Business cycles are alternating periods of economic recession and expansion.
The growth rate of the real gross domestic product (GDP) is one of the statistics used to measure business cycles.
Thus, an economy is generally said to be in recession after declines in its real GDP over, at least, two consecutive quarters.
The real GDP is an aggregate measure of the value added to the economy by its various sectors or industries.
In this post, I explore the relevance of measuring business cycle fluctuations using alternatively disaggregated data from the North American industry classification system (NAICS).
In 1997, the NAICS broke down the economy of Canada, Mexico, and the United States into 19 sectors, for national accounting purpose.
In 2007, a twentieth sector was added to the list.
(For a complete list of these sectors, see here.)
I have used disaggregated data to compute the multivariate distance of the current real GDP growth rates of the sectors of the Canadian economy from their historical averages.
This statistic, which is named after its author Mahalanobis distance, was used by Mark Kritzman and Li Yuanzhen (2010) to study financial turbulence.
Designating the current growth rates of real GDP across the sectors by the vector ,
their historical averages by the vector ,
and their covariance matrix by , the expression for the turbulence index proposed by Mark Kritzman and Li Yuanzhen is
The square root of the above expression is the Mahalanobis distance.
I will study the business cycle fluctuations in Canada using the Mahalanobis distance, for convenience reason, but I will refer to this statistic as turbulence index.
Figure 1, below, plots the turbulence index computed for the period 1997:M1-2018:M12.
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| Figure 1: GDP Growth Turbulence Index, Canada, 1997:M2-2018:M12 (263 months). |
The turbulence index peaks in January 2009, during the global financial crisis.
Some other most turbulent periods are: December 1997 - January 1998, which corresponds to the Asian financial crisis, and August 2003, which corresponds to the early 2000s recession.
On the other hand, the information technology bubble, mainly the months of June and September 2000 and August 2001, are the least turbulent periods.
One could set a threshold to dissociate in Figure 1 turbulent periods (recession) from non-turbulent periods (expansion).
An alternative to this deterministic approach is to fit the turbulence indices to a Markov-dependent mixture of two normal distributions.
| Recession | Expansion | |
|---|---|---|
| Mean | 5.445 | 3.911 |
| (18.18) | (45.66) | |
| Standard Deviation | .845 | .662 |
| (33.87) | (48.40) | |
| Unconditional Probability | 24.9% | 75.1% |
| (12.37) | (8.14) | |
| Persistence | 64.9% | 88.3% |
Table 1, above, presents the maximum likelihood estimates of the Markov-dependent mixture model.
It turns out that economic recession is characterized by both a high expected turbulence index and a high volatility of this index.
On the other hand, both the expected value and the standard deviation of the turbulence index are lower during economic expansion.
The unconditional probabilities in Table 1, which are also the stationary distribution of the Markov chain, indicate that recession is less recurrent than expansion: one-quarter of the time, the Canadian economy is in recession, and, three-quarters of the time, it is in expansion.
It also appears in Table 1 that recession is less persistent than expansion: there is a 35.1% probability that the Canadian economy exit an on-going recession the next period versus an 11.7% probability of entering into recession.
The -statistics in Table 1 are all greater than 1.64, their 5% critical value, which indicates that the estimates are significantly positive.
Figure 1 plots th histogram as well as the marginal distribution of the turbulence index.
The marginal distribution is a linear combination of two normal distributions: the distributions of the turbulence index during recession and expansion.
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| Histogram and Marginal Distribution of the GDP Growth Turbulence Index, Canada, 1997:M2-2018:M12. |
It appears in Figure 2 that the Markov-dependent mixture of the two normal distributions provides a good fit.
The Situation of the Canadian Economy in 2019
Will the Canadian economy experience a recession this year? To provide an answer for this question, I have estimated the probabilities of a recession and an expansion for the whole year using the Markov-dependent mixture of two normal distributions.| Recession | Expansion | |
|---|---|---|
| January | .137 | .863 |
| February | .190 | .810 |
| March | .218 | .782 |
| April | .232 | .768 |
| May | .240 | .760 |
| June | .245 | .755 |
| July | .247 | .753 |
| August | .248 | .752 |
| September | .249 | .751 |
| October | .249 | .751 |
| November | .249 | .751 |
| December | .249 | .751 |
For the whole 2019, the probability of an expansion of the economy is much higher than that of a recession.
The risk of a recession slightly increases each month but does not exceed 25% at the end of 2019.
An Alternative to the Growth Rate
The growth rate of real GDP, approximated by the first difference of its natural logarithm, is referred to as first-difference filter. The most popular filter used in the business cycle literature is the Hodrick and Prescott (HP) filter. I have detrended the disaggregated GDP using the HP filter to compute new economic turbulence indices. These new indices are plotted in Figure 3 below. |
| Figure 3: Economic Turbulence Index Computed using GDP Detrended with the HP Filter and their Expected Values during Recession and Expansion, Canada, 1997:M1-2018:M12. |
The turbulence indices computed using growth rates and those computed using the HP filter differ in magnitude. The most turbulent event that the Canadian economy experienced between 1997 and 2018, according to the former approach, is the global financial crisis. According to the latter approach ( i.e. the turbulence indices computed with the GDP detrended using the HP filter), the Asian financial crisis of 2003 is the most turbulent event. The expected value of the economic turbulence indices computed using the HP filter is 6.3 during a period of recession and 4.25 during a period of expansion.
Unlike the indices computed using the growth rate of real GDP, the standard deviation is lower during recession: 51 during recession and .63 during expansion.
The correlation coefficient between the economic turbulence indices computed using the GDP growth rate and the GDP detrended with the HP filter is .47.
