Appendix: Tell-tale Signals: A Customized Toolkit for Tracking the Economy By Jeremy Kronick, Steve Ambler and Mawakina Bafale

This exercise yields the following variables as having the best predictive power of a financial stress episode: 1) the deviation from trend of the ratio of household debt to disposable income; 2) the deviation from trend of the ratio of household debt to GDP; 3) the ratio of housing price to rent; 4) the deviation from trend of the ratio of housing price to rent; 2 5) the year-over-year growth rat. [...] The first principal component is the linear combination which explains the largest fraction of the variation in the data. [...] If we take the expected value of the right-hand side in period t, where we assume the expected value of the error term is zero, we get Therefore, since we can interpret the unweighted diffusion index as the percentage of industries in a given quarter that are expanding, we can make a similar statement regarding the interpretation of the principal components version. [...] The exact specifications are as follows.1 1) The basic Taylor rule: it = r‾ + πt + α(πt – π* ) + β(yt – y *t  ), where it is the policy rate, r‾ is the long-term real natural rate of interest, πt is the current inflation rate, π* is the inflation target, yt is the current level of real GDP, and y *t is the estimated level of full-capacity GDP. [...] Core inflation is one of the Bank of Canada’s preferred measures, CPI-median, which, from the Bank’s website, is “a measure of core inflation corresponding to the price change located at the 50th percentile (in terms of CPI basket weights) of the distribution of price changes in a given month.” 4) Forward-looking rule: The forward-looking rule is also similar to the basic Taylor rule except that i.