Does a high public debt really matter?

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Does a high public debt really matter?

Egbert Jansen

June 26, 2018

Abstract

This thesis aimed to investigate the effect of public debt on the growth of an economy. Therefore, this thesis examined the causal relationship between public debt and economic growth. This thesis consists of two different parts. The first part includes a replication of the study conducted by Reinhart and Rogoff with an additional set of data, which also contains the effect of the recent financial crisis. Additionally, more countries are added in order to increase the amount of observations. The second part of this thesis consists of a regression analysis of the public debt level on economic growth. This thesis corrects for the business cycle and the financial crisis to check whether the results are robust. The results found in this thesis suggest a positive relationship between the public debt level of a country and their economic growth rate.

Supervisor: Kees Haasnoot UvA - Economics Email: c.w.haasnoot@uva.nl

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Statement of Originality

This document is written by Egbert Jansen who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Acknowledgements

I would like to express my very great appreciation to soon to be Dr. Kees Haasnoot. Through-out this research my supervisor has been of much help. I would especially like to thank him for putting more time and effort in this process then expected from the university rules. In addition, I would like to offer my special thanks to Chantal for reading over my thesis. Lastly, I would like to thank everyone else for their support while writing my thesis.

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1 Introduction

In 2010, Reinhart and Rogoff wrote a paper about the relationship between public debt and GDP growth. The authors concluded that high public debt can lead to a substantial decline in economic growth, especially those countries who exceeded the 90% debt to GDP ratio (Reinhart & Rogoff, 2010). This paper, ”growth in a Time of Debt”, is frequently used as a scientific justification for austerity measures. Paul Ryan, a congressman and chair of the House Budget Committee in the United States, used this paper as a substantiation for his Federal Budget plan, which contained several cuts in the governmental spendings, and was approved by the House of Representatives. Furthermore, this paper is frequently cited by other policymakers such as the European Commission, especially after the financial crisis (Herndon et al., 2014). The years after the publication, the research methods and the selective use of available data received a lot of criticism. A critique written by Herndon, Ash and Pollin replicated the study done by Reinhart and Rogoff. The authors came to the conclusion that inappropriate weighting of summary statistic, coding errors and selective use of the data, led to an incorrect relationship between public debt and economic growth (Herndon et al., 2014).

During and after the financial crisis which started in 2007, a lot of countries changed their policy regarding governmental expenditure and governmental debt (Schuknecht et al., 2011). As the research of Reinhart and Rogoff only consists of data until 2009 and thus do not capture the financial crisis, it is of importance to add more years of data. Therefore, in this research, data going up until 2016 will be taken into consideration. The study done by Reinhart and Rogoff (2010) is proven to be done improperly, and many policymakers and politicians have based their policies on this study. It is therefore important that reliable research will be done about the relation between public debt and GDP, aiming for better policies to be made.

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Additionally, during the financial crisis the indebtedness of countries increased sharply: on average, around 25 percentage point (figure 1). This was caused by large budget deficits that countries ran to stabilize their economy. Besides that, automatic stabilizers contributed to even larger deficits (Mankiw, 2013). After the financial crisis, public debt is still a major topic for policy makers, especially in the European Union. The question still remains if public debt results in a lower GDP growth and if this is caused by a higher public debt. The financial crisis gives an unique opportunity to see the things that stand out. To see the outcomes that are very different from the rest, meaning that there is a major difference between the low debt countries and the high debt countries in their GDP growth.

Besides adding more years of data, it is important to add more countries to the dataset. Reinhart and Rogoff originally started with twenty countries. There is no clear argument why they used these twenty countries, except for the fact that their economies are advanced. Since there are more than twenty advanced economies, it would be compelling to expand the list of countries, including all the European Union members as well as the OECD countries. The total number of countries in this research will be 41, which will give more meaning to the outcomes.

Last but not least, even after the replication done by Herndon, Ash and Pollin, still some doubts remain about the method of Reinhart and Rogoff, and thus also Herndon et al., used to conduct the research. In this study, the methods and assumptions used by Reinhart and Rogoff will be carefully examind and, if necessary, the methods will be modified to increase the reliability of the study.

The relevance of this study is also demonstrated by the following debate about the influence of public debt on GDP growth. In Krugman’s early days as an economist, he believed that high public debt could lead to debt overhang and slowdown in economic growth (Krugman, 1988). Now, he is in favour of the argument that stimulating the economy, and thus a higher public debt level, could be beneficial for economic performance. Recently, he had an argument with the President of Estonia about the effect of public debt to GDP on economic growth. Estonia had extraordinary low debt to GDP levels, for more than twenty years in a row (Bourne, 2012). Their average GDP growth is around 6,5% each year. In comparison to Germany, which experienced an average growth rate that is around 1.5% each year, for the last twenty years. This while Germany is seen as the ”engine” of the economy of the Eurozone. Krugman argued that low debt levels, as a result of austerity measures, would affect economic growth. He used Estonia as an example, but he did not mention that over the past twenty years, Estonia experienced almost the biggest growth rates of the whole Eurozone and still has a low public debt to GDP level (Bourne, 2012). This debate emphasized how important thorough research is, because this debate shows that the topic is subject to change and that it is not always clear if a high/low public debt is harmful or not.

The research question of this paper is: What is the causal relationship between public debt and GDP? There are a couple of sub questions which have to be answered first. Starting with: what is the consequence of a high public debt level on GDP? Followed by: is there a public debt to GDP threshold for which GDP declines sharply? After answering these questions, this research can hopefully give an answer to the comprehensive question how public debt affects economic growth.

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2 Literature review

A lot of research has been done about the impact of public debt on GDP growth. This literature review will describe the most important articles about this topic and it will give an overview of the criticism that Reinhart and Rogoff received about their study. Additionally, this literature review will give a short overview about the determinants of economic growth. This overview is crucial for selecting useful variables used for the regression in the second part of this study, as it is necessary to look at other factors affecting economic growth besides public debt. This literature review is divided into sections in which the studies show similar results. The review will start with the studies that show that there is a negative relationship between public debt and economic growth. There will be looked at the mechanics that causes lower economic growth and the empirics that support these claims. In the second part of the review, the studies arguing that there is no causal relationship found between public debt and economic growth will be discussed. In the third part of this overview, the studies that describe the determinants of economic growth will be discussed.

