We construct a multivariate, mixed-frequencies model for short-term monitoring and forecasting public finances in Spain

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DOI 10.1007/s13209-010-0018-3
ORIGINAL ARTICLE
Short-term monitoring of the Spanish government
balance
Teresa Leal · Diego J. Pedregal · Javier J. Pérez
Received: 23 July 2009 / Accepted: 26 October 2009
' Spanish Economic Association and Fundación SEPI 2010
Abstract We construct multivariate, state-space mixed-frequencies models for the
main components of the Spanish General Government sector made up of blocks for
each one of its subsectors: Central Government, Social Security and aggregate of
Regional and Local government sectors. Each block is modelled through its total rev-
enue and expenditure categories, and encompasses a number of indicators, depending
on data availability. The mixed-frequencies approach is particularly relevant for the
case of Spain, given its institutional set-up and the specific data availability for the
different subsectors. All in all, we provide models detailed enough in coverage, while
at the same time manageable, to be used: (1) for real-time monitoring of fiscal policies
with a focus on quarterly developments of the General Government sector, (2) for the
monitoring of general government sub-sectors for which intra-annual data coverage
is limited (Regional and Local governments), (3) to bridge (translate) into National
Accounts available monthly information for the subsectors of the general government.
Keywords Fiscal forecasting · Fiscal policies ·Mixed frequency data ·
Kalman filter
JEL Classification C53 · E6 · H6
T. Leal
University of Huelva, Huelva, Spain
e-mail: mtleal@uhu.es
D. J. Pedregal
U. Castilla-La Mancha, Ciudad Real, Spain
e-mail: diego.pedregal@uclm.es
J. J. Pérez (B)
Banco de España, Madrid, Spain
e-mail: javierperez@bde.es
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1 Introduction
Monitoring public finances in the very short-run by means of high-frequency fiscal
data has not been an issue traditionally tackled in the literature, even though it is usually
part of the routine of practitioners. The fact that budgetary projections are prepared
in annual terms, given an annual budgetary cycle, in the framework of annual mod-
els, and the discretionary nature of many government measures set up for the entire
year, have traditionally limited the role of high-frequency fiscal data for monitoring
annual budgetary targets in the course of the year. The relative scarcity of intra-annual
data for the desired, policy-relevant government variables (typically referred to the
general government sector) has contributed to this situation as well. Thus, the stan-
dard practice for factoring-in new intra-annual fiscal information on revised annual
fiscal targets and projections is via informed, judgemental add-in factors (Leal et al.
2008).
In this framework, official annual fiscal targets and projections tend to display
well-documented political biases and/or large forecast errors (see Strauch et al. 2004;
Moulin and Wierts 2006; Annett 2006; Pina and Venes 2008; Jonung and Larch 2006;
Leal et al. 2008). In addition to political biases, fiscal forecast errors might be due
to a number of factors, in particular policy errors, owing to the implementation of
new fiscal policy measures, not yet announced by the forecast cut-off date, and eco-
nomic errors due to inaccurate forecasts of the macroeconomic variables that underlie
budgetary projections.
Even without judging the determinants of fiscal forecasts, some recent episodes
show large forecast errors linked to official annual fiscal projections. Take for exam-
ple the case of the Spanish General Government deficit in 2008. In this year, according
to the Spring 2009 EDP notification, the general government recorded a deficit of 3.8%
of GDP. By June 2008 most national and international institutions still projected a bud-
getary surplus for 2008, and only some institutions timidly turned their estimates to
small deficits for the whole year after the summer. Nevertheless, as late as October
2008 the government still estimated a deficit of 1.5% of GDP, slightly above the 1.6%
deficit projected by the European Commission around the same date (see EC 2008).
The same estimate for 2008 was kept as a reference by the government in the budget
law for 2009 that passed parliamentary approval at the end of December. At the begin-
ning of January, though, in the framework of the updated Stability Programme for
2008?2012, the government provided an estimated deficit for 2008 of 3.4% of GDP,
close to the final figure. A natural question arises: was the sharp, unanticipated revision
of the estimated deficit by the government indeed unpredictable or was it motivated
by some strategic behaviour??as the literature on politically-motivated fiscal fore-
casts might have suggested. In a related fashion, and more relevant for the aim of this
paper: given the available information at the time, would it have been possible for an
independent analyst to detect the fiscal deterioration in advance, at least in the course
of the last part of 2008?
On the development of early-warning tools for fiscal variables, a recent strand
of the literature has shown that intra-annual fiscal data, when modelled appropriately,
contains extremely valuable and useful information for forecasting annual fiscal aggre-
gates, enabling earlier detection of episodes of fiscal deterioration (or improvement)
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than traditional methods (Pérez 2007; Silvestrini et al. 2008; Onorante et al. 2009;
Pedregal and Pérez 2009; Leal and Pérez 2009).
The present paper aims at contributing to this branch of the literature in two direc-
tions. Firstly, it focuses with high detail on one single country (Spain) what enables
the development of a model for the General Government sector (GG) made up of
blocks for each one of its subsectors: the Central Government sector (CG), the Social
Security sector (SS) and the aggregate of the Regional and Local government sec-
tors (LG). To exploit the existing accounting identity between GG and its subsectors
(GG = CG + SS + LG), the variables total revenue, total expenditure and deficit are
modelled in our baseline model in such a way that Z = Z + Z + Z , where
GG CG SS LG
Z stands for any of the fiscal variables mentioned above. In addition, each subsector
is modelled through its total revenue and expenditure categories, and encompasses
a number of idiosyncratic indicators, depending on data availability. The extant lit-
erature either focused on the State subsector of the general government, or directly
on the aggregate of the general government for some representative, headlines fiscal
variables.
Secondly, along the lines of the models by Pedregal and Pérez (2009) for euro area
fiscal aggregates, the models presented in the current paper make use of annual, quar-
terly and monthly ESA95 fiscal figures and other relevant monthly fiscal indicators.
An optimal way to use these data is to build a single model that relates data at all
frequencies. Thus, we construct multivariate, state-space mixed-frequencies models
along the lines of Harvey and Chung (2000), Moauro and Savio (2005), Proietti and
1
Moauro (2006), and Frale and Veredas (2008). This is particularly relevant for the
case of Spain, given important differences in data availability for the different sub-
sectors of the general government. Quarterly ESA95 (European System of National
Accounts) figures are available only for the general government sector as a whole, for
the period starting in 1995, but not for any of its individual subsectors. For the subsec-
tors as defined in National Accounts only annual figures are available for the sectors.
A partial exception is the central Government sector, given that monthly ESA95 fig-
ures are available for its main component (the State sector) that comprises almost 90%
of the total. As regards the Social Security sector, there is monthly information, though
on a cash basis, for several variables. As regards the Regional and Local government
sectors, the availability of intra-annual information is extremely limited.
