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									                Government bond yield spreads and the euro

                                               Lorenzo Pozzi∗

                                             September 2009



                                                   Abstract

          This paper estimates a latent factor decomposition of the weekly 10 year government bond
      yield spreads of Belgium, France, Italy, and the Netherlands versus Germany over the pe-
      riod 1991-2006. Each spread is decomposed into a country-specific and a common factor.
      The country-specific factors and the country-specific factor loadings on the common factor
      are allowed to converge to a situation of full government bond market integration. The re-
      sults suggest that, in the period after the introduction of the euro, government bond market
      integration has increased
          JEL Classifications: E43, G12
          Keywords: government bond yield spreads, euro, state space methods




  ∗ Tinbergen   Institute and Department of Economics, Erasmus University Rotterdam, Burgemeester Oudlaan 50,
PO Box 1738, 3000DR Rotterdam, the Netherlands. Tel: +31 (0)10 408 12 56. Fax: +31 (0)10 408 91 61. Email:
pozzi@few.eur.nl. Website: http://people.few.eur.nl/pozzi.


                                                        1
1     Introduction

This paper analyzes the integration of euro area government bond markets by investigating the
importance of the common international risk factor in euro area government bond yield spreads.


    In the literature on (euro area) government bond yield spreads two approaches have been
followed to take this common factor into account.

    First, a number of studies investigating euro area countries include a proxy for this common
factor in their analysis (e.g., Codogno et al., 2003, and Favero et al., 2007).

    Second, a number of studies filter the common factor out of the government bond spreads
through the use of factor analysis and state space methods (e.g., Dungey et al., 2000).


    This paper follows the second approach. Using a state space approach I decompose the 10 year
government bond spreads of Belgium, France, Italy, and the Netherlands versus Germany into a
common factor and an idiosyncratic country-specific factor. Data used are weekly and cover the
period 1991-2006.

    The paper adds to the literature by investigating whether the country-specific factors and the
country-specific factor loadings on the common factor in the spreads have converged towards a
situation of full government bond market integration, i.e. a state that I define as characterized by
zero country-specific factors and equalized country-specific factor loadings on the common factor.


    The results suggest that the country-specific factors and factor loadings in the bond spreads
are significantly reduced for all four countries in the period after the introduction of the euro
implying a significant increase in euro area government bond market integration. I report, first,
a reduction of country-specific premiums (e.g. liquidity premiums) in bond spreads since I find
a decrease towards zero of the country-specific factors in the latent factor decomposition of the
spreads. Second, I report a decrease in the country-specific exposure to international risk since
I find a decrease towards a common value (of zero) of the country-specific factor loadings on the
common factor in the latent factor decomposition of the spreads.


    The outline of the paper is as follows. Section 2 presents the empirical specification and the
estimation method. Data issues are also discussed. Results from the estimations are reported in
section 3. The final section concludes.


                                                  2
2       Empirical specification, data, and estimation method

2.1         Empirical specification

I estimate the following system (where  denotes time and  denotes country with  = 1   ),

                                           +1 = +1 +  +1 +1                                     (1)

                                      +1 = +1  +   + +1 +1                               (2)

                                                  +1 =  +   +1                                     (3)

                                          +1 =  +    + +1                                      (4)



     Eq.(1) presents the decomposition of the government bond spreads +1 into an idiosyncratic
factor +1 and a common factor +1 where the latter is multiplied by country-specific and
time-varying factor loadings  +1 .


