We present an econometric analysis of underemployment and overemployment in the UK following and expanding on Tam (2010). In particular, we look at the relationship between the age of a worker and their probability of being underemployed or overemployed. We found a significant and positive association between age and underemployment and also between age and overemployment, once the influence of other confounding variables are accounted for. The first result is in contrast to what could be inferred from simple cross-tabulations.

**1. Introduction**

In the July 2010 issue of the Economic & Labour Market Review published by the Office for National Statistics, Helen Tam presents a statistical summary of the characteristics of the underemployed and the overemployed in the UK (Tam, 2010). Several tables and charts are included, which show the relationship between either underemployment or overemployment and a number of variables, such as age, gender, qualifications, etc., for the first quarter of 2010.

Cross tabulations are a straightforward way to convey information about more than one variable, but there is a risk that one may read too much into them - in particular, the existence (or otherwise) of any association between a number of covariates and a response variable. Hence, we present a full econometric model of underemployment and overemployment - using the same datasets and definitions as in Tam's paper. However, we are going to restrict the sample to people aged between 24 and state pension age (i.e. 60 for women and 65 for men). The reason for this is that results for people aged 16-23 look very different from those for the rest of the population, as many of them are not economically active or only partly engaged in the labour market - and the same applies to people over state pension age.

After this introduction, we briefly describe Tams paper, including the creation of the two variables under study: underemployment and overemployment. In section 3 we describe the econometric approach, whilst section 4 presents the findings. Section 5 concludes.

**2. Underemployment and Overemployment**

**2.a. Definition**

Based on the standard ILO definition of employment, Tam (p. 10, Box 1) classified employed people as underemployed if:

- they are willing to work more hours because they want a job additional to their current job, want another job with longer hours, or want more hours in their current job;

- they are available to start working longer hours within two weeks; and

- their `constructed hours' during the reference week did not exceed 40 hours (if they are under 18 years of age) or 48 hours (if they are over 18 years of age)

In turn, employed people are classified as overemployed if:

- they want to work fewer hours, either in a different job or in their current job; and

- they would accept less pay for shorter hours, either in a different job or in their current job

`Constructed hours' are the actual number of hours worked in the reference week, unless this was fewer than the number of usual weekly hours due to non-economic reasons, in which case constructed hours equal usual weekly hours.

We refer the reader to Tam's paper for further details about the variables within the Labour Force Survey used to estimate underemployment and overemployment, as well as for the weighting of the survey data.

**2.b. Characteristics**

We became initially interested in the relationship between age and underemployment and overemployment (Tam, op. cit., Table 1 and Table 2, respectively), which we reproduce below for people aged 25 and over. The tables show that the older the worker (especially men), the lower the underemployment rates and the higher the overemployment rates. The reader could be forgiven to conclude from this that underemployment and age are inversely related and that the opposite is true for overemployed people.

Tam's paper also shows that workers with higher qualification levels are less likely to be underemployed and more likely to be overemployed and also that there would be some association between under and overemployment and occupation groups: workers in elementary occupations would exhibit higher underemployment rates and lower overemployment rates than, for example, managers and senior officials. Furthermore, it also shows that the industrial sector would be somehow related to underemployment and overemployment rates and that residents in Northern Ireland would exhibit lower underemployment and overemployment rates than workers in Great Britain.

Given these reported two-way relationships between the variables, we decided to run econometric models to isolate the effect of each regressor onto either underemployment and overemployment once the effects of all the other confounding variables have been accounted for. The following section describes our econometric approach.

**3. The econometric approach**

By construction, underemployment and overemployment are both binary variables (i.e., a worker is either underemployed or not, or overemployed or not). Hence, we used multivariate logistic regression analysis, with the logit as link function. The independent variables are: age, age squared, sex, qualification level, industrial sector, government office region of residence, occupation, whether the person works full-time or part-time and the reported employment status - that is, whether he or she is an employee or self-employed.