All in all, we provide models detailed enough in coverage, while at the same time
manageable, to be used: (1) for real-time monitoring of fiscal policies with a focus on
quarterly developments of general government figures, (2) as an input for the prepara-
tion of annual fiscal projections, (3) to bridge (translate) into National Accounts avail-
able monthly information for the different subsectors of the general government, (4)
to make inferences on short-term developments of Regional and Local governments,
given the fact that quarterly information for the aggregate of the General Government
1
Other approaches for modeling data at different sampling intervals are the methods based on regression
techniques (Chow and Lin 1971; Guerrero 2003), the MIDAS (mixed data sampling) approach (see Ghysels
et al. 2006; Clements and Galvão 2008), the state space approaches of Liu and Hall (2001)andMariano
and Murasawa (2003), or the ARMA model with missing observations of Hyung and Granger (2008).
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sector is used in conjunction with monthly information for the Central and the Social
Security sectors.
The models could be easily applied to other euro area countries; in particular those
with a similar institutional setup and at least the same data coverage by subsectors
(like Germany or Italy). For the case of Spain, this paper has to be seen as a first
attempt to develop a short-term fiscal model for the General Government; subsequent
refinements of the model, especially by further enlarging the data coverage by sub-
sectors, are warranted. On different grounds, we see the usefulness of our models as
a benchmark for the interpretation of newly available data, and not as a substitute
of the in-depth analysis normally carried out by fiscal experts in policy institutions.
A detailed knowledge of institutional and special factors is a key ingredient for the
short-term analysis of fiscal data, which could be further exploited in conjunction with
the models presented in this paper.
The rest of the paper is organised as follows. Section 2 describes the data used.
Section 3 describes the models, Sect. 4 presents the main results of the paper, and
Sect. 5 concludes.
2 Database description
Table 1 shows the dataset employed in the paper. It comprises a total amount of 32
time series, taken from different official providers of statistics (IGAE, INE, BDSICE),
and covers the period 1985?2008. The data covers the General Government sector and
its subsectors. Part of the dataset is in line with ESA95 standards, while another part
follows public accounts (cash) accounting rules.
As regards direct data for the General Government sector (GG), we use annual
non-financial total revenue and expenditure from 1985 to 2008, as well as quarterly
non-financial total revenue and expenditure, from 1995Q1 to 2008Q4. It is worth
noticing that, surprisingly enough, the quarterly information is not available for the
2
sub-sectors comprising GG. All series are in ESA95 terms.
By far, the Central Government sector (CG) is the subsector with the best data cover-
age in terms of adherence to ESA standards. We use annual non-financial total revenue
and expenditure from 1985 to 2008, as well as monthly figures for most categories of
the State Sector (that comprises more that 90% of the total CG sector) from 1985 to
2008. In particular, we use on the revenue side: direct taxes, VAT, other indirect taxes,
and other revenues (so that the sum of the four items adds up to the total revenues of
the State sector). On the expenditure side: ?government consumption? (compensation
of employees plus intermediate consumption), capital expenditure, interest payments,
and other expenditures (so that the sum of the four items adds up to the total of
expenditures of the State sector).
For the Social Security sector (SS) we also use annual non-financial total reve-
nue and expenditure from 1985 to 2008 in ESA95 terms. The Spanish SS sector is
2
Annual ESA95 series for the GG sector and all its subsectors are available from the IGAE (Badespe data-
base). Within the period 1985?2008 the changeover from ESA79 to ESA95 was accounted for by applying
growth rates of the variables in ESA79 terms (first part of the sample) to the levels of the variables in ESA95
(last part of the sample).
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Table 1 Data sources
a b
Non-financial series ESA95 coverage Periodicity Sample period Basis Source Units
General Government S.13 GG Annual 1985?2008 ESA95 INE Mrd EUR
total revenue (BADESPE
database)
General Government total
expenditure
Central Government total S.1311 CG
revenue
Central Government total
expenditure
Social Security total S.1314 SS
revenue
Social Security total
expenditure
General Government total S.13 GG Quarterly 1995Q1?2008Q4 ESA95 ECB and Eurostat
revenue
General Government total
expenditure
Direct taxes S.1311 subsector Monthly 1985:1?2008:12 ESA95 IGAE and INE
VAT taxes (State)
Other indirect taxes
Other revenues
Government consumption
Capital expenditure
Interest payments
Other expenditures
Total cash non-financial S.1314 subsector (Social Cash BDSICE database
receipts Security System) (cod.731102G)
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Table 1 continued
a b
Non-financial series ESA95 coverage Periodicity Sample period Basis Source Units
Total contributory social BDSICE database (cod. 731210)
benefits
Total expenditure S.1314 subsector Public State Emp. Service
(Public State
Employment Service)
Taxes collected by the S.1312 LG BDSICE database (cod. 753100)
Central Government
sector on behalf
of the Regional
government
a
ESA European System Account, GG General Government, CG Central Government, LG Regional and Local governments? aggregate, SS Social Security sector
b
INE Spanish National Institute, ECB European Central Bank, IGAE General Comptroller of the State Administration
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basically composed of two parts. On the one hand, the ?Social Security System??
covering mainly social contributions, and contributory and non-contributory social
benefits?for which, monthly cash non-financial receipts and expenses are available
for the period under study. On the other hand, the SS sector comprises ?Other Admin-
istrations of the Social Security Funds?, which covers the ?Public State Employment
Service? (SPEE) and the ?Social Guarantee Fund? (FOGASA). In this respect, we
include in our analysis the monthly cash non-financial revenues and expenditures of
the SPEE.
The Regional and Local governments (LG) are by far the sub-sectors with less
available intra-annual data. In fact, no consistent time series covering a reasonable
time span are available for the spending side of the LG sector. For the revenue side,
available information comprises monthly cash data for the whole period regarding
taxes collected by the CG sector on behalf of the LG sector (Tributos cedidos y con-
certados). Nevertheless, this source does not cover all tax revenues managed by the
LG sector. As usual, we also include annual ESA95 total revenue and expenditure of
the LG sector, from 1985 to 2008.
From an accounting point of view total revenues and expenditures of the GG in
ESA95 terms are equal to the sum of ESA95 CG, SS and LG sectors? total revenues
and expenditures, respectively. This is a constraint that links all the annual ESA95
data described above. The database is affected by a process of decentralization by
which some duties in the hands of the Central Government and Social Security sectors
have been transferred to Regional and Local governments, following the particular
development of the territorial structure of Spain established in the 1978 Constitution.
The distribution of revenues and expenditures between the sectors has been altered by
subsequent changes in the financial arrangements between them, leading to successive
waves of decentralization (see Gordo and Hernández de Cos 2001). For the purpose of
this paper, with a special focus on forecasting, the most influential effect arises from
the 2002 financial arrangements between the Central Government and the Regional
Government sectors, entering into effect in January 2002.
