Revisiting Reinhart & Rogoff after the Crisis: A Time Series Perspective

TL;DR: The authors revisited the debate on whether or not higher debt levels impede growth rates and contribute by offering a time series perspective of a corrected data set and also a more recent and higher frequency source.

Abstract: This paper offers a straightforward and descriptive contribution to the recent and busy debate on fiscal discipline made popular by a seminal paper by Reinhart and Rogoff (2010) after policymakers have sought foundation and justification of a policy known as austerity measures following the recent sovereign debt crisis. We revisit the debate on whether or not higher debt levels impede growth rates and contribute by offering a time series perspective of a corrected data set and also a more recent and higher frequency source. We find that with further hindsight and from a time series perspective there is no support for the view that higher levels of debt cause reductions in economic activity.

Summary

1. Introduction

• The authors argue that the field has yet to present a coherent framework with consistent evidence for the existence of a 'debt-threshold' or a strong case for a significant and negative causal link between public debt and economic growth.
• Instead, their findings lend support to those who suggest a reverse causality, where slumps in economic activity are largely responsible for increases in public debt.

2. Relevant Literature

• Within the empirical literature, numerous approaches have been employed in the attempt to shed light on the debt-growth relationship.
• Whilst the authors acknowledge the wider scope of the literature, the purpose of this study is to concentrate on the empirical post-crisis strand which has the 'debt-threshold' hypothesis at its core.
• The authors argue that this particular strand of the literature has yet to present a coherent framework with consistent evidence for the existence of a 'debt tipping point' or a strong case of a significant and negative causal link between public debt and economic growth.
• The authors show this in the preceding paragraphs using the delineating factors of exploratory evidence, correlation and causality, endogeneity, and cross-country heterogeneity.

2.1. Exploratory Evidence

• In their influential study Reinhart and Rogoff (2010) suggest a debt threshold of 90% at which growth is reduced by half for a sample of OECD countries.
• Nonetheless, it would be unjust and rather convenient to hold Reinhart and Rogoff (2010) accountable for the direction into which the public, political or economic debate has been leaning, let alone for the economic consequence of austerity itself.
• Egert (2013) performs a descriptive analysis of the original Reinhart and Rogoff (2010) data, its corrected counterpart (Herndon et al., 2014) as well as a third data set by Egert (2012) where the author had matched government debt data presented in Reinhart and Rogoff (2010) with growth rates from the Barro and Ursula (2010) data set.

2.2. From correlation to causality

• Apart from this algebraic relationship, the endogenous connection between both variables becomes even more illustrative if the authors consider the fact that some policy interventions may explicitly further endogenise both variables:.
• This rational provides a more theoretical argument for a 'reverse causality' link from low growth to high debt where high deficit spending may be one but not the only driving force of crumbling GDP growth rates.
• As shown in Baek and Brock (1992) , such parametric and linear Granger causality tests are found to have low power against certain non-linear alternatives.

2.3. Endogeneity in a cross-country setting

• Panizza and Presbitero (2014b) instrument the debt-to-GDP ratio with the valuation effect of debt held in foreign currency and exchange rate movements.
• Their exogenous instrument for country i is the averaged debt-to-GDP ratio of all remaining (12−i) countries; a proposition which may cast doubts in terms of validity: Checherita-Westphal and Rother (2012) also employ endogenous instruments to combat the challenges of endogeneity by means of a GMM estimation framework.
• Unfortunately, the inclusion of lagged, endogenous instruments may not adequately address the endogeneity problem in this particular case as this method was initially designed with microeconomic purposes in mind.
• To summarise, empirical efforts to unfold the debt-to-growth relationship through a cross-country framework are challenged by their capability to adequately control for model simultaneity.

2.4. Heterogeneity

• Important implications arise around the issue of cross-country heterogeneity.
• Particularly for a set of homogeneous and strongly interconnected entities, cross-sectional dependence may severely bias estimation results.
• The importance of accounting for cross-country heterogeneity is also stressed by Chudik et al. (2015) who provide evidence of cross-sectional heterogeneity of the 'debtthreshold' hypothesis in a dynamic, heterogeneous panel set-up.
• The authors provide threshold estimates of between 60 to 80 percent for the full sample as well as 80 percent for the advanced economies and between 30 to 60 percent for developing countries respectively when not accounting for unobserved common factors.
• Their cross-sectionally augmented models fail to reject the hypothesis of no simple debt threshold.

