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2019 | OriginalPaper | Buchkapitel

7. Public Debt

verfasst von : Burkhard Heer

Erschienen in: Public Economics

Verlag: Springer International Publishing

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Abstract

During the 1980s and 1990s, we observed many public debt crises in Latin America and Asia. Prior to, during, and after the financial crisis of 2007–2008, we also observed many countries in the European Monetary Union (EMU) with severe public debt problems. Government debt has increased to unprecedented levels in the post-World War II era in the so-called “GIIPS” countries (Greece, Ireland, Italy, Portugal, and Spain). The Greek, Spanish, and Italian governments have had to pay premiums of 16, 3, and 3 percentage points on their public debt relative to Germany. Consequently, the president of the European Central Bank (ECB), Mario Draghi, initiated a program whereby the ECB extended 3-year loans in the amount of 1 trillion (!) euros to the Eurozone banking sector. Interest rates subsequently converged, but debt levels remain high and still amounted to 179%, 100%, and 132% of GDP in Greece, Spain, and Italy in 2015, almost 10 years after the onset of the crisis. As a second major second case of severe public debt, Japan had accumulated a gross public debt equal to approximately 240% of GDP by 2015.

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Vorheriges Kapitel Pensions

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The former President of the European Commission, Romano Prodi, referred to this pact as the “stupidity pact”.

The data for the gross and net debt-GDP ratios are taken from the IMF World Economic Outlook database. A more detailed description is presented in Appendix 7.3.

The empirical figures in this section are computed with the help of the Gauss program Ch7_data.g which is available as a download from the author’s homepage.

Annual nominal GDP amounted to $18.6 trillion in 2016.

Comparing the per capita incomes (as measured by the per capita GDP in constant prices) for these countries between the year 2000, prior to the introduction of the euro, and the year 2015 (7 years after the onset of the financial crisis), we find that it fell in Greece (−3.5%) and Italy (−7.1%), while it only slightly increased in Spain (+ 7.5%). By comparison, in Germany, per capita income increased by 18.3% during the period 2000–2015.

When you compare the present values of the debt-revenue ratio with those from the default years, bear in mind that prior to World War II, government revenue constituted a much smaller share of GDP than at present. In the US, for example, government revenue only amounted to 11–12% of GDP during the 1920s, while it was equal to 23.5% in 2015. Consequently, the debt-GDP ratios of the defaulting countries in the default years and in 2015 are even closer to one another.

For example, data for Australia, New Zealand, and Canada in the late 1940s were excluded.

The critique of Herndon, Ash, and Pollin (2014) is only directed at the 1949–2009 dataset for the 20 industrialized countries. Reinhart and Rogoff (2010) also consider two other datasets, including one for an extended period from 1791 to 2009.

In addition, they find that the lower growth performance prevails even for those countries that do not experience higher real interest rates because of their indebtedness. Accordingly, the growth-reducing effects do not stem exclusively from higher real interest rates.

In this regard, Polito and Wickens (2015) present a measure of sovereign credit ratings that is derived solely from the fiscal position of a country and its ability to repay future debt obligations. It is capable of identifying the European debt crisis and the deterioration of credit rating quality among GIIPS countries even 2 years prior to the release of official credit ratings.

In February 2012, the ECB president, Mario Draghi, started the tender “Big Bertha” whereby the ECB offered one trillion euros in 3-year loans to the banking sector. By mid-year, Mario Draghi went one step further and announced new measures, promising that they would be sufficient. In particular, Mario Draghi said, “within our mandate, the ECB is ready to do whatever it takes to preserve the euro. And believe me, it will be enough.”

For the countries with the empty entries in Table 7.1 – Argentina, China and Greece – no data on net debt are available in the IMF statistics.

Another debt-ratio measure of the sustainability of public finances that is the most relevant for the evaluation of emerging countries is the amount of external debt or debt denominated in foreign currency. A detailed description of external debt and historical periods of high external debt is provided by Reinhart and Rogoff (2009).

