Forecasting the UK top 1% income share in a shifting world

Abstract

UK top income shares have varied hugely over the past two centuries, ranging from more than 30% to less than 7% of pre-tax national income allocated to the top 1 percentile. We build a congruent dynamic linear regression model of the top 1% income share allowing for economic, political and social factors. Saturation estimation is used to model outliers and trend breaks, proxying underlying structural changes driving income inequality in the UK. We use the model to forecast the top 1% income share over the last 15 years, and compare to a range of forecast devices. Despite a well-specified constant parameter model conditioning on significant explanatory variables, the best performing forecasts are obtained from a random walk and a smoothed random walk. These results are explained by the presence of shifts in the income share over the forecast period, resulting in forecasts from equilibrium correction models converging to the wrong equilibrium. Our best prediction for 2026 based on the most recent data from 2021 (a 5-year ahead projection) is that the pre-tax top 1% income share will remain at the most recent realized value of 12.7%, but there is a large degree of uncertainty, with a 95% confidence band ranging from 10% to 15.7%.