The fundamental determinants of financial integration in the European Union

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÷Y_i                i = l,.∙Λ

Now, we are able to rewrite equation (10) as

(i-i^a")_i,_r = ζ_i÷β%,_t÷e_i,_r i = l,..,ΛT tιl,..,T (ii)

Note that we have comprised the common intercept β₀ and the country-specific effect γ_i together to ζ_i. The
reason for this is that because both terms are fixed constants we cannot identify or estimate them separately.
We will refer to ζ_i as the generalized country-specific effect to distinguish it from the country-specific effect
γ_i. 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 + X_i β + e_i i = l,..,N

Define matrix Q as Q=I_T-ee’/T where I_T 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 ε_i,t to be an independently, identically distributed random variable with mean zero and variance σ_ε².
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 ε_i,_t imply for ε_i:              (i) e ( e . ) = о i = ι,..,N

(2) E(e_ie') = o'∕₁ i = l,..,N

(3) E ( e _j e' ) = 0 ɪ , j = 1,..,N Λ i ≠ j
with I_t denoting the T by T identity matrix.

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