The name is absent

specification for the non-fundamental shock, chosen to produce a hump-shaped
effect:

ʌ ʌ ʌ

^{^}t = ^ωθι,t + (^{ω -} 1)θ2,t                             (4)

^θj,t = ^ρj^θj,t-1 ^{+ ε}t   (^j = ^1,2)                           (5)

where εθ is white noise.

Instead we use a Markov-switching specification, to replicate the impact of
a sudden burst in asset prices, characteristic of financial crises. We assume
there are two states. The two states aim at capturing the complex behaviour
of financial markets, which have quiescent periods, when they seem to be
driven by fundamentals, interspersed with periods of “irrational exuberance”.
Therefore, we assume that in the first state the shocks have no persistence:

θjt = εθ (j = 1,2)                             (6)

In the second, exuberant regime, shocks are mildly explosive. This is
achieved by multiplying Dupor’s autoregressive coefficients by 1.6, which yields
autoregressive coefficients close to 1.09:

O                O            -Λ

^θj^t = ¹ ∙^6ρj^θj,t-1 ^{+ ε}t   (^j = ^1,2)

When the economy moves from state 1 to state 2, investment-firms expect
profits to increase exponentially and a bubble develops. The bubble bursts
when the economy moves from state 2 back to state 1. The state of the economy
is assumed to evolve as a Markov chain with the following probability transition
matrix:

p11 p12

p21 p22

where p_ij = 1 - p_ii (when i 6= j ) and p_ij is the probability of moving from
state i in the current period to state j in the next period. In this model,
the policymaker is uncertain about the state of the economy in the next

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