LABOUR MOBILITY AND EARNINGS IN THE UK, 1992–2017 ∗

We combine information from the British Household Panel Study and the United Kingdom Household Longitudinal Study (also known as Understanding Society) to construct consistent time series of aggregate w ork er stocks, w ork er ﬂows and earnings in the United Kingdom o v er the period 1992–2017. We propose a method to harmonise data between the British Household Panel Study and United Kingdom Household Longitudinal Study, which we validate by checking the consistency of some of our headline time series with equi v alent series produced from other sources, notably by the Ofﬁce for National Statistics. In addition to drawing a detailed aggregate picture of the United Kingdom labour market o v er the past two and a half decades, we use our constructed data set to compare the impact of industry, occupation and employer tenure on wages in the United Kingdom. We ﬁnd that returns to occupation tenure are substantial. All else equal, ﬁve years of occupation tenure are associated with a 3.3% increase in wages. We also ﬁnd that industry tenure plays a non-negligible part in driving wage growth.


Generalities
The British Household Panel Survey (BHPS) is an annual longitudinal study which follows all adult members of around 10,000 households in the UK from 1991 until the end of 2008. 3 Because initial BHPS interviews were conducted gradually o v er the course of 1991, the crosssection sample size of BHPS is initially small and gradually increases until the end of 1991.Then, following the final BHPS interviews at the end of 2008, all remaining respondents were invited to participate in the UK Household Longitudinal Study (UKHLS, also known as Understanding Society ), a successor to BHPS which follows a larger sample of around 40,000 households and collects data on a broader range of topics.
Interviews for wave 1 of UKHLS began in 2009, with those BHPS sample members who accepted the invitation to join the UKHLS sample members joining in wave 2. Interviews for each BHPS wave were completed within one calendar year.By contrast, interviews for each wave of UKHLS take place o v er a period of 24 months, but these 24-month periods o v erlap to ensure that each individual is interviewed once a year.So, for e xample, wav e 1 interviews took place in 2009 and 2010, wave 2 interviews took place in 2010 and 2011, wave 3 in 2011 and 2012, and so on.Wave 11, which is the most recent release, contains information from interviews conducted in 2019 and 2020.A consequence of the o v erlapping wav es in UKHLS is that data for 2009 and 2020, the first and last years currently co v ered by the data, relate to only half of the UKHLS sample (as half of the sample did not have their wave 1 interview until 2010, and half of the responses to interviews conducted in 2020 will not be released until wave 12).Data in these years are therefore less reliable than other years of UKHLS.
Those sample size issues (small BHPS sample in 1991, discontinuity between the final BHPS interview in 2008 and the initial UKHLS interview in 2009, and smaller UKHLS samples in 2008 and 2019) will impact the construction of our analysis sample, as explained in Section 1.3 .
Cross-sectional weights are supplied by BHPS and UKHLS to ensure that each cross-section of both panels is representative of the UK population at the time.Those weights are designed to adjust for different probabilities that each individual is selected into the sample and different probabilities of sample attrition, including selective attrition of BHPS sample members between BHPS and UKHLS.We consistently use those weights in this paper.

Individual Employment Histories
While each sample member is interviewed at annual intervals, respondents are asked to report job histories since the time of their previous interview in each wave.We use these recalled job histories to construct a data set containing each individual's employment status and any transitions between states (or from one job to another) in each month of the period since their pre vious intervie w. 4 We face two main difficulties in our construction of monthly employment histories: inconsistencies between the reported end date of one employment spell and the start date of the next, and inconsistencies between information reported in different waves.First, in some cases, the date that an individual recalls ending one spell of employment, unemployment or inactivity does not match the date at which they report having started their next spell.This results in either a gap in the individual's employment history or a period where labour market spells o v erlap.In such cases, we systematically set the start date for all non-left censored spells equal to the end date of the previous spell.
Second, the job histories reported by individuals sometimes contradict information provided in previous waves.For example, an individual may have reported being employed at the time of their wave 1 interview, while reporting a retrospective calendar of activities in wave 2 that implies that they were non-employed at the date of their wave 1 interview.In such cases, we give precedence to information provided in older interviews o v er information pro vided subsequently, i.e., we give precedence to information provided about labour market spells provided at interviews closest to those spells.The rules that we apply to rectify inconsistencies in individual responses are thus in the spirit of the 'closest interview method' discussed by Smith ( 2011 ).
In Appendix B, we further examine the magnitude and nature of the adjustments that these corrections impose on the raw data.We also investigate the consequences of simply discarding inconsistent observations (rather than attempting to correct them) on some of the main aggregate series that we construct.

