




































American Economic & Social Review 

 Vol. 6, No. 2; 2020 

ISSN 2576-1269   E-ISSN 2576-1277 

Published by CRIBFB, USA 

 

31 

IS THE REINHART-ROGOFF DEBT THRESHOLD 

APPLICABLE TO ITALY? 
 

 

Dr. Yu Hsing 

Joseph H. Miller Endowed Professor in Business 

Department of Management & Business Administration 

College of Business 

Southeastern Louisiana University 

Hammond, Louisiana 70402, USA 

E-mail: yhsing@selu.edu 

 

ABSTRACT 

This paper employs an extended production function to examine the relationship between central 

government debt and economic growth in Italy. The results show that the threshold of the central 

government debt ratio for Italy is estimated to be 105.00%, which is greater than the 90% debt 

threshold proposed by Reinhart and Rogoff. Besides, a higher growth rate of labor employment 

or investment/GDP ratio would raise the growth rate. Hence, the debt threshold proposed by 

Reinhart-Rogoff underestimates the debt threshold for Italy. The finding suggests that the debt 

ratio of 131.09% in 2019 is well above the debt threshold and is likely to be unsustainable. 

 

Keywords: Fiscal Policy, Government Debt, Reinhart-Rogoff Hypothesis, Debt Threshold.  

 

INTRODUCTION 

During and after the global financial crisis, many countries engaged in fiscal expansion to 

stimulate their economies. Italy is no exception. The central government debt ratio rose rapidly 

from a low of 98.13% in 2007 to 110.10% in 2009. The debt ratios continued to rise and reached 

130.27% in 2014 and then stabilized around 130% - 131% after 2014. Whether a higher 

government debt ratio would increase or reduce the growth rate of real GDP has been studied 

extensively. Reinhart and Rogoff (2010a, 2010b) show that the threshold or turning point of the 

government debt ratio is 90%. Beyond 90%, a further increase in the debt ratio tends to reduce 

the growth rate. 

The purpose of this paper is to test whether the Reinhart-Rogoff hypothesis may apply to 

Italy. Is it possible to have a debt threshold or turning point of 90% of GDP for Italy? This paper 

has several different aspects. First, a production function is extended to include the government 

debt ratio. Second, the paper uses a quadratic function to test whether there may be an inverted 

U-shape relationship and a turning point. Third, the GARCH process is employed in empirical 

work to correct for potential autoregressive conditional heteroskedasticity.    

 

LITERATURE SURVEY 

Based on a sample of forty-four advanced and developing countries covering many years, 

Reinhart and Rogoff (2010a, 2010b) find that there is a weak relationship between the growth 

rate and the debt ratio when the debt ratio is less than 90% whereas a debt ratio greater than 90% 

causes the growth rate to decline. This threshold for the debt ratio is comparable in advanced and 



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32 

emerging economies. However, using the same data sample developed by Reinhart and Rogoff 

and different specifications, Minea and Parent (2012) find that the threshold for the debt ratio is 

115%. Herndon, Ash, and Pollin (2014) use the same data compiled by Reinhart and Rogoff and 

find that for 20 advanced countries, the negative effect of the public debt ratio above 90% on 

economic growth cannot be confirmed. According to Herndon, Ash, and Pollin, during 1946–

2009, countries with public debt ratios over 90% recorded an average growth rate of 2.2% 

instead of −0.1% as presented by Reinhart and Rogoff. The relationship between the economic 

growth rate and the public debt ratio differs substantially by country and period. Égert (2015a, 

2015b) indicates that the 90% debt threshold cannot be confirmed and that the thresholds or 

negative links may exist at a much lower debt level between 20% and 60%. The magnitude of 

the thresholds is uncertain. A nonlinear relationship is not robust and sensitive to model 

specifications. Parameter estimates vary across countries. Lee, Park, Seo, and Shin (2017) find 

no support for the 90% debt threshold. Using the post-WWII data developed by Reinhart and 

Rogoff, they show that the debt threshold maybe around 30%. Beyond 30%, the growth rate will 

decline by 1 percentage point. 

