The effect of sovereign debt on economic growth in developed countries with specific attention to the case of the US

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Debt Dynamics

The effect of sovereign debt on economic growth in developed countries with specific attention to the case of the US.

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Master Thesis

MSc Economics – International Economics and Globalization Faculty of Economics and Business

August 15, 2018

Author: Stephan L. van der Boom Student number: 10082891

Email: stephan.vanderboom@student.uva.nl Supervisor: Ms. N.J. Leefmans

Second Reader: Dr. D.J.M. Veestraeten Word count: 14166

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Statement of Originality

This document is written by Stephan Lucas van der Boom who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are 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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Abstract

Most developed countries have participated in debt accumulation in recent history. For a long time high debt levels were associated with wars and depressions across the globe. Around 1995 and onward the perception of debt in general shifted. An increased concern towards the effect of debt on economic growth has become apparent. This paper investigates the legitimacy of this concern by researching the relation between gross government debt and economic growth per capita. In particular, it tries to understand the nature of the effect of public debt on growth.

This is done through forming a comparative literature review and subsequently estimating the relation through an empirical format. The methodology that is used in this paper follows the example of the empirical approach of Checherita & Rother (2010. p. 28). In the approach, both the direct and indirect effect of debt on growth is estimated. The dataset of this paper consists of 16 developed countries over the period 1965-2019. In addition, the relation between debt and growth is investigated for the United States (US) specifically.

This paper seems to find no conclusive evidence for a nonlinear unbiased direct relation between gross domestic debt squared (relative to Gross Domestic Product (GDP)) and economic growth per head of the population for both samples. It does find anomalies in the results for both samples when it comes to the analysis of the indirect relation which is measured using four channels: i) the private saving channel, ii) the private and public investment channel, iii) the Total Factor Productivity (TFP) channel and iv) the long-term nominal and real interest rates channel. Finally, this paper finds (weak) evidence that historical context seems to be important to take into account whilst assessing the relationship between debt and economic growth.

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1. Introduction

Most developed countries have participated in debt accumulation in recent history. Financial markets have increased in size, services and accessibility, making it more attractive and attainable for sovereignties to take on debt. This has risen to such a level that in 2016 global debt, both private and public, amounted to a new record high of 164 trillion dollar. In relative terms this is around 225% of the global GDP (Gross Domestic Product) (Gaspar & Jaramillo, 2018. p.1).

For a long time high debt levels were associated with wars and depressions across the globe. Around 1995 and onward the perception of debt in general shifted. An increased concern towards the effect of debt on economic growth has become apparent (Mody, 2015. p.1). This paper tries to address this concern, both for a group of developed countries (including the US), and for the US specifically. It does so by researching the effect of public debt on growth for the US and on a set of European countries. Figure 1 shows the complete sample that this paper addresses and all their relative debt to real GDP positions.

Figure 1. Gross gov. debt to real GDP per capita - ratio for all individual countries in the sample

Figure 1 shows some interesting features. A shift in debt positions occurs for nearly all countries in 2007 and onwards. The recent global economic and financial crisis is to blame for such increases. Certain countries were affected more than others. Figure 2, for instance, shows that certain regions of Europe were affected more than others.

0 50 100 150 200 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

Austria Belgium Denmark

Finland France Germany

Greece Ireland Italy

Luxembourg Netherlands Portugal

Spain Sweden United Kingdom

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6 Figure 2. Gross government debt to real GDP per capita - ratio for all regions in the sample

From a first glance, it looks like Northern Europe (Sweden, Finland, Denmark) was least affected by the crisis. Western Europe (UK, Austria, Belgium, Ireland, Netherlands, France, Germany, and Luxembourg) saw a large increase in relative debt levels: from an average of 50% debt to GDP towards an average of above 80% of debt to GDP. After 2014 however, debt levels seemed to return to more stable levels for Western Europe. Southern Europe (Portugal, Spain, Italy, and Greece) was hit the hardest as it saw an average increase of almost 60 percentage points in the period 2007-2016. In 2016 Southern Europe hit a peak; the average level of debt to GDP for these countries was over 135%. However, this debt crisis of Southern Europe seems to have a diminishing trend after the year 2017.

In addition, figure 3 shows the differences between the countries that have been most affected by the debt crisis (GIIPS)1 and have been the topic of economic conversation for an extended period of time. The figure further shows the remaining countries in the Eurozone (non-GIIPS) and the US.

1_{GIIPS (Greece, Ireland, Italy, Portugal, Spain) countries are identical to the region Southern Europe of figure 2}

with the exception of Ireland.

0 20 40 60 80 100 120 140 160 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

Northern Europe Western Europe Southern Europe United States

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7 Figure 3. Gross gov. debt to real GDP p.c. - ratio for GIIPS vs Non-GIIPS countries in the sample

Note that debt is portrayed in relative terms rather than absolute terms in the above figures. This makes it easier to compare debt statistics between different countries in a cross-country analysis. Although the relative debt to GDP metric is chosen as default for the remainder of this paper, it still is important to note the absolute debt numbers before continuing. The US stands above all in absolute terms. 21.2 Trillion dollars of public debt was measured in 2018 for the US. This outweighs the 14.3 trillion dollars of public debt for all remaining countries in the sample combined.

Furthermore, in contrast to all other countries, the US seems to be on an ever increasing path of debt accumulation. This can be seen in figures 1-3. According to a recent blog of the International Monetary Fund (IMF), all developed countries are forecasted to come down in their debt to GDP ratio in the coming years. Only the US stands out and is forecasted to increase its debt position over the coming years (Gaspar & Jaramillo, 2018. p.3). This is why the US is chosen in this paper to be addressed specifically as well, next to addressing a larger group of developed countries.

This ever increasing debt level for the US consists, at the time of writing, of an absolute value of debt of over 21.2 trillion dollars. Around 15.6 trillion dollar of federal debt is public debt, this is held by individuals and corporations (40%), local or state governments (6%), Federal Reserve banks (15%), foreign governments and other entities (39%) outside the US government.2_{Around 5.7 trillion dollar is intragovernmental debt held by either/or government}

2_{Less federal financing bank securities.}

0 20 40 60 80 100 120 140 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

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trust funds, revolving funds, special funds and federal financing bank securities (US Treasury, 8/8/2018).

Next to that, the increase in debt levels for the US is driven by multiple factors. Increased government spending on infrastructure and a decrease in tax revenue are two examples (Financial Times, 20/12/2017). Next to the explicit government obligations there are other implicit obligations that are usually not recognized as official debt. Two examples are Social security and Medicare (Bohn, 2008. p. 27). Both of these are expected to increase the tax burden due to the rising dependency ratio in the US.

The following question arises if we look at the high debt-to-GDP levels: is it possible that debt has an effect on economic growth? Figure 4 and 5 give us a first insight in the relation between gross government debt3 and Trend GDP growth.

Figure 4. Debt to GDP ratio for the US Figure 5. US Trend GDP growth rate

The two variables shown in figure 4 and 5 do not seem to have a clear-cut relation. It could possibly be interpreted as an overall negative relation. Next to the above example of the relation of debt and growth for the US, the general relation between debt and growth for developed and developing countries is a topic of much debate. This will become clear in the literature review.

