This paper analyses possible targets for the Italian debt-to-GDP ratio with a small macroeconomic model. The role of international macroeconomic variables such as the US GDP growth, prices of raw materials, EUR/USD exchange rate, and ECB monetary policy stance and domestic policy instruments is analyzed in the debt dynamics. We find that external conditions play a fundamental role for the Italian fiscal consolidation. To reach a target of 100% of debt-to-GDP ratio by 2020, a further growth sustaining policy has to be implemented.Debt to GDP Ratio, Italian Economy, International Factors, SUR.

Casadio, Paolo

Paradiso, Antonio

Rao, B. Bhaskara

English

Research Papers in Economics

  1 
The dynamics of Italian public debt:  
Alternative paths for fiscal consolidation 
 
Paolo Casadio 
paolo.casadio@yahoo.it 
Intesa Sanpaolo Bank Group, Risk Management, Rome (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 
This paper analyses possible targets for the Italian debt-to-GDP ratio with a small 
macroeconomic model. The role of international macroeconomic variables such as the US 
GDP growth, prices of raw materials, EUR/USD exchange rate, and ECB monetary policy 
stance and domestic policy instruments is analyzed in the debt dynamics. We find that 
external conditions play a fundamental role for the Italian fiscal consolidation. To reach a 
target of 100% of debt-to-GDP ratio by 2020, a further growth sustaining policy has to be 
implemented.  
 
Keywords: Debt to GDP Ratio, Italian Economy, International Factors, SUR. 
 
JEL: E62, H63, H68, C30 
 
 
   2 
 
1. Introduction 
This paper analyses the dynamics of the Italian government debt-to-GDP ratio using a small-
scale model. Our approach follows earlier works of  Favero (2002), Favero and Marcellino 
(2005), and Hasko (2007). Adopting various scenarios for the exogenous variables viz., US 
GDP growth, oil price change, long term interest rates,  and Euro vs dollar exchange rate, we 
predict that the debt ratio can reach a target of 100% by 2020 for fiscal consolidation and 
sustainability. Section 2 presents the basic arithmetic of debt accounting. Section 3 presents a 
brief description of the model and its structure. Empirical results are in Section 4. Section 5 
shows that under plausible assumptions our target of 100%  ratio for debt to GDP 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 (T – G). The same relation holds if the variables are measured in real terms 
assuming that inflation rate is measured with the GDP deflator and we shall use this 
assumption in our estimation. Normally the budget dynamic is written in the form of a change 
in the ratio of public debt-to-GDP (b): 
1 t t t t t t b i g b pb               (2) 
where variables in lower case denote the same variables expressed as ratios to GDP, 
inflation rate, g real GDP growth. According to (2), for a given pb, a stronger real 
GDP growth, a lower nominal interest rate, and higher inflation rate will reduce the debt 
growth dynamics.   
 
