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Since the publication of  Friedman’s (1977)  Nobel lecture, the relationships between the mean function of the inflation stochastic process and its uncertainty, and between inflation uncertainty (IU) and real output growth have been the subject of much research, with some studies justifying this causality and some reaching the opposite conclusion or finding an inverse correlation between mean inflation and inflation volatility with causation in either direction. We conduct a systematic econometric study of the relationships between the first two moments of the inflation stochastic process and between IU and output growth using state-of-the-art approaches and proposes a time-varying inflation uncertainty measure based on stochastic volatility to consider unpredictable shocks. Further, we extend the literature by providing a new econometric specification of this relationship using two semi-parametric approaches: the frequency evolutionary co-spectral approach and continuous wavelet methodology. We theoretically justify their use through an extension of  Ball’s (1992)  model. These frequency approaches have two advantages: they provide the analyses for different frequency horizons and do not impose restriction on the data. While the literature focused on the US data, our study explores these relationships for five major developed and emerging countries/regions (the US, the UK, the euro area, South Africa, and China) over the past five decades to investigate the robustness of our inferences and sources of inconsistencies among prior studies. This selection of countries permits investigation of the inflation versus inflation uncertainty relationship under different hypotheses, including explicit versus implicit inflation targets, conventional versus unconventional monetary policy, independent versus dependent central banks, and calm versus crisis periods. Our findings show a significant relationship between inflation and inflation uncertainty, which varies over time and frequency, and offer an improved comprehension of this ambiguous relationship. The relationship is positive in the short and medium terms during stable periods, confirming the Friedman–Ball theory, and negative during crisis periods. Additionally, our analysis identifies the phases of leading and lagging inflation uncertainty. Our general approach nests within it the earlier approaches, permitting explanation of the prior appearances of ambiguity in the relationship and identifies the conditions associated with the various outcomes.

Causal relationships between inflation and inflation uncertainty