Furthermore, it is also of interest to see what exact effect debt on growth has, if any. Does it negatively affect the economy? To investigate this further, this paper follows the methodology of Checherita and Rother (2010).4 The research question is as follows:

3_{General government aggregated financial liabilities.}

4_{From now this 2010 paper will be referenced to as CR 2010.}

0 20 40 60 80 100 120 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2019 US Debt to GDP 0 0,5 1 1,5 2 2,5 3 3,5 4 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2019

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“What is the effect of sovereign debt on economic growth in developed countries and the US?” In their paper, CR 2010 uses a sample of 12 developed countries over the period 1970-2008 to estimate the relation between debt and growth. With this sample, CR 2010 looks to find if an empirical argument could be made that supports economic theory of debt negatively affecting growth in a nonlinear relation.

A nonlinear relation of debt to GDP and growth suggests that the coefficient of debt changes in sign (from positive to negative) as the public debt to GDP ratio increases past a certain threshold. This threshold is also called a debt turning point. This paper does not set out to find such a threshold considering the scope of the thesis. It does however try to find such a nonlinear relation for debt and growth. The nonlinear relation is relevant due to the fact economic theory suggests that it is possible for sovereign debt to negatively affect economic growth for very high levels of debt. A linear relation would in contrast have a constant coefficient of the debt to growth relation over time. In short, a linear relation does not say much about the possible negative impact of very high debt stock.

Next to the distinction of linear and nonlinear, there is a distinction between developed countries and developing countries. In the literature review both categories are extensively discussed. Furthermore, there lies a distinction between a direct relation between debt and growth and an indirect one. The direct one is the effect of debt on growth directly. The indirect relation of the effect of debt on growth can be measured by four channels: i) private saving channel, ii) investment channel, iii) Total Factor Productivity channel (TFP) and iv) the sovereign long-term nominal and real interest rates channel. These channels will be estimated separately in section 4.2 (all countries) and 4.4 (US specifically).

This paper estimates the linear, nonlinear, direct and indirect effect of gross government debt to real GDP per capita5 for the US and the remaining developed countries in the sample. It also adds an estimation that shows the importance of the span of time for estimating the relation properly. The estimations are done through multiple estimators: Pooled OLS, FE, FD, IV and SGMM.6 This is done to show the differences of all the estimators and to show possible bias in the estimations. One example of bias is reversed causality. When estimating if debt has an impact on growth one needs to take into account that growth also has an effect on debt. One possibility to correct for such endogeneity is to use the instrumental variable estimator (IV).

5_{Per capita: per head of the population.}

6_{Short for: Pooled Ordinary Least Squares, Fixed Effects, First Differencing, Instrumental Variable and}

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Moreover, this paper hopes to add to the existing literature by using a sample of 16 developed countries over the period 1965-2019. Note that the period is extended by using projections for the years 2018 and 2019. When compared to the paper of CR 2010, an additional four countries are added to the dataset and the timespan of the data is lengthened by 16 years. The added countries are: Denmark, Sweden, UK and the US.

Finally, the paper is structured as follows. In section 2 a literature review is presented in which an overview of existing literature with regards to the debt-growth relation is presented. Section 3 describes the methodology that this paper uses in estimating the debt-growth relation. The results of the estimations are then presented in section 4. Finally, the conclusion of this paper is presented in section 5.

2. Literature Review

This literature review aims to provide additional insights into the specifics of the indirect effect of debt and growth by explaining the theory behind the channels through which debt affects growth: i) private saving channel, ii) investment channel, iii) Total Factor Productivity channel (TFP) and iv) the sovereign long-term nominal and real interest rates channel. This is presented in sections 2.1.1 - 2.1.4. These indirect effects are part of the estimations that are performed and presented in section 4 for both the US and the remaining European countries. It might therefore be of relevance to understand the economic theory underlying it.

In addition, a disquisition of comparative literature on the debt- growth relation is presented in section 2.2. In this disquisition, a number of distinctive features of the papers are brought forward: the nature and the period of the samples, the methods of estimation, the nature of debt (public or private), the (in)direct effect of debt measured, the channels, and the debt turning points. Finally, the overall findings of the papers are presented. At the end of section 2.2, table 1 is presented with an overview of all of the features mentioned above, relative to the authors and papers associated with them.

Finally, section 2.3 presents the underlying reasons for this paper to focus on one methodology in particular. This methodology is similar to the methodology presented by CR 2010.

2.1. The four debt-growth channels

The implications and the interpretation of a certain estimation method are dependent on the theoretical basis underlining it. For instance; using a regression method to see if two variables are correlated only gives us a technical understanding of a possible correlation. However, this

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does not imply a causal relation. This causal relation needs to find root in theoretical understanding instead of economic methods. The relation between debt and economic growth should therefore first be grounded in economic theory before we continue with a technical analysis. Sections 2.1.1 – 2.1.4 provides economic theory relating to the indirect effect of debt on growth.

2.1.1. Private saving channel

The first channel mentioned by CR (2010, p. 6) in their working paper for the ECB (European Central Bank) is the private saving channel. Private saving and high debt levels are interrelated in the following way: the removal of deadweight debt7_{could possibly increase the propensity} to save for households (CR, 2010, p.11). In the economic theory developed by Meade, there is the so called Pigou-effect (Meade, 1958. p.166). It assumes that if debt were to be removed by raising capital tax revenue, the net income of a citizen would remain the same but the incentive to save of such a citizen would increase as the value of his property had been reduced. These added savings could be impetus for increased private investment. Moreover, private investment is believed to be a driver of economic growth.

2.1.2. Investment channel8

If it were the case that personal properties would reduce in value due the increase in capital taxes, it is likely that the incentives to work increase (Meade, 1958. p.166). Such incentive to increase work will stimulate labor supply. This will translate into increased marginal productivity of labor and consequently stimulate the economy.

Note that there is an optimal tax revenue level when it comes to taxation. There is a separate literature on the calculation of this level that extends beyond the scope of this thesis. A general inference could be made by look at the following figure. Figure 6 represents the Debt Laffer curve (Laffer, 2004. p.2). The intuition behind the curve is that increases in tax revenue will eventually reach a turning point. Surpassing this level of

tax-revenue optimality, incentives to work will decrease and consequently have a negative effect on the economy. This is similar and closely related to the nonlinear relation between debt and

7_{Deadweight deb: a debt that is incurred to allow for contemporaneous spending without being related to a}

value-adding asset. A case can be made that a share of national debt is deadweight debt due to government failure, i.e. economic inefficiency caused by government intervention.

8_{This is sometimes also referred to as the capital accumulation channel. A high debt stock could deter}

investment incentive and therefore reduce capital accumulation.

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growth. As mentioned before, both the linear and the nonlinear effect of debt on growth will be estimated in this paper. A nonlinear relation implies that increases of debt in the first instance have a positive effect9_{on growth until it eventually reaches a debt turning point. After this} point, the sign switches from positive to negative. All four of the channels are possible determinants of the sign switch.

One other possible explanation for the sign shift is the argument of debt overhang. Debt overhang occurs when “the inherited debt of some countries is larger than the present value of the resource transfer that their creditors expect them to make in the future” (Krugman, 1988. P.29). In this case, the country is not able to pay all of its obligations and consequently loses the incentive for reform. In this case, it will be in the investor’s interest to forgive a part of the debt in order to increase the probability of repayment of the remaining debt.

Moreover, a higher debt stock is closely related to a higher interest payment obligation. Simply put, the cost of borrowing will go up as debt stock increases. This could affect public expenditure and investment to decrease since a larger share of income has to be allocated to interest payment obligations. Then again, as debt stock diminishes, the cost of borrowing goes down which could incentivize fiscal policymakers to accrue more debt.

