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Violation of parallel trend assumption will lead to biased estimation of the causal effect.
This article discusses the parallel trends assumption at length and proposes a weighting method for DID when the parallel trend assumption may not hold.
The parallel trend assumption is the most critical of the above the four assumptions to ensure internal validity of DID models and is the hardest to fulfill.
The so-called common trend assumption is the key identifying assumption of this strategy.
The results were consistent with the primary analysis, confirming the accuracy of the parallel trend assumption.
Table 3 tests the common trend assumption with another set of regressions.
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Both applications reveal the fragility of the widely adopted common trends assumption.
Ignoring the parallel-trend assumption and estimating the DD anyway produces the same result – a 0.05 percentage point reduction in new Flexjob hires compared to all new hires in governmental units post-reform compared to comparison firms, both with and without controls, LPM or Probit (available on request).
The same as with all endogeneity problems, we cannot formally test the parallel trends assumption.
Since the parallel trends assumption cannot be empirically supported in the non-western immigrants sample, the estimates are unreliable.
When performing the individual DiD estimation on income, the parallel trends assumption is in the danger zone.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com