Angela Lee Duckworth, Eli Tsukayama, and Henry May have published an article entitled, "Establishing Causality Using Longitudinal Hierarchical Linear Modeling: An Illustration Predicting Achievement From Self-Control" (abstract) in the October 2010 issue of the new journal Social Psychological and Personality Science.
The authors are interested in the personality trait of self-control (which encompasses such abilities as persistence and delay of gratification) and whether it can actually be shown to cause academic achievement (GPA) during the years from fifth to eighth grade. Duckworth and colleagues acknowledge the difficulty early on:
"Manipulating personality in a random-assignment experiment could, in theory, establish its causal role for later outcomes but, alas, personality is not easily manipulated. To our knowledge, no empirical investigation to date has successfully manipulated trait-level self-control and measured subsequent effects on life outcomes" (p. 311).
The authors also carefully review the arguments for why longitudinal predictive models using path-analysis and structural equation modeling (controlling for prior levels of the dependent variable), though an improvement over cross-sectional correlations, are still vulnerable to unmeasured third variables. "Longitudinal growth-curve modeling using hierarchical linear models (HLM)" is then presented as offering "a partial solution to the third variable problem" (p. 312).
The core of the argument appears to be this: "By treating a predictor as a time-varying covariate in the prediction of trajectories, one can rule out the possibility of all time invariant confounds (e.g., relatively stable variables such as socioeconomic status). Specifically, if short-term changes in a predictor predict subsequent short-term changes in achievement, a confounding variable z would have to predict these changes and also be tightly yoked to changes in the predictor over time (i.e., the confound and predictor would have to go up and down together in synchrony over time)" (p. 312).
The authors indeed found self-control to predict GPA longitudinally (and not the reverse), concluding as follows:
"This longitudinal HLM study illustrated an innovative analytic strategy that effectively controlled for all time-invariant third-variable confounds... What our analyses did not rule out, however, is the possibility of an unmeasured time-varying third variable that changes in sync with self-control and causally determines subsequent academic performance" (p. 316; my emphasis added).
I would recommend this article for its excellent exposition on causality with non-experimental designs and for the approach it demonstrates. There are a lot of technical details in the article, as well, and even readers experienced with some of the general techniques used may find themselves having to pause periodically to wrap their minds around each specific analytic decision the authors describe.