2.1 Relationship public debt and economic growth

In their famous article, Reinhart and Rogoff (2010), examined the relationship between public debt and economic growth. They used an extensive data set existing of twenty countries that goes back to 1970. They divided the public debt to GDP ratio in four categories: less than 30%, 30%-60%, 60%-90% and more than 90%. They calculated the average and median GDP growth of the concerning categories. Reinhart and Rogoff argue that a high public debt to GDP ratio causes lower economic growth rates after reaching a threshold of 90% public debt to GDP. This is in line with other literature done by Krugman (1988), Kumar and Woo (2010), Cecchetti et al. (2011), Checherita-Westphal and Rother (2012) which shows that there is a negative correlation between high public debt and GDP growth. There are several channels by which high public debt level can affect economic growth, which will be discussed below.

2.1.1 Future income

Firstly, high public debt reduces national savings, which is caused by interest payments and debt repayments, resulting in a lower national income in the future. Due to this lower income, capital accumulation and thus economic growth is negatively affected (Elmendorf & Mankiw, 1998).

2.1.2 Investments

Economic growth could also be reduced as a result of higher interest rates. Higher interest rates are a direct result of uncertainty from investors. If they fear a possibility of default caused by high debt levels, they would charge a higher risk premium, which is an important component of the interest rate. If the debt of a country reaches a certain (high) level there could be no possibility to grow out of this debt anymore. This can be shown by the following formula: ∆b = d + (r − yy)b. ∆b is the change in government debt, d is the primary deficit, r is the real

interest rate, and yy is the real growth rate of the economy. There are situations in which a high

public debt (b) cannot be reduced, even with a budget surplus. This could happen when the interest rate is higher than the growth rate of the economy (2). The debt is unsustainable and will result in higher risk premia and higher interest rates, which crowds out investments (Carlin & Sockice, 2006).

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Figure 2: Government debt ratio. Real interest rates exceeding the growth rate (Carlin & Sockice, 2006)

Additionally, empirical research and econometric models show that a high public debt (in the future) could increase long-term interest rates (Gale & Orszag, 2002). Due to the uncertainty by investors and raising interest rates, investments will decline, especially because borrowing money for investments will be more expensive and lending money will be riskier (Gale & Orszag, 2002). The Solow Growth model shows that lower investments results in less economic output. Furthermore, the model shows that the steady-state capital stock will decrease, which results in less consumption (Mankiw, 2013). All of these mechanics will lead to less economic growth.

2.1.3 Uncertainty

Another channel by which economic growth is affected is uncertainty. As an increase in the public debt could lead to higher interest rates and larger debt repayments, there is a possibility of having higher taxations in the future to finance the government debt. As taxations are distortionary, this could result in lower investments and less consumption which negatively affects economic growth (Barro, 1979). Additionally, uncertainty could arise due to doubt about future prospect and policies which are reactions of the high debt level. Furthermore, a debt crisis could set off other types of crises, for example, a financial or currency crisis. All these aspects that cause uncertainty may result in less investments because of doubts about the future rate of return (Hemming et al., 2003).

2.1.4 Inflation

High public debt could arise due to the expansionary governmental policies which increase the demand of services and goods. Overstimulating the economy could result in higher prices and thus higher inflation. In general, people do not like increasing or unstable prices, which results in uncertainty and a drop in consumption, saving and investment. Additionally, a higher inflation causes higher cost for allocating resources due to problems in identifying relative prices, which could lead to misallocation of resources and lead to less economic growth (Briault, 1995). As the study of Barro (1995) shows, a ten percentage point increase in inflation could lead to an average decline of economic growth by 0,25 percentage point each year. As the short-term economic growth results are not very significant, the long-term affect may be larger (Barro, 1995).

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2.1.5 Labour productivity

As described above, a high public debt could lead to lower investments and less capital stock per worker. Due to these reductions, a slowdown in labour productivity will occur. As labour productivity is a huge determinant of output delivered by companies, the rise in total national income will slow down. Eventually, this will result in lower tax revenue and government spending, which directly affects economic growth. Also, due to the less output delivered by companies, unemployment will rise, which will affect the consumption of the workers and thus economic growth. Kumar and Woo examined these channels and concluded that economic growth declines as public debt increases. The most significant and important factor that, according to Kumar and Woo, contributed to the slowdown in economic growth is labour productivity (Woo & Kumar, 2010).

2.2 No relationship public debt and economic growth

A critique that the paper of Reinhart and Rogoff received, written by Herndon, Ash and Pollin (2014) argued that there is no such thing as public debt affecting economic growth. They did not find a significant negative correlation between public debt and GDP growth. There are more studies conducted that try to estimate the effect of public debt on economic growth. Panizza and Presbitero (2014) did not find a correlation when they corrected for endogeneity. A paper written by Bell, Johnston and Jones (2015) examined the causal relationship between public debt and GDP using multilevel models. When they controlled for linear time trends, there was no significant effect of high debt levels on GDP growth. As there is no finding of a relationship between a high public debt and economic growth, meaning that there are no mechanics that support this view, this section is relatively short. Although, there are several arguments that could explain why a high public debt level does not affect economic growth.

2.2.1 Inflation

As described above, a high public debt could result in higher inflation. As a result of higher inflation, the value of the debt will decrease such that it will be rewarding to finance governmental expenditure with debt. If the debt, to finance governmental expenditure, is used for investments for which the net present value is positive, higher debt could lead to higher economic growth in the future (Barro, 1995). Examples of investments that could lead to economic growth are investments in infrastructure, education and healthcare.

2.2.2 Credibility

Another point in favour of why high governmental debt does not affect economic growth, is credibility. It is not likely that, for example, the United States will default on their outstanding loans. One reason for this is that it has never occurred. A second reason is that the United States is always able to print her own money to cover the interest and repayment costs. So, as long as investors belief that a country is able, or will be able, to pay their interest and debt repayments, it will not cause uncertainty. No decline in investment will occur, hence economic growth will not be affected.

