The Causal Relationships between Inflation and Inflation Uncertainty

Since the publication of Friedmanís (1977) Nobel lecture, the relationship between the mean function of the inflation stochastic process and its uncertainty has been the subject of much research. Friedman postulated that high inflation causes increased inflation uncertainty. Ball (1992) produces macroeconomic theory that could justify that causality. But other researchers have found the converse causality, from increased inflation uncertainty to increased mean inflation, and postulated macroeconomic theory that could support their views. In addition, some researchers have found inverse correlation between mean inflation and inflation volatility with causation in either direction. These controversies are important, since they have different implications for economic theory and policy. We conduct a systematic econometric study of the relationship among the first two moments of the inflation stochastic process using state of the art approaches. We propose a time-varying inflation uncertainty measure based on stochastic volatility to take into account unpredictable shocks. Further, we extend previous related literature by providing a new econometric specification of this relationship using two semi-parametric approaches: the frequency evolutionary co-spectral approach and the 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 related literature always focused on the US data, our study explores this relationship for five major developed and emerging countries (the US, the UK, the Euro area, South Africa, and China) over the last five decades to investigate robustness of our inferences and investigate sources of prior inconsistencies in inferences 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 depict a significant relationship between inflation and inflation uncertainty that varies with time and frequency and offer an improved comprehension of the ambiguous inflation versus inflation uncertainty relationship. This relationship seems positive in the short and medium terms during stable periods, confirming the Friedman-Ball theory, while it is negative during crisis periods. In addition, 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.