To address potential distortions due to this decentralisation process, we disregard
a purely statistical approach consisting on balancing transfers among sectors on the
basis of raw data, due to lack of sufficient information. Instead, we decide to take a
simpler, econometric approach: all the affected time series are corrected beforehand
with the aid of models set up in a State Space framework along the lines described
in a following section. An intervention model is estimated with constraints in the
intervention parameters, in a way such that the addition of the declines in CG and SS
revenues and expenditures due to transfers equal the raising up of LG revenues and
expenditures. Therefore, the accounting constraints mentioned earlier are respected
(i.e. total GG series are untouched): revenues and expenditures in all sub-sectors are
corrected so that at the end the total revenues and expenditures withdrawn from the CG
and the SS sectors are exactly equal in amount to the increase in LG sector?s revenues
and expenditures. In addition, the corrections are implemented in such a way that all
3
the implied deficit (revenue minus expenditure) time series are unaffected.
3
Additional interventions were kept to a minimum, but some were needed on technical grounds (detected
using the standard program TRAMO): additive outliers on October?November 1986 on monthly capital
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General Government Revenue General Government Expenditure
450 450
400 400
350 350
300 300
250 250
200 200
150 150
100
100
50 50
0
0
1985 1990 1995 2000 2005
1985 1990 1995 2000 2005
General Government Balance
25
15
5
-5
-15
-25
-35
-45
1985 1990 1995 2000 2005
Fig. 1 Spanish General Government revenue, expenditure and balance, 1985?2007. ESA95 annual and
=
quarterly figures (bars quarterly shown as four-quarter moving sum). Billion C
Figures 1, 2, 3 and 4 show most of the variables used in the analysis: total revenues
and expenditures for the GG sector and for all its subsectors (in ESA95 terms and
also the available ?indicators?), and also the government deficits, computed as the
difference between revenues and expenditures.
Figure 1 shows the information available for the General Government: annual
ESA95 series up to the year 1994 and quarterly afterwards (shown as four-quarter
moving sums). Figures 2, 3 and 4 display the same information but by subsectors,
and also the monthly information available in each case. Left plots in each row of
these figures present the ESA95 annual series and the indicator variables (annualised
monthly variables); right plots in each row show the ESA95 annual figures (bars) and
monthly cash series in a monthly time axis (solid line, shown as 12-months moving
sums). Figure 2 displays the expected close level correspondence between the State
sector and the total Central Government sector series. Also as expected, Fig. 3 shows
a quite small level gap on the revenue side between the indicators and the ESA95
aggregates for the SS sector, while total expenditures? levels are commensurate. In
Fig. 4 it is obvious that the available monthly information for the LG sector does not
properly trace the evolution of the overall sector in ESA95 terms.
Footnote 3 continued
expenditure; additive outliers on August?September 1993 on monthly cash Social Security System?s expen-
ditures; additive outlier on December 1998; correction of the drastic change in the variance of the series
of interest payments at the beginning of the 1990s (due to changes in Treasury?s practices). Finally, the
impact of one-off proceeds relative to the allocation of mobile licenses (UMTS) was removed from the
ESA95 annual series and, accordingly, some adjustments were also implemented in the monthly indicators
to guarantee consistency.
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Central Government Revenue Central Government Revenue
180 180
160 160
140 140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
1985 1990 1995 2000 2005
1985 1990 1995 2000 2005
Central Government Expenditure Central Government Expenditure
180 180
160 160
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
1985 1990 1995 2000 2005
1985 1990 1995 2000 2005
Central Government Balance Central Government Balance
20 20
15 15
10 10
5 5
0 0
-5 -5
-10 -10
-15 -15
-20 -20
-25 -25
-30 -30
1985 1990 1995 2000 2005 1985 1990 1995 2000 2005
Years Months
Fig. 2 Spanish Central Government revenue, expenditure and balance, 1985?2007. Left plots in each row
ESA95 annual figures (solid line) and annualised sum of 12 months for the monthly variables (dashed line).
Right plots in each row ESA95 annual figures (bars) and sum of the four monthly indicators (solid line,
=
shown as 12-month moving sum). Billion C
Most of the intra-annual variables included in our analysis present strong seasonal
patterns. As regards government revenue variables, they largely reflect the calendar
of payments of the corresponding tax categories. Income taxes are partly paid every
month via withholdings on labour and capital income, but also follow an annual cal-
endar of payments. Corporate taxes tend to follow a quarterly pattern as the bulk of
the tax returns are reported quarterly by companies. Indirect tax collection, especially
as regards VAT, also follows regular seasonal patterns linked to quarterly tax state-
ments by firms and the annual refund of taxes. Government expenditures also reflect
regular seasonal patterns, mainly linked to compensation of employees (payments to
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Social Security Revenue
Social Security Revenue
160
160
140
140
120
120
100
100
80
80
60 60
40 40
20 20
0
0
1985 1990 1995 2000 2005
1985 1990 1995 2000 2005
Social Security Expenditure Social Security Expenditure
140 140
120 120
100
100
80
80
60
60
40
40
20
20
0
0
1985 1990 1995 2000 2005
1985 1990 1995 2000 2005
Social Security Balance Social Security Balance
18 18
16 16
14 14
12 12
10
10
8
8
6
6
4
4
2
2
0
0
-2
-2
-4
-4
1985 1990 1995 2000 2005
1985 1990 1995 2000 2005
Years
Months
Fig. 3 Spanish Social Security revenue, expenditure and balance, 1985?2007. Left plots in each row ESA95
annual figures (solid line) and annualised monthly cash series (dashed line). Right plots in each row ESA95
=
annual figures (bars) and monthly cash series (solid line, shown as 12-month moving sum). Billion C
government employees) and transfers to households (in particular old age pensions
and other pensions). For these reasons the selected models, as reported in the Sect. 3 of
the paper, take due account of seasonality; we model explicitly seasonal components
for all the variables in our models, and estimate all the relevant seasonal parameters
jointly with all other parameters of our models.
3 The State Space models
The mixture of frequencies, and the estimation of models at the monthly frequency,
implies combining variables that at the monthly frequency can be considered as stocks
with those being pure flows. An annual ESA95 series cast into the monthly frequency
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Local Government Revenue Local Government Revenue
140 140
120 120
100 100
80 80
60 60
40 40
20 20
0 0
-20 -20
1985 1990 1995 2000 2005 1985 1990 1995 2000 2005
Local Government Expenditure Local Government Balance
140 1
0
120
-1
100
-2
80
-3
60
-4
40
-5
20
-6
0 -7
1985 1990 1995 2000 2005 1985 1990 1995 2000 2005
Fig. 4 Spanish Local Government revenue, expenditure and balance, 1985?2007. Top plots ESA95 annual
figures (solid line) and annualised monthly cash series (left; dashed line); ESA95 annual figures (bars)
and monthly cash series (right; solid line, shown as 12-month moving sum). Bottom plots annual ESA95
=
expenditure and deficit. Billion C
is a set of missing observations for the first months of the year (January to November)
and the observed value assigned to the last month of each year (December). Theoret-
ically, the annual ESA95 series would be obtained from a monthly ESA95 series by
summation of the 12 months of a year (January to December) had them been available.
