Componentes estratégicos de la capacitación para el talento humano del Sistema de

The SDW supplies publicly available quarterly statistics for any memeber state within the EMU. The official documentation provides an exact equation for debt level in each of the countries. Namely,

Dt =Dt−1 +It−Nt+Mt (3.2.6)

• Dt : total government consolidated debt. • Nt : government primary surplus

• It : interest payable (accrued betweent−1and t) • Mt : deficit-debt adjustment (DDA)

see [110] (Table 1A, p. 11 and Table 2A, p. 39) or [16] (p. 11).

Several modification have been approved on government accounting methods, finally endorsed60 _{in a Council Regulation: a new methodology, the ESA2010 replaced}

former ESA95 in defining rules for debt computation and accounting under the Excessive Deficit Procedure (EDP).61.

ESA2010 provides debt to be evaluated at face value, while ESA95 defines debt level as that which "..reflects the sum of funds originally advanced, plus any subsequent advances, less any repayments, plus any accrued interest ([16], p. 383); ESA95 time series are thus to be used in order to match (3.2.6).

The DDA reconciles change in debtDt−Dt−1 with (gross) surplusNt−It by taking

into account adjustments due to statistical discordances (between members central banks and the ECB) and to peculiar accounting-based discrepancies. Details are provided in [110] (pp. 34-37).

The interest payable is defined as the difference between primary surplus and the surplus itself: following [49], we can define an implicit interest rate y˜t:

It= ˜yt·Dt−1 (3.2.7)

which will be also addressed to as internal or accounting rate. The dynamics of public accounting are then retrieved weighting all variables with nominal output level Gt. Notice that gdp ratios of primary deficit (as well as DDA) are commonly

weighted by the gdp level over a quarter G∗_t, while debt/gdp at time t is defined as the ratio between current level of debt and theaggregated gdp-level over latest year, namely Gt=

P3

k=0G ∗

t−k. The choice was to follow the second convention: define

gt =

Gt−Gt−1 Gt−1

(3.2.8) the quarterly growth rate of yearly aggregated nominal output, divide (3.2.6) byGt

and combine (3.2.7) and (3.2.8) with (3.2.6) to obtain:

60_{Commission Regulation (EU) No 220/2014. ESA stands forEuropean System of Accounts.} 61_{This latter takes place in case a government is in persistent deficit excess with respect to the}

provided floor and"provides for the necessary steps to be taken-.. (which)..could ultimately lead to imposing sanctions on the country concerned." (ECB,www.ecb.eu)

Dt Gt = (1 + ˜yt) Dt−1 Gt − Nt Gt + Mt Gt . (3.2.9)

Equation (3.2.9) can in turn be rewritten at first order by exploiting Taylor expansion 1

1±x ≈1∓x and removing cross-products among variables. This yields:

∆xt= (˜yt−gt)xt−1−nt+mt. (3.2.10) where we defined:62 nt:= Nt Gt , mt:= Mt Gt , xt:= Dt Gt

and equation (3.2.10) remains an identity63.

The quantity (˜yt − gt)xt−1 measures the snowball effect ([49], p. 11), that is, the self-reinforcing of debt accumulation due to the difference between the cost of borrowing and the growth rate the country is able to achieve.64 _{Further comments}

are necessary for what concerns the implied interest rate y˜t.

Eurostat rules state that It is accrued according to the debtor approach, that is,

the yield on each debt instrument which is issued is ".. the cost of borrowing as observed at the time the instrument is created. As a consequence, interest must be accrued using the market rate (yield-to-maturity) or the contractual rate available at inception of the instrument.."([16], pp. 86).

Moreover, the methodologies to imply single-instruments yield-to-maturity is custom ([16], pp. 353-354) and is the same which is used in the construction of the yield curve (appendix B). Each debt instrument can thus be considered as a financial operation whose yield is implied by assuming that the market is arbitrage-free (equation (C.1.2)).

Debt instruments serve also the purpose of implying a sovereign yield curve, as showed in chapter 2; in this case, considering the total set of issued instruments as an aggregated single financial operation, the yield at time tof such portfolio will be

y(t, T∗), being T∗ the duration of the compound portfolio.

The SDW do not offer observations65 _{on government debt duration; figure 3.3 shows}

the average (residual) debt maturity across countries, and the average of this latter over the periods 2001-2013 and 1995-2013, respectively.

