What makes life more expensive in Canada?

The consumer price index (CPI) for all items is a weighted average of the retail prices of some goods and services that are classified into eight product groups. In Canada, while the monthly CPI for all items declined by .66 % in April 2020, the CPI for some of its constituentindices grew (e.g., food by 1.12 %, household operations, furnishings and equipment by .24 %, alcoholic beverages, tobacco products and recreational cannabis by .12 %). The CPI for recreation, education and reading remained unchanged. So, the CPI for all items and its constituent indices do not behave the same way.

It appears in the table below that the CPI for all the product groups tend to rise every month, except for the one for clothing and footwear that usually declines during periods of recession (-.38 %). During periods of expansion, the CPI for clothing and footwear is also the one that tends to show the lowest growth rate (.04 %). So, to answer for the question addressed in title of this blogpost, one can exclude from the list this product group, straightaway.

Table: Expected Monthly Percentage Change in CPI, Canada, 1992:M2-2020:M4.

Product group	Expansion	Recession
Food	.20 %	.10 %
Shelter	.15 %	.12 %
Household operations, furnishings and equipment	.10 %	.10 %
Clothing and footwear	.04 %	-.38 %
Transportation	.17 %	.36 %
Health and personal care	.12 %	.10 %
Recreation, education and reading	.11 %	.12 %
Alcoholic beverages, tobacco …	.19 %	.63 %
All items	.14 %	.16 %

The monthly percentage change in the CPI for household operations, furnishings and equipment is expected to be the same during both periods of expansion and recession (.1 %). Furthermore, the expected percentage change in the CPI for this product group is below that of the CPI for all items. Therefore, household operations, furnishings and equipment is another product group to exclude from the list of what makes life more expensive in Canada.

On the basis of the values in the above table, the four candidate product groups are: (1) alcoholic beverages, tobacco products and recreational cannabis, (2) transportation, (3) food, and (4) shelter. Before drawing conclusions, here are two more observations from the above table.

The first other observation is that the expected monthly percentage change in the CPI for alcoholic beverages, tobacco products and recreational cannabis in a period of recession is the highest of all (.63 %). What could that mean? It could mean that people tend to drown their worries in drugs, during recessions, and the increase in the demand for this product group causes a rise in its price. The Gallagher family (who are some alcoholic fictional characters from the TV series Shameless) would retort: good times and bad, people drink and smoke. That is right, they just have to look at the above table to see that, during a period of expansion, the second highest monthly percentage change is that of the product group alcoholic beverages, tobacco products and recreational cannabis.

The second other observation is that the expected monthly percentage change in the CPI for shelter is lower during recession than during expansionary periods. This reminds that real estate crises often happen either when an economy is contracting or they cause this contraction, as during the 2007-08 subprime crisis.

The figure below shows the shares of the eight product groups in the monthly inflation rate during periods of expansion and recession. Shelter has the highest share during periods of expansion (28.8 %) and food has the highest share during periods of recession (26.7 %).

Figure: State-Dependent Shares of Eight Product Groups in the Monthly Inflation Rate

So, what makes life more expensive in Canada? All depends on the prevailing state of the business cycle. During periods of expansion, shelter followed by food and then transportation contribute the most to inflation. During this state of the business cycle, the expected percentage change in the CPI for shelter (.15 %) is lower than that of food and transportation, but its share in inflation is much higher. (To find the contribution of a product group the living cost, multiply its expected percentage change by its share in inflation.) During periods of recession, both shelter and food come after transportation and the product group alcoholic beverages, tobacco products and recreational cannabis. But, note that it is not everyone that consumes the later product group.

Dataset and Code

Inflation and Unemployment over the Business Cycle: Comparing evidence from Canada and the United States

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.

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.

Figure 2 : Empirical Distribution and State-Dependent Distributions of the the Inflation and Unemployment Rates, Canada, 2001:M3-2019:M12.

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.

Table 1: Expected values from a Markov-Dependent Mixture of Multivariate Normal models, Canada, 2001:M3-2019:M12.

	Expansion	Recession
Inflation Rate	.16 %	6.02 %
Unemployment Rate	.12 %	7.33 %

Table 2: Expected values from a Markov-Dependent Mixture of Multivariate Normal models, US, 2001:M3-2019:M12.

	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.

Dataset and Code

Inflation and Unemployment over the Business Cycle

I have analyzed the joint behavior of inflation and unemployment in Canada over a period of time ranging from March 2001 to December 2019 (226 months). My interest is to find out if there is any difference in the way these two variables behave during periods of economic expansion and contraction. This is done by fitting a two-state Markov-switching multivariate Student's t-model to the data.

The inflation and the unemployment rates have turned out to be more volatile over one state than the other. Decoding the states shows that the most volatile one corresponds to the periods of economic contraction that the Canadian economy experienced : the early 2000s crisis, the 2009 recession, and the oil price collapse of 2015. The volatility of the unemployment rate almost doubles during the high volatility state.

The figure below shows the densities of the inflation and the unemployment rates, and plot the marginal distributions of the fitted model. The second panel of this figure shows that the distribution of the unemployment rate is bimodal, with its lowest peak corresponding to the periods of economic expansion. It also appears that even though the Markov-switching multivariate Student's t-model has produced an accurate estimate of the expected value of the unemployment rate during periods of expansion, it overestimated its probability of occurence. The estimates for the inflation rate match the actual probabilities.

Figure : Densities and State-Dependent Distributions of the the Inflation and Unemployment Rates, Canada, 2001:M2-2019:M12.

The table below reports the expected values from the fitted models. The expected value of the inflation rate turns out to be higher during periods of expansion. On the other hand, the unemployment rate is lower during periods of expansion and higher during periods of contraction.

Table : Expected values from a Markov-Dependent Mixture of Multivariate Student's t-models, Canada, 2001:M2-2019:M12.

	Expansion	Recession
Inflation Rate	.16 %	6.01 %
Unemployment Rate	.12 %	7.28 %

The actual correlation between the inflation and the unemployment rates is positive during periods of economic expansion (.04) and negative during periods of contraction (-.02). This means that during periods of expansion, inflation is mostly driven by such supply-side factors as technological innovations, which lower prices and raise employment (decreasing unemployment, by so doing) at the same time. On the other hand, when the economy is contracting, inflation is mostly driven by factors affecting the demand-side of the economy such as preference shocks.

Dataset and Code