We analyze possible targets for the French debt-to-GDP ratio with a small model. The role of the US and German GDP growth, prices of raw materials, ECB monetary policy, and domestic policy is analyzed in the debt dynamics. We find that external conditions, together with policies to stimulate growth and to generate a government surplus, play a fundamental role in the French fiscal consolidation.Debt to GDP Ratio, French Economy, International Factors

Esposito, Piero

Paradiso, Antonio

Rao, B. Bhaskara

English

Research Papers in Economics

1 
 
The dynamics of French public debt: Paths for fiscal consolidations 
Piero Esposito 
p.esposito@sssup.it 
Sant’Anna School of Advanced Studies, Pisa (Italy)  
 
 
Antonio Paradiso 
anto_paradiso@hotmail.com 
Department of Economics, University of Rome La Sapienza, Rome (Italy) 
 
B. Bhaskara Rao 
raob123@bigpond.com 
School of Economics and Finance, University of Western Sydney, Sydney (Australia) 
 
Abstract 
We analyze possible targets for the French debt-to-GDP ratio with a small model. The role of the 
US and German GDP growth, prices of raw materials, ECB monetary policy, and domestic policy is 
analyzed in the debt dynamics. We find that external conditions, together with policies to stimulate 
growth and to generate a government surplus, play a fundamental role in the French fiscal 
consolidation.  
 
Keywords: Debt to GDP Ratio, French Economy, International Factors. 
JEL: E62, H63, H68 
 
 
 
 
 
 2 
 
 
1. Introduction 
The 2009 recession has worsened the French fiscal balances and its debt situation. Government 
deficit rose significantly to 7 % of GDP and the government debt ratio reached about 82% of GDP 
in 2010. Therefore, a fiscal consolidation plan is needed to place France’s public finances on a 
sustainable path. This paper analyses the dynamics of the French government debt-to-GDP ratio 
(debt ratio hereafter) using a small-scale model based on Favero and Marcellino (2005) and Hasko 
(2007). Adopting various scenarios for the exogenous variables viz., US GDP growth, German 
GDP growth, oil price changes and short-term interest rates, we predict that France’s debt ratio can 
reach a target of 80% by 2020. Section 2 presents the basic arithmetics of debt accounting. Section 
3 gives a description of the model. Empirical results are in Section 4. Section 5 shows that under 
plausible assumptions our target of 80% for the debt ratio can be achieved. Section 6 concludes. 
 
2. Arithmetic of debt accounting 
The dynamics of debt accumulation can be described with the identities in (1) and (2): 
11 t t t t t B B i B PB               (1) 
where  t B  nominal general government debt at the end of year t, i the nominal interest paid on 
government debt, PB  primary advance which equals tax revenue less government expenditure net 
of the interests paid on debt (T – G). The above holds if the variables are measured in real terms if 
inflation is measured with the GDP deflator. Normally the budget dynamics is written in the form of 
a change in the debt ratio (b): 
1 t t t t t t b i g b pb               (2) 
where  inflation rate, g real GDP growth. Variables in lower case denote their ratios to GDP. 
According to (2) a stronger real GDP growth, a lower nominal interest rate, and a higher inflation 
will reduce the debt growth. The following condition is needed to guarantee solvency and debt 
reduction: 
* * * * * () pb i g b                 (3) 3 
 
where the variables with * are their sample averages. 
 
3.  A small macroeconomic model 
Identity (2) is used by Favero and Marcellino (2005) and Hasko (2007) in a simultaneous equations 
model to account for interactions among the key variables and we follow their approach. Our model 
consists of five equations in which the endogenous variables are driven by four international 
variables viz., US GDP growth, German GDP growth, Oil price dynamics, and domestic short-term 
Central Bank monetary policy rate. Our model is as follows: 
1 2 3 4 5 1
US GER GER y
t t t t t t g pb g g g  (4) (Output equation) 
6 7 1 8 1 1 9 1 10 09
L pribal
t t t t t t pb pb i i g DUM   (5) (Fiscal rule) 
11 12 1 13 14 1 15 16
GER b
t t t t t t t b b g pb g   (6) (Public debt equation) 
17 18 1 19 2 20 1 21 22 1 t t t t t t t g oil oil  (7) (Inflation equation) 
23 24 1 25 26 1 27
L L i
t t t t t t i i i g   (8) (Long-term interest rate equation) 
 