Printing money to cover the interest and debt repayments will inflate the debt away due to inflation tax revenue (Pilbeam, 2013). However, there are limitations to for how long and how much the government can credibly print money (Fischer et al., 2002). If inflation becomes too high, people are less willing to keep their money, because in the future they will not able to buy as much as they are able to buy today with the same amount of money. Due to reduction in

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demand for real money, the revenues of the inflation tax revenues are reduced. Additionally, high inflation levels could lead to hyperinflation and result in an economic crisis (Carlin & Sockice, 2006).

In the Eurozone, there is a similar but slightly different situation. Countries that are part of the Eurozone share a common currency. A common currency has a lot of advantages that will not be described in this study. There are also disadvantages of sharing a common currency, such as sharing risks. The downside of this is that some countries could take advantage of the fact that the risk of the Eurozone is divided across all her members, which results in moral hazards problems. Countries that experience high public debt levels have confidence in the fact that, if there is a threat of default, the Eurozone will rescue them. This is for the reason that, if a high public debt country will default, it will also affect the credibility of other Eurozone members, which at the end can result in uncertainty and thus lower economic growth. Countries that experience high public debt levels have confidence in the fact that, if there is a threat of default, the Eurozone will come to rescue because otherwise, If a high public debt country will default, it will also affect the credibility of other Eurozone members, which, in the end can result in uncertainty and thus lower economic growth (Vries & Haan, 2016). Next to the governments of countries that experience high public debt, investors may also believe that the possibilities of a default is not very likely. This view could be support by the fact that, despite the high debt levels of several countries, the spread of the interest rates between Eurozone countries, since the introduction of the Euro, was almost zero. Only during the financial crisis, the interest rates of highly indebted countries began to rise. Now, mainly due to the ”whatever it takes” speech of Mario Draghi, president of the European Central Bank (ECB), the spreads returned to their levels as if it were before the financial crisis (Vries & Haan, 2016).

2.2.3 Conclusion literature on public debt

As previously shown, there is no clear-cut answer to the question if high public debt levels affect economic growth. It seems that various studies show different results, or even contradict each other. Therefore, it is of importance to further explore this area of research.

2.3 Literature on economic growth

A lot of (empirical) research has been done about the determinants of economic growth. This study will follow the research conducted by Bosworth and Collins (2003), which argues that it is best to use a fundamental set of explanatory variables as control variables to estimate which variables affect economic growth. A couple of these variables are already discussed above, such as consumption, investment and interest rates. Other fundamental variables that could affect economic growth will be discussed in this section.

The (initial) level of GDP per capita is an important variable that significantly affects eco-nomic growth. Countries with low level of GDP per capita seem to grow faster than countries with a lower level of GDP per capita. This is due to what is called the catching-up or convergence process (Sala-i Martin et al., 2004).

Another important variable that seems to affect economic growth is human capital. This can be measured by level of schooling or the governmental expenditures for schooling. Countries with citizens that have plenty of human capital are more likely to grow faster than countries with fewer human capital. This is due to the fact that countries with a lot of human capital are more appealing to investors, because the people of those countries are more likely to adopt ideas from all over the world and to participate in innovative enterprises (Grossman & Helpman, 1990).

Something that is closely related to the previous variable is technological improvement, which could be measured by the total expenditures for research and development (Sala-i Martin et al.,

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2004). Due to technological improvement, the cost of producing will drop which increases the efficiency.

The openness of a country is another variable that could affect economic growth, which can be measured by the sum of the export and imports (trade) as part of the GDP. Trade affects economic growth due to the fact that a country is able to specialise in making a product and exchange it for another product that is produced in another country. Due to this specialisation, a country is able to produce more, which positively affects economic growth (Sala-i Martin et al., 2004).

3 Structure of empirical part

The empirical part of this study is divided into two sections. The first part consists of the replication of Reinhart and Rogoff. The method, data and results of the replication will be discussed in the first part. The second part will consist of a regression of public debt on economic growth. The method, data and results of the regression will be discussed in the second part. The discussion and conclusion will cover the results of the replication part as well as the regression part.

3.1 Hypothesis

For the replication part of this study, I do not expect to find a significant negatively relation-ship between public debt and GDP growth after adding the years following the financial crisis. This is similar to the results found by Herndon, Ash and Pollin and in contrast with the results found by Reinhart and Rogoff. For the regression part, I do not expect to find a significant negative relationship between public debt and economic growth.

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4 Replication of Reinhart and Rogoff

4.1 Method

The first part of this study consists of an replication of the study done by Reinhart and Rogoff. To estimate the effect of a high public debt on GDP growth it is necessary to divide the debt to GDP ratio in four categories: less than 30%, 30-60%, 60-90% and more than 90%. After that, the years for which the public debt to GDP level belongs to that category can be added. It is then possible to calculate for how many years a country belongs to a certain category and what the average GDP growth of that category is for a specific country. After doing that, the average and median GDP growth of the whole category can be calculated.

Due to the fact that there are several gaps in the observations, there are two possible ways to calculate for how many years a country belongs to a certain category: averaging by country or averaging by country-years. In the first situation, each country counts as a single observation, despite the fact how many years it shows up in any of the four or five categories. In the second situation, an observation will be counted as a weighted country-year observation within the total of country years (Herndon et al., 2014). Reinhart and Rogoff only used the first possibility, Herndon, Ash and Pollin also did the second possibility. The second method seems to be the best way to calculate the average growth rate of a category. If you use the first method to calculate the average GDP growth in a category, and there is a country for which a category only consist of one year, and in that year the growth rate was exceptionally high or low, that single year will count as a whole country observation. If you use the second method, that single year will be weighted and the year will only count as a percentage of all the years. For example, in 1999 the Russian Federation experienced a GDP growth of 6.4%. This year belonged to the 90-120% debt to GDP category. As this was the only observation in that debt category, using the first method, the growth rate will account for 6.25% of the average growth of all countries in that debt category. By using the second method, the growth rate of that category will only account for 1% of the average growth of all countries in that debt category. This study will use both calculation methods to show what the impact of these different methods is on the results.

As an extension, Herndon, Ash and Pollin 2014 added a fifth debt to GDP category. They changed the more than 90% in 90-120% and added more than 120%. The reason for this is that Reinhart and Rogoff thought that the threshold for which GDP declines sharply is around 90% debt to GDP. Herndon, Ash and Pollin thought that the threshold was more around 120% debt to GDP. In this study, both methods will be applied.

