 effect of value added on wages, however. It is the case that the correlation is estimated in the presence of sector fixed effects, and so is identified off variation in value added over time within sectors. It is not therefore due to unobserved characteristics of sectors that are correlated with both value added and wages and which are constant over time. It cannot be completely ruled out, however, that other factors may have changed in the finance sector at the same time as the rise in value added, and it is those other factors that have actually increased the wage. In the following sections we therefore consider alternative possible explanations for the high and rising finance sector pay premium, including relatively higher levels of human capital and task biased technological change.

IV. Is the finance sector more skill intensive?
Higher wages in the finance sector could potentially be explained by better qualified workers in the finance sector relative to all other industries, and rising wage premiums explained 19 See SupplementaryTable S3 for results. Column 1 is the standard OLS equation, and column 2 is the standard fixed effects specification. Adding the industry value-added variable (column 3) reduces the estimated finance coefficient from 0.263 to 0.194. 20 Compare columns 4 and 5 of Supplementary Table S3. 21 See column 6 of Supplementary Table S3. 22 As an alternative test, we collapsed the income, age and region data in NESPD down to the two-digit sector level, so that it was at the same level of aggregation as the value-added data. A similar specification to column 6 in Supplementary Table S3 was then estimated, with the log of value added per hour interacted with all 59 twodigit sector dummies. The coefficients for two of the finance sector interactions with value added (65 'Financial intermediation' and 67 'Activities auxiliary to financial intermediation') were positive and statistically significant, with the latter particularly large at 1.62, the fourth largest of all the interaction coefficients (results available from authors on request). Note that sub-sector 67 is the one that contains fund management and security broking, the two sub-sectors with the largest interactions in the more disaggregated individual level analysis in Supplementary Table S3. by increasingly well-qualified workers, although these explanations seem unlikely given that we have found a significant premium across the whole distribution. It has been well documented that the total employment shares of graduates have increased in the labour market as a whole. For example Lindley and Machin (2012) using the Labour Force Survey (LFS) show that the employment share of graduates increased from 0.14 in 1996 to 0.23 in 2006 and to 0.31 in 2011. We would like to know how many of these graduates are employed in finance and, conditional on the overall increase in the supply of graduates, whether the number working in finance is rising. In doing so, we must of course acknowledge that the skills of graduates may change over time, and this effect may differ by subject, as Higher Education has expanded to include a wider spectrum of young people. 23 Thus any increase in the number of graduates over time may overstate the increase in skills to a sector. Data from the LFS show that the finance employment share amongst graduates has increased from 0.046 in 1994 to 0.060 in 2008, but then fell slightly to 0.058 in 2011. So before the start of the recession in 2008, there were relatively more finance workers amongst graduates than amongst the total private sector workforce (the proportion of all private sector workers employed in finance was 0.052 in 2008). Disaggregation by subject area 24 shows that the finance employment share is much larger for economics graduates, maths/computing graduates and management/business graduates, with the economists demonstrating the largest increases. 25 In 2011 over a quarter of all economics graduates were employed in the financial sector. Figures for maths/computing and management/business were 10% and almost 11% respectively. Given these subjects are by nature more numerical, this also suggests that in the long term there has been numerical skill upgrading (mainly from economics graduates) in the financial sector.
Given that we find some evidence of skill upgrading in the finance sector, which may therefore provide the explanation for the high and rising wage premium in that sector, we augment equations (1) and (2) with measures for highest qualifications using the 1997-2008/9 British Household Panel Survey (BHPS). The BHPS is a longitudinal data set that contains questions on highest qualifications as well as a measure of annual labour income, including bonuses, which was first asked in 1997. 26 Consequently we estimate 23 See Lindley and McIntosh (2015) for a discussion of such issues. 24 See Supplementary Figure S1. 25 The subject of degree question for much of this period in the LFS refers only to the undergraduate degree, with subject of postgraduate qualifications only added more recently. We therefore focus only on subject of first degrees here. For detailed definitions of the subjects listed in Figure 2 see Lindley and McIntosh (2015). 