I'd imagine that Government spending will have the primary impact if its not at public college. Other than that, it would appear that the recession during the 1980's led to a situation whereby not only did more students stay on to do the Leaving Cert where there had previously been a high number leaving for Employment after the old Group and Intermediate Cert's but it led to an increase in College applicants and attendance.
Usually it means more people stay on for college because its the choice between that and emigration. It may well mean that you have no hope of a permanent position though if money is tight in the colleges. More foreign (non-EU) students will be enticed into uni's and IT's to bring their cash fees too. thats all my crystal ball tells me!
I agree that a recession may influence greateer numbers staying on in third level. There may also be encouragement through government schemes for the unemployed to go back to education through relaxed qualification criteria for the Back to Education Scheme.