The Penrose hypothesis holds that there is an inverse relationship between the number of prison inmates and the number of psychiatric hospital beds in a population i.e. as one goes up, the other goes down. This was thought to be because there was a relatively-fixed proportion of people in a society in need of containment and if they were not in a psychiatric hospital they would be in a prison or vice versa. A number of studies have found that a fall in available hospital beds occured at the same time as a rise in prisoner numbers. Most of the authors of most of these studies concluded that the decline in psychiatric hospital populations was a cause of increased prison populations suggesting that the same people who may have been hospitalized at one time were later imprisoned. Other researchers observed the same relationship but argued that different factors affected the number of hospital beds and the number of prison places. However, despite the regular publication of national statistics for prisoners and psychiatric hospital patients there has been no study replicating Penrose's original one in 1939. An analysis of data from 179 countries by researchers in Australia found that in high-income countries there was no link betweeen prison population and the number of beds. In low- and middle-income countries there was a positive correlation i.e. as hospital beds went up so did prison places and vice versa . The researchers thought that this might be because countries built more of both as their economic circumstances improved.
Large, Matthew M and Nielssen, Olav - The Penrose hypothesis in 2004: patient and prisoner numbers are positively correlated in low- and middle-income countries but are unrelated in high-income countries Psychology and psychotherapy: theory, reserahc and practice March 2009, 82(1), 113-120