2. Data

Data on seasonally adjusted headline consumer price indices (CPIs) come from Datastream and national sources. We use data on professionals’ survey-based CPI inflation expectations. These are taken from Consensus Economics surveys for next-year CPI inflation expectations.

Data on output gaps (as a percentage of potential Gross Domestic Product (GDP)) were obtained from the Organisation for Economic Co-operation and Development (OECD), and linearly interpolated from annual data. Nominal effective exchange rate indices (broad indices, quarterly averages) are taken from the Bank for International Settlements (BIS), where an increase indicates an appreciation of the domestic currency. Brent oil prices (quarterly averages, US dollar per barrel) are from Datastream.

We consider the following 36 economies: the OECD economies Austria, Australia, Belgium, Canada, Chile, the Czech Republic, Denmark, Estonia, euro area, Finland, France, Germany, Great Britain, Greece, Hungary, Ireland, Israel, Italy, Japan, Latvia, Lithuania, Mexico, the Netherlands, Norway, New Zealand, Poland, Portugal, Slovakia, Slovenia, South Korea, Spain, Sweden, Switzerland and the United States, and the OECD candidate countries Bulgaria and Romania. The sample period is from 2000Q1 to 2021Q1 at quarterly frequency.

3. Method and results

To study the effects of inflation expectations on inflation, we estimate the following New-Keynesian Phillips curve based on the studies by Jasova et al. (Reference Jasova, Moessner and Takats2019, Reference Jasova, Moessner and Takats2020), using a panel of 36 economies:

(1) $$ {\unicode{x03C0}}_{\mathrm{it}}=\unicode{x03B8}\;{\pi}_{it}^e+\unicode{x03C1}\;{\unicode{x03C0}}_{\mathrm{it}-1}+\unicode{x03D5}\;{outputgap}_{it}+\mu\;\Delta {NEER}_{it}+\unicode{x03BB}\;{\unicode{x03C0}}_{\mathrm{t}}^{\mathrm{oil}}+{\alpha}_i+{\varepsilon}_{it.} $$

where $ {\unicode{x03C0}}_{\mathrm{it}} $ denotes quarter-on-quarter (q/q) seasonally adjusted CPI inflation at annualised rates (saar) in percent, calculated from log differences in quarterly seasonally adjusted CPIs in country $ i $ at time t; $ {outputgap}_{it} $ denotes the output gap; $ {\pi}_{it}^e $ denotes next-year CPI inflation expectations from Consensus Economics surveys, year-on-year (y/y) in percent; $ \Delta {NEER}_{it} $ is the q/q change in the nominal effective exchange rate in percent, calculated from the log change in the nominal effective exchange rate, with an increase indicating an appreciation of the currency; $ {\unicode{x03C0}}_{\mathrm{t}}^{\mathrm{oil}} $ denotes q/q oil price inflation (annualised) calculated from log-differences in quarterly oil prices. Finally, $ {\alpha}_i $ are country fixed effects to control for observed and unobserved country heterogeneity. We use robust standard errors clustered at the country level. Equation (1) is our baseline specification.

For robustness, we also estimate the following specification, where we replace oil price changes by time fixed effects, $ {\beta}_{\mathrm{t}} $ , in order to control for all observed and unobserved variation in common global factors,

(2) $$ {\unicode{x03C0}}_{\mathrm{it}}=\unicode{x03B8}\;{\pi}_{it}^e+\rho\;{\unicode{x03C0}}_{\mathrm{it}-1}+\unicode{x03D5}\;{outputgap}_{it}+\mu\;\Delta {NEER}_{it}+{\alpha}_i+{\beta}_t+{\varepsilon}_{it.} $$

For robustness, we also use the system generalised method of moments (GMMs) following Arellano and Bover (Reference Arellano and Bover1995) and Blundell and Bond (Reference Blundell and Bond1998) for panel data with endogenous explanatory variables.