In the same fashion, a quarterly ESA95 series cast at the monthly frequency encom-
passes missing observations for the first and the second month of each quarter, while
the quarterly observation would be assigned to the last month of each quarter. In the
same fashion, the quarterly ESA95 series would be obtained from a monthly ESA95
series by summation of the 3 months of each quarter had them been available.
3.1 Time aggregation in State Space models
Prior to the exposition of the particular formulation used in this paper (see next sec-
tion), this section explains how time aggregation can be implemented in a general
State Space framework (see e.g. Harvey 1989). Let?s consider the general multivariate
State Space system
{
x = x + Ew : Transition Equations
t t?1 t
(1)
?
z = Hx + v : Observation Equations
t t
t
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Here t is the time index measured in months; z denotes the m dimensional output
t
?
time series; x is the n dimensional state vector; w and v are serial and mutually
t t
t
independent Gaussian noises of dimensions k and l, respectively, with constant covari-
ance matrices; and, E and H are known system matrices of appropriate dimensions.
Without any loss of generality Eq. (1) is rewritten as
?
? x = x + Ew
t t?1 t
?
?
?? ? ? ? ? ?
r H v
t 1 1,t
(2)
?? ? ? ? ? ?
? e = H x + v
t 2 t 2,t
?
?
u
u H v
t t
Equations (1) and (2) are equivalent; the only difference is that the vector of output
variables is separated in three parts: r and e , that are scalar variables, and u that is
t t t
?
a vector comprising the rest of m ? 2 variables. Matrices H and v have been split
t
u
accordingly. In particular H , H and H stand for the first, second and the rest of
1 2
rows of H matrix in (1). Similarly v ,v and v stand for the first, second and the
1,t 2,t t
rest of observed noises. Still, models (1) and (2) are exactly equivalent to a model
in which the state vector is extended to include the first two output variables and the
vector of transition noises is also extended with the first two observed noises
?
? ? ? ?? ? ? ?? ?
? r 00H r 10H E v
t 1 t?1 1 1,t
?
?
?
? ? ? ?? ? ? ?? ?
? e = 00H e + 01H E v
t 2 t?1 2 2,t
?
?
?
x 00 x 00E w
t t?1 t
? ? ? ?? ? ? ? (3)
?
r 100 r 0
?
t t
?
?
? ? ? ? ?? ? ? ?
e = 010 e + 0 v
?
t t t
?
?
u
u 00H x I
t t
Time aggregation now may be incorporated by introducing a cumulator variable in
system (3). This is a variable defined as
{
0, t = every january
C =
t
1, otherwise
The final model including the temporal aggregation constraints is
?
? ? ? ?? ? ? ?? ?
A A
? r C 0 H r 10H E v
t 1 1 1,t
? t t?1
?
? A A
? ? ? ?? ? ? ?? ?
? e = 0 C H e + 01H E v
t 2 2 2,t
? t
t?1
?
?
x 00 00E wx
t
t t?1
(4)
? ? ? ?? ? ? ?
A A
?
? r 100 r 0
t t
?
?
A A
? ? ? ? ?? ? ? ?
? e = 010 e + 0 v
t
? t t
?
u
u 00H x I
t t
A A
Variables u in Eq. (4) are measured at a monthly rate, while r and e are only
t
t t
measured at the end of a year, i.e. they are observed every December, while they are
missing the rest of the months. Thus, the value of the variable for one year is the sum
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of the disaggregated measure for the 12 respective months. Comparison of Eqs. (3)
A
and (4) clearly shows that r in (4) for any year is the accumulation along that year of
t
the hypothetical monthly observations r in (3), if it were known. Every January the
t
cumulator variable reset the monthly accumulation.
Beware that though models (3) and (4) look analytically similar, they have different
time properties, since model (4) has one time varying system matrix due to the intro-
duction of the cumulator variable. Exogenous variables may be added to the model by
including a standard linear term to the observation equations in (4).
3.2 Models for the subsectors of the General Government
The basic model is of the Unobserved Component Model class known as the Basic
Structural Model (Harvey 1989), that decomposes a set of time series in unobserved
though meaningful components from an economic point of view (mainly trend, sea-
sonal and irregular). The model is multivariate, and may be written as
?
z = T + S + v (5)
t t t
t
?
Here T , S and v denote a trend, seasonal and irregular components, respectively.
t t
t
Equation (5) is in fact a set of observation equations in a State Space system, which has
to be completed by the standard transition or state equations. The general consensus
in this type of multivariate models in order to enable identifiability is to build SUTSE
models (seemingly unrelated structural time series). This means that components of
the same type interact among them for different time series, but are independent of any
of the components of different types. In addition, relations are only allowed through
?
the covariance structure of the vector noises w and v , but never through the sys-
t
t
tem matrices directly. This allows that trends of different time series may relate to
each other, but all of them are independent of both the seasonal and irregular compo-
nents.
The state equations qualify the dynamic behaviour of the components, and a full
model may be built by block concatenation of the individual components. The tran-
sition equations for models of the trend and seasonal components are a Local Linear
Trend and the Trigonometric Seasonal in Eq. (6),
( ) ( ) ( )
?
T T w
0
?
?Trend : = + E
T T
? ?
? D D w
? 0
t t?1 t
?
?
6
?
Seasonal : S = S ; i = 1, 2,...,6 (6)
t i
t
?
? i=1
( ) ( ) ( )
?
?
?
S S w
i i i
? 2pi i
? = + E ,?=
i T i
? ? ?
12
S S w
i i i
t t?1 t
with
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( ) ( ) ( )
II I0 cos ? I sin ? I
i i
= ;E = ; = , i = 1, 2,...,6
T T i
0I 0I ?sin ? I cos ? I
i i
?
In Eq. (6) D and S are additional states necessary to define the components; I
t
it
and 0 are the identity matrix and a square block of zeros of dimension m;w and
j
?
w ( j = 0, 1,...,6) are multivariate Gaussian white noises serially independent and
j
independent of each other; and ? (i = 1, 2,...,6) are the fundamental frequency of
i
the seasonal component and its harmonics.
The State Space form of a full BSM model written as Eq. (4) consists of a state vector
x composed by the concatenation of all the states regarding the trend components (T
t t
?
and D ) and all the states regarding seasonal components S and S (i = 1, 2,...,6) in
t it
it
Eq. (6). Matrix is the block concatenation of matrices and , i = 1, 2,...,6;E
T i
is the block concatenation of seven E matrices; and H is the horizontal concatenation
T
[ ]
of seven I0matrices.
