The Census and I-CeM

This research uses two sources of data. The first is the Integrated Census Microdata (I-CeM)—a database containing all the anonymized information from the British decennial censuses between 1851 and 1911 (except for 1871)—compiled and published by Schürer and Higgs (2014). The second is the I-CeM Names and Addresses database (Schürer and Higgs 2015), which contains data on the names and addresses of the individuals in the main I-CeM database that have been removed by the process of anonymization. This information is necessary to conduct record linkage.

The censuses of 1851 to 1911 recorded all the vital information that is needed for occupational mobility research, specifically name, age, sex, place of birth, and occupation, with reasonable reliability. This information was then transcribed and enriched by the I-CeM project via a computer program.⁶ This automatic processing, aside from achieving practical efficiency, ensured that decisions concerning the validity of the underlying data source have been applied consistently across the entire database. Of course, this process cannot be perfect. For example, it is not possible to reconcile all the geographical information in the database with that published in the Census Report by the General Register Office (Higgs et al. Reference Higgs, Jones, Schürer and Wilkinson2013).⁷

The most significant undertaking of I-CeM is the standardization of raw textual strings. There were over 7.3 million unique strings for occupations and over 6.7 million for birthplace information, which had to be processed and coded into numeric occupation codes. This enables the use of the I-CeM database for this study since occupations have been coded into a manageable range of categories, while birth places have been standardized to the parish level. Naturally, the automatic coding of this vast number of occupational strings will introduce errors, leading to some occupations being miscoded. Higgs et al. (Reference Higgs, Jones, Schürer and Wilkinson2013) assert that for at least 95 percent of individuals with an occupation title, the coding is “correct.” Other variables, such as marital status and household relationships, have also been standardized, coded, and checked for consistency.

Measuring Occupational Status

In order to measure the association and transmission of socioeconomic status from fathers to sons, occupations must first be assigned a score that reflects their positions in society. One way of doing this is to assign scores based on the Historical Cambridge Social Interaction and Stratification Scale (HISCAM). This scale was constructed by Lambert et al. (Reference Lambert, Zijdeman, van Leeuwen, Maas and Prandy2013) using patterns of intergenerational occupational connections by exploiting data on social connections—such as marriage, friendship, or parent-child relationships—between the incumbent occupations. The main assumption here is that people with similar social status will interact more often. Based on their methodology, they assign a score between 0 and 100 to each occupation, with higher scores indicating a higher social status. The scores are then rescaled such that when they are applied to the sample used in the construction of HISCAM, they should have a mean of 50 and a standard deviation of 10.

The data used to construct HISCAM cover the period between 1800 and 1938 and originate from seven countries—Belgium, Britain, Canada, France, Germany, the Netherlands, and Sweden. Different variations of the HISCAM scale have been created depending on the subset of the data used. For this paper, the “HISCAM_U2” scale, which is generated using only male records from these countries, is used. Table 1 shows a sample of some common occupations observed in the census with their respective HISCAM scores.

Table 1 SAMPLE OF OCCUPATIONS WITH HISCAM SCORES

Notes: “OCCODE” is the numeric code for occupational groupings in the I-CeM Occupational Matrix.

Sources: “OCCODE” and “Occupation description” come from I-CeM (Schürer and Higgs 2014, UKDA, SN 7481); “HISCAM” is taken from Lambert et al. (Reference Lambert, Zijdeman, van Leeuwen, Maas and Prandy2013).

To ensure that the occupational mobility (or immobility) observed is not simply a product of the way occupations are scored by HISCAM, an alternative system of scoring occupations will be used. The one chosen here is the CCC index constructed by Clark, Cummins, and Curtis (Reference Clark, Cummins and Curtis2023), using a set of 1.7 million marriage registers in England between 1837 and 1940. In comparison, Lambert et al. (Reference Lambert, Zijdeman, van Leeuwen, Maas and Prandy2013) had information from 990,000 marriages, of which only around 51,000 came from Britain between 1800 and 1938.

