Government Debt and GDP Growth: Is There a Threshold? - Economics · 2019-10-14 · DEBT AND GROWTH: IS THERE A THRESHOLD? 2 1. Introduction The aftermath of the recent Great Recession

Government Debt and GDP Growth: Is There a Threshold?

Jafar El Armali*

Department of Economics – Western University

April 29, 2019

Abstract

Is the relationship between government debt and subsequent economic growth non-linear? Is there

a debt threshold above which accumulating more debt becomes significantly detrimental for future

growth? Reinhart and Rogoff (2010) suggest that the answer to these questions is yes, and that

90% is a threshold for the debt-to-GDP ratio in advanced economies. However, Reinhart and

Rogoff’s analysis is better suited to understand the short-run (contemporaneous) relationship

between debt and growth. Subsequent empirical studies, in general, indicate that this result holds

for longer time horizons (usually five to ten year periods). Some papers point out the importance

of considering parameter heterogeneity when grouping a large number of countries with different

characteristics. Hence, this paper focuses on advanced European countries. It studies the debt-

growth relationship in this group of countries by applying a new method, the regression kink model,

as per Hansen (2017). Results support the existence of a non-linear relationship. The estimated

threshold is between 30% and 35%. These results are supplemented by results from analyzing the

United States time series data starting from late 18th century.

Keywords: GDP growth, government debt, debt-to-GDP, threshold

* [email protected]. I would like to thank Professors Ananth Ramanarayanan, Juan Carlos Hatchondo, and

Audra Bowlus for their helpful comments, support and guidance of this project.

DEBT AND GROWTH: IS THERE A THRESHOLD? 2

1. Introduction

The aftermath of the recent Great Recession has led government debt-to-GDP in advanced

economies to increase to levels not seen since after World War II (Woo and Kumar, 2015).

This has raised concerns about the impact of such an increase on the economic performance of

these countries. Reinhart and Rogoff (2010) mention that for advanced economies, when public

debt-to-GDP crosses 90%, further debt accumulation has a negative impact on economic growth.

Hence, the authors conclude that the relationship between government debt and economic growth

in this group of countries is characterized by the existence of a threshold, which means that it is a

non-linear relationship. However, Reinhart and Rogoff’s results describe the short-run relationship

between current debt and current growth.

Subsequent papers test the relationship between debt and GDP growth using longer period

averages, usually five years (e.g. Checherita-Westphal and Rother, 2012; Afonso and Jalles, 2013;

Panizza and Presbitero, 2014; Eberhardt and Presbitero, 2015; Égert, 2015; Woo and Kumar, 2015).

Overall, results indicate that the non-linear relationship holds for longer time horizons and different

groups of countries, with few exceptions. Nonetheless, some papers (in particular, Afonso and

Jalles, 2013; Eberhardt and Presbitero, 2015) point out the importance of considering parameter

heterogeneity when grouping a large number of countries with different characteristics.

Against this background, the goal of this paper is to test the impact of accumulating debt

beyond an estimated threshold, on subsequent GDP growth in advanced economies using a sample

of advanced European economies. I test the relationship between ten-year average debt-to-GDP

and the subsequent ten-year average growth in GDP per capita. Using ten year averages is meant

to smooth out the effects of the business cycle, and to emphasize the longer term impact of debt.

In addition, some papers find that the change in debt rather than the level of debt is what matters

for GDP growth (e.g. Chudik et al., 2017). Therefore, I also use the change in debt as an additional

explanatory variable in my growth regression model.

Hansen (2017) suggests that the regression kink model is an appropriate choice to model

the non-linear debt-growth relationship characterized by a threshold. The regression kink model is

a continuous regression model with slope discontinuity at the “kink” or threshold, as per Hansen.

This is different from the regression discontinuity design and discontinuous threshold regression

methods as in Hansen (1999), in which the regression function itself is discontinuous. Therefore,

I use a regression kink model design, and apply Hansen’s estimation methodology on a panel of


advanced European countries. To the best of my knowledge, this is the first study to use a

regression kink model to test the debt-growth relationship in a panel of countries.

Results support the existence of a non-linear relationship. The estimated threshold is

between 30% and 35%. These results are supplemented by results shown in the appendix, from

analyzing the United States time series data starting from late 18th century provided by Reinhart

and Rogoff.

The rest of the paper is organized as follows. A brief literature review for empirical studies

starting from and subsequent to Reinhart and Rogoff (2010), is provided in Section 2. Data and

methodology are presented in Section 3. Main results are reported in Section 4. Section 5 presents

the results from investigating the relationship between debt-to-GDP and the share of private

investment in GDP. A brief discussion of the results is presented in Section 6, while Section 7

provides a conclusion.

