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Adjusting for Selection Bias in Longitudinal Analyses Using Simultaneous Equations Modeling

The Relationship Between Employment Transitions and Mental Health

Steele, Fionaa; French, Roberta; Bartley, Melb

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doi: 10.1097/EDE.0b013e31829d2479


Evidence for a causal relationship between unemployment and health is stronger for mental than for physical health.1,2 However, longitudinal research has also shown greater risks of becoming and remaining unemployed among those with lower levels of psychological well-being3 and other unfavorable prior characteristics.4–6 A recent review concluded that “The promise that the research would identify health costs and benefits of economic policy…. remains unfulfilled and will likely remain so without stronger theory and greater methodological agreement.”7 Studies investigating the relationship between individuals’ health and changes in employment status over the life course may provide stronger evidence for a causal link, especially where regular repeated measurements are available for a long follow-up period.

Although longitudinal data allow detailed examination of the dynamics of the link between mental health and employment, bias due to selection effects remains a serious threat to causal inference. Selection into unemployment is conceptualized as occurring by two distinct mechanisms: direct and indirect selection.8 Direct selection (also known as health selection or reverse causality) asserts that poor health leads to difficulty in securing and maintaining employment, which results in an over-representation among the unemployed of less psychologically healthy people. Indirect selection on the other hand occurs when there are unmeasured individual characteristics (such as social or economic factors or personality) that influence both health and the risk of unemployment.

The potential for selection bias has long been recognized. The standard approach taken to allow for direct selection is to adjust for health measured before exposure to unemployment. A strong case for direct selection was made by Lundin et al,6 who found that excess mortality risk among Swedish men experiencing at least 90 days of unemployment relative to those in stable employment was considerably reduced after adjustment for previous psychiatric diagnoses and sickness absence. Other studies investigating support for direct health selection found effects of childhood height and behavioral maladjustment on adult unemployment among British men4 and effects of perceived poor health on employment transitions in several European countries.9

Adjustment for indirect selection is usually through inclusion of measured confounders such as indicators of socioeconomic circumstances during childhood or health-related attitudes and behaviors. For example, Lundin et al6 found that the association between unemployment and the risk of violent death was substantially weakened after adjustment for previous alcohol drinking and contact with police in childhood, which are plausible influences on both employment and mortality. In the case of panel studies that began in adulthood, however, early life measures are often unavailable, limiting the potential to adjust for confounding by measured characteristics. Thus, although a major strength of these studies is the availability of regular repeated measures of health and employment, and information on other family members in household panels, selection on unmeasured factors is likely to be more of an issue than in studies using birth cohort data.

One approach to the problem of indirect selection by unmeasured factors has been to adopt instrumental variable methods. This approach has been used to contrast health effects of unemployment due to wholesale plant closure with unemployment arising for other reasons, on the grounds that in plant closures workers are not selectively dismissed.10–12 These studies have found a weaker effect of unemployment on mental health for those who were made unemployed after their workplace downsized or during a period of recession (ie, for reasons external to the person and their circumstances).

This article investigates the relationship between men’s employment transitions and their mental health using annual data from the British Household Panel Survey for 1991–2009. The study aims to extend previous research by testing for both direct and indirect selection effects and by examining the impact of adjusting for selection biases on estimates of the effect of a change in employment status between years t−1 and t on mental health at t. We account for direct selection in two ways: (1) adjustment for mental health at t−1, and (2) allowing explicitly for an effect of health at t−1 on employment transitions between t−1 and t. Indirect selection is taken into account by jointly modeling mental health and employment transitions, allowing for shared unmeasured influences on the two processes.



We used data from the British Household Panel Survey which began in 1991 with a representative sample of approximately 5500 households with 10,300 residents.13 Adult household members (aged 16 or over) have been reinterviewed each year, and members of new households formed were also followed while resident with the original sample member. The current analysis was based on men of working age (16–64) after leaving full-time education. We restrict our focus to men because women’s work patterns are more complex due to the combination of paid and unpaid work over their life courses, with particular difficulty in differentiating unemployment and economic inactivity for women with children.14,15

Contributions from men with missing data were included where they were present for at least two consecutive waves because employment transitions were based on employment status at years t−1 and t and covariates (including lagged mental health) refer to a man’s status at t−1. The analysis sample contained 8784 men who contributed 69,576 person-year observations between 1991 and 2009.


