What is known so far?

Although there has been much comment upon the impact of Brexit on the labour market, little rigorous analysis has been undertaken. The most cited study is that which indicates that, at least in the period between spring 2019 and summer 2022, Brexit resulted in a reduction in labour supply of some 330,000 persons (Portes and Springford, Reference Portes and Springford2023). The number of EU workers fell by about 460,000; the number of non-EU workers increased by 130,000. The largest shortfall of non-UK workers was mostly in sectors that disproportionately employ less-skilled workers. With respect to declines in the number of EU workers themselves, a sectoral breakdown suggested that it was made up as follows:

• • in transportation and storage: around 128,000 (about 8% of sectoral employment)

• • in wholesale and retail: 103,000 (about 3% of sectoral employment)

• • in accommodation and food: 67,000 (about 4% of sectoral employment)

• • in manufacturing: 47,000 (about 2% of sectoral employment)

• • in construction: 46,000 (about 2% of sectoral employment)

• • in administration and support (which covers activities such as building cleaning and maintenance): 32,000 (about 2% of sectoral employment).

The study arrived at its results by calculating the average growth rate in the workforce by region of origin (UK/EU/non-EU) for the 2014–19 period and, in the first instance, assuming that growth rates in the EU/non-EU born workforce would have followed a similar trajectory to that of the UK-born workforce. With respect to COVID-related developments, where UK-born workforce numbers fell, it was assumed that numbers of EU and non-EU workers would have declined at the same rate. This provided a counterfactual to what actually did happen—the 330,000 being the net difference for workers of all origins.Footnote ⁴

Another study by the ECB, on the impact of Brexit on UK trade and labour markets, found a increase in UK post-pandemic labour market tightness that was mainly attributable to a smaller pool of available workers. A faster than expected recovery was responsible for a rise in labour demand once the economy had reopened, but the study suggested that labour supply played a particularly important role in explaining the tightness seen. By contrast, what that study termed ‘aggregate supply constraints’ and ‘labour mismatches’ were less important as an explanation. The analysis used the method of historical shock decomposition based on a Bayesian vector auto-regression (BVAR) (Forster van Aerssen and Spital, Reference Forster van Aerssen and Spital2023).

A third study concentrated specifically on the Beveridge Curve relationship. However, what it considered was not the period after the UK had left the EU but rather the period after the Brexit referendum (from the summer of 2016 onward) and up to the point before leaving occurred (until the end of 2019). It focused on three industries—construction, transport and storage, and information and communication—on the grounds that they were likely to be particularly hard hit by higher trade barriers, reductions in foreign direct investment flows, and reduced EU net migration after Brexit. Difference-in-difference analysis was employed, with the number of comparator countries being almost 30, comprising other EU countries but also Turkey and Switzerland. Over the years 2016–19, an inward shift of the Beveridge Curve for each of the three sectors was found.Footnote ⁵ Robustness checks, which supported the results, were made using the Synthetic Cohort Method (Amuedo-Dorantes and Begen, Reference Amuedo-Dorantes and Begen2023).

Approaches to the analysis

The objective of this article is to test whether there has been a Brexit effect on the U/V ratio in the UK. The analysis used was difference-in-difference analysis (henceforth DiD).

DiD is commonly employed to assess whether an intervention has an impact. The sort of intervention can be very varied, and it can be in many fields. It can involve a medical treatment—for example, a vaccination. Here, the question for investigation is whether, after an appropriate time, those who receive the vaccine are less likely to experience an illness than those who do not.Footnote ⁶ It has been used most famously in labour economics to test whether a raising of the minimum wage had an impact upon employment—with special reference to the low-wage sector of employment in fast-food restaurants (Card and Krueger, Reference Card and Krueger1994). More recently, it has been used to assess whether Brexit has had any effect on UK trade—both exports and imports (Freeman et al., Reference Freeman, Manova, Prayer and Sampson2022)—and to help assess the impact Brexit had on UK food price inflation (Bakker et al., Reference Bakker, Datta, Davies and De Lyon2023).

In all cases, the assumption is that the ‘untreated’ population—those not vaccinated, those fast food joints that were not subject to a rise in the minimum wage or those countries that did not experience the ‘shock’ of Brexit intervention—experienced the same broad developments as those that were ‘treated’. So, all units of investigation changed in some, similar, ways. The question was whether those units which were ‘treated’ changed more than those who were not and, if so, in what direction.

What is the period to be studied?

The Brexit referendum took place in June 2016. Attempts to settle the process of leaving were fraught, but a leaving date was set for the end of January 2020. A transition period lasting until the end of December 2021 was also established. Freedom of movement under the rules governing the UK as a member of the EU ceased to be operative as of December 2020. A new, ‘points-based immigration system’ became operative thereafter that set a premium upon the level of wages and qualifications (HM Government, 2020). The UK, however, formally ‘left’ the EU at the end of January 2021, so that the period from the start to the end of 2020 was one of ‘transition’.

