Has the Euro increased risk sharing across Euro
Area countries?
Alessandro Ferrari∗
1
Anna Rogantini Picco∗
Introduction
The aim of this paper is to evaluate the level of risk sharing across Euro Area countries over the last 25 years and to address the following two questions: i) whether risk
sharing has changed; ii) whether the introduction of the Euro has had any impact
on it. We begin our analysis by measuring risk sharing by means of the BrandtCochrane-Santa-Clara (BCS) Index, which relies on how much countries’ Stochastic
Discount Factors (hereafter SDF) are close to each other. This index helps us to get
a rough idea on whether and how risk sharing has changed over our sample period.
In order to decompose the channels through which risk is shared across countries we
use the GDP decomposition introduced by Asdrubali, Sorensen, and Yosha (1996).
What we find is that risk sharing has certainly not increased after the introduction
of the Euro and, in fact, it has decreased.
To tackle the second question we want to build counterfactual time series to reproduce what would have happened in terms of risk sharing had the Euro not been
introduced. In order to do so we use the Synthetic Control Method (SCM). This
method allows us to build synthetic time series with which to estimate a counterfactual level of risk sharing with the absence of the Euro. A comparison of risk sharing
estimations between actual and synthetic data allows us to infer whether the Euro
has had an impact on the level of risk sharing across Euro Area countries. We find
evidence suggesting that the introduction of the common currency limited the ability to smooth income variations, in particular by reducing the scope for smoothing
through international capital markets and fiscal transfers from governments.
Related Literature. In order to get a counterfactual of some countries’ macro
variables for the period after the introduction of the Euro we resort to SCM (for a
more thorough discussion on SCM see Section 2.1). The method has been firstly
introduced by Abadie and Gardeazabal (2003) to test for the impact of terrorism
in the Basque Country in the late 60s. Building on that seminal paper, it has been
further employed by Abadie, Diamond, and Hainmueller (2010) to estimate the effect of a large-scale tobacco control program that California implemented in 1988.
∗
European University Institute, Villa San Paolo, Via della Piazzuola, 43, I-50133 Florence,
Italy; Email: [email protected] and [email protected].
1
Billmeier and Nannicini (2012) use SCM to investigate the impact of economic liberalization on real GDP per capita in a worldwide sample of countries. Closer to
our focus, Campos, Coricelli, and Moretti (2014) make use of SCM to evaluate the
benefits from being part of the European Union.
For our risk sharing assessment, we refer to two methodologies. A first measure
is the the BCS index, proposed by Brandt, Cochrane, and Santa-Clara (2006). This
is an indicator of bilateral risk sharing which relies on the similarity of pricing kernels. BCS index is computed by Rungcharoenkitkul (2011) to assess risk sharing
among some Asian countries in the first decade of the 2000s. In order to better understand the channels through which risk sharing is accomplished, we adopt a second
methodology, which has been introduced by Asdrubali et al. (1996) to identify risk
sharing channels in the US over the period 1963-1990. Later on, their methodology
has been used by Furceri and Zdzienicka (2015) to analyze and compare risk sharing
among Euro Area countries with that across US states. However, even though the
US are the closest currency union to the Euro Area, we do not believe that risk
sharing estimations for the US are a good counterfactual for the Euro Area, as the
Euro Area does not share fiscal policy as opposed to the US, where transfers can be
used to smooth GDP shocks across states. The analysis of Furceri and Zdzienicka
(2015) is updated with more recent data by van Beers, Bijlsma, and Zwart (2014),
who try to assess the functioning of insurance mechanisms in the Euro Area, and
by Kalemli-Ozcan, Luttini, and Sørensen (2014) who consider separately countries
hit by the sovereign debt crisis in 2010.
2
Methodology
2.1
The Synthetic Control Method
One purpose of this paper is to assess whether the introduction of the common
currency had an effect on the level of risk sharing between member states. In order to meaningfully address this question one would need to have estimates of the
economic performance of the member states under the alternative scenario in which
the currency area had not been established.
Since it is not possible to have a real counterfactual for the treatment “introduction
of the Euro”, we resort to the SCM by Abadie and Gardeazabal (2003), which allows
the evaluation of a synthetic counterpart. This method is a data driven procedure
that has been used to estimate the effect of policy interventions in absence of a
natural counterfactual.1
Using Abadie and Gardeazabal’s notation, let X1 be a set of determinants of variables of interest for the Eurozone member states before the introduction of the Euro
and let X0 be the values of the same variables in all non Eurozone countries during
such a period. In addition, let V be a diagonal matrix representing the relevance of
1
For reference, see Abadie et al. (2010), Billmeier and Nannicini (2012), Campos et al. (2014),
and Saia (2016).
2
these predictors in determining the outcome variables, estimated via a factor model.
Abadie and Gardeazabal (2003)’s algorithm looks for a vector
of weights W ∗ that
P
minimizes (X1 −X0 W )0 V (X1 −X0 W ), subject to wi ≥ 0 and i wi = 1 for i = 1...N ,
N being the number of countries in the potential counterfactual pool. Finally, let
Y1 and Y0 be the outcome variables for the treated (Eurozone) and untreated (Rest
of the world) countries, then the method uses Y1∗ = Y0 W ∗ as counterfactual for the
outcome of the treated country.
This method relies on two identification assumptions: 1) the choice of the pre treatment covariates on which the matching is carried out should be such that the variables that are able to mimic the pre treatment path are included, but should not
rely on observables that anticipate the effect of the treatment itself; 2) the units in
the donor pool should not be affected by the treatment.
