In an earlier post [here], I have analyzed the joint behavior of inflation and unemployment in Canada, over periods of economic expansion and contraction.
In this post, I go on with this investigation using now data from the United States (US) and comparing then the new findings to the evidence from the Canadian economy.
Figure 1, below, shows the distribution of the inflation and unemployment rates in both countries over a period of time going from March 2001 to December 2019 (226 months).
The distribution of the inflation rate in Canada appears to have a fatter and longer tail.
In fact, in Canada, the monthly inflation rate over the period of interest fluctuated in the interval ±.54% whereas, in the US, it fluctuated between -.12% and .38%.
However, both distributions are leptokurtic (i.e., their tails are fatter than those of a normally distributed variable).
On the other hand, unlike the inflation rate, the distribution of the unemployment rate in the US is wider than its distribution in Canada.
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| Figure 1: Empirical Distributions of the Inflation and the Unemployment Rates in Canada and the US, 2001:M3-2019:M12. |
It also appears in Figure 1 that, in both Canada and the US, the distribution of the unemployment rate peaks at two different points.
This is what is called a bimodal distribution.
In Canada, the lowest mode ( i.e., the unemployment rate associated to the first peak) has a lower probability of occurence than the highest mode.
But, in the US, it is the lowest mode that has a higher probability of occurence.
Evidence 1: The distribution of the unemployment rate in Canada and the US is bimodal.
Evidence 1 implies that it is inappropriate to model the unemploymment rate assuming that it is a normally distributed variable.
A normally distributed variable is bell-shaped, which implies it peaks only at one point.
It is also inappropriate to model the inflation rate making such an assumption, due to the excess kurtosis in the data.
(By excess kurtosis, I mean the fat tails of their distributions.)
Therefore, an alternative and better way of modeling both the inflation and the unemployment rates is to use a Markov-switching multivariate normal model.
A Markov-switching model assumes different unobserved states of the economy, which have their own unconditional and transition probabilities.
Then, the conditional probability of an observation depends on the realized state.
Figure 2, below, plots the mixtures of two state-dependent normal distributions fitted to the inflation and the unemployment rates in Canada.
Figure 3 that follows plots the estimates for the US.
In both cases, the two-state Markov-switching normal model provides a better fit to the inflation rate than to the unemployment rate.
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| Figure 2 : Empirical Distribution and State-Dependent Distributions of the the Inflation and Unemployment Rates, Canada, 2001:M3-2019:M12. |
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| Figure 3 : Empirical Distribution and State-Dependent Distributions of the the Inflation and Unemployment Rates, US, 2001:M3-2019:M12. |
Tables 1 and 2, below, display the expected values of the inflation and the unemployment rates over the two states of the economy (expansion and contraction) respectively in Canada and the US.
In Canada, the standard deviation of the unemmployment rate is .26 during periods of expansion and .48 during periods of contraction.
In the US, this standard deviation is .76 and .97, respectively during periods of expansion and contraction.
On the other hand, the standard deviation of the inflation rate does not change much over the two states.
| Expansion | Recession | |
|---|---|---|
| Inflation Rate | .16 % | 6.02 % |
| Unemployment Rate | .12 % | 7.33 % |
| Expansion | Recession | |
|---|---|---|
| Inflation Rate | .17 % | 5.00 % |
| Unemployment Rate | .13 % | 8.56 % |
Evidence 2: The volatility of the unemployment rate in Canada and the US is lower during the periods of economic expansion than during the periods of contraction.
Evidence 3: The inflation rate in Canada and the US is tends to be higher during the periods of economic expansion and lower during the periods of contraction.
On the other hand, the unemployment rate tends to be higher during the periods of contraction.
While the correlation between the inflation and the unemployment rates is negative over the two states in the US, in Canada, it is negative only during the periods of contraction.
The use of higher-order Markov-switching models (i.e., models distinguishing between more than two states of the economy) has not helped improve the estimates of the marginal probabilities of the unemployment rate.