In addition, if the interest payment size increases due to a larger debt stock, the probability of country’s ability to fulfill such debt obligation decreases. This, in turn, increases a country’s probability of defaulting on its debt obligation. This increase in the probability of default will disincentive investors from taking on of debt.10_{In such a way, deadweight debt} could cause crowding out of public and private investment (CR, 2010. p. 11). This decrease in investment could consequently be deleterious for economic growth.

2.1.3. Total factor productivity (TFP) channel

TFP is the measure of the efficiency of all inputs to a production process. Technological improvements are often regarded as a sub-section of TFP.

Certain inefficiencies could therefore negatively affect TFP. Tax inefficiencies are one example. Meade mentioned that deadweight debt could have negative effects on production due to an implicit increase in future income taxation. This would be caused by interest payments that need to be met with such debt (1958, p.167). According to the concept of Ricardian equivalence, there is a seemingly net transfer of value going from the worker to the government

9_{At first the sign is positive due to capital mobility gains. This affects transitional growth positively (Patillo et}

al., 2002. p.12).

10_{This is similar to the case of debt overhang mentioned earlier. This latter argument is specified to new}

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if a government decides to take on debt. This is due to the fact that we expect the worker to be rational. With a rational forward-looking perspective, a worker would expect future increases in taxation to meet the costs of current excessive borrowing. This is a possible explanation for explaining why the worker would not change his/her working attitude. This, again, results in a seemingly net transfer of value going from the worker to the government. However, due to tax raising costs11, there is an overall loss in efficiency. This is an example of taxation inefficiencies affecting TFP.

Another claim that could be made is as follows. The efficiency of the input of investment could also be negatively affected. If policy makers believes that certain reforms, such as trade liberalization and fiscal adjustments, will mainly benefit foreign creditors, they might lose incentives to go through with these reforms. It is an example of a moral hazard problem that negatively affects the investment climate. This in turn, affects TFP and consequently economic growth negatively (Patillo et al. 2002. p.5).

2.1.4. Sovereign long-term nominal and real interest rates channel

As mentioned in section 2.1.2, interest size could be deleterious for growth. In addition, long-term interest rates could crowd out private investment as well. This is based on the theory that high debt levels increase interest rates. The empirical corroboration of this assumption is however diverse. There are studies that suggest that high debt and deficits could play a part in the rise of public long-term interest rates and default risk premiums (Ardagna et al. 2007, p.21), Laubach (2009. p.881), Codogno et al. (2003. p.526). The premise is that if debt levels are such that they increase the probability of default, the private investor will want a risk premium for the increase in default probability. This in turn will increase the flow of capital out of the private sector into the public sector. This in turn might lead to an increase in the private interest rates and have a diminishing effect on private spending (Elmendorf & Mankiw, 1999. p.36).

2.2. Empirical debt-growth literature

The topic of debt has long been an interesting field in economics as its outworking can directly affect policy. Some politicians gladly adhere to certain economic inferences that suggest expansive fiscal policy to the detriment of the governmental budget balance. Papers that are brought forward by politically-linked institutions therefore deserve additional scrutiny. A few of the papers in the review are from the IMF and the benchmark paper is from to the ECB.

One of the ways to nuance findings on the relation between debt and growth is to compare different studies and see how they differ, if at all. It is for this reason that a disquisition

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of comparative literature is presented in the following paragraphs. The content of the literature review contains 8 influential papers over the period 2002-2014. In these 8 papers, 11 samples are used. 5 Of these are samples of developing nations and the remaining 6 are samples of developed (industrialized) nations. Next to differences in samples, there are differences in: methodology, sample periods, distinguishing linear/non-linear relations, distinguishing direct/indirect effects, differences in debt-turning points etc.12 Note that the content the different papers are presented in a semi-chronological order.13

In their working paper for the IMF, Patillo, Poirson and Ricci research the non-linear effect of external debt on growth.14 They did so using a large dataset of 93 developing countries over the period 1969-1998 (Patillo, Poirson & Ricci, 2002, p.1).15 Patillo, Poirson and Ricci both use 3-year- and 10-year averages to correct for the effects of short run fluctuations and to check the robustness of the findings respectively. In their paper they estimate a dynamic panel data model with economic growth per capita as the dependent variable. The explanatory variable used is external debt16, the control variables are: lagged income per head of the population, the rate of investment, school enrollment, population growth, total factor productivity, openness, fiscal balance and terms of trade in growth terms (2002, p. 9). The model specification is estimated by using a comparable set of estimators that is also used in the CR 2010 paper. The first one is pooled OLS estimation. This estimation is highly likely to be biased since the method does not correct for endogeneity problems that might occur. Hence the second estimation method is done using the instrumental variable method. Schooling, investment, fiscal balance, openness and debt variables are all instrumented in order to prevent possible reversed causality bias. The instruments used are the lagged values of the endogenous regressors. These instruments could turn out to be ineffective if the endogenous regressors are persistent (Panizza & Presbitero, 2014. p.23). Moreover, the first two methods fail to account for the presence of country effects which in turn may affect the estimation by an omitted variable bias. The third estimation method used is the Fixed Effects method. This method distinguishes itself by allowing countries to have different intercepts. Lastly, Patillo, Poirson and Ricci use the System Generalized Method of Moments (SGMM) estimation for efficiency gains and to correct for endogeneity.

12_{See table 1 for a general overview.}

13_{The order is semi-chronological in the sense that it has exceptions for directly interrelating papers.}

14_{External debt is the amount of debt a country owes to foreign creditors. This consists of government external}

debt and private external debt.

15_{The These are countries from the regions Sub-Saharan Africa, Asia, Latin America and the Middle East}

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All four methods show an almost always negatively signed coefficient for the case in which the specification is linear and in half of the cases the coefficients are significant (2002, p.13). In addition, economic theory suggests that the relation between debt and growth is a non-linear one (see section 2.1.2). With this in mind, Patillo, Poirson and Ricci developed a nonlinear specification of the model using three steps. The first step is to include dummies into the regression to measure the level of debt where the sign of the explanatory variable (debt) becomes negative. The second step is there to find the marginal impact of debt on growth. This is done by employing a quadratic specification. This is to distinguish debt and debt squared. Finally, forming a spline specification is the third step. It allows to estimate the regression with a structural break. This break is in the locus of the debt turning point, i.e. the point where the sign of the impact of debt shifts from positive to negative (Patillo, Poirson & Ricci, 2002. pp. 14-15).

Having formed this new specification, Patillo, Poirson and Ricci found that debt appears to have a nonlinear effect on growth for their sample of developing countries. The debt turning points for these countries, on average, seem to lie around 35-40 percent of debt to GDP ratio. Furthermore, the results of the paper suggest that per capita growth would decrease by 0.5 to 1 percentage points if debt stock would double in size. These results are insightful but the authors also mention that it was hard to estimate accurately due to the limited variation that they could find in the data (2002, p.19). Lastly, they also mentioned that the quality of the data on the debt service variable looks questionable (2002, p.8). These disclaimers might possibly weaken the argument for a strong negative non-linear relation between debt and growth for developing countries in the sample of Patillo, Poirson and Ricci.

Patillo, Poirson and Ricci continued to study this topic and wrote another working paper for the IMF in 2004. In this paper they tried to distinguish the direct effect of debt on growth from the indirect effect of debt growth through two channels: i) the capital-accumulation channel and ii) the total factor productivity channel (2004, p. 3). These channels are near the same as two of the four channels described in the benchmark paper CR 2010. They differ however in a small distinction that is made for the first channel. This capital-accumulation channels is further split into physical-capital accumulation and human-capital accumulation. The methodology that is used in the 2004 paper is similar to that of the 2002 paper. The difference in the methodology namely lies in the estimation of the two channels. This is done through a method called growth-accounting. In this method output growth is decomposed such that a distinction can be made of the different contributions that the two channels have. It gives a detailed account of the main drivers that form growth of output per capita (2004, p.10). It

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does so by specifying the model in such a way that it is consistent which macro-fundamentals but shows the individual drivers of growth. This makes it possible to estimate the indirect effects of the channels in one model.

