I recently realized that I may have been remiss in at least one prior post because I did not adequately connect the crucial components of my rationale for, more or less, taking the multiplier estimated by Christina Romer and the Haavelmo Theorem at face value.
There is a reason that, generally speaking, the multiplier does not work out to exactly its advertised proportions in practice, which is intimately linked with the IS/LM model. One of the earliest models prior to the Keynesian/Hicksian IS/LM model was the "Keynesian Cross." Such a model, though useful for some purposes (certainly for illustration), does not capture much of the dynamic effects of deficit financing. The IS/LM is more sophisticated because it takes into account the role of the interest rate in coming to an equilibrium for the supply and demand of funds. Thus, with an upward-sloping LM curve and a downward-sloping IS curve, shifting the IS curve to the right will result in something that looks like the following graph:
The difference between the Initial IS Curve and the Stimulus IS Curve is the increase of the deficit times the multiplier. In the case of a liquidity trap, where the LM curve is perfectly interest elastic (the interest rate is constant regardless of the level of output), as occurs when the nominal interest rate is zero and unable to go lower, the increase in the deficit times the multiplier gives the increase in output. In most cases, this is not true, but look at the short-term interest rates for 3-Month Constant Maturity Treasury bonds:
As Paul Krugman has pointed out many times, the United States is in a liquidity trap, so the multiplier should translate directly into increased output per dollar spent.
What would happen if the United States were NOT in a liquidity trap? Then the change in the interest rate would cause deficit spending to displace some private borrowing. What would be needed for an increased deficit to result in less aggregate demand? The LM curve would need to be downward-sloping, meaning that the supply of funds would have to decrease with a higher interest rate. Do I believe in a negative multiplier? No.