Abstract:

 

This paper constructed annual series of the government revenues, expenditures, outstanding debt, GDP and interest payment for Japan from 1980 to 2017. It focused on three approaches to examine the debt sustainability. First, tests of ADF unit roots of each individual variables were run to see if they are stationary. Second, Engle-Granger and Johansen tests were run to see if there is a cointegrating relationship between government revenue and expenditure variables. Finally, the same tests were run for interest payment and GDP variables. The results suggest that most of individual variables are not stationary, that government revenue and expenditure exhibit cointegration relationship but not economically significant to show debt sustainability, and that interest payment and GDP have strong cointegrating relationship upon further modeling. Although results are somewhat mixed, this paper concludes that the Japanese government debt is more likely to be unsustainable at the current state in the long run.

 

This paper explores existing literature and explains its choices of variables in the following Review of Literature and Background to the Economic and Statistical Models, and Choices of Variables sections. Data Sources and Descriptions section sets out graphs of primary data and describes how they appear before running econometrical tests. Econometric Issues section lays out economic explanations for possible outcomes of econometrical tests. Lastly, Empirical Results on Modeling, Forecasting and Analysis section summarizes findings of econometrical tests with conclusions at the end of the paper.

 

This paper used OxMetrics Version (7), acknowledges citations to Doornik and Hendry (2013) in obtaining econometrical results.

 

 

 

Introduction, Motivation and Summary of the Conclusions:

 

Mounting debt has been a serious issue for many countries. Japanese government debt, which now stands more than 230% of debt to GDP ratio, is the highest in the world. Debt sustainability is very important since government’s fiscal capability of government expenditure is largely inhibited by how much it has to periodically pay back its outstanding debt and interest payments in the long run. Frequently, there have been political and economic debates on how to reduce the ratio and make the debt sustainable. This paper would analyze if Japanese debt is sustainable by testing critical variables, such as GDP, interest payment, government revenue and government expenditure, and come up with econometric models to examine the effects of each variable in the long run. It would also include some policy measures to provide solutions to the sustainability problem in the conclusion.

 

Japan’s debt has been a long historical problem since the 1990s. When the real estate bubble burst, large amount of government fiscal stimulus was introduced to revive the fragile economy. However, these expenditures, largely spent in infrastructure, have resulted in an explosive growth of debt, which now has caused many problems relating to fiscal policy and hikes in consumption tax. The Japanese government gross debt to GDP ratio has increased from 66.92% in 1990 to more than 200% in 2010, surpassing other countries like U.S. (93%), Germany (80%) and even Greece (129%), according to IMF and OECD figures.[1]

 

This paper found that except interest payment to GDP ratios, all of fiscal variables are non-stationary, indicating that interest payment to GDP could be sustainable while others all point that debt is highly unlikely to be sustainable. This paper also found out that the government expenditure and revenue do have cointegrating relationship but debt is not economically sustainable while interest payment and GDP show sustainability in the long run. In conclusion, preponderance of evidence indicates that Japanese debt is not sustainable in the long run.

 

Review of Literature:

 

There have been numerous approaches to modeling and forecasting sustainability of Japanese debt problem in previous research papers. For example, Kobe paper approached this problem by looking at sustainability problem, relations with foreign investors and coordination problem in the JGB market. The paper had found that the Japanese government would have to generate sufficient fiscal surplus for achieving debt sustainability and that the JGB market could become volatile once government financial institutions quit their role of primary purchasers of bonds.[2] Another research paper has found that the Japanese government debt poses serious challenges, and to stabilize the debt to GDP ratio, Japan needs to implement a tax rate hike with an extraordinary magnitude.[3] Most of recent research literature pointed out the severity of the problem in different ways, and concluded that Japanese debt is not sustainable in the long run.

 

On the other hand, debt sustainability papers on other countries, such as Kremers paper, focused on similar problems in the US by looking at whether long-run constraints on the accumulated stock of outstanding Federal debt have influenced the annual conduct of budgetary policy. It also discussed the government’s intertemporal budget constraint and optimal pattern of debt/GNP stabilization.[4] Simon paper, in contrast, primarily used two empirical frameworks have been used to test for fiscal sustainability in European countries. The first rests mainly on testing the stationarity of the various fiscal variables, while the second employs cointegration time series techniques and explores the existence of a long-run equilibrium relationship between the fiscal variables of interest.[5] This paper draws some of the techniques that they have employed and apply them in analyzing the Japanese debt sustainability.

