The effect is shown differently on nominal and real GDP. According to this Wells Fargo’s report, as Real GDP attempts to solely measure changes in output, the real labor costs, which are measured by hours worked, is what it reflects. Thus, when hours worked decline, so does output.
On the other hand, the nominal federal component of GDP is unchanged, as a result of accrued back-pay. This is reflected mechanically in the GDP accounts as a rise in the federal price deflator. This has happened before in the Q4-2013 shutdown, as shown by the red circle in the graph below.
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