Outcomes: Mental Health and Employment Status

The General Health Questionnaire is widely used as a screening instrument for minor psychiatric morbidity, specifically distress and anxiety.16 In this study, we use the short 12-item version as a measure of current mental health. At each wave, participants were asked to record whether they had recently experienced a particular symptom or feeling on a 4-point scale. We analyzed the summative score of the 12items based on Likert (0-1-2-3) scoring (centered around the mean of 10, standard deviation = 5.1), where higher scores indicate a higher degree of psychological distress.

We used self-reported employment status at each wave, grouped into three categories: employed (82% of person waves), economically inactive (12%), and unemployed (6%). The major reasons given for economic inactivity were long-term sickness and disability (46%), early retirement (33%), and return to full-time education (10%). Given the high prevalence of long-term ill health in this group, selection is a particular issue when assessing the association between economic inactivity and health. It is therefore important to distinguish between unemployment and economic inactivity rather than grouping into a single “non-employment” state. Employment transitions were identified by comparing a man’s status at years t−1 and t, resulting in a variable with nine categories for all possible transitions between the three states (including categories for no change in status).


The models for mental health and employment status at year t both contained the following covariates: age at t, marital status (married/cohabiting, single) at t−1, care responsibilities measured by the presence of coresident dependent children and age of youngest child at t−1 (<5, ≥5 years), and household occupational class at t−1 as a proxy for permanent income (manual, nonmanual). Household occupational social class was classified according to the current or most recent occupation; for men in a coresidential union at t−1 the highest occupation class of the partners was used. In addition the model for employment status included the unemployment rate in the local authority district as an indicator of local labor market conditions at t−1, calculated using the claimant count as a proportion of the total working age population in the local authority. Descriptive statistics for all variables used in the analysis are presented in eTable 1 (eAppendix C;

Statistical Methods

We begin by setting out dynamic random effects panel models for mental health and for employment transitions. We then discuss approaches for handling the “initial conditions,” a problem that arises when there is correlation between the lagged outcomes and person-specific random effects. Finally, we describe how the health and employment models together form a simultaneous equations model in which each outcome may directly affect the other over time. In this joint model, the individual random effects may be correlated across processes, thereby allowing for the possibility that mental health and employment transitions may be influenced by a common or correlated set of unobserved characteristics. In the application, simpler forms of this model were fitted to investigate the impact of successive adjustments for direct and indirect selection.

Model for Effects of Employment Transitions onHealth

The effects of employment transitions between t−1 and t on mental health at t, conditional on mental health at t−1, were estimated using a random effects dynamic panel model17:

where Hti is the mental health score of individual i at year t, β0 is an intercept, β1 is the effect of mental health at the previous wave,

is a vector of eight dummy variables for the change in employment status between t−1 and t (taking one category as the reference) with a row-vector of coefficients β2, xt-1i is a vector of time-varying covariates with coefficients β3,

is a normally distributed random effect representing unmeasured time-invariant individual characteristics, and eti is a normally distributed time-varying residual.

Model for Effect of Health on Employment Transitions

We denote the employment status of individual i at year t by Eti (coded as 1 = employed, 2 = economically inactive, and 3 = unemployed) with category probabilities

for k = 1,2,3. We specified a random effects multinomial logit model for Eti conditional on employment status at t  −  1,18 which is an extension of the random effects first-order Markov transition model for binary data.19 Lagged employment status is denoted by three indicator variables El,1i (l = 1,2,3), which are stacked into column vector Et−1i. The model for employment transitions is specified as a multinomial logit model that consists of two equations contrasting the probabilities of being economically inactive (k = 2) or unemployed (k = 3) with the probability of being employed (k = 1) at t:

where the inclusion of lagged employment status Et−1i, with coefficients

allows estimation of the probability of each possible type of employment transition between t–1 and t (including remaining in the same state). We specified the effect of mental health at t–1 as a quadratic function to allow for the possibility of nonlinear effects. For example, the effect of health on employment transitions might be apparent only among men exhibiting the highest levels of psychological distress. The lagged employment status dummies were interacted with Ht−1i and

to allow for differential effects of mental health across employment transitions. The above parameterization, with the full set of indicator variables for lagged employment status and their interactions with lagged health, is easier to interpret than taking a reference employment state and including main effects of health. The coefficients


define the quadratic effect of prior health on the log relative risk of being economically inactive (k = 2) or unemployed (k = 3) versus employed for men in each employment category at t−1. Finally, the model includes time-varying covariates zt−1i, with coefficients

and individual-level normally distributed random effects


A potential concern with the multinomial logit model is the independence of irrelevant alternatives assumption.20 In this application, for example, the irrelevant alternatives property implies that the relative risk of being economically inactive versus employed at time t does not depend on the risk of being unemployed at t. This assumption may be unreasonable if some employment categories are more similar than others due to shared unmeasured risk factors. For instance, we might expect similarity between the economically inactive and unemployed states if older men who were about to become unemployed took early retirement instead. Allowing for a nonzero correlation between


offers some protection against departures from this assumption, to the extent that dependency between a man’s risks of being in different employment categories is due to time-invariant characteristics.

Initial Conditions

The inclusion of lagged outcomes in equations (1) and (2) may invalidate the standard assumption that the individual random effects are uncorrelated with the explanatory variables. Although (1) and (2) define models for health and employment status at t > 1, outcomes at t = 1 are assumed exogenous. For most men in the study, however, the start of the observation period does not coincide with their entry into the labor market, in which case the unmeasured time-invariant factors influencing outcomes at t > 1 will in general also influence outcomes at t = 1. Simply conditioning on initial health and employment status and ignoring the shared dependency of outcomes at all t on individual random effects will lead to overstatement of the lagged effects, β1 in (1) and

in (2). Furthermore, the effects of other explanatory variables will also be biased due their correlation with the (lagged) outcomes, although the magnitude of the bias will typically increase with the strength of the lagged effect and decrease with the number of repeated measurements.21,22 The “initial conditions problem” arises from a type of endogenous selection mechanism whereby those who have poor mental health or are in a particular employment state at t = 1 are a nonrandom sample of the target population.23 It is therefore distinct from the direct and indirect selection mechanisms described earlier, although the same parameters will be affected.

One way to adjust for initial-conditions effects is to specify models for outcomes at t = 1 that share random effects and must therefore be estimated jointly with the models for t > 1 given by equations (1) and (2)24:

where λ(H), λ(E2), and λ(E3) are random effect loadings that allow the between-person residual variance to differ for t = 1 and t > 1.

Simultaneous Equations Model

The random effects simultaneous equations model for the relationship between changes in mental health and employment transitions is defined by equations (1)–(4). The equations for health and employment status are linked by allowing for nonzero “cross-process” correlations between the individual-specific random effects


. Specifically we assume that

follow a trivariate normal distribution with covariance matrix

Previous approaches that consider a model for only Hti are equivalent to estimating a joint model with the residual covariance terms σu (H,E2) and σu (H,E3) set to zero. By freely estimating these residual covariances, we allow for the possibility that changes in mental health and employment transitions are jointly determined. We would expect both covariances to be positive if men whose unmeasured characteristics predispose them toward poorer mental health

tend also to have a higher risk of being out of paid employment

. Positive residual covariances imply selection of men with poor mental health into unemployment and economically inactivity which, if ignored, will lead to overstatement of the negative consequences of being in (or moving to) these states.

