Research and analysis

Impacts of 2018 to 2019 Scottish Income Tax changes on intra-UK migration and labour market participation

Published 24 April 2024

1. Abstract

Our paper estimates changes in labour market participation and intra-UK cross-border migration of Scottish taxpayers following the Income Tax rate changes in Scotland in the tax year 2018 to 2019. These changes increased the average tax rate for higher earners and decreased the average tax rate for lower earners. We combine a difference-in-differences, supplemented with propensity score matching, and 2-stage-least-squares technique to HMRC’s Real Time Information (RTI) Pay As You Earn (PAYE) and Self Assessment data. We estimate labour market participation and intra-UK cross-border migration semi-elasticities across income bands.

For labour market participation, we use England, Wales and Northern Ireland, the rest of the UK (rUK), as a control group for Scottish taxpayers. For cross-border migration, we exploit the variation in the intensity of the tax change in Scotland and compare taxpayers across different income bands. Our results show no evidence of a change in labour market participation. We find some evidence of a decrease in net cross-border migration (from rUK to Scotland) in the first year of the policy change for Scottish taxpayers above the Higher rate threshold, with semi-elasticities ranging from 0.19 to 2.56 which increase with income.

2. Acknowledgements and disclaimer

The analysis presented in this report would not have been possible without the input of colleagues both within and outside of HM Revenue and Customs (HMRC). We are particularly grateful for the constructive comments provided by academics from both the Fraser of Allander Institute and the University of Westminster. We also thank officials from the Scottish Government, the Scottish Fiscal Commission and the Welsh Government, who have provided comments and constructive challenge at various stages of the project. The views expressed in this report are those of the authors and do not necessarily represent those of HMRC. Any remaining errors are the author’s own responsibility.

Authors: E. Nilsson; D. Cox; N. Duncan; and T. Glinert.

3. Executive summary

From the tax year 2018 to 2019, the Scottish Government introduced 2 new Income Tax bands, as well as increasing the rates for 2 of the existing bands. As a result, Scottish taxpayers on higher incomes experienced an increase in the proportion of income which is paid in tax, whilst taxpayers on lower incomes experienced a decrease in the proportion of income which is paid in tax.

In 2021, HM Revenue and Customs (HMRC) estimated the change in taxable income declared in Scotland in response to the introduction of the 5-band system in Scotland in 2018 to 2019. Our paper extends that analysis and attempts to estimate behavioural responses that relate to individuals withdrawing from the Scottish workforce completely. Specifically, we consider 2 key responses: changes in labour market participation and changes in intra-UK cross-border migration, which is defined as movements between Scotland and the rest of the UK (rUK).

For labour market participation, we compare Scottish taxpayers to a group of similar taxpayers from rUK where Income Tax rates remained the same. Taxpayers are grouped into 5 income bands based on their average yearly income before the introduction of the policy (from the tax year 2014 to 2015 to the tax year 2017 to 2018). These income bands are mostly aligned to the Scottish 5-band system, apart from the Higher (HR) and Top rate (TR) which are separated at £100,000 in order to increase the number of observations. For each income band, we measure the percentage point change in the proportion of the population in work, from the year before the policy was implemented to the year of and the year after implementation.

For intra-UK cross-border migration, we group individuals into income bands based on their income in the year before the policy change (2017 to 2018). These income bands are aligned to the Scottish 5-band system. We only include individuals working in each year of the data. For each income band, we measure the percentage point change in the proportion of the population migrating from the year before the policy was implemented to the year of and one year after implementation. Given that different income bands experienced varying degrees of changes in the proportion of income retained after tax, we compare taxpayers in one income band to similar taxpayers in another income band that experienced a different change in the proportion of income retained after tax.

We use HMRC’s Real Time Information (RTI) Pay As You Earn (PAYE) and Self Assessment data and measure labour market participation and cross-border migration changes separately. We estimate the percentage point change in the probability of participating or migrating relative to a 1% change in the proportion of income retained after tax (also known as the average rate of retention or ARR, which is equivalent to 100% minus the average tax rate or ATR). This is known as a semi-elasticity.

We find no evidence of a change in labour market participation following the Scottish Income Tax changes. The semi-elasticity estimates, which capture the percentage point change in labour market participation relative to the percentage change in the ARR, are not significantly positive. The estimates are generally close to 0 but the confidence intervals are in most cases wide suggesting that the results may not be precise. Therefore, while our results suggest no changes in labour market participation following the Scottish Income Tax changes, we conclude that the true changes are uncertain and that we have not been able to detect if there was a change. We consider limitations to the analysis in the discussion section (6.6).

We find some evidence of a decrease in net cross-border migration to Scotland for taxpayers earnings above the Higher rate threshold (HRT) following the Scottish Income Tax changes. The semi-elasticity estimates, which capture the percentage point change in net cross-border migration relative to the percentage change in the ARR, are approximately 2.56 for taxpayers above £500,000 in taxable income and 0.19 to 0.44 for taxpayers below £500,000 in taxable income in 2018 to 2019 (the year of the policy change). The semi-elasticities are generally increasing with income.

A semi-elasticity of 2.56 means that for a 1% decrease in the ARR of taxpayers earning above £500,000 you might expect to see a 2.56 percentage point increase in the probability of Scottish taxpayers earning above £500,000 moving from Scotland to rUK. For all Scottish taxpayers above the HRT, we estimate that our results correspond to approximately 1,030 taxpayers or £61 million in Scottish non-savings non-dividend (NSND) tax receipts moving from Scotland to rUK.

Our results are consistent with the academic literature and the findings remained fairly stable when adopting different methodological approaches. While the semi-elasticities are statistically significant, the confidence intervals are generally wide suggesting some uncertainty in the precise magnitude of the estimates. Additionally, the results are only reliable to the extent to which they are driven by the Scottish Income Tax changes in 2018 to 2019. Limitations to the analysis are considered in the discussion section (7.6).

We find no conclusive evidence of persistence in the changes in cross-border migration. The headline semi-elasticity estimates are generally insignificant in 2019 to 2020 (one year after the policy change). For individuals on lower incomes, we find no conclusive evidence of changes in cross-border migration following the Scottish Income Tax changes as there is a lot of variation in the results when adopting different methodological approaches.

4. Introduction and policy background

Income Tax has been partially devolved to Scotland since the tax year 2016 to 2017 and to Wales since the tax year 2019 to 2020. The Scotland Act 2016 gave the Scottish Parliament full power over rates and thresholds of NSND Income Tax, excluding the Personal Allowance (PA), collected in Scotland for the 2017 to 2018 tax year onwards. Therefore, a taxpayer living in the UK could face a different Income Tax regime depending on where they live. Income Tax on savings and dividends is not devolved and continues to be set by the UK Government. For more information on the background to the Devolved Income Tax powers in Scotland please see HMRC’s previous publication ‘Estimating Scottish taxpayer behaviour in response to Scottish Income Tax changes introduced in 2018 to 2019 (section 5).

For the tax year 2018 to 2019 the Scottish Government introduced 2 new Income Tax bands and their associated rates, as well as increasing the rates for 2 of the existing bands (switching Scotland from a 3-band to a 5-band system). Figure 1 shows the timeline of this change to the Scottish Income Tax system.

Figure 1: Timeline of the introduction of the 5-band Income Tax system

Note 1: The role of income tax in Scotland’s budget.

Note 2: This included an amendment to the Draft budget proposal which decreased the proposed HRT from £44,273 to £43,430.

Table 1 shows the Scottish Income Tax (SIT) system for the tax year 2017 to 2018 and table 2 shows the new SIT system for the tax year 2018 to 2019, assuming the standard UK Personal Allowance in place for these years.

Table 1: Scottish Income Tax NSND policy for the tax year 2017 to 2018

Tax band	Scottish threshold	Scottish Income Tax (SIT) marginal rate
Basic rate	£11,850	20%
Higher rate	£43,000	40%
Additional rate	£150,000	45%

Table 2: Scottish Income Tax NSND policy for the tax year 2018 to 2019

Tax band	Scottish threshold	Scottish Income Tax (SIT) marginal rate
Starter rate	£11,850	19%
Basic rate	£13,850	20%
Intermediate rate	£24,000	21%
Higher rate	£43,430	41%
Top rate	£150,000	46%

Besides Income Tax, National Insurance Contributions (NICs) are also charged on NSND income. However, for the purpose of this analysis, we are not examining nor including the effects of NICs, which are not devolved to the Scottish Parliament, nor are we considering any other taxes or deductions to income as they are not devolved.

The new SIT system means that the total amount of Income Tax a Scottish taxpayer is liable to pay in 2018 to 2019 will be different compared to 2017 to 2018 and different to the total amount of Income Tax owed by a rUK taxpayer in 2018 to 2019. Figure 2 demonstrates the typical effective tax rates (total Income Tax liabilities over total earned income) on NSND income in Scotland under the SIT system for the tax year 2017 to 2018, 2018 to 2019 and the rUK system for the tax year 2018 to 2019, excluding NICs.

Figure 2: Effective NSND Income Tax rates on employee earnings in Scotland for the tax year 2017 to 2018, for the tax year 2018 to 2019 and in rUK for the tax year 2018 to 2019

For incomes up to approximately £33,000 the effective tax rate has decreased between 2017 to 2018 and 2018 to 2019 (for a given level of income), and for incomes above approximately £33,000 the effective tax rate has increased. Compared to rUK, for incomes up to approximately £26,000 the effective tax rate is lower in Scotland in 2018 to 2019 and for incomes above approximately £26,000 the effective tax rate is higher in Scotland. Table 3 shows examples of the typical tax liabilities on NSND income in Scotland for the tax year 2017 to 2018, for the tax year 2018 to 2019, as well as rUK for the tax year 2018 to 2019, excluding NICs.

Table 3: Illustrative examples of tax liabilities in Scotland and rUK

NSND income (£)	Scotland 2017 to 2018 (1)	Tax liabilities (£) Scotland 2018 to 2019 (2)	rUK 2018 to 2019 (3)	Difference 2018 to 2019 (2)-(1)	Difference rUK 2018 to 2019 (2)-(3)
12,000	100	29	30	-72	-2
15,000	700	610	630	-90	-20
20,000	1,700	1,610	1,630	-90	-20
30,000	3,700	3,670	3,630	-30	40
40,000	5,700	5,770	5,630	70	140
50,000	9,100	9,184	8,360	84	842
70,000	17,100	17,384	16,360	284	1,024
100,000	29,100	29,684	28,360	584	1,324
130,000	45,700	46,843	45,100	1,143	1,743
150,000	53,700	55,043	53,100	1,343	1,943
500,000	211,200	216,043	210,600	4,843	5,443
1,000,000	436,200	446,043	435,600	9,483	10,443

Since the changes introduced in 2018 to 2019, further Scottish Income Tax increases were implemented in the tax year 2023 to 2024, reducing the Top rate threshold (TRT) from £150,000 to £125,140, raising the Scottish Higher rate (HR) from 41% to 42% and the Scottish Top rate (TR) from 46% to 47%. In December 2023, the Scottish Government also announced additional increases to be implemented in the tax year 2024 to 2025, introducing a 45% band for taxpayers earnings between £75,000 and £125,140, as well as increasing the Scottish TR from 47% to 48%.

Further Income Tax changes in rUK have also been implemented since 2018 to 2019, including the reduction of the Additional rate threshold (ART) from £150,000 to £125,140 in the tax year 2023 to 2024. This paper focuses on the changes introduced in 2018 to 2019 as outturn data is only available up to 2021 to 2022. Future research would be required to investigate the effects of later policy changes.

The introduction of the 5-band system in Scotland produced an opportunity to study the responsiveness of Scottish taxpayers based on a natural experiment where one nation within the UK changes their Income Tax rates compared to rUK. In 2021, HMRC published a paper estimating the response of Scottish taxpayers on the intensive margin from the 5-band policy.

Our paper seeks to extend this analysis by exploring responses on the extensive margin and also by including a further year into the analysis. Specifically, we consider responses in labour market participation and cross-border migration from rUK to Scotland. Our paper therefore seeks to contribute to the literature by being the first of its kind to study these taxpayer behaviours in the Scottish context and provide further insight into the area of devolved fiscal policy.

To carry out our study, we build a multi-year micro-level dataset using HMRC’s administrative data covering the tax years 2014 to 2015 to 2020 to 2021. We use individual-level employment data to measure labour market participation and individual-level location indicators to measure cross-border migration. Our strategy relies on a difference-in-differences (DiD) method where we compare labour market participation and cross-border migration outcomes across groups that were differently affected by the Income Tax reform.

For labour market participation, we compare taxpayers in Scotland to taxpayers in rUK, before and after the reform. For cross-border migration, we exploit the variation in the intensity of the ATR change in Scotland and compare taxpayers across different income bands, before and after the reform.

