14
in period t.30 The subscript i represents the countries in our sample (i=1,..,N) and subscript t is the time
subscript (t=1,..,T).
Before turning to the estimation results, we will briefly describe the estimation technique for the above
fixed-effects model (see Hsiao 1986, pp. 29-32 and Eijffinger, Van Rooij and Schaling, 1994). For
convenience, we introduce the following notation:
β = ( β 1 5 P 1 ’ P з ’••• )
xi,t =(O -*fiwr°)1∙,i-ι><∙,J, i = l,..,N t = l,..,T
C∙ =β0÷Yi i = l,.∙Λ
Now, we are able to rewrite equation (10) as
(i-ia")i,r = ζi÷β%,t÷ei,r i = l,..,ΛT tιl,..,T (ii)
Note that we have comprised the common intercept β0 and the country-specific effect γi together to ζi. The
reason for this is that because both terms are fixed constants we cannot identify or estimate them separately.
We will refer to ζi as the generalized country-specific effect to distinguish it from the country-specific effect
γi. Ensuing, we need the following notation:
( i - i Euro ) . = ( ( i - i Euro ) it , . . , ( i - i Euro )iτy i = l,..,N
e = ( 1 , ∙ ∙ , 1 )’
x i = ( X i , 1 ’ ∙ ∙ ’ X i , T ) I = 1,.. ,W
e i ~{ei,i’--’ei,T) i-l,..,N
Now equation (ii) can be written as3i
(i - i Eur° ) i = ζ ie + Xi β + ei i = l,..,N
(i2
Define matrix Q as Q=IT-ee’/T where IT denotes the identity matrix with dimensions T by T. Premultiplying
equation (i2) with Qhas the effect of transforming all observations into deviations of their individual means.
Performing this transformation on equation (i2) gives:
30 We assume the error term εi,t to be an independently, identically distributed random variable with mean zero and variance σε2.
Furthermore, we assume that the error term is independent of the regressors. Moreover, when we use F- and t-statistics, we implicitly
make the assumption that the error term is normally distributed.
31 The conditions for εi,t imply for εi: (i) e ( e . ) = о i = ι,..,N
(2) E(eie') = o'∕1 i = l,..,N
(3) E ( e j e' ) = 0 ɪ , j = 1,..,N Λ i ≠ j
with It denoting the T by T identity matrix.