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Say I have the following model:

$$y_{it} = \gamma_i + \delta {T}_{it} + \zeta Z_{i(k)} + \epsilon_{it}$$

where $y$ is some outcome for household $i$ in month $t$. $\gamma_i$ denotes household fixed effects. $T_{it}$ is treatment dummy. Say I have 240 months worth of data. The variable $Z$ represents a vector of time-varying covariates, but they vary across years.

Question:

I want to be very explicit about the variation, but I also don't want to confuse any readers. Is writing out $Z_{i(k)}$ appropriate, where $k$ is the subscript denoting the yearly variation? I figured this notation is a bit weird since I already stated that the time frequency was months, not years.

This question is about scientific reporting, so I believe it's apt for this community. I'm most concerned about the clarity of the model, in particular the subscripts.

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