We find that Scotland and rUK have different trends in labour market participation over time (non-parallel trends), and that individuals on different income levels in Scotland have different trends in cross-border migration over time, which means that a standard DiD design alone would produce inaccurate estimates. We supplement the DiD method with propensity score matching (PSM) and therefore only compare taxpayers who have comparable characteristics such as age, gender, sector, industry and historical labour market participation or cross-border migration trends.

We estimate the semi-elasticities which show the percentage point change in labour market participation and net cross-border migration in response to a 1% change in the percentage of income retained after tax. These are estimated for distinct income bands to allow us to estimate the behaviours of taxpayers at different levels of income, which is referred to as heterogeneous behaviour. To estimate the semi-elasticities, we apply the DiD approach to a 2-stage-least-squares (2SLS) method.

The first stage regression of our DiD 2SLS method instruments the ARR, the percentage of income retained after tax, by the treatment interaction dummy from the DiD, in order to capture the tax change induced by the reform. The second stage captures the change in labour market participation and cross-border migration, relative to the change in the ARR. This technique is often used in similar studies of taxpayer behaviour such as Martinez (2017) in their study of tax-induced cross-border migration in Switzerland. Similarly by Sigurdsson (2019) in their study of labour supply during an Income Tax holiday in Iceland.

The semi-elasticity relates the change in labour market participation or cross-border migration to the change in the income retained after tax following the policy. However, it is worth bearing in mind that there will inevitably be other unobservable factors driving differences between the treatment and control groups, in addition to the effects of the policy, that we cannot control for. These limitations are discussed in more detail throughout the paper.

The paper is structured as follows. Section 5 describes the data used for our study. Section 6 presents the labour market participation analysis, including related literature, the methodology applied, and the results followed by a discussion. Similarly, section 7 presents the analysis on intra-UK cross-border migration. Finally, section 8 concludes.

5. Data

5.1 Data source

Individuals are drawn from 2 of HMRC’s administrative data sources: RTI data and Self Assessment. RTI data covers PAYE individuals, and this data is submitted to HMRC by employers whenever they make a payment to their employees. It includes the amount of money paid to the employee, the Income Tax deducted from them on behalf of HMRC and the necessary information to identify the individual, such as their national insurance number (NINO). This is mandatory for all employers except for those who have no employees earning above the NICs or Income Tax threshold. A small number of individuals will also be excluded if their employments have been flagged as incorrect due to unusually high values, or due to sensitivity. Self Assessment data contains information on taxpayers who have filed a Self Assessment tax return. HMRC administrative data is subject to rigorous compliance checks, therefore quality is expected to be high. There could be minor discrepancies in the Self Assessment data due to late filers not having complete data.

Our dataset includes all individuals present in the RTI data and all Self Assessment individuals who declare NSND income. The dataset will therefore broadly include all individuals in the UK with NSND earnings (unless excluded for any of the reasons mentioned).

The dataset is a yearly panel and includes the tax years 2014 to 2015 to 2020 to 2021 (6 April to the following 5 April). This allows us to analyse trends in labour market participation and cross-border migration before the 5-band policy was introduced (2018 to 2019), as well as estimate responses up to 2 years after the policy was introduced. However, given that 2020 to 2021 coincides with the onset of the COVID-19 pandemic, we do not estimate effects in this year as this is deemed to be a significant confounding factor for participation and cross-border migration.

We have a balanced panel that includes one observation for each individual in each year of the panel, approximately 57.5 million observations per year (table A1, annex A). In the years when an individual is not present in RTI or Self Assessment, we have extrapolated an observation and assumed that they have no NSND earnings in that year.

We do not observe individuals who never enter the panel (individuals with no record in RTI or Self Assessment in any of the tax years 2014 to 2015 to 2020 to 2021 due to having no NSND earnings), and we do not observe individuals who have pension income outside of PAYE and not declared through Self Assessment.

The dataset includes the following information for each individual in each year: region (NUTS level 1, originally drawn from postcode data), income (NSND income only), sector (SIC code), gender, age and Scottish taxpayer indicator (‘s-flag’, from the tax year 2016 to 2017 onwards). For more information on how this data is sourced, please refer to HMRC’s previous publication ‘Estimating Scottish taxpayer behaviour in response to Scottish Income Tax changes introduced in 2018 to 2019’ (section 7). More information is also included in table A2 (annex A).

5.2 Labour market participation, migration and tax rates

We use the information available in the dataset to measure extensive margin outcomes. For labour market participation, we measure if individuals are working or not in each tax year based on their income. If an individual has a non-zero NSND income that is not from an occupational pension, we flag them as working in Scotland or rest of the UK (rUK). If an individual has no income, is missing from the dataset or has an income that is from an occupational pension, we flag them as not working in Scotland or rUK. Given that the data is yearly, we only observe entry and exit on an annual basis. For entry, this means that an individual will be observed as entering for the tax year in which they start working. For example, if an individual starts working in January 2018, or at any time within that tax year, they will be observed as entering in the tax year 2017 to 2018. For exit, an individual will be observed as exiting in the tax year after the exit took place. For example, if an individual stops working in January 2018, they will be observed as exiting in the tax year 2018 to 2019.

For cross-border migration, we compare individuals’ location between 2 consecutive tax years. We consider cross-border migration for individuals in work, based on the specifications outlined in the paragraph above, and flag an individual as migrating between Scotland and rUK if their location in one year is Scotland but their location in the previous year is not Scotland, or vice versa. For the tax years 2016 to 2017 and onwards, location is based on the s-flag which has a value of 1 if an individual is a Scottish taxpayer (located in Scotland) and 0 if the individual is not a Scottish taxpayer (located in rUK). For the tax years prior to this, we use the region variable to observe location as the s-flag does not exist for those years.

Both the region and s-flag variables are based on where an individual spent the majority of the tax year. The methodology used to measure intra-UK cross-border migration differs from that used in the ‘Intra-UK migration of individuals: movements in numbers and income’ analysis. More information on these differences is provided in section 7.2.

We use the income variable to calculate individuals’ tax liabilities in a given tax year. We apply the NSND Income Tax regime (rates and thresholds) to individuals’ income. This will be representative of individuals’ NSND Income Tax liabilities only and does not include other taxes individuals might be liable to such as NICs, savings or dividend tax. This also does not include any reliefs or benefits an individual could be in receipt of. The true effective tax rate for individuals that have other types of income subject to tax or individuals that receive certain tax reliefs/benefits will be different than the estimated effective tax rate. This means that the incentive to work or migrate could be different for these individuals. We assume that these differences are randomly distributed, given that the sample size is large. However, this assumption could be violated as Scotland has a different benefit system compared to rUK leading to a mismeasurement of the true tax incentive created by the policy change.

We use the ARR, 1 – ATR, as our explanatory tax variable. This is the proportion of income retained after tax. The ATR is calculated as individuals’ derived tax liabilities divided by their income.

6. Labour market participation

6.1 Related literature

This section summarises empirical literature on extensive margin elasticities that concentrate specifically on labour market participation responses to tax reforms that have taken place and measure said elasticities using quasi-experimental methods. The literature presented below generally finds small to no effects on labour market participation. The elasticities referred to capture the behavioural response in labour market participation in relation to the change in the tax.

Jäntti et al. (2013) use repeated cross sections of micro data from 13 developed (OECD) countries, including the UK, to estimate labour supply (labour market participation) elasticities. The cross-sectional data has a large number of tax reforms over time and across countries. They use a 2-stage-least-squares (2SLS) method, using group and time dummies as instruments for the average tax rate, and impute potential earnings in the state of work by regressing earnings on characteristics for those who have positive earnings. They find participation elasticities ranging from 0 to 0.4 for all individuals, with some not statistically different from 0.

Martinez, Saez and Siegenthaler (2018) study the effects of temporary 2-year Income Tax holidays in Swiss Cantons occurring throughout the periods 1997 to 2003. During these 2-year periods, the marginal Income Tax rates dropped from between 25% and 50% to 0%. They use yearly cross-sectional individual level data and estimate the causal effect of the net-of-tax rate (proportion of income retained after tax) on labour supply by instrumenting the net-of-tax rate on an indicator for the tax holiday in the Canton (the policy). They find no evidence of labour supply effects on the extensive margin. We note that this setting differs from the Scottish Income Tax policy in that it was temporary (rather than permanent), and this was known by the public.

Sigurdsson (2019) looks at a similar Income Tax Holiday in Iceland in 1987, where the marginal rate was 0% for one year. They build a population-wide dataset and exploit differences in pre-reform tax rates, comparing individuals in higher and lower tax brackets who faced different changes in tax rates. They use the same instrumental variable (IV) approach as Martinez, Saez and Siegenthaler (2018), instrumenting the net-of-tax rate by the policy interaction term and find an extensive margin elasticity of 0.07, which is smaller than the estimated intensive margin elasticity. Sigurdsson finds that these extensive effects are mainly driven by individuals under 25 and close to retirement. As in Martinez, Saez and Siegenthaler (2018), this study also differs from the Scottish setting as it concerns a salient, temporary measure.

Other literature focuses on labour market participation effects on specific demographic groups: Albert and Powell (2020) estimate an elasticity of 0.7 (men) and 3.9 (women) for older age workers in the United States of America, given their flexibility to retire, and Selin (2014) estimates elasticities of between 0.5 and 1 for Swedish women. While these papers find significantly larger elasticities for specific demographic groups, such as women, these demographic groups are likely to be underrepresented in the Scottish setting given that the Scottish reform was targeted at the higher end of the income distribution which has a higher proportion of male taxpayers (see Scottish Income Tax: distributional analysis).

Table 4 summarises the elasticities found across the referenced literature.

Table 4: Summary table of literature – labour market participation

Name of Paper	Tax base	Elasticity	Permanence
Martinez, Saez and Siegenthaler (2018)	All Swiss taxpayers	NA	Temporary
Sigurdsson (2019)	All Icelandic taxpayers	0.07	Temporary
Jäntti et al. (2013)	Cross-country	0 to 0.4	Permanent
Albert and Powell (2020)	Older workers in the US	0.7 (men) 3.9 (women)	Permanent
Selin (2014)	Swedish women	0.5 to 1	Permanent

6.2 Descriptive statistics

Table 5 shows the total working population in Scotland and rUK for the tax years 2014 to 2015 to 2020 to 2021, rounded to the nearest 500. Figure 3 and table 6 show the corresponding year on year growth rates in the working population. For the tax years 2016 to 2017 onwards we define location based on the s-flag and for the tax years prior we use the region variable.

Table 5: Working population in Scotland and rUK, 2014 to 2015 to 2020 to 2021 (Note 1), (Note 2)

	2014 to 2015	2015 to 2016	2016 to 2017	2017 to 2018	2018 to 2019	2019 to 2020	2020 to 2021
Scotland	2,601,500	2,632,000	2,610,500	2,628,500	2,638,500	2,631,000	2,544,000
rUK	29,216,000	29,964,500	30,272,500	30,724,000	31,285,500	31,397,500	30,372,500

Note 1: These figures may differ from other sources due to methodological differences.

Note 2: The Scottish Income Tax Outturn Statistics only includes taxpayers that pay Income Tax (after allowances and reliefs have been applied). This generally means that they have an income above the Personal Allowance. The figures in table 5 include all individuals in work (with NSND income) and will therefore also include individuals with an income below the Personal Allowance.

Figure 3: Year on year change in working population (%), Scotland and rUK, 2015 to 2016 to 2020 to 2021

Table 6: Year on year change in working population (%), Scotland and rUK, 2015 to 2016 to 2020 to 2021

	2015 to 2016	2016 to 2017	2017 to 2018	2018 to 2019	2019 to 2020	2020 to 2021
Scotland	1.2%	-0.8%	0.7%	0.4%	-0.3%	-3.3%
rUK	2.6%	1.0%	1.5%	1.8%	0.4%	-3.3%

Table 5, figure 3 and table 6 show that the total working population in rUK is consistently growing from 2015 to 2016 to 2019 to 2020, before decreasing in 2020 to 2021. Growth rates fall in 2016 to 2017, before increasing in 2017 to 2018 and 2018 to 2019 and then decreasing again in 2019 to 2020. A similar trend is visible in Scotland, but with negative growth in 2016 to 2017 and 2019 to 2020. The lower growth in 2016 to 2017 could be an initial effect of the referendum on the United Kingdom’s membership of the European Union (Brexit) taking place in this year. The negative growth in Scotland could also reflect the decline in oil and gas activity in the North Sea and subsequent recession as a result of a fall in oil prices, which had knock-on effects on local economies (Phillips, Waters and Wernham, 2023). The larger drop in the working population in 2020 to 2021 likely shows the effect of COVID-19 on the labour force. In 2018 to 2019, the year of the introduction of the 5-band policy, growth in the working population is positive in both Scotland and rUK but does decrease compared to the previous year in Scotland while increasing in rUK. This could indicate a drop in participation in response to the policy change.

