I’ve dedicated several posts recently to the subject of quasi-experimental designs and causal inference. I’ve tried to organize the following related links for a bigger picture.
First off, regression is often mischaracterized by a clinical view of assumptions related to linearity. However, as Angrist and Pischke state:
"In fact, the validity of linear regression as an empirical tool does not turn on linearity either...The statement that regression approximates the CEF lines up with our view of empirical work as an effort to describe the essential features of statistical relationships, without necessarily trying to pin them down exactly." - Mostly Harmless Econometrics, p. 26 & 29
For more discussion see:
In Mostly Harmless Econometrics, not only is linear regression rigorously developed and discussed, but quasi-experimental designs are given very heavy emphasis. As discussed in Cellini (2008):
… proxy variable, fixed effects, and difference in- differences approaches are becoming quite common. Indeed, these approaches have replaced basic multivariate regression as the new standard for education research in the economics literature”
The links below attempt to highlight at least in a heuristic sense, these methods and the issues they attempt to address:
Time Series Methods: