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  • What is the meaning of adding an non-binary interaction variable to a regression?

    When examining whether the impact of laws on Y differently in developed countries is to add an interaction variable.

    The general equation is:

    Leniency_law is a variable of interest in a Differentce-in-Difference setting, indicating 1 for the treatment and 0 for the control observation. pt_original is pt retrieved from this equation
    Dependent_variables= Leniency_law + Independent_variables + fixed effects + error term
    Examining whether the impact of laws on Y differently in developed countries is to add an interaction variable as
    Dependent_variables= Leniency_law + developed_dummy * Leniency_law + Independent_variables + fixed effects + error term
    where developed_dummy equalling to 1 if this observation is in developed countries.

    In the case above, the interaction variable is a binary one (receiving value of 0 or 1).

    However, in this Dasgupta, 2019, p. 2610,2611, Table 9, instead of the developed_dummy, they add a non-binary interaction variable called "Predicted conviction" as being asked here.

    The equation now becomes
    Code:
    Dependent_variables= Leniency_law + Prediction conviction * Leniency_law + Independent_variables + fixed effects + error term
    I am wondering what is the purpose of adding such "Predicted conviction"variable? Is Predicted conviction still a moderator variable? And how we explain the coefficient of Prediction conviction * Leniency_law
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