6.3 Methodology

Theoretical model of labour market participation

We draw upon a theoretical model of labour market participation (adapted from Saez, 2002; Jäntti et al., 2013; and Immervoll et al., 2007) to understand labour market participation incentives. We consider a static (one time period) model where individuals (i) maximise utility (u_i) which is a function of consumption and labour. Utility from working is the sum of consumption (c_i) less the disutility of working (v_i).

(1) u_i = c_i - v_i

The budget constraint includes earned income (z_i) and non-earned income (q_i), less taxes and transfers which is a function of earned income (T(z_i)). We assume no tax on non-earned income. This is a reasonable assumption in the setting of this analysis given that non-NSND income has the same tax treatment in all parts of the UK. Therefore, tax on non-NSND income is not a source of variation.

Substituting consumption for this budget constraint, the utility of working (u_Wi) and the utility of not working (u_NWi) are defined as:

(2) u_Wi = z_i - T(z_i) + q_i - v_i

(3) u_NWi = T(0) + q_i

An individual chooses to work if the utility of working exceeds the utility of not working:

(4) z_i - T(z_i) + q_i - v_i > T(0) + q_i

(5) z_i(1- a_i) - v_i > 0 where a_i = [T(z_i)+T(0)] / [z_i]

This tells us that for a given income, the participation decision is a function of the participation tax rate a_i: the increase in tax and loss in benefits relative to gross earnings when working. If T(0)=0, the participation tax rate is equivalent to the ATR.

To complete the model, we define 2 states: working=1 and not working=0.

(6) work_i = 1, v_i < z_i(1- a_i)

(6) work_i = 0, v_i ≥ z_i(1- a_i)

The probability that work_i=1, given that we observe z_i(1-a_i):

(7) P(work_i = 1 ǀ z_i(1- a_i)) = P(v_i < z_i(1- a_i) ǀ z_i(1- a_i)) = F(z_i(1- a_i))

The decision to work depends on F(z_i(1-a_i)), which refers to the distribution of v_i. Given a fixed income, for linear probability models (using decomposition of Random Utility Models from Train, 2009), the empirical counterpart shows that the probability to work P(work_i) for an individual i at period t is:

(8) P(work_it) = α + βlog(ARR_it) + ε_it

Where P(work_it) is defined to take on the value of 1 if the individual works and 0 if not working. The coefficient β is the semi-elasticity of participation: the percentage point change in the proportion in work (W_it) from a percentage change in the average rate of retention:

(9) β = [dW_it/W_it] / [dlog(ARR_it)/log(ARR_it)]

Identification strategy

To estimate changes in labour market participation, we rely on a DiD approach comparing individuals in Scotland (treated) to individuals in rUK (control) who were not subject to the policy. The control group provides us with the counterfactual difference (the change we would expect in the absence of the policy impact). We remove individuals migrating between Scotland and rUK throughout the panel in order to avoid leakage between treatment and control groups (this removes approximately 1% of the population). To recover the semi-elasticities, we apply the DiD approach to a 2-stage-least-squares (2SLS) method, where the ARR is instrumented by the DiD interaction term. Finally, we make use of PSM to ensure parallel trends pre-policy.

In order to estimate the change in labour market participation across different income levels (heterogeneous behaviour), we split individuals into income bands. We have used a similar method to Martinez (2017) and group individuals into income bands based on their average pre-policy income calculated as their average annual income over the 4 tax years 2014 to 2015 to 2017 to 2018. This provides a comprehensive measure of individuals’ pre-policy income and reduces the error resulting from individuals entering and exiting part-way through the tax year. The income brackets are generally based on the Scottish Income Tax thresholds in 2018 to 2019, apart from for HR and TR individuals who are split below and above £100,000 in average annual income. The £100,000 split is performed to ensure large enough within-group variation. Table 7 summarises the income band thresholds and the number of individuals in each income band.

Table 7: Income band thresholds and number of observations in the treated and control groups for the labour market participation analysis

Average annual income between 2014 to 2015 and 2017 to 2018	Treated individuals	Control individuals
£100,001+	29,868	530,168
£43,431 to £100,000	190,739	2,422,374
£24,001 to £43,430	613,046	6,635,792
£13,851 to £24,000	703,595	8,027,222
£11,851 to £13,850	159,679	1,946,912
Below £11,851 (Note 1)	1,218,958	17,156,660
Total £11,851+	1,696,927	19,562,128
Total	2,915,885	36,719,128

Note 1: Below £11,851 is not included in the analysis. We assume that individuals earning below the PA are not subject to Income Tax and therefore not impacted by the change.

Our pre-policy tax year is 2017 to 2018, and we measure the difference from this tax year to the post-policy tax years 2018 to 2019 and 2019 to 2020. As explained in the data section, one limitation of this method is that we only capture individuals who exit in the tax year after the decision is made and we do not capture individuals who exit part-way through a tax year. For entry, an individual will be counted as entering if they enter part-way through the tax year as we observe a positive income for them in that tax year. However, if an individual enters before the start of the post-policy tax year in anticipation of the policy, this will be captured as a pre-policy behaviour.

We note that the period between announcement and implementation was only 4 months, with an earlier Income Tax discussion paper published one month prior to announcement, giving limited time to react on the extensive margin. We therefore don’t expect this to have any material impact on the results.

For the regression analysis, we use a linear probability model with robust standard errors. Our reduced-form labour market participation responses are estimated using the following baseline DiD specification:

(10) W_it = δ₀ + δ₁T_i + δ₂P_t + δ₃(T_i × P_t) + ε_it

Where W_it is the work dummy, 1 if in work and 0 if not in work, T_i = 1[i = 1] is the treatment group dummy, 1 if Scotland and 0 if rUK, P_t = 1[t ≥ 2018 to 2019] is the post-reform dummy. The coefficient of interest δ₃ is the DiD estimator on the change in the probability of work, after the introduction of the reform in 2018 to 2019.

Instrumental variable approach

In order to obtain estimates for the semi-elasticities of labour market participation with respect to a change in the ARR, we use a 2SLS approach and instrument the ARR by the policy change (following the approach used in Advani et al., 2022; Martinez, 2017; Saez et al., 2012; and Selin, 2014). This method allows us to relate changes in labour market participation to changes in the ARR generated by the policy change.

Given that the policy change directly determined the change in the ARR, the strong first stage condition for IV is met. A strong first stage is demonstrated in table 8 (section 6.4) where the first stage results are non-zero and statistically significant, as well as in table B1 (annex B) which shows that the F-values relating to the results in table 8 are larger than 10 (F-values similarly test the significance of the instruments and an F-value above 10 generally means that the average outcomes are significantly different between the treated and control groups). As for the exclusion restriction, we assume that the policy change will only have impacted labour market participation through the change in the ARR as this was the policy intent.

In the first stage of our 2SLS DiD specification, we instrument the change in the ARR with the reduced-form treatment interaction dummy (T_i×P_t) from our DiD specification in equation 10. The first stage takes the form:

(11) log(ÂRR_it) = γ₁T_i + γ₂P_t + γ₃(T_i × P_t) + ε_it

Where ARR_it is the average rate of retention for individual i at time t and (log(ÂRR_it)) is the instrumented outcome of the log of the ARR. The second stage takes the form:

(12) W_it = β₀ + β₁T_i + β₂P_t + β₃(log(ÂRR_it) + ε_it

Where the coefficient β₃ in the second stage regression is the semi-elasticity of participation with respect to the ARR:

(13) [dW_it / dlog(ARR_it)] = [d(β₀ + β₁T_i + β₂P_t + β₃log(ARR_it) + ε_it) / dlog(ARR_it)] = β₃

The 2SLS method allows us to relate the change in labour market participation to the change in the ARR and recover a semi-elasticity mechanically. This method also means that we only capture the tax change induced by the reform as it, to some extent, addresses the main endogeneity issues: reverse causality as labour market participation status determines the ARR, omitted variable biases (such as simultaneous policy changes), and potential mismeasurements of the ARR. Finally, it takes into account that the treatment, the tax reform, may not have perfectly determined participation decisions.

Further identification assumptions

The baseline DiD methodology is valid on the assumption that, in the absence of the policy, labour market participation would change at the same rate in Scotland and rUK. Given that Scotland and rUK are divergent in key dimensions such as population growth and labour market characteristics, we account for non-parallel trends pre-policy by using propensity score matching (see Sigurdsson, 2019, for an example of using PSM in extensive margin analysis). We select a control group in rUK based on the characteristics: age, gender, sector, average income and historical labour market participation patterns. This allows us to compare Scottish taxpayers with a control group from rUK who are balanced along key characteristics.

We estimate propensity scores using a logistic (logit) regression, and match individuals using nearest-neighbour one-to-one matching (NN1). This means that each individual in Scotland is matched to one unique individual in rUK with the most similar characteristics. We use Abadie and Imbens (2006) to calculate standard errors for nearest neighbour matches.

We test the unconfoundedness and parallel trends assumption, that conditional on these explanatory variables, labour market participation outcomes would have been the same in both the treatment and control groups, by examining the parallel trends within each income band. We test common support by examining the overlap in the propensity score distribution between the treatment and control groups within each income band.

Graphs showing parallel trends and balance plots for each income band are included in annex B. Parallel trends and propensity score overlap are improved after matching. We find that employment trends in Scotland and rUK are visibly parallel pre-policy (pre 2018 to 2019) and that there is good overlap in propensity scores between the treatment and control groups after matching, indicating that the groups are balanced along matched characteristics on average.

6.4 Results

In table 8 we present our results for the labour market participation regression analysis. Table 8 shows the estimates of the policy effect on the tax rate (log(ARR) column), the first stage results, and the corresponding semi-elasticities for labour market participation (semi-elasticity column), the second stage results. F-values are presented in table B1 in annex B.

Table 8: Results of the labour market participation regression analysis

Income band	2018 to 2019 log(ARR)	2018 to 2019 Semi-elasticity	2019 to 2020 log(ARR)	2019 to 2020 Semi-elasticity
£100,001+	-1.01%***	-0.07	-1.55%***	0.28
	(-0.013, -0.008)	(-0.711, 0.565)	(-0.018, -0.013)	(-0.178, 0.742)
£43,431 to £100,000	-0.59%***	-0.04	-1.49%***	0.09
	(-0.007, -0.005)	(-0.445, 0.369)	(-0.016, -0.014)	(-0.085, 0.267)
£24,001 to £43,430	-0.28%***	0.20	-0.15%***	0.57
	(-0.003, -0.003)	(-0.283, 0.679)	(-0.002, -0.001)	(-0.446, 1.577)
£13,851 to £24,000	0.07%***	1.13	0.57%***	0.07
	(0.001, 0.001)	(-0.550, 2.819)	(0.005, 0.006)	(-0.149, 0.289)
£11,851 to £13,850	0.12%***	0.34	0.60%***	0.05
	(0.001, 0.002)	(-1.691, 2.380)	(0.006, 0.006)	(-0.370, 0.462)
All	-0.15%***	-0.11	0.03%**	-1.79
	(-0.002, -0.001)	(-0.621, 0.411)	(0.000, 0.001)	(-5.392, 1.812)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

The policy effect on the tax rate, log(ARR), is the percentage change in the ARR for the treated group (Scotland) relative to the control group (rUK). A negative effect implies a decrease in the ARR, paying more tax, relative to the control group and a positive effect implies an increase in the ARR, paying less tax, relative to the control group.

We find statistically significant changes in the ARR in Scotland relative to rUK for each income band and in aggregate (first stage results). The ARR has on average decreased in Scotland for individuals with an average income above £24,000 in 2018 to 2019 and 2019 to 2020. For lower incomes, the ARR has increased. This is expected given the nature of the policy change. As set out in the policy background section, the cut-off point in income for a negative compared to a positive change in the ARR in Scotland relative to rUK is around £26,000.

Therefore, some of the individuals in the £24,001 to £43,430 group will have experienced an increase in their ARR, albeit more have experienced a decrease. The absolute change in the ARR increases with income, up to 1% for individuals with incomes above £100,000 in 2018 to 2019. For most bands, the change in the ARR increases in 2019 to 2020, with individuals above £100,000 in income experiencing a decrease in their ARR of 1.55% on average.

The semi-elasticity of labour market participation with respect to a change in the ARR is the percentage point change in the probability of working given a one % change in the ARR. For individuals with an income above £24,000 who have experienced a decrease in their ARR on average, a positive elasticity shows that there was a decrease in participation following the decrease in the ARR, and a negative elasticity shows that there was an increase in participation following the decrease in the ARR.

For individuals with an income between £11,851 and £24,000 who have experienced an increase in their ARR on average, a positive elasticity shows that there was an increase in participation following the increase in the ARR, and a negative elasticity shows that there was a decrease in participation following the increase in the ARR.

