# Importance of Granger causality test

Granger causality is a method to examine the causality between two variables in a time series. “Causality” is related to cause and effect notion, although it is not exactly the same. It is a statistical concept which is based on the prediction. If X variable’s Granger causes Y, then past values of X should contain information that helps in predicting Y. In more simpler language; if X is influenced by the lagged values of both X and Y, then Y Granger causes X. Similarly, if variation in Y is impacted by its lag and the lagged values of X, then X Granger causes Y.

When Y Granger cause X and X Granger causes Y, this is known as bi-directional Granger causality. If only one Granger causes other, it is uni-directional Granger causality. If both the variables are independent of each other then there is no causality.

## Equations for Granger causality

The equations for Granger causality are as follows:

Where ε and n are random disturbances; serially uncorrelated with zero mean and unit variance. α, β a1,a2, .., ap, b1, b2, .., bp are parameters to be estimated.

## The hypothesis for checking causality

The hypothesis for checking the causality using Granger Causality test is as follows:

Null hypothesis: lagged x-values do not explain the variation in y {(x(t) doesn’t Granger-cause y(t)}

Alternative hypothesis: lagged x-values explain the variation in y.

(x(t) Granger-cause y(t))

It helps in investigating the patterns of correlation by using empirical datasets. In FDI study, Granger causality is used to check the robustness of results and to detect the nature of the causal relationship between FDI and GDP.

### Divya Dhuria

Research analyst at Project Guru
DIvya has a keen interest in policy making and wealth management. She is a Master in Economics from Gokhale Institute of Politics and Economics. She has been trained in the econometric techniques to assess different possible economic relationships. She hascontributed to the working paper on National Rural Health Mission at Institute of economic growth, Delhi. Along with academical growth, she likes to explore and visit different places in her spare time.

### Related articles

• How to perform unit root test? Unit root indicates a stochastic trend in the time series. Sometimes it is known as “random walk with drift”. A time series dataset will show a systematic unpredictable pattern if it has the unit root.
• How to test time series multicollinearity in STATA? The problem of multicollinearity arises when one explanatory variable in a multiple regression model highly correlates with one or more than one of other explanatory variables. It is a problem because it underestimates the statistical significance of an explanatory variable (Allen, 1997).
• Understanding normality test in STATA Time series data requires some diagnostic tests in order to check the properties of the independent variables. This is called 'normality'. This article explains how to perform normality test in STATA.
• How to perform Granger causality test in STATA? Applying Granger causality test in addition to cointegration test like Vector Autoregression (VAR) helps detect the direction of causality. It also helps to identify which variable acts as a determining factor for another variable. This article shows how to apply Granger causality test in STATA.
• Lag selection and stationarity in VAR with three variables in STATA This article incorporates Gross Fixed Capital Formation (GFC) and again performs the lag selection test and check for stationarity for both, GFC and PFC. Thus this article incorporates the VAR with three variables in STATA.
Discussions