Sample Selection
We construct monthly employment histories for all respondents in BHPS and UKHLS aged between 16 and 64 at the time of their interview.(Sample members therefore leave our sample on their 65th birthday and join our sample on their 16th birthday.)This selection is intended to make our analysis comparable with employment aggregates produced by the Office for National Statistics (ONS) based on the UK Labour Force Survey (UKLFS).
As explained above, cross-section sample sizes are smaller at the start of BHPS in 1991 (for dates when wave 1 interviews were not yet complete), and become smaller again in the most recent wave of UKHLS in 2019 (for dates in which some respondents had already completed their final interview and so had left our sample).We cut those small-sample dates and restrict our time window to the period January 1992 to January 2018.
Final BHPS interviews were conducted in the third quarter of 2008, and the first UKHLS interviews were not conducted until January 2009.In constructing our monthly series, we switch from using BHPS data to UKHLS data in October 2008.During this 'changeo v er' period between the two surv e ys, the only information we hav e is from the 9,230 BHPS sample members who agreed to participate in UKHLS (and were aged between 16 and 64).
Our final sample contains 88,690 individuals (a total of 5.02 million person-months) and 129,395 transitions between employment states.This total is made up of 27,093 individuals (2.03 million person-months) with 61,851 transitions for the period co v ered by BHPS from January 1992 until October 2008 and 70,863 individuals (2.98 million person-months) with 67,480 transitions for the period from October 2008 until January 2018 co v ered by UKHLS.As many as 9,345 individuals from the BHPS sample continued into the UKHLS sample.

Definition of Labour Market States
We consider four possible employment states which we label as follows: employed ( E), selfemplo yed ( S), unemplo yed ( U ), and inactive ( I ).In some of our analysis, we combine employment and self-employment into a single 'in work' state W = E ∨ S. We assign individuals to states in each month based on their self-reported status at the end of the month.The four states are defined as follows.
( 1 ) Employment ( E) includes all individuals who report being employed (part-time or full-time), in an apprenticeship, on maternity leave, working as unpaid family workers or participating in a go v ernment training scheme.This corresponds with the ONS definition of employment. 5ncluding women on maternity leave in the definition of employment is consistent with Smith ( 2011 ).
( 2 ) Self-employment ( S) includes all individuals who report being self-employed.
( 3 ) Unemployment ( U ) includes individuals who satisfy any of the following criteria: (1) report being unemployed, (2) report having searched for work in the four weeks prior to their interview while not being employed, or (3) report having claimed unemployment benefits while not reporting being employed.6( 4 ) Inactivity ( I ) includes all individuals who are not employed, self-employed or unemployed.
This includes people who (1) report being out of work due to long-term sickness, in fulltime education, caring for family members, in retirement, or for 'other reasons', (2) have 2023] labour mobility and earnings in the uk, 1992-2017 3075 © The Author(s) 2023.
not searched for work in the four weeks prior to their interview, and (3) have not claimed unemployment benefits.

BHPS/UKHLS Versus UKLFS
We use a combination of BHPS and UKHLS to document UK labour market indicators.An alternativ e would hav e been to use the UKLFS.What are the pros and cons of each data set?The UKLFS has a larger cross-sectional sample size (nearly three times as large as the UKHLS).It was not interrupted at such an unfortunate time as the end of 2008, and so does not require the 'splicing' that BHPS and UKHLS do.While those indisputably argue in fa v our of the UKLFS, we believe that the BHPS/UKHLS combination has fiv e ke y advantages (which are also emphasised by Smith, 2011 ).Those are (1) a higher frequency of observations: calendars of activities in BHPS and UKHLS allow the construction of monthly series, whereas it is only possible to construct series at quarterly frequency from the UKLFS.(2) A better tracking of respondents: BHPS and UKHS sample designs are such that if individuals mo v e their address or households, they will be tracked, whereas the UKLFS is an address-based sample and so does not track respondents if they move.(3) A longer time span: BHPS and UKHLS follow individuals for a much longer period than the UKLFS, with some respondents being present throughout the entire 1992-2016 sample period and are thus observed through most of their working life, while the UKLFS only follows each respondent for five quarters, which allows for a maximum of four labour market transitions.(4) Fewer proxy responses: the frequency of proxy responses is around 1% in BHPS and 8% in UKHLS, compared to almost 30% in the UKLFS.( 5) Face-to-face interviews: in BHPS and UKHLS, all individuals are interviewed f ace-to-f ace and separately (when possible), whereas in the UKLFS only the first interview is f ace-to-f ace and the other four interviews are carried out by telephone.Finally, one contribution of this paper is to provide an algorithm for data imputation and cleaning to produce reliable aggregate series based on the combination of BHPS and UKHLS.As explained below, one of our measures of reliability is closeness to the corresponding series published by the ONS based on UKLFS data.Given that BHPS and UKHLS co v er a much wider range of variables than the UKLFS, we think it is useful to produce reliable aggregate time series based on those two data sets, which can be used in conjunction with other variables in any economic analysis based on those same data sets.