2.5. Summary

• In this section the authors have surveyed a wide and contradictory field of academic research concerned with the importance of public debt for economic activity.
• The authors have focused on the most consistent and well developed body of 'debt literature' in advanced economies in terms of modelling choices.
• The authors reading of the literature is that the debt-growth relationship is both more complex and heterogeneous, when considered across countries and time periods, than initially assumed.
• What is more, it also raises the question as to whether gross debt is indeed the correct measure for this investigation in the first place, because of its inherent inability to consider the cross-sectional heterogeneity of national debt compositions.
• One interesting characteristic of the debate, to date, is that as the argument develops over time the consensus appears to be reversing, with later studies tending to disagree with the existence of the debt threshold.

3. Exploratory Data Analysis: A Time-series Perspective

• In this section the authors revisit the central claims made in Reinhart and Rogoff (2010) by employing a novel exploratory approach to visually disentangle the linkage between economic growth and public debt.
• The authors do this by using the corrected Reinhart and Rogoff (2010) data set following Herndon et al. (2014) which they contrast with up-to-date and higher-frequency OECD data.
• The authors offer a deliberately uncomplicated contradiction to the findings of Reinhart and Rogoff (2010) and the earlier supporting literature, by employing basic visual and exploratory techniques, in a similar way to Reinhart et al (2012) , allowing us to highlight channels and directions of causality, that might remain difficult to disentangle in more sophisticated empirical techniques.
• In doing so; the authors use an approach that they hope will facilitate wider access to this important debate, beyond the field of economics.
• The authors goal is to develop insights regarding the time-dependent causality pattern of debt and growth, their structural nature as well as any potential threshold effects of debt by comparing the patterns of the same set of countries and periods at different frequencies.

3.1. Inter-temporal Linkage of Debt and Growth

• In order to evaluate the relationship between public debt and time the authors introduce three regimes for debt and growth which they define based on the findings in the literature:.
• There also seems to be little visual evidence to suggest that the absorption of the financial crisis reflected by the decline in the growth rates seem to be associated with the debt regime of the corresponding countries in any way:.
• The authors try to address this issue in Figure 3 where they again use Reinhart and Rogoff (2010)'s annual data set and plot the levels of the debt-to-GDP ratio against time.
• If high public debt is causing low economic growth, the authors would assume to see more medium and low growth regimes associated with countries with higher debt levels.
• Rather than being typically present for extremely high levels of the sovereign debt ratio, periods of low economic growth seem to occur at similar time periods across countries (and have become more frequent in the 1980s to mid-1990s).

3.2. Non-linearities and Thresholds

• The authors acknowledge the argument that even if previous debt levels might not have been detrimental in causing low economic growth, as suggested in their analysis, this does not mean that sovereign debt induced economic slowdowns are an impossibility.
• This result is intuitive and is in line with their previous observations:.
• Crises can typically be characterised by a sharp drop in average growth rates and seem to generally lead to a debt build-up afterwards.
• Nevertheless, growth figures are nowhere near the negative aggregates reported in Reinhart and Rogoff (2010) for the 90% threshold, of which there appears to be very little evidence.

4. Conclusion

• The continuing debate over the imposition of measures to deal with sovereign indebtedness, since the financial crisis, has become centred on the seminal contribution by Reinhart and Rogoff (2010) .
• Since the publication of various inaccuracies in methodology pointed out by Herndon et al. (2014) amongst others, the argument has continued unabated.
• Secondly, after the financial crisis, it is evident that the number of higher debt regimes has exploded; offering support for reverse causality of debt caused by economic slumps.
• Thirdly, it seems that periods of low growth tend to be clustered around common time periods for many countries and not bound to country samples displaying particularly high levels of debt, thereby offering further support for reverse causality.
• The authors demonstrate that the average negative relationship between economic growth and the debt-to-GDP ratio strongly depends on the time dimension of consideration, and that accounting for business-cycle effects and short-term volatility accounts for much of the negative variation in growth figures.