 

Background to the Economic and Statistical Models, and Choices of Variables:

 

From the existing data set, the following government budget balance is constructed,

Government Budget Balance:

where  is the stock of interest-bearing debt outstanding at the end of period t,  is the government expenditure,  is the government revenue and  is the interest payment in period t-1. This variable was constructed based on Kremers paper, and was tested under the ADF test to examine the sustainability of budget balance in the long run.

 

These variables—government revenue (GR), government expenditure (GX), interest payment (IP), GDP and budge balance (BB)—were deliberately chosen, as they are directly associated with government debt and can show direct causations with debt rather than indirect variables like current account.

 

Data Sources and Description:

 

This paper made use of various data sources, including but not limited to Federal Reserve Economic Data St. Louis, OECD, World Bank, Japanese Ministry of Economy, Trade and Industry, Ministry of Finance, Bank of Japan and IMF. Most of economic data and index come from statistics released from Japanese government, banks and international organizations. In particular, a large amount of data came from the IMF, which included government revenue and expenditure.

 

Most of the data were denominated in different unit, so they had to be adjusted for 10 billion yen in value. Data sampling is from year 1980 to 2017, except for interest payment variable which only had data available from 1980 to 2015, and some of missing data on interest payment were extrapolated by taking average of the two periods. Also, while other research papers, such as Kremers, calculated the amount of interest payment by constructing “ ” where interest rate is multiplied by public debt in previous period, this paper used direct data of interest payment amount from World Bank data, as it is impossible to identify exact rate to apply for different debt with different maturity. In addition, small alphabetical characters indicate that they are logged variables while capital characters are level variables. Variables with D indicate that they are differenced variables.

 

Graphs of Variables (1) under Basic Description of Data Set indicates that the government expenditure begins to exceed the government revenue starting in 1990, and they have not converged ever since. In addition, it shows that total debt, debt to GDP ratio and interest payment all seem to be nonstationary and interest payment to GDP, balanced budget and balanced budget to GDP are difficult to guess without the ADF test to determine the stationarity. All of these variables would be tested with ADF and cointegration to fully determine whether they converge to the mean in the long run.

 

Graphs of Logged Variables (2) shows logged values of the variables. Budget balance and budget balance to GDP ratio have negative values in 1990s, which makes the data set discontinuous. Logged variables also show similar results in that the variables all seem to have be non-stationary except in the case of logged interest payment to GDP ratio.

 

Graphs of differenced variables (3) shows the first order differenced variables. It shows that once they are differenced, they seem to be stationary.

 

Econometric Issues:

 

Theoretical backgrounds for testing stationarity of debt to GDP ratio and conintegration testing is as follow: If the deficit series is non-stationary, then it means that it is growing without bound over time, which means that subsequent debt will also grow without bound rendering fiscal policy unsustainable. A stationary deficit means that the series is reverting to a certain mean overtime being in general close zero. If that were the case, then obviously fiscal policy and debt would be sustainable, since deficits will be under control. On the other hand, cointegration tests explore whether there is a long-run relationship between government revenues and expenditures. If such relationship exists, this means that the respective government is not spending without bound and is taking into account the amount of revenues it is generating. Subsequently, it will not have to resort to deficit financing to cover its expenses, and debt would be sustainable and will not grow without bound.[6] In addition to this, this paper would examine if the cointegrationg vector is either 1 or -1 and constant is 0, so that statistical cointegrating relationship is economically applicable to debt sustainability.

 

If conclusive evidence supports that public debt is stationary, then it is an indication for strict fiscal sustainability. Otherwise, Johansen test is run on cointegration between expenditure and revenue in a subsequent step. The application of the Johansen cointegration test requires subtracting one lag length since it is estimated in first differences. This is followed by the estimation of Vector Error Correction Models (VECM) allowing for multiple assumptions such as a trend in the data, a constant in the error correction term and a trend in the cointegration relation. If no significant cointegration relation between revenue and expenditure is found, we conclude that public finances are not sustainable. According to Afonso (2005) fiscal policy is sustainable, if the time series of expenditure and revenue are cointegrated and the hypothesis of a “normality vector” of [1,‐1] holds, i.e., a one‐percentage point increase in revenue leads to a one percentage point increase in expenditure (and vice versa). However, Koester and Priesmeier (2013) show that a significant element in the error correction term can be associated with fiscal unsustainability because the significant constant (trend) implies a (increasing) wedge between revenue and expenditure. This contributes to increasing deficits across time. In case of a significant cointegration relation, thus, debt is assumed to be sustainable.[7]

