Canada

I would guess that it is extremely difficult to quantify how much of an effect the tax has had on the housing market. Anything beyond a guess, however, would be outside of my qualifications — I would defer to those who have looked into this more appropriately. After a very quick, and cursory websearch, I found a paper that stated the following:

From the empirical analysis of overall market, we cannot detect the significant effect of Speculation and Vacancy Tax on the price of housing property in Vancouver after the implementation. Only the parameters of GDP of real estate growth and unemployment rate are reexamined to be statistically significant. We could observe the decrease of housing price in Vancouver from the price chart after the tax policy entered into force. The decrease is also reflected by the negative coefficient of City*Time although it is not significant. [...] Focusing on a specific region’s housing price, we still cannot detect that British Columbia’s Speculation and Vacancy Tax has significantly impact on the housing price of Vancouver West compared to Toronto Central. All the other factors mentioned by other researches are not statistically significant neither. [source (archive)]