Figures

Table B.1: Summary statistics

Figure 6: Average k-period-ahead GDP Growth rates vs. debt threshold levels τ, quarterly OECD data, 1996Q01 to 2018Q2

Figure D.8: Individual Country plots of debt-to-GDP ratio, Reinhart and Rogoff (2010), 1946 to 2009

Figure D.7: Individual Country plots of GDP Growth, Reinhart and Rogoff (2010), 1946 to 2009

Figure 1: GDP Growth, Reinhart and Rogoff (2010) data, 1946 to 2009

Figure 4: Debt-to-GDP ratio, quarterly OECD data, 1996Q01 to 2018Q2

Figure 3: Debt-to-GDP ratio, Reinhart and Rogoff (2010) data, 1946 to 2009

Figure D.10: Individual Country plots of debt-to-GDP ratio, quarterly OECD data, 1996Q01 to 2018Q2

Figure D.9: Individual Country plots of GDP Growth, quarterly OECD data, 1996Q01 to 2018Q2

Figure 5: Average k-period-ahead GDP growth rates vs. debt threshold levels τ, Reinhart and Rogoff (2010) data, 1946 to 2009

Figure 2: GDP Growth, quarterly OECD data, 1996Q01 to 2018Q2

Full text

The University of Manchester Research
Revisiting Reinhart & Rogoff after the Crisis: A Time Series
Perspective
DOI:
10.1093/cje/bez009
Link to publication record in Manchester Research Explorer
Citation for published version (APA):
Amann, J., & Middleditch, P. (2020). Revisiting Reinhart & Rogoff after the Crisis: A Time Series Perspective.
Cambridge Journal of Economics, 44(2), 343-370. https://doi.org/10.1093/cje/bez009
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Cambridge Journal of Economics
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Download date:09. Aug. 2022

Reprint submitted to Cambridge Journal of Economics 18 May 2019
REVISITING REINHART & ROGOFF AFTER THE CRISIS:
A TIME SERIES PERSPECTIVE
Abstract(
This paper offers a straightforward and descriptive contribution to the recent and busy
debate on fiscal discipline made popular by the seminal Reinhart and Rogoff (2010) paper,
after policymakers have sought foundation and justification for a policy known as austerity
measures, following on from the sovereign debt crisis of 2010. We revisit the debate on
whether or not higher debt levels impede growth rates and offer a time series perspective
of a corrected data set and a more recent higher frequency source. We find that with further
hindsight, and from a time series perspective, there is little to no support for the view that
higher levels of debt cause reductions in economic activity. In contrast to Reinhart and
Rogoff (2010), we suggest that economic slumps tend to cause debt build-ups rather than
vice versa.
Keywords: Austerity, Macroeconomic Policy, Fiscal Policy
JEL(Classification:"E60,"E62,"E65(
(
1. Introduction(
In the aftermath of the global financial crisis we revisit the popular debate on fiscal
discipline that has become crystallised around a controversial study by Reinhart and Rogoff
(2010), the findings of which suggest that countries with higher debt/GDP ratios (of above
90%) are associated with impeded growth rates. Our contribution to this debate is a time
series analysis that makes use of a more recent and higher frequency data source, obtained
from the OECD, alongside a corrected version of the original data from Herndon et al.
(2014), responsible for previous implications that austerity measures can be implemented
to reactivate an economy experiencing a deep recession.
In contrast to the majority of the literature on the debt growth nexus, our approach
is one that makes use of a deliberately simplistic time series perspective. We provide an
exploratory and descriptive presentation of the facts, in a similar way to Reinhart et al
(2012) and some of the earlier literature surrounding the Reinhart and Rogoff (2010)
findings. We do so alongside a comprehensive debt threshold analysis which we suggest
is perfectly adequate for the purpose of providing further evidence to this busy debate,
offering an alternative view on a topic that has been the subject of wide controversy inside
and beyond the field of economics. We consider our contribution a worthy addition to the