Moreover, Patillo, Poirson and Ricci add several different debt variables to capture the debt overhang effect. The total external debt stock variables comprise of the face value of debt stocks and the net present value of debt. Next to that, the contemporaneous debt service to exports ratio is also added as a control variable in order to isolate a crowding out effect. Both the debt overhang effect and the crowding out effect are directly linked to the first channel: the capital accumulation channel (see section 2.1.2 for details on the crowding out effect). Another part of the capital accumulation channel is human capital. This was measured by adjusting the workforce in such a way that it is corrected for education improvements of 7 percent of return for every additional year of schooling. This assumption was based on micro economic theory and empirical findings (2004, p.10).

Overall, the analysis uses panel regression for 61 developing countries over the period 1969-1998 which is somewhat similar but smaller compared to the dataset used in their paper of 2002. In their conclusion, Patillo, Poirson and Ricci find a result that is consistent with their previous study. On average, they find a direct large negative impact of debt on growth. Furthermore, doubling the debt from the debt turning point onwards will reduce growth per capita by about 1 percentage point (2004, p. 18).

The indirect effect of debt on growth, through the two channels, is similarly a negative relation. Both channels appear to have a strong negative relation with similar sizes of the effects of the relation. This however is not the case for the human-capital part of the total capital accumulation channel. This effect seems to be very small and insignificant. Moreover, close to one-third of the effect of debt at high debt stock levels is attributable to the physical-accumulation part of the physical-accumulation channel. Two-thirds is attributable to the TFP growth channel (2004, p.19).

Another study, written by Schclarek in 2004, is more in line with the results that Panizza and Presbitero brought forward in their paper written in 2014. In this paper, Schclarek attempts to study the relation of debt on growth through using both a developed countries-sample as a developing countries-sample. The samples consist of 59 developing countries and 24 developed countries. The data is averaged over a total of seven non-overlapping 5-year periods in the range of 1970-2002 (2004, p.6). In addition to examining the direct impact of debt on growth, Schclarek also estimates the indirect effect of debt on growth using three channels: TFP, capital stock growth rate per capita and the private savings rate. The four dependent variables of the

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study therefore are: real GDP growth per capita and the three aforementioned variables. This is very similar to the four channels brought forward in this paper and which were used in the model of CR 2010: private saving, public investment, TFP and sovereign long-term nominal and real interest rates (2010, p. 6).

Schclarek uses 15 debt indicators for the developing countries to form the explanatory debt variable. With regards to estimations, he forms 5 different sets of different explanatory and control variables. The first set controls for convergence by using the initial income per capita and the average years of schooling. The second set is an enhancement of the first set by adding the variables government size, inflation and openness to trade. The third set adds a variable for financial intermediary development. The fourth set adds the variable investment to GDP and population growth. Finally, the fifth set adds terms of trade in growth terms and fiscal balance to the regression (2004, p.7).

Furthermore, Schclarek estimates both the linear and the nonlinear effects of both public and external debt on growth. He finds a clear significant negative linear effect of public debt on growth for all sets except for set 2 for developing countries. Moreover, it seems that the relation is insignificant when it comes to private debt for developing countries. High levels of private external debt therefore do not seem to have a significant negative effect on growth (2004, p.9). Next to that, Schclarek mentions that his finding of a nonlinear effect of private debt on growth for developing countries is in stark contrast to that of the finding of Patillo, Poirson and Ricci in 2002. Schclarek performs the same nonlinear estimation while using the total external debt-to-GDP ratio with different debt turning points. However, he found no evidence to support an inverted-U shape relation between external debt and growth. Either the differences in the debt-turning points and/or the fact that Schclarek used 5 different sets to estimate the relation are a possible explanation for the discrepancy. He mentioned that only the fifth set directly corresponds to the Patillo et al. paper in a comparative way (2004, p.9).

Moreover, Schclarek did not find any robust negative linear or non-linear relation between public debt and growth for developed countries (2004, p. 15).

Reinhart & Rogoff used a different approach to assess the relationship between debt and growth. In their 2010 paper, they used samples for both developed countries (20) and developing (24) countries. These samples were extended in such a way that an historical analysis could be made. The time period for the sample of developed countries spanned between the years 1790-2009. The time period for the sample of the developing countries spanned between the years 1900-2009. In the paper, Reinhart and Rogoff look at the connection between

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public debt and average- and median growth outcomes (2010, p. 6).17

With regards to advanced countries, the authors distinguish the public debt to GDP data into 4 categories: i) up to 30%, ii) 30%-60%, iii) 60%-90% and iv) 90% and over. They then proceed to combine each category with the average- and median GDP growth that occurs in such a category. Then they point out that the fact that only the last category has a negative sign with respect to GDP growth (around -0.2). This is a remarkable finding since all other three categories have a positive average and median growth rate in the range of 2.8% to 4%. Note that they specifically made a comparison just for the United States. They found that the US has a lower growth rate in the fourth category than the average of all 20 developed countries. This growth rate was in the range of -.9% to 1.8% (2010, p. 10) compared to the range of 3.2% to 4% growth for all other three categories.

The sample for developing countries showed a striking resemblance with regards to the developed countries sample. They found that the first three categories fits the range of 4% to 5% of growth whereas the fourth category drops to the range of 1% to 3% of growth for the average and median levels.

Moreover, the average level of inflation for both samples increases from the range of 3.5% - 5% in the first category to a range of 6% – 17% in the fourth category (2010, p.14). Overall, Reinhart & Rogoff claim to have a found a distinct negative impact of debt on growth for both developed and developing countries when they pass the debt turning point of a 90% debt to GDP ratio (2010, p.22).

Herndon, Ash and Pollin replicated the research of Reinhart and Rogoff 2010 in 2013. In their paper they describe how Reinhart and Rogoff made significant measurement errors which corrupted their findings (2013, p.1). It is a critical analysis of the methods adapted by Reinhart and Rogoff in 2010. For example: they state that if the data were to be properly calculated, the actual differences in decreases of growth rates for developed countries in category 4 would be less negative, 2.2% instead of -0.1% (2013, p. 6). Herndon, Ash and Pollin list a number of faults they discovered in Reinhart & Rogoff 2010: data gaps, selective exclusion of available data, spreadsheet coding error, excluding 14 country-years out of 110 country-years in category 4 and weighing variables inappropriately while calculating summary statistics (2013, pp. 6-10). Reinhart & Rogoff later admitted the faults in their paper.

When all of the above are accounted for, the results of the analysis changes. There seems to be no clear debt turning point at a public debt to GDP level of 90%. Moreover, there is no

17_{In the figures presented in the Reinhart & Rogoff paper, there is also an inflation variable which is used to}

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sharp decline in growth rates in the corrected estimation past the debt turning point of category 4 (90%). Overall, Herndon, Ash and Pollin did not find any evidence, using the Reinhart & Rogoff methodology, to support the claim that high debt levels, both for developed and developing countries, have a strong negative impact on real economic growth (2013, p. 22). The “Impact of high and growing government debt on economic growth” paper of the ECB is the lead example for the empirical approach of this thesis (CR, 2010). In this paper, Checherita and Rother use a sample of 12 developed countries in the euro area over the period 1970-2008.18 While using this sample, CR 2010 distinguishes a linear relation from a nonlinear relation of debt to GDP and finds theoretical literature to support the last relation (2010, pp.10-11). Furthermore, they specify their empirical growth model to include a public debt to real GDP variable. Next to that, they add the following control variables for their basic estimation of a direct linear effect of debt on growth: fiscal indicators, long-term real interest rates, trade openness indicators, saving/investment rates, population growth and country and year- fixed effects. Most of the data are from the Annual Macro-Economic (AMECO) database (2010, p. 13).

