The Phillips Cure

House spending cuts hurt U.S growth -Goldman Sachs
By Richard Cowan
WASHINGTON | Wed Feb 23, 2011 4:50pm EST

[fair use skip]

“Under the House passed spending bill, the drag on GDP growth from federal fiscal policy would increase by 1.5pp (percentage points) to 2pp in Q2 and Q3 compared with current law,” according to Alec Phillips, who signed the analysis that is dated Tuesday.

Various intelligent bloggers have expressed doubt that the effect could be so large (no links). I think they are not just puzzled but Posnered, that they have made a factor of 16 error in their informal calculations. They seem to think that Phillips is assuming a huge gigantic multiplier since 2% of GDP is many times 61.5 billion.

Yes Phllips talks about quarter growth of quarterly GDP but don’t the two factors of four cancel ? No they multiply.

In forecaster speak 1.5% less growth for two quarters means growth at an annualized rate which is 1.5% lower for two quarters, that is GDP which is 0.75% lower in the second of the two quarters. Growth “in” a quarter doesn’t mean growth during that quarter but that quarter’s level compared to the previous quarter’s level (GDP is measured over a quarter). So Phillips is saying that GDP in the third quarter of 2009 will be 0.75% lower if the Republicans get their way than it would be if Obama gets his way.

That is 0.75% of quarterly GDP not of annual GDP so third quarter GDP will be lower by less than $ 30 billion. If the spending cuts were evenly spread over the 7 remaining months of fiscal 2011, then 3rd quarter public spending would be lower by more than $26 billion. The simple static multiplier (effect on GDP_t)/(change of G_t) is around one, which is not absurdly high. By the same assumption on spending, the multiplier for the second quarter would be about 0.5.

In fact it is hard to cut planned spending quickly, so if Phillips’s model were static (which it isn’t) then the multipliers would both be less than one.

Of course Phillips is using a dynamic model in which there is a hump shaped response to a demand shock with GDP gradually rising, peaking and returning to roughly where it would be (only roughly because of possible crowding out or hysteresis or whatnot but usually assumed to be exactly when modelling). The multiplier isn’t a relationship between Government consumption in a quarter and GDP that quarter — it is a dynamic effect which grows and dies out. But the implied summary multiplier is perfectly standard among Keynesians and “Everyone hoping to make money selling economic analysis”

By the way, Speaker Boehner’s office has made a wonderfully boneheaded assertion for the second day in a row.

A spokesman for House Speaker John A. Boehner of Ohio said the Goldman Sachs report represented “the same outdated Washington mind-set,” comparing it to the thinking behind the 2009 Recovery Ac.

Someone better gently remind that spokesman that Goldman Sachs is based in New York not Washington. Oh and if they’re so dumb, why are they rich ? Finally aren’t Republicans supposed to trust the private sector ?

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