2
literature, given that more sophisticated empirical studies have so far found inconclusive
support for the Reinhart and Rogoff (2010) ‘debt-threshold’ hypothesis and are oftentimes
confronted with severe empirical challenge. We find little to no evidence to support the
view that higher public debt levels dampen economic growth, and rather the converse case,
where depressions in output lead to higher debt, is more likely in line with other papers
that have stressed the reverse-causal nature of economic growth and public debt (Puente-
Ajovín and Sanso-Navarro, 2015; Lof and Malinen, 2014 and Irons and Bivens, 2010).
The financial crisis of 2007 brought an extraordinary slump in economic activity
and significant increases in gross government debt for many western developed economies.
Increased borrowing and the need to recapitalise financial institutions left governments
across Europe vulnerable in terms of borrowing ability, and consequently facing sovereign
debt crises. Even though the causality linkage between public debt and economic growth
is rather complex, and not yet fully understood, it is believed to be best described through
a bidirectional relationship: In conventional views, public debt build-ups through increases
in public spending, are assumed to have a positive short-run expansionary effect on
demand, but also a crowding out of capital and thus lower economic growth in the medium
to long-run.
On the other hand, low economic growth is also likely to induce higher public debt.
Given the rise in gross government debt figures across advanced nations, it is of little
surprise that scholars have tried to find an answer to the question of whether or not
economic growth can be stifled by excessive public debt. Up until the unfolding of the
financial crisis, there had been little research in this area. An influential study by Reinhart
and Rogoff (2010) found a link between public debt and economic growth with evidence
of a debt-threshold (of 90%) at which economic growth is reduced by half. This study is
not alone in the support of the debt-threshold hypothesis, see Cecchetti et al. (2011), Casni
et al. (2014), Baum et al. (2013), Woo and Kumar (2015) or Caner et al. (2010) for
examples.
In an environment of surging public debt and crumbling growth rates, international
organisations and policymakers have found their own interpretation of studies such as this
to legitimise rigorous public spending cuts, commonly referred to as austerity measures; a
term used to describe a form of fiscal discipline, and discussed in detail by Konzelmann
(2014). Whereas the effectiveness and legitimacy of austerity measures are widely
discussed in the public, economic and political arenas, the findings in Reinhart and Rogoff
(2010) have also provoked rigorous discussion in the field of applied economics, including
contradictions by Chang and Chiang (2012) and Panizza and Presbitero (2014a), and
serious technical challenges to the validity of the methodology, such as Herndon et al.
(2014), Kourtellos et al. (2013) and Minea and Parent (2012).
In this study we re-visit the busy debate on the causal relationship between
economic growth and sovereign debt by offering a two-fold contribution: In Section 2, we
compartmentalise the literature using the most recent empirical contributions surrounding
the field of fiscal discipline, discussing empirically motivated work in the context of
correlation, causality, endogeneity and cross-country heterogeneity. We argue that the field

3
has yet to present a coherent framework with consistent evidence for the existence of a
‘debt-threshold’ or a strong case for a significant and negative causal link between public
debt and economic growth. In Section 3, we emphasise the need for a more careful
evaluation in the context of heterogeneity patterns and threshold effects via a simple visual
analysis of two comprehensive data sets: We employ the corrected Reinhart and Rogoff
(2010) data provided by Herndon et al. (2014) and a more recent and higher frequency
OECD data source to provide a non-parametric and descriptive evaluation of both the
potential causal link between the variables as well as the ‘debt-threshold’ hypothesis.
A key advantage of extending our analysis to encompass the higher frequency data
source is the additional ability to consider higher frequency information including intra
annual fluctuations; although one might question the usefulness of this additional measure,
given the notorious persistence in debt and growth dynamics generally. In the context of
the Reinhart and Rogoff (2010) study, the usefulness arises from the time period in
question. The OECD sample benefits from increased scope and captures a period of
increased volatility witnessed since 2009. We therefore suggest that the perspective
provided by the OECD quarterly data is an enhanced one.
The use of lower frequency data can lead to confusion over the direction of
causality, a key issue in the context of this debate over the relationship between debt and
growth. The causal relationship can appear immediate in lower frequency data, and this
may explain the conflicting findings in the debt growth nexus literature, underlining the
value of exploratory analyses such as this study. By comparing different frequencies with
varying data coverage we illustrate a robustness in our findings that holds despite some
data discrepancies across both sets.
1
Given that debt levels have risen consistently from the
beginning of the financial crisis, and for many countries surpassing the 90% mark of the
sovereign debt-to-GDP ratio, this study benefits from a longer time series perspective on
the correlation between debt levels and economic growth; one which encompasses these
crucial debt build-ups in the latter part of the OECD sample. We find consistency across
both data sets and provide particular focus and comparison of the period leading up to the
financial crisis with that of the period of global recovery, where economic activity has
returned to more normal levels.
With the benefit of the extended scope provided by the two different data sets, we
illustrate that there is little to no evidence to support for the view that higher public debt
levels dampen economic growth. Instead, our findings lend support to those who suggest a
reverse causality, where slumps in economic activity are largely responsible for increases
in public debt. This becomes obvious as debt build-ups typically proceed economic
downturns, a pattern that regularly appears, irrespective of the actual debt level. At the
same time, even though actual growth outcomes are shown to be high in volatility, median
growth rates for countries above the 90% threshold are indistinguishable from their low-
debt counterparts.
As debt levels have risen consistently from the beginning of the financial crisis, and
for many countries surpassing the 90% mark of the sovereign debt-to-GDP ratio, this study
benefits from a longer and time series perspective on the correlation between debt levels

