This figure depicts the definitions of inflation forecasts used in various surveys. Panel A shows inflation forecasts for the euro area. Panel B shows inflation forecasts for the United States. The black line on each panel shows the realizations of the year-over-year inflation targeted by the ECB-SPF, defined as $$\pi_{t-12,t} = \ln \frac{P_t}{P_{t-12}}$$, where $$P_t$$ is the price index of the corresponding economy at time $$t$$. The grey line on each panel shows the realizations of the 4-quarter-average over 4-quarter-average inflation targeted by the US-SPF, defined as $$\tilde{\pi}_{t-12,t} = \frac{P_t + P_{t-3} + P_{t-6} + P_{t-9}}{P_{t-12} + P_{t-15} + P_{t-18} + P_{t-21}}$$. The red crosses on each panel indicate the approximated version of the grey line: $$\bar{\pi}_{t-12,t} = 1/4(\pi_{t-21,t-9}+\pi_{t-18,t-6}+\pi_{t-15,t-3}+\pi_{t-12,t})$$. This figure makes two points. First, both panels indicate that the four-quarter-average over four-quarter-average change in prices (grey line) is well approximated by $$\bar{\pi}_{t-12,t}$$ (red crosses). Second, the log change in prices (black line) and the approximation $$\bar{\pi}_{t-12,t}$$ (red crosses) are considerably different, with differences up to 1 percentage point, implying that the raw survey data, even if they target the same horizon, are not necessarily comparable.
This figure shows the original survey data. There are six panels in the figure, organized in two columns and three rows. The Left-hand side panels show the original data for the euro area from the ECB-SPF survey for 1-year 4 years ahead inflation forecasts. The right-hand side panels show the original data for the United States from the Survey of Primary Dealers (US-SPD) for the 5-year 5 years ahead inflation forecasts. Top panels show the point estimates for the inflation forecasts. The middle panels show original cumulative distribution function survey results for inflation rate forecasts along with their Beta-smoothed distribution. The bottom panels show our derived uncertainty measure about inflation rate forecasts. The ECB-SPF sample is from January 1999 to June 2016. The US-SPD sample is from March 2007 to June 2016.
Overall, in the post-crisis period, the raw survey data point out to a decline of long-horizon inflation expectations both in the United States and in the euro area, increase in inflation uncertainty in the euro area, and a decline in inflation uncertainty in the United States.
This figure displays, the factor loadings for conditional expectations and variances for forecast horizons up to 10 years. In the model, conditional expectations are assumed to be driven out by five latent factors and conditional variances -- by two latent factors. There are four panels in the figure, organized in two columns and two rows. The left-hand side panels show the factor loadings for the euro-area and the right-hand side panels show the factor loadings for the United States. Panels in the top row show the five lines that correspond to the factor loadings for conditional expectations. The solid black line shows the first factor loading. The dotted black line shows the second factor loading. The solid grey line shows the third factor loading. The dotted grey line shows the fourth factor loading, and the dashed black line shows the fifth factor loading. The first and third factors appear to be the most important driving conditional expectations in both areas, with their importance diminishing with the horizon. In the euro area, the second factor is also important. It is constant for any forecast horizon. Panels in the bottom row show the two lines that correspond to the factor loadings for conditional variances. The solid black line shows the first factor loading. The dotted black line shows the second factor loading. In the euro area, the first factor is more important driving the conditional variances, but the importance of both factors declines with the horizon. In the United States, the second factor is more important for driving conditional expectations. As in the euro area, the importance of both factors also declines with the horizon.