2. Literature Review

Reinhart and Rogoff (2010), RR hereafter, conclude that 90% is a threshold for the

debt-to-GDP ratio in advanced economies, above which there exists a significant drop in GDP per

capita growth. The result is based on descriptive statistics of annual GDP growth rates and

debt-to-GDP in 20 advanced economies for the period between 1946 and 2009. RR group their

data into four exogenous debt-to-GDP categories, and show that average and median growth rates

are particularly lower for the above 90% category.

Herndon et al. (2014), HAP hereafter, mention that RR’s results are inaccurate due to

omitted observations and to the way weights are assigned when calculating weighted averages.

However, as shown in tables 1-2 and figure 1 below, the results from HAP mirror RR qualitatively,

albeit with a smaller drop in growth above the 90% threshold.

Table 1

Average GDP growth for each debt-to-GDP category

Paper <30% 30-60% 60-90% >90%

RR (2010) 4.1 2.8 2.8 -0.1

HAP (2014) 4.2 3.1 3.2 2.2


Table 2

Median GDP growth for each debt-to-GDP category

Paper <30% 30-60% 60-90% >90%

RR (2010) 4.2 3.0 2.9 1.6

HAP (2014) 4.1 3.1 2.9 2.3

Fig. 1. Average and Median GDP growth for each debt-to-GDP category

In fact, two thresholds can be identified from the above tables and figure. The first is 30%,

after which average and median growth in both RR and HAP fall by 1% or more. The other is 90%.

However, the results from both papers are from descriptive statistics and involve no formal

econometric model or testing. Therefore, subsequent empirical studies attempt to test the debt-

growth relationship using different econometric techniques. For example, Baum et al. (2013) add

lagged debt-to-GDP to a set of explanatory variables usually used in a standard growth regression

model. The authors apply a (discontinuous) “dynamic threshold panel methodology” to test for the

relationship between debt-to-GDP and GDP growth in 12 European countries in the period from

1990 to 2010. The results support the existence of a debt threshold. The endogenously estimated

debt-to-GDP threshold is approximately 95%, below which the estimated coefficient is positive

and significant and above which it remains significant yet negative.

Nonetheless, even if the results from the above papers are taken as conclusive, they may

not reflect the effect of government debt on long-run economic growth. This is because in both

RR and HAP, the relationship examined is between current debt and current growth which is a

contemporaneous relationship as mentioned in RR. Even if lagged debt-to-GDP is used to address


the simultaneity/reverse causality concern, it still would not reflect the long-run effect of debt.

As Baum et al. (2013) point out: “We are analysing the impact of one-year lagged debt-to-GDP

ratios on annual real GDP growth rates. We thus obtain a near contemporaneous effect, which gives

us an idea of the short-term debt impact. Hence, a positive impact of debt on growth could be

interpreted as a stimulating effect of additional debt. However, the possibility that long-term effects

of high debt might be negative cannot be ruled out based on the yearly analysis” (p. 813).

As a result, other papers test the relationship between debt and GDP growth using longer

period averages. Checherita-Westphal and Rother (2012) use both current and five-year cumulative

GDP per capita growth as their dependent variable in growth regression models with country and

time fixed effects. The data in their paper is for 12 European countries for the period between 1970

and 2008. In both cases (current and five-year), they find a significant non-linear relationship

between lagged debt and subsequent growth. The estimated threshold is approximately between

80% and 105% depending on the model and period. Similar to Baum et al. (2013), the debt-to-

GDP estimated coefficient is positive/significant below the threshold and negative/significant

above the threshold. Similarly, Woo and Kumar (2015) test for the impact of initial debt on the

subsequent five-year average growth. Data used in Woo and Kumar is for a group of 38 advanced

and emerging economies for the period between 1970 and 2008. Their results show a negative and

significant effect of initial debt on subsequent growth, which is confirmed by cross-country

regression results using ten to thirty-year averages. When imposing exogenous thresholds to test

for possible non-linearity in the debt-growth relationship, the results show positive (yet

insignificant) coefficients below threshold and negative (significant) coefficients above threshold.

Some papers criticize the above results by pointing out the importance of considering

parameter heterogeneity and cross-sectional dependence. For example, Eberhardt and Presbitero

(2015) test the relationship between current GDP growth and lagged measures of physical capital

and debt-to-GDP using a factor model framework to allow them to capture parameter heterogeneity.

With a panel of 118 countries for the period between 1960 and 2012, and imposing two exogenous

thresholds (60% and 90%), the authors conclude that there is no universal threshold that applies to

all countries in their panel. Nonetheless, they report in their findings that higher debt-to-GDP ratios

are associated with lower long-run GDP growth overall. The absence of a common threshold is

not surprising given that the sample includes a large number of countries that differ considerably

in their stage of growth and quality of institutions. In addition, imposing an exogenous threshold

rather than estimating a threshold from the data may yield inaccurate results. Afonso and Jalles


(2013) is another paper that considers parameter heterogeneity and cross-sectional dependence.

