Time–frequency relationship between US inflation and inflation uncertainty: evidence from historical data

Abstract

We provide new evidence on the relationship between inflation and its uncertainty in the United States on an historical basis, covering the period from 1775 to 2014. First, we use a bounded approach for measuring inflation uncertainty, as proposed by Chan et al. (2013), and compare the results with the Stock and Watson (2007) and Chan (2015) methods. Second, we employ the wavelet methodology to analyze the comovements and causal effects between the two series. Our results provide evidence of a relationship between inflation and its uncertainty that varies across time and frequency. First, we show that in the medium and long runs, the Freidman-Ball hypothesis holds with a bounded measure of uncertainty, while if the Stock and Watson (2007) measure of uncertainty is used, the Cukierman-Meltzer reasoning prevails. Therefore, the findings are sensitive to the way inflation uncertainty is computed. Second, we discover mixed evidence about the inflation-uncertainty nexus in the short run, findings that explain the mixed results reported to date in the empirical literature.inflation precedes greater uncertainty in some periods. In this situation, however, the monetary authority contracts the money supply growth rate to control welfare loses, which causes inflation to fall.Although they differ in the direction of causality, the above-mentioned hypotheses all received validation by empirical studies. The mixed results documented by the empirical literature reflect differences in methodologies (linear or non-linear models), in the measures of inflation uncertainty (see Cukierman and Meltzer, 1986), or in the time horizon for the inflation expectations (see Pourgerami and Maskus, 1987).Against this background and to shed further light on the relationship between inflation and its uncertainty, we make four contributions to the existing literature. First, given the validation of different competing hypothesis by previous studies, we posit a non-linear link between the inflation rate and its uncertainty. Indeed, Kim (1993) shows that regime switching may provide the key element in explaining inflation uncertainty. Hypothesizing a high and low inflationary regime, however, seems too simplistic and arbitrary. Moreover, a strict focus on the time domain ignores the importance of the frequency-varying properties of inflation and its uncertainty. Fluctuations in the time profile of inflation uncertainty may differently affect policy decisions and consumers' behavior in the short run, compared with the long run (Barerro et al., 2017). In addition, common models assume stationary time series, which is not always the case. Therefore, to address these limitations, we propose a new analysis based on the wavelet method that combines the frequency and time domains. As far as we know, Bouoiyour and Selmi (2014) wrote the only paper that investigates the inflation-uncertainty nexus using the Maximal Overlap Discrete Wavelet Transform (MODWT) and a series of non-linear causality tests for Egypt. Our study differs in that we employ the Cont...

Causal relationships between inflation and inflation uncertainty

“…Overall, previous studies do not provide unanimous conclusions about the inflation-IU relationship, and their findings vary with the methodologies, countries, and samples under consideration. However, all previous studies, except Albulescu et al (2019) as shown in Table 3, tested this relationship using parametric models, which imply restrictions on specifying the relationship between inflation and uncertainty. Additionally, the sign and size of the IU effect on inflation depends on the a priori level of the central bank's commitment to inflation.…”

Output, Uncertainty and Fuel Prices in the EU Countries

“…In addition, the fuel price levels and not their increases have a positive impact on the economic growth. (1) is the first lag of the dependent variable; (ii) dummy variables are considered strictly exogenous; (iii) *, **, *** means significance at 10 %, 5 % and 1 %; (iv) iinflation rate, iuinflation uncertainty, yuoutput uncertainty, fuel1gasoline retail prices; dum_f1×fuel1interaction dummy between fuel1 and dum_f1 (which takes value 1 if the gasoline price increases in t compared to t-1 and 0 otherwise), cintercept. (1) is the first lag of the dependent variable; (ii) dummy variables are considered strictly exogenous; (iii) *, **, *** means significance at 10 %, 5 % and 1 %; (iv) iinflation rate, iuinflation uncertainty, yuoutput uncertainty, fuel2diesel retail prices; dum_f2×fuel2interaction dummy between fuel2 and dum_f2 (which takes value 1 if the diesel price increases in t compared to t-1 and 0 otherwise), c -intercept.…”

“…Whereas the link between inflation and its uncertainty is intensively tested with opposite findings by the early literature (e.g. Ungar and Zilberfarb, 1993), and by noteworthy recent papers (Albulescu et al, 2019), much less attention is paid to the impact of inflation uncertainty on economic output. The few recent studies in this area underline, in general, a negative impact of inflation uncertainty on the economic output, but several works find no significant relationship or, on contrary, report a positive influence of uncertainty on the economic output.For example, using a time-frequency approach and historical data, Albulescu A recent strand of the literature does not directly focus on the Friedman's (1977) second hypothesis but investigate the relationship between economic policy uncertainty (EPU) and economic output.…”

“…While most of these studies document a negative impact of inflation uncertainty on the output (e.g. Albulescu et al, 2019), other papers (e.g. Pintilescu et al, 2014) report inconclusive results.…”

“…Oil prices might have either a direct effect on economic growth influencing consumption and investment, or an indirect effect, influencing the production cost, the general prices, but also the inflation uncertainty. 1 As far as we know, Bhar and Mallik (2013) are the only scholars who consider the role of international oil prices in this equation. However, they check the impact of international oil price shocks and use dummy variables to see how jumps in oil prices impact the inflation and economic activity.…”