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  • lagged explanatory variable as a control in a DID model

    Hello ,
    Suppose I intend to use a difference-in-differences research design that exploits within-district variation in exposure to violent crime shock over time.
    And to account for heterogeneous treatment timings I run


    Code:
    did_multiplegt outcome district year x1 , placebo(1) dynamic(0) cluster(village_id) breps(999) trends_lin(district) longdiff_placebo robust_dynamic  controls( x2 x3 x4 girl_child)  graphoptions( ylabel(-.3(.1).1)  xlabel(-2(1)0) title() xtitle(Years from First Exposure) ytitle(Estimated Effects on outcome (SD)) legend(off))

    where x1 is the crimeshock indicator
    x2=crimeshock*female
    x3=lagged crimeshock
    x4* laggedcrimeshock*female


    Here I have included an indicator of lagged crime shock(indicator of crime shock in the previous year).
    1)Is this okay to include a lagged explanatory variable in such a model ?
    2) Is it alright to include the lagged interaction term as well?
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