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Interestingly, several types of institutions produce exactly as many PhDs as you’d expect given their enrollments - high research activity universities, doctoral universities, and baccalaureate colleges. When it comes to very high research activity universities and master’s universities, however, the former overperforms and the latter underperforms.

Enrollment by institution type
[ul][]26.2% Very high research activity
[
]12.9% High research activity
[]10.7% Doctoral university
[
]33.6% Master’s university
[li]16.6% Baccalaureate college[/ul][/li]Source: https://nces.ed.gov/programs/digest/d17/tables/dt17_317.40.asp (I excluded “special focus” colleges and CCs.)

Production of PhDs by undergrad institution type
[ul][]48.0% Very high research activity
[
]14.2% High research activity
[]4.43% Doctoral university
[
]18.0% Master’s university
[li]15.25% Baccalaureate college[/ul][/li]Source: WebCASPAR

The NSF noted precisely the same phenomenon in its 2013 study of PhD production.