Page - 68 - in The Austrian Business Cycle in the European Context

68 with z being the analysed time series and s, = 1 if the economy is in expansion and s, = 2 if it is in contraction, implying that the mean is above or below the average mean of the total series (32) ifs,= 1 ifs,= 2 The probability of being in either state of the cycle evolves ac- cording to a Markov chain defined by certain transition probabili- ties for switching from one state to the other (33) prob (s, = i Is,_ 1 = }) = £;,j e(O, 1) Vi, j = 1,2 Thus, the probability of being in expansion if the preceding period was also in expansion is (1-e1), or for a contraction following a contraction (1-s2), and the changes from one state to the other are s1 or s2 , respectively. The estimation of such Markov-switching models is quite compli- cated, since a global nonlinear process is combined with an un- observed component character. In practice, this is carried out with the Kalman filter technique in order to get Maximum- Likelihood estimators. As a result, probabilities for each observation of being in either state are obtained, which can be transformed into a binary vari- able indicating contraction or expansion periods. The advantage of this procedure, compared with the non-parametric ap- proaches, is that for all points in time it can be inferred whether the economy is expanding or contracting94• Furthermore, the size of deviation plays a role in the identification process, so that minor ups and downs can be excluded from the dating calendar. The advantage of obtaining probabilities for turning points may be a 9• Except for the very rare points where the probability for either regime is insignifi- cant.