Panel fixed-effects is the estimation technique used by CR 2010 for the basic estimation. CR 2010 further corrects for possible ‘reversed causality’ bias by adding instruments and estimating either through the Instrumental Variable (IV) method or the GMM method. The instruments are: i) up to 5 lags of the endogenous regressor (public debt as a percentage of GDP) and ii) the average of the public debt to GDP ratio of all other countries in the sample.

Using lagged variables is somewhat problematic since debt and growth tend to be persistent. This in turn could be detrimental for the exogeneity condition of the instrument. Also, instrument ii needs additional reservation when the following is taken into account. There is a possible spillover effect in the case of a global crisis. This means that the instrument could be endogenous because there is a link between debt levels of countries (2014. p. 23), since all countries endure the same shock. To account for possible persistence, CR 2010 also applies the First Differencing (FD) estimator (2010, p. 15).

Finally, CR 2010 describes four different channels that might indirectly affect economic growth: i) private saving, ii) public investment, iii) TFP and iv) sovereign long-term nominal and real interest rates. Since CR 2010 is somewhat of a benchmark paper with regards to this paper, more information on the methodology and the results of the channels is found in chapter 3. Furthermore, the empirical findings of CR 2010 show a highly significant non-linear relation

18_{Countries: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands,}

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between gross debt and economic growth per head of the population. Moreover, they found that at a certain debt turning point, the sign shifted from positive to negative. This meant that, above this turning point, gross debt had a negative effect on economic growth. Their robust conclusion is that the turning point lies in the range of a similar finding (Reinhart & Rogoff), namely between 90 and 100% of the debt to GDP level. The confidence interval on the lower bound shows that even a debt turning point of 70% debt to GDP is probable. Moreover, the results are less convincing when it comes to a linear relation between public debt and real GDP per capita. The results show that the linear relation is insignificant (2010, p. 23).

A more recent study on the effect of debt on growth was done by Lof and Malinen at the university of Helsinki (2013, p.1). They focused on developed countries rather than developing countries. In contrast to the benchmark paper CR 2010, Lof and Malinen found no clear negative relation between debt and growth. Both studies seem to use a sample with a comparable set of countries. Lof and Malinen use a sample of 20 developed countries of which (near) all 12 countries that are in the sample of CR 2010 are encapsulated in it. Only Luxembourg is left out (2013, p.3). Their time series extend to 1905-2008 for a subset of 10 countries and the remaining countries is comprised of annual data from 1954-2008.

They make a case, by their own account, that a dynamic model, such as a Vector Autoregressive Model (VAR), is suitable for estimating such long-run effects. They then use this panel VAR model to compute impulse-response functions between the dependent and independent variable: the growth rate of real GDP per capita and the growth rate of total gross government debt per capita respectively.

Before the panel VAR is estimated, they apply first-differencing. As the fixed effects drop out of the model, Lof and Malinen continue by estimating the differenced model using GMM. The lagged values of the endogenous regressors function as instruments (2013, p.4).

The result in the paper by Lof & Malinen suggest that the effect of debt on growth is “ambiguous, at best”. They did not find any long-term effect for any level of debt. This is a direct opposite of the findings of CR 2010. The estimation approach of Lof & Malinen however differs starkly. They only use a Vector Autoregressive model to show the significance of the direct effects. Furthermore, they find that the inverse, the effect of GDP per capita growth on debt, has a statistically significant negative effect (2013, p. 7). Moreover, they mention that the VAR method is not very informative when it comes to estimating the indirect effect of debt on growth through channels.

The last study examined in this paper, published in the Journal of Macroeconomics, found that it was simply unknown what the effects of public debt on growth are (Panizza &

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Presbitero, 2014. p.36). Panizza and Presbitero attempted to estimate the effect of debt on growth by using a different type of instrument in their instrumental variable estimation. Usually, a lag of the explanatory variable is used as an instrument when performing an instrumental variable analysis. Panizza and Presbitero decided to take a different approach. The instrument that they brought forward is a variable that encapsulates valuation effects that are brought about by exchange rate volatility. This is done through the matching of a detailed account of all currencies, in which the foreign debt is denominated, with data on bilateral exchange rates. It assumes that there is a direct effect of a country’s exchange rate on the debt to GDP ratio. This assumption is met in the presence of foreign currency debt (Panizza & Presbitero, 2014. p. 22). Most developed countries hold a share of some form of debt denominated in foreign currencies. The US specifically has a public debt position of which 30% of their debt is held by foreign investors (US Treasury, 8/8/2018). However, this debt is not denominated in foreign currency. There are other developed countries for which this is the case: France, Germany, Japan and the Netherlands (Panizza & Presbitero, 2014. p.24). A change in these foreign currencies would therefore not directly affect such a country’s debt position. This is a problematic feature of the instrument since it is not applicable to all developed countries and therefore does not provide any general inferential information. It is important to note that Panizza and Presbitero focused on developed countries rather than developing countries. In their sample they included seventeen OECD countries for the period 1993-2014.19_These countries are near identical to the countries that are used in the sample of CR 2010.

Furthermore, there is another problem with the instrument that they propose. A good instrument is both relevant and exogenous. Panizza and Presbitero show that their instrument is relevant for most countries in the sample by performing multiple weak- instrument tests. They fail however to prove that their new instrument is exogenous. This is due to the fact that valuation effects are axiomatically correlated with the exchange rate. This is problematic because the exchange rate might have an effect on economic growth. In their paper, Panizza and Presbitero try to correct for this problem by controlling for debt composition and for the exchange rate. Furthermore, they use a Bayesian method to make the case that small deviations from the exclusion restriction do not entail a significant bias in the estimation result (Pannizza & Presbitero, 2014. p. 22).

In their main regression, Panizza & Presbitero regressed the public debt to GDP ratio on the average growth of real GDP per capita (2014, p. 26). Similarly to CR 2010, they added

19_{Countries: Australia, Austria, Belgium, Canada, Germany, Denmark, Spain, Finland, France, Great Britain,}

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country and year fixed effects and a matrix of control variables. The control variables enlisted in the Panizza and Presbitero regression are: national gross savings, population growth, schooling, trade openness, inflation rate, dependency ratio, banking crisis and liquid liabilities/GDP. The main difference is the correction of the banking crisis control variable which is not used in the CR 2010 regression. Also, an important distinction is that Panizza and Presbitero fail to account for possible indirect effects of debt on growth by omitting any of the four channel variables that are encapsulated in the CR 2010 main regression. Furthermore, the main regression of Panizza and Presbitero is performed using an instrumental variable estimator with the variable valuation effects as instrument.

Their estimation however did not show a clear result. They did not find that debt, in the medium-run, had a negative effect on growth for advanced countries. Moreover, they recognized that the models used are never perfect and that it involves tradeoffs between efficiency and consistency (2014, p.37). Next to that, they could not find a convincing empirical proof of a link of causality between debt and growth in comparable literature. This finding finds resemblance in the Schclarek paper mentioned earlier.