Based on a sample of 18 OECD countries during 1980-2008, Cecchetti, Mohanty, and 

Zampolli (2011) find that the government debt threshold is 85%, suggesting that an increase in 

the government debt ratio beyond 85% tends to harm economic growth. They also show that 

when the corporate debt ratio is greater than 90% of GDP, there will be an adverse effect on 

growth.  

Checherita-Westphal and Rother (2012) examine the relationship between government 

debt and economic growth using a sample of 12 countries in the euro area. They find a threshold 

or turning point in the range of 90% - 100%, indicating that an increase in the government debt 

ratio tends to reduce economic growth if the debt ratio is greater than 90% - 100%. The threshold 

would start in the range of 70% - 80% based on the confidence interval. 

Baum, Checherita-Westphal, and Rother (2013) investigate the relationship between 

government debt and growth for twelve countries in the euro area. A higher debt ratio increases 

economic growth but has no impact when the debt ratio reaches about 67%. When the debt ratio 

is greater than 95%, a higher debt ratio reduces economic growth. 

Afonso and Jalles (2013) examine the impact of government debt on economic growth 

for 155 advanced and developing countries during 1970 – 2008. The debt threshold is estimated 

to be 59% for the eurozone and 79% for emerging economies. If the debt ratio increases by 10%, 

the growth rate would decrease by 0.2% if the debt ratio is over 90% and increase by 0.1% if the 

debt ratio is below 30%. 

Chirwa (2017) studies the relationship among government debt, growth, and other related 

variables for ten countries in the euro area.  The threshold is estimated to be 70% in the long run 

whereas government debt and economic growth have a negative relationship in the short run. 

Woo and Kumar (2015) show that if a 10-percentage point increase in the initial debt ratio tends 

to reduce the growth rate of real per capita GDP by 0.2 percentage points. A higher initial 

government debt ratio tends to cause a larger negative effect. The negative effect isowing tothe 

decrease in labor productivity growth. 

Lechtenberg (2017) analyzes the subject using a sample of 10 countries. Australia, 

Canada, Chile, Germany, and New Zealand have had low and declining debt ratios, and a higher 

debt ratio would not cause economic growth to decline in these countries. On the other hand, 

debt thresholds are found for France, Greece, Italy, the U.K., and the U.S. A higher debt ratio 



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33 

beyond the threshold tends to reduce economic growth in Greece, Italy, the U.K., and the U.S. 

but increase the economic growth rate for France.    

Comparing with public debt between Belgium and Italy, Sapir (2018) examines how 

these two countries have handled the debt issue. In the early 1990s, both countries have 

accumulated relatively high levels of public debt. After the Maastricht treaty took effect in 1993, 

both countries have improved their financial position to reduce the debt level to be eligible for 

the adoption of the euro. Before the launch of the euro, however, Italy’s debt position became 

worse mainly because Italy’s efforts stalked and did not pay enough attention to growth 

performance. During and after the global financial crisis and the Greek sovereign debt crisis, 

Italy took austerity measures, caused real GDP to decline, and raised the debt level. On the other 

hand, during the crisis, Belgium committed to fiscal discipline and debt sustainability. 

Reviewing Italy’s public debt during 1861-2018, Bastasin, Mischitelli, and Toniolo 

(2019) indicated that the relatively high public debt may not be sustainable and that the 

government needs to improve education, cut red tape, pursue investment-oriented fiscal 

expansion, and engage in structural reforms to enhance business competitiveness to promote 

growth. 

Using a large sample consisting of many advanced and developing countries, Swamy 

(2020) reveals that a 10-percentage point increase in the government debt ratio tends to result ina 

decrease in the average growth rate by 23 basis points and that the relationship between 

government debt and economic growth is nonlinear. The impact of government debt on 

economic growth varies by country, depending upon several major macroeconomic factors and 

debt regimes. 