The methodology applied to create this index is the same as the one used by Lambert et al. (Reference Lambert, Zijdeman, van Leeuwen, Maas and Prandy2013) for HISCAM. Using information from marriages, Clark, Cummins, and Curtis (Reference Clark, Cummins and Curtis2023) calculate how closely the holders of each occupation are associated with each other by social connections, such as marriages. Occupations that are far apart in terms of social connections, such as a Member of Parliament (MP) and a miner, will have very few social interactions between them (in other words, very few sons of MPs marry daughters of miners), thus they will be given vastly different scores. On the other hand, many marriages occur between bank clerks’ and teachers’ sons and daughters, so they are given similar scores. Again, the scores are between 0 and 100, with higher scores representing higher status.⁸

Finally, a prerequisite for calculating the Altham statistics—an alternative way of estimating social mobility employed in this paper and by many others in the literature—is to arrange occupations into a suitable number of social classes in a hierarchical order.⁹ This research uses HISCLASS—an international historical social class scheme based on the Historical International Classification of Occupations codes (HISCO) (van Leeuwen et al. Reference Van Leeuwen, Maas, Miles and Edvinsson2002; van Leeuwen and Maas 2011). Occupations in HISCLASS are ranked and assorted into 12 classes (with 1 being the highest) based on 4 dimensions: manual and non-manual divisions, skill level, degree of supervisory power, and economic sector. These 12 levels can be condensed into smaller schemes with fewer classes. To make comparisons with previous research easier, a four-class scheme will be used.¹⁰ Table 2 describes each of the 12 classes in HISCLASS and how they can be combined into the 4-class occupational categories, as shown by Antonie et al. (Reference Antonie, Inwood, Minns and Summerfield2022).

Table 2 HISCLASS LEVELS AND OCCUPATIONAL CATEGORIES

Sources: HISCLASS levels and descriptions are taken from van Leeuwen and Maas (2011); conversion to four-class occupational categories follows Antonie et al. (Reference Antonie, Inwood, Minns and Summerfield2022).

Census Linking Procedure

To conduct record linkage across the censuses, this project selects English-born sons aged 5 to 15 with fathers aged 30 to 55 at the start and tracks them across a 30-year period. Two linked samples are then produced. For the baseline sample, the sons are matched once at the end of the period when they are aged 35 to 45. For the multiple links (ML) sample, which is used to correct for measurement error, the sons are linked across every 10-year interval and the fathers are linked across one 10-year interval.¹¹ This is done for three periods: 1851–1881, 1861–1891, and 1881–1911.

Historical census record linkage is a complicated process due to the lack of a unique identifier like a Social Security Number across datasets. Matching relies heavily on intransient information such as name, birth year, and birthplace. Both the reporting and recording of this limited set of characteristics can be inconsistent. This creates the potential for false matches (Type I errors) and missed matches (Type II errors), and there is a trade-off between minimizing these two types of errors. Choosing an algorithm that eliminates as many false positives as possible while still achieving a satisfactory match rate is crucial for automated record linking (Ruggles, Fitch, and Roberts Reference Ruggles, Fitch and Roberts2018).

This paper adopts a prominent automated census linkage technique developed by Abramitzky, Boustan, and Eriksson (Reference Abramitzky, Boustan and Eriksson2014, Reference Abramitzky, Boustan and Eriksson2019)—henceforth ABE—which matches individuals over time by names (and their Jaro-Winkler string distances), places of birth (in this case parish), and inferred birth year from age.¹² The procedure is outlined in Online Appendix B. This paper opts for the more conservative approach in matching, which minimizes false positives at the expense of a smaller sample (fewer Type I errors, more Type II errors).

The adoption of a more conservative approach to linking is motivated by the findings of Bailey et al. (Reference Bailey, Cole, Henderson and Massey2020), who reviewed a number of prominent automated linkage methodologies (including ABE). They compared the intergenerational mobility elasticity estimates derived from algorithm-linked samples of two pairs of high-quality datasets to the estimate derived from hand-linked samples and a synthetic “ground truth” sample created by the authors.¹³ They concluded that reducing false matches is more important than generating a higher match rate for improving inferences with linked data, as evidenced by the extent of attenuation of the mobility estimates caused by the errors. Although different linking methods produce different samples, eliminating false matches renders estimates from different algorithms statistically indistinguishable.

