As of this week, the government shutdown is now the longest in U.S. history. Granted, it is only a partial shutdown. Previous wholesale shutdowns occurred in January 2018 over immigration (specifically saving DACA-Deferred Action for Childhood Arrival) which lasted 3 days and October 2013 (over saving Obamacare) which lasted 16 days.
These prior shutdowns can be used to estimate the economic impact of the current one. According to the Office of Management and Budget, the October 2013 government shutdown lowered real GDP growth by 0.2% to 0.6% - or somewhere between $2 billion and $6 billion in lost economic output. It is estimated the current shutdown is knocking off anywhere from 0.1% to 0.5% of GDP per day. It will take quite a while for the actual impact to show up in economic stats.