Jacobs, Ogawa, Sterken, and Tokutsu (2020) explore the relationship between public debt 

and economic growth for 27 EU members and 4 OECD countries during 1995-2013. They show 

that economic growth Granger causes public debt, but not vice versa. Slow economic growth 

causes more public debt. In high-debt economies, slow economic growth increases public debt, 

which causes a higher long-term interest rate, dampens interest-rate sensitive private spending, 

and increases public debt. Besides, they indicate that high-debt economies show greater impacts 

of economic growth on the debt ratio and that the low-debt countries exhibit greater effects of the 

debt ratio on economic growth.  

 

The Model 

Applying Ram (1986, 1989) and Goel, Payne, and Ram (2008), the growth rate of real GDP can 

be expressed as: 

 

GY = w(GL, GK, DY)          (1) 

 

Where 

GY= the growth rate of real GDP(Y) in Italy,  

GL = the growth rate of labor (L),  

GK   = the growth rate of capital (K), and 

DY = the government debt-to-GDP ratio.  

Due to the lack of data for capital, the growth rate of capital can be substituted by the ratio of 

investment spending to gross domestic product (IY) (Ram, 1986, 1989).  

 

GY = z(GL, IY, DY)            (2) 



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34 

 

The coefficient of GL measures the elasticity of Y with respect to L, and the coefficient 

of IY represents the marginal product of capital. The coefficient of GL and IY is expected to be 

positive, and the sign of the coefficient of DY is unclear. When DY is relatively low, an increase 

in the government debt ratio for infrastructural improvements may enhance economic growth. 

When the debt ratio is relatively high, a further increase in the debt ratio tends to raise the 

interest rate, cause the local currency to appreciate, hurt exports, and crowd out private spending.  

There may be a threshold or an inverted U-shaped relationship between GY and the government 

debt ratio. An analysis of the data also finds that growth rates declined a great deal due to the 

global financial crisis. Hence, a binary variable (B) is also added to the estimated equation: 

 

GY = δ0 + δ1GL + δ2  IY + δ3  DY + δ4DY2 + δ5B + ε (3) 

 

An inverted U-shaped relationship between GY and the debt ratio suggests that the sign 

of DY should be positive and the sign of DY2should be negative. 

The critical value (turning point) of the debt ratio corresponding to the maximum growth rate of 

real GDP is given by: 

 

DY∗ = δ3 2δ4                  (4) 

 

Where,  𝛿3 is the coefficient of DY and 𝛿4 is the coefficient of DY2. 

 

EMPIRICAL RESULTS 

The data were collected from the World Economic Outlook, International Financial Statistics, 

and Eurostat. The growth rate of real GDP is expressed as a percent. The growth rate of labor 

employment is expressed as a percent. Investment spending as a percent of GDP is used as the 

data for capital is not available. Central government debt is measured as a percent of gross 

domestic product. The sample ranges from 1981 to 2019. The data for the government debt ratio 

or the growth rate before 1981is not available. 

Figure 1 shows the growth rates of real GDP over time. It appears that growth rates of 

real GDP were less than 2% after the year 2006 and were negative in 2008 and 2009 due to the 

global financial crisis. Figure 2 describes the central government debt as a percent of GDP.  The 

debt ratio declined during 1996-2007, rose during 2008-2013, leveled off after 2013, and reached 

131.09% in 2019. Figure 3 exhibits a scatter diagram between the debt ratio and the growth rate 

of real GDP. It seems that the relationship is nonlinear. With a few outliers, the relation was 

positive when the debt ratio was relatively small and negative when the debt ratio was relatively 

high.   

Table 1 presents the estimated regression and related statistics. The GARCH process is 

employed in empirical work to correct for autoregressive conditional heteroskedasticity. 

Approximately 58.60% of the variation in the growth rate of real GDP in Italy can be explained 

by the five independent variables. These five explanatory variables have the expected sign and 

are significant at the 1% or 10% level. The growth rate of real GDP in Italy is positively affected 

by the growth rate of labor, the investment/GDP ratio, and the central government debt ratio and 

negatively affected by the central government debt ratio squared and the binary variable for years 

2008 and 2009.  