They have a sample of 155 countries between 1970 and 2008. However, unlike Eberhardt and

Presbitero, they test the null hypothesis of parameter homogeneity for subsets of the sample with

common characteristics for which it is plausible to expect homogeneity. In particular, they find

that the null cannot be rejected for countries that are members of the Euro-area and the OECD.

The authors report that for debt-to-GDP ratios less than 30%, the coefficient is positive and

significant. It turns into negative for debt-to-GDP ratios above 30%, and above 90%, the

coefficient increases in magnitude (while still negative and significant).

Pointing to endogeneity concerns, Panizza and Presbitero (2014) propose an instrument for

debt to test for the debt-growth relationship in a sample of OECD countries. In contrast to the

standard practice of testing the effect of lagged debt on subsequent GDP growth, the authors

construct an instrument, “valuation effects”, which they say captures the effects of real exchange

rate changes on the total value of debt (since an exchange rate movement changes the value of

foreign currency debt, and as a result of total debt). Using this instrument, they conclude that public

debt has no significant effect on GDP growth. However, two things can be noted. First, the authors

admit that their proposed instrument does not necessarily satisfy the exclusion restriction. Second,

five countries in their sample (United States, France, Germany, Japan and the Netherlands), have

no foreign currency debt as they mention.

Other papers construct measures of variables that are perceived to affect the relationship

between debt and growth, and interact them with the levels of debt to test whether the effect of

debt changes with these measures. For example, using data from 16 OECD countries, Proaño et al.

(2014) construct a “financial stress index” and interact it with lagged debt-to-GDP. The index is

meant to capture the degree of instability/uncertainty in the financial markets. They conclude that

higher debt-to-GDP is correlated with lower growth only in periods of “high stress” in the markets.

However, the authors use quarterly data in their testing, which makes it problematic to infer long-

run effects. Moreover, Dreger and Reimers (2013) construct a debt sustainability measure, and

interact it with debt-to-GDP. They conclude that for 12 European countries between 1991 and 2011,

the effect of increasing debt-to-GDP is positive yet insignificant when debt is sustainable, and

turns into negative and significant when debt is non-sustainable.

Finally, some papers (e.g. Pescatori et al., 2014; Chudik et al., 2017) point out that the

change in debt-to-GDP, rather than the level of debt-to-GDP, is the relevant variable to consider.

Pescatori et al. (2014) mention that countries with increasing debt perform worse on average,


in terms of growth, than countries with decreasing debt levels. Chudik et al. (2017) find that above

a debt-to-GDP threshold (like 90% for e.g.), further increases in debt-to-GDP have significantly

negative effects on GDP growth. A similar result is reported in Afonso and Jalles (2013).

The above survey is by no means comprehensive; however, it comprises a representative

sample of the empirical studies on the subject since 2010, to the best of my knowledge. Overall,

it can be inferred that higher levels of debt-to-GDP are indeed correlated with lower growth rates

in GDP per capita. This is applicable whether the period considered is annual, five-year, or

ten-year averages. The only paper in the above survey that concludes that no such relationship

exists (i.e. Panizza and Presbitero, 2014), does so based on a weak instrument, with a significant

portion of their sample having zero variation in that instrument.

Papers that interact the level of debt with other indicators, like the conditions of the

financial markets or debt sustainability, do not necessarily contradict the conclusion of negative

correlation between debt and GDP growth. In fact, they can be viewed as complementing results.

This is because these indicators may be the mechanisms through which higher levels of debt

negatively affect growth. Furthermore, the change in debt and the level of debt need not be

mutually exclusive when it comes to which variable is negatively correlated with GDP growth.

That being said, whether there exists parameter heterogeneity (i.e. whether different

countries or regions have different thresholds), remains a legitimate concern. This is a particularly

important consideration in studies that involve a relatively large number of advanced and

developing countries pooled in one sample. It is noteworthy that studies citing the parameter

heterogeneity concern, as in Eberhardt and Presbitero (2015), also conclude that higher levels of

debt are detrimental to growth. The concern is whether the same debt threshold applies to a large

set of countries. It is for that reason that I focus on advanced European economies in my study,

although this comes with the expense of having a smaller sample size.

3. Data and Methodology

The ideal way to avoid the parameter heterogeneity concern is to conduct a separate study

for each country using that country’s time series data. However, even for the country with the

longest span of time series data available (i.e. the United States), taking five-year averages for

example, results in a limited number of observations. This affects the significance of the estimated

coefficients, and makes inference problematic.