At the end of 1991 and early 1992, an asset price bubble burst in Japan and was followed by a long period of stagnation. The period 1990–2010 is sometimes referred to as Japan’s “Lost 20 years”.

The introduction of the European System of National and Regional Accounts (ESA 2010) obliged the EU countries to publish their implicit public debt.

Notice that estimates for implicit debt are subject to much stronger volatility than the official numbers on gross or net debt. Numbers on implicit debt are very sensitive with regard to reforms of the pension or health system and changes in the growth dynamics of a country. For example, Hagist, Moog, Raffelhüschen, and Vatter (2009) use the method of generational accounting to provide estimates of the implicit debt-GDP ratio in 2004 at the amount of 254% (France), 252% (Germany), 35% (Spain), 510% (UK), and 350% (US). Compared to the values in Table 7.3, their numbers are higher and the ordering of the implicit debt numbers is the same except for Spain, for which the authors report a drastically lower implicit debt-GDP ratio.

We should be extremely careful to assess the accuracy of the implicit debt numbers since all the data are self-reported by the individual EU countries. In January 2010, for example, the European Commission condemned Greece for falsifying its data on public finances and deliberate misreporting after the official 2009 deficit numbers had been revised from 3.7% to 12.5% of GDP in fall 2009 by the newly elected Greek government (which was led by the center-left PASOK).

Sometimes, $\tilde B_{t-1}$ or B _t−1 is used as the notation for the beginning-of-period-t government debt level because it is equal to the government debt at the end of period t − 1. We use the notation $\tilde B_t$ such that the time index is in accordance with that of the capital stock K _t at the beginning of period t in the Ramsey and OLG models from the previous chapters.

In Appendix 7.1, we also consider the case in which the government finances its deficit with the help of money, so-called seignorage. Since seignorage, however, only constitutes a small share of government finance in industrialized countries, we neglect it in the remainder of the main text. For example, King and Plosser (1985) estimate that seignorage amounted to 0.3% and over 2% of GDP in the US and Italy during the period 1952–1982, respectively.

In the literature, real government debt is often denoted by the lower-case variable b _t. Our notational convention in this book is that upper-case variables denote aggregate variables, while lower-case variables denote individual variables. For example, we will use the notation $b^s_t$ and b _t for the real bonds of the s-year-old individual and the per capita bonds in period t in subsequent sections.

In a Ponzi scheme, an investor (or government) raises a return to the old investors (or creditors) by raising revenue from new investors (or creditors) that are inconsistent. When the inflow of new investors stops, the scheme falls apart. A prominent historical example of such a pyramid scheme occurred in Albania in 1997 which lead to the bankruptcy of some 25 firms; the liabilities of the scheme amounted to approximately $1.2 billion (which was equal to half the annual GDP of Albania in 1997), and resulted in political unrests. As a consequence, the former economic advisor of Prime Minister Fatos Nano was arrested and imprisoned (see also Jarvis 1999). The no-Ponzi condition (7.6) excludes this possibility.

Clearly, the Stability and Growth Pact has been violated dozens of times since its creation. Frequently during the period 2001–2015, all EMU countries presented in Figs. 7.4 and 7.5 – France, Germany, Italy, and Spain – ran deficits in excess of 3% in some years.

The title from Barro’s article derives from the fact that, in his model, an individual’s consumption is proportional to net wealth. For this reason, if higher government debt increases net wealth, consumption rises, while savings decline.

In 1974, Robert J. Barro provided the theoretical foundation for hesitant speculation by Ricardo (1817) that it “is only by saving from income, and retrenching in expenditures, that the national capital can be increased.”

In the next section, we analyze the effects of debt financing of the pension reform during the demographic transition in a large-scale OLG model and show that the effects of debt financing are dramatic and result in substantial long-run output and welfare losses.

We distinguish between aggregate labor L _t and population size N _t to allow us to use the same specification of the production sector in the next section on the OLG model.

