ASSESSING THE FISCAL RISK OF BUDGETARY PROJECTIONS IN ITALY

Transcription

1 Ministry of Economy and Finance Department of the Treasury Economic Focus N 4 - May 2009 ISSN ASSESSING THE FISCAL RISK OF BUDGETARY PROJECTIONS IN ITALY Juan José Pradelli* ABSTRACT This note addresses the sources of fiscal risk -broadly defined as the possibility of deviations of fiscal outcomes from projections- as regard to the medium-term projections of Italy s public that are regularly reported in budgetary planning documents (e.g. the RPP). An analysis of historical projection errors covering the period suggests that: (i) on average, errors in projecting levels were negligible; (ii) over time, however, there was a tendency to overestimate and deficits in the late 1990s, and to underestimate them in the 2000s; and (iii) errors in projecting ns were heavily influenced by data revisions (which affect the growth-adjuste levels) and failures in predicting stock-flow ents. The note presents a projection for in a hypothetical worst-case scenario that introduces fiscal risks. This scenario assumes the RPP 2009 budgetary projections are hit by unexpected shocks, whose magnitude is the standard deviation of historical projection errors. JEL: H0, H6, H62, H63 Keywords: Fiscal Risk, Projections, Economic Focus: The Economic Focus series is aimed at promoting circulation and dissemination of the thematic notes produced within the Department of the Treasury (DT) of the Italian Ministry of Economy and Finance (MEF). The views expressed are those of the authors and do not necessarily reflect those of DT and MEF. * Consip SpA, Università degli Studi di Roma Tor Vergata e Center for the Study of State and Society CEDES. Corresponding author: Via XX Settembre 87, Rome - ITALY. Tel: juanjose.pradelli@tesoro.it I gratefully acknowledge Lorenzo Codogno, Manuela Nenna, Rita Ferrari, and Jules Leichter for their comments and suggestions. 1

2 I. INTRODUCTION Budgetary planning typically involves making projections on the future behaviour of fiscal and macroeconomic variables. Underlying such projections, there are judgements regarding possible events and developments whose realisation would have a bearing on the variables prospective behaviour. For instance, a projection of the public requires projections on tax revenues, government expenditure, interest rates, and GDP growth rates, which in turn make it necessary to foresee events related to fiscal policy, financial market conditions, patterns of corporate investment, and developments in the labour market. Uncertainty is an unavoidable feature of budgetary planning. More often than not, unexpected events occur and, as a consequence, projections ex ante differ from observations ex post. In this regard, IMF (2008) defines fiscal risk as the possibility of deviations of fiscal outcomes from what was expected at the time of the budget or other forecast. 1 The several revisions of growth and public finance projections following the unfolding of the current economic crisis are a main example of fiscal risk materialising ex post. The main sources of fiscal risk are macroeconomic shocks and contingent liabilities associated with unexpected events that have material effects on the public and lead to large differences between expectations and outcomes. For instance, negative shocks to fiscal balances, interest rates, GDP growth, terms of trade, and exchange rates usually result in a higher-than-expected -to-gdp ratio. Similarly, bailouts of state-owned enterprises, financial institutions, and non-financial corporations, as well as calls on government guarantees and legal claims, trigger the acknowledgement of contingent liabilities and may entail a substantial increase in public. At a technical level, the judgements underlying a budgetary planning exercise are often supported either by statistical models or by scenarios analysis. Each methodological approach provides specific measures of the uncertainty surrounding projections that can be used in assessing fiscal risk. Statistical models seek to produce point forecasts and confidence intervals. The notion of fiscal risk would be associated with the forecast error, whose probability distribution constitutes an analytical basis for quantifying fiscal risk. Constructing scenarios, instead, has the purpose of presenting specific outcomes that are expected to occur on the basis of informed opinion and practical expertise. Uncertainty is addressed by postulating alternatives to the baseline case and conducting a sensitivity analysis. In this context, unexpectedly-adverse developments would be identified with a worst-case scenario that envisages fairly unfavourable outcomes and hence delivers pessimistic projections. A quantitative measure of the fiscal risk is 1 See IMF (2008); Fiscal Risks Sources, Disclosure, and Management ; Fiscal Affairs Department; May. 2