4.2 Data

This study will add more data obtained from more years to get more accurate and reliable results. This data set contains the years ranging from 1995 to 2016. After 2009, many countries suffered from a financial and economic crisis. It seems logical to add the years after 2009 until 2016 to get a better understanding of the relationship between public debt and GDP growth. The research that has already been done only includes data until 2009. It was not possible to work with the same dataset used by Reinhart and Rogoff, who use the years ranging from 1979 to 2009, because the dataset is not publicly available. To obtain the years ranging from 1979 to 1995, it is necessary to use other sources than the Word Bank, such as different national governments, which will come with the disadvantage of not using the same characteristics to define public debt and economic performance. Therefore, this study only contains the years starting from 1995 because they are, without trouble, accessible from the World Bank. A second argument for excluding the years ranging from 1979 until 1995 could be that the data might be outdated. The world and economy has changed, and with the introduction of European union,

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more rules about fiscal policy and public debt are implemented. The years ranging from 1979 until 1995 would not give an accurate representation of the effect of public debt on economic growth in the world as it is today.

Another addition to the study is the extension of the countries that are used. The reliability of the results will increase due to the extension of the dataset. The dataset of Reinhart and Rogoff contains twenty advanced economies. They do not specify why they use only these twenty countries. This study will add another 21 advanced economies, based on the membership of the European Union and OECD. Now almost all advanced economies are part of the research. There are advanced countries that are not part of the study. This is because the data used for the replication was obtained from the World Bank and that there are gaps in the available data. This is due the fact that a country is not obliged to report their public debt levels. Despite the fact that a country is not obliged to report their public debt level to the World Bank, most countries do. However, for the countries that did not report their debt levels to the World Bank, it is possible to look at other sources, such as the IMF and local authorities, such as the ministry of Finance. Before merging debt data from the World Bank with debt data obtained from somewhere else, the methods that were used to calculate the debt levels are compared. Only if the methods were similar and the data corresponds between the two different sources, the data was used. If that was not the case, the country was not obtained in the study.

To obtain the yearly debt levels, it is necessary to calculate the average debt levels of the four quarters each year. The quarterly public debt database of the World Bank is used, for which countries report their debt level each quarter. Averaging is essential, because of the measurement that is used for economic growth, namely the average GDP growth per year. GDP growth per capita is not used because of the following reason; Reinhart and Rogoff only used the average GDP growth per year as a measurement for economic growth. Since the list of countries used in this study only consists of advanced economies for which the fertility rate does not differ significantly between countries, there is controlled for the positive effect that population growth could have on economic growth.

Reinhart and Rogoff use central governmental debt as a measurement for public debt. Some-times, when they did not find data about the central governmental debt, they used general government debt as a measurement. The central government debt incorporates the budgetary central government, such as ministries and government agencies. Social security funds and extra-budgetary accounts are included in the central government debt. However, the debt of state and local governments, such as province and municipalities, are not part of the central government debt. General government debt includes all the debt, domestic as external, of all the sectors of the government. As a result of decentralisation and the growing importance of local governments, it seems relevant to consistently use general government debt as a measurement for public debt. In the replication, both types of government debt will be used separated because this seems like a more transparent method, and compare the outcomes with the original paper. Both types of debt include domestic as well as external public debt. Due to better measurement variables, the conclusion of the replication could be more credible and transparent.

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4.3 Results

The replication of Reinhart and Rogoff shows different results in comparison with the original study. As shown in table 1, Reinhart and Rogoff argued that economic growth will decline sharply after reaching a public debt to GDP level of 90%, with an average shrink of -0.1% each year. The results of the replication yields different outcomes. Again, after reaching the 90% public debt to GDP ratio, the growth rates are reduced, but not as strong as Reinhart and Rogoff stated in their study. After reaching the public debt to GDP level of 90%, the average growth rate is 2.2% each year. Figure 3 shows the growth rates of the original study done by Reinhart and Rogoff. Figure 4 shows the growth rates of the replication. Figure 6 in the appendix shows a scatterplot which represents the underlying data that is used for this replication.

Furthermore, it is shown in table 1 as well that when you calculate the economic growth rates using the method averaging by country-years the results are slightly different. It seems that the impact of public debt on GDP growth is stronger, but not as strong as stated in the original study. The results that follow after using different measures for public debt are not significant. In the appendix figures 7 to 9 can be found, which shows the growth rates for each debt category and method that is used.

Public debt/GDP category

≤30% 30-60% 60-90% ≥90%

RR published results

Mean 3.8 2.9 3.4 -0.1

Median 3.9 3 3.3 2.3

Replication central government debt

Mean 3.6 2.6 2.2 2.2

Median 3.9 2.7 2.5 2.2

Replication central government debt (Country-Years)

Mean 3.7 2.6 2 1.4

Median 3.8 2.8 2.1 1.6

Replication general government debt

Mean 4.7 3 2.3 1.7

Median 4.9 3.1 2.8 1.5

Replication general government debt (Country-Years)

Mean 4.7 2.9 2.2 1.3

Median 4.6 3 2.4 1.6

Table 1: Recalculated GDP growth rates (1995–2016) and Reinhart & Rogoff GDP growth rates in percentages for 1979–2009 time period

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Figure 3: GDP growth (% per year) for each public debt category (Reinhart & Rogoff, 2010)

Figure 4: GDP growth (% per year) for each public debt category, data obtained from World Bank

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The replication yields different results after adding a fifth public debt to GDP category. Table 2 shows that after reaching a public debt to GDP level of 120%, the growth rate of the economy declines sharply, which is independent of the method that is used. This confirms the idea that public debt could negatively affects economic growth. Figures 10 to 13, available in the appendix, show the average growth rates for each public debt to GDP category.

