Analyzing U.S. GDP-Debt-Inflation Linkages in the Time-Frequency Domain

We add to the discussion on the role of debt-to-GDP and inflation on the U.S. real GDP per capita and its growth rate during the period from 1966 to 2022. We use Global Wavelet Power Spectrum, Multivariate Coherency and Partial Coherency, Phase-Difference and Gain. This framework enables us to work with heteroskedastic and non-stationary data. We find complex phasic and anti-phasic relations between business and growth cycles, versus debt and inflation. To summarize, most relationships (zero to 4-year frequency period) between debt and GDP per capita are characterized by anti-phasic leadership of debt cycles and the relationship between inflation and growth (zero to more than 8-year frequency period) it is also strongly characterized by the anticipation of inflationary cycles in the opposite direction. We also have interesting findings over NBER recessions, and our most recent evidence captures the effects of the pandemic