"It is amazing what happens when you assume that you live in a linear world. You say that the multiplier for government spending is 1.57.
Really? Over what range? Think of it this way: at which level of additional government spending would the path of U.S. real GDP be the highest?
(a) $100 billion in spending above the baseline
(b) $1 trillion in spending above the baseline
(c) $100 trillion in spending above the baseline
If you use a constant multiplier of 1.57, the right answer is (c). Yet we know that this is not the right answer. At $100 trillion in additional government spending, the United States would be operating like Zimbabwe, with similar results."
Indeed, why not go for a quadrillion dollars? That would make all Americans multi-millionaires!
This exercise in Bastiat-style Reductio ad absurdum teaches us two important lessons: First of all, there are no constant multipliers or other quantitative relationships in economics (except for functional ones, like 4% interest rate on a $100 million loan means $4 million in interest payments). Whatever "multiplier" that may have existed in one country in one time for a specific package will not hold in other countries, or the same country in a different time or even the same country at the same time with a different quantity. Any such relationship, even if estimated correctly (and there are good reasons to doubt that), is a historical fact for a specific circumstance, not a timeless theoretical relationship.
And secondly, fiscal stimulus will not necessarily have positive net effects, otherwise $100 trillion or quadrillion packages would bring us to unprecedented instant prosperity. The use of borrowing and/or "printing presses" will inevitably crowd out private investments and create price inflation, which will depress output.
That doesn't mean that the reverse is true, that all "fiscal stimulus" will be meaningless or have negative net effects. If focused on incentive improving tax cuts during a period of declining credit demand (like now), it will probably have positive net effects. But what it does mean is that "fiscal stimulus" will always have both positive and negative effects, and that for badly designed "fiscal stimulus" the negative effects are likely to be bigger, particularly if you take a long term perspective.