4
and economic growth. With the benefit of extended scope and hindsight, our study finds
no clear-cut evidence in favour of the debt-threshold hypothesis. Instead, it lends support
to those who suggest a reverse causality, where slumps in economic activity are largely
responsible for increases in public debt. Consequently, we conclude that our analysis
throws serious doubt over previous findings that austerity measures might assist in the
reactivation of an economy from a deep recession.
2. Relevant(Literature(
Within the empirical literature, numerous approaches have been employed in the attempt
to shed light on the debt-growth relationship.
2
Whilst we acknowledge the wider scope of
the literature, the purpose of this study is to concentrate on the empirical post-crisis strand
which has the ‘debt-threshold’ hypothesis at its core. We argue that this particular strand
of the literature has yet to present a coherent framework with consistent evidence for the
existence of a ‘debt tipping point’ or a strong case of a significant and negative causal link
between public debt and economic growth. We show this in the preceding paragraphs using
the delineating factors of exploratory evidence, correlation and causality, endogeneity, and
cross-country heterogeneity.
!"#" $%&'()*+(),-$./01231-
In their influential study Reinhart and Rogoff (2010) suggest a debt threshold of 90%
at which growth is reduced by half for a sample of OECD countries. More precisely, their
‘[...] main result is that whereas the link between growth and debt seems relatively weak
at ‘normal’ debt levels, median growth rates for countries with public debt over roughly
90 percent of GDP are about one percent lower than otherwise’ (Reinhart and Rogoff,
2010, p. 573). Even if it is clear that association or correlation between two variables by
no means implies a causal effect of one variable on the other, the authors are probably over
ambitious in arguing that, ‘[...] when gross external debt reaches 60 percent of GDP,
annual growth declines by about two percent; for levels of external debt in excess of 90
percent of GDP, growth rates are roughly cut in half ’ (Reinhart and Rogoff, 2010, p. 573).
The Reinhart and Rogoff (2010) paper has also sparked controversy through the
empirical replication of their study by Herndon et al. (2014) who reported that coding
errors, selective data exclusion and unconventional weighting of summary statistics lead
to an inaccurate representation of the relationship between public debt and GDP growth
for the data sampled. After correcting these deficiencies, the previously reported,
extraordinary debt threshold becomes significantly smaller, leading Herndon et al. (2014,
p. 278) to conclude that ‘policy-makers cannot defend austerity measures on the grounds
that public debt levels greater than 90% of GDP will consistently produce sharp declines
in economic growth’. Nonetheless, it would be unjust and rather convenient to hold
Reinhart and Rogoff (2010) accountable for the direction into which the public, political
or economic debate has been leaning, let alone for the economic consequence of austerity

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Revisiting reinhart & rogoff after the crisis: a time series perspective" ?