To address the parameter heterogeneity concern, while still having a sample big enough for

meaningful econometric analysis, I choose to restrict my attention to advanced European countries.

My sample is for 16 European countries with advanced economies, for the period from 1950 to

2016. In particular, I gather data for the following countries: Austria, Belgium, Denmark, Finland,

France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Spain, Sweden,

Switzerland, and the United Kingdom. Therefore, I exclude other advanced economies (like the

United States for example) and other European countries that had a different economic system

until the 1990’s. In the appendix, I present the estimation results for the United States using time

series data from RR with five-year and ten-year averages. The results in the appendix supplement

those presented in this paper. Data used in this paper come from the Penn World Table (PWT) 9.1

(Feenstra et al., 2015), The International Monetary Fund, and RR.

The countries in my sample have geographical proximity and shared history. In addition,

most of them adopted a common currency, and are supposed to meet The Maastricht criteria of 3%

maximum budget deficit, and 60% maximum debt-to-GDP (Polasek & Amplatz, 2003). Moreover,

most of the countries in the sample (with two or three exceptions) can be viewed as small open

economies. Where this does not necessarily guarantee parameter homogeneity, it makes the

estimated parameters less susceptible to the parameter heterogeneity concern relative to studies

that use a large pool of advanced and developing countries or even combine all advanced

economies with their geographical, historical and other differences. However, this choice means

limiting the number of observations in my sample.

3.1 The Econometric Model

The model used in this paper is a regression kink model based on Hansen (2017). I use

lagged debt-to-GDP, rather than current debt-to-GDP, as the main regressor of interest. This is for

two reasons. First, from a theoretical perspective, it is the starting level of debt (inherited from the

previous period) that is usually taken as a state variable by the decision maker in period t. Second,

using lagged debt-to-GDP helps address the reverse causality concern especially that each period

in my analysis comprises ten years (except for the last period, 2010-2016), which makes it unlikely

that average GDP growth in a given decade has an effect on the average debt-to-GDP in the

previous decade. Hence, with 𝑦𝑖𝑡 being the average growth rate of GDP per capita in country 𝑖 at

period t (where t is 10 years), 𝑑𝑖𝑡−1 being the lagged average debt-to-GDP in country 𝑖, and 𝛾

being the endogenously estimated debt-to-GDP threshold, the regression model is as follows:


𝑦𝑖𝑡 = 𝛽1(𝑑𝑖𝑡−1 − 𝛾)− + 𝛽2(𝑑𝑖𝑡−1 − 𝛾)+ + 𝛽3𝑋𝑖𝑡 + 𝛼𝑖 + 𝜗𝑡 + 𝜀𝑖𝑡 (1)

As in Hansen, (𝑑𝑖𝑡−1 − 𝛾)− and (𝑑𝑖𝑡−1 − 𝛾)+ are used to split the observations of lagged average

debt-to-GDP into below and above the estimated threshold so that two different coefficients are

estimated. Note that (𝑑𝑖𝑡−1 − 𝛾)− = {𝑚𝑖𝑛[𝑑𝑖𝑡−1 − 𝛾, 0]}, and (𝑑𝑖𝑡−1 − 𝛾)+ = {𝑚𝑎𝑥[0, 𝑑𝑖𝑡−1 − 𝛾]}.

In contrast to a regression discontinuity design (RDD), equation (1) is a continuous function in all

its arguments albeit the slope with respect to 𝑑𝑖𝑡−1 is not defined at 𝑑𝑖𝑡−1 = 𝛾 (Hansen, 2017).

𝑋𝑖𝑡 includes a set of explanatory variables usually used in growth regressions, in addition to the

change in average debt-to-GDP, as follows:

Natural log of initial real GDP, to capture conditional convergence.

Investment share of GDP in period t.

Government expenditure share of GDP in period t.

A measure of trade openness in period t (in particular, net exports/GDP).

Population growth in period t.

The change in debt-to-GDP in period t.

Intercept.

In addition, a dummy variable (𝐸𝑀𝑈𝑖) is included in the pooled OLS regression to capture

whether a country has become a part of the European Monetary Union. In the panel fixed-effect

regressions, 𝛼𝑖 is added first to capture country fixed effects. Then, 𝜗𝑡 is also added to capture time

fixed effects. Finally, 𝜀𝑖𝑡 is an error term.

The estimation strategy follows Hansen (2017). First, a grid of thresholds between 10%

and 90%, with increments of one, is generated. This guarantees that at least few observations in

the sample are above and below the bounds of the grid. For each point on the grid, the regression

coefficients are estimated. Then, the combination of the threshold and the associated coefficients

that minimize the sum of squared errors is selected. Further, I impose 60% as a threshold, as per

The Maastricht criteria, to test whether results change.


