Dots in the lower right quadrant correspond to series where traditional Granger-causality tests do not find evidence of predictive ability whereas Rossi’s (2005) robust Granger-causality test does find predictive ability. The upper-left and in the lower-right quadrants focus on cases in which the two tests disagree.
Dots in the lower left quadrant (close to the origin) correspond to series where Granger-causality is found by both traditional and robust tests. Dots in the upper right quadrant correspond to series where no Granger-causality is found by either traditional tests or by Granger-causality tests robust to instabilities. The dotted lines represent p-values of 5%, and divide the picture in four quadrants. Each dot in the figure corresponds to one of the series that we consider. Panel A in Figure 21.1 reports results for forecasting inflation and Panel B for output growth. To get a sense of how important instabilities are, Figure 21.1 reports scatterplots of the p-values of the traditional Granger-causality tests (on the horizontal axis) and of Rossi’s (2005) Granger-causality test robust to instabilities (on the vertical axis). For example, only selected interest rates Granger-cause inflation, although almost all interest rates do Granger-cause inflation if we take instabilities into account. Second, in several cases traditional Granger-causality tests do not find predictive ability whereas Rossi’s (2005) test does, thus indicating that there is Granger-causality once instability has been taken into account. For example, inflation does not Granger-cause output growth in most countries, but some measures of unemployment do. The table show which predictors are most useful. First, the traditional Granger-causality tests show that many of the predictors that we consider do help predicting both inflation and output growth since, in most cases, the p-values are close to zero.
56 The table shows two interesting empirical results. For each of the predictors that we consider (reported in the first column), transformed in several possible ways (described in the second column), and for each of the countries that we consider (described in the remaining columns), the table reports p-values of traditional Granger-causality tests (upper row) and p-values of Rossi’s (2005) Granger-causality test robust to instabilities (lower row, in parentheses), QLR T ∗, defined in Eq. Table 1 reports results of Granger-causality tests as well as Rossi’s (2005) Granger-causality tests robust to instabilities. Barbara Rossi, in Handbook of Economic Forecasting, 2013 4.1.1 Do Traditional Macroeconomic Time Series Granger-Cause Inflation and Output Growth?
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