Index construction - 2020

The methodology of these indexes follows a modified version of the methodology used to construct the Oxford Stringency Index.

For each indicator listed in Table 1, a value is assigned using an ordinal scale ranging from least restrictive (value of 0) to most restrictive (values of 2 to 6, depending on the indicator). The values are recorded based on a consistent set of coding requirements^{Footnote 1}. These requirements were determined based on values taken from Oxford and the joint evaluations of the project team, and they reflect consensus decisions and revisions that arose as coding progressed. In addition to the ordinal scales, each policy indicator has a geographic scalar indicating whether the policy is general (1) or targeted to a particular health region (0) within a province.

Once restrictions are differentiated by vaccine status, the restriction values are divided between the vaccinated and unvaccinated populations, and recorded based on the coding requirements for the separate restrictions announced by the province. The restrictions for the vaccinated and unvaccinated populations can then be reported separately. Additionally, the value for the total population can be constructed as the weighted sum of the vaccinated and unvaccinated variables. The weights are based on the vaccinated and unvaccinated proportions of the population eligible for vaccination.

To produce an index for a specific indicator, the ordinal values are scaled to fall between 0 and 100 using the largest ordinal value. In the Oxford approach, the changes between levels of restrictions are equal so that the coding sequence (0,1, 2, 3, 4) becomes (0, 25, 50, 75, 100), such that a unit change in the severity of the index corresponds to an increase of 25 percentage points.

However, in terms of their effects on the economy, mental health or societal stress, it is likely that stronger restrictions have a larger impact. To incorporate the increasing impact of progressively tighter restrictions, the present indicator-specific indexes are calculated after squaring the ordinal values. This means that the ordinal values (0, 1, 2, 3, 4) are rescaled (0, 1, 4, 9, 16) before being normalized (0, 6.25, 25.00, 56.25, 100.00). As a consequence, changes in the indexes are accentuated, particularly for periods when tighter restrictions come into effect.

Formally, the indicator-specific indexes $\left(I_{j,t}\right)$ are calculated as follows:

$I_{j,t}=100\frac{{V^2}_{j,t}-0.5(F_j-f_{j,t})}{{N^2}_j}$

where $V_{j,t}$ is the recorded policy value on the ordinal scale. $f_{j,t}$ is the recorded binary flag for indicator $j$ and takes a value of 1 if the restriction is general to the province or territory and a value of 0 if the restriction is targeted to a specific city or health region. $F_j$ is a binary variable and takes a value of 1 if that indicator has a flag variable and takes a value of 0 if the indicator does not have a flag variable.${\mathrm{ \; N}}_j$ is the maximum ordinal value of the indicator.

When policy is different for the vaccinated and unvaccinated populations, the indicator-specific indexes $\left(I_{j,t}\right)$ are calculated as follows:

$I_{j,t}=100\times (P_{vacc\_rate}\times \frac{{V^2}_{j,t,vacc}}{{N^2}_j}+(1-P_{vacc\_rate})\times \frac{{V^2}_{j,t,unvacc}}{{N^2}_j})$

where $P_{vacc\_rate}$ is the vaccination rate for fully vaccinated people as a share of the eligible population, $V_{j,t,vacc}$ is the recorded policy value for the vaccinated population, and $V_{j,t,unvacc}$ is the recorded policy value for the unvaccinated population.

After calculating normalized index values for each indicator, the COVID-19 restrictions index for a province at time $t$ is calculated by taking the average of the 15 policy-specific indexes:

$Covid-19RestrictionInde{x}_{j,t}=\frac{1}{k}\sum _{i=1}^k\left(I_{j,t}\right) , k=1,...,15$