International analysis of child poverty – ukmod/euromod modelling

Appendix B – Demographic and Labour market computation

B.1 Counterfactual: Demography

Scottish demographic data was matched to each of the comparator countries as part of the decomposition analysis. This involved adjusting the Scottish data to reflect family demographic characteristics reported for each comparator country.

Matching of Scottish data to comparator country data was based on: the relationship status of the family, the education of the household head and spouse, and the number of family members in different age brackets.

The matched data reflect close similarities with the comparator countries. Nevertheless, differences in measures of education reported for Scotland and comparator countries suggest that some distortions are likely to remain.

The results of the demographic comparison are explored in Section 4.

Our analytical approach involves reweighting the Scottish data to reflect demographic characteristics reported for comparator countries. This was achieved by matching each observation described for a comparator country to a set of Scottish observations.^[18] For each match, the record from the comparator country was then considered to “donate” its weight to the Scottish recipients, so that we end up with a dataset that is identical to the Scottish data in all respects other than the (weighted) distribution of the demographic characteristics considered for the matching process. This then permits identification of the contribution of demographics to measures for child poverty.

Matching was conducted exclusively on a selected set of demographic variables evaluated at the benefit unit level.^[19] The following set of benefit unit demographic variables were considered for the matching procedure:

• Relationship status: singles and couples.
• Age of head: under 26, 26 to 50, 51 to 75, and 76+.
• Age of spouse: under 26, 26 to 50, 51 to 75, and 76+ (same as age of head).
• Number of members under age 6: 0, 1, 2, and 3+.
• Number of members aged 6 to 15: 0, 1, 2, and 3+ (same as aged under 6).
• Number of members aged 16 to 17: 0, 1, 2, and 3+ (same as aged under 6).
• Number of members aged 18+: 0, 1, 2, and 3+ (same as aged under 6).
• Number of members aged 65+: 0, 1, and 2.
• Highest education of head: tertiary, upper-secondary, other.
• Highest education of spouse: tertiary, upper-secondary, other (same as education of head).

All of the characteristics noted above are discrete variables, permitting application of (coarsened) exact matching. Analyses proceeded as follows:

4. A recipient dataset was obtained from the original dataset of Scottish benefit units, where all benefit unit weights were initialised to 0.

5. For each benefit unit (BU) in the comparator country data (donor), a match (with replacement) was found to a set of Scottish benefit units (recipient pool) drawn from the recipient dataset defined following (1).

6. The donor sample weight was added to the weights of members in the recipient pool identified from (2) in proportion to their weights in the original Scottish dataset.

a. For example, if a recipient pool was comprised of two observations, A and B, where the weight of A in the original Scottish data was twice the weight of B, then two-thirds of the donor’s sample weight (described by the comparator data) would be added to the weight of recipient A and the remaining third to recipient B.

b. Where a match was not obtained for a comparator country donor, new observations for (synthetic) Scottish recipients were generated.^[20]

Summary statistics for the alternative input data sources are reported in Tables B1.1 and B1.2. These tables indicates a reasonably close correspondence between the population demographics described by the input data for Scotland and the alternative comparator countries (the “orig.” statistics reported in the table). Indeed this basic similarity was one of the considerations underlying the choice of comparator countries, as discussed in Section 2. Nevertheless, notable differences do exist for the distribution of highest education qualification, where there is a substantially lower incidence of upper secondary and tertiary education in Scotland relative to all of the comparator countries.