Both representations of the government budget are used in the literature. For example, Trabandt and Uhlig (2011) use the specification (7.9), while Heer and Scharrer (2018) use (7.3). The representation (7.9) has the advantage that we can use individual wealth ω _t = k _t + b _t, which is equal to the sum of the two assets, as the individual state variable, while Heer and Scharrer (2018) have to define $\tilde \omega _t = k_t + b_t/(1+r^B_{t-1})$ as the individual state variable to solve their model. Since the former is easier to interpret and more convenient to handle, we will use it in the following.

We commit a small notational sin here (since we have exhausted all arabic letters for the notation of variables in this book). In Sect. 4.5.2, we used the variable g _t to denote the mark-up. Here, it stands for real government consumption G _t divided by A _t N _t.

Since we define real debt per capita b _t with respect to the price level in period t − 1, P _t−1, the nominal interest rate is related to the real interest rate according to

$$\displaystyle \begin{aligned} 1+i_t^B = (1+r^B_t) (1+\pi_t)\end{aligned}$$

rather than by (7.4).

In particular, we define $c^1_t\equiv C^1_t/(A_t N_t)$ and $c^2_{t+1}\equiv C^2_{t+1}/(A_t N_t)$ where $c^1_t$ and $c^2_{t+1}$ denote household consumptions in period t and t + 1, respectively. See also Appendix 3.2 for a discussion of this assumption with respect to preferences and alternative specifications of the lifetime utility in the 2-period OLG model in the presence of economic growth.

In Problem 7.1, you are asked to consider the case in which the government transfers tr _t equally to both the young and the old generation.

In the following, we have already incorporated the result from the previous section that the two form of assets K _t and B _t need to generate the same rate of real return r _t.

We annualized the debt-output level by multiplying the model’s 30-year value B∕Y by 30.

In Theorem 20.1 on page 321, Azariadis (1993) proves that, in any asymptotically stable stationary equilibrium, capital intensity and per capita saving are decreasing functions of per capita national debt under the following assumptions: (1) Government purchases are zero, (2) consumption goods in young and old age are normal and gross substitutes, (3) a constant stock of per capita public debt is serviced by lump-sum taxes on old individuals, (4) labor supply is exogenous, and (5) production is characterized by constant returns to scale, and goods and factor markets are competitive.

Diamond (1965) shows in a competitive OLG model that, in steady state, higher debt reduces (increases) utility when the economy is efficient (in the case of over-accumulation of capital). However, as we noted in Chap. 3 on the OLG model and Chap. 6 on social security, it is rather unlikely that we would observe over-accumulation of capital in industrialized countries in face of the low population growth and the large unfunded public-pay-as-you pension systems. Therefore, debt is likely to decrease utility in steady state, as we will also find in the subsequent section for the case of the US economy.

See Appendix 3.1 for the computation of this Kuhn-Tucker problem.

In Problem 7.2, you are asked to derive the goods market equilibrium condition (7.42). Therefore, notice that consumption in both young and in old age, $c^1_t$ and $c^2_{t+1}$, is normalized (made stationary) by dividing by A _t. When you derive the goods market equilibrium, take care to sum total consumption according to $C_t= N_t A_t c^1_t+ N_{t-1} A_{t-1} c^2_t$.

If the discount factor R changes, of course, equilibrium values of the variables k, y c ¹, and c ² will adjust.

Trabandt and Uhlig (2011) show that the utility function (7.44) has the two properties: (1) It is consistent with long-run growth, and (2) it features a constant Frisch elasticity of labor supply ν ₁.

See Appendix 7.2 for the derivation.

Trabandt and Uhlig (2011) use the calibration period 1995–2007.

Please see also Fig. 6.8 in Chap. 6.

For the projection of future survival probabilities that serve as inputs into our subsequent quantitative analysis, we continue to use moving averages of four periods.

In 2016, the US social security contribution rates amounted to 6.2% for each the employer and the employee. Our endogenous value of τ ^p falls somewhat short of this value for two main reasons. (1) In the US, social security also encompasses disability insurance, which we do not model. (2) In addition, there is a maximum threshold level of wage income for which the individual pays social security contributions. In 2016, this limit amounted to $118,500. Accordingly, the effective average social security contribution rate on wage income is lower than 12.4%.