Since the use of phonetic names in census linking has come under criticism for the high rate of false positives produced when attempting to link Irish immigrants in the United States across the American censuses (Anbinder et al. Reference Anbinder, Connor, Gráda and Wegge2021), this paper opts for matching using string distances by adopting the Jaro-Winkler version of the ABE methodology. Moreover, to ensure that the results obtained in this paper are not significantly impacted by false matches, I have devised a method for estimating the rate of Type I errors and used this to construct a more conservative “true” sample for robustness tests.

The test for false positives exploits the fact that sons and fathers are matched across multiple census years in separate matching processes. For example, I match both sons and fathers from 1851 to 1861 and then identify sons who are found to be living with their fathers in both years. Then I can compare if the fathers I matched through census linking in 1861 are the same people as the ones co-residing with the sons in the census. The detailed procedure and results are outlined in Online Appendix C. The benefit of this way of testing for false positives is that unlike the conventional method of benchmarking a linked sample against a high-quality dataset (Bailey et al. Reference Bailey, Cole, Henderson and Massey2020; Abramitzky et al. Reference Abramitzky, Leah Boustan, Feigenbaum and Pérez2020; Anbinder et al. Reference Anbinder, Connor, Gráda and Wegge2021), which is rare to find given the historical nature, a double-linked sample is much more accessible.

There are a priori reasons to believe that false matches may be less of an issue with linking British censuses. While the U.S. data lacked detailed birthplace information, such that Abramitzky, Boustan, and Eriksson (Reference Abramitzky, Boustan and Eriksson2014, Reference Abramitzky, Boustan and Eriksson2019) could only match people based on the state of birth (equivalent to county level for England), the I-CeM database allows matching based on standardized parish of birth. The latter was also not available to Long (Reference Long2013), so they were not able to address the issue of some parishes having multiple or changing names. Moreover, Anbinder et al. (Reference Anbinder, Connor, Gráda and Wegge2021) recognized that matching Irish people may produce a higher rate of false positives due to a higher incidence of common names. Therefore, the likelihood of Type I error from the use of the ABE algorithm in linking the British censuses should be even lower.

Another issue with census linking is the representativeness of the linked data. Bailey et al. (Reference Bailey, Cole, Henderson and Massey2020) contend that linking, whether by hand or by machine, cannot produce a fully representative sample. This is because individuals are required to be “unique” by name, age, and birthplace, which necessarily means that it will be easier to match people with rarer and/or longer names. This may inadvertently introduce bias into the sample if people with these names systematically differ from people with common names. Moreover, people with higher levels of education may be easier to link since they can report their information more accurately and more consistently over time. The match rate may also vary with age, as the incidence of emigration and mortality differs between the young and the old—younger people are more likely to emigrate, while the rate of mortality increases with age.

However, the impact of a non-representative sample may be less significant than false positives. Bailey et al. (Reference Bailey, Cole, Henderson and Massey2020) show that reweighting the sample by inverse probability can effectively address the issue of sample selection bias.¹⁴ They also suggest that after removing the incorrect links, reweighting makes little difference. Abramitzky et al. (Reference Abramitzky, Leah Boustan, Feigenbaum and Pérez2020) also state that coefficient estimates and parameters of interest derived from different samples, weighted or otherwise, produced by the different algorithms they tested are very similar and do not change the interpretation.

Census Linking Outcomes

Table 3 shows the summary statistics for the baseline and the multiple-link samples for the periods 1851–1881, 1861–1891, and 1881–1911. For the baseline samples, between 290,000 and 610,000 father-son pairs have been successfully matched, which translates to a match rate of 21 to 29 percent. Upon restricting the sample to sons who can be matched across every census in the 30-year period with fathers who can be matched across a 10-year interval, the match rate decreases to between 5 to 8 percent. This still generates between 68,000 to 160,000 father-son pairs—a huge improvement on the sample size of Long (Reference Long2013), who had only 12,516 father-son pairs for 1851–81 and 4,071 pairs for 1881–1901.

Table 3 SUMMARY STATISTICS OF LINKAGE RESULTS, 1851–1911

Notes: “Population” includes all men aged 35–45 in 1881, 1891, and 1911 when comparing with the sons in the linked sample and all men aged 30–55 in 1851, 1861, and 1881 when comparing with the fathers; “ML” refers to the sample where sons are double- or triple-linked and fathers are double-linked; “Manufacturing” in Occupational Structure also includes Mining and Transport sectors; “Extra London” refers to the regions of Middlesex, Kent, Essex, and Surrey that are not included in “London”; “Greater London” refers to the entire regions of Middlesex, Kent, Essex, and Surrey; “Yorkshire” includes all Ridings of Yorkshire. All numbers are in percentages unless stated otherwise.