Lastly, they make the distinction that debt could have a negative effect on growth in a theoretical sense. Namely, if fiscal policy is such that it puts in place restrictive fiscal policy to correct for the possible volatility of the market, it might be deleterious for growth (2014, p.38). 2.3 Chosen methodology

CR 2010 is chosen in this paper as the benchmark paper20 for the following reasons. The first reason is that it is a relatively recent paper. It was written in 2010, in the aftermath of the 2008 global financial- and economic crisis, and after a number of papers that were mentioned in section 2.2. The second reason, is that its methodology was adjusted to developed countries rather than developing countries. This was helpful since the US is a developed nation. Finally, the last reason that the CR 2010 methodology was chosen, was due to the fact that they sought to estimate the direct, indirect, linear and nonlinear relations between debt and growth.

The next page shows table 1 in which a general overview of all of the papers mentioned above is given.

20_{In the sense that the methodology of this paper follows most of the empirical approach that is described in}

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23 R em ar k s Un reliab le d ata _- _Inco m p lete set o f Pu b lic d ata. _Measu rem en t e rr o rs n o t ac co u n ted fo r R ep licatio n o f R ein h ar t & R . 2 0 1 0 - On ly lo n g -ru n In str . E n d o g . - Deb t tu rn in g p . 35 -4 0 % d eb t-GDP 35 -4 0 % d eb t-GDP - - 90 % d eb t-GDP 90 % d eb t-GDP un clea r u n clea r 7 0 % d eb t-GD P 9 0 % d eb t-GDP - - In d ir ec t r elatio n th ro u g h ch an n els C h an n el relatio n - 2/2 n eg . an d s ig n . 1 /3 n eg . an d s ig n . 1 /3 n eg . an d s ig n . - - - - ¾ n eg . an d sig n . - - 2/4 n eg . an d s ig n . # ch an n els - 2 3 3 - - - - 4 - - 4 Dir ec t r elatio n p u b lic d eb t to GDP No n l. relatio n - - Lim ited su p p o rt In sig n . - - - - Sig n . - - Inco n clu si ve L in ea r relatio n - - Neg . & 5 /5 sig n . Po s. & 1 /5 sig n . Dec r. Ab o v e th r. Neg . Ab o v e th r. Mo d er ate ∆ ab . th r. Mo d er ate ∆ ab . th r. Neg . & In sig n . Po s. & in sig n . In co n clu si ve - Dir ect relatio n p riv ate d eb t to GDP No n l. relatio n Sig n . Sig n . L im ited su p p o rt In sig n . - - - - L in ea r relatio n Neg . & ½ sig n . Neg . & ½ sig n . Neg . & 1 /5 sig n . - Dec r. Ab o v e th r. Neg . ab o v e th r. Mo d er ate ∆ ab . th r. Mo d er ate ∆ ab . th r. - - - - T able 1. L it er at u re ov er v ie w Me th o d OL S/IV/FE /GMM OL S/IV/FE /GMM 5 s ets 5 s ets 4 ca teg o ries 4 ca teg o ries rep l. 4 ca teg o ries rep l. 4 ca teg o ries FE/I V/GM M/FD FD/GMM -VAR IV OL S/IV/FD /FE/GM M Per io d 1969 -1 9 9 8 1969 -1 9 9 8 1970 -2 0 0 2 1970 -2 0 0 2 1790 -2 0 0 9 1900 -2 0 0 9 1790 -2 0 0 9 1900 -2 0 0 9 1970 -2 0 0 8 1905 -2 0 0 8 1993 -2 0 1 4 1965 -2 0 1 9 Sam p le 9 3 d ev . 6 1 d ev . 5 9 d ev . 2 4 i n d u str . 2 4 d ev . 2 0 in d u str . 2 4 d ev . 2 0 in d u str . 1 2 in d u str . 20 in d u str . 1 7 i n d u str . 1 6 in d u str . Patill o et al. 2002 Patill o et al. 2004 Sch clar ek 2004 Sch clar ek 2 004 R ein h ar t & R . 2010 R ein h ar t & R . 2 0 1 0 Her n d o n et al. 2 0 1 3 Her n d o n et al. 2 0 1 3 C R 2 0 1 0 L o f & M. 2013 Pan izza & P. 2 0 1 4 T h is p ap er

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3. Methodology

In the introduction and the literature review we saw that there are multiple ways of looking at the debt-growth relation. Moreover, we saw a number of estimation methods that were used by different papers. As mentioned in section 2.3, the chosen methodology of this paper is very similar to the CR 2010 methodology. This will become clearer in sections 3.1 and 3.2. The methods to estimate both the direct and indirect effect of debt on growth are described in these sections respectively. Section 3.3 provides insights into possible bias in the estimation and section 3.4 describes the error term characteristics. Finally, section 3.5 presents all the limitations of the datasets that are used.

3.1. Estimation models

It is important to specify that most researchers on the debt to growth relation believe that the relation between debt and growth has a nonlinear nature. A nonlinear function, as is mentioned in section 2.1.2, has a debt-turning point at which the sign of the effect of debt changes from positive to negative (CR, 2010. p. 9). The turning point of debt relative to GDP is believed to be around 90% for developed countries (see table 1).21 A linear form of debt does not show a significant result in the effect of debt on growth in the CR 2010 paper. That is why the following equation holds a quadratic form of debt as well. Using this quadratic form, we can see the non-linear relation as well as the non-linear relation of debt and growth. The estimation equation in this paper is similar to the equation used by CR (2010, p. 13).

The independent variable (regressor) is the gross government debt per capita relative to GDP. Furthermore, there are multiple control variables in order to correct for omitted variable bias: the cyclically adjusted government revenue (a proxy for the average tax rate), population growth, the public and private saving rate, trade openness and the long-term real interest rate. The basic estimation equation is as follows:

𝑔_𝑖 = 𝛽₀+ 𝛽₁𝑑𝑒𝑏𝑡_𝑖𝑡2 + 𝛽₂𝑑𝑒𝑏𝑡_𝑖𝑡+ 𝛾₁𝑔𝑜𝑣_𝑟𝑒𝑣_𝑐𝑎𝑝_𝑖𝑡+ 𝛾₂𝑝𝑜𝑝_{𝑔𝑟𝑜𝑤𝑡ℎ}+ 𝛾₃𝑠𝑎𝑣𝑖𝑛𝑔_𝑝𝑢𝑏+ 𝛾₄𝑠𝑎𝑣𝑖𝑛𝑔_𝑝𝑟𝑖𝑣 + 𝛾₅𝑜𝑝𝑒𝑛𝑛𝑒𝑠𝑠 + 𝛾₆𝑙𝑡_𝑟𝑒𝑎𝑙_ + 𝜃_𝑡+ 𝜌_𝑖 + 𝜀_𝑖𝑡

Where 𝑔𝑖 represents the GDP growth rate per capita, 𝑑𝑒𝑏𝑡𝑖𝑡 is the gross government debt relative to GDP, 𝛾₁₋₅… are the control variables (mentioned above), 𝜃_𝑡 are the time fixed effects, 𝜌𝑖 are the country fixed effects and 𝜀𝑖𝑡 represents the error term.

There are multiple estimation techniques available to estimate the above relations. In

21_{As was mentioned in the introduction, the calculation of the debt turning point extends beyond the scope of}

this thesis. For more information on the calculation of the debt turning point, see (Patillo, Poirson & Ricci, 2002. pp. 14-15).

