This paper is a nontechnical introduction of how economists formulate matching problems. We discuss the relevance of notions such as stability and strategy-proofness, and examine these criteria in the context of the recent change of algorithms in Japanese doctor-hospital matching, which tried to address the problem of shortage of doctors in rural areas. Most of the discussions are based on Kamada and Kojima（2010）while some new examples and discussions are provided.

Many studies suggest that years of formal schooling completed is the most important correlate of good health. There is much less consensus as to whether this correlation reflects causality from more schooling to better health. The relationship may be traced in part to reverse causality and may also reflect “omitted third variables” that cause health and schooling to vary in the same direction. The past four decades have witnessed the development of a large literature focusing on the issue just raised. I deal with that literature and what can be learned from it in this paper.

We aimed to clarify the effect of relative wages on turnover varies by tenure among care staff working at long-term care facilities in Japan. First, we assessed whether a greater sensitivity to wages in other occupations is likely among workers with shorter job tenure than among those with longer tenure. We used matched employer-employee data from 1,633 long-term care facilities in December 2007. Care staff turnover was defined as the number of employees leaving each institute and was classified according to tenure (less than 1 year of tenure or 1 to 3 years of tenure), type of service (at home nursing care or institutional care), and type of employment (full-time or part-time). We found that, only among full-time workers in institutional care facilities, wages relative to other occupations had a significantly negative effect on the turnover of workers with less than 1 year of tenure; in contrast, no significant effects were observed on the turnover of workers with 1 to 3 years of tenure. This suggests that, for full-time workers in institutional care facilities, wage increases may be an effective way to retain workers with less than 1 year of tenure, but not for those with 1 to 3 years of tenure.