   3 
3. Modelling debt: A small macroeconomic model 
Identity (2) can be used in two different ways: as a single residual equation, incorporating the 
scenarios for primary balance, growth, inflation, and interest rate, determining the debt-to-
GDP dynamics or as an equation in a more complex model to account for interactions among  
the key variables.  More recently, Favero and Marcellino (2005), and Hasko (2007) estimated 
small-scale simultaneous equations models for this purpose and we follow their approach. 
Our model consists of five equations and the endogenous variables are driven by three 
international variables (US GDP growth, Oil price dynamics, EUR/USD exchange rate and 
domestic short-term Central Bank monetary policy rate). The model is as follows: 
1 2 1 3 4 5 1
US g
t t t t t t g pb g i i  (Output equation)    (3) 
6 7 1 8 9 1
pribal
t t t t t pb pb g b   (Fiscal rule)                            (4) 
10 11 1 12 2 13 14 2 1 15
Lb
t t t t t t t t b b b g b i      
            (Public debt equation)                        (5) 
16 17 1 18 1 19 1 20 t t t t t t g pb oil   (Inflation equation)  (6)     
21 22 1 23 2 24 25 26 27 1
L L L i
t t t t t t t t i i i i b euro    
          (Long-term interest rate equation)                   (7) 
where g real GDP growth, 
US g   real US GDP growth, oil  oil price percentage change 
(expressed in Euro), 
L i  nominal long term interest rates,  b debt-to-GDP ratio, i  
nominal short term interest rate,    CPI inflation rate, euro  Euro versus dollar exchange 
rate, and  pb  primary balance as percent of GDP. Data are yearly and the estimation period 
is from 1970 to 2010. Details of data are in the Appendix 
A brief explanation of the structure of the model is as follows. The output equation (3) 
embodies three effects: a restrictive fiscal policy effect ( 2 0) captured by an increase in 
the primary balance, a monetary policy effect ( 45 0) measured as the ECB monetary 
policy rate and an international business cycle effect ( 3 0) captured by US GDP growth 
rate. The fiscal policy effect is negative ( 2 0) due to the high tax rates in Italy. The short-  4 
term interest rate has also a negative overall effect on growth.
1 The primary balance equation 
(4) depends both on output growth and debt-to-GDP ratio in a positive way ( 8 0and  
9 0). Similar results are also found for Italy by Favero and Marcellino (2005). The debt-
to-GDP ratio is explained in equation (5). We consider the long term interest rate as a proxy 
for the average cost of debt because the Italian government debt duration is getting longer 
and closer to the duration of long-term bonds. All signs in the equation are as expected i.e., 
13 0, 14 0 , and  15 0.Inflation in equation (6) depends positively on oil price 
growth and output growth ( 20 0  and  18 0).
2 The primary balance exerts a negative 
effect on inflation ( 19 0). Two offsetting effects are to be accounted when considering the 
inflation response to the primary balances: a stimulus to inflation acting via costs (usually 
linked to an increase in indirect taxation) and a depressive effect due to the decrease of 
private spending due to the tax burden. We expect the latter effect to dominate. In the last 
equation ( 7 ) the long-term interest rates depends positively on the short-term interest rate 
( 24 0 ), on inflation ( 25 0), on debt-to-GDP ratio ( 26 0 ), and on the Euro 
exchange rate versus dollar ( 27 0 ). Finally, the higher the level of Italian debt the higher 
is the long-term interest rate due to higher risk-premiums attached to the Italian long-term 
bonds.  
5. Empirical results 
The system of equations (3) – (7) is estimated as a simultaneous equation model using 
Seemingly Unrelated Regression method (SUR) with annual data for the period 1970 - 2011. 
The results are in Table 1. The results are impressive. All the coefficients have the expected 
signs and are statistically significant. The residual diagnostic tests for no serial correlation 
(Portmanteau tests) and normality (Jarque-Bera) of residuals do not reject the null 
hypotheses. To check the reliability of the model to perform 10-years horizon forecasts, we 
also conducted the following exercise. We estimated the model from 1970 to 1999 and then  
forecasted for the next ten years, comparing the out-of-sample forecasted values with the 
                                                             
1 We used the long-term interest rate and also the real interest rate in the output equation, but the results were 
poor. Similar results were reported for Italy by Favero, Marcellino (2005). 
2 Output growth is preferred as indicator for the overall level of activity instead of unemployment rate or output 
gap; see Hasko (2007).   5 
historically recorded ones. The results are very satisfactory but not reported to conserve 
space.  
Table 1: SUR Estimates of Italian Debt Dnamics (1970 – 2010) 
1 2 1 3 4 5 1
US y
t t t t t t g pb g i i  (Output equation) 
1  2  3   4  5   2 R  
JB 
p-value 
   
