that there is an upper limit on consumption tax revenue when the amount of capital stock is variable, while tax revenue can be increased indefinitely in a model where the amount of capital stock (land) is fixed? The neoclassical growth model assumes that when the consumption tax rate rises, a tax distortion causes a drop in labor input and a similar decline in factors of production such as machinery. Therefore, tax increases cause consumption to fall to a significant degree and very little tax revenue growth can be achieved. However, the amount of land does not decrease just because there is less labor input. Therefore, in a model that accounts for the existence of land, consumption does not decline so much, and, as a result, tax revenue can continue to rise endlessly.

The result that consumption tax revenues can grow endlessly even while production and the labor force are limited is hard to believe because it is so counterintuitive. The key to solving this contradiction is that "taxes, once collected, soon become subject to taxation again." Consumption tax revenues are paid to Japanese citizens in the form of redemption of government debt and social security benefits. In the hands of citizens, those funds are consumed and taxed again. Therefore, consumption tax revenues and citizens' incomes can grow in step with each other, exceeding the size of the gross domestic product (GDP).

The fact that tax revenue can grow indefinitely if the consumption tax rate is increased points to the surprising fact that, in theory, "any size of public debt can be sustained by raising the consumption tax rate." This is because, although public debt cannot exceed the present value of future tax revenue, with a higher consumption tax rate, future tax revenue can grow endlessly, beyond future GDP.

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However, that result is strictly theoretical. Even if we accept that raising the consumption tax can support any size of public debt, there must be a combination of debt level and consumption tax rate that is optimal for society as a whole.

For example, as the consumption tax rate rises, consumption by citizens declines and ultimately approaches zero. This too is a tax distortion. Higher tax rates make consumer goods expensive, meaning that citizens buy less of them and increase leisurely activities that do not require the use of such goods. This causes the labor supply and the GDP to contract, ultimately dropping to zero when the tax rate is raised to infinity. Consumption also declines as the tax rate rises. Even if this results in more tax revenue, it is not a desirable state of affairs for society.

On the other hand, there are also merits to increasing public debt (i.e., issuing government debt). Government debt gives households and businesses a means to build up their savings. Households and businesses have to store up resources for times of need, but if they store up resources that could be used as a means of production (e.g., metals), production activity declines and is a waste for the overall economy. If government debt becomes a means of saving, such resources are used for production, which increases economic efficiency.

This effect is largely the same as what the Massachusetts Institute of Technology (MIT) Professor Peter Diamond pointed out in his 1965 paper in which he argued that government debt has the effect of smoothing out consumption among generations. Likewise, a 1998 paper by MIT Professor Bengt Holmstrom and Toulouse 1 Capitole University Professor Jean Tirole claimed that government debt increases economic efficiency when additional liquidity suddenly becomes necessary at businesses.

In recent years, it has been pointed out that, associated with financial crises, when asset bubbles collapse, issuing more government debt can mitigate the impact of the collapse on the real economy. Examples include a 2006 paper by MIT Professor Ricardo Caballero and Northwestern University Professor Arvind Krishnamurthy and a 2009 paper by Narayana Kocherlakota (president of the Federal Reserve Bank of Minneapolis).

The merits of issuing government debt, balanced against the demerits resulting from tax distortion, tell us that there is an optimal amount of government debt and an optimal consumption tax rate. When government debt and the consumption tax rate are both low, the merits have the edge, so it is best for society to raise the tax rate (and government debt). As tax rates rise, however, the merits diminish and the demerits increase. Social welfare is maximized when the tax rate is set to some value, beyond which social welfare declines. It is at that value that debt and the consumption tax rate are optimal.

The optimal level of debt and the consumption tax rate to support it vary considerably depending on the structure of economic models. It will take a very refined model to yield realistic values. In any case, it would take a very large increase in the consumption tax to make up Japan's public debt, which is close to 230% of GDP. Without doubt, that exceeds the optimal size.

>> Original text in Japanese

* Translated by RIETI.

February 14, 2014 Nihon Keizai Shimbun

March 12, 2014

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