 

In addition, conintegration test between interest payment and GDP is run, following the steps outlined above, to examine whether there is a long-run relationship between interest payment and GDP. This is where the paper makes contribution to previous literature, because no other tests examined cointegration relationship between interest payment and GDP. If such relationship exists, likewise, it would mean that the GDP could fully compensate for interest payments, and thus the government would not have to resort to deficit financing. Further error correction modeling, impulse indicator saturation (IIS) test, and forecasting are conducted with respect to ip and gdp to make the testing more comprehensive.

 

Empirical Results on Modeling, Forecasting and Analysis:

 

ADF Tests: Unit Roots, Stationarity, and Lag Specification

ADF Tests (1) under Tables shows that all of the variables, except interest payment to GDP ratio, have unit roots. It means that government revenue, government expenditure, gross debt, interest payment and budget balance are all non-stationary, and thus they grow without bound over time. This results indicates that Japanese debt is highly unsustainable if these economic variables were looked at from individual level.

 

First order ADF Tests (2) shows that when the variables are differenced once, except government expenditure, gross debt and gross debt to GDP, they do not have unit roots and thus become stationary.

 

Thus, the results of ADF tests indicate that Japanese government debt is not sustainable, even when GDP ratio is used, as economically critical variables all grow without tendency to revert to their means. In addition, it is found that interest payment and GDP variables need to be further tested for cointegration because of their stationarity in the first place.

Cointegration with Engle-Granger and Johansen Test:

 

Since government expenditure and government revenue are non-stationary, Engle-Granger test is run to examine if there is a cointegrating relationship between the two variables. Government expenditure and revenue are regressed with two lags, and the resulting residual is tested for unit root. The test result (3) shows that the residuals do not have unit root and thus stationary, indicating that there is a cointegration relationship. This cointegration relationship could indicate that even though two non-stationary times series are not converging overtime, the series might eventually converge in the long run, thus making government expenditure and revenue sum up to equal and debt sustainable.

 

To make sure that there is such relationship, the Johansen test is run. The Johansen test (4), however, shows that there is no cointegrating relationship between the government expenditure and revenue. These conflicting results could perhaps be due to a misspecification and scaling problem, and thus new Johansen test with trend variable and logged gr and gx variables are tested. The test result (5) shows that variable gr and gx have a cointegrating relationship. This is more likely to be a correct indication of existence of cointegration.

 

In addition, to test if this cointegration relationship makes debt sustainable, the cointegrating vector has to be either -1 or 1 and constant has to be 0. LR test of restrictions was run to see if the vector is +1, and the test results show that Chi^2(2) = 19.230 [0.0001]**, rejecting the null and the vector is not equal to +1. The same test was run to see if the vector is -1, and the test results show that Chi^2(2) = 11.046 [0.0040]**, rejecting the null and the vector is not equal to -1. The resulting beta on gx is -2.0594 and trend is 0.010263, and alphas in General Cointegration Test (6) show that although constant is near zero, the cointegrating vector is not equal to either 1 or -1. Thus, it can be concluded that although there is a statistical cointegration relationship, this relationship does not translate into an economic significance in explaining debt sustainability.

 

Thus, Johansen test concludes that government revenue and expenditure have long run relationship yet fiscal stability is not to be found. Most of research paper that addressed Japanese debt sustainability also indicated that there is no cointegrating relationship between government revenue and expenditure, and thus Japanese debt is not sustainable.[8] This paper would also follow this line of reasoning, and conclude that government revenue and expenditures only have statistical significance in cointegration and do not exhibit sustainability in debt.