3 provided, for instance, by the difference between the value of -to- GDP ratio in the baseline and worst-case scenarios. Assessing the fiscal risk of budgetary projections implies identifying unexpected events that could still happen in the future and quantifying their potential effects on fiscal outcomes, as for instance the effects on the level or n of public. These effects, in turn, would give rise to projection errors, i.e. differences between actual and projected values. The past experience in projecting budgetary variables is a valuable guide in assessing fiscal risk because unexpected events that occurred in the past might happen again in the future. Furthermore, the size of historical projection errors, which somehow measure the effects of those events, might offer a reasonable estimation of the magnitude of the impacts of future unexpected events. As the assessment of fiscal risk requires envisaging and analysing several possible events and developments that could affect the public finances, it greatly improves the information content, technical quality, and institutional transparency of the overall budgetary planning exercise. Therefore, governments should seriously consider introducing such an assessment into regular official documents reporting budgetary projections. This is indeed a motivation for this note, which provides a basic analysis of past projection errors and uses it to assess fiscal risk in the 2009 Relazione Previsionale e Programmatica (RPP 2009) projections. The work is organised as follows. Following this introductory section, section II presents a statistical model suitable for the analysis of projections and errors for the variables determining public dynamics. Section III reports evidence on historical projection errors and characterises some properties of their frequency distributions. Section IV presents a projection for in a hypothetical worst-case scenario that introduces fiscal risks; this scenario assumes the RPP 2009 budgetary projections are hit by unexpected shocks, whose magnitude is the standard deviation of historical projection errors. Section V concludes. II. THE STATISTICAL MODEL No one knows ex ante the magnitude of the deviation of future outcomes from current projections; otherwise, the deviation would be used to correct the projections and eventually there would be no projection error. At most, statistical models seek for a theoreticallybased probability distribution of the forecast error. It is feasible, on the other hand, to track the projection errors made in the past, i.e. the deviation of past outcomes from previous projections, and then compute the frequency distribution of these deviations. For practical purposes, the historical frequency distribution would be an empirical estimate of the probability distribution of the forecast error in the future. Tracking historical projection errors is worth doing for the purpose of managing fiscal risk. First, errors reveal unexpected events that 3

4 occurred in the past and might still constitute sources of fiscal risk in the future. Second, the frequency distribution of past deviations may suggest overhaul to the statistical models or to the criteria used in constructing scenarios. As an example, a statistical methodology for constructing a worst-case scenario in the projection of public is outlined below; the methodology exploits the frequency distribution of past deviations between the actual and projected values of fiscal and macroeconomic variables involved in the dynamics of public. Projections and errors Let us consider a simple model. For a variable X, denote X t t-1 the value of X at year t that is projected using information available at year t-1; hence X t t-1 is a one-period-ahead projection. Assume the true value of X at year t, denoted X t, becomes known at year t (say at the end of the year). In this basic setup, the one-period-ahead projection error is defined as X t - X t t-1, i.e. the difference between actual and projected values of X. In a statistical model, the forecast error X t - X t t-1 is a random variable with a probability distribution. For the sake of simplicity, we have introduced a one-period-ahead projection and error. It is also possible to consider a projection X t t-h for a value of X that is h years ahead with respect to the year of the information set being used. The associated h-period-ahead projection error is X t - X t t-h. It is worth noticing that a projection referred to a distant year is often riskier than a projection referred to a near year; hence, the projection error X t - X t t-h would have a variance larger than that of X t - X t t-1. Intuitively, in projecting the to-gdp ratio, errors are more likely when the information available at 2009 is used than when the information available at 2010 is used. Also for simplicity, we have assumed that X t becomes known at year t. In practice, however, there is a first release of data regarding the value of X in t, which is followed by subsequent revisions of the historical series. In other words, not only the true value X t may be still unknown at year t, it may even remain so for many years after t. It makes sense, therefore, to denote X t t the value of X at year t that is thought to have happened on the basis of information available at year t; X t t would be the first data release referred to X t which usually takes place soon after the end of year t. A subsequent revision that uses information available at year t+h is denoted X t t+h. The fact that X t is unknown even after year t ends makes it necessary to modify slightly the basic setup by defining the one-period-ahead projection error as X t t - X t t-1, i.e. the difference between the value of X in the first data release and the previously projected value. If a subsequent revision taking place in year t+h is considered, the corresponding error is X t t+h - X t t-1. The notion that the uncertainty surrounding long-term projections is larger than that of short-term projections holds. dynamics and projections An analysis of public dynamics involves projections of fiscal and 4

