I'm running a difference-in-differences analysis on monthly repeated cross sectional data.

I've been told to add a linear time trend to the DiD model to adjust for underlying trends:

Y_ijt = Bo + B1treatment_j + B2post_t + B3treatmentpost_ijt + B4*month_t

where month = number of months from the start of the study period

I'm wondering whether including a linear monthly time trend common to both groups is appropriate in a DiD analysis or whether the time trend may soak up trend changes in the post-period that are related to the treatment?

Note: I don't think this is relevant for the question but I will also adjust for calendar month for seasonality and a vector of individual level variables.

I'm running a difference-in-differences analysis on monthly repeated cross sectional data.

I've been told to add a linear time trend to the DiD model to adjust for underlying trends:

$$Y_{it} = B_0 + B_1 treatment_i + B_2 post_t + B_3 (treatment_i \times post_t) + B_4 month_t + \epsilon_{it}$$

where month = number of months from the start of the study period

I'm wondering whether including a linear monthly time trend common to both groups is appropriate in a DiD analysis or whether the time trend may soak up trend changes in the post-period that are related to the treatment?

Note: I don't think this is relevant for the question but I will also adjust for calendar month for seasonality and a vector of individual level variables.