For the latter reason the matching is carried out for one treated unit at the time,
meaning that we iteratively drop all but one Eurozone member states, so that the
procedure always involves one treated unit and N control units.
The choice of the covariates in matrix X is such that it maximizes the ability of
the synthetic control to reproduce the pre treatment behaviour of the treated unit.
The baseline matching function will always take the past value of the variable we
investigate, meaning that if we are evaluating what consumption would have been
in Germany without the Euro we will always start by matching on the consumption
of Germany in every pre treatment year. Further discussion on the advantages and
drawbacks of this strategy will follow in Section 3.
Our matching strategy reduces to matching on all the available lags of the dependent
variable and the pre-treatment period average of the other covariates we analyse.
These variables include, all in per capita terms, GDP, household final consumption,
government expenditure, national income and disposable national income. To give
a more precise example when we want to match the behaviour of per capita GDP
∗
we match on the following list of values: {GDPt }Tt=0 , C, G, DN I, N I where T ∗ is
the treatment year and bar on variables represents the pre-treatment average.
The intuition behind this method is that one can use the best linear combination of
untreated units, in terms of matching pre treatment behaviour, as a counterfactual
for the treated unit after the policy.
It is worth mentioning that the evaluation of the robustness of these estimates has
been discussed in the literature but no analytical result is available to compute the
standard deviation of these estimates, in particular because the estimated component is the weighting vector; robustness checks are then carried out via bootstrap,
randomly resampling the donor pool (see Saia (2016)), or via estimation of a difference in difference and testing for difference from zero of the outcome (see Campos
et al. (2014)). A third way to check robustness is to run placebo studies on units in
the donor pool to assess whether the method delivers spurious effect of the treatment.
A relevant assumption for the correct use of the Synthetic Control Method is that
the control group is unaffected by the treatment. This assumption can be trou-
3
blesome since, given the magnitude of the potential effect of the Euro, one might
indeed think that the introduction of the common currency indirectly affected all
the countries in the world, particularly the ones in our control group being OECD
countries with strong trade and financial linkages with our treated sample.
This concern is legitimate if we define as the treatment the introduction of the Euro
itself. However one can think of the total effect of the Euro for member states as
being the composition of two effects: i) the effect of the existence of the Euro; ii)
the effect of being a member of the currency union. Under this decomposition all
countries in the world are subject to the first effect, but only Euro Area member
states are subject to the second one. Hence, one could interpret our treatment as
being the membership of the Euro, conditional on the Euro existing.
2.2
Risk Sharing: the BCS Index and Consumption Correlation
In this paper we adopt SCM in order to produce a synthetic dataset of macroeconomic indicators. The first analysis we carry out is the estimation of consumption
behaviour under the two scenarios. Hence, we use SCM to predict what consumption
would have been in absence of the common currency. With this preliminary analysis
we want to check the direction of the change, if any, of risk sharing as measured by
the degree of similarity of SDF, denoted by M . Being this a preliminary analysis
carried out solely to inspect how risk sharing changes, we take a relatively agnostic
stance and assume that all countries in the Eurozone have the same deep parameters. This allows us to evaluate the two following objects, where subscripts T and S
denote treated, meaning with the Euro, and synthetic, meaning the counterfactual:
!−σ
cTi,t+1
T
(1)
Mi,t = β
cTi,t
!−σ
S
c
i,t+1
S
Mi,t
=β
(2)
cSi,t
Where we assume that preferences are CES with risk aversion σ, i denotes a country
index, and β is the discount factor.
Economic theory, under the assumption of no arbitrage and complete markets, predicts that, when two countries fully share risk, their stochastic discount factors
should be the same. Following this intuition Brandt et al. (2006) propose an indicator of bilateral risk sharing that relies on similarity of pricing kernels.
In particular the index takes the following form:
BCSi,j = 1 −
var(logMi,t+1 − logMj,t+1 )
var(logMi,t+1 ) + var(logMj,t+1 )
(3)
This metric ranges between −1 and 1 with a higher number meaning a higher degree
of risk sharing.
4
As a preliminary check we compute, under the same parametrization, the BCS
indices for both treated and synthetic samples to assess whether consumption fluctuations got closer with the introduction of the common currency. As a robustness
check we do the same exercise on the pre intervention period in order to check the
soundness of our matching. A sound matching would result in relatively similar
indices in both samples for the pre treatment period.2
In addition, we take another route to evaluate the SDF under the two regimes.
In the previous discussion we matched over consumption and computed the pricing
kernels with treated and synthetic data. The alternative strategy is to compute
the SDF on actual data and only then generate a synthetic counterpart. This competing procedure is potentially more convoluted because normally the matching is
carried out on levels, but the pricing kernel is a function of gross growth rates of consumption. To exemplify why this difference may be troublesome, consider you want
to check the stochastic discount factor of Germany under the two policy regimes.
Then, matching on consumption levels would optimally put weight on countries with
similar levels of per capita consumption, and in particular it is likely that the counterfactual is mostly made as a linear combination of developed countries. If instead
we match on the pricing kernel directly, which ultimately boils down to matching on
consumption growth, we may have that the counterfactual is made by countries with
completely different fundamentals which happened to display similar dynamic behaviour as pre treatment Germany. Ultimately both strategies are econometrically
correct, though their outcomes may vary considerably and one may have different
preferences on the two competing procedures. We do not take a stand on which of
the two is more advisable, though it is worth mentioning that, precisely because of
this reason, they may deliver very different results.
