Impulse–response functions in Markov-switching structural vector autoregressions: A step further

Commodity Prices and the Business Cycle in Latin America: Living and Dying by Commodities?

“…s t+h =j for all h) in which the shock occurs but they require the assumption that there is no more change in regime in the wake of the shock. This occurs when we assume that t h t / + ξ is a vector with one in the position j and zeroes elsewhere for all h. Second, Karame (2010) propose Markov-switching impulse responses that capture the possible different impact of a shock depending on the regime in which it occurs. However, this author supposes that the regime at the time of the shock is known with probability one (e.g.…”

“…Contrary to Ehrmann, Ellison, and Valla (2003) who propose regime-dependent responses, and to Karame (2010) who supposes that the regime at the time of the shock is known with probability one, our impulse responses are calculated at any point in history. Hence, the case of regime-dependent responses and the case where the shocks occur in a particular regime become special cases of our method.…”

An algorithm for generalized impulse-response functions in Markov-switching structural VAR

“…We then identify the second shock as an aggregate shock. We compare our GIRF to the ones provided by Erhmann et al (2003), Karamé (2010) and Camacho & Perez-Quiros (2011). Simulation parameters for initial values and future shocks are set respectively to A = 500 and B = 500, which allows to reach stable results.…”

“…Up to now, Ehrmann et al (2003) propose a regime-dependent IRF to study the response of the system conditionally to the regime in which the shock occurs and with no change in regime afterwards. Karamé (2010) generalizes their approach to whatever visited states in the wake of the shock. These approaches are very close to the traditional linear literature on IRF since they are based on several steps ahead predictions.…”

Macroeconomic Regimes and Regime Shifts

“…Suppose we first condition not just on the regime j at date t but also on a particular regime j 1 for date t + 1, j 2 for t + 2, and j m for t + m, and consider the value of Karamé (2010) noted that this (n × n) matrix can be calculated from the recursioñ Ψ m,j,j 1 ,...,jm = Φ 1,jmΨm−1,j,j 1 ,...,j m−1 + Φ 2,jmΨm−2,j,j 1 ,...,j m−2 + · · · + Φ r,jmΨm−r,j,j 1 ,...,j m−r for m = 1, 2, ... whereΨ 0j = I n and 0 =Ψ −1,. =Ψ −2,.…”