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this paper we will use the following estimators: OLS (pooled), Panel-fixed effects (FE), two staged least squares/Instrumental Variable estimation (2SLS/IV), System Generalized Method of Moments (SGMM), and First-Differencing (FD).

In pooled OLS all data points are used in a regression to see what the relation is between multiple variables. This is a simple estimation technique that can give us a quick indication of certain behaviors of variables over time. However, the technique is quite rough and can easily be misinterpreted. This could happen because all data points are pooled together to form one regression line. Even though OLS is likely to be biased, it does give a good benchmark which could be useful when comparing the different estimators. A basic equation of OLS:

𝑌_𝑖 = 𝛽₀ + 𝛽₁𝑋_𝑖 + 𝛽₂𝑊_1𝑖+ 𝛽₃𝑊_2𝑖… + 𝛽_1+𝑟𝑊_𝑟𝑖 + 𝜀_𝑖𝑡22

Where 𝑌_𝑖 is economic growth, 𝑋_𝑖 is the gross debt level, 𝑊_𝑘𝑖23_{are the control variables and 𝜀} 𝑖𝑡 is the error term. The difficulty with this method is that it does not account for possible differences between countries (heterogeneity bias). Panel-fixed effects (FE) is an estimation technique used to mitigate the heterogeneity bias mentioned in the above paragraph. It does so by including entity fixed effects in the regression (Stock & Watson, 2012. p.396). These unknown intercepts (one for each country) vary across countries but not over time.

The third estimation technique used in this paper is an instrumental variable regression (2-SLS/IV) (Stock & Watson, 2012. p.763). OLS and FE are insightful but are not fully encapsulating the relation between debt and growth. One of the reasons is that it is prone to be biased by the possibility of reversed causation. Normally, a Vector Autoregressive model would be sufficient to correct for this endogeneity problem. However, it also possible to use an instrument in an instrumental variable regression (2-SLS/IV) (Stock & Watson, 2012. p.763). The instrument variable in that case is correlated with an endogenous regressor (instrument relevance) and is uncorrelated with the regression error (instrument exogeneity) (Stock & Watson, 2012. p. 808). The strength of the instrument then determines the value of the instrument in explaining the dependent variable. This allows for a regression without the endogeneity problem of simultaneous causality which is present in Pooled OLS and FE.

There are two instruments used in this paper for the endogenous variable (gross debt) in order to mitigate the endogeneity problem of reversed causality. The first one is the time lag of the independent variable up to the 5th_{lag. The second one is the average debt of all the other} countries in the sample. These are the same instruments used in the CR 2010 paper.

22_{Typical OLS model (lecture 3, applied econometrics).}

23_𝑊

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Another estimation technique used in this paper is the System Generalized Method of Moments (SGMM). This method is believed to be a more efficient estimator than the 2SLS estimator due to its additional weighting matrix (CR, 2010. p. 14). In addition, SGMM is more efficient than the Differenced Generalized Method of Moments (DGMM), especially in case of weak instruments. DGMM takes moment conditions from the estimated first differences of the error term (𝜀_𝑖𝑡). SGMM does this as well and also of the levels of the residuals. Hence the increased efficiency (Stock & Watson, 2012. pp.768-772). Note that it is possible that GMM shows inconsistency in its estimations when the series are highly persistent (Panizza & Presbitero, 2014. p.23).

One way to estimate a persistent series is to use First-Differencing. Hence, the last estimation technique used in this paper, is the First-Difference method by which the first difference of a time series variable is taken and regressed upon (𝑌_𝑡− 𝑌_𝑡−1= 𝛿𝑌_𝑡∗) (Stock & Watson, 2012. p. 807).

3.2. Channel equations

In this section, the equations for the different channels with their corresponding control variables are presented. Note that in some of the cases lagged values are used. This has to do with the fact that some of the variables do not instantly affect the dependent variable. Furthermore, table 17 in the Appendix shows the abbreviations for all of the control variables mentioned below.24 The channel equations are as follows:

Equation 2 (channel 1: private saving ratio)

𝑠𝑎𝑣𝑖𝑛𝑔_𝑝𝑟𝑖𝑣𝑖𝑡 = 𝛽0+ 𝛽1𝑠𝑎𝑣𝑖𝑛𝑔_𝑝𝑟𝑖𝑣𝑖𝑡−1+ 𝛾1𝑑𝑒𝑏𝑡𝑖𝑡−12 + 𝛾2𝑑𝑒𝑏𝑡𝑖𝑡−1

+ 𝛾3𝑔𝑜𝑣_𝑟𝑒𝑣_𝑐𝑎𝑝𝑖𝑡−1+ 𝛾4𝑝𝑜𝑝_𝑔𝑟𝑜𝑤𝑡ℎ𝑖𝑡−1+ 𝛾5 𝑐𝑟𝑒𝑑𝑖𝑡_𝑝𝑟𝑖𝑣𝑖𝑡−1 + 𝛾6𝑙𝑡_𝑟𝑒𝑎𝑙_𝑖𝑖𝑡−1 + 𝛾7𝑡𝑟𝑎𝑑𝑒_𝑜𝑝𝑒𝑛𝑛𝑒𝑠𝑠𝑖𝑡−1+ 𝜃𝑡+ 𝜌𝑖 + 𝜀𝑖𝑡

Equation 3 (channel 2: private gross fixed capital formation) 𝑔𝑓𝑐𝑓_𝑝𝑟𝑖𝑣 = 𝛽₀+ 𝛽₁𝑔𝑓𝑐𝑓_𝑝𝑟𝑖𝑣_𝑖𝑡−1+ 𝛾₁𝑑𝑒𝑏𝑡_𝑖𝑡−12 + 𝛾₂𝑑𝑒𝑏𝑡_𝑖𝑡−1+ 𝛾₃𝑔𝑓𝑐𝑓_𝑔𝑜𝑣_𝑖𝑡

+ 𝛾₃𝑔𝑓𝑐𝑓_𝑔𝑜𝑣_𝑖𝑡−1+ 𝛾₄ln_gdp_cap_𝑖𝑡−1+ 𝛾₅𝑔𝑑𝑝_𝑐𝑎𝑝_𝑔_𝑖𝑡−1 + 𝛾6𝑔𝑜𝑣_𝑟𝑒𝑣_𝑐𝑎𝑝𝑖𝑡−1+ 𝛾7𝑐𝑟𝑒𝑑𝑖𝑡_𝑝𝑟𝑖𝑣𝑖𝑡−1+ 𝛾8𝑙𝑡_𝑟𝑒𝑎𝑙_𝑖𝑖𝑡−1 + 𝛾₉𝑡𝑟𝑎𝑑𝑒_𝑜𝑝𝑒𝑛𝑛𝑒𝑠𝑠_𝑖𝑡−1+ 𝜃_𝑡+ 𝜌_𝑖 + 𝜀_𝑖𝑡

Equation 4 (channel 2: government gross fixed capital formation)

24_{For a detailed account of the contributions of the covariates, see CR 2010, pp. 19-22. These are unaccounted}