The simultaneous equations model defined by equations (1)–(4) can be viewed as a random effects model for a bivariate response (Hti,Eti). Such models are sometimes referred to as multilevel multiprocess models and are increasingly used in the social sciences.25,26 The model described above can be fitted using routines for a mixture of continuous and multinomial responses with a hierarchical structure. All analyses presented here were carried out in the aML software, which implements maximum-likelihood estimation using Gauss–Hermite quadrature to integrate out the individual-level random effects.27

In order to estimate a simultaneous equations model, it is usually necessary to impose some identification conditions on the exogenous covariates in the model. To identify the effect of employment transitions between t−1 and t

on health at t would involve having at least one variable (an instrument) that predicts changes in employment status but not mental health, that is, a variable contained in

but not

. In general, it is difficult to find variables that satisfy this requirement in household-panel studies, as there is usually little information available on family background and early-life measures. In the case of longitudinal data, however, covariate exclusions are not formally required for adjustment of selection on time-invariant unmeasured factors.26,28 Identification of the effect of

is made possible by the presence of men who change employment status during the 19-year observation period. After accounting for the individual effects and their correlation, the remaining within-person variation in

represents the effect of an employment transition on mental health, adjusting for selection on individual-specific unmeasured variables (indirect selection). Similarly, identification of the effect of health at t−1 on employment transitions between t−1 and t relies upon within-individual variation in general health scores over time.


The model represented by equations (1)–(4) is the full simultaneous equations model with adjustments for direct and indirect selection (Model D in Table 1). To investigate the impact of allowing for different forms of adjustment, a sequence of models was considered, building up gradually to this model. All models include the covariates described earlier, and person-specific random effects to allow for unobserved between-person heterogeneity in the distress and anxiety score or employment transitions. The models also include equations for the initial conditions, which were estimated jointly with the dynamic models for outcomes at t > 1. However, allowing for initial conditions was found to have little impact on the results, most likely because of the long panel and the implicit assumption of autoregressive models that the influence of outcomes at t = 1 on subsequent outcomes diminishes with t.21 Summary statistics of the covariates, along with the full results for selected models, are given in eAppendix C (

Estimated Effects of Employment Status at t−1 and t (Relative to Remaining Employed) on GHQ at t, with Various Adjustments for Direct and Indirect Selection (95% CIs)

Models A–C in Tables 1 and 2 are special cases of Model D. The starting point is Model A, which makes no adjustment for direct or indirect selection. This model consists of equations (1) and (3) for Hti, but without conditioning on Ht−1i in (1). Furthermore, the model assumes that employment transitions ΔEt−1i are uncorrelated with unmeasured time-invariant influences on health

, so equations (2) and (4) do not form part of Model A. Model B extends Model A by including Ht−1i in the model for Hti to adjust for direct selection. Model C is a simultaneous equations model for health and employment transitions, and therefore adjusts for indirect selection. However, the model for employment transitions involves a simplification of equation (3) as it does not allow for effects of Ht−1i or

, a potential additional source of direct selection. Further details about the specification of Models A–D can be found in eAppendix A (

Estimated Effects of Selected Employment Transitions Between t−1 and t on GHQ at t, with Various Adjustments for Direct and Indirect Selection (95% CIs)

Table 1 shows estimates of the effect of employment status at wave t−1 and t relative to being employed at both waves (β2 in equation 1). The effect of making a transition between any of the three employment states may be derived from these estimates by subtraction. In the following discussion, we focus on the effects of transitions between employment and unemployment and between employment and economic inactivity (presented in Table 2).

Traditional Adjustment for Direct Selection

We began by investigating the support for direct selection by comparing the effects of employment transitions between t−1 and t on the anxiety point score at t before and after adjustment for anxiety score in the previous year (Models A and B of Table 2). Model B is analogous to the approach commonly taken in the literature, whereby a measure of prior ill-health is included to account for direct selection. These first two models do not adjust for the joint dependency of unemployment and ill-health or for a direct effect of health on subsequent employment. Adjustment for direct selection by including prior health leads to modest differences in the estimated effects of employment transitions on distress and anxiety: effects of transitions that increased anxiety score were overstated before adjustment whereas effects of transitions that lowered the anxiety score were understated. For example, the detrimental effect of becoming unemployed changed from 2.52 to 2.45 after adjustment. (A change of 2.5 is equal to half a standard deviation on the anxiety score distribution.)

