Theory Of Impulse Responses Function With Applications In Macroeconomic System

Impulse response function is a method of causal analysis, which is used widely along the development of the Vector Autoregression model. Looking back the application of impulse response function in China for nearly twenty years, there has three problems. The first problem is the arbitrary application on innovation decomposition; the second one is the arbitrary application of the criterion on the selection of lag order; the third one is about of the significance test of the impulse response coefficients. Based on the three problems, this paper investigates how impulse response function can be formally used in empirical analysis.First of all, the paper analyses the Choleskey decomposition method, the test of Wold casual chain, the asymptotical distribution of impulse response coefficient matrices, and the bootstrapping confidence intervals in the small sample. Secondly, it also introduces three method of innovation decomposition in the frame of structural VAR which are K-model, C-model, and AB-model, and the asymptotical distribution and bootstrapping confidence intervals of structural impulse response coefficients matrices. Thirdly, based on the Monte Carlo simulation method, the paper analyses the influence of the selection of criteria of lag order to impulse response function. Finally, on the bases of theoretical investigate results, the paper construct two SVAR models that respectively base on short term constraints and long term constraints, and find out the dynamic relation between real stock returns and inflation through structural impulse response function.Based on the theoretical analysis and empirical investigation above, the paper can obtain several conclusions. The first one is on the aspect of the innovation decomposition. In the empirical analysis, we should test the Wold causal chain firstly. If the test is significance, we can use the Choleskey decomposition; if it were not, we would specify the structural coefficients matrix and carry through the structural impulse response analysis. Meanwhile, for the purpose of the unique impulse response function, the structural coefficients matrix must be just-identified. The second one is on the aspect of the selection of lag order. Based on the outcome of the Monte Carlo simulation, HQ criterion can always make the best choice of the lag order whether the sample volume is large or not. The third one is the aspect of the efficiency of the estimation of impulse response coefficients. Since the span of Macroeconomic dataset in China are not large enough, bootstrapping confidence intervals can make more efficiently statistically inference than asymptotic confidence intervals.The theoretical innovations are mainly on the methods of innovation decomposition and the selection of the criterion of lag order. The first one is the test of the recursive relation between the variables; the second one is that we compare the influence of five selection criteria to the impulse response function through Monte Carlo simulation. On the aspect of application, we build two structural systems about the real stock returns and inflation, which are constraint in short term or in long term, and we analysis the dynamic relations between the two variables through the formally analysis method of impulse response function.