Methodology

We use 2 bottom-up statistical methods to estimate the high wealth income tax gap – the 'extreme value theorem' regression model for individuals and the multi-stage 'logistic linear regressions' model for companies. We step through the following methods and results and combine them in Table 1.

Calculation – high wealth individuals

There are 4 steps in the extreme value theorem to estimate the high wealth individuals tax gap.

Step 1: Identify the extreme population

Amendments for high wealth individual taxpayers follow a power law distribution, with the majority of total tax amendments in value terms represented by a small number of amended income tax returns.

We rank the amendments in descending order and identify the point where the cumulative sum of positive amendments is equal to or less than the total negative amendments.

We remove all these small amendments, which have no impact on the net value of total amendments. The remaining amendments are referred to as the 'extreme values'.

We calculate the number of extreme values as a ratio of all amendments to be used for extrapolation purposes in step 2.

Step 2: Estimate the unreported tax amount

We transform the amendment data of the extreme population to estimate a linear relationship between the value and rank of the amendments using a regression approach.

To estimate the unreported tax amount, we then extrapolate the relationship to the number of taxpayers expected to contribute to the extreme values in the wider population.

Step 3: Apply a non-detection uplift factor

We need to account for imperfections in the process that could lead to the final gap estimate not reflecting the true tax gap. To account for non-detection, we apply an uplift factor to the unreported tax amount in step 2.

Step 4: Consolidate the gap estimates

We calculate the gross gap by adding the:

• unreported amounts from step 2
• non-detection uplift from step 3
• non-pursuable debt.

We calculate the net gap by subtracting the total amendment amount from the gross gap. Then we add the net gap to the expected collections to estimate the total theoretical liability.

Summary of the estimation process – high wealth individuals

Table 2 shows the:

• individuals population count at step 1
• dollar values at steps 2 to 4.6
• percentage figure for the gross and net gaps at steps 4.7 and 4.8.

*Projected years

Calculation – high wealth companies

The following 5 step bottom-up regression is applied to estimate the High Wealth-linked companies tax gap.

Step 1: Establish a logistic regression trend

We analyse the income tax return data of companies that have been subject to amendment activities and adjust the data to account for selection bias. We identify the relevant characteristics of companies in general that would contribute to the prediction of whether a company has a tax gap.

Based on these characteristics, we assign each company a unique probability of having a tax gap. We then model each company to be compliant or non-compliant through a Monte Carlo simulation.

Step 2: Establish a linear regression trend

We analyse tax return data of known non-compliant companies to identify characteristics of companies that would contribute to the prediction of the tax gap size. We also apply weights to account for selection bias. Then we apply linear regression to each company to estimate the potential size of the gap.

The key difference between steps 1 and 2 is that step 1 calculates the likelihood of a company having a tax gap while step 2 calculates the size of each company's potential tax gap.

Step 3: Combine the results from the 2 regressions

We calculate the estimated unreported tax amount for each simulation by adding the step 2 non-compliance amount to the predicted non-compliance companies in step 1. We estimate total unreported tax (including amendments) by taking an average of the results from 20,000 simulations.

Step 4: Apply a non-detection uplift factor

We uplift the estimates preceding this step to account for non-compliance that isn't detected. This ensures that the final estimate is not understated.

Step 5: Consolidate the tax gap estimates

We calculate the gross gap by adding up the:

• unreported amounts from step 3
• non-detection uplift from step 4
• non-pursuable debt.

We calculate the net gap by subtracting the total amendment amount from the gross gap. We then add the net gap to the expected collections to estimate the total theoretical liability.

Summary of the estimation process – high wealth companies

Table 3 shows the:

• dollar values in millions at steps 1 to 5.6
• company population count at step 5.7
• percentage figures for the gross and net gaps at step 5.8 and 5.9.

*Projected years

Find out more about our overall research methodology, data sources and analysis for creating our tax gap estimates.

Limitations

The following caveats and limitations apply when interpreting this tax gap estimate:

• There is a considerable delay between an income year and the completion of our compliance activities for that year. This means gap estimates are subject to revisions for a considerable period. Amendment results for companies and individuals are projected for 2019–20 to 2021–22. They are expected to be subject to revisions overcoming years.
• Provisions are made for non-pursuable debt for all years, excluding 2017–18.
• There is no independent data source that can provide a credible or reliable macroeconomics-driven estimate (unlike indirect taxes).
• The true extent of non-detection is unknown and extremely challenging to measure. There is no international proxy we can apply to the individuals or companies in this population.

Updates and revisions to previous estimates

Each year we refresh our estimates in line with the annual report. Changes from previously published estimates occur for a variety of reasons, including:

• improvements in methodology
• revisions to data
• additional information becoming available.

Figure 2: Current and previous net high wealth income tax gap estimates, 2012–13 to 2021–22

This data is presented in Table 4 as a percentage.

Table 4: Current and previous net high wealth income tax gap estimates, 2012–13 to 2021–22