Preliminary Remarks
We denote labour market stocks consistently with the way we label labour market states.For example, we denote the total number of employed workers in a given month t by E t , the total number of self-employed by S t , etc.Following this notation, the total number of people who are in work in month t is W t = E t + S t .From those aggregate stocks, we derive the corresponding rates.The employment rate is defined as The rates of self-employment and inactivity are defined analogously.So is the total employment rate (including the self-employed), The unemployment rate equals U t W t + U t .All the series plotted in this paper are smoothed using a 24-month moving average filter centred in the current month.Moreo v er, as discussed abo v e the data are particularly noisy at the end of 2008 and through 2009, the period co v ered by the first wave of UKHLS.In all the charts below, we highlight this period using two vertical lines.Finally, in Appendix D, we replicate all the charts showing our aggregate series with added 95% confidence bands.

Employment, Unemployment, Self-Employment and Inactivity
Figure 1 shows our estimates of the monthly rates of total emplo yment, unemplo yment, selfemployment and inactivity.The ONS publishes series of those four rates based on the UKLFS.Figure 1 also shows those ONS series, for comparison. 7ur estimates of the rates of total employment and unemployment are, reassuringly, very close to the ONS series, even during the changeo v er period 2008 to 2010.The only noticeable discrepancy is that the BHPS/UKHLS-based employment rate dips a little lower than the ONS one in the immediate aftermath of the Great Recession.Our unemployment rate series mirrors that and peaks a little higher than the ONS series.There are small discrepancies between the two inactivity rate series, with the BHPS/UKLHS-based series being more volatile than the ONS one in the period where the quality of our data is low.Yet the two series of inactivity rates follow the same downward trend.
The self-employment rate series constructed using BHPS/UKHLS follows a similar trend to its ONS counterpart, ho we ver, the latter is around half a percentage point higher between 1995 and 2003, and almost two percentage points higher in the rest of the sample period (Figure 1 c).Contrary to the ONS total employment, unemployment and inactivity rate series, which represent individuals aged 16-64, the ONS uses all individuals aged 16 and abo v e to construct the selfemployment rate.By contrast, all our BHPS/UKHLS series, including the self-employment rate, are consistently based on individuals aged 16-64.Moreo v er, in our self-employment category, we only consider individuals who report themselves as self-employed, some of which could also hold a second, salaried job.These may explain some of the discrepancy between our self-employment series and the ONS one.In Appendix C we investigate this further and show the extent to which different ways of counting self-employment can affect the aggregate rate.

Preliminary Remarks
In this section we document the labour market flows into and out of employment, selfemplo yment, unemplo yment and inactivity.The first step in calculating transition rates is identifying and classifying all transitions.For example, we record the occurrence of a transition from unemplo yment to emplo yment if (1) the respondent w as unemplo yed in t − 1 and emplo yed at t, and (2) the respondent reports that they started a new employment spell in month t.We then calculate the weighted sum of each transition type in each month, using the cross-sectional weights supplied with BHPS and UKHLS.
We label all transitions in accordance with our notation for the stocks: for example, the aggregate number of transitions from unemployment to employment transition in month t is denoted as U E t .Transitions from unemployment to work, irrespective of self-versus salaried employment, will be denoted as U W t .Note that w ork ers often change jobs without experiencing any interim period of non-employment, giving rise to emplo yment-to-emplo yment ( E E t ) and selfemplo yment-to-self-emplo yment transitions ( SS t ).Job-to-job transitions, irrespective of selfversus salaried employment, will be denoted as W W t .
Finally, we construct the transition rate in each month t following the method suggested by Shimer ( 2012 ).F or e xample, we calculate the UW transition rate as λ U W t = − ln 1 − U W t U t−1 .Other transition rates are defined similarly.