4. Results

Based on the above methodology, three models are estimated: pooled OLS, panel country

fixed effects, and panel country & time fixed effects. This means that I estimate six models, models

1 to 3 with thresholds estimated from the data, and models 4 to 6 with 60% imposed as a threshold.

Results are presented in table 3 and figures 2 to 4.

Table 3

Regression Kink Model Estimates

(Dependent Variable: 10-year Average Growth in GDP per Capita)

Explanatory Variable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

Threshold (γ) 30% 35% 35% 60% 60% 60%

0.043

(0.022)

0.030

(0.017)

0.007

(0.016)

-0.007

(0.024)

-0.003

(0.015)

-0.017**

(0.007)

-0.027*

(0.009)

-0.020**

(0.006)

-0.023**

(0.007)

-0.025*

(0.013)

-0.020**

(0.008)

-0.022**

(0.007)

Log (initial real GDP) -0.604**

(0.118)

-1.907**

(0.316)

-3.507**

(0.969)

-0.576**

(0.139)

-1.750**

(0.317)

-3.430**

(0.987)

Investment share of

GDP

1.533

(1.146)

2.633**

(1.066)

3.749**

(1.160)

1.160

(1.209)

2.289**

(1.101)

3.588**

(1.185)

Government

expenditure share of

GDP

-0.769

(0.666)

-2.222**

(1.184)

-0.910

(1.224)

-0.727

(0.751)

-2.532**

(1.344)

-0.981

(1.300)

Trade Openness 0.339

(2.519)

3.108

(2.562)

4.964**

(2.652)

0.400

(2.714)

2.424

(2.704)

4.459**

(2.702)

Population Growth 0.162

(3.735)

-2.894

(3.107)

-1.784

(3.219)

0.118

(3.839)

-2.718

(3.681)

-1.609

(3.496)

Change in debt-to-GDP -0.032**

(0.013)

-.010

(0.009)

-.008

(0.013)

-0.032**

(0.014)

-.010

(0.009)

-.009

(0.013)

EMU 1.098**

(0.332)

1.004**

(0.344)

Country fixed effects no yes yes no yes yes

Time fixed effects no no yes no no yes

* Significant at the 90% confidence level.

** Significant at the 95% confidence level.

(𝑑𝑖𝑡−1 − 𝛾)−

(𝑑𝑖𝑡−1 − 𝛾)+


Fig. 2. 10-yr avg growth & avg lagged debt-to-GDP; scatterplot and the estimated kink model 1.

(Pooled OLS)


(Country Fixed Effects)



(Country and Time Fixed Effects)

Overall, the estimates from the first three models, those with endogenously estimated

thresholds, point out to a non-linear relationship (close to an inverted U shape) between average

growth in GDP per capita in a given decade and average debt-to-GDP ratio in the previous decade.

This is displayed in figures 2 to 4. The endogenously estimated thresholds are 30% in model 1 and

35% in models 2 and 3. Interestingly, this is in line with the first threshold that can be identified

when looking at figure 1 (i.e. the results from RR and HAP).

As shown in the results from the first three models, the coefficient of (𝑑𝑖𝑡−1 − 𝛾)− is

always positive. This is in line with the findings of Baum et al. (2013), Afonso and Jalles (2013),

and Égert (2015). As mentioned by Égert, this may indicate that at relatively low levels, debt can

be used to finance productive (growth-enhancing) public spending. However, the coefficient is

insignificant in all three models. In contrast, the coefficient of (𝑑𝑖𝑡−1 − 𝛾)+ is negative and

significant in all three models (at 10% confidence level in model 1, and 5% confidence level in

models 2 and 3). This result is in line with the overall conclusion from the literature review section.

It indicates that accumulating government debt beyond a certain threshold can put pressure on

subsequent GDP growth.


Other explanatory variables have the expected signs. Initial GDP has a negative and

significant coefficient in all models in line with the concept of conditional convergence.

Investment is positively correlated with GDP growth, with significant coefficients in models 2

and 3. Government expenditures (which include non-productive spending) negatively correlate

with GDP growth, although the coefficient is significant only in model 2. Trade openness is

positively correlated with GDP growth, with a significant coefficient only in model 3.

Population growth has mixed albeit insignificant coefficients, while joining the European

Monetary Union is positively correlated with GDP growth. The change in average debt-to-GDP

has a negative coefficient, which is in line with what is reported in Pescatori et al. (2014) and

Chudik et al. (2017). However, the coefficient is significant only in pooled OLS case.

