The purpose of this paper is to provide brief review of estimation methods for the standard consumption-based asset pricing model (CCAPM) and some of its serious empirical problems, namely, the two puzzles in the Japanese financial market. First, we introduce Hansen's (1982) generalized method of moments (GMM) estimator for estimating the parameter of the standard CCAPM. Second, we show the superiority of alternative GMM estimator, generalized empirical likelihood (GEL), by measuring the difference of the higher order bias on the standard CCAPM and indicate the GEL estimator suggest a possibility for solving the puzzles. Last, we suggest a few methods to examine the standard CCAPM for future research.