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Towards a Theory of Medium Term Life Satisfaction: Two-Way Causation Partly Explains Persistent Satisfaction or Dissatisfaction

Abstract

Long term panel data enable researchers to construct trajectories of life satisfaction (LS) for individuals over time. In this paper we analyse the trajectories of respondents (N = 3689) in the German Socio-Economic Panel who recorded their LS for 20 consecutive years in 1991–2010. Previous research has shown that at least a quarter of these respondents recorded substantial long term changes in LS (Headey et al. in Proc Natl Acad Sci 107.42:17922–17926, 2010a, in Soc Indic Res 112:725–748, 2013). In this paper, graphs of LS trajectories, and subsequent statistical analysis, show that respondents tend to spend multiple consecutive years above and, in other periods, below their own 20-year mean level of LS. They experience extended ‘good times’ and extended ‘bad times’. These results are contrary to set-point theory which views LS as stable, except for short term fluctuations due to life events. In the later part of the paper we attempt to move towards a theory of medium term life satisfaction. We estimate structural equation models with two-way causation between LS and variables usually treated as causes of LS, including health, physical exercise, frequency of social activities, and satisfaction with work and leisure. Results are interpreted as showing positive feedback loops between these variables and LS, accounting for extended periods of high or low LS. The models are based on a modified concept of ‘Granger-causation’ (Granger in Econometrica 37:424–438, 1969). The main intuition behind Granger-causation is that if x can be shown to be statistically significantly related to y in a model which includes multiple lags of y, then it can be inferred that x is one cause of y.

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Fig. 1
Fig. 2

Notes

  1. The sample size would have been almost halved to 1873 if the age restriction had not been lifted.

  2. The correlation between these two items varies from year to year, but is usually around 0.3.

  3. ‘Seldom’ or ‘never’ have been included as separate categories in more recent waves of SOEP.

  4. Disability status was not included in models in which the self-rated health scale was the x variable.

  5. The Big Five items have been included in SOEP every 4 years since 2005. In the case of respondents who have answered more than once, we have averaged their results and imputed the average for missing years. So we treat adult personality traits as fixed characteristics, as most psychologists would.

  6. OLS regression analysis is essentially a single equation technique. Regression estimates derived from multi-equation systems are likely to be biased, due to correlations between explanatory variables and error terms in some or all equations. A key assumption of OLS regression is that such correlations are zero.

  7. ML estimates are usually consistent and asymptotically normal under the (not very restrictive) assumption of conditional normality (StataCorp 2013). Only paths or covariances linking conditioning (i.e. control) variables may not be consistent and asymptotically normal (even then, the main problem lies just with estimates of standard errors). These paths are not usually of substantive interest. Substantive interest lies in paths (1) linking exogenous with endogenous variables and (2) between endogenous variables.

  8. From a mathematical standpoint, a model can be viewed as a set of constraints—or a set of restricted paths—limiting the possibilities of simply reproducing the input data. Attempts by a researcher to improve his/her model involve modifying these constraints to improve model fit…subject to the theory/hypotheses underlying the model.

  9. Model ‘stability’ is here used as a technical term. Previously we used the term in a different sense to refer to Scherpenzeel and Saris’s (1996) claim that two-way causation models of LS are unstable because apparently small differences in model specification can lead to substantially different estimates.

  10. Another limitation is that covariances between the error terms of equations cannot be estimated, so it becomes difficult to assess whether relationships are spurious.

  11. When convergence fails, exactly the same Chi square LR is produced repeatedly, model iteration after iteration.

  12. Kessler and Greenberg (1981) describe how a multi-wave panel model of this kind may in principle be identified by using equality constraints (i.e. by constraining sets of parameters to be equal to each other). In practice, this approach to identification only succeeds if relationships among variables are quite far from equilibrium (i.e. relationships differ substantially from wave to wave of the panel data). In panel surveys of life satisfaction, it is reasonably clear that relationships between LS and causal variables of interest are much the same from wave to wave. Estimation of models with both simultaneous and cross-lagged links is also likely to run into problems because of multicollinearity; the effects on LS of x at time t and x at t − 1 are likely to be too highly correlated for estimates to be reliable.

  13. It is accepted, of course, that differing 20-year trajectories can have the same mean and standard deviation. Our inspection of a very large number of trajectories indicated that few panel members recorded steady 20-year declines or steady increases in LS. The majority recorded trajectories with multi-year periods of both relatively high and relatively low LS, as shown in Figs. 2b, d, f. The statistical analysis below (Table 1) confirms this point.

  14. Another way of making the same point: among individuals who were above their own 1991–2010 grand mean of LS in any particular year, just over 25 % remained above it for all of the next four years. By chance only 6.25 % would have done so.

  15. With a large sample size, it is obvious that many statistically significant but substantively trivial effects are likely to be found.

  16. In the final run of this model the equality constraints on the BU and TD estimates for the equations for Exerciset+1 and LSt+1 were dropped. The reason is that these are not ‘Granger’ equations in that no ‘extra’ (2nd, 3rd) lags are available. Consequently, as Granger would predict, the estimates of the BU and TD links from these equations are considerably higher than from the equations with multiple lags, and are probably biased (Granger and Newbold 1974).

  17. Results for sub-sets of the population are not printed here; available from the authors.

  18. Again, no statistically significant differences were found between men and women, or older and younger people.

  19. As was the case for some of the models with only one x variable, just one pair of imposed equality constraints in this multivariate model was diagnosed as not strictly justified; the LR test result would be improved if they were dropped. Again, however, the measures of fit which reward parsimony—the TLI and RMSEA—provide countervailing evidence in favour of retaining the constraints.

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Headey, B., Muffels, R. Towards a Theory of Medium Term Life Satisfaction: Two-Way Causation Partly Explains Persistent Satisfaction or Dissatisfaction. Soc Indic Res 129, 937–960 (2016). https://doi.org/10.1007/s11205-015-1146-8

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Keywords

  • Life satisfaction trajectories
  • Set-point theory
  • Two-way causation
  • Positive feedback loops
  • Granger-causation