If we now substitute (3.41) and (3.43) into (3.39), the REH solution for the price level is obtained:

5pt 4Et-imt + Et_2mt + 1(vt - ) + -61Et_i(vt - ut) + 3Et_2(vt - ut ). (3.44)

This can be substituted into the AD equation (3.25) to obtain the expression for yt:

yt = mt - [iEt-imt + 3Et-2Mt (1/t Ut) Et-1(Vt Ut) 3Et_2(vt - ut)] + vt

= 3 [mt --Et--2mt] — — ut) — Et_i(vt — ut) — 3Et_2(vt - ut) + vt, (3.45)

where we have used the fact that Et_imt = mt.

74

= putinut.

I where we have used t e tit-2. Using (3.-iu ) a Mt Et-2Mt = 11

= 11 i. _ivation (3.48) is i:..

period ahead (i.e. Et t — 1 an innovati i qt _1, respectively)

innovation that occt.

t: .cir contract in p,:io If we substitute (3.41 Yt = liEt-i —

= + E tl