Public debt/GDP category

≤30% 30-60% 60-90% 90-120% ≥120%

Replication central government debt

Mean 3.6 2.6 2.2 2.5 -0.3

Median 3.9 2.7 2.5 2.2 0.7

Replication central government debt (Country-Years)

Mean 3.7 2.6 2 2.2 -0.6

Median 3.8 2.8 2.1 1.8 0.7

Replication general government debt

Mean 4.7 3 2.3 2.1 0.8

Median 4.9 3.1 2.8 1.6 1.4

Replication general government debt (Country-Years)

Mean 4.7 2.9 2.2 1.8 0.5

Median 4.6 3 2.4 1.8 1.5

Table 2: Recalculated GDP growth rates (1995–2016) and Reinhart & Rogoff GDP growth rates in percentages for 1979–2009 time period

It is difficult to give meaning to the results. First of all, the results of the replication could differ from the results obtained by Reinhart and Rogoff due to the errors they made in their methods. Secondly, independent of the methods used, the public debt is the only variable that is used to investigate the effect on economic growth. In addition, no control variables are used. Thirdly, it was not possible to use the same dataset used by Reinhart and Rogoff.

Despite the fact that the growth rates differ from the original study after reaching the public debt to GDP level of 90%, the trend seems to be the same as originally stated by Reinhart and Rogoff. The same holds after adding a fifth public debt to GDP category. Therefore, it could be argued that, despite the methodological errors made by Reinhart and Rogoff, the public debt level could have a negative effect on economic growth. Another conclusion that could be drawn from the results is about the public debt to GDP threshold for which economic growth declines sharply. Reinhart and Rogoff argue that this is the case after reaching the 90% public debt to GDP. If you add another public debt to GDP category, the threshold seems to be above 120%. Perhaps, the threshold has moved from 90% to 120% over time. This can be due to the fact that investors are now more certain about the expected rate of return on their investments than that they were in the past.

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5 Regression

The second part of this thesis consists of a regression to obtain information about the causal relationship between public debt and GDP growth. Therefore, it is necessary to use the deter-minants of economic growth, discussed in the literature review, which can be used as control variables. By using Stata, it is possible to examine if such a relationship exists. Reinhart and Rogoff did not use any regression analysis to estimate the effect that public debt could have on economic growth.

5.1 Data

The dependent variable of the regression is GDP growth per capita. This will be measured by using the yearly average real GDP growth of the 41 countries that are part of the dataset which is used for the replication in the first part of the study. The data is obtained from the World Bank and consists of the years ranging from 1995 to 2016. One of the independent variables is the public debt to GDP level. As described in the data section of the replication part of the study, there are two measures for public debt: central and general governmental debt. For each year, the average is taken for the four quarters for a specific year. The data is obtained from the World Bank and consists of the years ranging from 1995 to 2016.

Other fundamental variables that are discussed in the literature review will be used as control variables. All the control variables such as, GDP per capita, human capital (governmental expenditures for schooling in percentage of GDP), investment (in percentage of GDP), real interest rate, consumption (in percentage of GDP), openness (sum of import and exports in percentage of GDP), technological improvement (total expenditures for research and innovation in percentage of GDP) and annual inflation, are obtained from the World Bank and includes the years from 1995 to 2016.

5.2 Method and results

Since panel data is used, it is essential to check whether to use random or fixed effects. This has been done by using the Hausman Test. For all the models, fixed effects should be used. The test results of the Hausman test can be found in the appendix. Additionally, before running a regression, it is necessary to test for common econometric problems such as heteroskedasticity (Likelihood ratio test), autocorrelation (Wooldridge test) and cross sectional dependency (Pe-saran test). Because all of these three problems occur in this dataset, it is necessary to correct for them. The results of the test for econometric problems can be found in the appendix.

As can be seen in figure 5, there is one outlier at the top of the figure. This observation shows that Ireland experienced 25% economic growth in the year 2015. This was due to the fact that Apple moved to Ireland to benefit from Ireland’s more attractive tax system. As this exceptional economic growth rate is not explained by economic factors and only happened once, it seems to be logical to exclude this year from the data.

All the variables are centred to interpret the constants more easily. This means that a constant describes what the economic growth will be, if all the variables are at their mean. Additionally, the variable GDP per capita is divided by thousand. This will make the interpretation of the coefficient easier.

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Figure 5: Central governmental debt and GDP per capita growth (% per year), data obtained from World Bank

The first two regressions are simplistic and try to estimate the effect of public debt on GDP growth and whether it is significant. In the first regression, central governmental debt is used as a measure for public debt.

GDP GRi,t= αi,t+ β1CentralDebti,t+ β2GDP/CAPi,t+ i,t (1)

The second regression is almost the same, however general governmental debt is now used as a measure for public debt.

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The results of the regression can be found in table 3, which shows that both types of public debt yield almost the same results. The difference is that general governmental debt is significant at a 5% confidence level, and thus seems to negatively affect economic growth. This means that if general debt to GDP increases by 1%, the average growth per year of a country declines by 0.023%, ceteris paribus. Central governmental debt is only significant at a 10% confidence level and thus does not seem to explain economic growth well.

To test whether the results from regression 1 and 2 are robust, it is necessary to add control variables that could also affect economic growth. Regression 3 and 4 are the same, but differ in the measurement for public debt. The variables chosen for these regressions are based on the study done by Sala-i-Martin et al., (2004) which determines the fundamental variables (the most significant) that could affect economic growth. The control variables are: GDP per capita, central government debt, governmental expenditures on schooling (as human capital), real interest rate and governmental expenditures on research and innovation (as technological improvement). The econometric problems as described above are corrected for.

GDP GRi,t= αi,t+ β1GDP/CAPi,t+ β2CentralDebti,t+ β3HumanCapitali,t

+ β4InterestRatei,t+ β5ExpResearchi,t+ i,t (3)

and

GDP GRi,t= αi,t+ β1GDP/CAPi,t+ β2GeneralDebti,t+ β3HumanCapitali,t

+ β4InterestRatei,t+ β5ExpResearchi,t+ i,t (4)

The regression results are shown in table 3. In model 3 and 4, neither of the public debt is significant at a 5% confidence level. It seems that the public debt level does not have an effect on economic growth after correcting for other variables that could affect economic growth.

