This focuses on comparing data from 2000 and 2016. From the article:

> Since 2000, the number of people in private prisons has increased 47%, compared to an overall rise in the prison population of 9%.

2016 things changed a bit:

> At the federal level, a 2016 Obama Administration policy shift to reduce reliance and ultimately phase out private prison contracts was reversed by Attorney General Jeff Sessions in February 2017.

The article also answers whether this has any impact on the justice system:

> Changes in policy at the Department of Justice in 2017 that are likely to increase sentence length and expand prosecutions for drug and immigration offenses may contribute to the expansion of private facility contracting.

I picked that particular article because it wasn't especially kind to my point of view. Nevertheless, the last statement you quoted is speculation and we don't have any data to back it up.