5 macroeconomic variables and is often included in budgetary planning exercises. By definition, the at end of year t (referred to as final ) equals the at beginning of t (referred to as initial, which is also the final at t-1) plus the n during t. Formally, D t = D t-1 + DV t (1) where D t is the stock as percentage of GDP at the end of year t, and DV t is the n during t. Also by definition, DV t = D t - D t- 1. Analytically, the n is given by: DV t = Def t - y t / (1+y t ) * D t-1 + SFA t (2) where Def t is the overall deficit as percentage of GDP (i.e. expenditure plus interest bill minus revenues, or net borrowing); -y t /(1+y t ) * D t-1 is the mechanical contribution of nominal GDP growth to the reduction of the -to-gdp ratio (hereinafter referred to as growth-adjuste ), with nominal GDP growth rate denoted y t ; and SFA t is the stock-flow ent as percentage of GDP, which is a residual term that ensures consistency between changes in and budgetary concepts. 2 Expression (2) breaks down the n in -to-gdp ratio in t into the three components in the right side. 3 The one-period-ahead projection of final at t using information available at year t-1 is D t t-1, the first data release is D t t, and the projection error is the difference D t t - D t t-1. A similar notation applies to the variables DV t, Def t, -y t /(1+y t ) * D t-1, and SFA t. The projection of final D t t-1 must satisfy the expression (1) above, so D t t-1 = D t-1 t-1 + DV t t-1. The projection error D t t - D t t-1 must do it as well, so D t t - D t t-1 = (D t-1 t - D t-1 t-1 ) + (DV t t - DV t t-1 ). Hence, there are two factors that account for the projection error: (i) the error D t-1 t - D t- 1 t-1, which results from a revision of the historical series that differs from the first data release on the initial ; and (ii) the error DV t t - DV t t-1 (hereinafter referred to as unexpected n), which arises because of errors in projecting at t-1 the variables determining n at t (i.e. deficit, growth, and stock-flow ent). In other words, any failure in projecting the final must be due either to a revision of the first data release of the initial, to an error in projecting the n, or to both. III. ANALYSIS OF HISTORICAL PROJECTION ERRORS 2 Stock-flow ent includes several transactions and accounting ents, e.g. the net acquisition of financial assets, valuation effects associated with exchange rate fluctuations, corrections from interest accrued to interest paid, and corrections from liabilities transaction value to face value. For details, see European Commission and Eurostat (2002); ESA95 manual on government deficit and ; Office for Official Publications of the European Communities; Luxemburg; Part V. 3 Another expression for the n is DVt = PBt + (it-yt) / (1+yt) * Dt-1 + SFAt, where PBt is the primary balance as percentage of GDP; (it-yt) / (1+yt) * Dt-1 is the growth-adjusted interest bill, with nominal interest rate it and nominal GDP growth rate yt; and SFAt is the stock-flow ent as percentage of GDP. 5

