Money Growth & Inflation: Long-Run Evidence

The study's core focus is the long-run relationship between money growth and inflation, examined over the past two centuries. Cross-spectral coherence at the zero frequency (ω=0), representing long-term trends, is consistently high (close to one) across the US, UK, and several other nations. This indicates a strong, stable link where long-run money growth significantly explains long-run inflation variation. However, the cross-spectral gain at ω=0 shows substantial variation, often below unity. A unitary gain, consistent with the quantity theory of money, is observed only during inflationary periods such as World War I and the Great Inflation, notably absent during World War II. The post-1980s disinflation saw a consistent drop in the gain, with only one exception (Sweden's M3 aggregate). The research utilizes various monetary aggregates (M0, M1, M2, M3) and multiple countries to ensure robustness and broad applicability of the findings. The introduction of the concept of cross-spectral gain and coherence, and its connection to the quantity theory of money, sets the stage for the further investigation of the causes behind the observed variations.

The study employs cross-spectral analysis, a frequency-domain method providing precise numerical estimates of coherence and gain. The choice of this methodology is justified in contrast to band-pass filtering, which lacks the precision to quantitatively assess uncertainty in the relationship between money growth and inflation. The analysis considers both the frequency at ω=0 and a frequency band beyond 30 years, providing a comprehensive view of long-run dynamics. Data used include high-frequency series from the US and the UK (pre-World War I data). The specific data sources include the NBER Historical Database, FRED (Federal Reserve Economic Data), publications like Friedman and Schwartz (1970), and the Office for National Statistics (ONS). The analysis handles diverse monetary aggregates (M0, M1, M2, M3, M4) and various price indices (CPI, wholesale price index, GNP deflator, GDP deflator), spanning several decades, carefully adjusted for seasonality and converted to quarterly or annual data where necessary. The explanation of the methodology strengthens the study's credibility and provides context for the reliability of the obtained results.

Initial observations reveal a surprisingly stable long-run correlation between money growth and inflation, even across vastly different monetary regimes (from the Gold Standard to inflation targeting). This initially suggests a ‘structural’ relationship, hardwired into the economy. However, the authors caution against over-interpreting this using solely band-pass filters, highlighting the limitations of such techniques concerning uncertainty estimation. The analysis focuses on the US, UK, Norway, Australia, and Portugal, which show a near one-to-one correlation. Others (Switzerland, Italy, Netherlands) show some divergence. The study shifts to cross-spectral methods to calculate precise numerical gain and coherence estimates. This meticulous approach allows for more sophisticated and reliable results than previously possible, moving beyond simple visual correlations observed in time series graphs. This section sets the stage for more detailed analysis and interpretations, acknowledging and addressing potential limitations of earlier observational approaches.

The study investigates alternative explanations for the observed patterns, including those involving monetary policy changes. Under monetary policy determinacy, the gain and coherence are relatively unaffected by systematic policy changes, while indeterminacy is associated with lower values of both. The observed differing patterns between gain and coherence make the monetary policy explanation unlikely. Another possibility, explored in line with Lucas (1988) and Reynard (2006), involves systematic velocity shifts due to Fisherian interest rate movements. This too fails to adequately account for the observed data. The section concludes by introducing the use of rolling samples (25 years) to account for the time-varying nature of the relationship. The use of rolling sample estimates is justified by the unfeasibility or lack of established confidence intervals in alternative methods like evolutionary spectral analysis. This meticulous examination of alternative explanations demonstrates rigorous methodology and carefully addresses potential criticisms before proposing the core explanatory mechanism.

The paper initially explores whether changes in monetary policy can explain the observed variations in the cross-spectral gain between money growth and inflation. The analysis considers scenarios of both determinacy and indeterminacy within monetary policy frameworks. Under determinacy, the gain and coherence at zero frequency are largely unaffected by systematic monetary policy changes. In contrast, indeterminacy is typically associated with lower values of both gain and coherence. However, this indeterminacy explanation is deemed insufficient. It fails to account for the different patterns observed in the two cross-spectral statistics (gain and coherence) and relies on the implausible assumption that more stable monetary regimes (like the Gold Standard or the post-1980s period) were characterized by indeterminacy, while the Great Inflation period was characterized by determinacy—a notion most macroeconomists would likely find unconvincing. Therefore, the authors conclude that changes in systematic monetary policy alone cannot explain the observed fluctuations in the cross-spectral gain.

Given the inadequacy of monetary policy explanations, the paper proposes an alternative mechanism based on the interplay of velocity shocks and infrequent inflationary upsurges. This hypothesis, consistent with Estrella and Mishkin (1997), suggests that under normal, stable monetary regimes, velocity shocks predominantly impact the cross-spectral gain, causing it to be comparatively lower than the coherence. Infrequent inflationary upsurges (like those associated with World War I and the Great Inflation) temporarily mask the effects of these velocity shocks by increasing both gain and coherence toward one. These upsurges ‘swamp’ the noise introduced by velocity growth, temporarily revealing the underlying one-to-one relationship between money growth and inflation (associated with the quantity theory of money) which would otherwise remain hidden in the data. This mechanism offers a plausible explanation for the observed patterns of low gain and high coherence in periods of low and stable inflation.

