This paper uses the old-Keynesian representative agent model developed in Farmer (2010b) to answer two questions: 1) do increased government purchases crowd out private consumption? 2) do increased government purchases reduce unemployment? Farmer compared permanent tax financed expenditure paths and showed that the answer to 1) was yes and the answer to 2) was no. We generalize his result to temporary bond-financed paths of government purchases that are similar to the actual path that occurred during WWII. We find that a temporary increase in government purchases does crowd out private consumption expenditure as in Farmer (2010b). However, in contrast to Farmer's experiment we find that a temporary increase in government purchases can also reduce unemployment.
Full paper by Farmer and Plotnikov here. Overall, they find that a temporary increase in government purchases crowds out private consumption expenditure, but also reduces unemployment.