An average duration of 4.3 years concerning this eight-countries panel is obtained using datasets of the Organisation for Economic Cooperation and Development (OECD), although observations are often sparse, and lasts in the year 2010.

62_{ntandmtare roughly 1/4 of correspondentquarterlysurplus/gdp (DDA/gdp) defined in [14].} 63_{Discrepancies arise due to Taylor approximation: market data induce a maximum error of 7}

bp with respect to the true∆xt, thus (3.2.10) will still be considered an identity.

64_{Notice that (3.2.10) does not change even ifreal interest rate and output are considered.} 65_{An interesting review on debt size and composition across the EMU can be found in [77].}

1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 3 4 5 6 7

Figure 3.3: Time-evolution of average public debt maturity across Europe (red-squared); average from 1995 to 2013 is T = 5.78 years (blue-crossed) while average from 2001 is T = 6.48 (black-dotted). (Source: ECB and authors computations)

The choice is to compare y˜t with current market yield y(t, T) and set T = 5,

for at least two reasons. First of all, five years is the closest custom maturity to both the average debt maturity and its duration. Secondly, eventual movements in the slope and/or curvature of the term structure y(t, T) (including inversions) are better captured with a mid-term rate than with a longer termed one, due to the flattening of the curve asT goes to infinite [39].

Figure 3.4 shows the time-evolution of y˜t and yt for the countries under exam:

market yield yt reacts to the burst out of the crisis in reaching peaks of near 15%

on a yearly basis (concerning Portugal and Ireland); time-evolution of y˜t, on the

contrary, is rather smooth, very similar across countries and almost not reacting to any of the crisis side-effects.

Before 2008, y˜t stays above market yields, a fact that could be attributed to the

differences in debt maturity with respect to the choice T = 5. Observe that, in the case of Germany, market rate always stays lower than the internal rate, because a general lowering of interest rates.

Particularly, the internal ratey˜tdoes not embed credit risk premia but rather follows

an arranged (hence highly predictable) pattern that remains similar throughout the whole countries panel.

Next section will present adirect econometric approach aimed to answer the questions presented thus far. First of all, the vector model (y,y˜) is fitted so as to unearth eventual common features of the two rates which could help out to settle the internal rate of return within financial markets rates.

Secondly, a VAR model for both the couples (y, x) and (˜y, x) is set up, with the purpose of estimating ω out of equation (3.2.2), as well as the feeedback effects of rates on debt. It will be also useful to introduce another variable of interest, that is, debt variation (debt speed) ∆x.

01 03 05 07 09 11 13 5% 10% 15% BE 01 03 05 07 09 11 13 5% 10% 15% DE 01 03 05 07 09 11 13 5% 10% 15% ES 01 03 05 07 09 11 13 5% 10% 15% FR 01 03 05 07 09 11 13 5% 10% 15% IE 01 03 05 07 09 11 13 5% 10% 15% IT 01 03 05 07 09 11 13 5% 10% 15% NL 01 03 05 07 09 11 13 5% 10% 15% PT

Figure 3.4: 5-years sovereign yield yt (blue-dotted) and implied rate y˜t (green-squared)

BE DE ES FR IE IT NL PT y 2 3 1 1 2 4 2 3 ˜ y 2 3 3 2 4 2 2 2 x 2 2 3 3 2 3 2 2 s 2 − 4 2 2 4 1 3

Table 3.1: Unidimensional number of lags pˆj_{, estimated through the step-procedure}

described in section 1.1,pˆj_{≤4by construction.}

The reasoning behind comes from direct inspections of macroeconomic variables time evolution (figure 3.1). The examples of Portugal and Ireland, the latter showing a pre-crises consolidated debt 30%, suggest that a major source of increase in risk aversion (and credit risk premium) might be the speed at which this high level of debt is reached, rather than the level itself.

A VAR model of the form(y,∆x)is thus inferred using the set of relevant observation. The idea is that debt variation could affect directly y in shifting upwards the slope of demand curve, as explained in section 3.3.

Moreover, associating to each country the speed∆xat which it gets into debt could be also seen as another possible way of scoring countries: that is, the faster it runs up into debt, the higher its credit risk premium (or yield, see (3.2.4)) variation. It will thus be worth to discuss VAR models in the form (s,∆x), where spread vis-à-vis Germany s is selected as benchmark (see chapter 2).