Transitions In and Out of Work
We begin by focusing attention on transitions between work, unemployment and inactivity. 8Our comparison benchmark series in this case are based on the X02: Labour F orce Surv e y Flows Estimates data set published and updated every quarter by the ONS. 9 Those ONS series are available from 2001:Q4 and, as the name suggests, they are based on data from the UKLFS.Because of the difference in frequencies between the (quarterly) UKLFS and our (monthly) BHPS/UKHLS data set, the ONS set of flow rate series are not directly comparable with ours.Specifically, the time aggregation bias (caused by the fact that both data sets miss all sequences of more than one transition, such as a job loss followed by a new job accession, occurring within their respective unit time period) is likely to be much more severe at quarterly than at monthly frequency.
The impact of time aggregation on the level and cyclicality of estimated labour market flow rates has been studied in a number of contributions based on a variety of different data sets (Petrongolo and Pissarides, 2008 ; Elsby et al. , 2009 ; Fujita and Ramey, 2009 ; Nekarda, 2009 ).While all those authors conclude that the time aggregation bias affects the levels of estimated turno v er rates, they also concur in saying that the impact of time aggregation on the cyclicality of said turno v er rates is quantitatively small.
Based on that conclusion, for each transition rate, we attempt to make the UKLFS-based ONS series comparable to ours by rescaling the former such that its mean and standard deviation coincide with those of our series o v er the period where both series o v erlap.In other words, we adjust the levels of the ONS series, and compare the cyclical behaviour of those adjusted series with that of our own BHPS/UKHLS series. 10igure 2 shows the six series of transition rates between work, unemployment and inactivity.Overall, the trends of our transition rate series are very similar to those constructed by the ONS o v er the period co v ered by both.The behaviour of our various transition rates o v er the observation window is in line with what was documented elsewhere in the literature.The UW rate (Figure 2 b) increased from the end of the 1992 recession to a peak of almost 10% at the beginning of 2,000.It then started a gradual decline, followed by a sharp drop towards the end of 2008, from which it has yet to reco v er.The IW rate (Figure 2 d) follows a qualitatively similar cyclical pattern, albeit at a much lower level.
The WU job separation rate peaked at 0.65% in the 1992 recession, after which it declined steadily until 2008.It then increased sharply and suddenly during the Great Recession, but quickly resumed its trend decline after 2010, down to a low of around 0.25% since 2014.By contrast, the WI rate (Figure 2 c) was hump-shaped o v er the period 1992-2008, reaching its peak around 2001.But during and after the Great Recession, the WI rate evolved roughly parallel to the WU rate.
Finally, the UI transition rate (Figure 2 e) seemed to follow a slight upward trend from 1992 to 2008, before falling sharply during the Great Recession.It has since then stayed lower than its pre-recession level, just above 2%.The IU rate mirrored the UI rate qualitatively, although with quantitatively larger swings.

J ob-to-J ob Mobility
Figure 3 plots our job-to-job (WW) transition rate series, i.e., the rate at which either employed or self-emplo yed w ork ers mo v e directly from one job to another without experiencing any period of unemployment or inactivity in between.As for transition rates in and out of work, we use the (rescaled) quarterly job-to-job transition rates from the ONS's X02 data set as benchmark.

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labour mobility and earnings in the uk, 1992-2017 3079 © The Author(s) 2023.The behaviour of the WW rate o v er our observation window is qualitatively similar to that of the UW rate (Figure 2 b): increasing in the 1990s, reaching a peak around 2000, then gradually declining until 2008 to its early 1990s level, before falling sharply during the Great Recession and staying at historically low lev els ev er since.Quantitativ ely, howev er, the drop in the WW rate during the Great Recession is, in relative terms, much more dramatic than the drop in UW rates.

Taking Stock
One consistent message conv e yed by Figures 2 and 3 is that all the transition rates in and out of work (WU, UW, WW, WI, and, to a slightly lesser extent, IW) have been on a moderate, but clear downward trend, since around 2000.This echoes similar findings for the United States (see, among others, Fallick and Fleischman, 2004 ; Fujita et al. , 2018 ), which have fuelled a literature investigating a possible trend decline in business dynamism.The United States' decline in transition rates is generally accepted to have started in the early to mid-1990s, slightly earlier than what our data suggest for the UK.Yet the parallel is striking.

