Abstract
The central premise of life course research is the presumption that no period of life can be understood in isolation from prior experiences, as well as individual’s aspirations for the future. This chapter discusses causal inference methods as they relate to life course research, including regression, propensity score matching, instrumental variables, fixed effects, and quasi-experimental designs. We also discuss strategies for incorporating variation in response to treatment according to heterogeneity, time-variation, and mediation, which are important components to estimating effects over the life course with a causal framework. The chapter aims to explain the assumptions behind the methods we present, and includes intuitive explanations. We also demonstrate the use of the methods discussed with an empirical example using constructed data with a known data generating process of the effects of exposure to violence on educational attainment.
This research made use of facilities and resources at the California Center for Population Research, UCLA, which receives core support from the National Institute of Child Health and Human Development, Grant R24HD041022. The National Institutes of Health, Grant 1 R01 HD07460301A1, provided financial support for this research. The ideas expressed herein are those of the authors.
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Notes
- 1.
For example, displaced workers are likely to have lower wages than non-displaced workers even in the absence of displacement. However, if we were able to specify all the factors that influence the probability a worker was displaced and condition upon those factors, we could then assume conditional independence between displacement and workers’ wages.
- 2.
The counterfactual condition is the outcome that would have resulted had an observation experienced an alternative treatment assignment. For example, suppose we are interested in the labor market effects of college selectivity. We observe the wages of students who attend selective colleges, but we do not observe the wages of students who attend selective college, had they not attended those colleges and instead attended non-selective colleges. This unobserved outcome is the counterfactual.
- 3.
Lagged dependent variable models and fixed effects model are similar in that they both incorporate repeated measures of an outcome. They differ in that while fixed effects models assign special status to pre-treatment outcomes, by incorporating them into the dependent variable, lagged dependent variable models treat outcome observations from previous period(s) as simply another regressor in explaining the level of the post-treatment outcome.
- 4.
Sample and cell size consideration affect the feasibility of producing estimates. Comparisons are made between a subgroup that experience treatment at time t, and the subsample that has not experienced treatment up to time t. This implies that all individuals who experienced treatment before time t are excluded from the stated effect estimate. We thus need enough individuals experiencing treatment within those periods to produce reliable estimates. A wider interval benefits from the inclusion of more observations, which can yield more precise estimates, but means that our pre-treatment covariates have potentially reduced ability to predict the probability of treatment exposure.
- 5.
See Appendix A for further details on the constructed data.
- 6.
For simplicity, we do not consider heterogeneity in effects here. We assume that effects are homogenous. In applied life course, research, however, researchers should routinely question the underlying homogeneity assumption (Brand and Simon Thomas 2013).
- 7.
We do not assess how exposure to the treatment over time produces variation in individual effects. It is likely that ETV that occurs early in childhood relative to middle childhood or adolescence might influence the effects on our outcomes of interest.
- 8.
See the description of the simulation process in Appendix A. Simulated respondents for whom α i >β i prefer having more consumption (measured by labor activity) and less leisure, while simulated respondents for whom the opposite is true (i.e. α i <β i ) prefer more leisure and less consumption.
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Appendix A: Simulation Process
Appendix A: Simulation Process
This section explains the mathematical problem solved by simulated agents in the creation of the test data. Agents have preferences over consumption, leisure, and high school completion. They make choices each period over the allocation of time towards, education, labor or leisure given constraints on time availability and the consumption benefits of wage labor. The sequence of choices determines whether they graduate in four periods. This provides a non-linear data generating process with computable counterfactual outcomes, where we can assess our ability to make correct causal inference using the linear models presented above.
Formally, simulated agent i solve.
The objective function (1) takes the form of a Cobb-Douglas utility function expressing preferences over consumption, x t,i , and leisure, \( 1-{l}_{t,i}^a-{l}_{t,i}^w, \) plus an additional additive component capturing gains from graduation. Constraint (2) is a budget constraint limiting present period consumption to what is affordable given endowment e i and earned income, l w t,i w i , where w i is a wage rate.. Endowments are a small but fixed percentage of household income, while wage offers are random. G i,t is the time t value that agent i places on eventual graduation. The indicator function shows that agent i only expects to receive G i,t if he or she supplies some minimum amount of academic labor. Constraints (3) and (4) stipulate that all time and consumption allocations must be non-negative.
The solution to this problem takes the following form given state \( {s}_{t,i}=\left\{{e}_{t,i},{c}_{t,i},{a}_{i,}{G}_{i,t}\right\}: \)
The intuition behind this solution is as follows. The return function for academic labor is a non-differentiable step function and requires special care for that reason. There are only three possible optimal values for academic labor. First, one could supply \( \frac{c_{t,i}}{a_i} \) units of academic labor, which is just enough to receive the expected return G. Any time committed beyond this amount has no return, and would be better spent towards wage labor or leisure since α i > 0 and β i > 0. If it turns out that the simulated agent cannot feasibly supply the desired amount of academic labor such that
or that the agent has a higher present period gain if she devotes the time to wage labor or leisure such that
then \( {l}_{t,i}^{a*}=0 \) must be the optimal academic labor supply. In this case, any time allocation above 0 has a higher return as wage labor time or leisure time. From here, we utilize the concavity, continuity, and differentiability of the return function in {l w t,i , x t,i } to solve for (6) and (7) in terms of parameters and These formulas are sufficient for calculating the current period return to continuing education, and the current period return to dropping out. Simulated agents choose the option with the highest present period return.
This model adds interesting dynamics to the data. First, individual actions are highly sensitive to specifications of α i , β i and G t,i all of which are unobserved by the researcher. Also, these parameters are correlated with familial and community characteristics. Endowments e i are a function of household income. The dependence of these parameters on family characteristics should lead to an estimable degree of intergenerational transmission of advantage.
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Moore, R., Brand, J.E. (2016). Causality in Life Course Studies. In: Shanahan, M., Mortimer, J., Kirkpatrick Johnson, M. (eds) Handbook of the Life Course. Handbooks of Sociology and Social Research. Springer, Cham. https://doi.org/10.1007/978-3-319-20880-0_23
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