Sources: Author’s analysis of I-CeM (Schürer and Higgs 2014, UKDA, SN 7481) and I-CeM Names and Addresses (Schürer and Higgs 2015, UKDA, SN 7856).

A comparison of the key socioeconomic indicators suggests that both the baseline and the multiple links samples are very representative of the full population. In terms of occupational status—measured by HISCAM and CCC—and age, both the sons and their fathers show negligible differences from the wider population. The same is true for the sons’ first and last name lengths, and the number of kids and servants they have.

Other variables, such as household relationship status, marital status, occupational structure, and geographical distribution, are also presented. It may be worth noting that in terms of the geographical distribution of the linked sample, both by county of birth and by registration district of residence, matching tends to be biased against dense, urban regions such as London and Lancashire. This is to be expected since it is more difficult to find “unique” individuals in parishes with denser populations. As a result, the linked sample also tends to be more agricultural, especially for the more restrictive sample with multiple links. As Bailey et al. (Reference Bailey, Cole, Henderson and Massey2020) demonstrated, these issues can be corrected using inverse probability weights (see Online Appendix D for more detail), and later results will show that reweighting does not change the results significantly.

Calculating Intergenerational Elasticity (IGE)

A standard approach in estimating intergenerational mobility in the social mobility literature, particularly for the modern era, is to calculate the IGE of any measure of socioeconomic status by regressing the log of son’s outcome (Y _i,t ) on the log of the father’s outcome (Y _i,t–1):

(1) $${Y_{i,t}} = \alpha {\rm{ }} + \beta {Y_{i,t}}_{-{\rm{1}}} + {\rm{ }}{\varepsilon _{i,t,}}$$

where α is the constant, ε _i,t is a set of random factors, and the coefficient of interest is β, which is the IGE estimate. A perfectly mobile society will have an IGE of 0, indicating no association between the father’s outcome and the son’s outcome. Conversely, a very immobile society will have an IGE of close to 1.

The socioeconomic outcome of an individual observed in a given year consists of a permanent component and an uncorrelated transitory component. As such, our occupation-based measures of status may be noisy, so the occupational status of the father observed in a single year may deviate from his permanent status, which attenuates β toward 0:

(2) $${Y_{i,t-1}}\, = {Y_{i,t-{\rm{1}}}}\, + {u_{i,t-{\rm{1}}}}$$

To address the issue of classical measurement error, one method is to average multiple observations of the father’s status by T times:

(3)

This reduces the attenuation bias caused by errors-in-variables. Modern-day mobility studies often use an average of incomes from many years—a classic example being Mazumder (Reference Mazumder2005), who averaged fathers’ earnings as many as 16 times—but research on historical mobility is limited by data availability and the costs of linking censuses. Though the costs have fallen in recent years with the advent of big data and automated census linking, it is still difficult to obtain more than three observations of occupational status (over time) for a single individual as the census was taken only once per decade. More observations also mean greater sample attrition.

A second method is to instrument the father’s outcome with a second measure of the father’s outcome (Z _i,t–1), assuming that the transitory components of the occupational statuses (ε _i,t and µ _i,t ) observed are uncorrelated across different observations:

(4)

(5)

Both methods for correcting measurement error (averaging across multiple short-run observations or IV) have been implemented for modern-day studies (for instance, by Altonji and Dunn (Reference Altonji and Dunn1991), Solon (Reference Solon1992), Zimmerman (Reference Zimmerman1992) in the U.S. context, and Dearden, Machin, and Reed (Reference Dearden, Machin and Reed1997), Grawe (Reference Grawe and Corak2004) for the British context) and more recently, for historical studies by Ward (Reference Ward2023). The instrumental variables approach is shown to work as well, if not better than averaging across three father’s observations (Ward Reference Ward2023). To carry out the IV method, this paper instruments the father’s occupation at the start of each of the three periods (1851–1881, 1861–1891, and 1881–1911) with the father’s occupation observed in another census, 10 years apart.

