# Dynamic covariate balancing: Estimating treatment effects over time with potential local projections

**Davide Viviano, Jelena Bradic – 2023**

Main difference from standard local projections

- You estimate the LPs on the conditional expectation of potential outcomes rather than the conditional expectation of actual outcomes
- You estimate the LPs recursively, which requires first estimating the furthest out horizon and then using those calculations as part of your estimates for the shorter horizons
- Uses a method called dynamic covariate balancing to reweight observations to ensure covariate balance between treated and control units.

Why have this distinction

- The estimand of standard local projections doesn’t explicitly take a stance of the autocorrelation of the treatment variable. This makes interpretation of the LPs ambiguous, since interpreting what effect you are measuring requires a view on to what degree future treatments are influenced by past treatments and covariates. Note that this doesn’t mean that LPs are “wrong” in any way, merely that their interpretation is tricky and they may not be estimating the thing you want. The only way to interpret an LP as representation
*only*the effect of a singular treatment with no future treatments is if you assume treatments are independent over time (no autocorrelation). This is almost certainly not true unless you are using a properly constructed white noise shock variable with no autocorrelation. - This is an important distinction particularly when you have an explicit series of treatments that you want to estimate the effect of. In such situations, you need to be clear about about assigning effects to various treatments. Not so in the standard LP case, where you only care about a single, initiating treatment and whatever happens from there is fair game / not explicitly modeled
- In effect, this method lets you explicitly estimate the effect of a single treatment followed by no future treatments and the effect of two consecutive treatments. On the other hand, LPs estimate something in the middle – the effect of a single treatment, with no control over or insight into subsequent treatments.

Important assumptions

- This method takes no stance on modeling selection into treatment, i.e. propensity scores. The issue with propensity scores is that you can, of course, be wrong in your estimation an in addition they can be unstable in certain situations. The nice part about this method is that, via covariate balancing, you can achieve an as-good-as solution relative to propensity scores without literally knowing true propensity model and with lower variance.
- Because you model potential outcomes, the intertemporal dependence of treatments doesn’t matter, since by assumption potential outcomes are not affected by treatment. This lets you retain full control over the particular treatment effects you analyze
- Can be used on imbalanced panels