In order to get an idea of how risk sharing might have changed due to the introduction of the common currency we also compute bilateral correlations of consumption
across Euro Area members. Economic theory would suggest that a higher level
of risk sharing should increase correlation of consumption between countries while
their GDP correlation still being low. We are well aware that, in fact, economic
theory is not supported by the data and that often GDP correlation is much higher
than consumption correlation even across countries which are known to share risk.
However, what we are interested in is not much the level of correlation in itself, but
the difference in correlation obtained from the actual and the synthetic data. If the
introduction of the common currency has had an impact on risk sharing, we should
find that the difference in consumption correlation between actual and synthetic
data should be significantly different from zero.
2
Note that one of the assumptions of the SCM is that there was no anticipation effect for the
treatment.
5
2.3
Risk Sharing: GDP Decomposition
Given the preliminary inspection on how risk sharing changed due to the introduction of the Euro, the naturally ensuing question is whether we can track back
this change to different channels through which risk is shared. We carry out this
analysis following a methodology proposed by Asdrubali et al. (1996). The idea of
this analysis is to check which of the potential risk sharing channels absorb output
shocks. In particular this is implemented by decomposing GDP into the following
national account aggregates: Gross Domestic Product (GDP), Net National Income
(NI), Disposable National Income (DNI), and Private and Government Consumption (C+G). According to this decomposition, GDP can be disaggreagated as this
accounting identity:
GDP =
GDP NI DNI DNI+G
(C+G)
NI DNI DNI+G C+G
(4)
The ratios on the RHS can be given a very specific interpretation as channels through
accounts for income insurance stemming from
which risk is absorbed. Namely, GDP
NI
internationally diversified investment portfolios. NI measures the income (net of
depreciation) earned by residents of a country, whether generated on the domestic
territory or abroad, while GDP refers to the income generated by production activities on the economic territory of the country. Therefore, the first ratio captures the
private insurance channel due to private cross-border investments or, as KalemliOzcan et al. (2014) refer to, holding of claims against the output of other regions.
NI
, instead, can be interpreted as the public insurance channel due to
The ratio DNI
government taxes and transfers. DNI is the income that households are left with
DNI
after subtracting taxes and adding transfers. The ratios DNI+G
and DNI+G
account
C+G
for smoothing through public and private saving channels respectively.
In order to measure how variations in output is absorbed by each channel we
proceeds as in Asdrubali et al. (1996). We first take logs of equation 4, we difference
the series, and we multiply by the change of log GDP. Then, we regress the resulting
equations on ∆ log GDP, which allows us to estimate how much of a country GDP
shock is absorbed by each of these components. A zero coefficient in the regression
of consumption on GDP (equation 9) means that a shock to GDP is fully absorbed
through capital markets, fiscal transfers, public and private savings, thus leaving
consumption unchanged. A high coefficient of consumption in the same regression,
instead, means that only a minor part of the shock is absorbed through risk sharing,
while a significant part stays unsmoothed.
6
2.3.1
Estimation methods
We start our analysis by estimating the system of equations proposed by Asdrubali
et al. (1996):
∆ log GDPi,t − ∆ log N Ii,t = β m ∆ log GDPi,t + m
i,t
g
∆ log N Ii,t − ∆ log DN Ii,t = β ∆ log GDPi,t +
p
(5)
gi,t
∆ log DN Ii,t − ∆ log(DN Ii,t + Gi,t ) = β ∆ log GDPi,t +
(6)
pi,t
∆ log(DN Ii,t + Gi,t ) − ∆ log(Ci,t + Gi,t ) = β s ∆ log GDPi,t + si,t
u
∆ log(Ci,t + Gi,t ) = β ∆ log GDPi,t +
ui,t
(7)
(8)
(9)
where each β coefficient represents the share of the income shocks smoothed by a
given channel. In particular, β m accounts for the share of GDP shocks smoothed
by capital markets, β g by fiscal transfers, β p by public savings, β s by private savings. What is left, β u , is the unsmoothed part of the GDP shock. By construction
β m + β g + β p + β s + β u = 1. The estimation of coefficients for the above system
is carried out using the following methods: OLS with time fixed effects, OLS with
panel correlated standard errors, generalized method of moments, and seemingly
unrelated regressions.
In the rest of the paper our baseline estimation for the analysis of risk sharing
channels will be an OLS estimation with time fixed effects. We also perform OLS
with panel correlated standard errors, seemingly unrelated regression and GMM. In
particular in GMM, we separately estimate the above described relations using lags
of GDP growth as an instrument. In the reported results we use up to 3 lags of the
instrument. Also note that the estimation procedure, which follows Arellano and
Bond – see Roodman (2009) – automatically includes past values of the dependent
variable as instruments.
We show the results of these estimation strategies as computed in a difference in difference model, which is equivalent to separate estimation. Namely we stack together
our treated and synthetic samples and include the independent variable interacted
with the 4 possible combinations of treated/synthetic and euro/no euro. In particular our results should then be interpreted as follows: the coefficient associated
to the independent variable interacted with the treated dummy and the no euro
dummy, both taking value 1, represents the share of GDP variation smoothed by
a given channel for our actual data before the introduction of the euro; this coefficient should be compared with its synthetic counterpart, meaning the coefficient
of the ∆ ln GDP when the data is synthetic and before the Euro. If our matching
is successful we should not find a statistical difference between these two estimates.