Earnings
We construct series for average monthly labour income as the weighted sum of monthly labour income (using the BHPS and UKHLS cross-sectional weights), divided by the weighted sum of respondents reporting non-zero labour income in month t.This process produces estimates of nominal average labour income in each month t.We then construct real average labour income by deflating nominal labour income to 2015 GBP using the Consumer Price Index (CPI) All Items (D7BT) series produced by the ONS.We compare our estimates of real labour earnings to those produced by the ONS as part of its Average Weekly Earnings series (AWE), the series used by the Bank of England and HM Treasury to measure the inflationary pressure emanating from the labour market.Specifically, we use the KAB9: Weekly Earnings series, which is part of the AWE.When we make this comparison, we take the ONS estimate of nominal earnings and deflate using the same CPI series we use for our own BHPS/UKHLS series.
There is less information available on monthly pay in UKHLS than in BHPS.Monthly labour earnings are only available in UKHLS for any job the respondent holds at the time of interviewing .In BHPS, data on labour income is available for the individual's full employment history, including jobs which were held between the previous and current interviews.For the UKHLS period, we therefore calculate average earnings as the weighted total monthly earnings that we 2023] labour mobility and earnings in the uk, 1992-2017 3081 © The Author(s) 2023.observe, divided by the weighted total of individuals whose labour income we observe-i.e., we ignore individuals who are employed, but whose labour income we do not observe.11Figure 4 shows the average real weekly earnings series constructed from BHPS and UKHLS against the corresponding ONS series.The latter is only available from January 2000 onwards.Both series have parallel time profiles, and are very close in level.Nevertheless, on average there is a £10-20 difference (in 2015 GBP) between the two series. 12ur series confirms that, after o v er 15 years of steady growth, real labour earnings started falling in 2008 and have been subdued ever since (despite signs of reco v ery since early 2015), as has been widely documented and discussed in the public debate.

Returns to Occupation, Industry and Employer Tenure
We now illustrate the usefulness of our spliced BHPS/UKHLS data set in an application.Key advantages of our data set include its long longitudinal dimension and its reliable tracking of individuals across jobs o v er e xtended periods of time.Those attributes make our data set well suited to the study of individual career paths and earnings dynamics o v er the life cycle.Our specific application is on the comparative wage returns to occupation, industry and employer tenure.Neal ( 1995 ) and Parent ( 2000 ) have argued that the observed correlation between wages and employer tenure is attributable to the fact that wages grow with industry experience, which in turn is correlated with employer tenure and generally omitted from wage regressions.Ho we ver, Kambourov and Manovskii ( 2009 ) find that tenure in an industry has a very small impact on wages once the effect of occupational tenure is accounted for.Long before that, Shaw ( 1984 ) has already argued that investment in occupation-specific skills is an important determinant of earnings.Yet the empirical literature that followed up on her important insight remains surprisingly sparse, and our aim here is to contribute to it in the UK context.

Wa g e Function Estimation
In order to assess the respective impact of occupation, industry and employer tenure on wages, we follow Kambourov and Manovskii ( 2009 ) and estimate the following wage equation: where w i jmnt is the natural logarithm of the hourly wage of person i working with employer j in occupation m and industry n in month t.Emp ten , Occ Ten and Ind Ten denote tenure with the current employer, occupation, and industry, respectively.Additional control variables x it include an intercept term, 1-digit occupation and industry dummies, a marital status dummy, year dummies, education, sex as well as age.Finally, θ it is the error term.
We estimate ( 1 ) by ordinary least squares (OLS).Both our estimation method (OLS) and our specification of the wage equation ( 1) are slightly simpler than the preferred estimation method and specification of Kambourov and Manovskii ( 2009 ).For the joint sake of parsimony, clarity and brevity, we focus on OLS estimates of ( 1 ) in the main body of this paper.Ho we ver, in Appendix F, we run a series of regressions based on the same specifications as Kambourov  and Manovskii ( 2009 ), both as robustness checks and to produce results that are more directly comparable to theirs.

