Workshop in Applied Statistics presentation by In Song Kim, MIT.

===== Abstract =====

  Many social scientists use linear fixed effects regression models

  for causal inference with longitudinal data to account for

  unobserved time-invariant confounders.  We show that these models

  require two additional causal assumptions, which are not necessary

  under an alternative selection-on-observables approach.

  Specifically, the models assume that past treatments do not directly

  influence current outcome, and past outcomes do not directly affect

  current treatment.  The assumed absence of causal relationships

  between past outcomes and current treatment may also invalidate some

  applications of before-and-after and difference-in-differences

  designs.  Furthermore, we propose a new matching framework to

  further understand and improve one-way and two-way fixed effects

  regression estimators by relaxing the linearity assumption.  Our

  analysis highlights a key trade-off --- the ability of fixed effects

  regression models to adjust for unobserved time-invariant

  confounders comes at the expense of dynamic causal relationships

  between treatment and outcome.