Itofumi Takeuchi a Department of Economics, Nihon University, Chiyoda-ku, Tokyo, 102-8005, Japan   2-23-22 Honchyo Funabashi-shi,Chiba,Japan Funabashi-shi, Chiba, Chiba 273-0005 Japan   cdit26076@g.nihon-u.ac.jp             JEL Areas: C1 : Econometric and Statistical Methods: General C9 : Design of Experiments: General