One issue that comes up quite a bit in my research is when to begin counting a country as semi-presidential. I already alluded to this point in the posting on Turkey. Is Turkey now semi-presidential even though the current president was elected by parliament and even though he may be in office for five, or even seven years, until the first direct election takes place? I think we should count Turkey as semi-presidential now because the constitution has been changed and the definition used here relies solely on constitutional provisions. However, doing so means that we can have cases of semi-presidentialism where there has never been a direct presidential election.
Take Austria. In December 1928 Wilhelm Miklas was elected as president by parliament. In December 1929 the constitution was amended to include the direct election of the president. In 1934, the constitution was amended again and the direct election of the president was removed. In the meantime, democracy collapsed. For Polity, the last full year of democracy was 1932. So, the Austrian constitution was semi-presidential from 1929-34, but there was no direct presidential election in this period.
Another case is Burkina Faso. In 1970, a new semi-presidential constitution was adopted for the then Upper Volta. As far as I can tell, this system lasted until 1974. In this period there was no presidential election.
Another interesting example is Brazil from 1961-63. I will do a much fuller post about Brazil at some future date. For now, though, the presidential system was changed to a pure parliamentary system by a constitutional amendment in September 1961 only for the presidential system to be restored in January 1963. In this period there was no presidential election under the new system. So, for a short time Brazil had a directly elected president operating in a parliamentary constitution.
I count Brazil as parliamentary in this period in the same way that I count Austria and Burkina Faso (Upper Volta) as semi-presidential from 1929-34 and 1970-74 respectively. However, if one were to decide that a country only became semi-presidential at the point when the first direct presidential election occurred, then Austria and Burkina Faso (Upper Volta) would not be classed as semi-presidential and Brazil would be semi-presidential from 1961-63.