Adjustment for Indirect Selection

We next adjust for indirect selection by estimating Model B for distress and anxiety score jointly with the model for employment transitions. The joint model (Model C) allows for correlation between the individual random effects in the models for anxiety and employment. Before assessing the impact of joint modeling on effects of employment transitions on anxiety, we examine estimates of the random effect correlations as a test for indirect selection (Table 3). We found strong evidence of nonzero correlations between the random effect for anxiety and the random effects for the two employment equations, and both were positive as expected. Thus men whose unmeasured characteristics placed them at above-average levels of anxiety and depression tended also to have above-average chances of being out of employment. There was also a positive residual correlation between the log relative risks of being economically inactive or unemployed rather than employed.

Estimated Standard Deviations and Correlations of Individual Random Effects from Model D, the Joint Model of GHQ and Employment Transitions (95% CIs)

There were some substantial differences between Models B and C in the magnitude of the estimated effects of employment transitions on anxiety score (Table 2), particularly in the effect of moving from employment to economic inactivity (relative to remaining employed), which decreased from 0.92 to 0.58. Adjustment for indirect selection led to a smaller reduction in the effects of transitions between employment and unemployment: the effect of becoming unemployed decreased from 2.45 to 2.23 whereas the effect of moving out of unemployment into employment changed from –2.05 to –1.77.

The direction of these changes was in line with what would be expected from the positive correlations seen in Table 3. For example, before accounting for indirect selection, the “remaining employed” category had an over-representation of men who had experienced unemployment or economic inactivity less often than average throughout the study at any wave

, whereas the employed-to-unemployed category had an over-representation of those with above-average risk of being unemployed at any wave

. In the unadjusted model, the positive residual correlations between the unmeasured influences on the probability of being repeatedly unemployed

and the unmeasured influences on mental health

were ignored. As a result the mean anxiety score was deflated in the “remaining employed” group due to the disproportionate presence of men with better than average mental health

whereas the anxiety score was inflated in the employed-to-unemployed group due to an over-representation of men with poorer than average mental health

. The larger impact of adjustment for indirect selection on transitions between employment and economic inactivity is consistent with the larger residual correlation between anxiety and economic inactivity (vs. employment) than between anxiety and unemployment (0.38 and 0.27, respectively).

Additional Adjustment for Direct Selection

The final model (Model D of Tables 1 and 2) extends Model C by allowing for a direct effect of anxiety score at t−1 on employment transitions between t−1 and t. This additional adjustment for direct selection has little impact on estimates of the effects of employment transitions on anxiety (Table 2). The similarity between the estimates for Models C and D is in line with small effects of prior anxiety on subsequent employment transitions (see Table 4 and eFigures 1 and 2;

Estimated Effects of GHQ at t−1 on the Log Relative Risk of Economic Inactivity or Unemployment vs. Employment at t According to Employment Status at t−1, Model D (95% CIs)

Among those who were employed at t−1, the effect of anxiety score (as measured by the General Health Questionnaire [GHQ]) at t−1 on the log relative risk of being unemployed rather than employed at t is given by

(from coefficients of interactions between employed and GHQ and GHQ2 given in the final column of Table 4). The 95% confidence interval for the quadratic term (but not the linear term) excludes zero, which suggests that distress and anxiety increased the probability of job loss, but the effect was only apparent among men with severe depression. Similarly, those with the highest anxiety scores at t−1 were more likely than those with fewer depressive symptoms to become economically inactive rather than remain employed. (See eFigure 1 for predicted probabilities of transitions from employment by anxiety score; For men who were unemployed at t−1, there was a suggestion that higher anxiety was associated with a decrease in the risk of remaining unemployed rather than finding a job (see Table 4 and eFigure 2; It is likely that those with a higher anxiety score either recovered sufficiently to find work or left the labor force altogether.


