What is the interaction term in firm's industry case?

[Phuc Nguyen]

In Dasgupta, 2019, p.2012, 2013, they want to examine the impact of staggered leniency laws on firms' asset growth. Afterward, they went further as below:

Finally, in panel D, we look at recent industry growth. High growth industry can be associated with less collusion (...)We use the three-digit SIC industry median of sales growth as the proxy for maturity of an industry

In panel D, our main variable of interest is the interaction between the passage of the leniency laws and the median lagged 2-year sales growth in the firm’s industry. In Columns 1 our main variable of interest is the interaction term between the passage of the leniency law and the industry growth.

Note: The dependent variable above is asset growth

From my understanding, the industry growth variable is generated for each observation is the median of asset growth of all firms in THIS industry in THIS country in THIS year. I am wondering if it is the correct explanation.

Apart from that, what is the purpose of adding this interaction variable into the equation like that?

[Clyde Schechter]

n panel D, our main variable of interest is the interaction between the passage of the leniency laws and the median lagged 2-year sales growth in the firm’s industry.

From my understanding, the industry growth variable is generated for each observation is the median of asset growth of all firms in THIS industry in THIS country in THIS year.

So, no, it seems the industry growth variable for each observation is the median of asset growth of all firms in this industry in this country two years earlier.

Apart from that, what is the purpose of adding this interaction variable into the equation like that?

Apparently the people who developed this model believed that the effect of the leniency laws on asset growth would differ among industries, and specifically that the previous asset growth rate in the industry would influence the effect of the leniency laws. So they modeled that with that interaction term, which would be the simplest way of reflecting that belief in their model.