Many researchers would be interested in one question: If a change of X is made, will Y be influenced in response? However, while a lot of statistical methods are developed to analyze association between variables, how to find a causal relationship among variables is relatively neglected. The PC algorithm, developed on the basis of Pearl, Sprites, Glymour, and Scheines"s studies, is used to find the causal pattern of the real-world observed data. However, PC in Tetrad produces a class of directed acyclic graphs (DAGs) that are statistically equivalent under a normal distribution, and therefore such a distributional assumption causes a series of unidentifiable DAGs because of the same joint probability. In 2006 Shimizu, Hoyer, Hyvarinen, and Kerminen developed the Linear Independent Non-Gaussian Model (LiNGAM) to do a causal search based on the independently non-Gaussian distributed disturbances by applying higher-order moment structures. The research objective of this dissertation is to examine whether the LiNGAM is helpful relative to the PC algorithm, to detect the causal relation of non-normal data. The LiNGAM algorithm is implemented by first doing independent component analysis (ICA) estimation and then discovering the correct ordering of variables. Thus, the procedures of ICA estimation and the process of finding the correct causal orderings in LiNGAM are illustrated. Next, we do a causal search on the retail-level scanner data to investigate the pricing interaction between the manufacturer and the retailer by applying these two algorithms. While PC generates the set of indistinguishable DAGs, LiNGAM gives more exact causal patterns. This work demonstrates the algorithm based on the non-normal distribution assumption makes causal associations clearer. In Chapter IV, we apply a classical structural demand model to investigate the consumer purchase behavior in the carbonated soft drink market. Unfortunately, when further restrictions are imposed, we cannot get reasonable results as most researchers require. LiNGAM is applied to prove the existence of endogeneity for the brand"s retail price and verify that the brand"s wholesale price is not a proper instrument for its retail price. Therefore, consistent estimates cannot be derived as the theories suggest. These results imply that economic theory is not always found in restriction applied to observational data.
