Central banks have different objectives in the short and long run. Governments operate simultaneously at different timescales. Many economic processes are the result of the actions of several agents, who have different term objectives. Therefore, a macroeconomic time series is a combination of components operating on different frequencies. Several questions about economic time series are connected to the understanding of the behavior of key variables at different frequencies over time, but this type of information is difficult to uncover using pure time-domain or pure frequency-domain methods.To our knowledge, for the first time in an economic setup, we use cross-wavelet tools to show that the relation between monetary policy variables and macroeconomic variables has changed and evolved with time. These changes are not homogeneous across the different frequencies.

A body of work using the continuous wavelet transform has been growing. We provide a self-contained summary on its most relevant theoretical results, describe how such transforms can be implemented in practice, and generalize the concept of simple coherency to partial wavelet coherency and multiple wavelet coherency, moving beyond bivariate analysis. We also describe a family of wavelets, which emerges as an alternative to the popular Morlet wavelet, the generalized Morse wavelets. A user-friendly toolbox, with examples, is attached to this paper. ∞ −∞ |x(t)| 2 dt is usually referred to as the energy of x, the space L 2 (R) is known as the space of finite energy functions.We use the convention g(t) ↔ G(ω) to denote a Fourier pair, that is, we denote by the corresponding capital letter the Fourier transform of a given function. Hence, if ψ(t) ∈ L 2 (R), (ω) will denote its Fourier transform, here defined as (ω) := ∞ −∞ ψ(t)e −iωt dt. With this definition, ω is an angular (or radian) frequency. The relation to the more common Fourier frequency is given by f = ω 2π .

We use (cross) wavelet analysis to decompose the time-frequency effects of oil price changes on the macroeconomy. We argue that the relation between oil prices and industrial production is not clear-cut. There are periods and frequencies where the causality runs from one variable to the other and vice-versa, justifying some instability in the empirical evidence about the macroeconomic effects of oil price shocks. We also show that the volatility of both the inflation rate and the industrial output growth rate started to decrease in the decades of 1950 and 1960.

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a b s t r a c tWe assess the relation between the yield curve and the macroeconomy in the U.S. between 1961 and 2011. We add to the standard parametric macro-finance models, as we uncover evidence simultaneously on the time and frequency domains. We model the shape of the yield curve by latent factors corresponding to its level, slope and curvature. The macroeconomic variables measure real activity, inflation and monetary policy. The tools of wavelet analysis, the set of variables and the length of the sample allow for a thorough appraisal of the time-variation in the direction, intensity, synchronization and periodicity of the yield curve-macroeconomy relation.

This paper offers a plausible explanation for the close link between oil prices and aggregate macroeconomic performance in the 1970s. Although this link has been well documented in the empirical literature, standard economic models are not able to replicate this link when actual oil prices are used to simulate the models. In particular, standard models cannot explain the depth of the recession in 1974-75 and the strong revival in 1976-78 based on the oil price movements in that period. This paper argues that a missing multiplier-accelerator mechanism from standard models may hold the key. Copyright 2007 The Ohio State University.

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We show that dependence on foreign energy can increase economic instability by raising the likelihood of equilibrium indeterminacy, hence making it easier for fluctuations driven by self-fulfilling expectations to occur. This is demonstrated in a standard neoclassical growth model. Calibration exercises, based on the estimated share of imported energy in production for several countries, show that the degree of reliance on foreign energy for many countries can easily make an otherwise determinate and stable economy indeterminate and unstable.