Proportional attrition

This page explains how complex fluctuations in stakeholder counts are handled in the Regulatory Costing Calculator, specifically in situations where the annual stakeholder counts have been entered manually.

Note: Proportional attrition only applies in situations where the stakeholder count first increases and then decreases over time. If the analysis involves stakeholder counts that are always growing or always shrinking, then proportional attrition does not apply - those cases are handled more simply. Proportional attrition is only implemented to handle complex/irregular patterns in the stakeholder count, which are possible when users enter their stakeholder counts manually.

Using automatic growth

When using automatic growth in the RCC, users enter the initial stakeholder count and an annual growth rate. This rate can be positive, zero, or negative. If the growth rate is negative, then there are no new entrants throughout the analytical period, so the reduction in each year is always achieved by shrinking the count of the existing stakeholders. For example, the count could start at 100 and decrease by 1% every year. The 1% reduction would always come from those in the initial group of 100.

Using manual growth

With manual entry, the stakeholder count for a particular group could involve any mix of increases and decreases throughout the analytical period. If the count fluctuates between increases and decreases, then a method is required to determine the breakdown of a reduction in the stakeholder count between the existing stakeholders and the new entrants. For example, if the stakeholder count increases in Year 2 and Year 3 but then decreases in Year 4, it is necessary to decide whether the decrease comes from the existing stakeholders, the new entrants, or a mix of both. There are a few different methods that could be employed, with each having pros and cons related to i) expected realism; ii) analytical complexity; and iii) data requirements.

In theory it would be possible to assume that a reduction in the stakeholder count always comes from existing stakeholders ('first in, first out') or that it always comes from the new entrants ('last in, first out'). These methods are relatively low in analytical complexity, but they may not be realistic and they may not be justified without supporting data. They also may break down in certain edge cases.

The method that is used in RCCv4 is called "proportional attrition", explained below. This method has a moderate level of realism and analytical complexity, and no additional data requirements.

Conceptual explanation

When the stakeholder count increases between any two years, that means there are some new entrants (i.e., that is how "new entrants" are defined in the RCC). The new entrants in each year form new "cohorts." Proportional attrition is based on an analysis of changes in cohort sizes over time. If the stakeholder count shrinks or stays the same between any two years, that means there are no new entrants that year. In these situations you could say that there is no new cohort, or that there is a new cohort of size 0.

At a high level, for each year in the analysis, a weight between 0 and 1 will be calculated. These weights will be multiplied by the business count of each cohort to see how many of them make it to the subsequent year. After the weight has been applied, each cohort will either stay the same size (if there is positive or zero growth in the stakeholder count) or it will shrink (if there is a reduction in the stakeholder count). Once a weight less than 1 has been applied, all affected cohorts will be reduced permanently. Subsequent new entrants will form new cohorts, but they do not 'top up' previous cohorts that have reduced in size.

The weight for each cohort in each year is determined by first calculating the year-over-year percentage change in the stakeholder count for that group. Between any two years, if there is positive or zero growth in the stakeholder count (i.e., not a reduction), then all cohorts stay the same size. In these cases the percentage change is set to 0 since the previous cohorts are not actually going to change (rather, new cohorts will be formed), so the previous cohort counts are simply multiplied by 1. On the other hand, if there is a decrease in the stakeholder count between any two years, then all previous cohorts are multiplied by [1+(Percentage Change in Stakeholder Count)], and this latter term will be a value less than 1. Multiplying each cohort by a value less than 1 will shrink them all, and the sum of the reductions in each cohort will equal the total reduction in the count for that stakeholder. This method of distributing the reduction in the stakeholder count means that each cohort shrinks proportionally, relative to its share of that group's stakeholder count in the previous year. This is the meaning behind the term "proportional attrition."

Example

For a particular stakeholder group, at the end of Year 1 the count is 100 and at the end of Year 2 the count is 110. There are 10 new entrants in Year 2, so Cohort 1 is 100 and Cohort 2 is 10. Imagine that the count drops to 99 at the end of Year 3. This would be a 10% reduction compared to the count at the end of the previous year (99/110 - 1). There are no new entrants in Year 3, so Cohort 3 = 0. Cohorts 1 and 2 are both multiplied by 0.9 (1 - 0.1), so Cohort 1 shrinks from 100 to 90 (100*0.9) and Cohort 2 shrinks from 10 to 9 (10*0.9). Combined, the sum of the reductions in Cohort 1 and Cohort 2 is 11 (10 + 1), which equals the reduction from 110 to 99 in the stakeholder count. More stakeholders left Cohort 1 than Cohort 2 because Cohort 1 is bigger. In Year 4, if the stakeholder count drops again, the new reduction would be applied to the remaining counts from Cohorts 1 and 2. In other words the reductions are applied cumulatively (i.e., they "stack").

Technical explanation

The RCC calculations keep track of how many stakeholders from each cohort are remaining in every period of the analysis, because the same cohort(s) may experience a reduction multiple times.

In every year in the analysis and for each cohort, a cohort weight is calculated. This weight is the product of all [1+(Percentage Change in Stakeholder Count)] values, after that cohort has entered the market. To reiterate, increases in the stakeholder count form new cohorts, so in these cases the percentage change for previous cohorts is 0. When the stakeholder count increases, the remaining counts from each cohort are simply multiplied by 1 (meaning they stay the same size).

In Excel, these cohort weights are calculated using the PRODUCT function. For example, the number of Existing Stakeholders at the end of Year 4 could look like this: (Initial Count at Registration)*PRODUCT(1, 1, 0.9, 0.8). In successive years in the analysis, more [1+(Percentage Change in Stakeholder Count)] terms are included in the PRODUCT function. This ensures that successive reductions are applied cumulatively. As more values are added into the PRODUCT function, the cohort weight will either stay the same as it was in the previous year, or it will shrink. If there is an increase in the stakeholder count, then a new value of 1 is added to PRODUCT, which does not change the result compared to the previous year. Importantly, this means that any prior reductions are carried forward; e.g., PRODUCT(1, 0.9, 1). If there is a decrease in the stakeholder count, then a new value less than 1 is added to the product, which shrinks each affected cohort relative to its count in the previous year.

Reminder

If the stakeholder count decreases every year in the analysis, then proportional attrition is not needed because all of the reductions would come from Cohort 1. If the stakeholder count increases every year in the analysis, then proportional attrition is not needed because there would be no reductions to distribute among the existing stakeholders and new entrants.