Compared to 2012 policy, the fiscal cliff deal principally consisted of increased taxation of extremely high income and large inheritances. I would not expect this to affect consumption much. However, it also included expiration of the partial payroll tax holiday with an increase in payroll taxes of 2%. This corresponds to a regressive tax increase of $115 billion. A new Keynesian could argue that the timing of taxes doesn't matter, since consumers knew that something like that would happen. But I can't.
A now standard estimate of the government spending multiplier is 1.5. To the most paleo of paleo Keynesians, this should be 1/(1-c) (where c is the marginal propensity to consume) giving c = 1/3. The tax increase multiplier should be c/(1-c) = 0.5 so the impact on GDP should have been about 0.5*115/16768 roughly = 0.4 %
This corresponds to a reduction in the annualized growth rate of 1.6%.
I have a problem. It isn't terrible. The predicted effect is small enough that it could be obscurred by the ordinary fluctuations in quarterly growth rates. But it seems to me that it should have been noticeable.
Moving on from 1937 to the 1960s the second most paleo possible Keynesian notes that increased aggregate demand causes increased investment through the accelerator. A payroll tax increase does not have this effect. The government expenditure multiplier is 1/(1-c-b) where b is the effect on investment, but the tax increase multiplier is still c/(1-c).
I estimate b = 0.29 (this is just from a regression of investment/GDP on the lagged annual GDP growth rate and a trend). I have gone too far, with a c=0.04 and a tiny multiplier.
OK where did I get the 1.5? Well always from looking at papers which look across US states or across mostly European countries. The multiplier for a large almost closed economy like the whole USA should be larger. I will guess 1/(1-c-0.29) = 2 so c is about .2 so c/(1-c) is about 1/4 and the effect on annualized growth about 0.8% which is not tiny but now well within the normal variation of growth rates.
I guess the bottom line of this silly exercize is that we can't learn anything from one data point regressions. I am talking about one quarterly growth rate and there is almost no information in it.