Introducing our common inflation expectations index - Capital Economics
US Economics

Introducing our common inflation expectations index

US Economics Focus
Written by Paul Ashworth

In a world where the Phillips curve is flat, inflation expectations become the key driver of actual inflation over the medium term. But getting a true handle on inflation expectations is difficult because of the large number of diverse measures that are available. Our new common inflation expectations (CIE) index cuts through the noise by using novel quantitative methods to construct a single unifying monthly measure of medium-term expectations. What we find is that, although expectations are still slightly lower than what is needed for the Fed to hit its 2% inflation target, they have rebounded markedly in recent months and, if that trend continues, it won’t be long before the Fed should start to be concerned about a sustained overshoot in actual inflation.

  • In a world where the Phillips curve is flat, inflation expectations become the key driver of actual inflation over the medium term. But getting a true handle on inflation expectations is difficult because of the large number of diverse measures that are available. Our new common inflation expectations (CIE) index cuts through the noise by using novel quantitative methods to construct a single unifying monthly measure of medium-term expectations. What we find is that, although expectations are still slightly lower than what is needed for the Fed to hit its 2% inflation target, they have rebounded markedly in recent months and, if that trend continues, it won’t be long before the Fed should start to be concerned about a sustained overshoot in actual inflation.
  • We use a dynamic factor model to construct a single common inflation expectations (CIE) index from a large dataset of 22 separate measures of inflation expectations, which builds on recent work by the Fed’s own staff. Our dataset includes TIPS breakeven inflation compensation rates, inflation swaps rates, and survey-based measures collected from households, businesses and professional forecasters. Our model is monthly, however, which makes it timelier than the Fed’s quarterly updates, and we also take a different approach to presenting the index, which we think makes it easier to interpret shifts in our index in terms of the FOMC’s 2% target for PCE inflation.
  • After dropping to a 20-year low in the early stages of the pandemic last year, our CIE index has rebounded markedly in recent months (see Chart 1), which stands in stark contrast to the Fed’s own index that has barely risen at all. But the latter is a quarterly index with the data only going up to the end of last year, which means it doesn’t yet capture the recent surge in market-based measures of inflation compensation since early January, when victory for the Democrats in the Georgia Senate run-off elections opened the door to additional fiscal stimulus on an almost unprecedented scale.

Chart 1: CE Common Inflation Expectations Index (%)

Source: Capital Economics


Introducing our common inflation expectations index

With the output gap having less of an impact on inflation in recent years, inflation expectations have become arguably the key driver of actual inflation dynamics, with central banks including the Fed paying ever closer attention to how those expectations are evolving.

Although, unlike the output gap, inflation expectations are directly observable, the drawback is that there is no all-encompassing single measure of expectations. Instead, what we have available is a broad range of survey measures that cover the expectations of households, businesses and professional forecasters, as well as measures derived from inflation-indexed financial market instruments. Those competing measures also cover a range of time horizons.

Given the different language used in the questions in those surveys, in practice it is often hard to reconcile one survey measure with another. It is even more difficult to translate those survey responses into a measure of expectations for the Fed’s preferred PCE inflation measure specifically. At the same time, the measures derived from the spreads between inflation-protected and nominal Treasury bonds and, by extension inflation swaps rates, are better characterised as measures of inflation compensation. They are not pure measures of inflation expectations, since those rates are affected by shifts in various liquidity, inflation uncertainty and term premiums too.

In this Focus, we develop an index of common inflation expectations using a dynamic factor model, which builds on recent work by the Fed’s staff. (See here.) The aim is to take the broadest possible range of inflation expectations measures and to distil the co-movement in those series into one single common factor. Whereas the Fed projects its index of Common Inflation Expectations (CIE) onto one of its component series – namely the long-run inflation expectation series from the Survey of Professional Forecasters – we take a different approach. We think it makes more sense to fit the CIE index to the actual core PCE inflation rate. First, since our factor seems to fit well and, more importantly, because it allows a much easier interpretation of our index of inflation expectations relative to the Fed’s 2% target.