This paper offers a straightforward and descriptive contribution to the recent and busy debate on fiscal discipline made popular by the seminal Reinhart and Rogoff ( 2010 ) paper, after policymakers have sought foundation and justification for a policy known as austerity measures, following on from the sovereign debt crisis of 2010. The authors find that with further hindsight, and from a time series perspective, there is little to no support for the view that higher levels of debt cause reductions in economic activity. In contrast to Reinhart and Rogoff ( 2010 ), the authors suggest that economic slumps tend to cause debt build-ups rather than 

Q2. What future works have the authors mentioned in the paper "Revisiting reinhart & rogoff after the crisis: a time series perspective" ?

When analysing the inter-temporal linkage between growth and debt, their time series analysis provides crucial evidence on the much debated possibility that growth can be endogenous on the level of external public debt. The authors build this argument, firstly, on the observations that the times series plots for growth in GDP, over the last six decades, reveal a downward trend over the sample ; a fact which could be the actual explanation for any negative correlation between debt and growth. Thirdly, it seems that periods of low growth tend to be clustered around common time periods for many countries and not bound to country samples displaying particularly high levels of debt, thereby offering further support for reverse causality. In addressing the question of the existence of a debt threshold, the authors find no evidence that countries will experience significant reductions in GDP growth after surpassing a certain percentage of the debt-to-GDP ratio. 

Q3. What is the immediate issue arising from the article?

An immediate issue arising is the obvious endogeneity problem resulting in an estimation bias of(2)which the authors derive in Appendix C. 

Q4. What is the significance of cross-sectional dependence?

Particularly for a set of homogeneous and strongly interconnected entities, cross-sectional dependence may severely bias estimation results. 

Q5. How many countries have used the Granger causality test?

In a sample of 16 OECD countries spanning 30 years Puente-Ajovín and Sanso-Navarro (2015) apply a panel bootstrap Granger causality test developed by Kónya (2006) which accounts for cross-country heterogeneity as well as cross-sectional dependence. 

Q6. How does the authors find evidence of a common cross-country debt threshold?

Using a dynamic Common Correlated Effects (CCE) Mean Group estimator which allows for varying country-level coefficients they find no empirical evidence of a common cross-country debt threshold. 

Q7. What is the purpose of this study?

Whilst the authors acknowledge the wider scope of the literature, the purpose of this study is to concentrate on the empirical post-crisis strand which has the ‘debt-threshold’ hypothesis at its core. 

Q8. What makes the threshold argument problematic in the eyes of the authors of this study?

What makes the threshold argument problematic in the eyes of the authors of this study is that through their ad-hoc selection rule, Reinhart et al. (2012) identify 26 debt-overhang periods for only 13 out of their sample of 22 advanced countries and furthermore note that ‘[...] many debt overhangs result from costly wars. 

Q9. What is the way to address this issue?

A straight-forward way common within the literature to address this issue is by treating both GR and D as endogenous by means of a vector autoregressive (VAR) model of the form(3a)(3b)where (pGR, pGR) denotes the selected lag length for the endogenous variables. 

Q10. What is the main reason why the authors fail to reject a non-Granger causality?

Another study which analyses a Granger causal relationship is Irons and Bivens (2010) who study the debtgrowth nexus for the case of the USA and fail to reject non-Granger causality going from debt to growth but finds significant evidence of a reverse causality link from growth to debt. 

Q11. What does the author say about the relationship between debt and growth?

they report that the association of debt and growth tends to weaken for higher levels of debt, particularly when controlling for peer country growth rates. 

Q12. How does Baum et al. (2013) find evidence of a significant increase in the debt?

As discussed before, Baum et al. (2013) find evidence of a considerable increase in the significant debt threshold (from 66 to 72 and 96 percent for the non-dynamic and dynamic panel respectively) if the crisis years 2008 to 2010 are added to the analysis. 

Q13. How do they approach the challenges of endogeneity?

Checherita-Westphal and Rother (2012) also employ endogenous instruments tocombat the challenges of endogeneity by means of a GMM estimation framework. 

Q14. What is the main result of Reinhart and Rogoff’s study?

More precisely, their ‘[...] main result is that whereas the link between growth and debt seems relatively weak at ‘normal’ debt levels, median growth rates for countries with public debt over roughly 90 percent of GDP are about one percent lower than otherwise’ (Reinhart and Rogoff, 2010, p. 573).