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 Relationship between Unemployment Rate and Economic Growth across Canada

Among the ten provinces of Canada, Quebec showed the highest unemployment rate, in April 2020 (17 %). In January and February, the province of Quebec along with Manitoba and British Columbia recorded the lowest unemployment rate in Canada. In February 2020, the level of the unemployment rate in Quebec was 4.5 %, the lowest since 1976. The extent of the spread of the COVID-19 explains the high unemployment rate in Quebec. As a matter of fact, Quebec accounts for more than half of the confirmed cases of COVID-19 in Canada (44 197 cases out of 79 502, as of May 20). Most of these cases (about half) are in the region of Montreal that generates the third of Quebec's gross domestic product (GDP).

In the Prairie Provinces (i.e. Manitoba, Saskatchewan, and Alberta), the unemployment rates in April 2020 nearly doubled, compared to their historical averages (see Figure 1). For example, in Alberta, the unemployment rate was 13.4 % in April, versus an historical average of 6.4 %. In April, the unemployment rate in Alberta was the highest in the Prairies and also a record high in the history of this province.

Figure 1: Unemployment Rates across Canada.

The picture of the situation is different in Atlantic Canada (i.e. Newfoundland and Labrador, Prince Edward Island, Nova Scotia, and New Brunswick). In Newfoundland and Labrador, the unemployment rate in April 2020 (15.9 %) was very close to its historical average (16 %). This reminds that unemployment rate has often been very high in this province. (See my blogpost Unemployment Rate in Newfoundland and Labrador.) Prince Edward Island is the only province in Canada where the unemployment rate during the outbreak of COVID-19 has been lower than the historical average. As of May 20, only 27 cases of COVID-19 have been found in this province.

Throughout Canada, three economic sectors have been mainly affected by the lockdown restrictions: (1) accommodation and food services, (2) construction, (3) forestry, fishing, mining, quarrying, oil and gas. In the sector of accommodation and food services, between January and April 2020, the unemployment rate rose from 9 % to 44.7 % in Quebec, from 2 % to 30.9 % in Manitoba, from 4.7 % to 35 % in Saskatchewan, and from 5.9 % to 38.9 % in British Columbia.

In the sector of forestry, fishing, mining, quarrying, oil and gas, between January and April 2020, the unemployment rate rose from 8.7 % to 27.9 %, in Quebec. In the construction sector, while in Quebec the unemployment rate rose from 11.3 % in January to 40.3 % in April, it only rose from 5.4 % to 14 %, in Ontario.

In a previous post [here], I have used the Okun's law to predict GDP growth from changes in unemployment rates using data for Canada as a whole. In this post, I take things a bit further by estimating the Okun's law using instead data of the ten provinces (panel data). I have kept the short-run effect of unemployment on real GDP unchanged across the provinces and allow for heterogeneity only in the intercept. (This is referred to as a least squares dummy variable model, in econometrics.)

Figure 2 shows as scatter plot the changes in the annual unemployment rates and the corresponding GDP growth rates in the ten provinces, between 1981 and 2018. The blue line in this figure represents the predictions from the Okun's law. The estimate of the short-run effect of unemployment on real GDP is -1.45, which means a 1 percentage point increase in unemployment rate causes a 1.45 % decrease in real GDP. This estimate is close to the one obtained previously using aggregate data for Canada (-1.4). But, the explanatory power of this panel data model is much higher. It explains 58.5 % of the variability in the data versus 35 % for the model that uses aggregate Canadian data.

Figure 2: Okun's Law: Percentage Point Change in Unemployment Rate and Real GDP Growth Rate, Canadian Provinces, 1981-2018.

The table below reports the predictions of the real GDP growth rates for the ten provinces for the first quarter of 2020 and April 2020.

Table: Predictions of real GDP Growth Rates for the Provinces of Canada based on a Panel Data Model.

Province	First Quarter of 2020	April 2020
Newfoundland and Labrador (NL)	1.4 %	-4.1 %
Prince Edward Island (PE)	2.3 %	-.9 %
Nova Scotia (NS)	1.6 %	-2.6 %
New Brunswick (NB)	1.9 %	-4.7 %
Quebec (QC)	.9 %	-11.2 %
Ontario (ON)	1.5 %	-2.8 %
Manitoba (MB)	1.8 %	-5.2 %
Saskatchewan (SK)	.7 %	-3.7 %
Alberta (AB)	1.9 %	-3.8 %
British Columbia (BC)	1.5 %	-3.8 %

The Okun's model that uses panel data predicts a positive real GDP growth across Canada for the first quarter of 2020. This contrasts with the predictions I made previously using the aggregate Canadian data. On the other hand, it predicts negative growth rates across Canada for April 2020. However, it is worth pointing that these forecasts do not take into account the effects of the various economic stimulus programs initiated by the federal and the provincial governments in response to COVID-19.

Dataset and Code