Within this general structure, the specific models estimated for each one of the
subsectors of the General Government will be:
Model CGBlock: model of type (6) for the CG sector. r and e refers to annual total
t t
revenue and total expenditure of the CG sector in ESA95 terms. u comprises eight
t
monthly variables: four on the revenue side (State sector direct taxes, VAT, other
indirect taxes, and other revenues) and four on the expenditure side (State sector
government consumption, interest payments, capital expenditure, and other expendi-
tures).
Model SSblock: model of type (6) for the SS sector. r and e refers to annual total rev-
t t
enue and total expenditure of the Social Security sector in ESA95 terms. u comprises
t
one monthly revenue variable and one monthly expenditure variable.
Model LGblock: model of type (6) for the LG sector. r and e refers to annual total rev-
t t
enue and total expenditure of the sector in ESA95 terms. u only contain one monthly
t
revenue indicator.
In order to reduce the dimensionality of the models (in terms of parameters to be
estimated), some constraints have been imposed among the unobserved components
of r, e, and u, that can be partly rationalized on the basis of economic priors. First, the
structure of the covariance matrix for the noises affecting the seasonal components is
assumed diagonal, i.e. all the seasonal components are assumed independent of each
other. The main motivation for this assumption is the fact that cash and accrual vari-
ables differ in the way they are computed within the year, i.e. seasonal components
reflect mainly differences in accounting standards.
Second, the covariance matrices for the noises in the trend levels, the trend slopes
and the irregulars are specified according to the following constraints: (1) the ones
corresponding to r and e are correlated, (ii) the block of revenue indicators in u is
modelled jointly but independent of the block of expenditures, (3) the block of expen-
diture indicators in u is modelled jointly but independent of revenues, (4) r is only
related to the corresponding block of revenue indicators, (5) e is only related to the
corresponding block of expenditure indicators. Thus, we allow for full interdepen-
dence of total revenues and total expenditures in ESA terms (the key variables), while
at the same time incorporate dimensionality-reducing constraints between the blocks
of revenue and expenditure indicators.
123
SERIEs
3.3 Model including the General Government and all the subsectors
A final model (Model GG) will be a joint model for the full dataset, with the following
properties: (1) quarterly information about GG total revenue and total expenditure
from the first quarter of 1995 onwards is incorporated into the model, (2) it is built by
orthogonal block concatenation of the individual models for the subsectors discussed
in the previous subsection.
Model GG is specified in order to produce a joint explanation of the problem. The
model is multivariate in a weak sense, since the only connection among different
sectors is given by the fact that the sum of the three subsectors? total revenue and
4
expenditure is equal to the total revenue and expenditure of the GG sector. In addi-
tion to the joint estimation of the blocks, the joint model allows the integration of the
available quarterly information for the General Government sector while, as stated in
a previous section, there is no quarterly information available for the subsectors. Thus,
a new cumulator variable has to be defined
?
? 0, t = every January (monthly data) or
?
C = first month of every quarter (quarterly data)
t
?
1, otherwise
In order to explain how Model GG is set up, consider a system formed by the concat-
enation of three systems of type (6) for the CG, SS and LG sectors (models CGBlock,
SSBlock and LGBlock, the latter with u empty) in Eq. (7)
t
{
X = X + EW
t t t?1 t
(7)
Z = HX + CV
t t t
Here capital letters stand for the vertical concatenation of the state vector, noises and
endogenous variables, while bar letters indicate diagonal block concatenation of cor-
responding matrices. General Government ESA95 variables have to be added to the
system, bearing in mind that the data is annual up to 1994 and quarterly afterwards.
?
Application of time aggregation techniques by means of the cumulator variable C
t
gives
?
? ? ? ?? ? ? ?
?
? R C 0 H R H E
R t R
t t?1
t
?
?
? ?
? ? ? ?? ? ? ?
? E = 0 C H E + H E W
t E t t?1 E t
? t
?
?
? X X
E
t 00 t?1
t
(8)
? ? ? ?? ? ? ?
?
?
0
? R
10 0 R
t t
?
?
?? ? ? ?? ? ? ?
? E =
01 0 E + 0 V
t t
t
?
?
Z 00 H X C
t t
4
More complex models were entertained, in which relations among sectors were specified explicitly via
the covariance matrices of the components, but the estimation problems at that stage were too discouraging.
In the end, the information added for the estimation of this model is quarterly information for part of the
sample in two aggregated time series, i.e. too little information for the amount of additional parameters to
be estimated.
123
SERIEs
Here R is annual/quarterly GG revenue; E is GG expenditure; H is a row vector
t t R
formed by the addition of rows in H corresponding to the aggregated revenue of CG,
SS and LG sectors; and H is a row vector formed by the addition of rows in H
E
corresponding to the aggregated expenditure of CG, SS and LG.
3.4 Estimation of State Space models
Given any model written in State Space form, the estimation problem consists of
finding the first and second order moments (mean and variance) of the state vector,
conditional to all the data in a sample. The widespread general tools to perform this
operation in a State Space framework are the Kalman Filter and the Fixed Interval
Smoothing algorithms (full accounts can be seen, e.g. in Harvey 1989; Pedregal and
Young 2002).
One classical problem is that the application of the recursive algorithms above
requires the knowledge of all the system matrices. In most cases, though not always
necessarily, there will be some unknown elements, usually called hyper-parameters,
which must be estimated by efficient methods. There exist a number of ways to deal
with this problem, though Maximum Likelihood in time domain is the most wide-
spread estimation method, mainly because of its strong theoretical basis. Assuming
that all the disturbances in the state space form are normally distributed, the Log-
likelihood function can be computed using the Kalman Filter via ?prediction error
decomposition? (Schweppe 1965; Harvey 1989). There is not any need for especial
considerations about the estimation of models with time aggregation constraints. Since
this is a classical estimation procedure the topic is not pursued further in this paper
(see Harvey 1989; Pedregal and Young 2002). Some diagnostic checks of the annual
revenue and expenditure residuals of the models estimated by Maximum Likelihood
are shown in Table 2. All tests show clearly absence of any kind of problem in the
residuals, since there is no evidence of serial dependence, residuals are Gaussian and
no evidence of heteroskedasticity can be found.
4 Empirical exercise
4.1 Forecast performance statistics: current year forecasts
In order to replicate the real-time constraints faced by real-time analysts, we adopt
the timing rules displayed in Table 3, following the standard dates of dissemination
of data at the different frequencies. In the table we show the available information in
each quarter of a given year. Annual ESA95 figures for year t ? 1 are first released by
the national statistical office in March/April of year t but the validation processes by
Eurostat of figures reported by national statistical agencies render April/May as the
actual date in which usable/reliable figures are available to an outside analyst. Thus,
from a quarterly observation perspective, it is fair to assume that the annual figure for
year t ? 1 is only available in the second quarter of year t. In a related fashion, the
quarterly ESA95 figure for the fourth quarter of year t ? 1 would only be available in
the course of the second quarter of year t. Regarding monthly cash accounts, we follow
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Table 2 Diagnostic checks of annual revenue and expenditure residuals of all models
Sector Variables Q (1 year) Q (2 years) Jarque-Bera P (Jarque-Bera) P (Heterosk.)
