The purpose of this paper is to explore the use of cause-and-effect tests, also known as Granger-causality tests, to evaluate linear dependence between two variables. The paper will discuss the theoretical basis for the tests, their advantages and disadvantages, and provide examples of the tests in practice.
The theory of causality has been studied in various fields of science, including economics and finance. In economics, cause-and-effect tests are used to determine whether one variable has an effect on another. This is done by testing for linear dependencies between two variables. The most commonly used cause-and-effect tests are the Granger-causality tests, which were developed by Clive Granger in 1969.
The Granger-causality tests use linear regression techniques to test for linear dependencies between two variables. The test is based on the assumption that one variable can be used to predict another. If the regression coefficient is found to be statistically significant, then it is assumed that the two variables are linearly dependent.
The advantages of using the Granger-causality tests are that they provide a simple and easy to understand method for testing for linear dependencies between two variables. Additionally, the tests are relatively easy to interpret, since the results can be interpreted as either a cause or an effect.
Despite their advantages, the Granger-causality tests have some drawbacks. For example, the tests are limited to linear dependencies and can not detect nonlinear relationships between two variables. Additionally, the tests assume that the two variables are independent, which may not always be the case.
To illustrate the use of the Granger-causality tests, consider the following example. Suppose that there is a relationship between stock prices and GDP growth. To test for a linear dependency between these two variables, a Granger-causality test can be used. The test would involve running a regression with stock prices as the dependent variable and GDP growth as the independent variable. If the regression coefficient is found to be statistically significant, then it can be assumed that there is a linear dependency between the two variables.
In conclusion, the Granger-causality tests are a useful tool for testing for linear dependencies between two variables. The tests are relatively simple to understand and interpret, and can be used to determine whether one variable is causing the other. However, the tests are limited to linear dependencies and can not detect nonlinear relationships between two variables.
References
Granger, C. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.
Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1-3), 159-178.