This paper studies asymptotically optimal estimation and testing procedures for moment condition models using the theory of large deviations (LD). Minimax risk estimation and testing are discussed in details. The aim of the paper is three-fold. First, it studies a moment condition model by treating it as a statistical experiment in Le Cam's sense, and investigates its large deviation properties. Second, it develops a new minimax estimator for the model by considering Bahadur's large deviation efficiency criterion. The estimator can be regarded as a robustified version of the conventional empirical likelihood estimator. Third, it considers a Chernoff-type risk for parametric testing in the model, which is concerned with the LD probabilities of type I errors and type II errors. It is shown that the empirical likelihood ratio test is asymptotically minimax in this context.