6. Determinacy of the Rational Expectations Equilibrium
In consequence, we obtain the subsequent matrix form for the system of equations:
Ay = Bx + u,
where the vectors of unknowns y, x and the vector of disturbance terms u read as follows:
(62)
|
y:= |
^ xt πt,H πt,F ʌ |
, x := |
' Et [xt +1 ] ■ Et[ x*+1] |
, u := |
'—Et [∆ at+1Γ Ut * 0 |
|
it-1 |
it |
ω1 vt | |||
|
ʌ Lh-1J |
ʌ L i* J |
L -(ω* )-1 v* J |
The coefficient matrices A, B, however, read:
|
1 |
0 |
0 |
00 |
0 |
0 | ||
|
0 |
1 |
0 |
00 |
0 |
0 | ||
|
-μ |
0 |
1 |
00 |
0 |
0 | ||
|
0 |
* -μ |
0 |
10 |
0 |
0 |
, | |
|
0 |
0 |
1 |
-1 1 |
-1 |
1 | ||
|
0 |
0 |
α ω |
00 |
1 |
0 | ||
|
0 |
ι* ω* |
0 |
_ * * 0 ω* |
0 |
1 | ||
|
1 |
0 |
ρ-1 |
0 |
■& |
-ρ-1 |
0 | |
|
0 |
1 |
0 |
ρ- |
1 μ* |
0 |
_ |
ρ-1 |
|
0 |
0 |
β |
0 |
0 |
0 |
0 | |
|
B := |
0 |
0 |
0 |
β |
0 |
0 |
0 |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 | |
|
0 |
0 |
0 |
0 |
0 |
ω-1 |
0 | |
|
0 |
0 |
0 |
0 |
0 |
0 |
( ω* )-1 |
In order to determine the eigenvalues of the system of equations (62), it has to be rearranged in the
following form:
y = Mx + v, (63)
where M := A-1B and v := A- 1u. Moreover, A-1 denotes the inverse of A, which exists because
det(A) = 1 = 0.
The matrices A-1 and M and the vector v read as follows:
18
More intriguing information
1. The name is absent2. The Context of Sense and Sensibility
3. Transfer from primary school to secondary school
4. Innovation Policy and the Economy, Volume 11
5. Evolutionary Clustering in Indonesian Ethnic Textile Motifs
6. Langfristige Wachstumsaussichten der ukrainischen Wirtschaft : Potenziale und Barrieren
7. A Bayesian approach to analyze regional elasticities
8. TECHNOLOGY AND REGIONAL DEVELOPMENT: THE CASE OF PATENTS AND FIRM LOCATION IN THE SPANISH MEDICAL INSTRUMENTS INDUSTRY.
9. The name is absent
10. Why unwinding preferences is not the same as liberalisation: the case of sugar