6 The methodology for constructing worst-case scenarios is based on the frequency distribution of historical projection errors. At this stage, the previous experience in projecting and budgetary aggregates is analysed in order to characterise the projection errors. Due to the lack of long time series for the variables of interest, the analysis is limited to a few moments of the frequency distribution, such as means, standard deviations (SD), and correlations. Table 1 below presents the one-period-ahead projection, the first data release, and the projection error for each of the four terms in the n equation (2), covering the period. Projected values are taken from the RPP; first data releases for correspond to the Bank of Italy Annual Report (BoI), while those for overall deficit and nominal GDP growth correspond to the Relazione Generale sulla Situazione Economica del Paese (RGE). 4 The stock-flow ent is always calculated as a residual in order to ensure the n equation (2) is fulfilled. stock Table 1 Year (1)=(2)+( 3) One-period-ahead projection Xt t-1 (RPP) First data release Xt t (BoI and RGE) Projection error Xt t - Xt t-1 (2) (3)=(4)+( 5)+(6) (4) (5) ent (6) (7)=(8)+( 9) (8) (9)=(10) +(11)+(1 2) (10) (11) ent (12) (13)=(14 )+(15) (14) (15)=(16 )+(17)+( 18) (16) (17) Mean Max Min SD Variance ent (18) Errors in projecting stock To start with, consider the one-period-ahead projection and first data release for the final, i.e. D t t-1 and D t t. The corresponding series are reported in columns 1 and 7 of Table 1, and Figure 1 below depicts them. The projections pointed to a decreasing in the period and to a fairly stable in (with a slight increase since 2006). According to the first data releases, indeed declined in , but often at a pace slower than expected; subsequently, stabilised, but at a level higher than expected (with the exception of 2007). Errors in projecting final are reported in column 13 and depicted stock 4 To clarify the sources, consider the case of the n in -to-gdp ratio during 2007: the projected value is taken from the RPP 2007 (published in 2006) and the first data release is taken from the Bank of Italy 2007 Annual Report (published in 2008). Table 5 reported in the Appendix presents the latest revision of all the series. 6

7 in Figure 2 below. The tendency to overestimate in and to underestimate it in is apparent in the direction of the bars., however, the projections neither underestimated nor overestimated the level of final : the average projection error over was -0.1 percentage points (pp) per year. The largest projection errors were observed in 2001, when was underestimated by 2.8 pp, and in 2007, when it was overestimated by 2.9 pp. Figure Projected final (% of GDP) Source: Own calculations on the basis of MEF data. Data release final (% of GDP) Figure Error in final (pp) Error in Error in initial (pp) 7

8 Source: Own calculations on the basis of MEF data. It was mentioned before that two factors account for an error in projecting final : a revision of the first data release of the initial, and an error in projecting the n (i.e. the unexpected n). 5 Figure 2 also shows both factors (series reported in columns 14 and 15 of Table 1). The initial assumed in the projections of final often exceeded the revised data; on average, projections indicated an initial 0.7 pp higher than that eventually reported in the revisions. On the other hand, the projections of n tended to underestimate the changes eventually observed. On average, an annual 2.1 pp reduction in was projected, but the first data releases reported only a 1.4 pp reduction (see columns 3 and 9); hence, the average projection error was 0.7 pp. These figures explain why the average projection error of final, which is the sum of both factors, was the negligible -0.1 pp value mentioned above. 6 Figure 2 shows another important point: the errors in projecting n were more volatile than the errors arising from data revisions of initial (SD are 2.5 pp and 1.3 pp, respectively, as reported in columns 14 and 15 of Table 1); but since the two series tended to move in opposite directions, they partially offset each other. The two series were negatively correlated with Pearson coefficient -0.53, leading to errors in final projections having a SD of 2.1 pp. Errors in projecting n Consider now the one-period-ahead projection and first data release for the n, i.e. DV t t-1 and DV t t. The corresponding series are reported in columns 3 and 9 of Table 1, and shown in Figure 3 below. No regular pattern can be easily identified in the behaviour of the series. n 5 The revision issue explains why columns 2 and 8 in Table 1 are not the lagged series reported in columns 1 and 7, respectively. 6 Differences are due to rounding. The effect of subsequent data revisions is apparent in Table 5 reported in the Appendix: using the latest data revision, the average error in projecting final is -1.7 pp and the revision of initial accounts for -2.4 pp. 8

