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