Some stylized facts from the business cyle literature are:
(1) the real Gross Domestic Product (GDP) is nearly as volatile as total hours worked equal,
(2) the high positive correlation between total hours worked and real GDP,
(3) hourly wage is less volatile than productivity, and
(4) the absence of correlation between hourly wage and real GDP.
The business cycle literature is the branch of macroeconomics concerned with explaining and predicting economic recessions and expansions.
In an earlier post [here], I have suggested measuring business cycle fluctuations applying the turbulence index to disaggregated real GDP from the North American industry classification system (NAICS).
The NAICS consists of 20 sectors.
The turbulence index, which is named after its author Mahalanobis distance, was used by Kritzman and Yuanzhen (2010) to study financial turbulence.
Designating the current distribution of an economic variable, say the growth rate of real GDP, across the 20 sectors of the NAICS by the vector ,
their historical averages by the vector ,
and their covariance matrix by , the expression for the turbulence index is
The square root of the above expression is the Mahalanobis distance.
This statistic has successfully helped identify the most and the least turbulent periods of the Canadian economy.
In this post I keep exploring the relevance of measuring business cycle fluctuations using the turbulence index.
This time, I am computing and analyzing the turbulence index for some labor market variables, which are: the average and total hours worked, hourly wage, and labor productivity.
The labor productivity is the ratio of the real GDP and total hours worked in each sector.
Figure 1, below, shows the turbulence indices of the growth rates of real GDP, wage, average hours worked, and labor productivity.
Among other things, one can identify the year 2009 as the moment where the turbulence indices of the variables GDP, average hours worked, and labor productivity reach their hight levels.
The turbulence index of the growth rate of real wage has not peaked during the global financial crisis because employers could not legally reduce the hourly wages of their staff.
This is called downward wage rigidity.
 |
| Figure 1: Turbulence indices of GDP and some Labor Market Variables, Canada, 2002:M2-2018:M12 |
To study the behavior over the business cycle of the labor market variables and the real GDP, I have used a Markov-dependend mixture of multivariate normal distributions.
This enables computing in one-go the average values of their turbulence indices, their standard deviations, and their correlations (or covariances) during periods of economic expansion and recession.
Figure 2, below, plots the histograms of some of the turbulence indices and the fitted marginal distributions.
 | ||
|
The Markov-dependent mixture of multivariate normal distributions suggests that most of the time (precisely 70.5 % of the time), the Canadian economy is in expansion and 29.5 % of the time , it is in recession
Furthermore, both states of the business cycle turn out to be very persistent, as the chance that a period of expansion ends is only 1.2 % and the probability of exiting a period of recession is 3 %.
Table 1 and Table 2 respectively present the standard deviations of the turbulence indices of the macroeconomic variables and their correlation coefficients with the turbulence index of real GDP growth.
| Expansion | Recession | |
|---|---|---|
| GDP | .828 | .915 |
| Total Hours Worked | .817 | 1.176 |
| Average Hours Worked | .988 | .944 |
| Wage | .841 | .874 |
| Productivity | .782 | .772 |
Indeed, it appears in Table 1 that the turbulence index of real GDP is nearly as volatile as the turbulence index of total hours worked, but this holds only during periods of economic expansion.
During recessions, the volatility of the turbulence index of total hours worked is much higher.
On the other hand, the turbulence index of the average hours worked is more volatile than that of real GDP, during both periods.
Furthermore, the turbulence index of hourly wage is more volatile than that of productivity.
This latter finding is at odds with the single-state stylized fact produced by Cooley and Prescott (1995) who used the Hodrick-Prescott (HP) filter to extract the cyclical components of the macroeconomic variables.
One could see in Table 2 that, during periods of economic expansion, the correlation between the turbulence indices of hourly wage and real GDP is low as Cooley and Prescott (1995) pointed out.
But, during recessions, this correlation is somewhat higher.
There is no high correlation between total hours worked and real GDP, as the business cycle literature points out.
| Expansion | Recession | |
|---|---|---|
| Total Hours Worked | .013 | .051 |
| Average Hours Worked | .036 | .208 |
| Wage | .057 | .176 |
| Productivity | .088 | .188 |
It also appears in Table 2 that the correlation between the turbulence indices of the labor market variables and the turbulence index of real GDP growth are lower during periods of economic expansion than during recessions.
A possible explanation is that during periods of expansion, the economy is at its full potential and unemployment fluctuates around its natureal rate.
Consequently, raising the level of employment does not much impact on output.