9 Figure Projected Source: Own calculations on the basis of MEF data. Data release A more interesting picture arises when analysing the three variables that account for ns: the overall deficit, the growth-adjusted initial, and the stock-flow ent. It is worth making a preliminary observation as regard to the importance of each variable in the determination of n. Consider the projection series indicated in columns 3 to 6 of Table 1: over the period, projections delivered an average annual reduction of 2.1 pp; the bulk of this n was accounted for by the growth-adjuste (which induced a reduction of 4.8 pp), followed by the overall deficit (which led to an increase of 2.5 pp); the stock-flow ent s contribution was a negligible increase of 0.2 pp. Consider now the first data release series reported in columns 9 to 12 of Table1: the average annual reduction was eventually 1.4 pp; the growth-adjuste made the largest contribution (inducing a reduction of 4.2 pp), followed by the overall deficit (leading to an increase of 2.9 pp); a negligible reduction of 0.1 pp was due to the stock-flow ent. Notice then that the stock-flow ent had a very limited influence on ns, both projected and eventually observed. However, the errors in projecting stock-flow ent had a large impact on the errors in projecting n: the average projection error for stock-flow ent was -0.3 pp, while figures for overall deficit and growth-adjuste were 0.4 pp and 0.6 pp, respectively. Further details are provided by Figures 4, 5, and 6 below that depict the one-period-ahead projections and first data releases corresponding to the three components of n (series are reported in columns 4 and 10, 5 and 11, and 6 and 12 of Table 1). 9

10 Figure Projected overall deficit (% of GDP) Source: Own calculations on the basis of MEF data. Data release overall deficit (% of GDP) Figure Projected growth-adjuste (% of GDP) Source: Own calculations on the basis of MEF data. Data release growth-adjuste (% of GDP) 10

11 Figure Projected stock-flow ent (% of GDP) Source: Own calculations on the basis of MEF data. Data release stock-flow ent (% of GDP) Projections on overall deficit performed fairly well in , but there was a tendency to slightly underestimate deficits in On average, the projection error was 0.4 pp with SD 1.0 pp. As far as growth-adjuste projections are concerned, the tendency to underestimate figures was systematic all over the period (this variable has a negative sign as long as nominal GDP grows). On average, the projection error was 0.6 pp with SD 1.1 pp. ly, the stock-flow ent projections and outcomes were very different, leading to an average projection error of -0.3 pp with high SD of 1.7 pp. Interactions between errors in projecting the three variables and the n are illustrated in Figure 7 below. Errors in projecting overall deficit and growth-adjuste tended to move in the same direction and therefore reinforced their effect on unexpected ns; in particular, the two variables were positively correlated with a Pearson coefficient Errors in projecting stockflow ent were very volatile and rather independent from the other variables; indeed, nil Pearson coefficients correspond to the correlation between errors in projecting stock-flow ent and errors in projecting overall deficit and growth-adjuste. 11

12 Figure Error in Error in stock-flow ent (pp) Source: Own calculations on the basis of MEF data. Error in growth-adjuste (pp) Error in overall deficit (pp) A decomposition of variance of errors in projecting n is reported in Table 2 below. The influence of unexpected stock-flow ents was relatively large since their variance accounts for the bulk of the variance of unexpected ns. Variance decomposition Table 2 Value Index Variance of errors in projecting n Variance of errors in projecting overall deficit growth-adjuste stock-flow ent * Covariance of errors in projecting overall deficit & growth-adjuste overall deficit & stock-flow adjustement stock-flow adjustement & growth-adjuste Errors in projecting nominal GDP growth Projections of growth rate of nominal GDP are an important part of a budgetary planning exercise. In particular, nominal GDP growth is a determinant of the dynamics because it directly affects the growth-adjuste and indirectly influences overall deficits through tax revenues. The positive correlation observed above between errors in projecting these two variables is partially due to both depending on nominal GDP growth and the fact that errors in growth projections are recurrent. Focusing on the direct influence on growth-adjuste exerted by nominal GDP growth itself, Table 3 below presents projections, first data releases, and projection errors for these variables. Nominal GDP growth 12