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In regression 5 and 6, more control variables are added to check for robustness. The extra variables are based on the regression in the study done by Checherita-Westphal and Rother (2012) and include: investment, openness (sum of import and exports as share of GDP), consumption and inflation. Additionally, an ordinal variable is added to model 5 and 6. This represents the public debt to GDP threshold of 120%, to test whether this holds and corresponds to the outcomes obtained from the replication part of this study. For all the observations of which the public debt level is below 120%, the value of the variable is 0. For the observations that the public debt level is above 120%, the value is 1. As can be seen below, regression 5 and 6 differ in the measurement for public debt. Again, there is corrected for econometric problems.

GDP GRi,t= αi,t+ β1GDP/CAPi,t+ β2CentralDebti,t+ β3HumanCapitali,t

+ β4InterestRatei,t+ β5ExpResearchi,t+ β6Investmenti,t+ β7T radei,t

+ β8Inf lationi,t+ β9Consumptioni,t+ β10CDebt>120i,t+ i,t (5)

and

GDP GRi,t= αi,t+ β1GDP/CAPi,t+ β2GeneralDebti,t+ β3HumanCapitali,t

+ β4InterestRatei,t+ β5ExpResearchi,t+ β6Investmenti,t+ β7T radei,t

+ β8Inf lationi,t+ β9Consumptioni,t+ β10GDebt>120i,t+ i,t (6)

As shown in table 3, both public debt in model 5 and 6 are not significant at a 5% confidence level and thus not seem to affect economic growth. Furthermore, the public debt thresholds of 120% are not significant. In both models, most control variables are significant which seems to affect economic growth.

Total expenditures on research and development, which is one of the control variables, is shown to be significant at a 1% confidence level in model 3, 4, 5 and 6, but seems to negatively affect economic growth. Additionally, the same result is found when looking at the variable government expenditure on schooling, although this is found to be less significant. To test whether these results hold, it is necessary to test for multicollinearity between the expenditures on research and development and the expenditure on schooling. This could be tested by looking at the Variance Inflation Factors (VIF) and using the rule of thumb that states that if the VIF is below 10, there is no multicollinearity. It is shown that for these two variables, there seems to be no multicollinearity (VIF = 4.31).

An explanation for the negative coefficient could be that countries that spend a lot on research and development and schooling, already have a high GDP per capita. This is shown in the scatterplot which can be found in the appendix, figure 14. Countries with a higher GDP per capita tend to grow slower in comparison to countries with a lower GDP per capita, due to catch up growth and convergence.

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Table 3: Regression Table

(1) (2) (3) (4) (5) (6)

model 1 model 2 model 3 model 4 model 5 model 6

Central Debt -0.0198∗ 0.00720 0.0163 (-1.81) (0.81) (1.18) GDP per capita -0.139∗∗∗ -0.138∗∗ -0.149∗∗ -0.0864 -0.232∗∗∗ -0.181∗∗ (-3.01) (-2.60) (-2.20) (-0.98) (-3.13) (-2.24) General debt -0.0233∗∗ -0.0151 0.00106 (-2.18) (-1.13) (0.09)

Real interest rate -0.216∗∗ -0.169∗ -0.161∗ -0.119∗

(-2.12) (-2.03) (-1.96) (-1.71) School exp -0.995 -1.139∗ -1.066∗ -1.166∗∗ (-1.59) (-1.89) (-1.85) (-2.15) Research exp -3.749∗∗∗ -2.597∗∗∗ -4.965∗∗∗ -4.061∗∗∗ (-2.86) (-2.84) (-3.01) (-3.64) Trade 0.0642∗∗ 0.0679∗∗∗ (2.51) (3.67) Investment 0.306∗∗∗ 0.339∗∗∗ (4.84) (5.00) Consumption 0.192∗ 0.275∗∗∗ (1.95) (2.99) Inflation -0.00436 -0.0184 (-0.10) (-0.40) Central debt >120% 0.454 (0.40) General debt >120% 0.218 (0.25) Constant 2.193∗∗∗ 2.356∗∗∗ 0.319 1.154 -0.0153 0.311 (4.79) (5.21) (0.35) (1.35) (-0.02) (0.39) Observations 765 786 263 291 263 291 t statistics in parentheses ∗_{p < 0.1,}∗∗_{p < 0.05,}∗∗∗_{p < 0.01}

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5.2.1 Correcting for business cycle

The results obtained so far do not seem to imply that the public debt level of a country significantly affects economic growth. A possible explanation for this could be that only the short term effects have been looked at, and that the business cycle has not been corrected for. This also means that the effect of the financial crisis is not included in the regression. To correct for the business cycle and to check whether the results found so far are also robust in the long run, it is needed to create five periods, which contain five years of observations. For each of these periods the averages of the variables are calculated. For example, the average economic growth for the years ranging from 1995 to 1999 for one country is calculated and put in period 1. The same holds for the other countries, years and variables.

The following regressions are the same as presented in model 1 to 6. The only difference between these models is that the averages of certain periods are used. This means that the observations will drop to 1/5 of the original observations. There has been corrected for the econometric problems as described above. The variables are centred and GDP per capita is dived by thousand. The results are represented in table 4.

After correcting for the business cycle, the public debt level in model 9 and model 10 seems to be at least significant at a 5% confidence level and negatively affect economic growth. Although, the coefficient is so small, around -0.005, that it should not be taken into serious consideration. This means that with an increase of 100% point of the public debt to GDP level, the average growth rate of the economy will only decrease by 0.5% point, ceteris paribus. After controlling for other variables in model 11 and model 12, the public debt level seems not to be significant anymore. Due to the fact that in model 11 and model 12 the public debt is not significant and due to the fact that in model 9 and 10 the effect is small, it could be concluded that there is no effect of public debt on the growth of the economy.