Our Phillips curve estimates for Equations (1) and (2) are shown in Table 1. We can see that in both specifications, the coefficient on the output gap is significantly positive, implying that in our cross-country, dynamic panel setting the New-Keynesian Phillips curve is “alive and well” (see also Coibion and Gorodnichenko, Reference Coibion and Gorodnichenko2015b). We can also see that the coefficient on lagged inflation is significantly positive, so that our dynamic panel specification is appropriate. We find that inflation expectations have a significantly positive effect on inflation at the 1% significance level, with a coefficient which is similar for both specifications, at 1.17 and 1.15, respectively. Oil prices have a significantly positive effect on inflation at the 1% level. Moreover, exchange rate depreciations lead to significantly higher inflation, as would be expected, also at the 1% significance level in both specifications.

Table 1.

CPI inflation versus inflation expectations

Note: Fixed effects panel estimation; sample period: 2000Q1-2021Q1. ***/**/*denote statistical significance at 1/5/10% confidence level. Robust standard errors clustered at the country level.

We next study whether the effects of inflation expectations on inflation depend on the inflation environment. We do so by adding an interaction term of inflation expectations with inflation lagged two periods, according toFootnote ³

(3) $$ {\unicode{x03C0}}_{\mathrm{it}}=\unicode{x03B8}\;{\pi}_{it}^e+\unicode{x03C1}\;{\unicode{x03C0}}_{\mathrm{it}-1}+\unicode{x03D5}\;{outputgap}_{it}+\mu\;\Delta {NEER}_{it}+\unicode{x03B3}\;{\pi}_{it}^e\;{\unicode{x03C0}}_{\mathrm{it}-2}+\unicode{x03BB}\;{\unicode{x03C0}}_{\mathrm{t}}^{\mathrm{oil}}+{\alpha}_i+{\varepsilon}_{it.} $$

The results for Equation (3) are shown in Table 2. For robustness, we also show the corresponding results in Table 2 when replacing oil price changes by time fixed effects in Equation (3). For both specifications, the effect of inflation expectations remains significantly positive at the 1% level. We find that the coefficient on the interaction term of inflation expectations with inflation lagged two periods is significantly positive at the 1% significance level, with a magnitude which is similar for both specifications, at 0.018 and 0.019, respectively. These results imply that inflation expectations have a stronger effect on inflation when inflation is higher. The coefficients on the remaining variables continue to be significant and have the expected signs.

Table 2.

CPI inflation versus inflation expectations: with interaction term

Note: Fixed effects panel estimation; sample period: 2000Q1-2021Q1. ***/**/*denote statistical significance at 1/5/10% confidence level. Robust standard errors clustered at the country level.

For robustness, we also estimate Equations (1) to (3) using system GMM. The corresponding results are shown in Table 3, and we can see that the results are generally robust to using this method, both when including and when excluding the interaction term of inflation expectations with inflation lagged two periods.

Table 3.

CPI inflation versus inflation expectations: system GMM estimation

Note: System GMM estimation using the studies by Arellano and Bover (Reference Arellano and Bover1995) and Blundell and Bond (Reference Blundell and Bond1998) dynamic panel estimator; sample period: 2000Q1-2021Q1. ***/**/*denote statistical significance at 1/5/10% confidence level. Robust standard errors.

^a Reports p-values for the null hypothesis that the instruments used are not correlated with the residuals.

^b Reports p-values for the null hypothesis that the errors in the first difference regression exhibit no second-order serial correlation.

We therefore find evidence that inflation expectations have a significantly larger effect on inflation when inflation is high. This suggests that second-round effects via the effects of higher inflation expectations on inflation are more of a problem in a high-inflation environment.

3.1. Quantile regressions

In order to study whether the effects of inflation expectations on inflation depend on the level of inflation, we next also estimate quantile regressions for the specification of Equation (1), at the 10th, 25th (lower quartile), 50th (median), 75th (upper quartile) and 90th percentiles. This allows us to determine whether the effects of inflation expectations on inflation differ when inflation is in the upper tail of the inflation distribution, compared with at the median level or in the lower tail of the distribution.