13 Table 3 One-period-ahead projection Xt t-1 (RPP) First data release Xt t (BoI and RGE) Projection error Xt t - Xt t-1 Year Nominal GDP growth (%) d initial Nominal GDP growth (%) d initial Nominal GDP growth (%) d initial Mean Max Min SD Variance Figure 8 below illustrates series of projection errors and points out that nominal GDP growth was systematically overestimated all over the period: in the projections, the average annual growth rate was 4.4 percent, while in the first data releases, the average was 3.9 percent; thus, the average projection error was -0.5 pp. Regarding the initial, it was already mentioned that projections exceeded data revisions, leading to an average projection error of -0.7 pp. ly, systematic overestimation in both nominal GDP growth an led to systematic underestimation in the growth-adjuste projections, which is apparent in the direction of the bars. 7 Hence, the average error in projecting growth-adjuste was 0.6 pp. 7 There is a change in sign and a non-linear relation involved in the formula -yt /(1+yt) * Dt-1. 13

14 Figure Error in growth-adjuste (pp) Error in initial (pp) Source: Own calculations on the basis of MEF data. Error in nominal GDP growth rate (pp) IV CONSTRUCTING WORST-CASE SCENARIOS The moments characterizing the frequency distribution of historical projection errors are now used to construct a worst-case scenario. This scenario modifies the baseline case, taken from the RPP 2009, by assuming unexpected shocks affect the dynamics by hitting the three variables that determine the n, i.e. overall deficit, growth-adjuste, and stock-flow ent. The magnitude of the shocks is calibrated using the SD of the historical projection error corresponding to each variable. Fiscal risk is then measured by the deviation of the -to-gdp ratio in the worst-case scenario from that in the baseline case. Table 4 below presents the RPP 2009 scenario, taken as the baseline case, with projections for all the variables discussed in the previous section (see columns 1 to 6). Worst-case scenarios Table 4 Year (1)=(2)+( 3) Projections Xt 2008 in RPP 2009 (2) (3)=(4)+( 5)+(6) (4) (5) ent (6) Projections assuming values in columns (4)-(5)-(6) are adjusted by adding the SD of historical projection errors (7)=(8)+( 9) (8) (9)=(10) +(11)+(1 2) (10)=(4) +SD with SD=1.0 (11)=(5) +SD with SD=1.1 ent (12)=(6) +SD with SD=1.7 Projections assuming values in columns (4)-(5)-(6) are adjusted by adding the SD of historical projection errors (13)=(14 )+(15) (14) (15)=(16 )+(17)+( 18) (16)=(4) +SD with SD=1.0 (17)=(5) +SD with SD= ent (18)=(6) +SD with SD=1.7 Columns 7 to 12 constitute a worst-case scenario in which unexpected 14