 

Other variables of particular interests are interest payment (IP) and GDP, since their ratio indicated stationarity in the previous graphs. The same testing procedure is run for interest payment and GDP variables to find out whether there is a cointegrating relationship between IP and GDP. Engle-Granger test (7) indicates that the residuals from regressing GDP and IP have no unit root, and thus indicate that they have a cointegrating relationship. Johansen test (8) indicates that there is no cointegrating relationship between the interest payment and GDP with rank order of 1. Separate Engle-Granger and Johansen tests for IP and GDP showed conflicting results. This could be due to a misspecification, missing variable or scaling issue. Therefore, further modeling on interest payment and GDP was conducted to test cointegrating relationship.

 

Further Modeling:

 

This time Johansen test was run with logged interest payment and logged GDP to remove scaling issue, in addition to adding trend and the newly created dummy variable, i1998, as the graph for data indicates that there is a peak in the interest payment in 1998. Autoregressive Distributed Lag (ADL) Model was constructed following Johansen test by reducing AD (2,2) -> AD (1,1) through various steps.

 

The resulting new Johansen test (9) indicates that there is one cointegrating vector, with error correction term being ECM = ip – 3.92235 – 0.369851*gdp – 0.897609*i1998 – 0.00972574*Trend when interest payment is regressed on two lags, GDP with two lags, year dummy variable 1998 and trend. Feedback test of cointegration is (T-value of -4.10) very significant ADL Model (1), indicating strong cointegrating relationship.

 

Autoregressive Distributed Lag model was constructed starting from 1. ADL Model (10). In 1. ADL Model (10), the two parameters, gdp_1 and Trend do not show statistical significance, and are thus dropped from the regression. In 2. ADL Model (11), likewise, Dip_1 and Dgdp_1 are dropped because of their low t-value. In the end, 3. ADL Model (12) shows final model, where error correction model is expressed as the following:

ECM = Dip – 0.000636935 – 0.342187*i1998 – 0.166107*Dgdp + 0.39339*ECM_1;

 

Impulse Indicator Saturation (IIS) Tests:

 

Impulse Indicator Saturation test was run to test if any year other than 1998 was structurally affecting the regression model. As the critical value became smaller, the number of significant year variable also decreased. At critical value 0.0001, year 2007, 2009 and 2011 were found to be significant (13). The effects of year 2007 and 2009 may be significant due to the global financial crisis, and may have influenced the modeling. Thus, it makes logical sense that the model would be able to pick up on the delta due to the global financial crisis in those years by including those year dummy variables in the final model, and figure out the magnitude of the crisis and their effects on the model. The final model including the year dummy variables is shown in the table (14).

 

Forecasting:

 

The final model with year dummies in error correction model is used for forecasting future Dip movement. Root mean square of error for 5 period forecast is 0.032447 and 0.014522 for 3 period. Thus, 3 periods forecast indicates better forecasting model as there is a less root mean square of error, which could be due to a limited number of samples used for forecasting. The forecasting graph (15) does not, however, show any significant findings related to the future of interest payment, and thus forecasting did not add any weights to the final conclusion in debt sustainability.

 

Conclusions:

 

This paper was interested in finding out whether Japanese government debt is sustainable over long period of time. The time series properties of fiscal variables of interest, such as budget balance, interest payment, government expenditure and government revenue, along with their GDP ratio, have revealed that they have unit roots, making budget deficit unsustainable.

 

Cointegration tests of gr and gx have shown that they have cointegrationg relationship but fail to show debt sustainability. The government revenue and expenditure start to show diverging relationship in the early 1990s, with large increase in government spending in public construction projects which peaked in the 2000s. Furthermore, the current Japanese government suffers from increased social security expenditure which has been financed by public debt since the late 1990s. The econometric tests and qualitative analysis of the current Japanese government show that debt is unlikely to be sustainable in the long run,

 

Further modeling of the Japanese debt indicates that interest payment and GDP do have a strong cointegrating vector, which could make the Japanese debt sustainable in the long run. This indicates that although fiscal status is negative, interest payment could be sustainable with GDP growth and decreasing interest payment burden.

 

In conclusion, time series properties of economic variables show sustainability in covering interest payment with GDP but other variables, such as government revenue, expenditure and budget balance, reveal that debt is not sustainable. Forecasts on interest payment and GDP do not show conclusive indication of future of the interest payment, but with cointegrating relationship, it is reasonable to expect that interest payment at least could stay sustainable.