Results
Column 5 in Table 1 reports our OLS estimates of the coefficients of interest-the returns to occupation, employer, and industry tenure-in ( 1 ).We find that the returns to occupation tenure, at about 0.65% per year (or 3.3% o v er fiv e years), are almost three times as large as the returns to industry tenure and an order of magnitude larger than the returns to employer tenure.The fact that occupation tenure is the most important source of wage growth echoes the main findings of Kambouro v and Mano vskii ( 2009 ).Ho we ver, in contrast to Kambourov and Manovskii ( 2009 ), we find that industry tenure also has a sizeable effect on wages though the effect is weaker than the effect of occupation tenure.
In Table 1 , column 6, we take advantage of the longitudinal dimension of our data to include w ork er fixed effects into ( 1 ).Doing so roughly doubles the estimated impact of employer tenure on wages, while halving those of industry and occupation tenure.This suggests that high-wage 2023] labour mobility and earnings in the uk, 1992-2017 3083 © The Author(s) 2023.
w ork ers (in a fixed effect sense) tend to have longer occupation tenure.Exactly why that is cannot be inferred from ( 1 ),13 but the main qualitative conclusion of Kambourov and Manovskii  ( 2009 ) stands: even though employer and industry tenures have non-negligible positive impacts on wages, the effect of occupation tenure is more than twice as large. 14he first four columns in Table 1 show estimation results for alternative specifications of the wage equation in which employer, industry and occupation tenure are variously dropped from the list of regressors.Perhaps unsurprisingly, those results suggest that employer tenure picks up a large part of the wage effects of industry and occupation tenure when those are omitted from the regression.Again, those results mostly corroborate the findings of Kambourov and Manovskii  ( 2009 ) on United States data.

Conclusion
In this paper, we combine information from the BHPS and UKHLS to construct consistent time series of aggregate w ork er stocks, w ork er flows and earnings in the UK o v er the 1992-2017 period for all w ork ers as well as for two separate education groups.
We propose a method to harmonise data between the BHPS and UKHLS, which we validate by checking the consistency of some of our headline time series with equi v alent series produced from other sources, notably by the ONS.This allows us to put together what, to our knowledge, is the first aggregate analysis of UK labour market stocks, flows, and earnings based on a 'spliced' BHPS/UKHLS data set.
Our main findings are summarised in the introduction to this paper.We do not repeat them here.Aside from our substantive results, we hope that this paper will help demonstrate the usefulness of a combined BHPS/UKHLS data set for the study of UK labour markets.While the analysis in this paper is almost entirely confined to the aggregate level, it is based on harmonised indi vidual-le vel employment history data which is ready to be used for micro-level analysis.decades)-typically much longer than the single year individuals are asked to recall at subsequent interviews.
A related problem is that, in many cases, individuals have not reported their full employment history at their first interview.Instead, they only report the start date of their current labour market spell.Because employment spells last much longer on average than non-employment spells, including pre-interview labour market histories in our data would lead us to systematically o v erestimate the number of employed individuals in the pre-interview period (and underestimate the unemployed and inactive).
Potentially reflecting both of these reasons, we found that including recalled job histories for the period before individuals' first interviews resulted in a significant upward bias in the employment rate (and corresponding downward biases in the unemployment and inactivity rates) relative to national statistics. 15econd, we use individual weights supplied in BHPS and UKHLS to construct our estimates of aggregate stocks and flows to ensure they are representative of the UK population.Unfortunately, no weights are provided for pre-panel years and therefore it is not possible to make pre-panel years representative.

Appendix B. The Extent of Adjustment by the Algorithm
To check, assess the extent to which our algorithm adjusts the raw data, we reconstructed employment histories without applying the parts of the algorithm which set the start date of spells equal to the end date of previous spells-simply using the start and end dates recorded in the data, without any attempt to resolve inconsistencies or fill gaps.We still dropped all dates for an individual before the first interview and after their most recent one.We then calculated the number of times our algorithm changes the employment status recorded for an individual in a given month.
Figure B1 shows the number of changes our algorithm makes o v er time, e xpressed as a proportion of all employment spells recorded in each month.The vast majority of changes made 2023] labour mobility and earnings in the uk, 1992-2017 3085 © The Author(s) 2023.by the algorithm are to fill missing employment spells, meaning that Figure B1 shows the number of job spells we would have to discard without the algorithm.
To further illustrate the impact of our adjustment algorithm, we compare the transition rates described in Section 3 to those we would have obtained if, instead of using the closest interview method, we simply discarded all observations with missing information or inconsistencies.This method is useful to illustrate the consequences of selection bias.Figure B2 shows that mobility between work and either unemployment or inactivity is almost systematically, and quite severely, and a term OJ i jt which is an indicator variable of individual i not being in their first year of employment with their current employer j .Exactly why possible non-linear effects of employer tenure are specified differently than those of occupation or industry tenure is not entirely clear to us. 16