The results that are computed with the Gauss program Ch7_US_debt.g fluctuate around the line presented in Fig. 7.12 due to numerical inaccuracies. We, therefore, interpolated the results by a smooth cubic function. The vertical distance between the computed values and the line in Fig. 7.12 is on the order of 10⁻⁵.

Of course, the total effect on labor supply would be much different if higher debt were instead financed by distortionary labor income taxes.

The reader is asked to verify this by adjusting the parameter value in the program Ch7_US_debt.g.

There are multiple other effects on savings; for example, the age composition of the labor force changes and average productivity increases in the older labor force ceteris paribus. Moreover, the savings rate of the 20–24-year old workers is below the average savings rate of the workers (as presented in Fig. 7.11).

If we increased the number of periods during which the government resorts to debt financing of additional expenditures to 50 years, our economy would collapse. In this case, labor income taxes would be insufficient to finance government expenditures in the long run and the fiscal space would shrink to zero. In other words, the maximum tax revenues at the peak of the Laffer curve are insufficient to balance the government budget in this case. See also Sect. 6.6 for the concept of the fiscal space.

Recall our discussion of the intertemporal government budget constraint in Sect. 7.3.

Remember that we assume that households are born at age 20.

In addition to the factors considered in our model, D’Erasmo, Mendoza, and Zhang (2016) also include endogenous utilization of capital and limited tax deprecation allowances of capital. As a consequence, they are able to more accurately model the (stronger) capital response to higher capital income tax rates. The two-country setup also allows them to model the externality of higher domestic capital taxes on the foreign country. Since capital is mobile, the revenue from higher capital income taxation is reduced. As we do not consider the use of capital income taxes to finance higher debt in our analysis, we refrained from implementing these important model components.

İmrohoroğlu, Kitao, and Yamada (2016) perform a sensitivity analysis for the returns on government debt and find that “if the interest rate on government debt is higher than the 1% assumed for the benchmark case, the resulting impact on fiscal balance can be disastrous”.

In the early work on sovereign default, the default costs are usually assumed to be linear in output, while in latter work such as Arellano (2008) and Aguiar, Chatterjee, Cole, and Stangebye (2016), the focus has shifted to non-linear default costs that increase in output. Non-linear default costs help to improve the performance of these types of models with respect to the replication of empirical facts, particularly with regard to the volatility of interest spreads, which often serve as a measure of default. For example, Aguiar, Chatterjee, Cole, and Stangebye (2016) identify a “crisis” episode with a period that features an interest rate spread of government debt in the top 5% of the distribution of quarterly changes. Mendoza and Yue (2012) provide a model with a micro-foundation of non-linear costs in which domestic producers cannot import foreign intermediate inputs during periods of default.

The results from this literature are sensitive to the stochastic nature of the shock. Most of these models assume a deterministic trend, which, at a minimum, seems questionable for a multitude of developing countries; alternatively, a stochastic growth rate is considered. With the assumption of deterministic growth, the economy is more responsive to a negative output shock because it implies a recovery to trend and, therefore, a higher future level of output. As a consequence, the government issues more debt to intertemporally smooth consumption.

As one exception to the assumption of one sovereign, Cuadra and Sapriza (2008) incorporate the presence of two parties, e.g., a left-wing versus a conservative party, into a model of a political economy. Both parties give preferential treatment to their voters, which consist of two types of households, each preferring a different public good. The incumbent party also has an incentive to finance its expenditures by borrowing and impose potential default risk on its successor.

In general, the possibility of smoothing consumption with the help of domestic credit markets is also not considered in these types of models.

In the benchmark model of Eaton and Gersovitz (1981), the government remains excluded from international capital markets after a default.

See, for example, Arellano (2008) on risk-averse investors, Alfaro and Kanczuk (2007) and Aguiar and Amador (2016) on different maturities of government debt, Durdu, Nunes, and Sapriza (2013) on news shocks, Gosh, Kim, Mendoza, Ostry, and Qureshi (2013) on fiscal policy rules, Asonuma (2016) on exchange rates, Cuadra and Sapriza (2008) on political economy, and D’Erasmo (2012) on reputation.