The observed differences in relation to educational attainment reported in Tables B1.1 and B1.2 are somewhat surprising. Eurostat data, for example, indicate that the proportions of populations aged 15 to 64 with “less than primary, primary and lower secondary education (levels 0-2)” between 2011 and 2019 were generally comparable between the UK and the comparator countries, where Denmark was reported to have appreciably higher rates of lower education.^[21] Furthermore, the Scottish Census 2011 indicates that 26% of people aged 16 and over had a university degree of professional qualification, which is double the associated figure reported in Tables B1.1 and B1.2. Recent quality reviews of the Family Resources Survey (FRS) - upon which the current analysis is based – have identified issues with reported education status, which may go some way toward explaining the disparities identified here.^[22]

Furthermore, Scottish data report a higher incidence of disability than do the comparator countries. Note, however, that disability was not considered for the matching reported here, motivated in part by difficulties in ensuring international comparability of measurement, and in part because identification of disability from the FRS is based on a labour market (rather than demographic) variable. Treatment of cross-country differences associated with the labour market are considered separately to demographics, and are reported in Appendix B.2.

Source: Authors’ calculations on input data for UKMOD (Scotland) and EUROMOD (Croatia, Slovenia, Denmark and Finland).

Notes: SC: Scotland, HR: Croatia, SI: Slovenia, DK: Denmark, FI: Finland. “orig.” denotes weighted population statistics described by original input data. “match” denotes weighted statistics described by Scottish data re-weighted data following population matching. * denotes statistics not considered as part of the matching procedure. Data for Scotland derived from the Family Resources Survey (FRS) for 2012 and 2022. Data for all other countries derived from the European Union Survey of Income and Living Conditions (EU-SILC) for 2012 and 2019. See Appendix A.1 for further detail. All statistics describe population percentages except “Age” and “Years of education”, which report years.

Notes: See Table B1.1.

Concerning the set of variables considered for matching (those without stars in the table), the average absolute difference between the population averages reported for 2011 in Scotland and Croatia is 8.8 percentage points, and 8.5 percentage points for Slovenia. These differences fall to 0.9 and 1.6 percentage points respectively in the matched datasets. Similar results were obtained for all comparator countries based on data for 2024.^[23] The residual variation reported for the matched data are due to a range of considerations including top-coding of household members in the matching process, the creation of synthetic recipients (not reported in the table) and rounding of population weights.

B.2 Counterfactual: Labour market

Counterfactual projections for employment and earnings were created to compare the impact of the Scottish labour market with the comparator countries. This was achieved through a combination of four statistical models in order to estimate the likelihood of employment and unemployment, the hours worked, and the pay per hour worked for families.

The probit model estimating employment has lower explanatory power for some of the comparator countries, which is attributed to very high rates of employment observed in these countries. The probit model estimating unemployment for those not in work has a greater explanatory power than the model estimating employment. However, of note, the number of those not in work in Scotland described as unemployed are much lower than the comparator countries, likely due to the means-testing and activity requirements imposed on benefits receipt in Scotland.

The results of the counterfactual projection for labour is explored in Section 4.

As discussed in Section 2, counterfactual projections for employment and earnings in Scotland that are designed to reflect conditions in comparator country labour markets are used as part of the decomposition analysis reported in Section 4. These labour market counterfactuals are generated based on four statistical models estimated for each comparator country:

• Probit equation defining the likelihood of being employed
• Probit equation defining the likelihood of being unemployed for those not employed
• Linear regression for (log) hourly wages estimated for those in employment^[24]
• Linear regression for hours worked per week for those in employment

Regression estimates for each of these models are reported below.

Tables B2.1 and B2.2 report estimates for the probability of being employed in 2011 and 2024 respectively. Tertiary education is the only variable associated with statistically significant coefficient estimates for all combinations of countries and years, where estimates imply higher likelihoods of employment. Other variables for which estimates are typically significant include age squared (Age x Age) which tends to be negative reflecting the hump-shaped profile of the working lifetime, professional and associate professional occupations, which are associated with higher rates of employment, and length of preceding employment history (months of work) which also tends to increase likelihood of employment.

The regression summary statistics reported at the bottom of Tables B2.1 and B2.2 indicate that the assumed regression specification has greater explanatory power in Scotland and Croatia than the remaining countries considered for analysis. This observation, however, can be attributed to the very high rates of employment observed in 2024 in Slovenia, Denmark and Finland. These high rates of employment result in regression estimates that tend to generate false positive predictions.