Research has suggested that after the referendum and even before Brexit actually occurred, there were some Brexit-induced changes in the labour market. First, insofar as it was measured, net migration from the EU declined. It did not become negative, but it did decline by nearly 60% (Sumption and Walsh, Reference Sumption and Walsh2022). Second, over the same period, and indeed since 2013, unemployment had also been falling. More importantly, the UK Beveridge Curve, as measured by the V/U relationship, had started to move inwards between 2016 and 2019. Not only an examination of graphics shows this, but other research supports it (Amuedo-Dorantes and Begen, op cit).

Complicating matters was the fact that the start of 2020—the beginning of the transition period—was coterminous with the onset of the COVID pandemic. All countries were hit by that shock. In most, the pandemic resulted in severe restrictions to economic and social activities. In some countries, the response of governments was the introduction or extension of provisions enabling short-time working (Kurzarbeit/‘furloughs’, etc.); in others, it was to extend or improve unemployment compensation to provide for those who had been (temporarily) laid off (Casey and Mayhew, Reference Casey and Mayhew2022). In some cases, workers who had come from abroad left and returned to their home countries. All this has potential implications for the V/U relationship.

The extent of COVID-induced restrictions across a selection of broadly similar countries is summarised in Figure 2. It is by no means clear that those in the UK were either more, or less, severe than in most of these.

Figure 2. Lockdown intensity (weighted average of vaccinated and non-vaccinated).

The difference-in-difference analysis

For any given outcome variable, Y_it, the population difference-in-difference effect is given by the difference in the outcome variable for treated and control units before and after the intervention.

(1) $$ {\displaystyle \begin{array}{l}\mathrm{DiD}=\left\{\mathrm{E}\left({\mathrm{Y}}_{\mathrm{i}\mathrm{t}}=1|{\mathrm{D}}_{\mathrm{i}\mathrm{t}}=1=1,{\mathrm{Z}}_{\mathrm{i}}=1,{\mathrm{X}}_{\mathrm{i}}\right)-\mathrm{E}\left({\mathrm{Y}}_{\mathrm{i}\mathrm{t}}=1|{\mathrm{D}}_{\mathrm{i}\mathrm{t}}=1=0,{\mathrm{Z}}_{\mathrm{i}}=0,{\mathrm{X}}_{\mathrm{i}}\right)\right\}\\ {}\hskip2pc -\left\{\mathrm{E}\left({\mathrm{Y}}_{\mathrm{i}\mathrm{t}}=0|{\mathrm{D}}_{\mathrm{i}\mathrm{t}}=0=0,{\mathrm{Z}}_{\mathrm{i}}=1,{\mathrm{X}}_{\mathrm{i}}\right)-\mathrm{E}\left({\mathrm{Y}}_{\mathrm{i}\mathrm{t}}=0|{\mathrm{D}}_{\mathrm{i}\mathrm{t}}=1=0,{\mathrm{Z}}_{\mathrm{i}}=0,{\mathrm{X}}_{\mathrm{i}}\right)\right\}\end{array}} $$

There are presumed to be two periods—a ‘before treatment’ period where D_i,t = 0 and a ‘post treatment’ period where D_i,t = 1. Units for investigation, i, are divided into two groups—a treated group, where Z_i = 1, and a control group to which the treatment is not delivered, where Z_i = 0. The treatment indicator requires the absence of any intervention in the baseline for either group (D_i,t = 0 = 0|Z_i = 1, 0) and a positive intervention for the treated group in the follow-up (D_i,t = 1 = 1|Z_i = 1). Any observable covariates can be added using the variable X_i, but their inclusion is not a necessity.

The data

Data on vacancies and unemployment (seasonally adjusted) were drawn from OECD Labour Force Statistics, Eurostat Labour Force Statistics (Ireland, the Netherlands, Norway, and Spain), Statistics Canada and the Australian Bureau of Statistics. This gave a dataset of a maximum of 18 countries. Quarterly data were available for the period 2010q1 onwards. The termination date for analysis was 2022q2—so, effectively, 18 months after the UK had formally left the EU. At this point, the number of vacancies per unemployed person in the UK was one.

Czechia was included in the initial data set. However, for much of the period from the early 2010 to the late 2010s, that country had an extremely high vacancy rate—higher than that of any other countries examined—and also very low unemployment. This was remarked upon by many observers, but no good explanation was given.Footnote ⁷ For this reason, Czechia was dropped from the analysis. This left 17 countries, of which all but five were members of the EU (at least prior to Brexit). Of the remainder, two were members of the EEA (Norway and Switzerland) and three were non-European (Australia, Canada and the US).