The output equation is explained by international business cycle effects ( 3 4 5 0, 0) 
captured by US (
US g ) and German (
GER g ) GDP growth rates and by primary balance (pb). A 
fiscal consolidation (a rise of the primary balance due to either an increase in government revenues 
or a cut in government spending) has in general a negative impact on economic growth. However, 
Rohn (2010) considers that the direct negative effect on aggregate demand could be potentially 
counterbalanced by a positive indirect effect if fiscal consolidation signals lower future public debt 
and taxes, as well as decreasing precautionary savings. In particular, this effect can be large if 
public debt is high. For France the indirect effect seems to be historically larger as one can see in 
figure A2 in the Appendix. The relationship between GDP growth and primary balance is strongly 
positive with a highly positive cross-correlation (0.63). Then, we expect a positive coefficient for 
the primary balance in the output equation ( 2). The primary balance depends positively on both 4 
 
output and the spread between long-term and short-term interest rates ( 8 0and  9 0). Higher 
rates on long-term government bonds imply higher costs of public debt service, forcing an increase 
in government revenues (or a cut in government spending) in order to contain public debt growth. 
We consider the long term interest rate as a proxy for the average cost of debt because the French 
government’s debt duration is getting closer to the duration of long-term bonds; see Figure A3 in 
the Appendix. A dummy (DUM09) is added to capture the financial crisis of 2009.  The debt ratio is 
explained by GDP growth, inflation and an international business cycle indicator (
GER g ). All signs 
in the equation are as expected, i.e.  13 0, 15 0, and  16 0. Inflation in equation (7) 
depends positively on oil price growth and output growth ( 20 0  and  21 22 0 ).
1 In the 
last equation the long-term interest rate depends positively on the short-term one ( 25 0), on 
inflation ( 26 0 ) and on output growth ( 27 0 ). 
4. Empirical results 
The system of equations (4) – (8) is estimated simultaneously with the Seemingly Unrelated 
Regression method (SUR) with annual data for the period 1970 - 2011. The results are in Table 1 
and are impressive. All the coefficients have the expected signs and are significant. The residual 
diagnostic test for absence of serial correlation (Portmanteau test) does not reject the null 
hypotheses and the normality test (Jarque-Bera), fails only for the long-term interest rate equation. 
This  non-normality is perhaps caused by outliers which produce an excessive kurtosis. Favero and 
Marcellino (2005) posit that the use of dummies could improve diagnostic tests but it could weaken 
its forecasting performance. Since forecasting is our main goal, we prefer not to introduce such 
dummies. 
In order to test the forecasting properties, we estimated the model from 1970 to 1999 and then 
forecasted for the next ten years, comparing the forecasted values with the historically recorded 
ones. The results are very satisfactory. To conserve space we report in appendix only the plot of the 
historical debt ratio versus the forecasted debt ratio (Figure A1).  
 
                                                             
1 Output growth is preferred to unemployment or output gap as indicator for the overall level of activity; see Hasko 
(2007). 5 
 
 
Table 1: SUR Estimates of French Debt Dynamics (1970 – 2010) 
1 2 3 4 5 1
US GER GER y
t t t t t t g pb g g g  (Output equation) 
1  2  3   4  5   2 R  
JB 
p-value 
   
0.0147 
(0.003) 
[4.273] 
0.4430 
(0.118) 
[3.741] 
0.1876 
(0.077) 
[2.424] 
0.3920 
(0.080) 
[4.907] 
-0.2806 
(0.083) 
[3.375] 
0.660  0.385     
6 7 1 8 1 1 9 1 10 09
L pribal
t t t t t t pb pb i i g DUM  (Fiscal rule) 
6  7   8   9   10  2 R  
JB 
p-value 
   
-1.5159 
(0.236) 
[6.424] 
0.3647 
(0.094) 
[3.869] 
0.2332 
(0.082) 
[2.849] 
0.4911 
(0.084) 
[5.813] 
-3.190 
(0.529) 
[6.031] 
0.849  0.832     
11 12 1 13 14 1 15 16
GER b
t t t t t t t b b g pb g  (Public debt equation) 
11  12  13  14  15  16  2 R  
JB 
p-value 
 
7.7448 
(1.172) 
[6.609] 
0.9438 
(0.018) 
[52.846] 
-0.8448 
(0.190) 
[4.495] 
-0.7064 
(0.156) 
[4.483] 
-0.2664 
(0.077) 
[3.450] 
-0.500 
(0.140) 
[3.547] 
0.993  0.156   
17 18 1 19 2 20 1 21 22 1 t t t t t t t g oil oil  (Inflation equation) 
17  18  19  20  21  22  2 R  
JB 
p-value 
 