For our treatment period we should then compare the coefficient associated with
∆ ln GDP of actual data with the one of the synthetic data, which tell us the share
of income variation smoothed by the given channel after the Euro. If the Euro had
an effect on this channel the two estimates should be statistically different. All our
specifications have time fixed effects, unless specified otherwise.
Provided we have a good match for pre-treatment period, we can be relatively sure
7
that the common trend assumption is fulfilled. We provide an example of this in
Figure 3 which shows the last dependent variable, ∆log(C + G) (the one that delivers us the coefficient of the unsmoothed component) for both the treated and the
synthetic group over the whole sample period.
2.4
Data
The data that we use for our analysis are taken from the OECD National Account
Statistics. In particular, we use household final consumption expenditure for C, general government expenditure for G, gross domestic product computed following the
so called output approach for GDP, net national income for NNI, and net disposable
income for DNI.
Our dataset covers 31 countries from 1960 to 2014. As the Synthetic Control Method
requires the data not to display missing values, in order to keep for the matching all
the countries in our sample, we limit our matching window to the period 1990-1998.3
This limitation leaves us with 21 countries for which we have a complete set of data
for the variables we need. Out of these 21 countries 11 are Eurozone member states,
hence treated, while 10 are OECD countries that are not in the currency area.
The weighting matrices resulting from the synthetic control method are displayed
in Tables 1 and 2.
3
Results
3.1
BCS Index and Consumption Correlations
As discussed in the methodology section we perform two different approaches to
first inspect the potential change in risk sharing generated by the introduction of
the common currency: the first implements the matching on the consumption data
and then computes the SDF out of the actual data and the synthetic series; the second, instead, relies on the computation of the SDF from the consumption data and
then on the application the SCM to generate a synthetic version of the SDF directly.
As mentioned above the difference between these two approaches boils down to
using the SCM on levels of consumption or on growth rates. Both methodologies
produce a very good matching on the pre-treatment window, even though, given
that we aim at generating a series that closely resembles the level of consumption,
the first approach performs poorly when we compute the ensuing SDF. On the other
hand, we are able to match relatively well the dynamics of the SDF by matching on
consumption growths and then computing our object of interest. Figure 1 show the
actual and synthetic SDF for Greece over the period 1990-2011.
3
With the aim of increasing the number of countries in the donor pool for the synthetic control
matching, we also tried to use World Bank data series. However, we encountered some problems
in accounting divergence with the OECD data, hence for the moment we limited our analysis to
the OECD data series.
8
The results of the latter procedure are displayed in Tables 3-6. The first three
tables represent the bilateral differences between the BCS index computed from actual data and its synthetic counterpart for the full sample, the matching window
and the treatment period respectively. In order to better summarize our results,
in Table 3 we provide summary statistics for the three matrices in Tables 4-6. In
particular, we observe that the full sample result points towards a reduction of the
ability to share risk due to the introduction of the Euro, though the coefficient is
not significant using standard inference. The same object for the matching period
is extremely close to zero, suggesting that our matching procedure does reasonably
well in generating the synthetic series. Finally, for the treatment period we find
again a negative coefficient, suggesting that risk sharing decreases, though the size
of the standard errors implies that this result is not significantly different from zero.
A comparison between consumption correlations obtained from actual and synthetic
data leads us towards a similar conclusion. Tables 7-10 show the difference between
bilateral consumption correlation computed from the actual and the synthetic data.
Table 8 displays the difference for the sample period 1990-1998, i.e. before the introduction of the Euro. The fact that all the differences are not significantly different
from zero confirms the good quality of our match. Table 9 and Table 10 show the
difference in consumption correlations for the sample periods 1999-2007 and 20082011, respectively. Since many are significantly different from zero and negative
means that consumption correlation computed with the actual data is lower than
that computed with the synthetic data. A lower consumption correlation means that
consumption smoothing happens at a lower degree with the Euro than without. One
might think that during the crisis the general confidence loss in the economy led
to a lower cross-country risk sharing. However, 9 shows that even in the pre-crisis
period after the introduction of the Euro consumption correlations computed with
actual data are lower than consumption correlations computed with synthetic data
(the difference in negative and significantly different from zero). Summary statistics
of Tables 8-10 are reported in Table 7. Even though in the sample periods 1999-2007
and 2008-2011 the difference between correlations of the actual and synthetic data
are not significant on average, there are still many bilateral correlation difference
which are significantly different from zero.
3.2
Risk Sharing Channels
Figure 2 shows the actual and synthetic series of household and government consumption expenditure for Finland. The two series are very close in the matching
period spanning from 1990 to 1998, and then start to diverge over the treatment
period. Even if only household and government consumption series for Finland are
displayed here, actual and synthetic series for the national account aggregates and
the countries that we considered look similar to those reported. Given that the aim
of synthetic control method is to get a synthetic series which is as close as possible to the actual one for the matching window, our matching proves to be successful.
9
The obtained actual and synthetic series are used to estimate Equations 5-9. Table
11- 15 display the results of our estimations for the full sample period, i.e. 1990-2011.
Four specifications of the model are shown, both for the actual (Treated) and the
synthetic (Control) series. Each table shows both the estimations for the treated
and the control group in the period before (Pre-tr) and after (Post-tr) the introduction of the Euro (Treatment). The third and the sixth row of each table exhibits
the p-value of a Wald test on whether the treated and control group coefficients are
significantly different from each other.