None of the semi-elasticities are significantly positive. Estimates are generally small, close to 0, and some have a negative sign. Therefore, we find no evidence of changes in labour market participation following the changes to Scottish Income Tax. Some of the estimates are large compared to those found in the literature. However, the wide confidence intervals suggest that the results may not be precise and some of these regressions may have lower power, regardless of the true effect.

In table 9, we present the semi-elasticities for labour market participation for each income band by subgroup: male, female, age over 50 and age below 50.

Table 9: Labour market participation semi-elasticities by subgroup

Semi-elasticity: 2018 to 2019	Male	Female	Age 50+	Age below 50
£100,001+	-0.09	0.04	0.05	-0.16*
	(-0.810, 0.621)	(-1.307, 1.388)	(-1.177, 1.285)	(-0.349, 0.021)
£43,431 to £100,000	-0.17	0.31	-0.06	0.03
	(-0.670, 0.336)	(-0.358, 0.983)	(-1.077, 0.959)	(-0.090, 0.153)
£24,001 to £43,430	0.10	0.38	1.04	-0.07
	(-0.476, 0.674)	(-0.485, 1.247)	(-0.443, 2.520)	(-0.187, 0.041)
£13,851 to £24,000	1.45	0.92	1.91	-0.09
	(-1.398, 4.290)	(-1.151, 2.996)	(-1.331, 5.156)	(-0.518, 0.339)
£11,851 to £13,850	1.45	0.20	0.58	-0.08
	(-9.696, 12.598)	(-1.609, 2.016)	(-5.439, 6.589)	(-0.510, 0.349)

Semi-elasticity: 2019 to 2020	Male	Female	Age 50+	Age below 50
£100,001+	0.35	0.00	0.78	-0.09
	(-0.186, 0.882)	(-0.842, 0.851)	(-0.199, 1.758)	(-0.205, 0.030)
£43,431 to £100,000	-0.04	0.42***	0.31	0.01
	(-0.250, 0.178)	(0.116, 0.717)	(-0.145, 0.774)	(-0.046, 0.061)
£24,001 to £43,430	0.11	1.54	-4.99*	0.04
	(-1.026, 1.244)	(-0.560, 3.633)	(-10.560, 0.584)	(-0.125, 0.196)
£13,851 to £24,000	0.14	0.02	0.06	-0.05*
	(-0.196, 0.470)	(-0.273, 0.309)	(-0.479, 0.607)	(-0.106, 0.000)
£11,851 to £13,850	0.32	-0.08	0.05	-0.05
	(-0.479, 1.127)	(-0.566, 0.401)	(-1.052, 1.159)	(-0.143, 0.053)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

There is a lot of variation in the estimates and some uncertainty given the smaller population sizes. In general, most estimates are not significantly positively. The negative significant results at the 1% level are unintuitive and therefore likely to be driven by confounding factors. There is one strong result of 0.42 for the female group in the £43,431 to £100,000 income band in 2019 to 2020, suggesting a potential decrease in labour market participation after the Scottish Income Tax changes.

6.5 Robustness

To test the robustness of the results, we run a placebo regression where we test the analysis for a subset of individuals with an average income below the PA, between £10,000 and £11,850, who were not affected by the Scottish Income Tax changes. We use the DiD with propensity score matching method and compare individuals in Scotland to individuals in rUK. The results of the DiD regression with work as the outcome variable are presented in table 10.

Table 10: Work DiD results, £10,000 to £11,850 income band (below PA)

	2018 to 2019	2019 to 2020
Work	-0.001	-0.002
	(-0.003, 0.002)	(-0.004,0.001)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

We find no statistically significant changes in the proportion of the population in work in Scotland relative to rUK, in 2018 to 2019 or 2019 to 2020, satisfying the placebo validity test in both years. This is expected as there was no tax change during the time period for individuals below the PA.

6.6 Discussion

We find no evidence of a change in labour market participation following the Scottish Income Tax rate changes in 2018 to 2019 or 2019 to 2020. We consider this a plausible result given that leaving the labour market entirely or entering the labour market as a result of a 0.1% to 1.5% change in an individual’s overall tax liability is a seemingly drastic response. As shown in table 3, the change is less than £100 for individuals with an income of £50,000 and below, around £600 for individuals with an income of £100,000 and £1,300 for individuals with an income of £150,000. This result is broadly consistent with the literature, although some of the literature looks at temporary, rather than permanent, changes to the tax system.

We observe parallel trends in participation for all income groups in Scotland and rUK post-matching, and therefore assume that DiD is valid. Additionally, the 2SLS method controls, in part, for issues of endogeneity. For some income groups, such as £100,001+, £43,431 to £100,000 and £24,001 to £43,430, the graphs showing labour market participation trends (annex B) visually suggest that there might have been a change in labour market participation after the policy was implemented. However, the regression results show no statistically significant divergences between Scotland and rUK. The estimates are in most cases close to 0, but the standard errors are large. Therefore, while our results suggest no change in labour market participation following the Scottish Income Tax changes, we conclude that the true changes are uncertain and that if there was a change, we have not been able to detect it.

We consider some additional limitations. Firstly, the results could be dependent on the choice of the counterfactual. In particular, this analysis measures only changes in average Income Tax rates and does not capture effective tax rates. In reality, individuals are subject to a range of other taxes and benefits which could influence tax-induced behaviour. While we compare individuals on similar income levels and therefore expect these incentives to be roughly the same between the treated and control groups, there are some benefits that are devolved and could differ between Scotland and rUK. The semi-elasticities estimated are only based on Income Tax changes, so the true magnitude of the ‘effective’ semi-elasticities are likely to be different.

Secondly, this analysis has focused on short term changes as it only observes changes in 2 years after the policy change. Labour market participation could be more elastic in the long term, which this analysis has not been able to detect within the 2 year time frame.

Finally, there are also other wider economic factors that could influence individuals’ labour market participation decisions that differ between Scotland and rUK, such as factors related to job security and flexibility. This paper has used a dataset that is limited to annual observations and only able to control for high-level demographic characteristics such as age, gender and employment. Other policies simultaneous to the period studied may also have had an impact on labour market participation decisions. For example, the Early Learning and Childcare (ELC) expansion in Scotland could have contributed to an increase in labour market participation in Scotland.

There could also be early effects associated with the UK leaving the European Union that might vary between Scotland and rUK. These are all potential confounders (unmeasured third variables that influences both the supposed cause and supposed effect) that we have not been able to fully control for, apart from through the demographic characteristics previously mentioned.

7. Cross-border migration

7.1 Related literature

This section summarises empirical literature on tax induced cross-border migration studies from different tax reforms that have taken place. The majority of the literature available focuses on reforms in federal countries such as the United States of America. Generally, the literature finds some evidence of responses in within-country migration among higher earners with elasticities ranging from 0.1 to 6.5. The elasticities referred to capture the behavioural response in migration in relation to the change in the tax rate. We only consider literature on within-country migration as this is the most comparable to migration between Scotland and rUK. There does exist other literature on international migration (see Kleven et al., 2020, for a comprehensive review), but this is out of scope here. For a more in-depth literature review on tax induced cross-border migration and how it relates to the Scottish context, please see the Scottish Government’s paper ‘Understanding the Behavioural Effects from Income Tax changes’.

Young and Varner (2011) focus specifically on higher earners and examine the response to a millionaire tax in New Jersey, United States of America, which raised the Income Tax rate on top earners by 2.6 percentage points to 8.97 percentage points, one of the highest tax rates in the country. They use a DiD strategy on state tax micro-data comparing individuals above $500,000 affected by the tax to individuals between $200,000 and $500,000 who are also high earners but not affected by the tax. This compares individuals in the 95th-99th percentile to those in the 99th percentile. They find small responses, with semi-elasticities (the percentage point change in migration in response to a percentage change in tax) generally below 0.1.

Cohen, Lai and Steindel (2012) considered the same policy and suggested that Young and Varner (2011) failed to control for a number of important factors affecting migration and used a population that was too restricted. They concluded that Young and Varner’s (2011) estimates were likely an underestimate. While these studies are relevant in the context of Scottish top earners, New Jersey has a larger tax base, is in close proximity to other major cities, and has a lower Income Tax rate compared to Scotland.

We also consider other studies that concern smaller and more integrated regions that are likely to be more comparable to the Scottish context. Martinez (2017) that looks at a regressive local Income Tax cut in a Swiss Canton benefiting the top 1% of the Canton. They use a difference-in-differences, 2SLS method with individual tax data and compare individuals with incomes above the threshold for the tax cut to those just below this threshold. They find large migration elasticities (inflow of individuals with respect to the average net-of-tax rate) ranging from 3.2 to 6.5.

Agrawal and Foremny (2019) also look at within-country migration following a Spanish reform that granted regions the authority to set autonomous Income Tax rates, resulting in substantial tax differentials across local authorities. They use administrative data and a general equilibrium model with fixed effects to estimate the effect of the tax rate on migration, conditional on moving. They estimate a migration semi-elasticity of 1.7 for higher earners.

However, we note that some recent studies (see Kleven et al., 2020, and Zhang and Hewings, 2019) suggest that the applicability of empirical studies on tax induced cross-border migration is generally limited, given that the results are highly contextual and often dependent on non-tax factors that differ across regions and time.

Table 11 summarises the elasticities found across the referenced literature.

Table 11: Summary of literature - cross-border migration

Name of Paper	Tax base	Elasticity
Young and Varner (2011)	US incomes of top 1%	0.1
Martinez (2017)	Switzerland incomes of top 1%	3.2 to 6.5
Agrawal and Foremny (2019)	Spain high incomes	1.7

7.2 ‘Intra-UK migration of individuals: movements in numbers and income’ analysis

For descriptive statistics on cross-border migration flows between Scotland and rUK please refer to the ‘Intra-UK migration of individuals: movements in numbers and income’ analysis.

The cross-border migration figures in this paper will be different to those presented in the ‘Intra-UK migration of individuals with taxable income’ analysis due to different methodologies, specifically:

• population in scope - the intra-UK migration dataset will include all individuals with any taxable income in HMRC administrative data including savings and dividends income. It also includes individuals with non-savings non-dividends income from workplace pensions. In this paper, we only consider migration for individuals with NSND income (excluding income from workplace pensions)

• geographical information - the intra-UK migration analysis uses postcode information to measure location. In this paper, we use regional data for 2014 to 2015 and 2015 to 2016, which is also derived from postcodes, but we use the s-flags to measure location from the tax years 2016 to 2017 onwards. Previous analysis shows that postcodes and s-flags have approximately a 98% match. The s-flags identify Scottish taxpayers based on where an individual resided in the course of a tax year and are the most accurate measurement of an individual’s ‘taxable’ location. Scottish taxpayer status applies for a whole tax year – it is not possible to be a Scottish taxpayer for part of a tax year

• when the geographical information is recorded - the intra-UK migration analysis measures an individual’s location as of the end of a tax year, whereas in this paper, we measure location as the location where an individual has spent the majority of the tax year. Taking the location an individual resides in the majority of the tax year is analogous to an s-flag

The differences between the 2 methods do not impact the robustness of this paper’s analysis. Rather, they present different ways to observe and analyse migration trends. The findings in this paper are specific to non-pension NSND taxpayers only and look at taxable location (rather than geographical location) in each tax year.

7.3 Methodology

Theoretical model of cross-border migration

We start with the same static model as for participation and apply it to the (binary) migration choice: to stay in the origin location (o) or to move to the destination location (d), assuming the individual is in work (adapted from Martinez, 2017).

Utility in the origin location (u_oi) is equal to the net-of-tax income of individual i in location o. The potential utility in the destination location (u_di) is the after-tax income of individual i in location d, less the disutility of moving (w_i). We assume that income is fixed:

(13) u_oi = z_i - T_o(z_i) + q_i

(14) u_di = z_i - T_d(z_i) + q_i - w_i

An individual will choose to move if the utility in the destination location exceeds the utility in the origin location:

(15) (z_i(1-a_d)) + q_i + w_i > (z_i(1 - a_o)) + q_i

(16) (z_i(1-a_d)) - (z_i(1 - a_o)) - w_i > 0

The migration decision is a function of the difference in the net-of-tax income between origin and destination. We define 2 states: migrate=1 and not migrate=0:

(17) migrate_i = 1, w_i < (z_i(1-a_d)) - (z_i(1 - a_o))

(17) migrate_i = 0, w_i ≥ (z_i(1-a_d)) - (z_i(1 - a_o))

The probability that migrate=1, given that we observe net-of-tax income in both locations, is defined as:

(18) P(migrate_i = 1 ǀ ((z_i(1 – a_d)) – (z_i(1 – a_o))) = P(w_i < (z_i(1 – a_d)) – (z_i(1 – a_o)) ǀ (z_i(1 – a_d)) – (z_i(1 – a_o))) = F((z_i(1 – a_d)) – (z_i(1 – a_o)))

The decision to migrate depends on the difference in the average rate of retention (ARR) between the 2 locations. Empirically, we assume the decision is driven by the ARR the individual is subject to (F(z_i(1-a_i )), which is dependent on location. Given a fixed income, for linear probability models (using decomposition of Random Utility Models in Train, 2009), the empirical counterpart shows that the probability to migrate P(migrate_i) for an individual i at period t is:

(19) P(migrate_it) = α + β log(ARR_it) + ε_it

We define P(migrate_it) as the net cross-border migration probability: it takes the value of 1 if the individual in-migrates (from rUK to Scotland), -1 if the individual out-migrates (from Scotland to rUK), and 0 if the individual does not migrate. The coefficient β is the semi-elasticity of migration: the percentage point change in net cross-border migration (M_it) from a percentage change in the ARR:

(20) β = [dM_it / M_it] / [dlog(ARR_it)/log(ARR_it)]

Identification strategy

To estimate changes in cross-border migration, we rely on a DiD approach comparing individuals in Scotland across different income levels, exploiting the variation in the intensity of the average tax rate (ATR) change in Scotland. Using this method, causal effects could be estimated from the differential treatment intensity, provided that they generate differential responses. To recover the semi-elasticities, we apply the DiD approach to a 2SLS method, where the ARR is instrumented by the DiD interaction term. Finally, we make use of PSM to ensure parallel trends pre-policy.