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labour mobility and earnings in the uk, 1992-2017 3091 © The Author(s) 2023.Table F1.Returns to Tenure, Specification of Kambourov and Manovskii ( 2009 ).Finally, Kambourov and Manovskii ( 2009 ) assume the following structure for the disturbance term: In other words, they decompose the disturbance term θ i jmnt into an individual w ork er effect α i , a w ork er-emplo yer match effect γ i j , a w ork er-occupation match effect φ im , a w ork er-industry match effect ψ in , and an error term it .While Kambourov and Manovskii ( 2009 ) start by estimating ( F1 ) by OLS, they also worry about the possibility that 'good' matches, in the sense of matches with high specific effects γ i j , φ im or ψ in , may tend to be more stable, implying that the various measures of tenure might each be correlated with at least one of the components of θ i jmnt .
To address that particular concern, Kambourov and Manovskii ( 2009 ) apply an instrumental variable procedure adapted from Altonji and Shak otk o ( 1987 ) and Parent ( 2000 ). 17We do not by the quadratic specification of the tenure profile'.Parent ( 2000 ) says 'the rationale for the inclusion of such a variable is that the first year of tenure might be of special significance in terms of investments in job-related skills'. 17Tak e emplo yer tenure for example.Emp Ten i jt is by Emp Ten i jt − Emp Ten i jt , where Emp Ten i jt is the average tenure of individual i during their current spell of work at employer j.For example, if an individual has a job for five months, the employer tenure variable will take values { 1 , 2 , 3 , 4 , 5 } o v er the fiv e months.The av erage employer Fig. G1.Dashed Line: Transition Rates from Smith ( 2011 ), Solid Line: Transition Rates Using Spliced BHPS/UKHLS, Dash-dot line: transition rates using Spliced BHPS/UKHLS with Smith ( 2011 ) definitions of stocks.
comment on the properties of that particular IV protocol in this paper: we only apply it to our own data set for comparability with Kambourov and Manovskii ( 2009 ).
tenure for that spell is three, and so the IV takes values {−2 , −1 , −0 , 1 , 2 } .All tenure variables (including the non-linear terms and the variable OJ i jt ) are instrumented in the same way.

