I estimate a spending multiplier of around 0.4 within the same year and about 0.6 over two years. Thus, if the government spends an extra $300 billion in each of 2009 and 2010, GDP would be higher than otherwise by $120 billion in 2009 and $180 billion in 2010.Few economists think that the velocity of money is stable enough to predict with any accuracy what would happen if the money stock increased by10%. Why should the multiplier be any more predictable?
When one factors in the typical relationship between tax rates and tax revenue, the multiplier is around minus 1.1. Hence, an increase in taxes by $300 billion lowers GDP the next year by about $330 billion.
Update: More here and here.