Quantile regressions weigh observations in the neighbourhood of the quantile of interest more heavily, and weigh other observations less heavily, corresponding to a reduction in sample size. We adopt the quantiles‐via‐moments estimation method of Machado and Santos Silva (Reference Machado and Santos Silva2019), using their xtqreg command in Stata, as in the study by Kiley (Reference Kiley2021).

The results of the quantile regressions for Equation (1) are shown in Table 4. We can see that for the median regression (50th percentile), the coefficient of inflation expectations is similar to that for the mean fixed effects panel regression shown in Table 1, at 1.15 compared with 1.17, and it is also significant at the 1% level. Figure 1 shows the results for the coefficients of inflation expectations for q/q inflation by percentile together with 90% confidence intervals. We can see that the coefficient of inflation expectations on q/q inflation is higher at larger percentiles, but not significantly so at the 10% level. For each of the percentiles, the coefficients on the other variables all remain significant and with the expected signs.

Table 4.

CPI inflation (q/q) versus inflation expectations: quantile regressions

Note: Fixed effects panel estimation; sample period: 2000Q1-2021Q1. ***/**/*denote statistical significance at 1/5/10% confidence level.

Figure 1.

Effects of inflation expectations on inflation (q/q) by percentile. Notes: Responses of CPI inflation to 1 percentage point increase in inflation expectations, in percent. Estimates using quantile regressions based on equation (1). Effect on CPI inflation (q/q saar), with 90% confidence intervals.

In order to study the effects of inflation expectations on inflation over a longer horizon, we also estimate these quantile regressions when using local projections based on the study by Jordà (Reference Jordà2005),

(4) $$ {\unicode{x03C0}}_{\mathrm{it};\mathrm{h}}=\unicode{x03B8}\;{\pi}_{it}^e+\unicode{x03C1}\;{\unicode{x03C0}}_{\mathrm{it}-1}+\unicode{x03D5}\;{outputgap}_{it}+\mu\;\Delta {NEER}_{it}+\unicode{x03BB}\;{\unicode{x03C0}}_{\mathrm{t}}^{\mathrm{oil}}+{\alpha}_i+{\varepsilon}_{it.} $$

where $ {\unicode{x03C0}}_{\mathrm{it};\mathrm{h}} $ denotes the seasonally adjusted annualised CPI inflation rate at time t over h quarters in country $ i $ at time t, calculated from the log-difference between the CPI index at time t-1+h and the CPI index at time t-1. Here, h=1 corresponds to the q/q seasonally adjusted annualised inflation rate $ {\unicode{x03C0}}_{\mathrm{it}} $ used above, and h=4 corresponds to year-on-year (y/y) inflation.

The results of the quantile regressions at the yearly horizon (h = 4) for Equation (4) are shown in Table 5. Also shown in column I of Table 5 for comparison are the results of the mean fixed effects panel regression for Equation (4). We can see that for the median regression, the coefficient on inflation expectations is again similar to that for the mean fixed effects panel regression, at 0.75 compared with 0.76, and it is also significant at the 1% level.

Table 5.

CPI inflation (y/y) versus inflation expectations

Note: Fixed effects panel estimation; sample period: 2000Q1-2021Q1. ***/**/*denote statistical significance at 1/5/10% confidence level.

Figure 2 shows the results for the coefficients of inflation expectations for y/y inflation by percentile together with 90% confidence intervals. We can see that the coefficients of inflation expectations are larger at higher percentiles of the inflation distribution. We find that at the yearly horizon, the coefficient of inflation expectations is significantly larger at the 10% level for the upper tail of the inflation distribution (the 90th percentile) than for the lower tail of the inflation distribution (the 10th percentile). Again, for each of the percentiles, the coefficients on the other variables all remain significant and with the expected signs. These results therefore also suggest that second-round effects via the effects of higher inflation expectations on inflation are more of a problem in a high-inflation environment.

Figure 2.

Effects of inflation expectations on inflation (y/y) by percentile. Notes: Responses of CPI inflation to 1 percentage point increase in inflation expectations, in percent. Estimates using quantile regressions based on equation (4). Effect on CPI inflation (y/y), with 90% confidence intervals.