For example, D’Erasmo, Mendoza, and Zhang (2016) assume that the (annual) logarithmic government expenditure-GDP ratio follows an AR(1) process with an autoregressive coefficient of 0.8802 and a standard deviation of 1.7%, while the output costs of a default amount to a minimum of 2% and increase linearly with government expenditures. Default occurs with a probability of 1%.

As a different interpretation of their model, D’Erasmo, Mendoza, and Zhang (2016) argue, “in the European debt crisis, a Greek default can be viewed as redistributing from German tax payers to Greek households” (on p. 2559).

D’Erasmo and Mendoza (2016) also show that default is more costly in the presence of physical capital and, hence, an endogenous portfolio choice by the household.

Aiyagari and McGrattan (1998) find that the optimal debt-GDP ratio amounts to approximately 2/3 in the US, which is close to the post-war average level. In Problem 7.4, you are asked to compute the insurance mechanism that is provided by the public debt system in a simple three-period OLG model with income uncertainty. In essence, the provision of public debt in a non-Ricardian economy increases the interest rate, meaning that the return on savings increases, and a (stochastic) drop in income can be more easily compensated.

One reason for the difficulties in integrating endogenous default into the standard DSGE model (that can be overcome) is the inherent non-linear nature of the sovereign’s optimization problem. The choice is binary (default versus honoring debt payments), and the equilibrium bond price is a highly non-linear function of the state of the economy. In addition, Gordon and Guerron-Quintana (2018) note that policy functions (and the value functions of the sovereign) might become non-monotone in the presence of capital accumulation and long-term government debt; the latter is necessary for matching empirical spread and default statistics. As a consequence, the linearization method for solving the DSGE model that we introduced in Chap. 2 is no longer applicable.

There exist many definitions of seignorage in the literature; for example one different definition also encompasses interest-bearing government bonds held by the central bank, which we included in the variable B _t. For an overview, see Section 4.2 in Walsh (2010).

The data were downloaded from https://fred.stlouisfed.org/series/GDPA and https://fred.stlouisfed.org/series/BASE and are also included in the Gauss program Ch7_data.g.

More specifically, Eq. (7.47) represent the first-order conditions of the s-year-old household who was born in period t − s + 1. Therefore, we are able to present the first-order conditions of all s-year old households, s = 1, …, J, who are alive in period t.

Notice that (7.67a) states the capital market equilibrium. In particular, we use the stationarity condition $\tilde \omega '=\tilde \omega $, so that (7.67a) is the analog to the capital market equilibrium condition (1 + n)k _t+1 = s _t. In order to make this correspondence even more evident, consider the economy with just two periods, J = 2. In this case, the individual savings of the young generation at age 1 at the end of period t amount to $\tilde \omega ^1_{t+1}$. The savings of the old households at age 2 at the end of period t are equal to zero so that total savings are equal to $N_t(1) \tilde \omega ^1_{t+1}$. Therefore, in capital market equilibrium

$$\displaystyle \begin{aligned} \tilde \varOmega_{t+1} = N_t(1) \tilde \omega^1_{t+1}.\end{aligned}$$

After division by N _t+1, (7.67a) follows noticing that N _t(1)∕N _t+1 = μ ¹∕(1 + n) and $\tilde \varOmega _{t+1}/N_{t+1}=\tilde \omega '=\tilde \omega $ in steady state. The same reasoning applies to the computation of $\tilde b$ in (7.68) below.

The set-up of the equation for bequests is motivated in Chap. 6 and, in particular, Appendix 6.1. Notice that accidental bequests also include net interest payments at the end of period t + 1.

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Titel: Public Debt
verfasst von: Burkhard Heer
Verlag: Springer International Publishing
Buch: Public Economics
Print ISBN: 978-3-030-00987-8

Electronic ISBN: 978-3-030-00989-2

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-00989-2_7