Null findings

What happens when we have a null finding? I was puzzled over this post from John Cochrane on a paper by Dupor and Li:

Bill Dupor and Rong Li have a very nice new paper on fiscal stimulus: "The 2009 Recovery Act and the Expected Inflation Channel of Government Spending" available here.

New-Keynesian models are really utterly different from Old-Keynesian stories. In the old-Keynesian account, more government spending raises income directly (Y=C+I+G); income Y then raises consumption, so you get a second round of income increases.

New-Keynesian models act entirely through the real interest rate.  Higher government spending means more inflation. More inflation reduces real interest rates when the nominal rate is stuck at zero, or when the Fed chooses not to respond with higher nominal rates. A higher real interest rate depresses consumption and output today relative to the future, when they are expected to return to trend. Making the economy deliberately more inefficient also raises inflation, lowers the real rate and stimulates output today. (Bill and Rong's introduction gives a better explanation, recommended.)

So, the key proposition of new-Keynesian multipliers is that they work by increasing expected inflation. Bill and Rong look at that mechanism: did the ARRA stimulus in 2009 increase inflation or expected inflation? Their answer: No.

I wasn't sure if the paper was about the stimulus, i.e. based on the model there was no effects of stimulus on inflation or whether this was a test of the New Keynesian model. The post seems to read as though the paper was making a case that the stimulus did not work although I sort of read between the lines for this. The comments seem to indicate this was a test of the model which indicates then that the model is somewhat off.