This figure illustrates the fitting properties of the model. There are ten panels in the figure, organized in two columns and five rows. The left-hand sides panels show the fitting properties for the euro-area surveys. The right-hand side panels show the fitting properties for the United States' surveys. The first row of panels in the figure shows realized inflation rates, based on the HICP and the headline CPI, for the euro area and the United States, respectively. In the second and lower rows, the black dots correspond to survey observations. The dark grey lines correspond to model-implied quantities. The light grey-shaded areas represent 2-standard-deviation confidence intervals. Pink bars indicate euro-area CEPR recessions and blue bars indicate US NBER recessions. The second row of panels shows the model fit for the 1-year ahead inflation forecasts. The third row of panels shows the model fit for the variances of the 1-year ahead inflation forecasts. The left panel of the fourth row shows the model fit for the 1-year 4 years ahead inflation forecast in the euro area. The right panel of the fourth row shows the model fit for the 5-year 5 years ahead inflation forecast in the United States. The left panel of the fifth row shows the model fit for the variance of the 1-year 4 years ahead inflation forecast in the euro area. The right panel of the fifth row shows the model fit for the variance of the 5-year 5 years ahead inflation forecast in the United States. The euro-area survey observations correspond to the ECB-SPF. The survey observations for the 1-year ahead inflation forecasts in the United States correspond to the US-SPF survey. The survey observations for the 5-year 5 years ahead correspond to the Blue Chip Surveys prior to March 2007 and to the US-SPD afterwards. Overall, the figure shows that the model fits first and second moments of survey forecasts reasonably well, with a few minor exceptions.
This figure plots the one-year ahead ECB-SPF and US-SPF survey-based histograms (bars on the charts), their Beta-smoothed counterparts (dashed lines), and the 1-year ahead model-implied distributions (solid lines). The grey bars and lines correspond to an early date in the sample (February 2005 and January 2005 for the euro area and the US), the red bars and lines correspond to a late date in the sample (April 2016 and January 2016 for the euro area and the US). For the model-implied distributions, two-standard-deviation confidence intervals are reported. These standard deviations reflect uncertainty associated with the estimation of the latent factors $$X_t$$ using the Kalman smoothing algorithm. Overall, the figure shows that inflation forecast distributions shifted to the left in the past decade reflecting higher probabilities of the lower inflation rates in future. Relative to a decade ago, the euro-area survey distributions flattened out pointing to a higher uncertainty associated with inflation forecasts. In contrast, US survey distributions became more ``pointed'' indicating a lower uncertainty associated with the inflation forecasts.
This figure displays the term structure of model-implied expected spot and forward inflation rates. There are four panels in the figure. The left-hand side panels show the term structure of the inflation forecasts in the euro area. The right-hand side panels show the term structure of the inflation forecasts in the United States. The top two panels display expected annualized inflation rates up to a horizon of 10 years. The bottom two panels similarly display the 1-year forward inflation forecasts starting from 1 to 10 years ahead. The black lines show the term structure for February 2005 (for the euro area) and January 2005 (for the United States). The red lines show the term structure for April 2016 (euro area) and January 2016 (United States). The grey areas with solid and dashed borders represent the 5th and 95th quantiles associated with the respective conditional distributions for early and late dates in the sample, respectively. Overall, the figure shows that over the past decade inflation expectations moved down. However, expectations in the near term (1 to 3 years) shifted more relative to those in the longer term (8 to 10 years).
This figure displays the term structure of model-implied conditional variances. There are four panels in the figure. The left-hand side panels show the term structure of the variance of inflation forecasts in the euro area. The right-hand side panels show the variance of the term structure of inflation forecasts in the United States. The top two panels show the variances of annualized inflation forecasts up to a horizon of 10 years. The bottom two panels show the variances of the 1-year forward inflation forecasts starting from 1 to 10 years ahead. Displayed variance reflects uncertainty around inflation forecasts. The black lines show the term structure for February 2005 (for the euro area) and January 2005 (for the United States). The red lines show the term structure for April 2016 (euro area) and January 2016 (United States). The grey areas with solid and dashed borders represent the 5th and 95th quantiles associated with the respective conditional distributions for early and late dates in the sample, respectively. Figure shows that, over the past decade, uncertainty associated with inflation forecasts in the euro area increased, especially for near-term inflation. At the same time, uncertainty associated with US inflation forecasts dramatically diminished, especially at the shorter horizons.