Table 11 shows the OLS estimates. In the pre-treatment period coefficients of the
treated and control group are never significantly different from each other, implying
that the quality of our match is good. In the pre-euro subsample (1990-1998), most of
the risk sharing happens through private savings, while a smaller part goes through
public savings and fiscal transfers. The unsmoothed portion of risk is around 47%.
In the post treatment period (1999-2011), the difference between the coefficients
of the capital market channel and the unsmoothed portion becomes significant. In
particular, while the coefficient of capital market channel is insignificant for the
treated sample, it is significant and equal to 18.9% for the control group. This
means that without the Euro, capital markets would have had a remarkable role is
absorbing the risk. Even more significant is the difference between the unsmoothed
coefficients. Namely, the the unsmoothed portion of risk in the treated group is
73.9% against only 36.8% for the control group. This implies that the Euro has
significantly lowered the level of risk sharing across Euro Area countries, at least
in comparison to our counterfactual experiment. The higher degree of absorption
would have happened according to our estimates through capital markets.
Estimates obtained with OLS and panel-correlated standard errors as well as
with SUR confirm the results of the baseline model. GMM estimates, instead, are
somewhat different. While the coefficients of public and private risk sharing channels
are similar to the estimates obtained with the other methods both in terms of value
and significance, what changes is the coefficient of capital market channel. While
with OLS the control group coefficient after the treatment becomes significant, with
the GMM it is smaller and insignificant.
Apart from GMM the other method consistently deliver the result that our control group after the treatment would have guaranteed a statistically significantly
higher level of risk sharing and this would have happened mainly through capital
markets, public and private savings.
A general and legitimate concern regarding our estimates is that they may be prone
to measurement error driven bias. This may be particularly worrisome given that
we are estimating our parameters on data we may have generated with error. As it
is well known, random measurement error generates attenuation bias, which would
bring our risk sharing channel for the counterfactual data closer to zero than the
true parameter. Firstly, this cannot be the case for all the parameters given the
identity nature of our problem. In particular, assuming that we generate our series
with random error, we can only have that the first 4 parameters suffer from attenuation bias, while the last one in fact can be computed as a residual. If the first 4
10
parameters are closer to zero than their true counterpart, this implies that the the
unsmoothed share must be higher than the true value. Since we consistently find
that the unsmoothed parameter is lower in the counterfactual experiment than in
the true data and we have no reason to believe that the true data is subject to the
same measurement error, then our estimated difference in smoothed income variation can only be a lower bound to the actual value.
By the same token, our estimated changes in the risk sharing channels can be viewed
as lower bounds since we consistently find that the channels would be more effective
in the counterfactual and given the potential attenuation bias we may find we may be
underestimating this change. The only case in which this measurement error in our
synthetic data can be alarming is for the pre treatment period of the international
capital markets and fiscal transfer channels, in which we find a higher estimate for
the synthetic data than for the actual one, implying that if we were to measure the
coefficient without bias the two would be further apart. In particular, the difference
between treated and control estimate for the international capital markets channel,
which is already statistically different from zero, would be even larger.
4
Conclusion
This paper assesses the effect of the introduction of the common currency on the
ability to smooth consumption for Eurozone member states. We do so by building a
dataset of counterfactual macroeconomic variables for the Eurozone countries without the Euro via Synthetic Control Method.
We run a number of econometric procedures, including the evaluation of bilateral
correlations of consumption, the Brandt-Cochrane-Santa Clara Index, and the decomposition introduced by Asdrubali et al. (1996) to evaluate the existence of this
effect and the channels through which it may have occurred. Our results show evidence of a decrease in risk sharing across Euro area countries for the period after the
introduction of the Euro. Bilateral consumption correlations calculated from synthetic data are higher than those computed from actual data, indicating that with
the introduction of the Euro consumption smoothing has decreased. In particular,
we find that international capital markets and fiscal capacity of governments would
have had a larger ability to absorb income variations.
In order to find additional evidence on what might have caused the reduction in
risk sharing we would like to proceed as follows. First of all, we conducted our
analysis using OECD data. In order to see how sensitive the matching to produce
synthetic data is to the countries’ donor pool that we use, we plan to conduct the
same analysis using data from the World Bank.
Furthermore, we plan to improve our measures of risk sharing. In particular, we
would like to get a better estimate of SDF. As we are well aware, there are several
difficulties related to SDF estimation. In this paper we resorted to a consumption
based estimation, but in further research we would like to use the term structure of
11
interest rates as in Rungcharoenkitkul (2011).
Finally, given our findings of a decrease in risk sharing over the period following
the introduction of the Euro, it would be of primary interest to inquire which could
be the determinants of this phenomenon. Indeed, a higher degree of financial and
goods market integration across Euro area countries would prompt us to think that
risk sharing should increase. Taken our results into account, we would like to get a
deeper understanding of why this is not the case.
12
A
Synthetic Control Method
Figure 1 – Actual and synthetic series of Greek SDF
Note: The matching window is 1990-1998.
Figure 2 – Actual and synthetic series
(a) Household Consumption
(b) Government Consumption
Note: The matching window is 1990-1998.