15 shocks hit the overall deficit, growth-adjuste, and stockflow ent in the period. The shock corresponding to a variable is equal to the SD of the historical projection error of that variable (reported in the series label). Thus, the exercise boils down to projecting under the hypothesis that the ns in would be 3.8 pp higher than what the RPP 2009 has projected. 8 In , higher overall deficits and stock-flow ents, together with lower growth-adjuste, lead to ns larger than those in the baseline scenario; in , instead, ns coincide in both scenarios. Because of the shocks accelerating the public dynamics, the worst-case scenario shows a level of final in 2013 that is 11.4 pp above the level reached in the baseline case. Columns 13 to 18 report another worst-case scenario in which unexpected shocks hit the same variables and have the same magnitude, but now lasting until Consequently, ns are always higher and the 2013 final level exceeds by 22.8 pp the level of the baseline case. 9 Figure 9 below illustrates the projections corresponding to the RPP 2009, the two worst-case scenarios described above, and their optimistic counterparts. Figure RPP2009 Projected final (% of GDP) +/- SD in (% of GDP) +/- SD in (% of GDP) Serie2 Source: Own calculations on the basis of MEF data. 8 The working hypothesis treats shocks to the three components of n as if they were mutually independent. This is a fairly accurate approximation for practical purposes because, as shown in Table 2, the stock-flow ent is nearly uncorrelated with overall deficit and growth-adjuste, while the correlation between these two has indeed a small effect on the variance of the projection errors of n (it explains around 20 percent of the variance). 9 In an alternative exercise, it has been assumed that a shock hits the dynamics although with a direct impact on n rather than on its three components. The shock was then calibrated to be equal to the SD of the projection error of n, which is 2.5 pp as reported in Table 1 and thus lower than the 3.8 pp shock implicit in the main text. In the alternative exercise, when the shock occurs over , the reaches 99,4 percent of GDP in 2013; and when it occurs over , the is percent of GDP in

16 Caveats This simple methodology presents two weaknesses. First, the use of SD of historical projection errors to modify the baseline case does not allow to attach a probability to the occurrence of the worst-case scenario projections. IMF (2008) and the US Congressional Budget Office (2007) tackle this issue by using the percentiles of the frequency distribution of the historical projection errors corresponding to variables involved in n and budget balances. 10 Percentiles resulting from observed frequencies are, of course, suitable for an interpretation in terms of probability of occurrence. Nevertheless, IMF (2008) constructs a historical frequency distribution using heterogeneous data from different countries. As cross-section and time series data are being mixed, the IMF results are too rough to be used in a budgetary planning exercise of any specific country. The US Congressional Budget Office (2007), instead, focuses on US data but only the 25-year period is available for the analysis. Second, since the degree of uncertainty regarding projected values depends on how distant these values are in the future, i.e. on the length of the projection horizon, it is not appropriate to use a statistic corresponding to the frequency distribution of one-period-ahead projection errors over all the years in the budgetary planning s horizon. Hence, an analysis of projection errors associated to two, three, or more periods ahead should be undertaken to characterize a set of frequency distributions from which different statistics can be computed and then applied to each year of the planning horizon. This procedure, nevertheless, could be difficult to implement because of series of projections being too short. Despite of using short time series, the US Congressional Budget Office (2007) makes an effort to characterize the frequency distribution of one- to five-period-ahead projection errors. An extension Taking into account the second caveat discussed above, an analysis of two- and three-period-ahead projection errors has been undertaken in order to estimate different SDs and to apply them to the corresponding year of the budgetary planning horizon. 11 In doing this, the shocks size is allowed to vary over time. Figure 10 illustrates the projections for the worst-case scenarios and their optimistic counterparts. 10 See CBO (2007); The Uncertainty of Budget Projections: A Discussion of Data and Methods ; The Congress of the United States; March. 11 Data are reported in Tables 7 and 8 in the Appendix. 16

