What social and institutional factors determined the role of government in the late nineteenth and early twentieth century?
The major social factor that would have determined this was the dedication of many Americans to the idea of laissez-faire government. The majority of Americans at this time believed (although this was fading as the Progressive Era began) that government should stay out of the economy.
The major institutional factor was a simple lack of capacity on the part of the government. The government was much smaller than it is now. It would not have had the ability to take a much more activist approach even if it had wanted to.
For these reasons, the role of government in the economy in this time period was quite limited.