     For +1 I assume that lim→+∞ +1 = 0. I therefore model +1 as an (1) process,
i.e. ∗                ∗
      +1 =  +    + +1 with 0     1, multiplied by a deterministic convergence

operator +1 where lim→+∞ +1 = 0. Thus, +1 = ∗ +1 . To obtain eq.(2) write
                                                       +1

∗
 +1 =  (1 −   ) + +1 (1 −   ) where  is the lag operator. Multiplication by +1

then gives +1 = +1  (1 −   ) + +1 +1 (1 −   ). Multiplication of both sides of this
expression by (1 −   ) gives eq.(2). For  I use the following logistic specification1 ,

                                    = exp [  ( −   )] (1 + exp [  ( −   )])                   (5)

where    0 is the rate of convergence. Since    0 I find  = 0 for  → +∞ and  = 1 for
 → −∞. In a sample of size  the fact that    0 implies that  ≈ 0 for     and that
 ≈ 1 for     . The parameter   with 1      determines the mid-point of the change.


     For  +1 I assume that lim→+∞  +1 =  where  is common across countries. Hence in
eq.(3) I model  +1 as a constant  plus a country-specific constant   that is multiplied by the
convergence operator  defined above.
    1 See   e.g. Pozzi and Wolswijk (2008) who model the idiosyncratic components in government bond risk premia
instead of government bond spreads.




                                                             3
    As can be seen in eq.(4) I assume that the common component +1 follows a standard (1)
process with 0     1.


    The error terms in the system +1 ( =   with  = 1  ) follow (1 1) processes
(e.g., Dungey et al., 2000),
                                                           12
                                                +1 = +1  +1                               (6)

    where  +1 ∼ (0 1) and where

                                     +1 =  [+1 ] =   +   2 +   
                                                                                              (7)


    with    0, 0     1, 0     1, and 0    +    1. The unconditional variance of +1
                                                        

is given by   (1 −   −   ).
                            



    From the model the start of the convergence process is characterized by +1 = 1. This implies
+1 = ∗
         +1 and  +1 =  +   . After complete integration +1 = 0 so that +1 = 0 and

 +1 = , i.e. the country-specific factors have disappeared and the country-specific impacts of
the common component are identical across countries.


2.2     A look at the data

All data are taken from Datastream/Thomson Financial. The available data cover the period
6/28/1991 to 8/4/2006 (789 weekly observations). I average daily data to weekly data to avoid
day-of-the-week effects (e.g., Dungey et al., 2000). For the spreads +1 I use the yield to maturity
of 10 year government bonds issued by country  (i.e. Belgium, France, Italy, and the Netherlands
so that  = 4) minus the yield to maturity of the benchmark country (i.e. Germany). To remove
exchange rate changes from the spreads before the introduction of the euro on 1/1/1999 I subtract
from these spreads the difference between the 10 year fixed interest rates on swaps denominated
in currency of country  and those denominated in DEM (e.g., Codogno et al., 2003).


    In Figure 1 the joint movement of the spreads suggests that they are driven by a common
component. Moreover, from table 1, the correlation between the spreads is higher after the intro-
duction of the euro indicating that the idiosyncratic components in the spreads have become less
important.




                                                          4
2.3         Estimation

2.3.1       Method

I obtain estimates for the unobserved states +1 and +1 , for the conditional variance series
+1 and +1 , for the convergence operator series +1 , and for the parameters in the model
by putting the model described in section 2.1 in state space form.2 Estimates of the state vector
are obtained with the Kalman filter and smoother while parameter estimates are obtained by
maximum likelihood. The time-varying conditional variances complicate the otherwise standard
Gaussian linear state space framework. To deal with this I follow the approach by Harvey et al.
(1992) and augment the state vector with the shocks +1 and +1 . The Kalman filter then
provides estimates of the conditional variance of the shocks, i.e. estimates for +1 and +1 .


2.3.2       Identification

First, note that eq.(1) can be written as +1 = +1 ∗ ++1 +  +1 +1 . The first term
                                                         +1

in this expression +1 ∗ can be multiplied and divided by a constant , i.e. (+1 )(∗ )
                          +1                                                              +1

so that a new term is obtained which is equally plausible. Hence the system is unidentified. To
avoid this I set 1 = 1 (∀). The same problem holds for the second and third terms. To identify
these terms I impose an unconditional variance of unity on +1 , i.e 2 = 1. This amounts to
                                                                        

setting   = 1 −   −   (e.g., Dungey et al., 2000). Second, the sign of the factor loadings  +1
                        

cannot be identified because of the sign invariance of the factor variance decompositions of the
spreads. Therefore, I impose  +1  0 by setting   0 and    0 (∀). Third, since only 
constants can be estimated but the model contains  + 1 constants I identify the constants by
setting  = 0.