We investigate net cross-border migration rates from rUK to Scotland for individuals in the Starter rate (SR), Intermediate rate (IR), Higher rate (HR), Top rate (TR) and above £500,000 in income, compared to individuals in the Basic rate (BR) where there was no change in the marginal Income Tax rate (which remained at 20%). While individuals in the BR may also have experienced a change in their ATR due to the introduction of the SR, we find that this group experienced the smallest change overall (close to 0%) and should therefore have a small to no change in net cross-border migration following the policy change. We remove individuals moving across income bands throughout the estimation period in order to avoid leakage between the groups being compared.

We look at the working population only (individuals in work in every year of the panel) who are present in Scotland in at least one tax year of the panel. Individuals are grouped based on their income in 2017 to 2018 (pre-policy tax year). Table 12 shows the income thresholds and number of observations in each income group.

Table 12: Income band thresholds and number of observations for the cross-border migration analysis

Annual income in 2017 to 2018	Number of individuals
£500,001+	671
£150,001+ (TR)	8,642
£43,431 to £150,000 (HR)	185,784
£24,001 to £43,430 (IR)	438,339
£13,851 to £24,000 (BR)	346,531
£11,851 to £13,850 (SR)	18,323
Below £11,851 (Note 1)	237,520
Total £11,851+	997,619
Total	1,235,139

Note 1: Below £11,851 is not included in the main analysis. We assume that individuals earning below the Personal Allowance are not subject to Income Tax and therefore not impacted by the change.

Our pre-policy tax year is 2017 to 2018, and we measure the difference from this tax year to the post-policy tax years 2018 to 2019 and 2019 to 2020. Location is measured as the location where the individual spent the majority of the tax year (using the s-flag). Therefore, we estimate cross-border tax migration (where the individual was liable to tax). One limitation of this method is that if an individual migrated towards the end of a tax year, this will not be captured until the following tax year. However, if migration changes occurred before the policy came into effect in anticipation of the policy (towards the end of 2017 to 2018), this will be captured as a post-policy change (in 2018 to 2019).

For the regression analysis, we use a linear probability model with robust standard errors. Our reduced-form cross-border migration responses are estimated using the following baseline DiD specification:

(21) M_it = δ₀ + δ₁T_i + δ₂P_t + δ₃(T_i × P_t) + ε_it

Where M_it is the migration dummy, 1 if migrating in (from rUK to Scotland), -1 if migrating out (from Scotland to rUK) and 0 if remaining in the same location, T_i = 1[i = 1] is the treatment group dummy, 1 if AR/HR/IR/SR and 0 if BR, P_i = 1[t ≥ 2018 to 2019] is the post-reform dummy. The coefficient of interest δ₃ is the DiD estimator on the change in cross-border migration, after the introduction of the reform in 2018 to 2019.

An alternative method we considered using was regression discontinuity design (RDD), comparing migration responses immediately above and below certain income levels where the marginal change in the tax rate was different above and below, such as the TRT and the PA taper. By comparing observations lying closely on either side of these incomes, it is possible to estimate the average treatment effect, based on the intuition that these individuals are similar but experienced different intensities of treatment. However, when we plotted the probability of migration above and below these incomes, we did not observe a clear structural break which is a key requirement for RDD to be applicable (example in annex C). We concluded that the RDD method was not suitable and would only allow us to estimate local cross-border migration effects.

Instrumental variable approach

In order to obtain estimates for the semi-elasticities of net cross-border migration with respect to a change in the ARR, we use a 2SLS approach and instrument the ARR by the policy change (following the approach used in Advani et al., 2022; Martinez, 2017; Saez et al., 2012; and Selin, 2014). This method allows us to relate changes in net cross-border migration to changes in the ARR generated by the policy change.

Given that the policy change directly determined the change in the ARR, the strong first stage condition for IV is met. A strong first stage is demonstrated in table 13 (section 7.4) where the first stage results are non-zero and statistically significant, as well as in table D2 (annex D) which shows that the F-values relating to the results in table 13 are larger than 10 (F-values similarly test the significance of the instruments and an F-value above 10 generally means that the average outcomes are significantly different between the groups compared). As for the exclusion restriction, we assume that the policy change will only have impacted cross-border migration through the change in the ARR, as this was the policy intent.

In the first stage of our 2SLS DiD specification, we instrument the change in the ARR with the reduced-form treatment interaction dummy (T_i×P_t) from our DiD specification in equation 21. The first stage takes the form:

(22) log(ÂRR_it) = γ₁T_i + γ₂P_t + γ₃(T_i × P_t) + ε_it

Where ARR_it is the ARR for individual i at time t and (log(ÂRR_it)) is the instrumented outcome of the log of the ARR. The second stage takes the form:

(23) M_it = β₀ + β₁T_i + β₂P_t + β₃(log(ÂRR_it) + ε_it

Where the coefficient β₃ is the semi-elasticity of migration with respect to a change in the ARR:

(24) [dM_it / dlog(ARR_it)] = [d(β₀ + β₁T_i + β₂P_t + β₃log(ARR_it) + ε_it) / dlog(ARR_it)] = β₃

This method allows us to relate the change in net cross-border migration to the change in the ARR and recover an elasticity mechanically. This method also means that we only capture the tax change induced by the reform as it, to some extent, addresses the main endogeneity issues: reverse causality as location determines an individual’s ARR, omitted variable bias (such as simultaneous policy changes), and potential mismeasurements of the ARR. Finally, it takes into account that the treatment, the tax reform, may not have perfectly determined migration decisions.

Further identification assumptions

The baseline DiD methodology is valid on the assumption that, in the absence of the policy, net cross-border migration trends across the different income bands would have run parallel. We account for non-parallel trends pre-policy by using propensity score matching (PSM) (see Sigurdsson, 2019, for an example of using PSM in extensive margin analysis). We select a control group from the BR based on the characteristics: age, gender, sector and historical cross-border migration patterns. We estimate propensity scores using a logistic (logit) regression.

We match individuals using nearest-neighbour one-to-one matching (NN1) with replacement. This means that each individual in the income band is matched to one individual in the compared income band with the most similar characteristics. We also use nearest-neighbour 2 (NN2) matching as a robustness check (section 7.5). We use Abadie and Imbens (2006) to calculate standard errors for nearest neighbour matches.

We test the unconfoundedness and parallel trends assumption, that conditional on these explanatory variables, cross-border migration outcomes would have been the same in the income bands being compared, by examining the parallel trends for each income band. We mechanically test the parallel trends by regressing net cross-border migration changes in the pre-policy tax years. We use a DiD approach, comparing net cross-border migration outcomes between 2015 to 2016 and 2016 to 2017, 2015 to 2016 and 2017 to 2018 as well as 2016 to 2017 and 2017 to 2018. We test common support by examining the overlap in the propensity score distribution between the income bands being compared.

Parallel trend graphs, balance plots and pre-policy regression results are included in annex D. We find good overlap in propensity scores between income bands after matching, indicating that the groups are balanced along matched characteristics on average. We find visually parallel trends for most groups and no statistically significant differences in pre-policy cross-border migration trends, indicating that the parallel trends assumption holds.

7.4 Results

In table 13 we present our results for the net cross-border migration regression analysis. Table 13 shows the estimates of the policy effect on the tax rate (log(ARR) column), the first stage results, and the corresponding semi-elasticities for net cross-border migration (semi-elasticity column), the second stage results. F-values are presented in table D2 in annex D.

Table 13: Results of the cross-border migration regression analysis

Income band	2018 to 2019 log(ARR)	2018 to 2019 Semi-elasticity	2019 to 2020 log(ARR)	2019 to 2020 Semi-elasticity
£500,001+	-2.04%***	2.56***	-2.49%***	0.48
	(-0.023, -0.018)	(0.921, 4.192)	(-0.027, -0.023)	(-0.683, 1.639)
TR	-2.14%***	0.44**	-2.38%***	0.00
	(-0.023, -0.020)	(0.099, 0.777)	(-0.025, -0.023)	(-0.285, 0.285)
HR	-1.54%***	0.19***	-2.12%***	0.04
	(-0.016, -0.015)	(0.101, 0.272)	(-0.022, -0.021)	(-0.025, 0.095)
IR	-0.55%***	0.14**	-0.71%***	0.08*
	(-0.006, -0.005)	(0.021, 0.262)	(-0.007, -0.007)	(-0.010, 0.171)
SR	0.25%***	0.02	0.37%***	0.10
	(0.002, 0.003)	(-0.932, 0.976)	(0.003, 0.004)	(-0.523, 0.730)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

The policy effect on the tax rate, log(ARR), is the percentage change in the ARR for the income band relative to the BR. A negative effect implies a decrease in the ARR, paying more tax, relative to the BR and a positive effect implies an increase in the ARR, paying less tax, relative to the BR.

We find statistically significant changes in the ARR relative to the BR for each income band (first stage results). The ARR has on average decreased for individuals in the IR, HR and TR and increased for individuals in the SR. The change in the ARR generally increases with income.

The semi-elasticity of cross-border migration with respect to a change in the ARR is the percentage point change in the probability of migrating (net) given a one % change in the ARR. For individuals in the IR and above, who have experienced a decrease in their ARR on average, a positive elasticity shows that there was a decrease in net cross-border migration (more individuals leaving or less individuals entering) following the decrease in the ARR and a negative elasticity shows that there was an increase in net cross-border migration (less individuals leaving or more individuals entering) following the decrease in the ARR. For individuals in the SR, who have experienced an increase in their ARR on average, a positive elasticity shows that there was an increase in net cross-border migration following the increase in the ARR and a negative elasticity shows that there was a decrease in net cross-border migration following the increase in the ARR.

The semi-elasticities are generally small, but significant in 2018 to 2019 for the £500,001+, TR, HR and IR income groups. The semi-elasticities increase with income. The £500,001+ group has the largest semi-elasticity of 2.56. This means that for each 1% decrease in the ARR there was a 2.56 percentage point decrease in net migration. The standard errors are large, meaning that there is quite low precision. For example, for the £500,001+ group, the upper and lower bounds (95% confidence intervals) range from 0.9 to 4.2, for the TR group they range from 0.1 to 0.8 and for the HR group from 0.1 to 0.3. The wider ranges for the highest income groups are also a result of the smaller population sizes and more within-group variation.

For the SR, the semi-elasticities are not statistically significant. However, we note that the range of the estimates given by the confidence intervals are wide, suggesting low precision of the results.

In 2019 to 2020, the semi-elasticities decrease compared to 2018 to 2019 for the higher income groups and are no longer significant. In the IR, we see a small significant semi-elasticity in 2019 to 2020. This could indicate that there is some persistence or delay in the change in net cross-border migration from 2018 to 2019, however given that the elasticity is close to 0 and only significant at the 10% level this is uncertain.

For the IR, HR, TR and £500,001+ groups, we consider in- and out-migration separately in table 14. In-migration is defined as migration from rUK to Scotland and out-migration is defined as migration from Scotland to rUK. We run a DiD regression on in- and out-migration to detect the underlying changes, where they both take the value of 1 or 0. This means that a positive change implies an increase in in- or out-migration, and a negative change implies a decrease in in- or out-migration.