-0.3983 
(0.251) 
[1.590] 
1.2255 
(0.137) 
[8.910] 
0.3010 
(0.127) 
[2.377] 
0.2391 
(0.076) 
[3.160] 
0.0272 
(0.003) 
[8.051] 
-0.0165 
(0.010) 
[2.951] 
0.963  0.925   
23 24 1 25 26 1 27
L L i
t t t t t t i i i g  (Long-term interest rate equation) 
23  24  25  26  27   2 R  
JB 
p-value 
Skewness 
p-value 
Kurtosis 
p-value 
0.8003 
(0.277) 
[2.888] 
0.4123 
(0.062) 
[6.645] 
0.4070 
(0.048) 
[8.383] 
0.1840 
(0.038) 
[4.887] 
0.0643 
(0.048) 
[1.326] 
0.972  0.000  0.124  0.00 
System residual Portmanteau tests for autocorrelations 
Q-Stat (Lag 1) 
(Prob. value) 
Q-Stat (Lag 2) 
(Prob. value) 
Q-Stat (Lag 4) 
(Prob. value) 
Q-Stat (Lag 6) 
(Prob. value) 
 
0.727  0.436  0.248  0.180   
Notes: Standard errors and t-ratios are in parentheses and brackets respectively 
 
5. Scenarios and debt-to-GDP dynamic forecasts 
Table 2 summarizes the assumptions of three scenarios (baseline, upward/optimistic, and 
downward/risky) for the exogenous variables together with the results for the endogenous variables. 
In an upside scenario in which both the domestic and global economies are stronger than expected, 6 
 
oil prices could grow well above US$200 per barrel.
2 The first three columns assume no policy 
intervention, while in the last column the outcome of a realistic policy intervention, in accordance 
with favorable international and monetary policy conditions, is shown.  
 
Table 2: Scenarios and Macroeconomic Analysis for 2011 - 2020 
  Baseline 
scenario 
Upside 
scenario 
Downside 
scenario 
Policy 
intervention 
Scenario 
Nominal short-term interest 
rate 
3.5%  4%  3%  3.5% 
2020 Oil price in US dollar 
and Euro  
Nominal  
206$ (155€) 
Nominal 
247$ (186€) 
Nominal  
171$ (129€) 
Nominal 
247$ (186€) 
Real 
184$ (139€) 
Real 
202$ (152€) 
Real 
139$ (105€) 
Real 
202$ (152€) 
Real US GDP growth  2%  2.4%  1.6%  2.4% 
Real GER GDP growth   1.8%  2.2%  1.4%  2.2% 
2020 Public Debt (% of GDP)  94%  90%  97%  78% 
Primary balance (% of GDP)
 *   -1.06%  -1.00%  -1.13%  0.16% 
Nominal long-term interest 
rate
*  
4.12%  4.49%  3.75%  4.43% 
Inflation
*   1.24%  1.55%  0.92%  2.26% 
Real GDP growth
*   1.53%  1.70%  1.38%  2.40% 
General Government balance 
in % of GDP
*  
4.67% 
(4.72%) 
4.86% 
(4.47%) 
4.35% 
(4.28%) 
3.37% 
(2.91%) 
* * * * * 0 pb i g d   -2.29  -2.11  -2.33  0.340 
Note: Real values for Oil price change are calculated assuming an international average inflation 
of 2.2% for the period 2011 – 2020. 
* Average values over the period. In parentheses the last 
government balance value in 2020. 
 
 
 
We simulate accommodating monetary policy (3.5%, below the 4% assumed in the upside scenario) 
in a positive international scenario (2.4% of US GDP growth and 2.2% for German GDP growth 
until 2020). In this situation, we assume the French government to raise its surplus by 0.4% and 
increase the baseline GDP growth by 0.2% every year from 2011 to 2020. With these policy mixes 
                                                             
2 Charles Maxwell of Weeden and Co., a renowned expert in the energy markets, predicts an oil price of 300$ in 2020. 
This value could be strong, but if the world economy will recover from the recession and economies, such as India and 
China, will continue to experience  double-digit or close growth, then a value well above 200$ could feasible.  7 
 
the GDP growth is in line with US GDP growth (2.4%), inflation will increase to above 2% 
(because of sustained growth) and, most importantly, the debt ratio will decrease below 80% in 
2020, fulfilling the Maastricht restrictions (below 3% of GDP) from 2017 (the deficit ratio in 2020 
is 2.91%). Without the implementation of this policy, the debt ratio ranges from 90% to 97%, 
depending on the scenario. The patterns of the variables in various scenarios are depicted in Figure 
1. 
 
