Friday, March 15, 2024
HomeHealth LawMust we accept as true with staggered difference-in-differences estimates? – Healthcare Economist

Must we accept as true with staggered difference-in-differences estimates? – Healthcare Economist


That’s the query posed in paper via Baker, Larcker and Wang (2022). I summarize their key arguments underneath.

The validity of…[the DiD]…means rests at the central assumption that the noticed development in keep watch over gadgets’ results mimic the rage in medicine gadgets’ results had they now not gained medicine. Because the authors write:

First, DiD estimates are independent in settings with a unmarried medicine era, even if there are dynamic medicine results. 2d, DiD estimates also are independent in settings with staggered timing of medicine task and homogeneous medicine impact throughout companies and through the years. In spite of everything, when analysis settings mix staggered timing of medicine results and medicine impact heterogeneity, staggered DiD estimates are most likely biased.

Oftentimes, DiD is carried out the use of an strange least squares (OLS) regression founded type as follows:

When there are greater than two teams and greater than and a pair of time classes, regression-based DiD fashions normally depend on two-way constant impact (TWFE) of the shape:

The place the primary two coefficients are unit and time frame
constant results. Word that earlier analysis from Goodman-1st Baron Verulam
(2021)
presentations that static kinds of the TWFE DiD is if truth be told a “weighted
moderate of all conceivable two-group/two-period DiD estimators within the information.”

When medicine results can trade through the years (“dynamic
medicine results”), staggered DiD medicine impact estimates can if truth be told
download the other signal of the real ATT, although the researcher had been ready to
randomize medicine task (thus the place the parallel-trends assumption
holds).

The cause of it’s because Goodman-1st Baron Verulam
(2021)
presentations that the static TWFE DiD is if truth be told is composed of three elements:

  • Variance-weighted moderate medicine impact on
    the handled (VWATT)
  • Variance-weighted moderate counterfactual tendencies
    (VWCT)
  • Weighted sum of the trade within the moderate
    medicine at the handled inside of a treatment-timing organization’s post-period and
    round a later-treated unit’s medicine window (ΔATT)

The primary time period is the time period of hobby.  If the parallel tendencies happens, then VWCT =0.  The final time period arises as a result of, below static
TWFE DiD, already-treated teams as successfully used as comparability teams for later-treated
teams.  If DiD is estimated in a
two-period type, then again, this time period disappears and there is not any bias. However,
if medicine results are static (i.e., now not converting through the years after the
intervention), then ΔATT = 0 and TWFE DiD is legitimate. 

The demanding situations, then again, happens when medicine results are
dynamic.  On this case ΔATT

0 and the TWFE DiD is biased.

So what can also be accomplished? The authors be offering 3 answers:

  • Callaway and Santa’Anna (2021). Right here, the authors permit one to estimate medicine impact for a specific organization (medicine at time g) the use of observations at time τ and g-1 from a blank set of controls.  Those are mainly not-yet handled, last-treated, or never-treated teams. 
  • Solar and Abraham (2021).  A equivalent technique is used as in CS, however always-treated gadgets are dropped, and the one gadgets that can be utilized as efficient controls are the ones which might be never-treated or last-treated. Additional, this means is absolutely parametric.
  • Stacked regression estimators. Cengiz (2019) implements this means.  The objective is to “create event-specific “blank 2 × 2” datasets, together with the result variable and controls for the handled cohort and all different observations which might be “blank” controls throughout the medicine window (e.g., not-yet-, last-, or never-treated gadgets). For every blank 2 × 2 dataset, the researcher generates a dataset-specific figuring out variable. Those event-specific information units are then stacked in combination, and a TWFE DiD regression is estimated at the stacked dataset, with dataset-specific unit- and time-fixed results… In essence, the stacked regression estimates the DiD from every of the blank 2 × 2 datasets, then applies variance weighting to mix the medicine results throughout cohorts successfully.”

Whilst there was a large number of math on this submit, if researchers follow those choice DiD estimators, the authors correctly suggest that “researchers must justify their number of ‘blank’ comparability teams—not-yet handled, final handled, or by no means handled—and articulate why the parallel-trends assumption is prone to follow”.

You’ll learn the entire article right here.



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