Using annual data collected over a 19-year period, we find a strong relationship between employment transitions and subsequent mental health: becoming unemployed has a negative consequence for mental health, whereas moving out of unemployment into work is associated with an improvement in mental health. Any tendency for macroeconomic changes to increase rates of psychological ill-health in the population is of considerable public health significance.29 In 2004, 23% of the total burden of disease in the United Kingdom was attributable to mental disorder (including self-inflicted injury), compared with 16% for cardiovascular disease and 16% for cancer, as measured by Disability Adjusted Life Years.30 As a result of the current financial crisis, the unemployment rate increased from 5% (1.6 million) at the start of the recession in 2008 to a peak of 8% (2.7 million) at the end of 2011—its highest level in 17 years.31 By November 2012, there were still 2.5 million unemployed, a rate of 7.7%.32 The analysis presented in this article allows for a conservative but robust estimate of the resulting additional burden of psychological distress.

Taking account of direct and indirect health selection by jointly modeling changes in employment status and health over time does not alter the broad substantive conclusions outlined above. Including the previous year’s distress and anxiety score in a model of the relationship between employment status and mental health, and allowing for a direct effect of prior anxiety score on subsequent employment changes, has tested the extent to which direct selection by poorer preexisting mental health may have been at work. However, adjustment for prior anxiety score had only a modest impact on estimates of the effects of employment transitions on subsequent anxiety, and employed study participants with poor mental health in any year were not found to be very much more likely to become unemployed the following year. There was, as expected, a higher probability of exit from employment to economic inactivity (very often due to permanent sickness) among these participants. Somewhat more surprisingly, unemployed participants with higher anxiety scores were less likely to be classified as unemployed at the following wave; rather they were more likely to be either inactive or employed. One potential explanation for this observation, and for the small effect of prior anxiety score on employment transitions, is the measurement of anxiety scores and employment status only annually. This may have led to missed employment transitions between waves. For example, a man who is observed as employed at both t−1 and t may have experienced a spell of unemployment in between. Suppose that the true effect of high anxiety at t−1 is to increase the probability of becoming unemployed between t−1 and t and decrease the probability of remaining employed. For men who lose their job but regain employment by t, the transition into unemployment is missed, which would lead to understatement of the detrimental effect of poor mental health on the probability of remaining employed.

Evidence is much stronger for indirect selection, that is, the presence of unmeasured characteristics of a man that result in a higher than average risk of both nonemployment and poor health. This can be seen by the attenuation of the estimated effects of transitions between employment and unemployment or economic inactivity on mental health when the person-specific residuals in the models for mental health and employment status are allowed to correlate. The impact of allowing for indirect selection is especially marked for estimates of the effects of entering and exiting the labor market, which is expected due to the high proportion of long-term ill and disabled men in the economically inactive category.

There are likely to be other processes underlying the relationship between employment and mental health that we have not been able to capture in our model. First, the methods do not allow for selection on time-varying unmeasured factors, for example, some “shock” at t−1 that influences both employment status and mental health. Second, we have not taken into account the well-known anticipatory effects of unemployment, that is, the threat of future unemployment may lead to increased stress before becoming unemployed. In that case, effect of job loss would be understated as anxiety would have worsened before the event.

Future work should consider the possible complex processes of selection both into occupations and into employment status over the course of a work career. There is evidence that men with higher status jobs suffer a worse reaction to a transition into unemployment than those in less prestigious occupations.33 It is also important to extend the analysis to women, with modifications to the models to distinguish full-time and part-time employment and to allow the relationship between health and employment transitions (and potentially selection effects) to vary according to whether a woman has dependent children.

The methods reported in this article may be more widely applied in the use of longitudinal panel data in the study of health inequality. Most of the existing evidence on how the large differences in health between social and income groups arise has come from less rich data and rather simpler methods, resulting in considerable uncertainty as to the policy implications to be drawn. Although it is widely acknowledged that health inequality probably results from complex interactions over the life course, a great deal remains to be understood.


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