Table 14: Results for the cross-border in- and out-migration DiD analysis

Income band	In-migration 2018 to 2019	In-migration 2019 to 2020	Out-migration 2018 to 2019	Out-migration 2019 to 2020
£500,001+	-0.018**	-0.009	0.034**	0.003
	(-0.035, 0.000)	(-0.024, 0.006)	(0.007, 0.062)	(-0.021, 0.027)
TR	0.004*	0.006*	0.014***	0.006**
	(0.000, 0.009)	(0.002, 0.011)	(0.008, 0.019)	(0.001, 0.012)
HR	0.006***	0.006***	0.009***	0.007***
	(0.005, 0.007)	(0.005, 0.007)	(0.008, 0.009)	(0.006, 0.008)
IR	0.004***	0.003***	0.004***	0.004***
	(0.003, 0.004)	(0.003, 0.004)	(0.004, 0.005)	(0.003, 0.004)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

We find that for the £500,001+ group, the significantly positive semi-elasticity in 2018 to 2019 is primarily driven by an increase in out-migration (Scotland to rUK), along with a smaller fall in in-migration (rUK to Scotland). For the TR, we find that the significantly positive semi-elasticity in 2018 to 2019 is driven by an increase in out-migration. For the HR and IR, there is a statistically significant increase in out-migration, driving the significantly positive semi-elasticities. However, there is also a significant increase in in-migration which is unexpected and could suggest the presence of a confounder (an unmeasured third variable that influences both the supposed cause and supposed effect). We see the same changes in the 2019 to 2020 results for the IR, HR and TR.

Finally, table 15 presents the results for net cross-border migration for the HR and TR by subgroups: ages 20 to 30, ages 30+, female and male. It shows the estimates of the policy effect on the tax rate (log(ARR) column) and the corresponding semi-elasticities for net cross-border migration (semi-elasticity column).

Table 15: Results of the net cross-border migration regression analysis for the HR and TR by subgroup

TR	2018 to 2019 log(ARR)	2018 to 2019 Semi-elasticity	2019 to 2020 log(ARR)	2019 to 2020 Semi-elasticity
Age 20 to 30	-2.84%***	3.37	-3.48%***	0.87
	(-0.039, -0.018)	(-0.790, 7.529)	(-0.045, -0.024)	(-2.210, 3.951)
Age 30+	-2.13%***	0.37**	-2.36%***	-0.02
	(-0.023, -0.020)	(0.032, 0.699)	(-0.025, -0.022)	(-0.306, 0.256)
Female	-2.24%***	0.34	-2.55%***	-0.21
	(-0.025, -0.019)	(-0.392, 1.063)	(-0.029, -0.023)	(-0.840, 0.427)
Male	-2.17%***	0.50**	-2.42%***	0.26
	(-0.023, -0.020)	(0.079, 0.911)	(-0.026, -0.023)	(-0.081, 0.608)

HR	2018 to 2019 log(ARR)	2018 to 2019 Semi-elasticity	2019 to 2020 log(ARR)	2019 to 2020 Semi-elasticity
Age 20 to 30	-2.58%***	0.91***	-3.25%***	0.24**
	(-0.027, -0.025)	(0.611, 1.205)	(-0.034, -0.031)	(0.010, 0.466)
Age 30+	-1.46%***	0.08*	-2.03%***	0.01
	(-0.015, -0.014)	(-0.008, 0.168)	(-0.021, -0.020)	(-0.053, 0.068)
Female	-1.57%***	-0.07	-2.31%***	-0.17***
	(-0.016, -0.015)	(-0.225, 0.081)	(-0.024, -0.022)	(-0.273, -0.072)
Male	-1.58%***	0.38***	-2.13%***	0.18***
	(-0.016, -0.015)	(0.276, 0.480)	(-0.022, -0.021)	(0.108, 0.251)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

There is a lot of variation in the results, and some uncertainty given the smaller population sizes, especially for the age 20 to 30 and female groups. For both the HR and TR, the semi-elasticities (second stage results) are largest for individuals aged 20 to 30 and male. This could indicate a larger responsiveness among these demographic groups, albeit the semi-elasticity for the TR 20 to 30 age group is not significant.

Males and those aged 30+ are the largest proportion of individuals in these income groups, and their results do not differ substantially from the headline results. This suggests that the larger changes in especially the 20 to 30 age group do not appear to be confounding the results.

7.5 Robustness

Matching methods

The headline results use nearest neighbour matching where one individual in the income band is matched to one individual in the BR. As a robustness check, we also run the regressions using nearest-neighbour 2 matching (NN2), where 2 individuals in the BR are matched to one individual in the income band. Given that the income bands have fewer observations than the BR, this method provides us with a larger BR sample to compare to. In table 16, we present the results from the regression analysis using NN2 matching.

Table 16: Results of the net cross-border migration regression analysis using NN2 matching

Income band	2018 to 2019 log(ARR)	2018 to 2019 Semi-elasticity	2019 to 2020 log(ARR)	2019 to 2020 Semi-elasticity
£500,001+	-1.96%***	2.13***	-2.50%***	0.36
	(-0.022, -0.018)	(0.633, 3.631)	(-0.027, -0.023)	(-0.658, 1.380)
TR	-2.05%***	0.40*	-2.57%***	0.05
	(-0.022, -0.019)	(0.091, 0.718)	(-0.027, -0.024)	(-0.181, 0.289)
HR	-1.40%***	0.23***	-2.19%***	0.04
	(-0.014, -0.014)	(0.150, 0.318)	(-0.022, -0.021)	(-0.010, 0.093)
IR	-0.44%***	0.59***	-0.56%***	0.16***
	(-0.004, -0.004)	(0.453, 0.728)	(-0.006, -0.006)	(0.060, 0.262)
SR	0.29%***	0.51	0.43%***	0.34
	(0.003, 0.003)	(-0.213, 1.225)	(0.004, 0.005)	(-0.122, 0.807)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

When using NN2 matching, the semi-elasticities are similar to those obtained using NN1 matching for the HR, TR and £500,001+ groups. The results for 2018 to 2019 are similar in magnitude and statistically significant. The results for 2019 to 2020 are close to 0 and not statistically significant. For the IR group, the NN2 matching semi-elasticities are much larger than those using NN1 matching and also statistically significant in both years. For the SR group, the semi-elasticities are larger in magnitude, but statistically insignificant.

Placebo regression

As an additional robustness check, we run a placebo regression where we compare individuals in the BR to individuals below the Personal Allowance (PA) who were not directly affected by the Income Tax changes. We use the same DiD with propensity score NN1 matching method and compare the BR (‘treated group’) to the PA (‘control group’). The results for the DiD regression comparing net cross-border migration outcomes before and after the policy change are summarised in table 17.

Table 17: Changes in net cross-border migration following the Scottish Income Tax changes, BR compared to below the PA

	2018 to 2019	2019 to 2020
Net migration	-0.0003	-0.0118***
	(-0.001, 0.0005)	(-0.013, -0.011)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

We find no significant changes in net cross-border migration in 2018 to 2019. In 2019 to 2020, the regression results show a statistically significant divergence between the 2 groups, with net migration falling in the BR relative to the below PA group. This suggests that there is a confounding factor present in 2019 to 2020 that could be impacting the headline results. The placebo analysis satisfies the validity test for 2018 to 2019 but not for 2019 to 2020.

Below the Personal Allowance as a control group

Given that we identify a potential confounding factor in 2019 to 2020 when comparing the BR to individuals below the PA, we replicate the analysis for all income bands using the below PA group as the control group instead of the BR. We use the same DiD with NN1 propensity score matching method. Parallel trend graphs, balance plots and pre-policy regression results are included in annex E. We find good overlap in propensity scores between income bands after matching, indicating that the groups are on average balanced along matched characteristics. We find no statistically significant differences in pre-policy migration trends, indicating that the parallel trends assumption holds. The regression results are presented in table 18.

Table 18: Changes in net cross-border migration following the Scottish Income Tax changes, below PA as the control group

Income band	2018 to 2019 log(ARR)	2018 to 2019 Semi-elasticity	2019 to 2020 log(ARR)	2019 to 2020 Semi-elasticity
£500,001+	-1.87%***	3.03***	-1.93%***	0.62
	(-0.020, -0.017)	(1.245, 4.815)	(-0.021, -0.018)	(-0.898, 2.136)
TR	-1.77%***	0.46**	-2.05%***	0.37**
	(-0.019, -0.017)	(0.062, 0.868)	(-0.022, -0.019)	(0.045, 0.700)
HR	-1.21%***	0.21***	-1.74%***	0.15***
	(-0.012, -0.012)	(0.103, 0.324)	(-0.018, -0.017)	(0.073, 0.223)
IR	-0.31%***	0.01	-0.13%***	1.20***
	(-0.003, -0.003)	(-0.204, 0.234)	(-0.001, -0.001)	(0.668, 1.718)
SR	0.37%***	-0.64*	0.96%***	-0.26*
	(0.004, 0.004)	(-1.335, 0.053)	(0.009, 0.010)	(-0.513, 0.002)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

The semi-elasticities in the £500,001+, TR, and HR groups in 2018 to 2019 are similar to the headline results. For the IR, the 2018 to 2019 semi-elasticity is close to 0 and insignificant.

Compared to the headline results, the semi-elasticities in 2019 to 2020 are larger and significant in the IR, HR and TR income groups. This is driven by the increase in net cross-border migration in the below PA group relative to the BR group in this year, as shown in table 17. For the IR, the semi-elasticity in 2019 to 2020 is significantly larger than the headline result and the semi-elasticities found for the other income bands in that year. For the SR, the semi-elasticities are very different to the headline results in both years, as they are now negative and significant at the 10% level.

The robustness checks show a lot of fluctuation in the results for the IR and SR depending on matching method (NN1 or NN2) and choice of control group. This could be due to the change in the ARR for these groups being small, resulting in a small denominator for the semi-elasticity. In practice, this means that small fluctuations in the change in net cross-border migration can lead to large changes in the resulting semi-elasticity. Additionally, these populations are more similar to the BR in terms of historical migration patterns. Changes in the propensity score matching methodology can therefore lead to significant changes in the make-up and subsequent trends of the matched BR population.

7.6 Discussion

Interpretation of results

We find some evidence of a change in intra-UK cross-border migration for individuals above the Scottish Higher rate threshold (HRT) in the first year of policy implementation, following the Scottish Income Tax rate changes in 2018 to 2019. The size of the change is reasonable, broadly consistent with findings in the literature and generally increasing with income group. We confirm parallel trends in net cross-border migration for all income groups pre-policy using placebo regressions (annex D), and therefore assume that DiD is valid. Additionally, the 2SLS method controls, in part, for issues of endogeneity.

For individuals above the Scottish HRT, compared to individuals in the Scottish BR band, net cross-border migration decreased. This implies that more individuals moved from Scotland to rUK and/or less individuals moved to Scotland from rUK following the policy change. In particular, we find that this is primarily driven by an increase in individuals moving from Scotland to rUK, which could be to reduce their tax burden and would be consistent with economic theory. For the £500,001+ band we also find a statistically significant fall in in-migration in 2018 to 2019, which is consistent with the assumption that the highest earning individuals in rUK chose not to move to Scotland to avoid the higher tax burden.

However, for the other income bands we find an increase in in-migration (rUK to Scotland) following the Income Tax changes, albeit smaller increases than for out-migration (Scotland to rUK). These increases are likely to be driven by factors besides the Income Tax changes, suggesting that there might be other underlying factors contributing to changes in migration trends in these years that are not being controlled for, either in the HR and TR income bands or in the BR counterfactual band.

When testing the headline results using 2 other approaches, NN2 matching and individuals below the PA as the counterfactual, the results are broadly consistent and statistically significant for the HR, TR and £500,001+ income bands. We find some evidence that the semi-elasticities vary by characteristics such as age and gender with the largest changes seen for young and male individuals.

We estimate the largest cross-border migration semi-elasticities for taxpayers earning above £500,000. The headline semi-elasticity for this group is 2.56 and ranges from 2.13 to 3.03 depending on the control group and matching method used. This result is central when compared to estimates found in the literature, 0.1 to 6.5 (Young and Varner, 2011 and Martinez, 2017). However, the confidence intervals for these estimates are in general large, suggesting that we could be over- or underestimating the change in cross-border migration flows. This will be driven by small sample sizes and large within-group variations, especially for the HR, TR and £500,001+ income bands.

Two years after the policy was implemented, we find no evidence of divergences in cross-border migration trends, with most of the headline results being statistically insignificant. This suggests that it was a short-term change for those taxpayers that migrated following the Income Tax changes but does not appear to be a persistent long-term outcome. However, the placebo test comparing individuals in the BR to individuals below the PA shows a significant change in net cross-border migration in 2019 to 2020. This suggests the presence of a confounder which we have not been able to control for. Therefore, we have not been able to identify a valid control group for 2019 to 2020.

When using individuals below the PA as the control group, we estimate larger semi-elasticities in 2019 to 2020 for the higher income groups. This might suggest some persistence in the changes in cross-border migration 2 years after the Income Tax changes. However, given the presence of a potential confounder, we conclude that the results for 2019 to 2020 are uncertain.

We find no reliable evidence of a change in net cross-border migration for SR or IR taxpayers. For the SR, the headline results show no statistically significant changes. When using individuals below the PA as the counterfactual group we find negative and unintuitive results. For the IR, the headline results suggest a small, significant change in both years. However, this result varies significantly when testing the alternative approaches of NN2 matching and using the PA as the counterfactual group. Given the sensitivity present for these 2 income bands, we conclude that the results are too uncertain to infer any conclusive changes in cross-border migration trends.