This may seem to be an unusual use of the IV method, given that the purpose of using the instrument is not for causal identification. However, there is an established tradition of using IV methods to correct for measurement error. Fuller (Reference Fuller1987) outlined that where the independent variable x _t is measured with errors, we can correct for the attenuation bias caused by such errors using an instrument W _t ; a possible choice for W _t is a measurement of x _t obtained by an independent method. Indeed, this is the approach taken by Solon (Reference Solon1992), who used a father’s years of education as an instrument for a father’s earnings in a single year. Ward (Reference Ward2023) adapts this approach to the nineteenth century by using the father’s occupational status measured in a different year as an instrument for the father’s occupational status observed in one year.

The validity of such an instrument lies in the fact that it provides additional information for measuring our independent variable, the father’s true socioeconomic status. Though this second measure of the father’s status may produce additional measurement error, as long as these errors are uncorrelated with each other—a standard assumption in the literature—the IV estimator will remain consistent (Solon Reference Solon1992; Modalsli and Vosters Reference Modalsli and Vosters2019; Ward Reference Ward2023).

A potential limitation to this strategy is that the instruments available are often endogenous. In Solon’s (1992) case, the father’s education may be positively but imperfectly correlated with the son’s status, and in this paper, a father’s occupation in a second census may also be positively correlated with the son’s future occupational status. If this was the case, then the IV estimator will be upward-inconsistent, so the IGE obtained using the IV approach becomes an upper-bound estimate for the true level of father-son association in status, and the OLS estimate becomes a lower-bound since it is downward-inconsistent (Solon Reference Solon1992; Mitnik Reference Mitnik2020).

Another concern with the IV approach is that life-cycle variations in socioeconomic status could have an impact on the IGE estimated. Haider and Solon (Reference Haider and Solon2006) show that attenuation or amplification bias to β could occur if the incomes of sons are observed at younger or older ages; this can be mitigated by measuring status at mid-life—around early 40s (Haider and Solon Reference Haider and Solon2006; Modalsli and Vosters Reference Modalsli and Vosters2019). This falls within the middle of the age range (35 to 45) from which the son’s occupational status is taken in this paper. Moreover, additional checks show that the IGE estimated using the occupational status of sons observed at different census years is quite similar (see Online Appendix H), so lifecycle effects are not significant enough to cast doubts on the results and their interpretations.

Measuring Mobility Using Altham Statistics

Several papers in the literature on social mobility in the nineteenth and twentieth centuries relies on an entirely different approach, based on the construction of mobility tables—a two-way contingency table plotting the father’s social class against the son’s social class (Long Reference Long2013; Long and Ferrie Reference Long and Ferrie2013; Pérez Reference Pérez2019; Antonie et al. Reference Antonie, Inwood, Minns and Summerfield2022). The diagonals in the table represent the number or share of sons who do not show mobility— those who held an occupation belonging to the same social class as their fathers at a similar stage in their life cycles. The cells above the diagonals contain the upwardly mobile, and the cells below the diagonals contain the downwardly mobile. Mobility rates can be calculated by aggregating all individuals with the same mobility pattern. For instance, the rate of upward mobility is simply the percentage of all upwardly mobile sons as a share of the total number of father-son pairs.

However, simply comparing the mobility rates between different mobility tables is not enough to inform us whether one society is more mobile than another. This is because raw mobility rates are affected by the marginal frequencies of the two tables. Thus, it cannot distinguish whether differences in mobility are caused by the different distributions of occupations in the two mobility regimes or by the differences in the strength of association between fathers’ and sons’ outcomes.

One measure that could account for differences in the marginal frequencies between two tables and quantify relative mobility is the Altham statistic, devised by Altham (Reference Altham1970) and coded into Stata by Altham and Ferrie (2007). For two tables P and Q with r rows and s columns, the Altham statistic sums the squares of the differences between the natural logarithms of the cross-product ratios in the two tables:

(6)

Tables with very similar mobility patterns will produce a d(P,Q) value of close to 0, and a very large value if the two tables are very different. The likelihood ratio G ² statistic with (r – 1)(s – 1) degrees of freedom is used to establish statistical significance and whether we can accept that d(P,Q) ≠ 0.