 
 
Figure 1: Forecasts of macroeconomic variables for period 2011 – 2020. 
 
-3.0%
-2.0%
-1.0%
0.0%
1.0%
2.0%
3.0%
2
0
0
3
2
0
0
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0
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g_BASE g_UP g_DOWN g_INT
 
60.0%
65.0%
70.0%
75.0%
80.0%
85.0%
90.0%
95.0%
100.0%
2
0
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9
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2
0
d_BASE d_UP d_DOWN d_INT
 
-5.5%
-4.5%
-3.5%
-2.5%
-1.5%
-0.5%
0.5%
2
0
0
3
2
0
0
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2
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0
2
0
pb_BASE pb_UP pb_DOWN pb_INT
 
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
2
0
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2
0
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2
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5
2
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1
9
2
0
2
0
Infl_BASE Infl_UP Infl_DOWN Infl_INT
 8 
 
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
5.0%
5.5%
2
0
0
3
2
0
0
4
2
0
0
5
2
0
0
6
2
0
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2
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7
2
0
1
8
2
0
1
9
2
0
2
0
Lint_BASE Lint_UP Lint_DOWN Lint_INT
 
Notes: BASE = Base scenario, UP = Upside scenario, Down = Downside scenario, INT = Policy intervention 
scenario. 
 
6. Conclusions 
In this paper we used a small-scale econometric model in order to study possible patterns of the 
French debt ratio in the next ten years. Our results show that, even in presence of external positive 
scenarios, the debt ratio will not decrease to less than 90%. Our simulation showed that a policy 
intervention aimed at both pushing the GDP growth rate not below 2.3% and generating little 
government surplus is needed to bring the debt-to-GDP ratio below the 80% threshold.  
 
Data Appendix 
  Definitions and Data Source: 1970 - 2010 
Variable  Definition  Source 
b   Debt-to GDP ratio  AMECO - EUROSTAT 
(AE) 
  Percentage change of Consumer Price Index  OECD Statistics 
(OCED) 
g   Real GDP growth  AE 
US g   Real US GDP growth  Federal Reserve 
Economic DATA 
(FRED) 9 
 
GER g   Real German GDP growth  AE 
pb  Primary balance (Total government revenues 
minus government spending excluding interest 
payments). 
AE 
i   Nominal short-term interest rate  OCEDS 
L i  
Nominal long-term interest rate  OECDS 
oil   Oil price (WTI - expressed in Euro) percentage 
change  
FRED 
 
 
 
References 
Favero, C. A., Marcellino, M. (2005), Modelling and forecasting fiscal variables for the Euro Area, 
Oxford Bullettin of Economics and Statistics, 67, pp 755 – 783. 
Hasko, H. (2007), Public debt dynamics in selected OECD countries: the role of fiscal stabilization 
and monetary policy, in “Fiscal Policy: Current Issues and Challenges”, Symposium sponsored by 
the Bank of Italy. 
Rohn, O. (2010), New evidence on the private saving offset and Ricardian equivalence, OECD 
Economics Departments Working Papers, No. 762, OECD publishing. 
 
Appendix A 
Figure A1: Historical debt-to-GDP-ratio versus forecasted debt-to-GDP-ratio 10 
 
10
20
30
40
50
60
70
80
90
1970 1975 1980 1985 1990 1995 2000 2005 2010
d d forecasted  
 
Figure A2: GDP growth (g) versus primary balance (pb) 
-6
-4
-2
0
2
4
6
80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10
g pb  
 
 
 
 
 
Figure A3: Official deficit-to-GDP-ratio versus our calculated deficit-to-GDP-ratio 11 
 
0
1
2
3
4
5
6
7
8
9
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Our deficit-to-GDP-ratio Official deficit-to-GDP-ratio
 

Modelling and forecasting fiscal variables for the Euro Area,

New evidence on the private saving offset and Ricardian equivalence,

Public debt dynamics in selected OECD countries: the role of fiscal stabilization and monetary policy, in “Fiscal Policy: Current Issues and Challenges”, Symposium sponsored by the Bank of Italy.

The dynamics of French public debt: Paths for fiscal consolidations

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