What we find is that our CIE index has rebounded markedly in recent months. Although we believe it is still at a level consistent with a core PCE inflation rate of slightly below 2% right now, expectations would not have to rise much further before Fed officials should start to be concerned.

Our aim is to publish regular updates on this new index of common inflation expectations on our US macro service. In addition, we will be adding the data for download to our online portal CE Interactive. (See here.)


Table 1: Inflation Expectations Variables

Financial market measures

TIPS 5-Year Breakeven Rate

TIPS 10-Year Breakeven Rate

TIPS 20-Year Breakeven Rate

TIPS 5-Yr-5Yr-Forward Breakeven Rate

1-Year Inflation Swap Rate

3-Year Inflation Swap Rate

5-Year Inflation Swap Rate

7-Year Inflation Swap Rate

10-Year Inflation Swap Rate

Household survey-based measures

Uni of Michigan 1-Year

Uni of Michigan 5-Year

Conf Board 1-Year

NY Fed 1-Year

NY Fed 3-Year

Business survey-based measures

Atlanta Fed Business ULC Growth Exp 1-Year

Atlanta Fed Business ULC Growth Exp 5-10 Year (Q)

Professional forecasters survey-based measures

CPI 1-Year (Q)

CPI 5-Year (Q)

CPI 5Yr-5Yr-Forward (Q)

CPI 10-Year (Q)

PCE 5-Year (Q)

PCE 10-Year (Q)

Source: CE (Q) denote quarterly rather than monthly series


Data

Our model incorporates 22 separate measures of inflation expectations that cover a wide range of time horizons and sources; including breakeven inflation compensation rates (derived from the spread between TIPS and regular Treasury yields), inflation swap rates, and survey-based measures collected from households, businesses and professional forecasters. (See Table 1 for a full list and the Data Appendix for charts of all the series.)

Methodology

Our CIE index is constructed by estimating a dynamic factor model to extract a single common factor. The general framework exploits the fact that the relevant data series have strong co-movement so their dynamics can be summarised by a single latent common factor, which evolves over time. Similar in approach to the dynamic factor models that are increasingly used in the nowcasting literature to forecast GDP, this framework can cope with a large number of variables with mixed frequency series, in our case monthly and quarterly data. It can also deal with unbalanced data series, which allows for missing observations in some variables that creates a “ragged edge”, reflecting the varying start and end dates for different series.

We estimate the model using quasi-maximum likelihood estimation. (See here and here.) In other applications of dynamic factor modelling, like GDP nowcasting, the modeller also needs to estimate how many factors should be used to explain a sufficient degree of the movement in the included series. But in this case, we do not test for the presence of multiple factors since, by definition, we are trying to uncover a single common factor for inflation expectations. We assume the factor is characterised by an AR(3) process, since the highest frequency date we employ is monthly.

In a dynamic factor model each series is modelled as the sum of two orthogonal components; the first factor captures the co-movement of all the series, which is driven by an unobservable component (the signal), and the second factor is treated as an idiosyncratic residual (noise). We refer to the estimated common factor as the CIE index and to the idiosyncratic residuals as shocks. Following the convention in the literature, all data series are transformed to have zero mean and unit standard deviation.

We remove all outliers (setting their value to missing), which we define as observations that are more than two standard deviations from the series mean. The primary purpose of doing that is to improve the stability of the estimation, but it also makes intuitive sense, since medium-term inflation expectations should shift only gradually over time. The biggest impact of omitting the outliers is to remove the effects of the temporary collapse in TIPS breakeven inflation compensation rates during the financial crisis in late 2008 and the early stages of the pandemic in late March 2020. In both cases, we believe those collapses were due to liquidity issues in financial markets, which affect TIPS yields more than regular Treasury yields, rather than a genuine reassessment of inflation expectations by financial market participants. The model is estimated over the sample period January 1999 to March 2021.