Models for individual sectors (Model CG block, Model SS block, Model LG block)
CG Revenues 0.46 0.65 6.09 0.04 0.11
Expenditures 0.14 1.59 1.22 0.54 0.45
SS Revenues 0.15 1.59 4.07 0.13 0.45
Expenditures 0.02 0.15 1.49 0.47 0.47
LG Revenues 0.32 1.22 2.47 0.29 0.35
Expenditures 0.05 0.67 0.65 0.72 0.25
Overall model (Model GG)
CG Revenues 0.87 1.06 1.05 0.59 0.24
Expenditures 0.003 0.25 1.66 0.44 0.49
SS Revenues 0.09 2.04 3.92 0.14 0.43
Expenditures 0.14 1.28 1.15 0.56 0.48
LG Revenues 1.56 1.70 0.84 0.65 0.32
Expenditures 0.17 2.23 1.58 0.45 0.24
Q (1 year) and Q (2 years) stand for the Ljung and Box Q statistic of serial correlation for 1 and 2 years,
respectively. Jarque-Bera and P (Jarque-Bera) are a gaussianity test and its P value, respectively. P (Het-
erosk) is the P value of a standard ratio of variances test
Table 3 Timing rules
Q1 year t Q2 years t Q3 year t Q4 year t
(March) (June) (September) (December)
Available annual (A) A (March) A (April) A A
t?2 t?1 t?1 t?1
Available quarterly (Q) Q Q (April) Q Q
3,t?1 4,t?1 1,t 2,t
Available monthly (M) Jan. t Jan.?April t Jan.?July t Jan.?October t
the assumption of availability with a lag of two months. We deem this convention also
as a fair heuristic representation of reality.
In order to carry out the forecasting exercise, we add to the list of models described
in the previous section the following models: (1) annual random walk (ARW hence-
forth), (2) quarterly random walk (QRW henceforth), consisting of adding the last
four quarters available of the series when quarterly data is available (i.e. General
Government) and equals the ARW forecasts when the forecast origin coincides with
5
the end of each year. The QRW alternative allows to test against an alternative
5
Random walk models were selected because they are standard, benchmark alternatives in the forecasting
literature. In the case of our particular empirical setup other standard benchmark alternatives, like a AR(1)
applied to quarterly ESA95 series, were discarded on the basis that, due to the limited sample available
(for quarterly data the sample starts in 1995Q1) the estimation of simple AR(1) models turned out to show
high RMSEs. This finding is consistent with the fact that, given the non-stationary nature of the modelled
series (series in nominal terms), more complex ARIMA structures could have been needed. For the sake of
simplicity and focus of the empirical exercises, we preferred to stick to standard, simpler alternatives like
the QRW.
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SERIEs
purely based on quarterly GG information. The ARW alternative is the standard naive
benchmark.
Then we perform a rolling forecasting exercise in which the selection of the fore-
cast origin and the information set available at each date are carefully controlled for.
In particular we evaluate the forecasts generated from four forecast origins per year
from March 2001 to September 2007 (this makes up to 28 projections at each forecast
horizon). The first forecast origin is March 2001, and following the timing convention
outlined before (see Table 3) the annual information available covers up to the year
1999, the quarterly information up to 2000:Q3, and the monthly information up to
January 2001. The second forecast origin is June 2001, with annual information up to
2000, quarterly up to 2000:Q4 and monthly up to January?April 2001. Then we move
the forecast origin to September 2001 and so on and so forth until September 2007.
We leave out of the exercises in this section the year 2008, that will be analysed in
isolation in a subsequent section.
Finally, we present two standard, quantitative measures of forecasting performance.
Firstly, we look at the ratio of the root mean squared errors (RMSE) of the different
alternative models with respect to the ARW model. Secondly, we also look at the
Diebold and Mariano test, and test for the null hypothesis of no difference in the
accuracy of two competing forecasts. We make sure that a reasonable proportion of
the sample is employed when the first out-of-sample forecast is computed to reduce
the bias generated by ignoring parameter uncertainty (see for example Clark and
McCraken 2001); the forecasting exercise is performed on the moving window 2001?
2008, while the full sample covers 1985?2008.
We focus on the forecast performance of annual projections, i.e. forecasts generated
from each forecast origin for the end of the current year. Table 4 shows the results for
the end-of-the-year forecasts performed using the alternative models. It shows first the
RMSE ratios of the different alternative models to the ARW alternative and, second
the Diebold?Mariano tests of equal forecast accuracy for each pair of models.
One set of evidence on the usefulness of intra-annual information is provided by
the fact that the RMSE ratios of model QRW over ARW is 0.85, implying that a blind
use of quarterly ESA95 information would improve forecasts for the end of the year.
As regards the rest of RMSE ratios the results clearly show that all alternatives with
intra-annual update beat the ARW. The ratios range from 0.32 of Model GG to the
0.85 of LGblock. The best results are those for the overall GG, due to the fact that
the best forecasts by sectors correspond to CG, that represent the biggest proportion
of the overall General Government sector. In 2006 the proportion of revenue (expen-
diture) was 43.8% (43.7%) for CG, 37.5% (36.2%) for SS and 18.7% (20.1%) for LG.
As regards the ratios between pairs of the other alternatives except ARW, all models
beat QRW. The RMSE of Model GG and the addition of all the block results for GG to
QRW are 0.37 and 0.43, respectively. Regarding the results of the Diebold?Mariano
test, all models outperform the ARW model significantly. Either model GG or the sum
of forecasts of the three individual models for the subsectors produce significant better
forecasts than the QRW model. It is also worth noticing that model GG systematically
produces better RMSE ratios than the block models, and thus we may conclude that
including ESA95 quarterly information into the analysis is important for improving
forecasting results.
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Table 4 Forecast performance statistics: current year forecasts
RMSE/ARW Diebold?Mariano tests CG + SS + LG Block
ARW Full
GG
??
Full 0.318 ?2.308 ??
??
CG + SS + LG Block 0.366 ?1.988 0.344 ?
? ?? ??
QRW 0.851 ?1.667 2.403 2.191
CG
??
Full 0.439 ?2.139 ??
?
CG Block 0.553 ?1.685 0.176 ?
SS
??
Full 0.597 ?1.988 ??
??
SS Block 0.663 ?2.292 0.192 ?
LG
?
Full 0.838 ?1.793 ??
?
LG Block 0.853 ?1.678 0.646 ?