Qualification levels in the Labour Force Survey fall into the following six categories: no qualification, other qualifications, GCSE grades A-C or equivalent, GCE A level or equivalent, higher education, and degree or equivalent.

Industrial sectors are divided into the usual 9 main categories: agriculture & fishing, energy & water, manufacturing, construction, distribution, hotels & restaurants, transport & communication, banking, finance & insurance, public administration, education & health, and other services. However, given the low numbers of people employed in agriculture & fishing and energy & water, we grouped these two sectors within the manufacturing sector. Hence, in all our models, this variable only has seven categories instead of nine. We have dropped those who work outside the UK (which make up around 0.04% of all observations each year).

The variable occupation comprises the following nine categories: managers and senior officials, professional occupations, associate professional and technical, administrative and secretarial, skilled trades occupations, personal service occupations, sales and customer services, process, plant and machine operatives, and elementary occupations.

We have also allowed for six interactions between the explanatory variables under the assumption that there might exist some relationships between them which would affect their individual impact on either underemployment and overemployment. We introduced the following interactions: age and qualification levels, sex and full/part time work, occupation and qualification levels, occupation and full/part time work, occupation and reported economic activity, occupation and full/part time work, reported economic activity and occupation, and reported employment status and full/part time work.

The Labour Force Survey dataset for the first quarter of 2004 does not include the recorded responses for the highest level of qualification following a change in the survey frequency from seasonal-quarter to calendar-quarter in 2006. However, the Office for National Statistics provided us with the data for January and February 2004 for the corresponding variable (HIQUAL), which we used in our estimations^{1}.

Another methodological issue is the treatment of the `no answers' and `don't know' categories, which do not exceed 1 per cent of all responses for any of the variables considered in any year. We use multiple imputation to allocate them to one of the different categories of the variable in question - thus treating these records as missing at random^{2}.

We estimated the models for each year and looked at the variations of the regression coefficients over time to see whether the relationships between the explanatory variables and underemployment or overemployment have changed during the period 2002-2010.

Finally, we also looked at the composition of both underemployment and overemployment in terms of whether people wanted to work more or fewer hours in their current jobs or in different (or additional) jobs, but we found the proportions did not change significantly over the period under study - hence we decided against carrying out compositional data analysis as the exploratory results deemed this unnecessary.

We ran models for underemployment and overemployment with sex (and its interactions) as an explanatory variable, which was significant. However, post-estimation analysis suggested that we should consider running separate models for men and women. Therefore, in the following section we present separate results for men and women.

**4. Results**

As mentioned above, the cross-tabulations in Tam's paper would suggest that, generally speaking, the older the worker, the lower the underemployment rates and the higher the overemployment rates. In contrast, we found that age would be *positively* related to the probability of being classified as underemployed, both for men and women, once we take into account all the other confounding factors - and this same qualitative result is observed for each first quarter since 2003^{3}.

Table 3 reports the odds ratios from the econometric models for 2010. Odds ratios are expressed relative to the odds for one particular reference group, which depends on the variable in question. For example, working part-time is the reference group for the variable *part/full-time*, and therefore the odds ratios reported in the table express the probability for full-time workers relative to part-time workers of being underemployed or overemployed.

An odds ratio of 1 of being either underemployed or overemployed indicates that the predicted probability of being either underemployed or overemployed is the same for the different categories of the variable. Odds ratios greater than 1 denote higher probability, and vice versa. For male underemployment, for example, the odds ratio for *part/full-time* is 0.395, which indicates that men working full-time are less likely to be underemployed than men working part-time, all else considered.

The *p-value *columns report the statistical significance of the odds ratios to their left. The only variables for which the odds ratios are not significant at the 10 per cent level are: Qualification Level for male underemployment, the South East region and Sectors J-K for overemployment, and Wales for male underemployment. All the other odds ratios are statistically significant at the 1% level, except that for London for overemployment, which is significant at the 8.5% level.

