Dependent variable with many zeros in a difference-in-differences model

Question

There is a question with a similar title: How do I estimate a differences in differences model when the dependent variable has many zeros?

However, mine is a little different. Let's assume I have a dependent with 20% of zeros in the treatment group in the pre-treatment period; and 40% of zeros in the control group in the pre-treatment period. Then I observe that I have 10% of zeros in the treatment group in the post-treatment period and 30% of zeros in the control group in the post-treatment period (i.e. in both case the proportion of zeros decreased by 10 percentage points).

Is it wrong then to say that since both treatment and control groups have the same decrease in the number of zeros between the two periods, the difference-in-difference coefficient should not be biased?

Answer 1

Not at all.

I see no reason why such result can be equivalent to the assumptions made for an unbiased estimator in diff-in-diff regressions, namely: 1) a correctly specified equation; 2) average of error term equals zero and 3) error term not correlated with independent variables (the paralell-trend assumption).

This result you observe do not replace any of these assumptions, let alone all of them.

Please refer to these notes for more details.