Ratio of RMSE of each method against an annual random walk (ARW), and Diebold?Mariano test for the
null hypothesis of equal forecast accuracy of two forecast methods. The numbers in each cell of the DM
test represents the loss differential of the method in its vertical column as compared to the method in the
horizontal line
The Diebold?Mariano statistic follows a N (0,1) distribution. A single (double) asterisk denotes rejection
of the null hypothesis at the 10% (5%) significance level
The main lessons to be drawn from Table 4 are: (1) all models with intra-annual
update beat ARW, (2) models including monthly indicators beat QRW, (3) overall,
model GG tends to give better results for the fiscal variables of the individual subsec-
tors than the block model counterparts.
4.2 Forecast performance statistics: now-casting and current quarter forecasts
In Table 3 we focus on forecasts for the whole year, while in Table 5 we turn to
the related issue of now-casting and one-quarter-ahead forecasts, also relevant for
decision-taking in real time.
In real-time, policy makers face the following problems. First, form a public finance
point of view, annual targets are set in terms of National Accounts? definitions and
refer to the General Government sector, while the flow of incoming information tend
to follow cash recording practices (the case of monthly Social Security and Regional
governments? figures) or is related to a given sub-sector of the General Government
(the case of ESA95 monthly Central Government figures). At the same time, from
the point of view of macroeconomic forecasting, quarterly national accounts form the
articulating framework of short-term macroeconomic forecasts.
From these perspectives, the methodology and the approach developed in this paper
would provide a useful tool for policy makers and real-time forecasters if, on the basis
of incoming fiscal information, our models were able to provide fair current quarter
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Table 5 Forecast performance statistics: nowcasting and current quarter forecasts
RMSE/QRW Diebold?Mariano tests P value
??
Nowcasts 0.565 ?3.495 0.0005
??
One quarter ahead 0.727 ?3.074 0.0021
Ratio of RMSE measures for quarterly General Government sector of model GG (Full) (nowcasts and one
quarter ahead) against a quarterly random walk (QRW) forecast, and Diebold?Mariano test for the null
hypothesis of equal forecast accuracy of two forecast methods. Nowcasts are computed by assuming all the
monthly information up to the quarter to be forecast; one quarter ahead forecasts are computed by assuming
the information available at that point in time according to Table 2. The numbers in each cell of the DM
test represents the loss differential of the method in its vertical column as compared to the method in the
horizontal line
The Diebold?Mariano statistic follows a N (0,1) distribution. A single (double) asterisk denotes rejection
of the null hypothesis at the 10% (5%) significance level
estimates (now-casting if all the months of the quarter were available) and fair one-
quarter-ahead projections of fiscal aggregates in National Accounts.
These are exactly the exercises whose results are provided in Table 5. Now-casts
are computed by assuming all the monthly information up to the quarter to be forecast;
one quarter ahead forecasts are computed by assuming the information available at
that point in time according to Table 3; QRW consists of replacing the forecast for the
next quarter by the latest quarter of the same type available within the dataset. The ratio
of RMSEs is the ratio of the RMSE of model GG (now-casts and one quarter ahead)
against a quarterly random walk (QRW) forecast, and the Diebold?Mariano test shows
a comparison of the same two methods. The numbers clearly show how model GG
outperforms a quarterly random walk in the two investigated respects (now-casting
and one-quarter ahead forecasts); the relative behaviour of model GG is even better
than the one displayed for current year forecasts (see Table 4).
4.3 A real-time illustration
Figure 5 completes the information shown in Tables 4 and 5 by presenting the behav-
iour of the models in the most recent period, the year 2008, that was not included in the
previous forecasting exercises. We decided to leave 2008 out of the forecast sample
because it provides an episode of a dramatic deterioration of the general government
balance that moved from a surplus of 1.9% of GDP in 2008 to a deficit of 4.1% of
GDP in 2008, according to the revised estimates published in Autumn 2009.
We illustrate the mechanical behaviour of our time series models, against published
government targets/estimates, and published forecasts by the European Commission
(EC). This implies leaning against the mixed-frequency models, as in the course of the
year a number of discretionary fiscal policy measures affecting 2008 were announced
and implemented. In real-time, these measures, forward-looking in nature, could have
been included in our time series models. The exercise is a full real-time exercise, in
that the series/forecasts used in all cases were those available in real-time.
In the first quarter of 2008 the government still presented a general government sur-
plus as a target; with information up to February/March of 2008, the models would have
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SERIEs
Panel A
40
2007Q3
30
2008Q1 Model forecast with forecast
20 2007
origin March 2008
2006
2007Q4
[Information set: 2006;
2007Q3; January 08]
10
ACTUAL GENERAL GOVERNMENT 2008Q2
DEFICIT (as in April 2009)
Model forecast with forecast
0
origin June 2008 [Information
set: 2007; 2007Q4; April 08
-10 Model forecasts with forecast
º
origin September 2008
2008Q3
[Information set : 2007;
-20 2008Q2; July 08]
Model forecast with forecast
origin December 2008
-30
[Information set : 2007;
2008Q2; October 08]
-40 Model nowcast with forecast
origin February 2009
2008
[Information set : 2007;
-50 2008Q3; December 08]
2005 2006 2007
Panel B
40
2007Q3
30
2008Q1 Model forecast with forecast
20 2007
origin March 2008
2006
2007Q4
[Information set : 2006;
2007Q3; January 08]
10
ACTUAL GENERAL GOVERNMENT 2008Q2
DEFICIT (as in April 2009)
0
European Commission forecast
date of publication 1 April 2008;
-10
outcome for 2007 known.
2008Q3
Model forecast with forecast
-20 origin December 2008
European Commission fo [Information set : 2007;recast date
of 2008Q2; October 08] publication: 3 November 2008.
-30
European Commission forecast Model nowcast with forecast
date of publication: 19 January 2009; origin February 2009
-40
updated Stability Programme figure [Information set : 2007;
2008
for 2008 known. 2008Q3; December 08]
-50
2005 2006 2007
Panel C
40
2007Q3
30
2008Q1 Model forecast with forecast
20 2007
origin March 2008
2006
2007Q4
[Information available : 2006;
2007Q3; January 08]
10
ACTUAL GENERAL GOVERNMENT 2008Q2
DEFICIT (as in April 2009)
0
Model forecasts with forecast
origin September 2008
Government target - Stability
[Information set : 2007;
Programme for 2008 (December 2007)
-10
2008Q2; July 08]
2008Q3
Model forecast with forecast
-20 origin December 2008
[Information set : 2007;
Government estimate - Budget Law for
2008Q2; October 08]
2009 (December 2008)
-30
Model nowcast with forecast
Government estimate - Stability Programme
origin February 2009
-40
for 2009 (January 2009)
[Information set : 2007;
2008
2008Q3; December 08]
-50
2005 2006 2007
Fig. 5 Spanish General Government balance (billion euros) and alternative sets of projections for the end
of 2008: Full model projections, European Commission projections and Government projections. Forecast
origin and information set available shown
123
SERIEs
provided little signals of the appearance of a deficit in 2008, even though the estimates
were below the government?s (see Panel C). With subsequent information covering
up until April, and disregarding discretionary fiscal policy measures announced at
that time, the time series models would have already pointed to a small deficit for
2008 (triangle in Panel A). Indeed, EC projections, taking account of policy measures
announced in April, were already capturing the turning point, even though by April
2008 the EC still projected a small surplus. For the subsequent months, the mechanical
application of the time series methods would have traced very well the deterioration
subsequently incorporated by EC projections and government successive estimates
for 2008.
