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  • Correct specification for a time-related variable in DiD fixed effects regression

    I am using a Diff-in-Diff regression design to evaluate the impact of a county-level tax hike (i.e. treatment variable) on tobacco sales (i.e. outcome variable) in a given county, relative to counties in the control group.

    However, 16 months after the treatment county raised its tobacco tax, a state-wide value added tax (VAT) increase on tobacco was also implemented that affects both my treatment and control observations. My question is how can I account correctly account for the state-wide tax and disentangle its impact from the main policy I am interested in measuring, which is the county-level tobacco tax. I have created two dummy variables to incorporate this into my model but I am not sure if I am correctly coding the two dummy time variables.
    Here is a data example:
    ```
    dataex tobacco_sales month post_vat_time post_vat_implementation treated_neighborhood
    ---------------------- copy starting from the next line -----------------------
    [CODE]
    * Example generated by -dataex-. For more info, type help dataex
    clear
    input float(tobacco_salesmonth post_vat_time post_vat_implementation treated_neighborhood)
    155 76 0 0 1
    441 1 0 0 0
    12 4 0 0 0
    238 18 0 0 0
    81 34 0 0 0
    604 110 1 0 0
    553 111 1 0 0
    ```

    First, to capture whether the state-level tax impacted treated observations differently than control observations , I construct a variable, which equals 1 for post-VAT in treated observations , and 0 for post-VAT in treated observations . I created the variable as follows:
    ```
    gen post_vat_implementation= post_vat_time*treated_neighborhood
    ```

    Second, to measure the state-level tax policy on both treatment and control observations, I add a dummy time variable that equals 1 for post-VAT, and 0 pre-VAT.
    ```
    gen post_vat_time= (month>=16 & !missing(month))
    ```

    Does the coding of either variable allows us to separate the effects of the county-level tax on tobacco, versus the state-level VAT increase policy?
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