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

Does the Consumer Price Index Accurately Measure Changes in the Living Cost?

The consumer price index (CPI) in Canada declined by .66 %, in April this year compared to the previous month. On a year-over-year basis (i.e., compared to April 2019), it declined by .15 %. This is the first year-over-year decline in the CPI observed in the month of April, since 1992. The average year-over-year inflation rate (i.e., percentage change in the CPI) for the month of April is 1.74 %. I am wondering if the CPI or the inflation rate of April 2020 really makes sense as a measure for the living cost during the lockdown of the Canadian economy.

Basically, the CPI is a weighted average of the retail prices of the goods and services consumed by households. These goods and services are classified into eight product groups. The table below shows the averages and the values in April 2020 of the year-over-year percentage change in each of these eight product groups' CPI.

Table: Year-over-Year Percentage Change in CPI, Canada, 1992:M2-2020:M4.

Product group	Average	April 2020
Food	2.24 %	3.49 %
Shelter	1.87 %	1.32 %
Household operations, furnishings and equipment	1.26 %	.24 %
Clothing and footwear	.06 %	-4.40 %
Transportation	2.44 %	-4.39 %
Health and personal care	1.45 %	1.42 %
Recreation, education and reading	1.44 %	-.26 %
Alcoholic beverages, tobacco …	2.93 %	.41 %
All items	1.80 %	-.15 %

In April, the year-over-year percentage change in the CPI for food was 3.49 %, which is much higher than its historical average of 2.24 %. The year-over-year percentage change in the CPI for shelter was also high (1.32 %) but below its historical average of 1.87 %. These two product groups along with alcoholic beverages, tobacco products and recreational cannabis were mainly the goods deemed essential and mostly the only ones that were available to households, during the lockdown imposed by the federal and the provincial governments to stop the spread of the COVID-19.

The fact that their CPIs rose on a year-over-time basis and, at the same time, the year-over-year inflation rate fell casts a doubt on the use of the CPI for all items as measure of the cost of living. It is true that the CPI for clothing and footwear and that for transportation fell by 4.4 % on a year-over-year basis, which has dragged down the inflation rate, but these goods and services were not those people in Canada mainly purchased during the lockdown.

One also ends up at the same conclusion, looking instead at the monthly growth rates of the CPI for these product groups. In April 2020, the CPI for food grew by 1.12 % compared to March, the monthly CPI for alcoholic beverages, tobacco products and recreational cannabis grew by .12 %. Shelter was the only product group deemed essential whose CPI declined (-.34 %). One can still sustain that the .34 % decline in the CPI for shelter has caused a decline in the living cost during the lockdown, as both the year-over-year and the monthly inflation rates were suggesting. To rule out this possibility, I have computed the shares of each of the eight product groups in the monthly inflation rate. They are plotted in the pie chart below. (I have computed these shares by performing a linearly constrained optimization.)

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

It turns out that shelter is the product group that accounts for the largest share of the monthly inflation rate in Canada (27.5 %). Food accounts for 16.5 % while alcoholic beverages, tobacco products and recreational cannabis accounts for 5.7 %. Health and personal care accounts for the lowest share of the monthly inflation rate (4.7 %).

Even though shelter accounts for the largest share in the inflation rate, its contribution to the change in the living cost in April was only -.09 % (i.e., -.34 % x .275) whereas the contribution of food was .18 % (i.e., 1.12 % x .164) and that of alcoholic beverages, tobacco products and recreational cannabis was .01 (i.e., .12 % x .057). My conclusion is that the CPI is a good measure of the level of prices, but it cannot accurately measure the change in the living cost in periods of economic lockdown.

Dataset and Code

The Law of Demand Illustrated

Basically said, the law of demand is the economic prediction that the price of a good or a service increases along with its demand. To illustrate this, I am going to use the consumer price index (CPI) of traveler accommodation in Canada. This price index measures the change in the current price of the overnight or short stay in hotels or motels in comparison to a reference year.  

CPI of Traveler Accommodation, Canada, 2007:M1-2014:M6 (2002=100), Source: Statistics Canada

Each year, from April, the price of the travel accommodation starts increasing gradually to reach a peak in August. Thereafter, it starts falling progressively to reach an off-peak in December. It then resumes increasing in January to finally fall again in March.

Obviously, the factor that could explain these periodic fluctuations in the price of the traveler accommodation is the tourist season. The tourist season in Canada is between April and October. During that period, bookings and tourist arrivals in hotels or motels soar with peaks in summer. As a consequence of the increase in the occupancy rate in the industry, the price charged also increases.

February is also a busy month in the industry due to the success of winter festivals and sport activities. 