With all the possible available information at the monthly frequency included in
the model (December 2008 for the monthly indicators), the model would have now-
casted a deficit quite close to the final (first) estimate provided by the statistical agency
(Panel A of Fig. 5, ?Model now-cast? box). This is the case, notwithstanding the fact
that intra-annual fiscal information for the Regional and Local governments is quite
scarce in our models (as in reality), and a good part of the deterioration of the deficit of
the general government, ex-post, was due to the more-than-usual negative contribution
of these sub-sectors. It is interesting to note that the way intra-annual developments
in the Regional and Local governments are internalised in the model is via quarterly
General Government figures. Taking into account that, given our tight timing rules,
only 2008Q3 was assumed to be available to produce the ?Model now-cast? projec-
tions for 2008, one can conclude that the estimates of our model are reasonable enough,
and promising for real-time decision taking.
5 Conclusions
We construct multivariate, state-space mixed-frequencies models for the Spanish Gen-
eral Government sector made up of blocks for each one of its subsectors: the Central
Government sector, the Social Security Sector and the aggregate of the Regional and
Local government sectors. Each block is modelled through its total revenue and expen-
diture categories, and encompasses a number of indicators for each subsector, depend-
ing on data availability. In this sense, our model makes a fair coverage of the Central
Government sector, while the blocks for the Social Security sector and the Regional
and Local governments encompass a more limited coverage due to data availability.
The mixed-frequencies approach is particularly relevant for the case of Spain, given
the specific data coverage of the different subsectors of the general government.
All in all, we provide evidence that our models are appropriate tools: (1) for real-
time monitoring of fiscal policies with a focus on quarterly developments of general
government figures, (2) for the monitoring of general government sub-sectors for
which intra-annual data coverage is limited (Regional and Local governments), (3)
to bridge (translate) into National Accounts available monthly information for the
subsectors of the general government.
Acknowledgments We thank seminar participants at the Bank of Spain, the Editor (Eduardo Ley) and
two anonymous referees for useful comments and suggestions. Pedregal acknowledges financial support of
the Spanish Education and Science Ministry (project: SEJ2006-14732 (ECON)).
123
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References
Annett A (2006) Enforcement and the stability and growth pact: how fiscal policy did and did not change
under Europe?s fiscal framework. IMF Working Papers 06/116, International Monetary Fund
Chow GC, Lin A (1971) Best linear interpolation, distribution and extrapolation of time series by related
series. Rev Econ Stat 53:372?375
Clark TE, McCraken MW (2001) Tests of equal forecast accuracy and encompassing for nested models.
J Econom 105:85?110
Clements MP, Galvão AB (2008) Macroeconomic forecasting with mixed frequency data: Forecasting US
output growth. Working Paper 616, Department of Economics, University of London
European Commission (2008) Economic forecast?Autumn 2008. European Economy 6/2008, Director-
ate-General for Economic and Financial Affairs
Frale C, Veredas D (2008) A monthly volatility index for the US real Economy. ECORE DP 2008/15
Ghysels E, Santa-Clara P, Valkanov R (2006) Predicting volatility: getting the most out of return data
sampled at different frequencies. J Econom 131:59?95
Gordo L, Hernández de Cos P (2001) The Financing Arrangements for the Regional (Automomous)
Governments for the Period 1997?2001. Working Paper 0003, Research Department, Bank of Spain
Guerrero VM (2003) Monthly disaggregation of a quarterly time series and forecasts of its unobservable
monthly values. J Official Stat 19:215?235
Harvey A (1989) Forecasting structural time series models and the Kalman Filter. Cambridge University
Press, London
Harvey AC, Chung CH (2000) Estimating the underlying change in unemployment in the UK. J R Stat Soc
Ser A 163:303?339
Hyung N, Granger C (2008) Linking series generated at different frequencies. J Forecast 27:95?108
Jonung L, Larch M (2006) Fiscal policy in the EU: are official output forecasts biased? Econ Policy 491?534
Leal T, Pérez JJ, Tujula M, Vidal JP (2008) Fiscal forecasting: lessons from the literature and challenges.
Fiscal Stud 29:347?386
Leal T, Pérez JJ (2009) Un sistema ARIMA con Agregación Temporal para la Previsión y el Seguimiento
del Déficit del Estado. Hacienda Pública Española 190:27?58
Liu H, Hall SG (2001) Creating high-frequency national accounts with state space modelling: a Monte
Carlo experiment. J Forecast 20:441?449
Mariano RS, Murasawa Y (2003) A new factor of business cycles based on monthly and quarterly series.
J Appl Econom 18:427?443
Moauro F, Savio G (2005) Temporal disaggregation using multivariate structural time series models.
Econom J 8:214?234
Moulin L, Wierts P (2006) How credible are multiannual budgetary plans in the EU? Fiscal Indicators,
Banca d?Italia, pp 983?1005
Onorante L, Pedregal DJ, Pérez JJ, Signorini S (2009) The usefulness of infra-annual government cash
budgetary data for fiscal forecasting in the euro area. J Policy Model (in press)
Pedregal DJ, Pérez JJ (2009) Should quarterly government finance statistics be used for fiscal surveillance
in Europe? Int J Forecast (in press)
Pedregal DJ, Young PC (2002) Statistical approaches to modelling and forecasting time series. In: Clements
M, Hendry D (eds) Companion to economic forecasting. Blackwell Publishers, Oxford, pp 69?104
Pérez JJ (2007) Leading indicators for euro area government deficits. Int J Forecast 23:259?275
Pina A, Venes N (2008) The political economy of EDP fiscal forecasts: an empirical assessment, Working
Papers 2008/23, Department of Economics at the School of Economics and Management (ISEG),
Technical University of Lisbon
Proietti T, Moauro F (2006) Dynamic factor analysis with nonlinear temporal aggregation constraints. J R
Stat Soc Ser C Appl Stat 55:281?300
Schweppe F (1965) Evaluation of likelihood function for Gaussian signals. IEEE Trans Info Theory 11:61?
70
Silvestrini A, Salto M, Moulin L, Veredas D (2008) Monitoring and forecasting annual public finance deficit
every month: the case of France. Empir Econ 34(3):493?524
Strauch R, Hallerberg M, Von Hagen J (2004) Budgetary Forecasts in Europe?the track record of stability
and covergence programmes. European Central Bank WP 307
123