Inflation and monetary dynamics in the USA: a quantity-theory approach

Abstract

In this article we investigate the long-run link between inflation and money growth in the United States since 1960. A measure of the long-run inflation trend is constructed, which bears the interpreation of ‘monetary’ inflation rate and is directly related to the excess nominal money growth process (money growth less output growth), as postulated by the quantity theory. Consistent with the memory characteristics of the series, their fractional integration and cointegration properties are taken into account in empirical modelling. The proposed measure is then compared with several existing measures of ‘core inflation’, aimed at capturing long-run inflation dynamics but unrelated to money growth. The ‘monetary’ long-run inflation rate performs well in out-of-sample forecasting exercises especially over a 2–3-year horizon, yielding valuable information to monetary policymakers.

Notes

¹ Nelson, 2003 provides an insightful discussion of the quantity theory proposition in the context of the recent monetary policy literature.

² When 0 < d < 0.5 the process is stationary long-memory with all autocorrelations positive and decaying towards zero at a (slow) hyperbolic rate.

³ See also Morana (2002, 2004b).

⁴ Note that the same results hold for the case in which the u vector is I(b), with b > 0 and d − b > 0, since Δ ^d u ∼ I(b − d), implying over differencing and hence a null spectral matrix at the zero frequency.

⁵ Since f(0) is of reduced rank k, only k eigenvalues are greater than zero.

⁶ The u _t vector is I(b) when the cointegrating residuals are I(b) or when the largest order of fractional integration of the cointegrating residuals is I(b). Note in fact that the u _t vector is computed as a linear combination of the cointegrating residuals.

⁷ The p-values for the LR test are computed as in Davies (1987) to account for the non-standard asymptotic distribution of the test.

⁸ The finding of no structural change in US inflation contrasts with recent evidence of both long memory and structural change or both structural change and unit root behaviour provided by Bos et al . (1999) and Cook (2005), respectively, who employ monthly data. The analysis of quarterly data also partially contrasts with what obtained using the annual data. In fact, the Kokoszka and Leipus (2000) test points to significant structural breaks in the nominal variables but not in the real variables, while the augmented Engle and Kozicki test points to a spurious break process for output only. On the other hand, the Dolado et al . (2004) test points to spurious structural change for all series. A possible explanation for these findings is that results may be sensitive to the frequency of sampling, and that more reliable conclusions may be drawn from lower frequency data, being structural change associated with infrequent changes in the level of the series.

⁹ Standard errors have been computed assuming that the same asymptotic distribution holding under weak dependence holds also in the case of long memory, i.e. , where m denotes the bandwidth.

¹⁰ The analysis has been carried out also using monthly data, since the temporal aggregation properties of long memory processes warrant that the persistence features of the series are unaffected by the frequency of sampling. The monthly dataset counts 533 observations, a sample size which allows for efficient estimation of the fractional differencing parameter. The results (available from the authors upon request) are fully consistent with those obtained using quarterly data.

¹¹ In order to investigate the impact of possibly neglected structural change on the performance of the estimator, a Monte Carlo exercise has been carried out. This exercise aims to evaluate the consequences of neglecting a break process, as the one detected by the Markov switching model, for the inflation series. The results (available from the authors upon request) suggest that the estimator is not affected by a neglected break process.

¹² The test has been performed in the framework of an ARFIMA-GARCH model. The results are available from the authors upon request.

¹³ A current debate in monetary economics concerns the implications of monetary policy regimes on the endogeneity of the inflation and money growth rates. According to Svensson (2003), nominal money growth would be exogenous relatively to inflation under strict money growth targeting, while inflation would be exogenous relatively to nominal money growth under strict inflation targeting. However, as argued by Nelson (2003), even when money is not used as a policy instrument, monetary policy decisions have an impact on money growth dynamics. For instance, an open market operation which increases the policy rate aiming at a given level of inflation will slow money growth by reducing directly the monetary base. Hence, also in this latter case money growth can be regarded as ‘quantity-side’ indicator of monetary conditions. Then, what explains the final impact on inflation is only a matter of the transmission mechanism. Hence, since we do not aim at investigating the features of the transmission mechanism from the chosen monetary policy instrument to output and eventually inflation, our analysis is valid independently of the monetary policy regime.

¹⁴ To evaluate robustness, the persistence and cointegration properties have been also evaluated for the M1 and M2 monetary aggregates, yielding similar results, available from the authors upon request. Overall, the findings suggest that the long-run linkages are stronger for M3.

¹⁵ As a further robustness check we have carried out a Monte Carlo experiment to evaluate the impact of a neglected break process, as the one detected by the Markov switching model for inflation, on the performance of the estimator. The results suggest that the estimator is robust to neglected breaks, and are available from the authors upon request. Moreover, the estimation of the cointegration relationship has also been carried out on the candidate break-free inflation and excess nominal money growth processes. The evidence is against the break-free processes: in fact, the estimated parameter points to a negative long-run relationship between the two series, suggesting misspecification.