0.0049 
(0.005) 
[0.921] 
-0.2122 
(0.080) 
[2.645] 
0.6260 
(0.086) 
[7.315] 
0.5415 
(0.093) 
[5.829] 
-0.5713 
(0.083) 
[6.901] 
0.715  0.600     
6 7 1 8 9 1
pribal
t t t t t pb pb g b  (Fiscal rule) 
6  7   8   9   2 R  
JB 
p-value 
     
-5.4804 
(1.054) 
[5.200] 
0.6700 
(0.089) 
[7.521] 
0.3427 
(0.087) 
[3.960] 
0.0539 
(0.011) 
[4.708] 
0.889  0.363       
10 11 1 12 2 13 14 2 1 15
Lb
t t t t t t t t b b b g b i  (Public debt equation) 
10  11  12  13  14  15  2 R  
JB 
p-value 
 
15.8360 
(2.187) 
[7.240] 
1.3554 
(0.082) 
[16.442] 
-0.5056 
(0.074) 
[6.872] 
-1.0594 
(0.119) 
[8.889] 
0.4223 
(0.092) 
[4.589] 
-0.3612 
(0.078) 
[4.643] 
0.956  0.263   
16 17 1 18 1 19 1 20 t t t t t t g pb oil  (Inflation equation) 
16  17  18  19  20  2 R  
JB 
p-value 
   
0.0023 
(0.001) 
[0.427] 
0.7904 
(0.059) 
[13.390] 
0.2585 
(0.124) 
[2.079] 
-0.2054 
(0.109) 
[1.892] 
0.0432 
(0.007) 
[5.822] 
0.926  0.157     
21 22 1 23 2 24 25 26 27 1
L L L i
t t t t t t t t i i i i b euro  (Long-term interest 
rate equation) 
21  22  23  24  25  26  27   2 R  
JB 
p-value 
-0.0506 
(0.020) 
[2.555] 
0.8567 
(0.108) 
[7.895] 
-0.2977 
(0.089) 
[3.331] 
0.2625 
(0.059) 
[4.420] 
0.2189 
(0.050) 
[4.352] 
0.0464 
(0.014) 
[3.319] 
0.0066 
(0.004) 
[1.898] 
0.966  0.242 
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) 
 
0.399  0.551  0.556  0.134   
Notes: Standard errors and t-ratios are in the parentheses and square brackets respectively 
   6 
5. Scenarios and debt-to-GDP dynamic forecasts 
Table 2 summarizes the outcomes of three scenarios considered for the exogenous variables 
(baseline, an upward/optimistic, and a downward/risky scenario) together with the results of 
endogenous variables. The first three columns assume no policy intervention and in the final 
column the outcome of a realistic policy intervention 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 
4%  3.5%  3%  3.5% 
2020 Oil price 
in US dollar 
and Euro  
Nominal  
200$ (165€) 
Nominal 
180$ (138€) 
Nominal  
165$ (126€) 
Nominal 
180$ (138€) 
Real 
161$ (124€) 
Real 
144$ (111€) 
Real 
132$ (101€) 
Real 
144$ (111€) 
Real US GDP 
growth 
2.2%  2.6%  1.6%  2.6% 
EUR/USD 
Exchange rate  
1.3  1.3  1.3  1.3 
2020  Public 
Debt  (%  of 
GDP)
* 
106%  102%  109%  100% 
Primary 
balance (% of 
GDP)
 *  
2.38%  2.44%  2.30%  2.2% 
Nominal long-
term  interest 
rate
*  
5.0%  5.2%  4.8%  5.1% 
Inflation
*   2.3%  2.7%  2.0%  2.9% 
Real  GDP 
growth
*  
1.5%  1.8%  1.1%  2.0% 
General 
Government 
balance  in  % 
of GDP
*  
2.67%  2.88%  2.44%  3.0% 
Note: Real values for Oil price change are calculated assuming an international 
average inflation of 2.2% for period 2011  – 2020. 
*  Average values over the 
period. 
 
