[1] Shinshu Univ, Fac Econ & Law, Matsumoto, Nagano, Japan
[2] Shinshu Univ, Dept Econ, Matsumoto, Nagano, Japan
[3] Hosei Univ, Fac Econ, Tokyo, Japan
[4] Univ Texas Austin, McCombs Sch Business, Austin, TX 78712 USA
[5] Harvard Univ, Harvard Business Sch, Dept Econ, Cambridge, MA 02138 USA
[6] Harvard Univ, Ctr Math Sci & Applicat, Cambridge, MA 02138 USA
[7] Natl Bur Econ Res, Cambridge, MA 02138 USA