Causal relationships between inflation and inflation uncertainty

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.

A Variance Inequality for Meromorphic Functions Under Exterior Probability

The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses called Exterior probabilities have been investigated. It has been shown that under such probabilities, measurement variance of a measurable function around a 1st order pole on a complex manifold, consists of two separable parts - one that decreases with diminishing scale of the lenses, and the other that increases. It has been discussed how this framework can lend mathematical support to ideas of non-deterministic uncertainty prevalent at a quantum scale. In fact, the aforementioned variance decomposition allows for a minimum possible variance for such a system irrespective of how close the measurements are. This inequality is structurally similar to Heisenberg uncertainty relationship if one considers energy/momentum to be a meromorphic function of a complex spacetime.

The Relational Turbulence Model: A Meta-Analytic Review

A series of 27 meta-analyses was conducted to synthesize theoretical predictions, to date, of the relational turbulence model (RTM), which has informed relational turbulence theory (RTT). In line with theorized predictions, 12 random-effects meta-analyses (k = 9–15; n = 1,395–5,493) confirmed that RTM variables (i.e., self uncertainty, partner uncertainty, relationship uncertainty, and partner interference), on average, correlated with topic avoidance, depressive symptoms, and relationship satisfaction. An additional 15 random-effects meta-analyses (k = 4–41; n = 930–8,975) were conducted to pool an average correlation matrix among self uncertainty, partner uncertainty, relationship uncertainty, partner interference, partner facilitation, and relational turbulence. This pooled correlation matrix was used to test a meta-analytic structural equation model of the RTM commonly specified in the literature. Global and local fit statistics indicated the meta-analytic data fit the RTM well. Collectively, these results offer empirical and theoretical evidence for the RTM across nearly 2 decades of research and provide insights for future scholarship guided by the axioms and propositions of RTT.

Abstract-algebraic interpretations of the energy–time uncertainty relation prove quantization of time

In modern physics, the general theory of relativity (GTR) successfully predicts the vital structure of gravity. The GTR confirmed that gravity is the distortion of four-dimensional spacetime [Formula: see text] by massive bodies. Such a prediction of the GTR is one of the vital successes towards the development goals of modern physics. Though, the central foundation for all the calculations of the GR is the hypothesis of continuum spacetime. In this paper, the author introduces a theorem of the quantum mechanical theory of time (QMT) to test whether the metric time is discrete or continuous. To prove the theorem, the author applied the set theory of cardinal numbers on the energy–time uncertainty relationship. The proof of the theorem confirmed that the metric time is discrete, and has an intrinsic quantum nature. The result implied that the continuum spacetime assumption of the GTR is found fundamentally erroneous. Therefore, spacetime is discrete and needs to be analyzed by the principles of quantum mechanics (QM).

A Longitudinal Test of Relational Turbulence Theory

Relational turbulence theory (RTT) proposes causal relationships across cognitive, emotional and communicative variables. Although many tenets of this theory have been tested individually, there has not yet been a comprehensive, predictive examination of RTT. Using structural equation modelling, this study longitudinally tested several propositions and axioms of RTT. Results are largely in line with many of RTT's predictions. Time 1 relational uncertainty predicted time 2 biased cognitions. Time 1 facilitation from a partner predicted time 2 negative emotions. Negative emotions cross-sectionally related to both the enactment and valence of relational communication episodes. Relational turbulence theory's proposed feedback loop received partial support, such that time 1 communication valence (but not engagement) predicted time 2 partner uncertainty, relationship uncertainty and partner facilitation. Results are discussed in terms of theory expansion and refinement.