The “non-partisan” (but pro-government) Congressional Budget Office has assessed the economic effects of the five-week partial shutdown of the government that started on December 22, 2018, and ended on January 25, 2019. According to CBO,
real (that is, inflation-adjusted) gross domestic product (GDP) in the fourth quarter of 2018 was reduced by $3 billion (in 2019 dollars) in relation to what it would have been otherwise…. In the first quarter of 2019, the level of real GDP is estimated to be $8 billion lower than it would have been….
Although most of the real GDP lost during the fourth quarter of 2018 and the first quarter of 2019 will eventually be recovered, CBO estimates that about $3 billion will not be.
In truth, real GDP will rise as a result of the inactivity of government bureaucrats. By how much? Not a lot, relative to real GDP, which is measured in the trillions of dollars. But it will rise, as I explain in “Keynesian Multiplier: Fiction vs. Fact“, because there is a negative relationship between government spending and real GDP, other things being equal:
kT = ∆Y/∆F = -0.340Y0
kT = the true multiplier
Y = real GDP
F = fraction of GDP spent by governments at all levels, including transfer payments (e.g., Social Security, Medicare, and Medicaid)
Y0 = real GDP in the period during which F changes
Even a slight decrease in government spending has an out-sized — and beneficial — effect on GDP.