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Table 4: Regression table: correcting for business cycle

(7) (8) (9) (10) (11) (12)

Central Debt -0.00831 -0.00468∗∗ -0.00583 (-1.10) (-2.49) (-1.31) GDP per capita -0.156∗∗∗ -0.146∗∗∗ -0.351∗∗∗ -0.321∗∗∗ -0.268∗∗∗ -0.239∗∗∗ (-3.19) (-3.32) (-12.84) (-22.77) (-6.77) (-7.80) General debt -0.0130 -0.00501∗∗∗ -0.00256 (-1.64) (-2.87) (-0.88)

Real interest rate -0.174∗∗∗ -0.161∗∗∗ -0.171∗∗∗ -0.158∗∗∗

(-6.54) (-7.38) (-6.11) (-7.90) School exp -0.330∗ -0.290∗ -0.336 -0.359∗ (-2.04) (-1.99) (-1.16) (-2.03) Research exp 1.205∗∗ 1.018 1.418∗∗∗ 0.860 (2.62) (1.58) (3.13) (1.53) Trade -0.00380 0.000429 (-0.35) (0.23) Investment 0.144∗∗ 0.0625 (2.19) (1.23) Consumption 0.174∗ 0.118 (1.77) (1.66) Inflation 0.0988∗∗∗ 0.0586∗∗ (3.84) (2.22) Central debt >120% -0.127 (-0.14) General debt >120% -0.589 (-1.33) Constant 7.198∗∗∗ 6.969∗∗∗ 12.51∗∗∗ 11.52∗∗∗ 10.01∗∗∗ 9.062∗∗∗ (4.25) (4.70) (15.36) (21.53) (7.64) (8.87) Observations 181 186 79 88 76 85 t statistics in parentheses ∗_{p < 0.1,}∗∗_{p < 0.05,}∗∗∗_{p < 0.01}

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5.2.2 Time lags

Another way to check if the results found so far are robust is to use time lags. It is possible to lag the independent variables that are used in model 7 to 12 with one period. This means that the current effects of the independent variables will be estimated, on the dependent variable five years later. This is also justifiable because, in theory, almost all the variables seem to affect economic growth in the long run. That means that, for example, expenditure on schooling will not have a positive effect on the growth of an economy directly, but only after a few years. This holds for all the variables used in the models except for trade and consumption. When using time lags it is not possible to correct for autocorrelation, heteroskedasticity and cross country dependency. The results of the regressions with a time lag are represented in table 5.

The results show that the public debt to GDP level is significant at a 5% confidence level in all the models. Due to the fact that the coefficients are positive, it seems that public debt positively affects economic growth. In all the models the coefficients are approximately 0.03 which means that for an increase in the public debt to GDP level of 100% point, economic growth will increase with 3% points, ceteris paribus. An explanation for the fact that an increase in public debt could positively affect economic growth is that governmental spending and thus governmental investments could positively affect economic output.

The results that are found in the latest regression are the opposite of the results found in the replication part of the study. This could be due to the fact that in the replication part of the study the variance over time is not taken into account. There has only be looked at the variance of countries. In the regression part of the study, there is also looked at the variance over time, using panel data which could lead to different and more reliable results.

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Table 5: Regression table: using time lags

(13) (14) (15) (16) (17) (18)

L.Central Debt 0.0284∗∗∗ 0.0302∗∗ 0.0438∗∗∗ (3.59) (2.45) (2.91) L.GDP per capita -0.142∗∗∗ -0.163∗∗∗ -0.143∗ -0.130∗∗ -0.139 -0.164∗∗ (-3.55) (-4.59) (-2.01) (-2.08) (-1.62) (-2.05) L.General debt 0.0308∗∗∗ 0.0307∗∗∗ 0.0414∗∗∗ (4.73) (3.01) (3.82)

L.Real interest rate 0.185∗∗ 0.171∗∗ 0.118 0.106

(2.31) (2.32) (1.50) (1.55) L.School exp -0.202 -0.173 -0.672 -0.458 (-0.47) (-0.44) (-1.10) (-0.99) L.Research exp 0.178 -0.295 -1.045 -0.511 (0.13) (-0.26) (-0.76) (-0.48) Trade 0.0188 0.0188 (0.65) (0.84) L.Investment 0.186∗ 0.141∗ (1.96) (1.74) Consumption -0.208∗ -0.240∗∗∗ (-1.80) (-2.76) L.Inflation 0.0763 0.122∗∗∗ (1.40) (2.73) L.Central debt >120% 0.0986 (0.06) L.General debt >120% -0.798 (-0.80) Constant 6.397∗∗∗ 7.153∗∗∗ 6.024∗∗ 5.554∗∗∗ 5.751∗∗ 6.726∗∗∗ (4.86) (6.15) (2.66) (2.93) (2.14) (2.78) Observations 140 147 79 88 76 85 R2 _0.196 _0.268 _0.353 _0.348 _0.542 _0.548 Adjusted R2 _-0.153 _-0.027 _-0.146 _-0.092 _0.047 _0.138 t statistics in parentheses ∗_{p < 0.1,}∗∗_{p < 0.05,}∗∗∗_{p < 0.01}

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5.2.3 Reverse causality

The last part of this regression sections consists of a test for reverse causality. It could be reasoned that economic growth would reduce the public debt to GDP level. This can be explained by the fact that the public debt level is measured as part of the GDP; meaning that if the GDP rises, the public debt to GDP level will decline. Additionally, it could be reasoned that, due to the fact that there is economic growth, the government is able to reduce her public debt level. For this reason, also lower economic growth (or a shrinkage) could possibly result in a higher public debt level. Most of the control variables are not used because the only channel through which they could affect the public debt level is through economic growth. To test whether this is accurate the following regressions are used. Again there is correct for the business cycle and time lags are used. The results are represented in table 6.

GDP GRi,t= αi,t+ β1CentralDebti,t+ β2GDP/CAPi,t+ i,t (19)

And

CentralDebti,t = αi,t+ β1GDP GRi,t+ β2GDP/CAPi,t+ i,t (20)

In model 19 central debt is significant at a 1% confidence level and has an positive affect on economic growth. This corresponds with the results found in the regression mentioned above. Model 20 represents the reverse causality. Economic growth is significant at a 1% confidence level and negatively affects the public debt level. The R2_{of model 20 is larger than the R}2_{of model}

19. Additionally, the T-values of the coefficients in model 20 are larger than in model 19. This could mean that the model (20) which represents the reverse causality is better in explaining the variance than the initial model and thus that economic growth could affect the public debt level rather than vice versa.