Looking at the results from imposing 60% as a threshold (models 4 to 6), the overall

relationship between GDP growth and lagged debt-to-GDP becomes negative. However,

the coefficients of (𝑑𝑖𝑡−1 − 𝛾)− are insignificant in models 4 and 5. The coefficient is negative and

significant in model 6, but is smaller in magnitude than the coefficient of (𝑑𝑖𝑡−1 − 𝛾)+. Therefore,

the main conclusion holds. Beyond a certain level of debt-to-GDP, the results show that

accumulating more debt has a negative and significant effect on subsequent GDP growth.

The coefficients of the remaining explanatory variables in models 4 to 6 are similar in terms of

direction and significance to those obtained from models 1 to 3.

An interesting point to note from table 3 is the following. Despite that the coefficients of

all other explanatory variables change in magnitude or significance or both across different models,

the coefficient of (𝑑𝑖𝑡−1 − 𝛾)+ does not. Not only does the coefficient of (𝑑𝑖𝑡−1 − 𝛾)+ remain

significant in all models, it also has a stable estimate of approximately -0.02 across the 6 models.

5. Investigating the usual suspect: The effect of debt-to-GDP on private investment

Given that the above results point out to a non-linear relationship between GDP growth

and lagged debt-to-GDP, I ask the following question: Does this non-linearity extend to the

relationship between private investment and government debt? A positive answer to this question

can reveal one of the mechanisms through which accumulating debt above threshold may harm

subsequent growth.


To answer this question, I rewrite equation (1) with the investment-to-GDP ratio, averaged

over ten years, as the dependent variable. However, results from regression kink models are overall

insignificant. It is worth mentioning that some of the estimated coefficients of above threshold

lagged debt-to-GDP have a positive sign1.

Since the results using regression kink models are insignificant, I test the relationship using

a RDD threshold model to double check the results. In particular, I rewrite equation (1) as follows,

(𝐼𝑁𝑉

𝐺𝐷𝑃)𝑖𝑡 = 𝛽0 + 𝛽1𝐼(𝑑𝑖𝑡−1 > 𝛾) + 𝛽2(

𝐺𝑜𝑣. 𝑆𝑝.

𝐺𝐷𝑃)𝑖𝑡 + 𝛽3𝑝𝑜𝑝𝑔𝑟𝑖𝑡 + 𝛽4𝑡𝑟𝑜𝑝𝑖𝑡 + 𝛽4𝑐ℎ_𝑑𝑖𝑡 + 𝛼𝑖 + 𝜗𝑡 + 𝜀𝑖𝑡 (2)

where 𝐼(𝑑𝑖𝑡−1 > 𝛾) is an indicator for whether average lagged debt-to-GDP is above threshold,

(𝐺𝑜𝑣. 𝑆𝑝.

𝐺𝐷𝑃)𝑖𝑡 measures the share of government spending from GDP, 𝑝𝑜𝑝𝑔𝑟𝑖𝑡 is population growth,

𝑡𝑟𝑜𝑝𝑖𝑡 measures trade openness, and 𝑐ℎ_𝑑𝑖𝑡 is the change is average debt-to-GDP in country i and

period t. As before, an indicator for joining the European Monetary Union (𝐸𝑀𝑈𝑖) is added to the

pooled OLS regression, while 𝛼𝑖 (country fixed effects) is added to the first panel fixed effects

model (FE 1) and 𝜗𝑡 (time fixed effects) is added to the second panel fixed effects model (FE 2).

I estimate equation (2) using two thresholds, 35% (endogenously estimated in section 4),

and 60%, the debt-to-GDP threshold as per The Maastricht criteria. Results are shown in table 4.

The coefficient of 𝐼(𝑑𝑖𝑡−1 > 𝛾) is negative and significant in most of the models, with a magnitude

of approximately -0.1. However, the coefficient is insignificant when adding time fixed effects in

the model with 𝛾 = 35%. Since the coefficients are also insignificant using the regression kink

model, one cannot conclude with a degree of confidence that higher average lagged debt-to-GDP

leads to lower subsequent investment.

Nonetheless, it is noteworthy that in this set of regressions, the coefficient of the change in

average debt-to-GDP has a stable coefficient that is negative and significant. This could be a

channel that explains the results in papers indicating that a positive change in current debt is

negatively correlated with GDP growth. Similar results are reported in table 3, although the

coefficients are mostly insignificant. Results in table 4 also present some evidence of the

“crowding out” effect of government spending on investment, since the coefficient is always

negative and significant. It is also noteworthy that investment is negatively correlated with trade

1 Results are not presented here to save space, and are available upon request.


openness. Finally, population growth and joining the European Monetary Union do not seem to

have significant effects on the investment share of GDP.