 

Many scholars have pointed out ways to deal with the problems of the Japanese government debt sustainability and suggested potential solutions. For example, visiting scholar of the Edwin. O. Reischauer Center for East Asian Studies, Kazutaka Kuga, have pointed out the severity of the Japanese debt problem, and suggested both long term and short term solutions. In the short run, the Japanese government could implement austerity measure and impose tax on capital, which could negatively affect the recently reviving Japanese economy. In the long run, structural reforms in social security and fiscal policies, along with labor reforms and policies aimed at increasing productivity of the Japanese economy such as increasing labor participation of women, could make the Japanese government debt sustainable. As various econometric tests on data from 1980 to 2017 indicate that the Japanese debt is highly unlikely to be sustainable, the Japanese government must make the right choices right now in making fiscal reforms to address budge balance problem.[9]

 

 

List of references:

 

Jeroen J.M. Kremers, January 1988, U.S. Federal Indebtedness and the Conduct of Fiscal Policy

Tomomi Miyazaki, July 2017, the Sustainability of Japan’s Government Debt: A Review

Takero Doi, August 2011, NBER Working Paper Series, Japanese Government Debt and Sustainability of Fiscal Policy

Simon Neaime, July 2014, Sustainability of Budget Deficits and Public Debts in Selected European Union Countries

William R. Cline, October 2014, Sustainability of Public Debt in the United States and Japan

Walter Eucken Institut, Fiscal Sustainability of the German Laender Time Series Evidence

Kazutaka Kuga, the Budget of the Government of Japan, How is it Coexisting with High Debt Load?

Christopher Mupimpila, January 2015, The Causality between Government Revenues and Expenditures in Botswana

 

Data Appendix:

 

Data Sources:

International Monetary Fund:

https://www.imf.org/external/pubs/ft/weo/2017/01/weodata/weoseladv.aspx?a=&c=158&s=GGR%2cGGR_NGDP%2cGGX%2cGGX_NGDP

World Bank:

https://data.worldbank.org/indicator/GC.XPN.INTP.RV.ZS

 

Plots:

Basic Description of Data Set:

  • Graphs of Variables

Graphs of Variables

  • Graphs of Logged Variables

Graphs of Logged Variables

 

  • Graphs of Differenced Variables

Graphs of Differenced Variables

 

Tables:

  • ADF Tests

ADF Tests for variables

  • First Order ADF Tests

ADF Tests for first order differenced variables

  • Engle-Granger Test of GR and GX

Engle-Granger Unit Root Test of GR and GX

  • Johansen Test of GR and GX

Johansen Test of GR and GX

  • Johansen Test of gr and gx with trend variable

Johansen Test of gr and gx with trend

  • General Cointegration Test of gr and gx

General Cointegration Test

  • Engle-Granger Test of IP and GDP

Engle-Granger Unit Root Test of IP and GDP

  • Johansen Test of IP and GDP

Johansen Test of IP and GDP

  • New Johansen test, Long Run Static Equation

Static Long Run Equation for ip

  • 1 New ADL Modeling

ADL Model (1) Dip

  • 2 New ADL Modeling

ADL Model (2) Dip

  • 3 New ADL Modeling, Final Error Correction Model

ADL Model (3) Dip

  • IIS Test

IIS Test

  • Final Model with Year Dummies

Final Model with Year Dummies

  • Forecast

Forecast

 

[1] Takero Doi, August 2011, NBER Working Paper Series, Japanese Government Debt and Sustainability of Fiscal Policy

[2] Tomomi Miyazaki, July 2017, the Sustainability of Japan’s Government Debt: A Revie

[3] Takero Doi, August 2011, NBER Working Paper Series, Japanese Government Debt and Sustainability of Fiscal Policy

[4] Jeroen J.M. Kremers, January 1988, U.S. Federal Indebtedness and the Conduct of Fiscal Policy

[5] Simon Neaime, July 2014, Sustainability of Budget Deficits and Public Debts in Selected European Union Countries

[6] Simon Neaime, July 2014, Sustainability of Budget Deficits and Public Debts in Selected European Union Countries

[7] Simon Neaime, July 2014, Sustainability of Budget Deficits and Public Debts in Selected European Union Countries

[8] Christopher Mupimpila, January 2015, The Causality between Government Revenues and Expenditures in Botswana

[9] Kazutaka Kuga, the Budget of the Government of Japan, How is it Coexisting with High Debt Load?

 

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