   7 
In Table 2 the debt-to-GDP ratio ranges from 102% to 109% depending on the 
scenario. The main mechanism behind the debt-to-GDP reduction relies on growth of Italian 
economy. The positive effect of growth is only partially offset by the increase in the long-
term interest rates. The Italian growth performance depends heavily on the international 
scenario, so that the best performance in terms of debt dynamics is conditioned by 
international business cycle and a favorable oil prices. An important role is played by the 
European Central Bank monetary policy. 
In the final column of Table 2 we conducted a policy intervention exercise with the 
aim to reach a 100% of debt-to-GDP ratio compatible with 3% deficit limit of Maastricht.  In 
the most optimistic scenario, we calibrate a mix of interventions needed to reduce debt-to-
GDP ratio of 2%  in order to reach a target value of 100% of debt-to-GDP ratio in 2020. 
From 2011 to 2020 if the Italian government increases the GDP growth to 0.15%  and cuts 
taxes to 0.12%  of GDP, then the debt-to-GDP ratio will reach the 100% in 2020 (Figure 1) 
and the  Maastricht restriction of 3% will also hold.  
Figure 1: Forecasts of macroeconomic variables for period 2011 – 2020. 
-6.0%
-5.0%
-4.0%
-3.0%
-2.0%
-1.0%
0.0%
1.0%
2.0%
3.0%
4.0%
g_UP g_BASE g_DOWN
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
Infl_UP Infl_BASE Infl_DOWN
 
3.5%
4.0%
4.5%
5.0%
5.5%
6.0%
Lint_UP Lint_BASE Lint_DOWN
-1.0%
-0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
Pb_UP Pb_BASE Pb_DOWN
   8 
90%
95%
100%
105%
110%
115%
120%
125%
Debt_UP Debt_BASE Debt_DOWN
90%
95%
100%
105%
110%
115%
120%
125%
Debt_INT
 
Notes:  BASE  =  Base  scenario,  UP  =  Upside  scenario,  Down  =  Downside  scenario,  INT  =  Policy 
intervention scenario. 
5. Conclusions 
In this paper we used a small-scale econometric model for Italy to find a reasonable policy to 
reduce the debt ratio to 100% of GDP within a ten years. Our simulation results indicate that 
an external positive scenarios is necessary for the international variables to bring down the 
debt to GDP ratio under 105%. A dynamic international economy together with favourable 
oil prices and not too strong Euro are essential requirements. Furthermore, an expansive 
stance by ECB monetary policy helps to reach fiscal targets, reducing Italian interest 
payments. The most important domestic variable in the debt-to-GDP reduction process is the 
growth of domestic output. We showed that a policy intervention aimed to stimulate the  
GDP growth over 1.8% allows to reach the target 100%  debt-to-GDP ratio. 
 
 
 
   9 
Data Appendix 
 
  Definitions and Data Source: 1970 - 2010 
Variable  Definition  Source 
b   Debt-to GDP ratio  AMECO - EUROSTAT 
  Percentage change of Consumer Price Index  OECD Statistics 
g   Real GDP growth  AMECO - EUROSTAT 
US g   Real US GDP growth  Federal Reserve 
Economic DATA 
(FRED) 
pb  Primary  balance  (Total  government  revenues 
minus  government  spending  excluding  interest 
payments). 
AMECO - EUROSTAT 
i   Nominal short-term interest rate  OECD Statistics 
L i  
Nominal long-term interest rate  OECD Statistics 
oil   Oil  price  (WTI  -  expressed  in  Euro)  percentage 
change  
FRED 
euro   EUR/USD exchange rate  DATASTREAM 
(USEURFT) 
 
 
 
 
 
 
   10 
 
References 
Favero,  C.  A.  (2002)  How  do  European  monetary  and  fiscal  authorities  behave?,  CEPR 
Discussion Paper, No. 3426. 
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,  Public  Finance  Workshop,  Bank  of  Finland  Research 
Department, pp. 133 -172. 
 
 
 

The dynamics of Italian public debt: Alternative paths for fiscal consolidation

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