Abstract
K. Morimune proposed a modified limited information maximum likelihood (MF-LIML) which possesses exact moments and is asymptotically unbiased to O (T-1). The j-th best subset problem is formulated for the variable selection problem of MF-LIML. The solution to the first best subset problem (j=1) or the ultimately best subset among the J solutions obtained by solving the first to the J-th best subset problems (e. g., J=10) in one computer-run is proposed as a pragmatical solution to the variable selection problem for MF-LIML. The proposed variable selection procedure can make the laborious work of estimation by MF-LIML less time-consuming, labor-consuming and costly.