Tables B2.3 and B2.4 report estimates for similar regression models as reported in Table B2.1, but focussing on likelihood of unemployment among people who were not employed. In this regard, estimates for Scotland stand in stark contrast as appreciable minorities of people not employed are described as unemployed, rather than the clear majorities reported in comparator countries. This feature of the data may reflect the emphasis on means-testing and activity requirements imposed on benefits receipt in the UK.

The regression models for unemployment reported in Tables B2.3 and B2.4 appear to exhibit greater explanatory power than those for employment, in the sense that correct predictions exceed those of a naïve model by a wider margin.^[25] As suggested above, this improved explanatory power can be attributed, at least in part, to the greater variation described by the respective samples (which are more evenly split between those unemployed and those not).

Otherwise, the estimates reported in Tables B2.3 and B2.4 tend to associate higher rates of unemployment with women than men, and a hump-shaped profile with age that responds to the same pressures of retirement later in life as discussed above for rates of employment. In these respects, estimates for Scotland are comparable with those of the comparator countries.

Estimates for (log) hourly wage rates are reported in Tables B2.5 and B2.6. The summary statistics reported at the bottom of the table for these models indicate greater precision in Scotland and Croatia than in the other comparator countries. Nevertheless, the models estimated for all countries and time periods exhibit a reasonable degree of explanatory power, as suggested by the large number of statistically significant regression coefficients. Women are associated with statistically significant higher hourly wage rates than men, and there is a clear hump-shape in the hourly wage rate profile with age. All of the occupational categories identified in the regression (professional, associate professional, secretarial) are associated with higher hourly wage rates. At first glance, the occupational gradient of hourly wages may appear odd, but note that this is likely to reflect reverse relationships with hours of employment.

Tables B2.7 and B2.8 report estimates for hours of employment among the employed population. The R-squared statistics reported at the bottom of Tables B2.7 and B2.8 indicate that the models considered for hours of employment possess little explanatory power, especially for Croatia and Slovenia. This is in spite of the relatively large number of explanatory variables considered for the description of hours worked. Nevertheless, associated values for root-mean-squared-errors (RMSE) – which describe variation of the respective regression residuals – are between 13% (Croatia, 2024) and 22% (Denmark) of the mean hours of employment, giving confidence that much of the population variation is helpfully described by the considered set of covariates.

All else equal, the estimates suggest that employed women report significantly higher numbers of hours than do men in all of the regression specifications, with the largest differences reported for the UK followed closely by Finland. As for other estimates discussed above, hours of employment tend to describe a hump shape over the life-course. Significantly higher hours are also estimated for “associate professional” and “secretarial” occupations, and increase with the reported number of months in work. Other estimates reported in the table are more variable.

Source: Authors’ calculations on input data for UKMOD (Scotland) and EUROMOD (Croatia, Slovenia, Denmark and Finland).

Notes: SC: Scotland, HR: Croatia, SI: Slovenia, DK: Denmark, FI: Finland. “coef.” reports estimated coefficients. “s.e.” reports robust standard errors. Estimates noted with an * are not significant at 95% confidence interval. Data for Scotland derived from the Family Resources Survey (FRS) for 2012 and 2022. Data for all other countries derived from the European Union Survey of Income and Living Conditions (EU-SILC) for 2012 and 2019. Regression predictions evaluated at the 50% threshold.

Notes: See Table B2.1.

Notes: See Table B2.1. Sample further limited to observations not employed.

Notes: See Table B2.1. Sample further limited to observations not employed.

Notes: See Table B2.1. Sample further limited to observations not employed. Mean ln wages are in national currencies.

Notes: See Table B2.1. Sample further limited to observations not employed. Mean ln wages are in national currencies.

Notes: See Table B2.1. Sample limited to employed population.

Notes: See Table B2.1. Sample limited to employed population.