3       Results

In table 2 I present the results of estimating the system given by eqs.(1) to (7). In figure 2 the
smoothed estimates for +1 are presented for all countries. In figure 3 the smoothed estimates
for +1 are reported. In figure 4 the estimates for +1 are presented.3
    2 The   state space representation of the model is available from the author by request.
    3 Figures   for the estimated GARCH series +1 and +1 are available from the author by request.




                                                          5
    From table 2 I note that there are significant convergence effects since  is significantly lower
than zero for all countries. The estimates for  and  imply an estimated series +1 for each
country (see figure 4). It is obvious from this figure that the convergence of the government bond
spreads towards full government bond market integration has occurred after the introduction of
the euro for all countries. However, full convergence to zero had not yet occurred by the end of
the sample period. While the magnitude of +1 and  +1 is much lower after the introduction
of the euro the non-zero values found for +1 at the end of the sample period for all countries
suggest that the idiosyncratic components still had a non-negligible impact.


    To investigate the adequacy of the presented model I report the Akaike Information Criterion
for model comparison. I calculate this statistic for the model given by eqs.(1) to (7) () and for
three alternative models.   denotes this statistic for a model with no convergence effects, i.e.
when +1 = 1 ∀ .   denotes this statistic for a model with logistic convergence in +1
only and a time-invariant but country-specific  +1 , i.e.  +1 =   .   denotes the statistic
for the same model as for   but with an euro dummy in  +1 (which takes on value 1 before
1/1/1999). According to the comparison of these statistics, the model presented in this paper -
with (logistic) convergence effects on both +1 and  +1 - is preferred.



4     Conclusions

I use weekly data over the period 1991-2006 to decompose the 10 year government bond spreads
of Belgium, France, Italy, and the Netherlands versus Germany into a common component and an
idiosyncratic component. Convergence operators are used to investigate government bond market
integration.


    The results suggest that, after the introduction of the euro, both the country-specific factors
and the country-specific factor loadings on the common factor in the bond spreads have converged
towards zero for all four countries. Full convergence to zero of these components had not yet
occurred by the end of the sample period however.




                                                  6
References

Codogno, L., C. Favero, and A. Missale (2003): “Yield spreads on EMU government bonds,”
  Economic Policy, 18, 503—532.

Dungey, M., V. Martin, and A. Pagan (2000): “A multivariate latent factor decomposition
  of international bond yield spreads,” Journal of Applied Econometrics, 15, 697—715.

Favero, C., M. Pagano, and E. von Thadden (2007): “How does liquidity affect government
  bond yields ?,” CSEF Working Paper 181.

Harvey, A., E. Ruiz, and E. Sentana (1992): “Unobserved component time series models with
  ARCH disturbances,” Journal of Econometrics, 52, 129—157.

Pozzi, L., and G. Wolswijk (2008): “Have euro area government bond risk premia converged
  to their common state ?,” mimeo.



Web References

   http://ideas.repec.org/a/bla/ecpoli/v18y2003i37p503-532.html

   http://ideas.repec.org/a/jae/japmet/v15y2000i6p697-715.html

   http://ideas.repec.org/p/sef/csefwp/181.html

   http://ideas.repec.org/a/eee/econom/v52y1992i1-2p129-157.html

   http://ideas.repec.org/p/dgr/uvatin/20080042.html



Tables and Figures




                                               7
   Table 1: Correlation matrix of corrected 10 year government bond spreads versus Germany  (weekly
data).

                               Full sample                   Sample after introduction euro

                          6/28/1991 to 8/4/2006                    1/1/1999 to 8/4/2006

                    BE        FR       NL         IT       BE         FR        NL        IT

         Belgium      1        -         -        -         1          -         -        -

         France    0.2884      1        -         -       0.8780       1         -        -

     Netherlands   0.6106    0.1987     1         -       0.8891     0.8193     1         -

          Italy    0.3095    -.4663   -.0735      1       0.8608     0.7978   0.7264      1




                                                      8
      Table 2: Maximum likelihood estimation of the common factor model with GARCH errors and con-
vergence effects (eqs. 1-7).