To see which table is more mobile, the same procedure is carried out again to estimate d(P,I) and d(Q,I), where table I is just a matrix of ones, representing complete independence of rows and columns. In other words, d(P,I) and d(Q,I) measure the distance of tables P and Q from perfect mobility. If d(P,I) > d(Q,I) and d(P,Q) > 0, relative mobility is greater in table Q than in table P. To correct for measurement error in Altham statistics, Ward (Reference Ward2023) proposes that only those whose fathers are observed to be in the same class more than once should be kept in the sample.

Main Results—IGE Estimates

Table 4 illustrates the main findings of this paper. The IGE of log occupational status for the baseline sample is shown in Columns (1), (4), and (7) for the periods 1851–1881, 1861–1891, and 1881–1911.¹⁵ The OLS estimates of the β for the sample with multiple links (where sons can be linked across multiple censuses) are shown in Columns (2), (5), and (8).¹⁶ Standard errors are shown in parenthesis; all estimates are statistically significant at the 0.01 level. The β for the sample with multiple links is slightly higher than the β for the baseline sample across all periods. This may indicate that linking sons across multiple years, rather than just once across the 30-year interval, reduces the likelihood of false positives and hence the attenuation bias associated with false matches, though the difference is not huge.

Table 4 INTERGENERATIONAL ELASTICITIES OF OCCUPATIONAL STATUS (HISCAM), 1851–1911

Notes: Standard errors in parenthesis; all estimates are statistically significant to p<0.01; “ML” stands for Multiple Links and denotes whether sons and fathers can be linked across multiple censuses.

Sources: Author’s analysis of I-CeM (Schürer and Higgs 2014, UKDA, SN 7481) and I-CeM Names and Addresses (Schürer and Higgs 2015, UKDA, SN 7856).

More importantly, the results clearly suggest that measurement error associated with occupational status cause significant downward bias in historical mobility estimates. Columns (3), (6), and (9) show the estimates of IGE after instrumenting one father’s occupation with a second father’s occupation (detailed regression output with first-stage results can be found in Table 5). After accounting for errors-in-variables through the instrumental variable approach, the association between the father’s and son’s occupational status increases from around 0.41 to between 0.62 and 0.68—an increase of 53 to 64 percent. This is a considerable revision on previous estimates by Long (Reference Long2013), whose estimates of IGE of occupational earnings stood between 0.26 and 0.37 for the periods 1851–1881 and 1881–1901. It is important to note too that even without using the IV approach, the extent of mobility is lower than what Long had estimated, as the OLS β ranges from 0.38 to 0.41.

Table 5 DETAILED IV RESULTS (WITH FIRST STAGE), 1851–1911

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Sources: Author’s analysis of I-CeM (Schürer and Higgs 2014, UKDA, SN 7481) and I-CeM Names and Addresses (Schürer and Higgs 2015, UKDA, SN 7856).

Part of the discrepancy may be explained by the differences in the linked sample. My sample, which is much larger in size, may have been more representative and less prone to Type I errors, which would explain the higher β estimated vis-à-vis Long (Reference Long2013). Most of the differences, however, came from using the instrumental variable approach. This reinforces the concerns over the attenuation bias caused by measurement error in many existing estimates of social mobility—they could be overestimating mobility by twice as much, if not more.

While the OLS estimates show no changes in the rate of occupational mobility over time, the IV estimates suggest that England was becoming gradually more mobile over the course of the nineteenth century. This might be explained by the effects of measurement error weakening over time as occupations become more stable and people become more adept at reporting their personal information. Nevertheless, the decline is quite modest in magnitude.

Table 6 provides some additional results. When a different occupational score index (CCC score) is applied, there is still a significant extent of attenuation in the β estimated using the conventional OLS formula, caused by measurement error. The β rises from between 0.52–0.53 to between 0.63–0.71—21 to 34 percent higher—after instrumenting with a second father’s observation. Interestingly, the CCC β obtained using the IV approach is akin to the one for HISCAM, except for the 1881–1911 period, which might be expected given that both indices are constructed using similar methods. The fact that the OLS coefficients for CCC are much higher, and likewise the IV coefficients for the last period, suggest that the CCC index may be a better measure of occupational status for England during this period, though more work is required to attest to this. Regardless, the results confirm that there is a sizeable reduction in the degree of openness versus earlier estimates of intergenerational mobility.