Table 4

RDD Model With Exogenous Threshold

(Dependent Variable: 10-year Average Investment Share of GDP in logs)

Explanatory Variable Pooled

OLS FE 1 FE 2

Pooled

OLS FE 1 FE 2

Threshold (γ) 35% 35% 35% 60% 60% 60%

IIIdebt -0.122**

(0.035)

-0.090**

(0.041)

-0.037

(0.057)

-0.108**

(0.041)

-0.126**

(0.047)

-0.093*

(0.050)

Government expenditure

share of GDP

-0.121*

(0.068)

-0.318**

(0.129)

-0.386**

(0.165)

-0.149**

(0.069)

-0.306**

(0.127)

-0.319*

(0.165)

Trade Openness -0.550**

(0.184)

-0.956**

(0.232)

-0.928**

(0.297)

-0.550**

(0.189)

-0.975**

(0.226)

-0.881**

(0.280)

Population Growth -0.208

(0.419)

-0.318

(0.540)

-0.242

(0.563)

-0.0802

(0.431)

-0.244

(0.535)

-0.159

(0.543)

Change in debt-to-GDP -0.002**

(0.001)

-0.002*

(0.001)

-0.002**

(0.001)

-0.002**

(0.001)

-0.002**

(0.001)

-0.003**

(0.001)

EMU 0.005

(0.037)

-0.003

(0.038)

Country fixed effects no yes yes no yes yes

Time fixed effects no no yes no no yes



6. Discussion

The results in this paper point out to a non-linear relationship between government debt-

to-GDP and subsequent GDP growth. In the context of an endogenous growth with productive

government spending, this means that accumulating debt above threshold may lead to permanently

lower long-run growth rates (i.e. lower growth rates on the balanced growth path) as noted by

Barro and Sala-i-Martin (2004). It remains vital to investigate the channels through which this

relationship works. On one hand, government debt can be used to enhance growth by funding

public investments in needed infrastructure projects for example. On the other hand, if high levels

𝐼(𝑑𝑖𝑡−1 > γ)


of debt-to-GDP drive up the interest rate spread faced by the government as well as domestic

private borrowers, then this would depress private investment (and public investment too) which

leads to lower subsequent economic growth.

This paper presents suggestive (yet inconclusive) evidence that private investment is one

of the channels at work in the debt-growth relationship. Woo and Kumar (2015) report a similar

result and mention that this leads to lower labour productivity growth and hence lower GDP per

capita growth. Checherita-Westphal and Rother (2012) present empirical evidence of significant

effects of government debt on private saving, public investment, and total factor productivity.

Pescatori et al. (2014) point out that higher levels of debt are correlated with more volatility in

GDP. Reinhart and Rogoff (2011) highlight the importance of considering the interactions between

debt, banking and inflation crises. This could also be a potential channel through which higher

levels of debt-to-GDP lead to lower subsequent growth. Therefore, it is important to further explore

these different channels empirically, in order to better understand the debt-growth relationship.

Moreover, there exists a gap in the literature from a theoretical perspective. To the best of

my knowledge, there are only few theoretical papers that formalize the relationship between debt-

to-GDP and GDP growth taking the productive public spending channel into consideration.

However, these studies impose unrealistic fiscal rules in arriving to their conclusions (e.g.,

Checherita-Westphal et al., 2014; Teles and Mussolini, 2014). Therefore, there is a need to develop

theoretical growth models with government borrowing and productive spending that build on

empirical findings and do not impose unrealistic fiscal rules. This topic, in addition to the empirical

estimation of different channels in the debt-growth relationship, is the subject of my ongoing

research.

7. Conclusion

This paper presents new evidence that the relationship between government debt-to-GDP

and subsequent GDP growth is non-linear. It is characterized by the presence of a threshold,

below which the relationship is either positive or non-existent, and above which it turns to negative.

The estimated threshold is between 30% and 35%. This result is based on applying the regression

kink model estimation method from Hansen (2017) on a panel of advanced European economies.

This result is supplemented by the result from applying the same method on the United States

time series data as shown in the appendix. This is in line with results from different empirical

studies on the subject. It is worth mentioning that, to the best of my knowledge, all recent studies


that restrict attention to a sample of European countries find that the relationship between debt and

growth in these countries is non-linear. The result presented in this paper reinforces this conclusion

using a new estimation method, and a different sample of countries and time coverage.

I use ten-year averages in this paper as my aim is to capture the long term aspect of the

debt-growth relationship. It is important to differentiate short run from long run effects as each

have different implications, and are treated differently in theoretical models. Papers that use one

year or less as the period of analysis can tell us about the short run effects of higher debt.