While we do find some evidence of a change in cross-border migration following the Scottish Income tax changes in 2018 to 2019 for Scottish taxpayers above the HRT, we note that these results are reliable to the extent to which they are driven by the Scottish Income Tax changes in 2018 to 2019. We consider some additional limitations to the analysis.

Firstly, the results could be dependent on the choice of the counterfactual. HR and TR taxpayers are likely to be subject to and react differently to certain incentives compared to BR taxpayers or individuals below the PA. In particular, this analysis measures only changes in average Income Tax rates and does not capture effective tax rates. In reality, individuals are subject to a range of other taxes and benefits which could influence tax-induced behaviour. The semi-elasticities estimated are only based on Income Tax changes, so the true magnitude of the ‘effective’ semi-elasticities are likely to be different.

Secondly, there are also other wider economic factors that could influence individuals’ migration decisions that differ between higher income and lower income individuals. In particular, individuals on higher incomes might have more job security and flexibility to make tax-motivated decisions, whereas individuals in lower income bands might be more constrained in their options and choices. This paper has used a dataset that is limited to annual observations and only able to control for high-level demographic characteristics such as age, gender and employment.

Other policies simultaneous to the period studied may also have had an impact on migration decisions. For example, the Early Learning and Childcare (ELC) expansion in Scotland could have contributed to an increase in net migration to Scotland. Divergences in land transaction taxes at the time could have incentivised movements across borders for those looking to purchase a property. These are all potential confounders that we have not fully been able to control for, apart from through the demographic characteristics previously mentioned.

Illustrative implications for NSND Income Tax

In table 19 we estimate the illustrative NSND Income Tax impacts from cross-border migration only for the Higher rate (HR), lower Top rate (TR) (£150,001 to £500,000) and £500,001+ income groups using the headline elasticities estimated. This only includes the NSND Income Tax impact and excludes NICs and other non-devolved taxes. Cross-border migration has no direct impact on Scotland through non-devolved taxes as these are collected by the UK Government regardless of whether the individual is a Scottish or rUK taxpayer. There could be some indirect effects, such as through the Block Grant Adjustment (BGA).

For simplicity, we assume an initial migration rate of 0%. The percentage point change therefore relates to the percentage change in net migration as a result of the Income Tax change. We use total NSND income and average ATRs from the raw dataset used in the analysis. We apply the elasticity to the change in the ARR from the first stage headline regressions to find the % change in migration. We apply the % change in migration to total NSND income (in 2017 to 2018). Finally, we apply the new ATR in 2018 to 2019 to estimate the NSND tax impact:

(25) % Behaviour = Elasticity x % ∆ARR_{2018 to 2019}

(26) ∆NSND Income = % Behaviour x Total NSND Income_{2017 to 2018}

(27) ∆NSND Tax = ∆NSND Income x % ATR_{2018 to 2019}

We also include an estimate for the number of people that the change represents, by multiplying the percentage behavioural change by the total number of people in the income band:

(28) ∆# Individuals = % Behaviour x Total # Individuals_{2017 to 2018}

Table 19: Illustrative tax impact, HR, TR (£150,001 to £500,000) and £500,001+ group (Note 1), (Note 2)

	£500,001+ (TR)	£150,001 to £500,000 (TR)	HR
(A) Population in band	1,210	13,710	291,520
(B) Total income in band	1,644,000,000	3,048,600,000	18,692,500,000
(C) ATR	44%	39%	22%
(D) Change in ARR	-2.0%	-2.1%	-1.5%
(E) Elasticity	2.56	0.44	0.19
(F=D*E) Behaviour	-5.2%	-0.9%	-0.3%
(G=B*F) Lost income (£)	85,800,000	28,600,000	53,700,000
(H=C*G) Lost tax (£)	37,800,000	11,100,000	11,700,000
(I=A*F) Net loss in population	60	130	840

Note 1: All £ figures rounded to the nearest hundred thousand. All population figures rounded to the nearest 10.

Note 2: The population in band figures may differ from the Scottish Income Tax Outturn Statistics due to methodological differences. For example, the Scottish Income Tax Outturn Statistics applies allowances and reliefs which may place individuals in other tax bands.

For the tax year 2018 to 2019, we estimate a loss in NSND Income Tax from cross-border migration of approximately £12 million, or 840 individuals, for the HR band and £11 million, or 130 individuals, for the lower TR band (£150,001 to £500,000). For the upper TR band (£500,001+), this would imply a larger tax impact of approximately £38 million, or 60 people. The outturn figures for Scottish Income Tax paid by HR and TR taxpayers in 2018 to 2019 are £4,764 million and £2,004 million respectively. The total outturn figure for Scottish Income Tax in 2018 to 2019 is £11,549 million.

The estimates for NSND Income Tax lost from cross-border migration therefore account for approximately 0.2% and 2.4% of the HR and TR tax base respectively, and 0.5% of the total Scottish Income Tax base. These estimates are based on the headline semi-elasticity estimates. We use the 95% confidence intervals for these estimates to exemplify the range of estimates for the loss in NSND Income Tax as a result of cross-border migration. Table 20 shows the central, lower and upper bound estimates for each income band.

Table 20: Illustrative tax impacts - central, upper and lower bound estimates, HR, TR (£150,001-£500,000) and £500,001+ group

(£)	Lower	Central	Upper
£500,001+ (TR)	13,600,000	37,800,000	62,000,000
£150,001 to £500,000 (TR)	2,500,000	11,100,000	19,700,000
HR	6,300,000	11,700,000	17,000,000
Total	22,400,000	60,600,000	98,700,000

In total, we estimate a loss in NSND Income Tax from cross-border migration of £60.6 million (central estimate), ranging from £22.4 million (lower bound estimate) to £98.7 million (upper bound estimate). This is equivalent to approximately 0.5% (central estimate) of the total Scottish Income Tax base, ranging from 0.2% (lower bound estimate) to 0.8% (upper bound estimate).

These impacts are for illustrative purposes only and do not represent true changes to Income Tax receipts as a result of cross-border migration in response to the policy. The true tax impact will depend on the total income of the individuals migrating. The estimated elasticities are also contextual. Other Income Tax changes would not result in exactly the same proportional changes.

Our estimated semi-elasticities and modelling approach for the illustrative tax impacts differ from methods used by the Scottish Fiscal Commission (SFC). Specifically, the SFC capture extensive margin behavioural responses, including changes in labour market participation and cross-border migration, primarily through their average effective tax rate (AETR) factors. These factors apply directly to the changes in Income Tax liabilities as a result of changes in tax policy excluding a change in the taxpayers marginal rate. The SFC assume no extensive margin responses for individuals earning below the Basic rate limit (BRL), a factor of 0.06 for individuals above the BRL to £150,000 in taxable income and a factor of 0.25 for individuals above £150,000 in taxable income.

For changes to a taxpayers top marginal Income Tax rate, the SFC apply their Taxable Income Elasticities (TIEs). The TIEs are multiplied by the percentage change in the marginal Income Tax rate to provide the expected change in taxable income. The SFC’s TIEs range from 0.015 to 0.75 and increase with income. Finally, the SFC also apply a framework to capture revenue effects of additional intra-UK migration responses on top of those already captured in the AETR factors and TIEs. This framework applies an elasticity of 0.06 for taxpayers above the HRT and 0.25 for taxpayers above £150,000 in taxable income to the tax differential between Scotland and rUK. As such, the SFC capture extensive margin responses (including labour market participation and intra-UK cross-border migration) through these 3 channels.

These differences do not impact the results found in this paper but mean that a direct comparison between the elasticities used by the SFC and those estimated in this paper will not be accurate. The semi-elasticities estimated in this paper are loosely comparable to the SFC’s AETR factors.

8. Conclusion

Our paper has attempted to estimate how responsive labour market participation and intra-UK cross-border migration are to Income Tax changes, by exploiting the quasi-experimental variation created by the Scottish Income Tax rate changes in 2018 to 2019. The recently published paper ‘Intra-UK migration of individuals: movements in numbers and income’ provides an overview of general cross-border migration trends between Scotland, Wales and rUK. Our paper has taken this further by attempting to reveal the causal relationship between the Scottish Income Tax changes in 2018 to 2019 and changes in net cross-border migration, which cannot otherwise be detected by solely examining the general trends.

Our paper finds no evidence of changes in labour market participation and some limited evidence of a decrease in net cross-border migration (number of immigrants minus the number of emigrants) for Scottish taxpayers above the Higher rate threshold following the Scottish Income Tax changes. The changes we have identified in the context of the introduction of the 5-band system in Scotland in 2018 to 2019 are likely to be different in other contexts and tax regimes.

The labour market participation semi-elasticities are generally close to 0, statistically insignificant, and broadly consistent with the wider literature. These results seem reasonable given that the change in the average tax rate (ATR) was small relative to policies studied in the wider literature. It is likely that labour market behaviour on the intensive margin, as studied in HMRC’s previously published paper ‘Estimating Scottish taxpayer behaviour in response to Scottish Income Tax changes introduced in 2018 to 2019’, is more elastic and easier to adjust compared to labour market behaviour on the extensive margin.

The cross-border migration semi-elasticity estimates range between 0.19 to 2.56 for taxpayers above the Scottish Higher rate threshold (HRT) and increase with income. These estimates are statistically significant, stable across specifications, and broadly consistent with the wider literature. The change in the ATR for Scottish taxpayers above the Scottish HRT following the introduction of the 5-band system ranges from 1.5% to 2%, which has a small impact on the yearly tax burden. We consider 3 explanations for the findings and why it is reasonable that this tax rate change could have had an impact on net cross-border migration.

First, within-UK mobility costs, such as administrative and cultural barriers, are low. Higher earning taxpayers may also already have multiple residencies in both Scotland and rUK making the move relatively easy, in theory. Second, the long-term impact of an increased tax burden over multiple years could be perceived as a significant loss in net-of-tax income. Third, the increase in Income Tax rates could have set a precedent, leading to taxpayers expecting further increases in the future. Additional Scottish Income Tax increases were introduced in the tax year 2023 to 2024 and announced to be introduced in 2024 to 2025.

However, the precise size of the estimated semi-elasticities is uncertain. The confidence intervals are in general wide. For cross-border migration, there is also some uncertainty in the results for individuals below the HRT and for 2019 to 2020 (second year of policy implementation). As discussed throughout the paper, we also note that the estimates are reliable only to the extent to which they are driven by the Scottish Income Tax changes in 2018 to 2019. The results could be dependent on the choice of the counterfactual as the treated and control groups might be subject to different incentives not captured in this analysis. We are only able to control for high-level demographic characteristics such as age, gender and employment. Finally, there are also other wider economic factors and simultaneous policies that could have impacted labour market participation and cross-border migration decisions during the time period studied.

9. References

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10. Annexes

10.1 Annex A – Observations and variables

Table A1 provides the number of observations in the dataset, including the number of observations that have NSND income, for the tax years 2014 to 2015 to 2020 to 2021.

Table A1: Number of observations (Note 1), (Note 2)

Observations	with NSND income	with no NSND income	Total
2014 to 2015	43,849,470	13,704,125	57,553,595
2015 to 2016	44,825,697	12,727,898	57,553,595
2016 to 2017	45,462,640	12,090,955	57,553,595
2017 to 2018	45,857,573	11,696,022	57,553,595
2018 to 2019	46,331,486	11,222,109	57,553,595
2019 to 2020	46,706,634	10,846,961	57,553,595
2020 to 2021	45,573,013	11,980,582	57,553,595

Note 1: These figures may differ from other sources due to methodological differences.

Note 2: The Scottish Income Tax Outturn Statistics only includes taxpayers that pay Income Tax (after allowances and reliefs have been applied). This generally means that they have an income above the Personal Allowance. The figures in table A1 include all individuals in work (with NSND income) and will therefore also include individuals with an income below the Personal Allowance.

Table A2 defines each variable in the dataset and how it has been sourced.