                                             Country-specific parameters                               Common parameters
                        Belgium               France             Netherlands            Italy
                        0.9716               0.9811               0.7003              0.9954                 0.9667
                        (0.0077)             (0.0062)             (0.0644)            (0.0035)                (0.0076)
                        0.0063               0.0012               0.0262              0.0008                     -
                        (0.0020)             (0.0011)             (0.0075)            (0.0011)                    -
                       -0.0068               -0.0115             -0.0224              -0.0340                    -
                        (0.0003)             (0.0021)             (0.0054)            (0.0051)                    -
                        737.82               681.38               725.65              713.31                     -
                        (0.0053)             (34.821)             (14.735)             (8.596)                    -
                       2.5E-5               0.0001               2.4E-5              3.3E-6                 0.0055   


                        (8.8E-6)             (3.5E-5)             (6.4E-6)            (1.4E-6)                (0.0036)
               
                        0.1459               0.3699               0.4291              0.1253                 0.0994
                        (0.0455)             (0.0651)             (0.0714)            (0.0138)                (0.0204)
               
                        0.7906               0.5397               0.5551              0.8739                 0.8951
                        (0.0515)             (0.0677)             (0.0703)            (0.0139)                (0.0211)
                        0.0252               0.0222               0.0223              0.0223                     -
                        (0.0049)             (0.0045)             (0.0043)            (0.0044)                    -
                           -                    -                    -                   -                   1.7E-8
                            -                    -                    -                   -                  (1.4E-6)
                                                           Goodness of fit
                                                                  -18.2915
                   
                                                                  -18.2687
                                                                 -18.2510
                   
                                                                  -18.2003
      Note: Hessian based standard errors between brackets.  For the common state the point estimate and standard

error of     are obtained from the restriction   = 1 −   −   .  denotes the Akaike Information Criterion for
the full model with convergence effects on      and  ,   is the statistic if  converges but  is country-specific
and contains an euro dummy,         is the statistic if  converges but  is country-specific but constant over time,
and     is the statistic if there is no convergence, i.e. if  = 1 ∀ . A model with a smaller  is
preferred.



                                                             9
            Figure 1: Corrected 10 year government bond spreads versus Germany

 2 .5




    2




  1. 5




        1




 0 .5




    0




- 0 .5
   J un-91             J un-94                 J un-97                  Jun-00                   Jun-03                J un-06


                                 B elg ium               Fr an c e          N e t he r lan d s              It a l y




                      Figure 2: Idiosyncratic state  for all countries

 2.5




   2




 1.5




   1




 0.5




   0




-0. 5
   J un-91             J un-94                 J un-97                  J un-00                   J un-03               J un-06



                                  B el gi um              Fr a n c e         N et her l ands                Ital y




                                                                   10
                                       Figure 3: Common state 


              9




              4




             -1




             -6




            - 11




            - 16
             Jun- 91       Jun- 94           Jun- 97                Jun- 00              Jun- 03              Jun- 06




Figure 4: Convergence dynamics of the idiosyncratic components  and the idiosyncratic factor
loadings   (convergence operators  )

            1.2



               1



            0 .8



            0 .6



            0 .4



            0 .2



              0
             J un- 91      J un-94         Jun-97                   J un-00              J un-03              J un- 06


                                B elgium          Fr a n c e            N et her lands             It a l y




                                                               11

								
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