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labour mobility and earnings in the uk, 1992-2017 3093 © The Author(s) 2023.Results are summarised in Table F1 .Because Kambourov and Manovskii ( 2009 ) specify wages as non-linear of employer, industry and occupation tenure, we present the returns of each type tenure at various horizons as estimated either by OLS or IV.Estimates of the returns to employer tenure factor in the OJ i jt indicator of tenure greater than one year, which is part of the specification in Kambourov and Manovskii ( 2009 ).Full regression results are available on request.
When estimated by OLS on our UK data, the non-linear specification of Kambourov and  Manovskii ( 2009 ) continues to suggest that occupation tenure is the most highly correlated with wages.Ho we v er, it also suggests that employer and industry tenure both play non-ne gligibleand quantitatively roughly comparable-roles as drivers of wages.This corroborates the results obtained from our simpler, linear specification (Table 1 ), although the non-linear specification tends to assign a quantitatively larger role to employer tenure.Next turning to IV estimates, we see that instrumenting the various tenure measures as described in Altonji and Shak otk o ( 1987 ), Parent ( 2000 ) and Kambourov and Manovskii ( 2009 ) largely wipes out employer tenure as a determinant of wages, while inflating the coefficients on industry and occupation tenure, which are now of roughly equal magnitude. 18ur reading of those results is that, while specification seems to matter quantitatively, Kambouro v's and Mano vskii's result about occupation tenure being a much more important driver of wage growth than employer tenure is also found in our UK data.Ho we ver, contrary to Kambourov  and Manovskii ( 2009 ), our data suggests that industry tenure plays a quantitatively non-negligible role as a determinant of wage growth.Note that, in addition to the fact that our data pertains to a different country than Kambourov's and Manovskii's, it is also the case that we have a considerably larger, and representative, data set.Moreover, we have data on a much longer time horizon compared to their study and we also keep all workers (we only exclude self-employed workers) in our sample, whereas Kambourov and Manovskii ( 2009 ) only keep white male workers who are heads of household and aged between 16 and 64.
Figures G1 and G2 show the comparison between flow rates and aggregate unemployment rate using our definitions of variable versus Smith ( 2011 ) definitions.Regarding the difference in transition rates with Smith ( 2011 ), these differences are partly caused by our different way of defining employment statuses, especially inactivity.In Smith's definition, inactivity includes retirement, family care, long-term sickness or disability, full-time education, national or war service, and 'anything else' (approximately 32% of her sample).By contrast, we also require individuals to have not searched for work or claimed unemployment benefits in the four weeks prior to their interview.This narrower definition of inactivity results in lower average inactivity rates compared to Smith ( 2011 ) (around 24% of our sample) and higher transition rates from inactivity to unemployment and work.The dividing line between inactivity and unemployment is ine vitably some what arbitrary.We chose our definitions of unemployment and inactivity on two grounds.First, our definitions are closer to those upon which the ONS bases its own aggregate labour market series.Given that those ONS series are the reference measures of employment and unemployment rates in the UK, it is important that our own series match those measures.Second, while Smith's IW transition rates (Figure H2   and UW rates.Another difference is that the US rate is more volatile than the UW rate, showing a few sizeable spikes, notably one towards the end of the Great Recession. Transition between self-employment and inactivity (Panels I1 c, d), although somewhat volatile, show no particular trend o v er the period considered.
Finally, Panels I1 e and I1f show transition rates between self-employment and employment.The SE rate is hump-shaped o v er the pre-recession period, much like the general WW rate (Figure 3 ) but, unlike the WW rate, it does not collapse during the Great Recession: rather, it seems to have started on a slow downward trend around 2008.As for the ES rate, it has been on a slow but steady upward trend since the start of the sample.
Summing up, the U-shape of the self-employment rate o v er period 1992-2017 documented on Figure 1 c in the main body of the paper results from a somewhat complex combination of various inflo ws and outflo ws: a fall in transitions from unemployment into self-employment, partly compensated by fewer transitions into unemployment and by more transitions from employment.Zooming in on the aftermath of the Great Recession, a period during which the self-employment rate has increased in the UK (Figure 1 c), we can see that this increase in the stock of selfemplo yed w ork ers came with increased 'impermeability' of the state of self-employment, i.e., with a fall in all the associated inflow and outflow rates.Yet clearly, o v er that period, the impact of the combined fall in outflow rates from self-employment into unemployment, inactivity and employment dominated the contemporaneous fall in inflow rates.

Univer sity Colleg e London & Institute for Fiscal Studies, UK University of Bristol, UK
Additional Supporting Information may be found in the online version of this article:

Fig. B2 .
Fig. B2.Separation and Job Finding Rates Using Different Data Correction Methods.
FiguresG1 and G2 show the comparison between flow rates and aggregate unemployment rate using our definitions of variable versusSmith ( 2011 ) definitions.Regarding the difference in transition rates withSmith ( 2011 ), these differences are partly caused by our different way of defining employment statuses, especially inactivity.In Smith's definition, inactivity includes retirement, family care, long-term sickness or disability, full-time education, national or war service, and 'anything else' (approximately 32% of her sample).By contrast, we also require individuals to have not searched for work or claimed unemployment benefits in the four weeks prior to their interview.This narrower definition of inactivity results in lower average inactivity rates compared to Smith ( 2011 ) (around 24% of our sample) and higher transition rates from inactivity to unemployment and work.The dividing line between inactivity and unemployment is ine vitably some what arbitrary.We chose our definitions of unemployment and inactivity on two grounds.First, our definitions are closer to those upon which the ONS bases its own aggregate labour market series.Given that those ONS series are the reference measures of employment and unemployment rates in the UK, it is important that our own series match those measures.Second, while Smith's IW transition rates (FigureH2f) stayed roughly constant around 0.2% up until 2008, our series have a downward trend from 1992 to 2008 followed by a sharp increase

Fig. H2 .
Fig. H2.Transition Rates with No Moving Avera g e.

Table 1 .
Earnings Function Estimates, OLS.Standard errors in parentheses.The dependent variable is the natural logarithm of wages.All tenures measured in years.Additional covariates include 1-digit occupation and industry dummies, year dummies, marital status, education, sex and age.* * * statistically significant at the 1 percent tolerance level.