, in that permanent shocks to inflation are ruled out. the counterexample is if inflation follows a random walk process, whereby shocks have permanent effects on inflation, then uncertainty, as measured by the standard deviation from the distribution of future outcomes, rises linearly with the forecast horizon. applying theory to the real world in the years up to and including the first year of the pandemic, inflation had been running consistently below the fomc ’ s 2 percent longer - run target. then, in the spring of 2021, inflation readings surged, bringing the personal consumption expenditures ( pce ) inflation rate to around 6 percent, where it has remained through the first nine months of 2022. consumer price index ( cpi ) inflation rose by even more. this episode represents a unique opportunity to assess the three criteria of well - anchored expectations during a period of high and volatile inflation. 4 in empirically assessing the sensitivity and level of longer - run inflation expectations, one must specify what forecast horizon corresponds to the “ long run. ” surveys don ’ t typically ask about inflation in the “ long run, ” but rather the inflation rate over a specific period of time. a reasonable and oft - used benchmark of longer - run inflation expectations is to look at inflation five or more years in the future. such a forecast horizon is sufficiently long enough for typical business cycle dynamics and the effects of monetary policy on inflation to have played out, although under some circumstances, this may fall short of the “ long run ” implied by theory. over the past year and a half, measures of longer - run inflation expectations have been insensitive to the rapid rise in inflation. figure 1 shows the time series of these measures of longer - run inflation expectations. this includes median expectations from the survey of professional forecasters ( spf ) for inflation measured by the pce price index 6 - 10 years in the future ; breakeven inflation rates 6 - 10 years in the future as implied by nominal and inflation - protected u. s. treasury securities ; and the university of michigan survey of inflation expected over the next 5 - 10 years. 5 realized 12 - month cpi inflation is also shown in the figure for reference. as seen in figure 1, spf longer - run inflation expectations have remained remarkably stable over the past year and a half, while the market - based measure and the michigan survey rose modestly during 2021 before retracing some of those gains this year. because the michigan survey asks about inflation over

. interestingly, during the period of sustained low inflation before the pandemic, the market - based and michigan measures declined, and their current levels are similar to those seen prior to that decline. assessment of the uncertainty criterion for well - anchored inflation expectations is more challenging given data limitations. in theory, prices on inflation options contracts could be used to infer investors ’ distributions of beliefs about future inflation. 9 however, there have been virtually no trades recorded in the u. s. market for inflation caps and floors since 2015. over that time, the “ prices ” reported for these options were based on models — not transaction prices — and cannot be used to measure investors ’ inflation uncertainty during the current episode. instead, i will turn to the sce, which asks about consumers ’ uncertainty of by continuing to use our site, you agree to our terms of use and privacy statement. you can learn more about how we use cookies by reviewing our privacy statement. inflation expectations, as well as options on future interest rates, which provide some indirect insights into markets ’ uncertainty of future inflation. over the past year and a half, two aspects of increased inflation uncertainty are evident in the sce : an increase in disagreement in mean expectations across respondents and an increase in the width of respondents ’ reported inflation distributions. although disagreement does not directly correspond to uncertainty, research has identified it as a useful indirect indicator. 10 figure 2 and figure 3 illustrate the increase in disagreement across sce respondents over the past several years. figure 2 shows the share of respondents who have deflation expectations — that is, they expect inflation to be at or below zero percent — either one, three, or five years in the future. 11 as discussed in research with my colleagues at the new york fed, 12 there has been a striking increase over the past year in the share of respondents who expect deflation three and five years in the future. 13 at the same time, as shown in figure 3, the share expecting inflation above 4 percent grew, but part of the increase has since reversed. based on the most recent reading in september 2022, about a quarter of respondents have deflation expectations five years in the future, nearly as large as the share expecting inflation above 4 percent at the five - year horizon. following the onset of the pandemic, aggregate uncertainty — which combines disagreement and individual uncertainty — increased but has also become more symmetric. figure 4 shows the aggregate distributions of inflation three years in the future based on the sce