# A Study on the Causal Relationship between Economic Variable Using VAR Model

## Abstract

In this study, we analyzed the causal relationship among the Korean Won to US Dollar exchange rate (ER) and the consumer price index (CPI) provided by the Bank of Korea, and the KOSDAQ index provided by the Korea Exchange (KRX). The sample data were monthly data from January 1, 2005 to December 31, 2018. As the research model, we used the vector autoregressive model (VAR model), which is a vector time series model, to perform Cointegration Test, Granger Causality Test, Impulse Response Function Analysis, and Variance Decomposition Analysis. The results are as follows. The cointegration test of the economic time series variables CPI, KOSDAQ, and ER shows that there is no cointegration relationship between Trace and Maximum Eigenvalue statistics. In the Granger causality test, each of the variables shows that the significance probability of the chi-square statistic is smaller than the significance level of 0.05, indicating that there is a bidirectional linear dependency respectively, which is influenced by the past values of the self and the other two variables. The analysis of whether it affects volatility shows that the significance probability of the F-statistic is smaller than the significance level of 0.05, and therefore the model has predictive power. The results of impulse response function analysis to see how long the predictive power persists shows that the impulse of the CPI on the KOSDAQ negatively affects up to time lag 4 and disappears, and on the ER up to the time lag 2. In addition, the variance decomposition analysis of prediction error was performed to estimate the extent to which the changes in the CPI, the KOSDAQ, and the ER interact with each other. The result shows that, after the sixth lead, the CPI has an explanatory power of about 97% for itself, the KOSDAQ has an explanatory power of about 98% for itself, and other variables do not affect the CPI and the KOSDAQ. The ER does not affect the CPI, has an explanatory power of about 12% for the KOSDAQ, and about 87% for itself.