26 The BHPS is a sample of over 5,000 households in the UK, conducted annually since 1991 and contains information on human capital and socio-economic characteristics of each individual in the household. From 1997 onwards the survey also collected information on annual labour income and bonuses. The data on annual earnings in the BHPS is constructed from monthly and weekly earnings rather than being directly asked. From 1997 there was a separate question asked regarding the value of all bonuses received in the last 12 months. Following Bell and Van Reenen (2010), we add this value to the respondent's annual labour income to produce total annual labour income including bonuses. where F k is a dummy that is equal to one if worker i is employed in the finance sector, and has highest qualification k at time t, and zero otherwise. 27 There are four highest qualification groups; graduates, some college, 2 plus A-levels 28 and other/no qualifications. Again our controls in vector X are region of residence, gender, age and age squared, but we also now condition on marital status. Equation (5) differs to equation (4) only in that it also includes worker level dummies and thus provides fixed effects estimates. The estimates of from equations (1) and (2) are provided in the first and third columns of Table 6, whilst the second column provides the estimates of the coefficients from equation (4) and the fixed effects estimates of the coefficients from equation (5) are presented in the final column. The OLS conditional log annual wage differential over the period is 48%, while the second column shows that this is 76% for graduates and 78% for individuals with some college. The final two columns provide the FE estimates. These suggest a similar sized financial labour income differential within each education group. Conditioning on unobserved heterogeneity, the finance premiums are lower than the OLS estimates for all education groups, which is suggestive of unobserved wage-enhancing characteristics, such as greater cognitive ability. However, we cannot say how much of the unobserved heterogeneity observed here is a consequence of cognitive skill differences, to which we now turn.
In summary, the data suggest that the finance sector does employ an above-average proportion of higher-qualified workers, with some evidence that the sector is increasingly attracting the more numerate graduates. Qualification levels, as an indicator of skills, are therefore a potential explanation of the high and rising finance sector wage premium. The 27 We interact working in finance with the highest qualification in this way, because highest qualification does not vary with time for the vast majority of our subjects, and so would be picked up by the individual fixed effects in equation (5) if entered on their own. Equation (4) is then specified in the same way for comparison purposes. If instead we add the highest qualification variables to an OLS specification as in equation (1), then the estimated finance coefficient falls from the 0.393 reported in Table 6 column 1, to 0.308, revealing that part of the finance sector wage premium is due to differing stocks of qualifications between the finance and non-finance sectors, but that a significant premium remains even after controlling for qualification differences. 28 A levels are national qualifications obtained at the end of upper secondary schooling.
regression results, however, show that although qualifications go some way to explaining the size of the finance sector wage advantage, a significant premium remains, which is similar in size within each education group. This result compares with the analysis of Philippon and Reshef (2012) who similarly find an increasing skill-intensity in the finance sector at the same time as the increase in relative wages, but that the former cannot fully explain the latter, given an increase in the finance sector relative wage post-1990 that is greater than that predicted by the increase in skill-intensity.

V. Do finance sector workers have higher cognitive skills?
In this section we look further into the characteristics considered as unobserved in the previous section, and investigate to what extent the finance premium might be a consequence of high and rising cognitive skills amongst finance workers, paying particular attention to differences in numeracy and reading skills. We start by looking at whether finance workers have better skills on average and whether any such gap is increasing. We draw upon the British cohort study (BCS) which is a sample of men and women born in 1970 and the national child development study (NCDS) where respondents were born in 1958. The most recent sweeps of the BCS and NCDS were undertaken in 2008, when the BCS (NCDS) respondents were aged 38 (50) and questions were asked about various socioeconomic and work characteristics of the respondents. The surveys provide information on gross pay, highest educational qualification, industry of employment, marital status, gender and region of residence.

Differences in childhood test scores
Given that finance workers could be more numerate as adults because their job involves more numerical tasks, we use childhood test scores for mathematics and reading taken when the respondents were aged 10 and 11, rather than adult test scores. The