One of the difficulties in estimating multipliers is that during normal times, government spending and taxes do not change too much so it is difficult to isolate their effects on the economy. Economists Robert Barro and Charles Redlick went back in the historical record to look at times when government expenditures and taxes did change substantially: during the buildups and aftermaths of major wars.
In their work, they typically found much smaller multipliers for defense expenditures, typically less than one. This means that increases in government spending did increase the economy, but less than the amount of government spending itself. It also implies that there must have been crowding out of other components of spending. They found that multipliers were larger when there was more unemployment in the economy. Barro and Redlick also suggest that other researchers found larger associations between government spending and GDP because they had the causality backward nondefense spending often rises when GDP grows rapidly. Untangling these issues is a difficult task for social scientists.