# Case 6.5 Granger Causality

Granger causality statistics determine whether past values of one variable helps to predict another variable. For example, if the lagged value of the independent variable X, help in predicting the value of the explanatory variable Y_(t+1), then X granger causes the Y. On the other hand, if the independent variable X does not help to predict Y, then the coefficients on the lags of X will all be zero in the reduced form Y equation.

7. Empirical results

7.1 Optimal lag length selection tests

Before testing for the relationship among the selected variables, the optimal lag length is determined. The current study uses three different information criterion procedures, Akaike information criterion (AIC), Schwarz information criterion (SBIC) and Hannan-Quinn information criterion (HQIC), in order to get the optimal lag length. Too many lags could increase the error in the forecasts; too few could leave out relevant information (Stock and Watson, 2007).

Table 2, presents the results from the optimal lag length selection tests, for the variables private net savings, government net savings rate, GDP per capita growth, young dependency ratio, old dependency ratio, inflation growth rate, liabilities growth rate and interest rate, proxied as the long term government bond yield.

Lags AIC SBIC HQIC

1 -28.6713 -28.459

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Due to the fact that the disturbances may be contemporaneously correlated, these functions do not explain how variable i reacts to a one time increase in the innovation to variable j after t periods, holding everything else constant. In order to explain this, the orthogonalized ordering of exogenous shocks is applied so that the assumption to hold everything else constant is reasonable. Unrestricted VARs use a Cholesky decomposition to orthogonalize the disturbances and thereby obtain structurally interpretable