13
B
Weighting matrices
Table 1 – Weighting matrix OECD
Control
Australia
Canada
Japan
Korea
Mexico
NewZealand
Sweden
Switzerland
UK
US
Austria
33
2
Belgium
Finland
France
25.70
33
39.40
Germany
Greece
Ireland
44.10
Italy
26.70
Netherlands
Portugal
Spain
2.500
50.40
2.400
32.90
24
2.900
1.800
14
9
11.30
12.20
40.20
33.20
28.90
5.700
8.300
6.700
35.10
44.50
7.100
0.500
12
40.30
27.70
10.40
46.40
17.40
16.20
47.70
38.80
48.50
5.600
12.90
36.70
45.10
56
27.30
33.40
Table 2 – Weighting matrix World Bank
Control
Brazil
Cameroon
Central African Republic
Chile
Comoros
Costa Rica
Denmark
Japan
Jordan
Lebanon
Madagascar
Mexico
Rwanda
Senegal
Sweden
Switzerland
Turkey
C
C.1
Austria
Finland
14.30
France
Germany
Italy
Netherlands
Portugal
Spain
1.600
13.30
1
65.50
5.900
42.60
31.30
19
3.300
0.100
3
3.100
1.200
4.900
59
14.50
50.70
2.700
55.50
26.40
3
1.600
3.800
18.30
2.200
70.70
15
6.800
3.700
32.40
12.80
1.700
2.200
2.400
85.50
13.20
18.80
17
6.100
4
9.900
48.20
0.500
1.700
BCS
With total consumption
Table 3 – BCS index differences (BCSt − BCSs ): summary statistics
1990-2011
Mean t-stat
BCSt − BCSs
-0.265
-.379
1990-1998
Mean t-stat
-.105
14
-.522
1999-2011
Mean t-stat N
-0.316
-.355
110
Table 4 – BCS index differences (BCSt − BCSs ): sample period 1990-2011
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
.
.
-.399
(-.939)
-.398
(-.945)
-.634
(-1.464)
-.510
(-1.170)
-.492
(-1.375)
-.373
(-1.038)
-.413
(-1.001)
-.260
(-.661)
-.436
(-1.102)
-.327
(-.821)
.
.
-.449
(-1.038)
-.245
(-.569)
-.517
(-1.204)
-.272
(-.689)
-.230
(-.580)
-.162
(-.379)
-.087
(-.207)
-.172
(-.405)
-.127
(-.302)
.
.
-.576
(-1.332)
-.484
(-1.137)
-.285
(-.729)
-.179
(-.458)
-.439
(-1.009)
-.156
(-.374)
-.303
(-.721)
-.290
(-.677)
.
.
-.657
(-1.512)
-.294
(-.790)
-.113
(-.303)
-.272
(-.639)
.042
(.105)
-.159
(-.391)
-.101
(-.244)
.
.
-.722
(-1.969)
-.454
(-1.234)
-.323
(-.773)
-.370
(-.922)
-.264
(-.655)
-.443
(-1.093)
.
.
-.085
(-.195)
-.418
(-1.046)
.036
(.086)
-.480
(-1.133)
-.252
(-.610)
.
.
-.087
(-.220)
.069
(.163)
-.038
(-.091)
.256
(.621)
.
.
.165
(.395)
-.217
(-.515)
-.265
(-.611)
.
.
.110
(.253)
.308
(.730)
.
.
-.165
(-.387)
.
.
Table 5 – BCS index differences (BCSt − BCSs ): sample period 1990-1998
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
.
.
-.431
(-.655)
-.683
(-1.189)
-.088
(-.130)
-.306
(-.463)
.404
(.800)
.131
(.266)
-.226
(-.350)
-.083
(-.152)
.010
(.023)
-.004
(-.007)
.
.
-.432
(-.644)
-.527
(-.836)
.012
(.017)
.396
(.719)
.042
(.071)
.107
(.152)
-.188
(-.302)
.060
(.109)
.138
(.218)
.
.
-.670
(-1.154)
-.942
(-1.40)
-.175
(-.287)
.143
(.210)
-.367
(-.540)
.202
(.297)
-.555
(-.872)
-.214
(-.313)
.
.
-.644
(-1.014)
.115
(.218)
.201
(.395)
-.246
(-.395)
-.003
(-.006)
-.327
(-.729)
-.144
(-.249)
.
.
.034
(.062)
-.142
(-.237)
-.453
(-.642)
-.340
(-.544)
.175
(.322)
-.345
( -.545)
.
.
.500
(.759)
.169
(.303)
.308
(.454)
-.357
(-.536)
.021
(.032)
.
.
.298
(.484)
.078
(.113)
-.284
( -.410)
.335
(.486)
.
.
-.111
(-.176)
-.280
(-.499)
.074
(.116)
.
.
-.103
(-.154)
.257
(.364)
.
.
-.347
(-.527)
.
.
15
Table 6 – BCS index differences (BCSt − BCSs ): sample period 1999-2011
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
D
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
.
.
-.381
(-.699)
-.191
(-.350)
-.702
(-1.284)
-.557
(-1.007)
-.699
(-1.537)
-.507
(-1.092)
-.418
(-.791)
-.283
(-.555)
-.629
(-1.220)
-.408
(-.834)
.
.
-.431
(-.799)
-.184
( -.335)
-.712
(-1.322)
-.430
(-.885)
-.331
(-.662)
-.167
(-.307)
-.022
(-.041)
-.290
(-.539)
-.197
(-.387)
.
-.564
(-1.022)
-.264
(-.490)
-.320
(-.682)
-.259
(-.558)
-.311
(-.573)
-.061
(-.120)
-.260
(-.492)
-.284
(-.547)
.
.
-.676
(-1.252)
-.406
(-.838)
-.239
(-.492)
-.249
(-.455)
.082
(.156)
-.202
(-.374)
-.121
(-.232)
.
.