For example, we can infer about the effects of using debt to finance fiscal stimuli in times of

recession. In contrast, using longer periods such as five or ten years (common in the growth

literature) or more (when data permits) can tell us about the effects of higher debt on the long-run

growth rate. This could be the balanced path growth rate, or the growth rate on the transitional path

depending on the assumptions used.

It remains interesting to explore the mechanisms through which this relationship works.

Many candidates are put forward as potential channels through which higher debt affects growth.

More empirical studies are needed to estimate and confirm the significance of each channel.

In addition, there is a need to develop a theoretical model that can guide the analysis. Building on

an endogenous growth model with productive government spending à la Barro (1990) is a

promising venue which I pursue next in this research project.


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euro area. Journal of International Money and Finance, 32, 809-821.

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Appendix

Reinhart and Rogoff (2010) gather data for debt-to-GDP, GDP growth, and inflation rates

in the United States from 1790 to 2009. This is probably one of the longest time series data

available for one country. Using this dataset, Hansen (2017) reports a 43.8% threshold for debt-to-

GDP in the United States. Below the threshold, the coefficient is positive and above the threshold

it turns into negative, which indicates a non-linear relationship. These results are not subject to the

parameter heterogeneity critique since they come from data on one country.

The period used in Hansen is one year, which means that these results may reflect a

short-run relationship with business cycle fluctuations nuisance. Hence, I use the full time series

with the same model from Hansen to test the relationship using five-year and ten-year averages.

Unfortunately, even with such a relatively long time series, the number of observations remains

relatively small (43 in the five-year case, and 21 in the ten-year case). This affects the significance

of the results. The basic model used for estimation is as per equation (3) below:

𝑦𝑡 = 𝛽0

+ 𝛽1(𝑑𝑡−1 − 𝛾)− + 𝛽2(𝑑𝑡−1 − 𝛾)+ + 𝛽3𝑦𝑡−1 + +𝜀𝑡 (3)

where 𝑦𝑡 is the average growth rate of GDP per capita in period t (where t is 5 years or 10 years),

𝑦𝑡−1 is the lagged average growth rate of GDP per capita, while (𝑑𝑡−1 − 𝛾)− and (𝑑𝑡−1 − 𝛾)+

are same as before. Further, to make use of all data, I add average inflation rates to the regression.

Finally, I add the change in average debt-to-GDP.

Results are shown in table A1. Estimates have wide confidence intervals even at the 10%

confidence level, which is expected sue to the limited number of observations. Nevertheless,

results are strikingly similar to the European countries’ results presented in this paper. Below

threshold coefficients are positive, while above threshold coefficients are negative, indicating a

non-linear relationship. This is displayed in figures A1 and A2. In addition, the estimated

thresholds are 42% for the five-year case and 38% for the ten-year case which are lower yet close

to the threshold estimated by Hansen.

Although these results are inconclusive, given the relatively small sample size, they

supplement the results reported in this paper as well as other papers. The conclusion is again that

accumulating debt beyond a certain tipping point leads to a negative relationship between debt and

subsequent growth. As long as the ratio of debt-to-GDP is maintained below that tipping point,

there is some evidence that governments can use debt financing to boost growth via productive

spending. However, the relationship is in general statistically insignificant below threshold.

Another point worth mentioning is that while the threshold may differ by country or region, the


results from estimating different models in this paper for both Europe and the United States point

out to a range of 30% to 40%. This indicates that governments in these countries must aim to

maintain a long-run average of debt-to-GDP around that range.

Fig. A1. 5-yr avg growth & avg lagged debt-to-GDP; United States time series data.

Fig. A2. 10-yr avg growth & avg lagged debt-to-GDP; United States time series data.


Explanatory Variable Model 1 (5-yr) Model 2 (5-yr) Model 3 (10-yr) Model 4 (10-yr)

Threshold (γ) 42% 42% 38% 38%

0.016

(0.647)

0.017

(0.237)

0.014

(0.021)

0.014

(0.020)

-0.040

(0.138)

-0.049

(0.057)

-0.030

(0.063)

-0.019

(0.133)

Lagged GDP per Capita Growth -0.083

(0.212)

-0.062

(0.193)

0.212

(0.256)

0.258

(0.249)

Change in debt-to-GDP -0.019

(0.049)

0.055

(0.013)

Inflation 0.098

(0.332)

-0.080

(0.144)

Table A1

Regression Kink Model Estimates - United States Time Series

(Dependent Variable: Average Growth in GDP per Capita)



𝑑𝑖𝑡−1 − 𝛾 −

𝑑𝑖𝑡−1 − 𝛾 +

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Government Debt and GDP Growth: Is There a Threshold? - Economics · 2019-10-14 · DEBT AND GROWTH: IS THERE A THRESHOLD? 2 1. Introduction The aftermath of the recent Great Recession