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UK Income Inequality and Taxation, 2000--2023: A $κ$-generalised Distribution Analysis

Samuel Forbes

Abstract

We analyse the UK income distribution from 2000 to 2023 using HMRC annual percentile data for both pre-tax and post-tax income. We fit a prefactor-adjusted $κ$-generalised specification to the data by weighted non-linear least squares and use inverse transform sampling to generate simulated income populations. The results suggest a redistribution of income shares over the period: the bottom 40\% appears to have increased its share, the middle-upper part of the distribution (50th--90th percentiles) lost share, the top 10\% remained broadly stable, and the top 1\% increased its share of pre-tax income. Because the modified specification is defined only above a positive threshold, conclusions concerning the lower tail should be interpreted with some caution. Using simulated 2023 pre-tax incomes to examine tax reform scenarios, we find that revenue-equivalent tax increases on high-income earners must be more than four times as large as comparable increases on lower-income earners. This suggests that, despite increased concentration at the top, the UK tax base remains driven primarily by the large number of taxpayers outside the very top of the distribution.

UK Income Inequality and Taxation, 2000--2023: A $κ$-generalised Distribution Analysis

Abstract

We analyse the UK income distribution from 2000 to 2023 using HMRC annual percentile data for both pre-tax and post-tax income. We fit a prefactor-adjusted -generalised specification to the data by weighted non-linear least squares and use inverse transform sampling to generate simulated income populations. The results suggest a redistribution of income shares over the period: the bottom 40\% appears to have increased its share, the middle-upper part of the distribution (50th--90th percentiles) lost share, the top 10\% remained broadly stable, and the top 1\% increased its share of pre-tax income. Because the modified specification is defined only above a positive threshold, conclusions concerning the lower tail should be interpreted with some caution. Using simulated 2023 pre-tax incomes to examine tax reform scenarios, we find that revenue-equivalent tax increases on high-income earners must be more than four times as large as comparable increases on lower-income earners. This suggests that, despite increased concentration at the top, the UK tax base remains driven primarily by the large number of taxpayers outside the very top of the distribution.

Paper Structure

This paper contains 9 sections, 34 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Fitting the Income Distribution
  3. Data
  4. $\kappa$-generalised Distribution
  5. Fitting
  6. Inverse Sampling
  7. Inequality
  8. Taxation
  9. Conclusion

Figures (11)

  • Figure 1: Nominal UK pre-tax and post-tax income percentiles, 2000--2023 (excluding 2009). Source: HMRC govuk_percentile_income_before_after_tax_2025.
  • Figure 2: Income fits (black dashed lines) to UK pre-tax and post-tax income percentiles for 2023 using the modified $\kappa$-generalised specification.
  • Figure 3: Income fits (black dashed lines) to UK pre-tax and post-tax income percentiles for 2023 using the modified $\kappa$-generalised specification, shown over four income intervals.
  • Figure 4: Gini and Theil indices of the simulated pre-tax and post-tax income populations over the years 2000--2023, excluding 2009.
  • Figure 5: Decile UK pre-tax and post-tax income shares from 2000--2023, excluding 2009.
  • ...and 6 more figures

Theorems & Definitions (3)

  • Definition 1: $\kappa$-exponential and $\kappa$-logarithm clementi2016distributionclementi2023kaniadakis
  • Definition 2: $\kappa$-generalised income distribution clementi2016distributionclementi2023kaniadakis
  • Definition 3: Modified $\kappa$-generalised specification