-.898
(-2.036)
-.543
(-1.202)
-.192
(-.371)
-.308
(-.618)
-.465
(-.924)
-.465
(-.979)
.
.
-.403
(-.742)
-.531
(-1.039)
-.069
(-.132)
-.516
(-.978)
-.238
(-.450)
.
.
-.228
(-.448)
.056
(.104)
-.139
(-.265)
.105
(.206)
.
.
.193
(.359)
-.237
(-.430)
-.342
(-.630)
.
.
.180
(.331)
.327
(.627)
.
.
-.152
(-.279)
.
.
Consumption correlations
Table 7 – C correlation differences (ρt − ρs ): summary statistics
1990-1998
Mean t-stat
ρt − ρs
-.0183
-.061
1999-2007
Mean t-stat
-.410
16
-1.03
2008-2011
Mean t-stat N
-0.316
-1.56
110
Table 8 – Difference in correlation between actual and synthetic consumption:
sample period 1990-1998
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
0
.
-.019
(-.06)
.025
(.13)
.033
(.12)
-.014
(-.05)
-.042
(-.14)
.126
(.41)
-.037
(-.05)
-.054
(-.16)
-.162
(-.43)
-.017
(-.07)
0
.
-.118
(-.44)
.043
(.10)
.041
(.09)
-.186
(-.51)
-.069
(-.24)
.013
(.02)
-.028
(-.20)
-.421
(-.97)
-.035
(-.08)
0
.
.146
(.45)
.121
(.32)
-.009
(-.04)
.020
(.09)
.001
(.00)
-.173
(-.54)
-.112
(-.44)
.090
(.33)
0
.
-.036
(-.12)
.042
(.15)
.298
(.76)
-.024
(-.04)
.002
(.00)
.015
(.03)
-.040
(-.20)
0
.
-.020
(-.04)
.272
(.56)
-.225
(-.35)
.043
(.09)
.002
(.00)
-.075
(-.26)
0
.
.043
(.14)
.185
(.28)
-.266
(-.61)
-.073
(-.30)
.022
(.09)
0
.
.002
(.00)
-.163
(-.47)
-.104
(-.28)
.234
(.64)
0
.
.009
(.01)
.114
(.16)
.094
(.14)
0
.
-.484
(-1.03)
-.104
(-.21)
0
.
-.040
(-.10)
0
.
Note: t statistics are in parentheses.
Table 9 – Difference in correlation between actual and synthetic consumption:
sample period 1999-2007
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
AT
BE
FI
FR
DE
GR
IE
IT
NL
PT
ES
0
.
-.797
( -.49)
-.116
(-2.11)
-.130
(.01)
.123
(-.37)
-.304
(-.70)
-1.271
(-.51)
-.220
(-.35)
-1.342
(-.32)
-1.554
(-2.86)
-1.380
(-.10)
0
.
-1.326
(-3.11)
-.082
(.24)
-.541
(-.95)
-1.779
(-.41)
-.199
(-.14)
-1.404
(.07)
-.177
(-.33)
-1.471
(-2.61)
-1.731
(.27)
0
.
-.672
(-2.19)
-.229
(-.90)
-.006
(-3.46)
-1.654
(-3.27)
-.004
(-2.31)
-1.737
(-2.40)
-1.275
(-2.42)
-.991
(-2.39)
0
.
-.234
(-1.15)
-1.390
(-.14)
-.635
(.13)
-.801
(.05)
-.485
(.05)
-1.765
(-2.03)
-1.887
(-.13)
0
.
-.922
(-1.07)
-1.263
(-1.00)
-.243
(-1.23)
-.822
(-.84)
-1.991
(-2.24)
-1.905
(-1.33)
0
.
-1.911
(-.48)
.163
(-.08)
-1.888
(-.49)
-.933
(-2.13)
-.621
(-.12)
0
.
-1.617
(.31)
-.077
(-.25)
-.816
(-2.13)
-1.152
(.24)
0
.
-1.724
(-.19)
-.976
(-1.75)
-.661
(.05)
0
.
-1.049
(-2.68)
-1.326
(.03)
0
.
-.056
(-1.98)
0
.
Note: t statistics are in parentheses.
17
Table 10 – Difference in correlation between actual and synthetic consumption:
sample period 2008-2011
AT
BE
FI
FR
DE
GR
IE
IT
(-.31)
NL
PT
ES
AT
BE
FI
FR
DE
GR
IE
0
.
-.0922
(-.77)
-.9490
(-.25)
.0049
(-.12)
-.1401
(.15)
-.2559
(-.28)
-.1616
(-1.17)
-.0994
(-1.42)
-.0509
(-1.57)
-1.262
(-1.76)
-.0315
(-1.35)
0
.
-1.2882
(-1.42)
.0458
(-.13)
-.4475
(-.67)
-.1078
(-2.97)
-.0256
(-.29)
.0132
(-.01)
-.0483
(-.28)
-1.125
(-1.83)
.0498
(-2.71)
0
.
-1.1148
(-.58)
-.4461
(-.23)
-1.3714
(-.00)
-1.285
(-2.10)
-1.1618
(-.65)
-1.0626
(-2.98)
-.9908
(-1.20)
-1.2058
(-.87)
0
.
-.4113
(-.40)
-.0453
(-1.88)
.0372
(-.88)
.0100
(-.21)
.0118
(-.48)
-1.0378
(-3.10)
-.0127
(-4.36)
0
.