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𝑔𝑓𝑐𝑓_𝑔𝑜𝑣 = 𝛽₀+ 𝛽₁𝑔𝑓𝑐𝑓_𝑔𝑜𝑣_𝑖𝑡−1+ 𝛾₁𝑑𝑒𝑏𝑡_𝑖𝑡2 + 𝛾₂𝑑𝑒𝑏𝑡_𝑖𝑡+ 𝛾₃𝑔𝑓𝑐𝑓_𝑝𝑟𝑖𝑣_𝑖𝑡 + 𝛾₄𝑔𝑜𝑣_𝑏𝑎𝑙_𝑖𝑡−1+ 𝛾₅𝑔𝑜𝑣_𝑟𝑒𝑣_𝑝𝑟𝑖𝑣_𝑖𝑡−1+ 𝛾₆𝑔𝑑𝑝_𝑐𝑎𝑝_𝑔_𝑖𝑡−1 + 𝛾7𝑙𝑡_𝑟𝑒𝑎𝑙_𝑖𝑖𝑡−1+ 𝛾8𝑡𝑟𝑎𝑑𝑒_𝑜𝑝𝑒𝑛𝑛𝑒𝑠𝑠𝑖𝑡−1+ 𝜃𝑡+ 𝜌𝑖 + 𝜀𝑖𝑡 Equation 5 (channel 3: Total factor productivity)

𝑇𝐹𝑃 = 𝛽₀+ 𝛽₁𝑡𝑓𝑝_𝑔_𝑖𝑡−1+ 𝛾₁𝑑𝑒𝑏𝑡_𝑖𝑡2 + 𝛾₂𝑑𝑒𝑏𝑡_𝑖𝑡+ 𝛾₃𝑔𝑑𝑝_𝑐𝑎𝑝_𝑔_𝑖𝑡−1+ 𝛾₄𝑝𝑜𝑝_𝑔𝑟𝑜𝑤𝑡ℎ_𝑖𝑡−1 + 𝛾₅𝑐𝑟𝑒𝑑𝑖𝑡_𝑝𝑟𝑖𝑣_𝑖𝑡−1+ 𝛾₆𝑙𝑡_𝑟𝑒𝑎𝑙_𝑖_𝑖𝑡−1+ 𝛾₇𝑡_𝑜_𝑡_𝑔_𝑖𝑡−1+ 𝜃_𝑡+ 𝜌_𝑖 + 𝜀_𝑖𝑡 Equation 6 (channel 4: Long term real sovereign interest rates)

𝑙𝑡_𝑟𝑒𝑎𝑙_𝑖𝑖𝑡 = 𝛽0+ 𝛽1𝑠𝑡_𝑟𝑒𝑎𝑙_𝑖𝑖𝑡+ 𝛾1𝑑𝑒𝑏𝑡𝑖𝑡2 + 𝛾2𝑑𝑒𝑏𝑡𝑖𝑡+ 𝛾3𝑔𝑜𝑣_𝑝𝑟𝑖𝑚𝑎𝑟𝑦_𝑏𝑎𝑙𝑖𝑡

+ 𝛾4𝑔𝑑𝑝_𝑐𝑎𝑝_𝑔𝑖𝑡−1+ 𝛾5𝑦_𝑔𝑎𝑝_𝑡𝑟𝑒𝑛𝑑𝑖𝑡 + 𝛾6𝑐𝑎_𝑏𝑎𝑙𝑎𝑛𝑐𝑒𝑖𝑡+ 𝛾7𝑜𝑝𝑒𝑛𝑛𝑒𝑠𝑠𝑖𝑡 + 𝛾₈𝑟𝑒𝑒𝑟_𝑖𝑡+ 𝜃_𝑡+ 𝜌_𝑖 + 𝜀_𝑖𝑡

Equation 7 (channel 4: Long term nominal sovereign interest rates)

𝑙𝑡_𝑛𝑜𝑚_𝑖𝑖𝑡 = 𝛽0+ 𝛽1𝑠𝑡_𝑛𝑜𝑚_𝑖𝑖𝑡+ 𝛾1𝑑𝑒𝑏𝑡𝑖𝑡2 + 𝛾2𝑑𝑒𝑏𝑡𝑖𝑡+ 𝛾3𝑔𝑜𝑣_𝑝𝑟𝑖𝑚𝑎𝑟𝑦_𝑏𝑎𝑙𝑖𝑡

+ 𝛾₄𝑔𝑑𝑝_𝑐𝑎𝑝_𝑔_𝑖𝑡−1+ 𝛾₅𝑦_𝑔𝑎𝑝_𝑡𝑟𝑒𝑛𝑑_𝑖𝑡 + 𝛾₆𝑐𝑎_𝑏𝑎𝑙𝑎𝑛𝑐𝑒_𝑖𝑡+ 𝛾₇𝑜𝑝𝑒𝑛𝑛𝑒𝑠𝑠_𝑖𝑡 + 𝛾₈𝑟𝑒𝑒𝑟_𝑖𝑡+ 𝛾₉𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛(𝐺𝐷𝑃 𝑑𝑒𝑓𝑙. )_𝑖𝑡+ 𝜃_𝑡+ 𝜌_𝑖+ 𝜀_𝑖𝑡

3.3. Robustness tests

According to Panizza & Presbitero it is important to check for weak instruments and further robustly check for endogeneity before any inferences can be made (2014. P.37).

In the endogeneity test we are testing the null hypothesis that the gross debt variables are exogenous. This test shows that if the null hypothesis is not rejected, we could have used an OLS regression instead. OLS requires that the explanatory variable is exogenous, ie. that the variable is uncorrelated with the regression error term (Stock & Watson, 2012. P. 807). Table 2 shows that, in the case of estimating the direct effect of debt on growth using 2SLS, both the Durbin score statistic as well as the Wu-Hausmann statistic have very small p-values. This allows us to reject the null-hypothesis and means that OLS is not suited to use as an estimation method due to the fact that gross debt can be treated as an endogenous variable.25 This is in line with economic theory and empirical research. The most prominent reason is due to the effect of reversed causality bias (or simultaneous causality). This bias essentially is due to the fact that the role of debt and growth as independent and dependent variable can be switched

25_{https://www.youtube.com/watch?v=lbnswRJ1qV0 was helpful in performing and understanding the robustness}

(28)

28

(respectively) such that it is not possible to say that the explanatory variable (independent) is explaining part of the variance of the dependent variable in a one-way manner. In short, there is a causal link from growth to debt and therefore debt is correlated with the error term (Stock & Watson, 2012. P. 811).

Table 2. Tests for endogeneity

Table 3 shows the strength of the instruments. The first one is the time lag of the independent variable up to the 5th lag. The second one is the average debt of all the other countries in the sample. We are looking for the correlation between the instruments and the endogenous variable. The partial R-squared measures the correlation between debt and the instruments after the effects of the control variables are partialled out. The R-squared value is 0.5493 which is not very high but not low as well. Furthermore, the F-statistic is 55.5737 which is bigger than any of the critical values shown. So we can reject the null hypothesis that the instruments are weak.26

Table 3. Strength of instruments

26_{In the regression performed for the robustness checks, gov_debt2 was used solely as endogenous variable. This}

is done due to the similar properties gov_debt2 and gov_debt have.

Wu-Hausman F(1,231) = 50.2713 (p = 0.0000) Durbin (score) chi2(1) = 52.3676 (p = 0.0000) Ho: variables are exogenous

Tests of endogeneity

LIML Size of nominal 5% Wald test 4.84 3.56 3.05 2.77 2SLS Size of nominal 5% Wald test 26.87 15.09 10.98 8.84 10% 15% 20% 25% 2SLS relative bias 18.37 10.83 6.77 5.25 5% 10% 20% 30% Ho: Instruments are weak # of excluded instruments: 5 Critical Values # of endogenous regressors: 1 Minimum eigenvalue statistic = 55.5737

gov_debt2 0.9771 0.9707 0.5493 55.5737 0.0000 Variable R-sq. R-sq. R-sq. F(5,228) Prob > F Adjusted Partial First-stage regression summary statistics