Why don't the U.S. BLS labor force statistics for individual states sum to the national values?
The U.S. Bureau of Labor Statistics explains (citation):
State estimation procedures are designed to produce accurate data for each individual state. BLS independently develops a national employment series; state estimates are not forced to sum to national totals. Because each state series is subject to larger sampling and nonsampling errors than the national series, summing them cumulates individual state level errors and can cause significant distortions at an aggregate level. Due to these statistical limitations, BLS does not compile a "sum-of-states" employment series, and cautions users that such a series is subject to a relatively large and volatile error structure.
Metropolitan Area Employment and Unemployment
US Labor Force Statistics - Current Population Survey