17 Figure RPP2009 Projected final (% of GDP) +/- time-varying SD in (% of GDP) +/- time-varying SD in (% of GDP) Source: Own calculations on the basis of MEF data. V CONCLUSIONS The main findings of the note regarding the historical projection errors made in the period are the following. First, on average, errors in projecting levels were negligible. Second, despite of a seemingly good projection performance, there was a tendency to overestimate and deficits in the late 1990s and to underestimate them in the 2000s. Third, the errors in projecting ns were heavily influenced by data revisions (which affect the growth-adjusted initial levels) and failures in estimating stock-flow ents. Developing better methods to estimate stock-flow ents is key to improve projections. As far as the projection introducing fiscal risk is concerned, on the basis of the RPP 2009 outlook, the note estimates that Italy s public in 2013 could increase from an expected 91.9 percent of GDP to percent if the fiscal accounts are hit by unexpected shocks of a magnitude similar to the SD of past projection errors. The 2013 could increase further, reaching percent of GDP, if unexpected shock persist all over the period. A few caveats are in order to highlight technical and political limits of a statistical methodology aimed at introducing a fiscal risk assessment into a scenario-based budgetary planning exercise. (i) Historical fiscal and macroeconomic series may be too short, thus preventing the construction of reliable frequency distributions of projections errors for different time horizons; hence, the worst-case scenario and the fiscal risk measure should be taken with caution. (ii) Alternative breakdowns are possible for the variables determining the public dynamics, e.g. real GDP growth and GDP deflatorbased inflation as components of the nominal GDP growth, expenditure and tax revenues as components of the overall deficit, etc. Hence, a decision should be made regarding which breakdown stock 17

18 helps the most in emphasizing the main sources of fiscal risk. (iii) It is likely that different projection methodologies were used in the past for conducting budgetary planning exercises even in the same governmental office, so there is no unique model whose past predictive power could be assesses by a statistical methodology. Instead, the analysis of historical projection errors should be considered as an informal assessment of the staff s capacity to produce good projections and foresee key events influencing fiscal and macroeconomic developments, in broad terms. (iv) The presentation and discussion of fiscal risks should be done carefully and succinctly in order to avoid fuelling a misleading criticism to the baseline projections, which actually reflect the events that are more likely to happen according to the staff s judgement. 18

19 APPENDIX Table 5 Year (1)=(2)+( 3) One-period-ahead projection Xt t-1 (RPP) Latest revision Xt 2008 Projection error Xt Xt t-1 (2) (3)=(4)+( 5)+(6) (4) (5) ent (6) (7)=(8)+( 9) (8) (9)=(10) +(11)+(1 2) (10) (11) ent (12) (13)=(14 )+(15) (14) (15)=(16 )+(17)+( 18) (16) (17) Mean Max Mix SD Variance ent (18) Table 6 One-period-ahead projection Xt t-1 (RPP) Latest revision Xt 2008 Projection error Xt Xt t-1 Year Nominal GDP growth (%) d initial Nominal GDP growth (%) d initial Nominal GDP growth (%) d initial Mean Max Min SD Variance

20 Table 7 Year (1)=(2)+ (3) Two-period-ahead projection Xt+1 t-1 (RPP) First data release Xt+1 t+1 (BoI and RGE) Projection error Xt+1 t+1 - Xt+1 t-1 (2) (3)=(4)+ (5)+(6) (4) (5) ent (6) (7)=(8)+ (9) (8) (9)=(10) +(11)+(1 2) (10) (11) ent (12) (13)=(14 )+(15) (14) (15)=(16 )+(17)+( 18) (16) (17) Mean Max Min SD Variance ent (18) Table 8 Year Three-period-ahead projection Xt+2 t-1 (RPP) First data release Xt+2 t+2 (BoI and RGE) Projection error Xt+2 t+2 - Xt+2 t-1 (1)=(2)+ (3) (2) (3)=(4)+ (5)+(6) (4) (5) ent (6) (7)=(8)+ (9) (8) (9)=(10) +(11)+(1 2) (10) (11) ent (12) (13)=(14 )+(15) (14) (15)=(16 )+(17)+( 18) (16) (17) Mean Max Min SD Variance ent (18) 20

21 Ministry of Economy and Finance Department of the Treasury Directorate I: Economic and Financial Analysis Address: Via XX Settembre, Rome Websites: dt.segreteria.direzione1@tesoro.it Telephone: Fax: Copyright: 2009, Juan José Pradelli. The document can be downloaded from the website and freely used, providing that its source and author are quoted. Editorial Board: Lorenzo Codogno, Mauro Marè, Libero Monteforte, Francesco Nucci Organisational coordination: Marina Sabatini