We use univariate GARCH models of inflation and output growth and monthly data for the G7 covering the 1957e2000 period to test for the causal effect of real and nominal macroeconomic uncertainty on inflation and output growth, and the effect of inflation on inflation uncertainty. Our evidence supports a number of important conclusions. First, inflation is a positive determinant of uncertainty about inflation. Second, output growth uncertainty is a positive determinant of the output growth rate. Third, there is mixed evidence regarding the effect of inflation uncertainty on inflation and output growth. Hence, uncertainty about the inflation rate is not necessarily detrimental to economic growth. Finally, there is not much evidence supporting the hypothesis that output uncertainty raises inflation.

We use a bivariate generalized autoregressive conditionally heteroskedastic (GARCH) model of inflation and output growth to examine the causality relationship among nominal uncertainty, real uncertainty and macroeconomic performance measured by the inflation and output growth rates. The application of the constant conditional correlation GARCH(1,1) model leads to a number of interesting conclusions. First, inflation does cause negative welfare effects, both directly and indirectly, i.e. via the inflation uncertainty channel. Secondly, in some countries, more inflation uncertainty provides an incentive to Central Banks to surprise the public by raising inflation unexpectedly. Thirdly, in contrast to the assumptions of some macroeconomic models, business cycle variability and the rate of economic growth are related. More variability in the business cycle leads to more output growth.

The relationship between inflation and inflation uncertainty is investigated in six European Union countries for the period 1960–99. Exponential generalized autoregressive conditional heteroscedasticity models are used to generate a measure of inflation uncertainty and then Granger methods are employed to test for causality between average inflation and inflation uncertainty. In all the European countries except Germany, inflation significantly raises inflation uncertainty as predicted by Friedman. However, in all countries except the UK, inflation uncertainty does not cause negative output effects, implying that a common European monetary policy applied by the European Central Bank might lead to asymmetric real effects via the inflation uncertainty channel. Less robust evidence is found regarding the direction of the impact of a change in inflation uncertainty on inflation. In Germany and the Netherlands, increased inflation uncertainty lowers inflation, while in Italy, Spain and, to a lesser extent, France increased inflation uncertainty raises inflation. These results are generally consistent with the existing rankings of central bank independence.

This paper considers a formulation of the extended constant or time-varying conditional correlation GARCH model that allows for volatility feedback of either the positive or negative sign. In the previous literature, negative volatility spillovers were ruled out by the assumption that all the parameters of the model are nonnegative, which is a sufficient condition for ensuring the positive definiteness of the conditional covariance matrix. In order to allow for negative feedback, we show that the positive definiteness of the conditional covariance matrix can be guaranteed even if some of the parameters are negative. Thus, we extend the results of Nelson and Cao (1992) and Tsai and Chan (2008) to a multivariate setting. For the bivariate case of order one, we look into the consequences of adopting these less severe restrictions and find that the flexibility of the process is substantially increased. Our results are helpful for the model-builder, who can consider the unrestricted formulation as a tool for testing various economic theories.

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