Table A2: Variables

Variable	Description	Source
Income	Non-savings non-dividends (NSND) income. For Pay As You Earn (PAYE), an individual’s annual income is assumed to be the sum of their monthly pay across the tax year. Multiple employments are summed together. For Self Assessment, we use total NSND income as captured by the filing deadline for each tax year. For individuals with both an RTI and Self Assessment record, we have prioritised their Self Assessment income over their RTI pay in any given year as their Self Assessment NSND income will capture all forms of income, including their employment income from RTI.	Real Time Information (RTI) and Self Assessment Outturn data
S-flag	Scottish taxpayer indicator. This is based on where an individual resides for the majority of a tax year. Further information on who pays Scottish Income Tax can be found on the GOV.UK website. The s-flags in our dataset for both RTI and Self Assessment taxpayers are drawn from, and therefore consistent with, the HMRC data used to construct the Scottish Income Tax Outturn Statistics. Individuals without an s-flag are assumed to be residing in the rest of the UK (rUK).	Scottish Income Tax Outturn data
Age and Sex	Age and Sex is sourced from HMRC’s RTI data for both RTI and Self Assessment taxpayers wherever possible. Age is taken as their age at the end of the tax year in question. Sex will be the sex provided to HMRC by the individual’s employer.	RTI data
Sector	For each individual and tax year, we have sourced a Standard Industrial Classification of Economic Activities (SIC) code and placed these into the twenty-one sections of industry as defined on the Companies House website. For RTI individuals, we have sourced a SIC code based on their employment. For an individual with multiple employments, we have taken the SIC code attached to their employment with the highest amount of pay in that tax year. For Self Assessment taxpayers, an individual’s main source of income is the factor that determines their industry classification. For example, for a Self Assessment individual whose main source of income is classified as employment pay, we have sourced a SIC code on record based on their employer. For a Self Assessment individual whose main source of income is classified as being a sole trader, we have sourced their SIC code on record based on their trade income. Individuals with income from an occupational pension are flagged as a Pensioner.	RTI and Self Assessment data
Region	Nomenclature of Territorial Units for Statistics (NUTS) level 1 classification which covers Wales, Scotland, Northern Ireland and 9 regions of England. For RTI individuals, we have sourced the classification assigned to each individual’s monthly pay. We have subsequently taken their annual NUTS 1 to be the NUTS 1 for the majority of the tax year. It can therefore be thought of as the concentration of income where it spent the majority of the tax year in question. For Self Assessent individuals, we use the recorded postcode that was active for the individual for the tax year in question. These postcodes are matched to the equivalent NUTS 1 classification.	RTI and Self Assessment data

10.2 Annex B – Labour market participation parallel trends, balance plots and F-values

Figures B1, B3, B5, B7 and B9 below show the trends in labour market participation (proportion of the population in work) for Scotland and rUK for each income band from 2014 to 2015 to 2019 to 2020, before and after matching. Before the introduction of the 5-band system in 2018 to 2019, the figures generally show non-parallel trends between Scotland and rUK before matching and parallel trends after matching. After the introduction of the 5-band system in 2018 to 2019 and 2019 to 2020, the figures generally show small to no deviations in labour market participation trends between Scotland and rUK after matching.

Figures B2, B4, B6, B8 and B10 show the propensity scores before (left) and after matching (right) for each income band. On the left, the figures show the density of propensity scores for the treated (Scotland) and control (rUK) groups before matching, where we generally see that there are sizeable differences in the density of propensity scores. On the right we see significant overlap between the treated and matched control groups.

Figure B1: Trends in labour market participation (% in work) Scotland compared to rUK using NN1 matching - £100,001+ income band

Figure B2: Propensity score overlap before and after matching (NN1) - £100,001+ income band

Figure B3: Trends in labour market participation (% in work) Scotland compared to rUK using NN1 matching - £43,431 to £100,000 income band

Figure B4: Propensity score overlap before and after matching (NN1) - £43,431 to £100,000 income band

Figure B5: Trends in labour market participation (% in work) Scotland compared to rUK using NN1 matching - £24,001 to £43,430 income band

Figure B6: Propensity score overlap before and after matching (NN1) - £24,001 to £43,430 income band

Figure B7: Trends in labour market participation (% in work) Scotland compared to rUK using NN1 matching - £13,851 to £24,000 income band

Figure B8: Propensity score overlap before and after matching (NN1) - £13,851 to £24,000 income band

Figure B9: Trends in labour market participation (% in work) Scotland compared to rUK using NN1 matching - £11,851 to £13,850 income band

Figure B10: Propensity score overlap before and after matching (NN1) - £11,851 to £13,850 income band

Table B1 shows the F-values of the first stage regressions for the labour market participation regression analysis for each income band.

Table B1: F-values for labour market participation 2SLS regression analysis

Income band	2018 to 2019	2019 to 2020
£100,001+	F(3, 117088) = 146.47	F(3, 116403) = 599.73
£43,431 to £100,000	F(3, 750713) = 497.38	F(3, 747213) = 2157.86
£24,001 to £43,430	F(3, 2419298) = 510.06	F(3, 2407890) = 1177.58
£13,851 to £24,000	F(3, 2739204) = 129.85	F(3, 2718476) = 1968.92
£11,851 to £13,850	F(3, 607669) = 849.81	F(3, 601502) = 2418.82
All	F(3, 6633988) = 92.14	F(3, 6591500) = 275.52

10.3 Annex C – Regression discontinuity design (RDD)

Figure C1 shows the line of best fit for income and net cross-border migration for individuals with an income between £100,000 (start of PA taper) and £123,700 (end of PA taper) as well as £123,700 and £150,000 (TRT). We observe no significant structural break in net cross-border migration at an income of £123,700.

Figure C1: Plot showing relationship between income (£) and net cross-border migration (percentage points), above and below the Personal Allowance taper (£123,700)

10.4 Annex D – Migration parallel trends, balance plots, and placebo regressions

Figures D1, D3, D5, D7 and D9 below show the trends in net cross-border migration (as a % of the total income band population) for each income band compared to the BR from 2015 to 2016 to 2019 to 2020, before and after matching. Before the introduction of the 5-band system in 2018 to 2019, the figures generally show non-parallel trends between the income bands before matching and parallel trends after matching. After the introduction of the 5-band system in 2018 to 2019 and 2019 to 2020, the figures generally show a deviation in net cross-border migration for the £500,001+ (figure D1), AR (figure D3) and HR (figure D5) income bands compared to the BR in 2018 to 2019 after matching, but no deviation in 2019 to 2020. For the IR (figure D7), we see a small deviation in both 2018 to 2019 and 2019 to 2020. For the SR (figure D9), we see no significant deviation in either year.

Figures D2, D4, D6, D8 and D10 show the propensity scores before (left) and after matching (right) for each income band. On the left, the figures show the density of propensity scores for the treated and control groups before matching, where we generally see that there are sizeable differences in the density of propensity scores. On the right we see significant overlap between the treated and matched control groups.

Figure D1: Trends in net cross-border migration from rUK to Scotland - £500,001+ income band compared to BR income band using NN1 matching

Figure D2: Propensity score overlap before and after matching (NN1) - £500,001+ income band compared to BR income band

Figure D3: Trends in net cross-border migration from rUK to Scotland - TR income band compared to BR income band using NN1 matching

Figure D4: Propensity score overlap before and after matching (NN1) - TR income band compared to BR income band

Figure D5: Trends in net cross-border migration from rUK to Scotland - HR income band compared to BR income band using NN1 matching

Figure D6: Propensity score overlap before and after matching (NN1) - HR income band compared to BR income band

Figure D7: Trends in net cross-border migration from rUK to Scotland - IR income band compared to BR income band using NN1 matching

Figure D8: Propensity score overlap before and after matching (NN1) - IR income band compared to BR income band

Figure D9: Trends in net cross-border migration from rUK to Scotland - SR income band compared to BR income band using NN1 matching

Figure D10: Propensity score overlap before and after matching (NN1) - SR income band compared to BR income band

Table D1 shows the regression results for the pre-policy difference-in-differences regressions comparing changes in net-cross border migration for all income bands compared to the BR, after NN1 propensity score matching. Specifically, changes from 2015 to 16 to 2016 to 2017, changes from 2016 to 2017 to 2017 to 2018 and changes from 2015 to 2016 to 2017 to 2018. We find no statistically significant differences for any of the income bands compared to the BR.

Table D1: Regression results for pre-policy migration difference-in-differences with the BR as the control group

	2015 to 2016 to 2016 to 2017	2016 to 2017 to 2017 to 2018	2015 to 2016 to 2017 to 2018
£500,001+	0.007	0.01	0.006
	(-0.03, 0.05)	(-0.02, 0.05)	(-0.03, 0.05)
TR	-0.0001	0.001	0.001
	(-0.01, 0.01)	(-0.008, 0.01)	(-0.01, 0.01)
HR	-0.0001	0.0001	0.0002
	(-0.002, 0.002)	(-0.001, 0.002)	(-0.002, 0.002)
IR	0.00003	-0.00001	-0.00005
	(-0.001, 0.001)	(-0.001, 0.0007)	(-0.001, 0.001)
SR	-0.001	-0.0002	0.0008
	(-0.004, 0.002)	(-0.003, 0.002)	(-0.003, 0.004)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1

Table D2 shows the F-values of the first stage regressions for the cross-border migration regression analysis for each income band.

Table D2: F-values for cross-border migration 2SLS regression analysis

Income band	2018 to 2019	2019 to 2020
£500,001+	F(3, 2680) = 224163.22	F(3, 2680) = 221885.78
TR	F(3, 34564) = 622784.02	F(3, 34564) = 624940.98
HR	F(3, 743132) = 899864.27	F(3, 743132) = 901002.24
IR	F(3, 1753352) = 2507743.31	F(3, 1753352) = 2325378.01
SR	F(3, 73288) = 100744.87	F(3, 73288) = 104787.85

10.5 Annex E – Migration parallel trends, balance plots, and placebo regressions: Below PA as the control group

Figures E1, E3, E5, E7 and E9 below show the trends in net cross-border migration (as a % of the total income band population) for each income band compared to the below PA income band from 2015 to 2016 to 2019 to 2020, before and after matching. Before the introduction of the 5-band system in 2018 to 2019, the figures generally show non-parallel trends between the income bands before matching and parallel trends after matching. After the introduction of the 5-band system in 2018 to 2019 and 2019 to 2020, the figures generally show a deviation in net cross-border migration for the £500,001+ (figure E1) income band compared to the below PA income band in 2018 to 2019 after matching, but no deviation in 2019 to 2020. For the AR (figure E3) and HR (figure E5), we see a deviation in both years. For the IR (figure E7) we see no deviation in 2018 to 2019, but a deviation in 2019 to 2020. For the SR (figure E9), we see no significant deviation in either year.

Figures E2, E4, E6, E8 and E10 show the propensity scores before (left) and after matching (right) for each income band. On the left, the figures show the density of propensity scores for the treated and control groups before matching, where we generally see that there are sizeable differences in the density of propensity scores. On the right we see significant overlap between the treated and matched control groups.

Figure E1: Trends in net cross-border migration from rUK to Scotland - £500,001+ income band compared to below £11,850 (below PA) income band

Figure E2: Propensity score overlap before and after matching (NN1) - £500,001+ income band compared to below £11,850 (below PA) income band

Figure E3: Trends in net cross-border migration from rUK to Scotland - TR income band compared to below £11,850 (below PA) income band

Figure E4: Propensity score overlap before and after matching (NN1) - TR income band compared to below £11,850 (below PA) income band

Figure E5: Trends in net cross-border migration from rUK to Scotland - HR income band compared to below £11,850 (below PA) income band

Figure E6: Propensity score overlap before and after matching (NN1) - HR income band compared to below £11,850 (below PA) income band

Figure E7: Trends in net cross-border migration from rUK to Scotland - IR income band compared to below £11,850 (below PA) income band

Figure E8: Propensity score overlap before and after matching (NN1) - IR income band compared to below £11,850 (below PA) income band

Figure E9: Trends in net cross-border migration from rUK to Scotland - SR income band compared to below £11,850 (below PA) income band

Figure E10: Propensity score overlap before and after matching (NN1) - SR income band compared to below £11,850 (below PA) income band

Table E1 shows the regression results for the pre-policy difference-in-differences regressions comparing changes in net-cross border migration for all income bands compared to the below PA income band, using NN1 propensity score matching. Specifically, changes from 2015 to 2016 to 2016 to 2017, changes from 2016 to 2017 to 2017 to 2018 and changes from 2015 to 2016 to 2017 to 2018. We find no statistically significant differences for any of the income bands compared to the below PA band.

Table E1: Regression results for pre-policy migration difference-in-differences with below PA as the control group

	2015 to 2016 to 2016 to 2017	2016 to 2017 to 2017 to 2018	2015 to 2016 to 2017 to 2018
£500,001+	-0.01	0.009	0.02
	(-0.05, 0.03)	(-0.03, 0.04)	(-0.02, 0.06)
TR	-0.0007	0.003	0.004
	(-0.01, 0.01)	(-0.005,0.01)	(-0.01,0.01)
HR	0.00001	0.0001	0.0001
	(-0.002, 0.002)	(-0.001, 0.002)	(-0.002, 0.002)
IR	0.00003	0.00006	0.00003
	(-0.001, 0.001)	(-0.001, 0.0008)	(-0.001, 0.001)
SR	0.0005	0.0009	0.0004
	(-0.003, 0.004)	(-0.002, 0.003)	(-0.003, 0.004)

95% confidence intervals in parentheses. ***p<0.01, **p<0.05, *p<0.1