-.5676
(-1.12)
-.5386
(-1.69)
-.5210
(.21)
-.3614
(-.80)
-1.1774
(-15.33)
-.5115
(-5.57)
0
.
-.0998
(-5.02)
-.0265
(-2.28)
-.1464
(-4.13)
-.8560
(-1.08)
-.0386
(-.76)
0
.
.0707
.
-.0605
(-.09)
-.8784
(-1.07)
.0620
(-1.49)
IT
NL
PT
ES
0
.
-1.1782
(-.99)
.0081
(-1.36)
0
.
-1.0174
(-.22)
0
.
0
-.04256624
(-2.50)
-.8967
(-.80)
.0105238
(-.52)
Note: t statistics are in parentheses.
E
Risk sharing channels
Figure 3 – ∆ln(C + G) for treated and control group
Note: The matching window is 1990-1998.
18
Table 11 – OLS estimated risk sharing channels - sample period 1990-2011
Capital markets
Pre-tr
Control
Treated
Post-tr
Control
Treated
Fiscal transfers
Public savings
Private savings
Unsmoothed
-.022
(-0.32)
-.054
(-0.67)
.040
(1.72)
-.005
(-0.20)
.139∗∗∗
.345∗∗∗
( 4.56)
.001
( 0.05)
(4.42)
.058
(0.63)
.496∗∗∗
(6.59)
-.000
( -0.00)
.124
(1.52)
-.003
(-0.03)
-.012
(-0.47)
-.015
(-0.52)
-.112∗∗
(-3.11)
.009
( 0.24)
-.031
( -0.34)
-.173∗
( -1.69)
.032
(0.37)
.183∗
(1.85)
Note: t statistics are in parentheses.
∗
p < 0.1,
∗∗
p < 0.05,
∗∗∗
p < 0.01.
Table 12 – OLS with PCSE AR(1) estimated risk sharing channels - sample
period 1990-2011
Pre-tr
Control
Treated
Post-tr
Control
Treated
Capital markets
Fiscal transfers
Public savings
Private savings
Unsmoothed
-.021
(-0.27)
-.054
(-0.58)
.041∗
.154∗∗∗
(1.84)
-.006
(-0.23)
(5.36)
-.005
(-0.14)
.346
(4.21)
.058
(0.56)
.496∗∗∗
(5.63)
-.002
(-0.02)
.122
(1.28)
-.002
(-0.02)
-.014
(-0.56)
-.013
(-0.45)
-.127∗∗∗
(-3.53)
.020
( 0.45)
-.031∗∗∗
(-0.30)
-.174
(-1.44)
.026
( 0.24)
.189
(1.47)
Note: t statistics are in parentheses.
∗
p < 0.1,
∗∗
p < 0.05,
∗∗∗
p < 0.01.
Table 13 – OLS PCSE HET estimated risk sharing channels - sample period
1990-2011
Pre-tr
Control
Treated
Post-tr
Control
Treated
Capital markets
Fiscal transfers
Public savings
Private savings
Unsmoothed
-.022
(-0.30)
-.054
(-0.59)
.040∗
(1.87)
-.005
(-0.20)
.139∗∗∗
(5.28)
.001
(0.05)
.345∗∗∗
(5.21)
.058
(0.63)
.496∗∗∗
(7.18)
-.000
(-0.00)
.124
(1.46)
-.003
(-0.03)
-.012
(-0.49)
-.0159
(-0.53)
-.112∗∗∗
(-3.49)
.009
(0.24)
-.031
(-0.39)
-.173∗
(-1.70)
.032
(0.39)
.183∗
(1.73)
Note: t statistics are in parentheses.
∗
p < 0.1,
∗∗
p < 0.05,
19
∗∗∗
p < 0.01.
Table 14 – GMM estimated risk sharing channels - sample period 1990-2011
Capital markets
Pre-tr
Control
Treated
Post-tr
Control
Treated
Fiscal transfers
Public savings
Private savings
Unsmoothed
-.040
(-0.35)
-.045
( -0.31)
.060
(1.63)
-.085
(-1.86)
.212∗∗∗
(4.94)
-.062
(-1.16)
.298
(2.42)
.194
(1.26)
.469∗∗∗
(4.07)
-.000
(-0.01)
.045
(0.36)
.046
(0.30)
-.044
(-1.09 )
.069
(1.42)
-.157∗∗
( -3.31)
.060
(1.05)
.108∗∗
(0.80)
-.382∗∗
(-2.32)
.047
(0.37)
.205
(1.33)
Note: t statistics are in parentheses.
∗
p < 0.1,
∗∗
p < 0.05,
∗∗∗
p < 0.01.
Table 15 – SUR estimated risk sharing channels - sample period 1990-2011
Pre-tr
Control
Treated
Post-tr
Control
Treated
Capital markets
Fiscal transfers
Public savings
Private savings
Unsmoothed
-.022
( -0.33)
-.054
(-0.69)
.040∗
.139∗∗∗
.345∗∗∗
( 1.77)
-.005
( -0.20)
(4.70)
.001
(0.06)
(4.56)
.058
(0.65)
.496
-.000
-
.124
( 1.56)
-.003
(-0.03)
-.012
(-0.48)
.009
(-0.54)
-.015
( -3.21)
-.112∗∗
(0.25)
-.031
(-0.35)
-.173∗
( -1.75)
.032
.183∗
(3.64)
Note: t statistics are in parentheses. ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01. The bottom right number in brackets
(3.64) is the test statistic of a Wald test performed on the coefficient.
20
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