To my knowledge, there is no such study. It would be quite the undertaking to do one.
One of the reasons why I am in favour of the government digitizing its services is that health care, for example, could be improved. We may have to invest in technology, for example, but there would be a return on the investments, since health care would be more efficient.
To my knowledge, no such study exists. First, it is difficult to imagine the future without digitization. Second, even though there would be a significant cost, there would surely be a return on the investments.