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35 

A 1 percentage point increase in labor would result in an increase in the growth rate by 

0.5031 percentage points. If the investment-GDP ratio rises 1 percentage point, the growth rate 

would increase by 0.3388 percentage points. The quadratic relationship between the growth rate 

and the central government debt ratio indicates that the critical value of the central government 

debt ratio corresponding to the turning point is estimated to be 104.997%. During 2008-2009, 

growth rates of real GDP in Italy declined by 5.5745 percentage points.  

 

 
 

Figure 1. Growth rates of real GDP over time 

 

 
 

Figure 2. The government debt ratio over time 

 

-6

-4

-2

0

2

4

6

1985 1990 1995 2000 2005 2010 2015

GROWTH_RATEGROWTH_RATE

50

60

70

80

90

100

110

120

130

140

1985 1990 1995 2000 2005 2010 2015

DEBT_RATIODEBT_RATIO



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36 

 

 
 

Figure 3. Scatter diagram between the debt ratio and the growth rate of real GDP 

 

Table 1. Estimated regression for the growth rate of real GDP in Italy 

 

Variable Coefficient Probability 

Intercept -83.2978 0.0000 

The growth rate of labor 0.5031 0.0010 

Investment/GDP ratio 0.3388 0.0735 

Central government debt ratio 33.4988 0.0001 

Central government debt ratio squared -3.5990 0.0002 

Binary variable -5.5745 0.0000 

R squared 0.5860  

Sample period 1981-2019  

Number of observations 39  

Methodology GARCH  

Notes: The binary variable equals 1 during 2008-2009 and 0 otherwise. 

 

To sum up, the results in this paper show that the growth rate of real GDP has a positive 

relationship with the growth rate of labor, the investment/GDP ratio and a negative relationship 

with the binary variable during the global financial crisis during 2008-2009. The growth rate and 

the debt ratio exhibit a quadratic relationship with a threshold or turning point at 105.00%. 

In comparison, the finding of a threshold or turning point of 105.00% in this study is less 

than the 115% threshold estimated by Minea and Parent (2012) but greater than the 90% 

threshold proposed by Reinhart and Rogoff (2010a, 2010b) and other findings (Égert, 2015a, 

2015b; Lee, Park, Seo and Shin, 2017; Cecchetti, Mohanty, and Zampolli, 2011; Checherita-

Westphal and Rother, 2012; Baum, Checherita-Westphal and Rother, 2013; Afonso and Jalles, 

2013; Chirwa, 2017). The result in this study is in contrast with the results reported by Wu and 

-6

-4

-2

0

2

4

6

50 60 70 80 90 100 110 120 130 140

DEBT_RATIO

G
RO

W
TH

_R
AT

E

DEBT_RATIO

G
RO

W
TH

_R
AT

E



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37 

Kumar (2015) and Swamy (2020), which show that a higher government debt ratio hurts the 

growth rate.  

 

SUMMARY AND CONCLUSIONS 

This paper has applied an extended production function to examine the relationship between the 

central government debt ratio and the growth rate of real GDP in Italy. Reinhart-Rogoff (2010a, 

2010b) suggests that when the debt ratio is greater than 90% of GDP, a further increase in the 

debt ratio would slow down the growth rate. The main focus is to test whether the Reinhart-

Rogoff hypothesis may apply to Italy.  

Results show that their relationship is nonlinear and that there is a turning point or 

threshold estimated to be 105.00%. When the debt ratio increases and is less than 105.00%, the 

growth rate would rise. Conversely, when the debt ratio increases and is greater than 105.00%, 

the growth rate would decline.  Comparing with the current debt ratio of 131.09% in 2019, a 

further increase in the debt ratio would hurt economic growth. The estimated threshold suggests 

that the debt threshold of 90% proposed by Reinhart and Rogoff does not apply to Italy. 

Besides, the growth rate of real GDP is positively associated with the growth rate of 

employment and the investment/GDP ratio, and it declined during the global financial crisis 

during 2008-2009.  

Hence, to promote economic growth, Italy’s debt ratio needs to decrease because the 

current debt ratio is unsustainable. To pursue fiscal discipline and to reduce government deficits 

and debt, government spending needs to slow down or decline, and taxes need to increase. To 

enhance growth, authorities need to improve human capital by providing more training and 

quality education.     

 

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