Table 6: Regression table: reverse causality

(GDP per capita growth) (Central debt level (% of GDP)

model 19 model 20

L.Central Debt 0.0284∗∗∗

(3.59)

L.GDP per capita -0.142∗∗∗ 0.134

(-3.55) (0.39)

L.GDP per capita growth -6.244∗∗∗

(-8.08) Constant 6.397∗∗∗ 53.75∗∗∗ (4.86) (4.89) Observations 140 159 R2 _0.196 _0.428 Adjusted R2 -0.153 0.221 t statistics in parentheses ∗_{p < 0.1,}∗∗ _{p < 0.05,}∗∗∗_{p < 0.01}

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5.3 Concluding thoughts

To sum up, in all the regressions, the public debt to GDP level does not significantly negatively affect economic growth. This is in contrast with what is found by Reinhart and Rogoff (2010) but in line with the hypothesis and the replication part of this study. However, there certainly seems to be a positive relationship between the public debt level and economic growth. As can be found in the regressions when correcting for the business cycle and by using time lags, a higher public debt could result in higher economic growth. Additionally, when testing for reverse causality, the outcome that economic growth affects the public debt level seems to be stronger than the outcome the other way around.

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6 Discussion

This thesis examined if the public debt level of a country has an effect on the growth rate of the economy. The motivation for this thesis is based on the study done by Reinhart and Rogoff (2010) describing a strong negative relationship between the public debt level and economic growth. However, the literature shows that there is no clear-cut answer to this question, especially because some studies argue that there is a negative relationship between public debt and economic growth, while others did not find such a relationship. This thesis consists of two different parts. The first part includes a replication of the study conducted by Reinhart and Rogoff, and the second part of this thesis consists of a regression analysis of the public debt level on economic growth

The replication part of this study shows different results in comparison to the results found by Reinhart and Rogoff. Nonetheless, the trend that a higher public debt causes lower economic growth is still present. The results found in the regression part of this thesis do not show any negative relationship between public debt and economic growth. After correcting for the business cycle it looks like there could even be a positive relationship between public debt and economic growth.

The differences found between the results could be due to the fact that the data used in the replication part of this study only explained the variance of countries and did not take into account the variance over time. However, the data that is used in the regression part did take into account the variance of countries as well as the variance over time.

There are also differences between the results of the regressions which are conducted in this research. The first two regressions did not find a significant result of a relationship between public debt and economic growth. While the third regression, in which time lags are used, concluded that there could be a positive relationship between public debt and economic growth. Due to the fact that time lags are used, it is not possible to correct for all the econometric problems as carried out in the first two regressions. Furthermore, in the second and third regression, periods with the average of five years are used. This lead to a drop of the observations to 1₅ of the observations in the initial situation. It could be that the results are less reliable due to the low number of observations.

In the literature review, many channels described how a high public debt level could negatively affect economic growth. These theories seem logical, but the results found in this thesis do not support this perspective. An explanation for this could be that the theories and channels by which public debt affects economic growth still hold, however, only at very high public debt levels. If investors lose their confidence in the idea that the countries can pay their interest and debt repayments, which is often the case when a county has a very high public debt level, these channels will work. It could be that uncertainty about the height of the public debt level is the only thing that matters, which results in lower economic growth. The measurement of uncertainty is quite difficult and was not part of this study. Therefore, future research should focus on this matter, and in particular about the difference of uncertainty in the Eurozone and other countries. This because the individual Eurozone members differ in the ability to conduct their own monetary policy in comparison to countries that are not part of the Eurozone.

As previously mentioned, There could be a reverse causality, which means that the growth of the economy could affect the public debt level of a country. However, this is difficult to determine as the public debt level is presented as part of GDP. Therefore, by definition, the public debt level will rise or fall if the GDP changes. To determine if there really is a reverse causal relationship, future research should focus on this topic to give a more substantial answer to the question about the relationship and direction between public debt and economic growth.

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of Reinhard and Rogoff as scientific justification for austerity measures. However, when looking at the results of this thesis, such a justification does not hold. The results show that a higher public debt level could even have a positive effect on the growth of the economy. This does not imply that policymakers can just spend governmental money, but that it is not a conclusion set in stone that a high public debt level results in lower economic growth.

7 Conclusion

This research aimed to investigate the effect of public debt on the growth of an economy. It consists of two parts namely: a replication of the study conducted by Reinhart and Rogoff, and a regression analysis of the public debt level on economic growth.

The results in the replication part of this study showed a weak but negative relationship between public debt and economic growth. This is in contrast with the study of Reinhart and Rogoff who argue that there is a strong negative relationship. The difference between the results of this thesis and the study of Reinhart and Rogoff could be explained by the errors they made in their methods.

In order to investigate if the results found in the replication are significant and robust, a regression analysis is executed, as described in the second part of this thesis. The results show that there is no negative relationship between public debt and economic growth. In fact, the results suggest that there is a positive relationship between public debt and economic growth, which could be due to the fact that governmental spending will stimulate the economy.

The difference between the results of the replication part and the regression analysis are due to the fact that, in the replication part, the variance over time is not taken into account. Therefore, the results obtained by the replication are less reliable than the results obtained by the regression analysis, which did take into account the variance over time.

To conclude, there is a significant relationship between the public debt level and the growth rate of the economy. However, this relationship is not negative, as suggested by Reinhart and Rogoff, but positive as shown by the regression analysis in part two of this thesis.

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8 Appendix

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Figure 7: GDP growth (% per year) for each public debt category (averaged by country)

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Figure 9: GDP growth (% per year) for each public debt category (averaged by country-years)

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Figure 11: GDP growth (% per year) for each public debt category (averaged by country)

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Figure 13: GDP growth (% per year) for each public debt category (averaged by country-years)

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P-values for testing for econometric problems Hausman test model 1: 0.0090 model 2: 0.0046 model 3: 0.0027 model 4: 0.0034 model 5: 0.0034 model 6: <0.001

Cross sectional dependency test

Model 1: <0.001 Model 2: <0.001

Model 3: insufficient observations Model 4: insufficient observations Model 5: insufficient observations Model 6: insufficient observations

Wooldridge test Model 1: <0.001 Model 2: <0.001 Model 3: <0.001 Model 4: <0.001 Model 5: <0.001 Model 6: <0.001

Likelihood ratio test

Model 1: <0.001 Model 2: <0.001 Model 3: <0.001 Model 4: <0.001 Model 5: <0.001 Model 6: <0.001

Does a high public debt really matter?