What did these researchers discover?

NBFR: 
We propose a new source of cross-sectional variation that may identify causal impacts of government spending on the economy. We use the fact that a large number of federal spending programs depend on local population levels. Every ten years, the Census provides a count of local populations. Since a different method is used to estimate non-Census year populations, this change in methodology leads to variation in the allocation of billions of dollars in federal spending. Our baseline results follow a treatment-effects framework where we estimate the effect of a Census Shock on federal spending, income, and employment growth by re-weighting the data based on an estimated propensity score that depends on lagged economic outcomes and observed economic shocks. Our estimates imply a local income multiplier of government spending between 1.7 and 2, and a cost per job of $30,000 per year. A complementary IV estimation strategy yields similar estimates. We also explore the potential for spillover effects across neighboring counties but we do not find evidence of sizable spillovers. Finally, we test for heterogeneous effects of government spending and find that federal spending has larger impacts in low-growth areas.

I have not read the paper, it is gated. 

According to federal law, The census and the yearly population estimates result in  changes for federal funds that are population based.  So, each year funds are re-matched to population.  This should help the local economies, and it does, say the researchers.

Does this research say anything about hysterical Kanosian pension stuffers?  No, those folks plan bail outs for their favorite programs.