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The phrase "has lagged" is correct and can be used in written English.
It is typically used in the present perfect tense to indicate that something has fallen behind or is not progressing at the expected pace. Example: Despite efforts to improve efficiency, our production has lagged behind our competitors for the past quarter.
Exact(60)
O'Brien has lagged.
One waterway has lagged, however.
Performance has lagged lately.
But the timeline has lagged.
Implementation of the plan has lagged.
State growth has lagged behind national growth.
of modern information systems, has lagged behind.
Investment has lagged behind the region's needs.
Still, the state has lagged in enforcement.
Investor perception has lagged that change.
But spending has lagged behind expectations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com