Table 6 ADDITIONAL ESTIMATES OF IGE

Notes: Standard errors in parenthesis; all estimates are statistically significant to p<0.01; all occupations are scored using HISCAM-U2 unless otherwise stated; “Main results” refer to the results shown in Table 4; “Time-adjusted” estimates are produced using the “HISCAM-E” and “HISCAM-L” schemes to score occupations differently for fathers and sons to reflect the changes in socioeconomic status associated with each occupation; “CCC scores” estimates are produced when occupations are scored by the CCC scheme devised by Clark, Cummins, and Curtis (Reference Clark, Cummins and Curtis2023); “Weighted” estimates are produced when the linked sample is reweighted according to population characteristics, following the procedure outlined in Online Appendix D; “NYSIIS” estimates are obtained when IGE is estimated using a linked sample produced by the standard ABE algorithm that matches individuals using their phonetic names (NYSIIS) rather than string distances; “False positive check” estimates are produced when individuals who are likely to be false positive matches are dropped from the sample, according to the procedure outlined in Online Appendix C. Sources: Author’s analysis of I-CeM (Schürer and Higgs 2014, UKDA, SN 7481) and I-CeM Names and Addresses (Schürer and Higgs 2015, UKDA, SN 7856).

Allowing occupational scores to vary over time to adjust for the changes in the socioeconomic status associated with each occupation also makes a modest improvement to the β estimated. HISCAM provides two alternative scales constructed using historical records from different periods: “HISCAM-E” for an early period of 1800 to 1890 and “HISCAM-L” for a later period of 1890 to 1938 (Lambert et al. Reference Lambert, Zijdeman, van Leeuwen, Maas and Prandy2013). The “Time-Adjusted” OLS and IV estimates for 1861–1891 and 1881–1911 are produced when sons’ occupations are scored using the HISCAM-L scale and fathers’ occupations are scored using the HISCAM-E scale. Both estimates are higher than when fathers’ and sons’ occupations are scored using the same HISCAM-U2 scale. The difference is greater for the 1881–1911 period and significant to the 95 percent confidence interval.

In addition, estimating β using different samples constructed for robustness checks produced very similar results. The “Weighted” sample refers to the multiple links sample with inverse probability weights assigned according to the procedure outlined in Online Appendix D. The “NYSIIS” sample is produced using the phonetic name version of the ABE matching algorithm, as outlined in Online Appendix B. Lastly, the “False Positive Check” sample refers to the multiple links sample after removing those who were deemed likely to be false positives, using the method discussed in Online Appendix C. As the table highlights, none of these changes affect the results enough to warrant a reconsideration of this paper’s findings.

Finally, Figure 1 shows the comparison of my results for the period 1851–1881 with Long (Reference Long2013), and the difference each change in the data and the methodology makes to the estimates of intergenerational mobility. As expected, the IV strategy contributes to most of the difference between my estimates and those of Long (Reference Long2013). However, it is evident that other changes in data and methodology, including using the full 1851 census rather than a 2 percent sample, also raise the estimated IGE. This suggests that, among other things, the use of a sample overestimates the true extent of intergenerational mobility, even without correcting for measurement error, which may have been caused by a higher incidence of false positives.¹⁷

Figure 1 COMPARISON OF MY RESULTS FOR 1851–1881 WITH LONG (2013)

Notes: “2% Sample w/ ± 5 Birth Year” refers to using a 2 percent sample of the 1851 census and allowing for birth year to differ by at most plus or minus five years—this is the approach taken with census linkage in Long (Reference Long2013), which I have also replicated in my work; I use the same 2 percent sample that I have created through randomization but with the further restriction of only allowing the birth year to differ by two years to produce the “2% Sample w/ ± 2 Birth Year” estimate; “Full Census” estimate is taken from Table 4, Column (1); “Full Census w/ Multiple Links” is taken from Table 4, Column (2); “IV” estimate is taken from Table 4, Column (3); “CCC” is the estimate obtained using both the IV strategy and the CCC scores instead of HISCAM.

Sources: Long (Reference Long2013) and author’s analysis of I-CeM (Schürer and Higgs 2014, UKDA, SN 7481) and I-CeM Names and Addresses (Schürer and Higgs 2015, UKDA, SN 7856).