This figure shows the time series of the model-implied conditional means and variances of the forward inflation rates. There are 6 panels in the figure, organized in two columns and three rows. The left-hand side panels show the time series for conditional means. The right-hand side panels show the time series for conditional variances. The top row shows 1-year 4 years ahead forward inflation rates, the middle row shows 1-year 9 years ahead inflation rates, the bottom row shows 5-year 5 years ahead inflation rates. On each panel, grey lines correspond to the time series of the euro-area inflation rates. Black lines correspond to the time series of the US inflation rates. $$\pm2$$ standard-deviation bands reflect the uncertainty associated with factors $$X_t$$. Pink bars indicate euro-area CEPR recessions and blue bars indicate US NBER recessions. The figure indicates that, overall, US inflation expectations shifted down over our sample period from January 1999 to June 2016, albeit with considerable volatility especially for the 5-year 5 years ahead inflation rate. The latter volatility peaked during the financial crisis period around 2008. Inflation expectations in the euro area have been increasing approximately up to 2008 and declined afterwards. The volatility of the inflation forecasts in the euro-area increased for all presented horizons after the financial crisis.
This figure displays probabilities that future inflation rates will fall between 1.5 and 2.5 percent. The figure has three panels. The top panel shows the time series of such probabilities for the 1-year 4 years ahead inflation rates for the euro area, United States, and their respective difference along with their 2-standard-deviation confidence bounds that reflect the uncertainty associated with the estimation of latent factors $$X_t$$. The middle figure shows the time series of probabilities for the 1-year 9 years ahead inflation rates, and the bottom figure -- probabilities for the 5-year 5 years ahead inflation rates. Black lines represent US probabilities, grey line represent euro-area probabilities, and dotted lines -- the difference in the two probabilities. The dashed red vertical line indicates the timing of the ECB clarification of its inflation objective, in May 2003. The solid red vertical line indicates the timing of the specification of the inflation objective by the Federal Reserve, in January 2012. Pink bars indicate euro-area CEPR recessions and blue bars indicate US NBER recessions. Overall, figure indicates that the probability of future US inflation rates increased over time, while the probability for future inflation rates in the euro area declined somewhat. Towards the end of our sample, both probabilities are statistically similar indicating that inflation expectations are similarly anchored in the euro area and Untied States.
This figure presents probabilities that inflation rates will fall between 1.5 and 2.5 percent. The figure has three panels. The top panel shows the time series of such probabilities for the 1-year 4 years ahead inflation rates for the euro area, United States, and their respective difference along with their 2-standard-deviation confidence bounds that reflect the uncertainty associated with factors $$X_t$$. The middle figure shows the time series of probabilities for the 1-year 9 years ahead inflation rates, and the bottom figure -- probabilities for the 5-year 5 years ahead inflation rates. Black solid lines represent US probabilities implied by the joint-area model estimation. Black dashed line represents US probabilities implied by the single-area model estimation, which involves only US survey data. Grey solid lines represent euro-area probabilities implied by the joint-area model estimation. Grey dashed lines represent euro-area probabilities implied by the single-area model estimation, which involves only euro-area survey data. For the US, the estimation of the single-area model is based on the data spanning the period from 2007 to 2016. The dashed red vertical line indicates the timing of the ECB clarification of its inflation objective, in May 2003. The solid red vertical line indicates the timing of the specification of the inflation objective by the Federal Reserve, in January 2012. Pink bars indicate euro-area CEPR recessions and blue bars indicate US NBER recessions. Overall, the figure indicates very similar anchoring probabilities for both types of model estimation, with the minor exception of the US case, when the single-area estimation implies slightly lower probabilities than the joint-area estimation, for the 1-year 4 years ahead and for the 1-year 9 years ahead inflation rates, after the financial crisis. However, US probabilities implied by both single-area and joint-area model estimation converge toward the end of our sample period.