The Consumer Price Index across Canada

To measure change in the cost of living, Economists use the consumer price index (CPI). This statistic is a weighted average of the prices of a fixed and representative basket of items consumed by urban households. These items include, inter alia, food, shelter, clothing, housing, transportation, health and personal care, and education.  The CPI indicates the average percentage change in prices at a given time in relation to a base year. In this article I give a brief portrait of the evolution of the CPI across the ten provinces and three territories of Canada over a period of 422 months ranging from September 1978 to October 2013.  I point out the parts of our country where the change in the cost of living tends to be higher than the national average.

The provinces and territories of Canada are:

• The Atlantic Provinces: Newfoundland and Labrador (NL), Prince Edward Island (PE), Nova Scotia (NS), New Brunswick (NB),
• Central Canada: Quebec (QC), Ontario (ON),     
• The Prairie Provinces: Manitoba (MB), Saskatchewan (SK), Alberta (AB),
• The West Coast: British Columbia (BC),
• The Northern Territories: Yukon (YT), the Northwest Territories (NT), and Nunavut (NU).

The Evolution of Prices across Canada

The figure below plots the national CPI and those of all the provinces and territories grouped by region. One can notice that:

Figure: Log of Consumer Prince Index, All Items, 2011 basket, 2002=100, Canada, Provinces and Territories, 1978:M9-2013:M10, Data Source: Statistics Canada.



 

• In all over Canada, prices are trended upward,
• At times, prices in some provinces and territories are lower or higher than the national average.


The Deviation of Provincial and Territorial CPIs from the National Average

I have analyzed the percentage deviation of each province’s and territory’s CPI from the national average. In Table 1, below, I have reported both the means and standard deviation of these series.

Table 1, Means and Standard Deviations of the Difference between the Log of Provinces’ and Territories’ CPIs and the Log of the National CPI, 1978:M9-2013:M10.



After some statistical tests performed on the means reported in Table 1, I find out that changes in the cost of living tend to be

• Above the national average in Newfoundland and Labrador, the Prince Edward Island, Nova Scotia, New Brunswick, Quebec, British Columbia, Yukon, and the Northwest Territories,  
• Below the average in Ontario, Manitoba, Saskatchewan,  Alberta, and Nunavut.

I compare my results to the ranking of the most expensive cities in Canada. I am interested in finding out whether the highest changes in the cost of living take place in provinces whose major cities are ranked among the ten most expensive in the country.  

Table 2: The Most Expensive Cities inCanada

It appears in Table 2, above, that three cities in Ontario, three others in Alberta, and one city in Saskatchewan appears in the top ten list. But these three provinces are parts of Canada where the change in the cost of living tends to be lower than the national average. This leads me to conclude that the highest increases in the cost of living are not always taking place in such most expensive provinces as British Columbia but also in more affordable places such as the Atlantic Provinces or part of the Northern Territories.

 

The relationship between the Provincial and the National CPIs

Table 3, below, displays the partial correlation coefficient between the provincial and national CPIs. The partial correlation between the national CPI and that of a given province measures the intensity of the relation between these two variables isolating the effects of other provinces’ CPIs.

Table 3: Partial Correlation Coefficients between the Provincial and National CPIs, Canada, 1978:M9-2013:M10.

The partial correlation coefficients with the national CPI are positive across all provinces.  However the partial correlation between the national CPI and those of the Prince Edward Island and New Brunswick are weak and turn out not to be statistically significant. This means changes in prices in these two provinces do not much influence the national average.  To better understand this latter evidence I display in Table 4 below the shares of each of the ten provinces’ gross domestic product (GDP) in the national GDP.  One can see that the GDP of the Prince Edward Island and New Brunswick represent respectively, on average, .31 % and 1.91 % of the national GDP. Moreover, without any surprise, one can relate the strength of the partial correlation to the importance of the share of the provincial GDP.  

Table 4: Average Percentage Share of the Provincial GDPs in the National GDP, Canada, 1981-2010, Annual

Observe from Table 4 that the ten provinces account for 99.48 % of the national GDP. The other .52 % is the share of the three territories and Canadian residents living outside the country.

Another insight from the results in Table 3 is that a monetary policy aiming at fighting in inflation, i.e., a generalized increase in price level, nationwide will not have the same effects in all the provinces. It might even be ineffective or just produce little effects in such places as the Prince Edward Island and New Brunswick.
 

Summing up,

• Changes in the price level are generally above the national average in the Atlantic Province, Quebec, the West Coast, and part of the Northern Territories.
• A monetary policy aiming at curbing inflation will not have the same effects across all Canada and may be ineffective some Atlantic Provinces.