Special Report. Where are we in the cycle? Economics and Strategy. What does the yield curve say? Summary. What are the probabilities of recession?

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1 Economics and Strategy May 18, 017 Where are we in the cycle? Summary The odds of a recession in Canada or the U.S. in the years ahead is a contentious question in the economic community and the media. Some observers emphasize that the slope of the yield curve of government bonds remains distinctly positive, suggesting very little chance of recession. Others point to the age of the current expansion in arguing for a much higher probability. For this study, we defined the maturity of an expansion in relation to the spread between the unemployment rate and the NAIRU. Based on that interpretation, we compared the present situation with a sample going back to 190 in order to gauge the chances of a U.S. recession. Give that the U.S. has only recently entered in the mature phase of expansion, our calculations show a historical probability of less than 0 over the next 1 months. Repeating this exercise for Canada, we found a probability of only within a year, since by our definition the Canadian expansion has not yet entered its mature phase and because the sample consists of only five recessions since This seems low compared to the U.S., especially given the correlation of those two economies. A sample encompassing all of the G7 countries (8 recessions) seems more appropriate to us. The historical record for these countries yields a 1 probability of a Canadian recession within 1 months. What are the probabilities of recession? Our team periodically sets out the economic scenario that we consider the most probable for the coming quarters. At present our baseline scenario is one of continuing expansion in Canada and the U.S. over the next two years. Despite some divergences about the vigour of the expansion, most economists share this view. However, the chances of a recession are never zero. Could it be that we are overoptimistic? That a recession is in the cards for the coming quarters? Under current conditions, what odds should we attach to that alternative scenario? In this Special Report we consider the probabilities of recession in the near and medium term. What does the yield curve say? Over time, the slope of the U.S. Treasury yield curve from months to years has become established as a reliable predictor of U.S. recessions. Inversion of this portion of the curve has often heralded economic downturns. Accordingly, the New York Fed has developed a model based solely on this indicator that it regularly updates to gauge the likelihood of recession within 1 months 1. Applying this model, the probability of the U.S. falling into recession in the next year is only (chart). U.S.: No signal of economic downturn from the yield curve slope Probability of recession within one year Probit model based on slope of the yield curve Percentage points NBF Economy and Strategy (data via Bloomberg) U.S. Treasury -year yield minus -month yield That being said, many economists question the usefulness of this model when the policy rate is close to zero, as it is today. In current conditions, i.e. with -month Treasuries yielding less than 1, the yield of -year Treasuries would have to drop to unprecedented lows for the curve to invert. For example, an inversion as pronounced as that of December 1980, seven months before the U.S. economy tipped into recession, would require a -year yield near -1. about 7 basis points beneath its record low. An expansion getting on in years Probability of recession Odds of may seem low, especially for an expansion that is 9 months old as at present. Indeed, the current expansion is now the third-longest in the U.S. and the fourth-longest in Canada since 19 (chart) capital_markets/prob_rec.pdf

2 U.S. and Canada: Intervals between economic downturns since 19 In months U.S NBF Economy and Strategy (data from National Bureau of Economic Research and C.D. Howe Institute) Canada But is the age of an expansion in itself a good reason to fear imminent recession? After all, only 1 months separated the U.S. recessions of 1980 and When we build a model based on duration of an expansion, we find its predictive power to be much lower than that of the yield curve. This finding is consistent with the argument set out last year by Glenn D. Rudebusch of the San Francisco Fed, who studied economic expansions since World War II using a lifeexpectancy model borrowed from actuaries and concluded that the hypothesis stating that these periods must eventually die of old age is wrong. Be that as it may, our model based on the age of an expansion put the probability of recession within a year at (chart), much higher than that suggested by the slope of the Treasury yield curve. U.S.: The age of the expansion plays a role but... Probability of recession within one year Probit model based on duration of expansion Another view of the maturity of an expansion So the current expansion is getting long in the tooth. Does that necessarily make it mature? To weigh this question we defined an expansion as mature from the moment unemployment rate falls below NAIRU (Non-Accelerating- Inflation Rate of Unemployment). The NAIRU, also known as the natural rate of unemployment, is the unemployment level at which inflation is not rising nor declining. It usually happens when the economy is operating at full capacity. In these occasions, the remaining unemployed are essentially in transition (frictional unemployment) or unfit for businesses needs (structural unemployment). Since 190, the time interval between the moment the unemployment rate falls below NAIRU and the beginning of a recession has averaged months. As of now, the current expansion has only just entered its mature period; the U.S. unemployment rate fell below NAIRU just three months ago (chart). U.S.: Another perspective on the timing of economic cycles Observed unemploymentrate vs. NAIRU (non-accelerating-inflation rate of unemployment) Average duration of expansion after unemployment rate falls below NAIRU: months 7 Unemployment rate NAIRU 0 the model has very limited explanatory power NBF Economy and Strategy (data via Bloomberg) The length of the current expansionary phase is thus not a reflection of its maturity, but the result of a lengthy recovery. As the following chart illustrates, it took more than 9 months from the bottom of the recession of for the unemployment rate to drop below NAIRU. The extreme slowness of this recovery, the longest since World War II (chart), attests to the severity of the last recession, but also suggests that the expansion could continue for a while yet. Its R is only 9, compared to 8 for the yield curve model. Will the Economic Recovery Die of Old Age?, G. D. Rudebusch, 01 NAIRU estimated by the Congressional Budget Office (CBO).