To validate the velocity shock and inflationary outburst hypothesis, the researchers utilize estimated Dynamic Stochastic General Equilibrium (DSGE) models. These models are calibrated using Bayesian estimates for the Euro area and the United States, focusing on full-sample periods to capture the long-run dynamics of the phenomena under investigation. Simulations using these DSGE models demonstrate that velocity shocks have a disproportionately larger impact on the gain than on the coherence, leading to comparatively low gains at zero frequency under low and stable inflation. Conversely, introducing infrequent, large inflationary episodes similar to historical events (like the Great Inflation) demonstrates a marked increase in both gain and coherence toward one. The simulations effectively reproduce the empirical patterns observed in the data, lending strong support to the proposed mechanism. This model-based validation strengthens the paper's conclusions about the underlying drivers of cross-spectral gain fluctuations.

The study utilizes cross-spectral estimates for rolling samples, specifically 25-year windows, to analyze time variation in the relationship between money growth and inflation at very low frequencies. This approach is chosen because alternative methods are deemed either unfeasible or lack established methods for calculating confidence intervals. 'Evolutionary' spectral analysis, while producing similar results, relies on asymptotic theory for confidence intervals, which are known to have poor coverage in traditional spectral analysis. The use of bootstrapping for confidence intervals, absent in evolutionary spectral analysis, is a key reason for choosing rolling samples. This methodological choice ensures greater reliability and accuracy in analyzing the time-varying nature of the economic relationship. The explanation of the rationale for selecting this specific methodology enhances the transparency and credibility of the research.

Empirical evidence using rolling samples reveals consistent high coherence (close to one) between money growth and inflation for most countries and monetary aggregates (M0, M1, M2, M3, M4), particularly in the post-World War II era. The exception is Italy's M2. A hump-shaped pattern around the Great Inflation is evident in the mass of the bootstrapped distribution exceeding 0.99. For the UK, coherence is uniformly high based on the monetary base, except for the early 20th century and the period between WWII and the early 1960s. Results using M3 show two periods of significantly lower coherence. Canada's results mirror those of the US, with uniformly high coherence and a hump-shaped gain around the Great Inflation, followed by a decline. Japan and the Euro area also display remarkably high coherence, while the gain decreases post-Great Inflation. Sweden shows minimal time variation in both gain and coherence. Norway exhibits a weaker coherence between the 1940s and 1960s, but it is uniformly high in recent times. The diversity of the countries and monetary aggregates examined ensures a comprehensive and robust analysis of the phenomena.

The data used are drawn from a variety of sources including the NBER Historical Database, FRED (Federal Reserve Economic Data), publications by Friedman and Schwartz (1970), and the Office for National Statistics (ONS). Specific data series used include various monetary aggregates (M0, M1, M2, M3, M4) and price indices (CPI, wholesale price index, GNP deflator, GDP deflator) for different countries. The time periods covered are extensive, spanning from the 1800s to the early 2000s. The data undergoes careful processing and conversion, including linking various series to create continuous time series. For example, a US quarterly seasonally adjusted M2 series was created by linking the M2 series from Balke and Gordon (1986) with M2SL from FRED. The detailed description of the data and its processing enhances the study's reproducibility and validity. The range of data sets employed reinforces the generality of the results obtained.

The research utilizes Dynamic Stochastic General Equilibrium (DSGE) models to investigate the relationship between money growth and inflation. The structural parameters of the DSGE models are calibrated using Bayesian estimates from Benati (2008) for the Euro area and the United States. The choice to use full-sample estimates from Benati (2008), rather than estimates from more recent, stable periods, is justified because the results obtained are qualitatively similar, and using full-sample estimates allows for a more comprehensive analysis across different monetary regimes. The models incorporate elements such as an intertemporal IS curve, a Phillips curve with indexation to past inflation, and various monetary policy rules (Taylor rule, price level targeting rule, alternative money growth rules). The specific parameterizations are crucial for the model's ability to reproduce the empirical findings regarding the cross-spectral gain and coherence, and the choice of these parameters is carefully explained and justified within the study's context.

The study explores the role of different monetary policy rules in shaping the cross-spectral gain and coherence. The Taylor rule, a widely accepted representation of monetary policy in recent decades, is particularly analyzed. A crucial finding is that a low gain at zero frequency under a Taylor rule necessitates the economy to be in a state of indeterminacy. This creates a significant implication: to explain the observed decrease in the gain after the 1980s disinflation, one would have to believe that the economy was under determinacy during the Great Inflation but shifted to indeterminacy afterward—a proposition deemed highly improbable by most macroeconomists. The analysis of alternative monetary policy rules, like price-level targeting rules, further underscores the limitations of monetary policy alone in fully explaining the observed cross-spectral patterns.

The study uses stochastic simulations of the calibrated DSGE model to analyze the joint impact of velocity shocks and infrequent inflationary outbursts. Simulations are run for 130 years at a quarterly frequency. The model incorporates a velocity shock term, allowing the researchers to investigate its impact on the cross-spectral gain and coherence. The simulation of an infrequent inflationary episode, designed to mimic the Great Inflation, involves modelling trend inflation using a bell curve to capture the temporary nature of the inflationary upsurge. Rolling estimates of gain and coherence are calculated for 25-year windows. The simulations reveal that, consistent with the empirical findings, velocity shocks have a much larger impact on the gain than on the coherence, leading to a low gain despite high coherence under stable inflation regimes. Large, infrequent fluctuations in trend inflation, on the other hand, boost both gain and coherence towards one, thereby temporarily revealing the underlying one-to-one relationship predicted by quantity theory, which is otherwise masked by velocity shocks.