Once we account for the influences of all the other covariates and the interactions, we find that the older the worker, the more likely they are to be underemployed - this is both the case for men and women. It is also the case that the older the worker, the more likely they are to be overemployed. However, underemployment rates for male workers suggest that there would be a negative association between their age and their underemployment status.

Furthermore, we found that, for men, the highest level of qualification attained is not related to the likelihood of being underemployed. Tam's paper does not break down the data for qualification levels by gender, but the paper suggests that lower levels of qualification would be associated with a higher probability of being underemployed. Our findings contradict these inferences. We have checked whether this remained the case in other waves of the Labour Force Survey; therefore we ran the same models for the first quarter of every year since 2002, and we only found a negative association between age and underemployment for men in 2002 (for women the association was always positive, as it was between age and overemployment irrespective of gender)^{4}.

We also looked on the marginal effect of age on underemployment and overemployment - that is, how the probability of being underemployed or overemployed changed as the age of the worker varied, once the effects of all the other independent variables were considered^{5}. An increase in age by 5 years increases the probability of being underemployment or overemployed for both men and women; however, for men the probability of being overemployed increases much more than that of being underemployment, and the converse is true for women (Table 4).

Given that the probability of being underemployed and overemployed increases with the age of the worker, we estimated whether this relationship has changed since the onset of the current recession in 2006 until Q1 2010. We found that the discrete changes in the probability of being underemployed as the workers' age increases have been more pronounced since 2006 (Figure 1), whereas the effects of a change in the age of a worker on the probability of their being overemployed have weakened since 2006 (Figure 2). In other words, an older age has made it increasingly more likely to be underemployed and less likely to be overemployed since the start of the current economic contraction -all else considered.

Gregg and Wadsworth (2010) report that during a recession the employment situation of younger workers is more likely to worsen than that of older workers and also that the numbers of people working part-time who report that they would like full-time work increases. We can only speculate here that during an economic downturn older workers are not as likely to be made redundant as their younger colleagues, but are offered to work reduced hours^{6}, and this may be reflected in the increased likelihood of being underemployed and the reduced likelihood of being overemployed for older workers in 2010 compared to 2006 and 2008. Future work will look into whether the probability of becoming underemployed or overemployed - that is, the flows from being in employment but not under or over employed to being under or over employed over a certain period of time- is contingent on the age of the worker and other factors, including changes in the number of hours worked^{7}.

**5. Conclusions**

Tam (2010) presented a summary of the main characteristics of underemployment and overemployment in the UK according to a number of factors. This paper complements it by carrying out an econometric analysis in order to estimate the effects of each explanatory variable.

The main result of this paper is that the age of the worker is positively associated with the probability of being underemployed: men and women are more likely to be underemployed the older they are. Furthermore, the probability of being underemployed is not uniform across age bands, but it becomes higher the older the workers are. This result constitutes a departure from the associations shown in Tam (2010). Another result not in line with those reported in Tam's paper is that qualification levels are not significantly associated with underemployment for men.

**Figure 1: Discrete changes in the Probability of Underemployment by 5-year changes in
age, Q1 2006-2010**

**Figure 2: Discrete changes in the Probability of Overemployment by 5-year changes in
age, Q1 2006-2010**

The results for the variable age mean that for those workers who work fewer than 48 hours a week and are willing to work more hours in their current jobs or in an additional or a new job, the more likely it is that they are willing to do so the older they are. Moreover, it is also more likely for older workers to want to work fewer hours in their current jobs or in a different job even if this implies less pay than for younger workers.

A final, general comment: cross-tabulations are sometimes overused, especially when more than one covariate is considered. They can help guide statistical analysis, model specification, and assumptions regarding distributions, but they cannot replace statistical modelling. Presenting associations between each covariate and a response variable as results or findings can be, and often is, seriously misleading.

**Professor José Iparraguire is Chief Economist and Ms Hui-Yu a former intern researcher at Age UK.**

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