3 Recession probability by maturity of expansion U.S. Historical probabilities based on unemployment rate vs. NAIRU Year Years Years Above NAIRU by more than 0. Above NAIRU by more than 0. but a maximum of 0. Above NAIRU by a maximum of 0. Below NAIRU by a maximum of 0. Below NAIRU by more 0. The hypothesis that the probability of recession correlates with the maturity of an expansion as measured by the unemployment rate relative to NAIRU was studied by the research firm Macroeconomic Advisers (MA). The authors of the study used historical labour-market data going back to 190 in order to assess the probability of a recession occurring over different time spans. To obtain a little more granularity in the unemployment rate than was presented in the MA study, we repeated its exercise for the United States. Our results were similar. We found that, when the unemployment rate exceeds NAIRU by whatever margin, the odds of a recession within a year are very low, i.e. less than (chart, below). We then applied this approach to Canada using data going back to Since the current Canadian unemployment rate of. is marginally above NAIRU, the historical probability of recession is only within a year and 1 within three years (second chart below). As it happens, our results show probabilities of recession below those of the U.S. for almost all unemployment rates. Canada: Unemployment rate and NAIRU since However, the odds rise significantly when the unemployment rate falls below NAIRU. At this writing the U.S. unemployment rate is., 0. points below NAIRU. Such a situation is historically associated with a 19 probability of recession within 1 months and 70 probability of recession within three years (chart) Unemployment rate NAIRU Recession Probabilities, B. Herzon and J. Prakken, 01 The NAIRUs used for countries except the U.S. are those estimated by the OECD

4 Recession probability by maturity of expansion Canada Historical probabilities based on unemployment rate vs. NAIRU Could our approach underestimate the risk of recession in Canada? Truly, is it reasonable to consider that Canada has significantly lower recession probabilities than the United States given the strong correlation between the two economies (chart)? Year Years Years 7 Above NAIRU by more than 0. Above NAIRU by more than 0. but a maximum of 0. Above NAIRU by a maximum of 0. Below NAIRU by a maximum of 0. Below NAIRU by more 0. investors suffered major losses on the stock markets. The resilience of the labor market in Canada probably contributed in tipping the balance for experts. The fact remains that the Canadian economy has been relatively spared since 1970, based on the official number of recessions that have been identified. A larger sample To remedy the weaknesses of a sample with only recessions, we repeated the exercise for all G7 countries. This allowed us to base ourselves on a history of no less than 8 recessions whose dates were determined by ECRI (Economic Cycle Research Institute) using a single analysis framework. For consistency, NAIRU estimated by the OECD were used. The evolution of the unemployment rates of the different countries as well as these recession periods are presented in the Annex section. If the results so obtained are applied to Canada, the current probability of recession within a year rises to 1 (chart), slightly less than the 19 estimated for the U.S.. The three-year probability rises to 7. This estimate seems intuitively more appropriate. Canada and U.S.: Highly correlated economic cycles Change in real gross domestic product y/y Shaded area= U.S. recessions Correlation: 8 In fact, the low probability of a recession in Canada is partly due to the fact that the country has experienced fewer recessions than its southern neighbor. In Canada, there has been a recession every 9. years since 1970, compared with.7 years in the United States since 190. Since 1970, the C.D. Howe Institute has estimated that recessions have occurred in Canada; the NBER counts 7 such occurrences in the United States. It should be understood that the two bodies responsible for defining periods of recession base their respective decisions on a multitude of economic indicators analyzed by experts. Knowing this, the line can sometimes be thin between what is considered a recession per se and what is judged to be a mere economic downturn. For example, it is likely that, for the 001 episode in Canada, the verdict of no recession was given after intense debate. Even though that period wasn t labelled a recession, the economy still experienced a significant slowdown and U.S. Canada

5 Conclusion The odds of a recession in Canada or the U.S. in the years ahead is a contentious question in the economic community and the media. Some observers emphasize that the slope of the yield curve of government bonds remains distinctly positive, suggesting very little chance of recession. Others point to the age of the current expansion in arguing for a much higher probability. For this study, we defined the maturity of an expansion in relation to the spread between the unemployment rate and the NAIRU. Based on that interpretation, we compared the present situation with a sample going back to 190 in order to gauge the chances of a U.S. recession. Give that the U.S. has only recently entered in the mature phase of expansion, our calculations show a historical probability of less than 0 over the next 1 months. Repeating this exercise for Canada, we found a probability of only within a year, since by our definition the Canadian expansion has not yet entered its mature phase and because the sample consists of only five recessions since This seems low compared to the U.S., especially given the correlation of those two economies. A sample encompassing all of the G7 countries (8 recessions) seems more appropriate to us. The historical record for these countries yields a 1 probability of a Canadian recession within 1 months. Matthieu Arseneau and Jocelyn Paquet

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