• ## Methodology

The high wealth income tax gap estimate is derived through applying two bottom-up statistical methods:

• 'extreme value theorem' regression model for individuals
• two-stage logistic and linear regressions for companies (the 'logistic linear regressions' model).

The following sections step through the method and results for the two separate models, before being combined as shown in Table 1.

### Calculation – high wealth individuals

There are four steps in using 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 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

The gross gap is calculated by adding the unreported amounts from Step 2, non-detection uplift from Step 3 and non-pursuable debt. The net gap is calculated by subtracting the total amendment amount from the gross gap. The net gap is then added to the tax paid to estimate the total theoretical liability.

For 2015–16 and onwards, the gross gap estimates are projected using the average gross gap percentage for 2012–13 and 2013–14. This is due to the delay between the lodgment and amendment of tax returns.

#### Summary of the estimation process – high wealth individuals

Table 2 displays the individuals population count at Step 1 and dollar values at Steps 2 to 4.6. Steps 4.7 and 4.8 show the percentage figure for the gross and net gaps.

Table 2: Summary of estimation process for high wealth individuals

Step

Description

2012–13

2013–14

2014–15

2015–16

2016–17

2017–18

1

Total population

9,825

9,856

9,861

9,865

9,840

9,709

2

Total expected amendments (\$m)

171

228

290

242

260

284

3

Non-detection (\$m)

115

146

184

167

174

191

4.1

Non-pursuable debt (\$m)

2

2

2

2

2

2

4.2

Gross gap (\$m)

288

376

476

412

436

476

4.3

Amendments (\$m)

102

111

68

123

125

94

4.4

Net gap (\$m)

186

265

408

288

311

383

4.5

Tax paid (\$m)

3,036

4,126

4,224

4,416

4,671

5,062

4.6

Total theoretical liability (\$m)

3,221

4,391

4,632

4,704

4,982

5,445

4.7

Gross gap (%)

8.9

8.6

10.3

8.8

8.8

8.8

4.8

Net gap (%)

5.8

6.0

8.8

6.1

6.2

7.0

### Calculation – high wealth companies

There are five steps involved in applying logistic linear regressions to the company population:

#### Step 1: Establish a logistic regression trend

We analyse the income tax return data of companies that have been subject to amendment activities. We apply weights to the data to account for selection bias in our data. We identify the relevant characteristics of companies in general that would contribute to the prediction of whether or not a company has a tax gap.

Based on these characteristics, each company is assigned a unique probability of having a tax gap. Each company is then modelled to be compliant or non-compliant through a Monte Carlo simulation.

#### Step 2: Establish a linear regression trend

We analyse the income tax return data of companies known to be non-compliant, to identify relevant characteristics of companies that would contribute to the prediction of the size of a tax gap. Weights are also applied to account for selection bias. The linear regression is then applied to each company to estimate the potential size of the tax 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 two regressions

The estimated unreported tax amount for each simulation is calculated 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 is not detected. This ensures that the final estimate is not understated.

#### Step 5: Consolidate the tax gap estimates

The gross gap is calculated by adding up the unreported amounts from Step 3, non-detection uplift from Step 4 and non-pursuable debt. The net gap is calculated by subtracting the total amendment amount from the gross gap. The net gap is then added to the tax paid 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. Step 5.7 shows the company population count. Step 5.8 and 5.9 show the percentage figures for the gross and net gaps.

Table 3: Summary of estimation process for high wealth companies

Step

Description

2012–13

2013–14

2014–15

2015–16

2016–17

2017–18

1

Total population

15,414

16,051

16,912

17,897

18,496

18,946

1–3

Unreported tax including amendments (\$m)

193

221

237

247

282

282

4

Non-detection (\$m)

133

146

158

164

186

190

5a

Non-pursuable debt (\$m)

1

1

1

2

1

1

5b

Gross gap (\$m)

327

367

396

413

468

473

5.c

Amendments (\$m)

64

44

46

37

48

48

5.d

Net gap (\$m)

263

323

350

375

421

425

5.e

Tax paid (\$m)

3,376

3,816

4,288

4,585

4,947

5,111

5.f

Total theoretical liability (\$m)

3,639

4,139

4,638

4,960

5,368

5,536

5.g

Gross gap (%)

9.0

8.9

8.5

8.3

8.7

8.5

5.h

Net gap (%)

7.2

7.8

7.6

7.6

7.8

7.7

### 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 relating to that year. This means that gap estimates may remain subject to revisions for a considerable period. Company results for 2016–17 onwards, and individual results for 2015–16 onwards are projected. They are expected to be subject to revisions over coming years.
• 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 is extremely challenging to measure. There is no international proxy that can be applied to the individuals or companies in this population.

### Updates and revisions to previous estimates

We published the high wealth income tax gap for the first time in March 2020. The chart below shows that the updated net gap estimates this year are largely similar to the estimates published last year. This is except for 2014–15 which has been revised up by around 1.1 percentage points from an improvement in the model that captures amendment amounts more accurately.

Figure 2: Current and previous net high wealth income tax gap estimates, 2011–12 to 2017–18

This data is presented in Table 3 as a percentage.

Table 4: Current and previous net high wealth income tax gap estimates, 2011–12 to 2017–18

Year

2011–12

2012–13

2013–14

2014–15

2015–16

2016–17

2017–18

2019

8.8%

6.6%

7.7%

7.1%

7.3%

7.7%

n/a

2020

n/a

6.5%

6.9%

8.2%

6.9%

7.1%

7.4%