The estimation

Different versions of the V/U relationship were constructed, each of which has been used for analysis of Beveridge Curves. These were

1. 1) V/U, where V is the absolute number of vacancies and U is the absolute number of unemployed peopleFootnote ⁸;

2. 2) Vacancy rate/Unemployment rate, where the vacancy rate is the number of vacancies divided by the number of jobs, and the unemployment rate is the number of unemployed people divided by workers plus the unemployed; and

3. 3) (V/U)/Unemployment rate, where V/U is defined as in 1, and unemployment rate is defined as in 2.

These three variables are highly correlated.Footnote ⁹ They serve as the dependent variables in the various models tested. The UK is the ‘treated group’ (Z = 1 in Eq (1)), and the point of treatment (D = 1 in Eq (1)) was chosen to be either date of the treaty setting leaving or that date when Brexit actually occurred.

Covariates selected were three. The first was the share of workers aged 50–64—intended to take account of the recognised large drop in the number of older workers post the pandemic. As well as losing over a third of a million workers as a result of Brexit (Portes and Springford, op cit), many had commented upon the loss of a further third of a million older people from the labour force in the period following the onset of COVID (for example, Boileau and Cribb, Reference Boileau and Cribb2022). The second was the share of selected industries (manufacturing, transport and hotels and restaurants) within total output. These were chosen to take account of the fact that some industries might be particularly dependent upon non-domestic labour.Footnote ¹⁰ The third was the share of business investment as a percentage of GDP. Its level relative to other countries has been much commented upon (Resolution Foundation, 2023). A reduced inability to employ capital rather than labour might mean that, faced with increases in demand, employers are more likely to try to hire more staff. For each of these covariates, values were averages taken across the period 2010 to 2019—i.e., in the pre-treatment period.

Two breakpoints were used for the analysis. The first was after 2019q4—i.e., from 2020q1 onwards. This was used because this was the date set in the initial withdrawal treaty that confirmed that leaving would occur. The second was after 2020q4—i.e., from 2021q1 onwards. The withdrawal treaty set leaving to take place as of the end of January 2021. After that, new rules about worker movement and the new points-based system became operative. It is to be noted that the first of the breakpoints closely overlapped the onset of COVID—many lockdown measures in many countries commenced at the end of 2020q1 or at the very start of 2020q2.

The results

Models were constructed for each of the two breakpoints—after the date of leaving had been formally settled and after the UK had left the EU. The data set was also split, whereby one data set included all 17 countries, the second only European (but not necessarily EU) countries, and a third only EU countries (UK included).Footnote ¹¹

Models using the formal settlement of a leaving date generated few positive results. This was regardless of the inclusion, or otherwise, of non-European countries and regardless of which of the three dependent variables was used. Introducing the covariates of age structure, industry composition or business investment investment had no impact.

Models using the actual date of leaving did generate significant results—and they did so for each of the dependent variables employed. Including the share of the labour force aged 50–64 was found to be relevant—the variable was positively signed, so that countries with a higher proportion of older workers experienced a higher V/U ratio than others at the end of the observation period. This was a result that was expected. Including the importance of manufacturing within the economy was also relevant—the variable was negatively signed, so that countries where manufacturing was more important experienced a lower V/U ratio than others. Including the level of business investment as a share of GDP was also significant and, as expected, the coefficient was also negatively signed. Results are shown in Table 1a-c.

Table 1a. Regression results for V/U (absolute values)

Non-significant coefficient in italics.

Table 1b. Regression results for Vrate/Urate (vacancy rate/unemployment rate)

Non-significant coefficient in italics.

Figure 3. V/U 2001q2 to 2023q2.

Table 1c. Regression results for V/U over Urate (vacancies/unemployment all over unemployment rate)

Non-significant coefficients are in italics.

Table 2a. Impact of Brexit on V/U rates after Brexit occurs

Derived from Table 1a. Row 2 is rate minus diff-in-diff coefficient

Table 2b. Impact of Brexit on V/U rates after Brexit occurs

Derived from Table 1b. Row 2 is rate minus diff-in-diff coefficient.

Table 2c. Impact of Brexit on V/U rates after Brexit occurs

Derived from Table 1c. Row 2 is rate minus diff-in-diff coefficient.

According to Tables 2a-c, the models including the covariates explain about one-fifth of the variance in the dependent variable. Two of the three models suggest that the V/U ratio was about a quarter higher than it would have been in the absence of Brexit; one that it was a third higher. If the recorded level at the end of the observation period was one vacancy for every unemployed person, the suggestion is that the level would have been between 0.8 and 0.75 vacancies per person unemployed. This would have been lower than the equivalent ratio of the Netherlands (nearly 1.4) and Norway (1.2) by the end of the follow-up period but would still have been above Germany and Austria (both under 0.7).