Results

In Table 2 we present the R2 values, the in-sample fit, which tells us how well the model fits each variable. (The in-sample fit is 1 minus the variance of shocks for each variable.) A higher value indicates the CIE factor explains more of the movement in that series. A reading of 100 would imply that the factor explains all the movement in our variable. The charts in our Data Appendix also include the factor projections (DFM fitted values) for each variable as well as the actual series.

Table 2: Contribution to the CIE index

Variable

R2 Values

Financial market measures

TIPS 5-Year Breakeven Rate

83.4

TIPS 10-Year Breakeven Rate

94.1

TIPS 20-Year Breakeven Rate

94.3

TIPS 5-Yr-5Yr-Forward Breakeven Rate

69.5

1-Year Inflation Swap Rate

26.5

3-Year Inflation Swap Rate

57.4

5-Year Inflation Swap Rate

86.4

7-Year Inflation Swap Rate

94.5

10-Year Inflation Swap Rate

90.1

Household survey-based measures

Uni of Michigan 1-Year

47.5

Uni of Michigan 5-Year

33.6

Conf Board 1-Year

8.6

NY Fed 1-Year

28.7

NY Fed 3-Year

35.2

Business survey-based measures

Atlanta Fed Business ULC 1-Year

10.9

Atlanta Fed Business ULC 5-10 Year

53.9

Professional forecasters survey-based measures

CPI 1-Year

15.8

CPI 5-Year

41.9

CPI 5Yr-5Yr-Forward

18.7

CPI 10-Year

21.0

PCE 5-Year

25.3

PCE 10-Year

19.7

Source: CE

What we find is that every variable contributes to our CIE index factor, though the financial market measures, TIPS and swaps, contribute the most. Moreover, the longer-term expectations measures have consistently greater contributions than the shorter-term measures. The 10- and 20-year TIPS breakeven inflation rates and the 7- and 10-year swaps rates are the only variables with R2 values in excess of 90. The weakest contribution among the financial market variables is for the 1-year inflation swap rate, at 26.

That pattern is what we would have expected, given that short-term inflation expectations are driven more by the current inflation rate, which itself is often skewed by sizeable, but temporary, shocks to the volatile components like food and energy. Otherwise, these results imply that our estimated CIE index is a good measure of medium-term inflation expectations and that it isn’t overly influenced by short-term temporary swings in actual inflation.

The estimated R2 values for our survey-based variables are, on the whole, significantly lower than those for the financial market variables. This reflects their more idiosyncratic nature and the fact that they tend to be shorter-term measures, often covering just the next 12 months, which means they are also more influenced by the near-term volatility in actual inflation. The Conference Board’s measure of households 1-year ahead expectations and the Atlanta Fed’s businesses 1-year ahead ULC expectations variables make particularly weak contributions to our CIE index. (See Charts 12 and 15 in the Appendix.) In contrast, the NY Fed’s relatively new household survey measures appear to be a good gauge of inflation expectations and the Atlanta Fed’s measure of medium-term businesses ULC expectations shares much more co-movement with the CIE index.

Finally, the measures based on the Philly Fed’s survey of professional forecasters appear to track surprisingly little of the variation in our CIE index, particularly the 10-year ahead expectations variables. (See Charts 17 to 22 in the Appendix.) As professional forecasters ourselves, we wonder whether there is a bias among respondents in these surveys who, subject to peer pressure, automatically write in the central bank’s inflation target rather than what value they actually expect inflation to average over that time horizon. Forecasting that a central bank would hit its inflation target, particularly over the medium term, is a matter of faith for many private sector economists.

Our CIE index

Dynamic factor models generate “formless” factors that use so-called factor loadings to generate fitted values for all the variables in the dataset. In this case, however, we are trying to generate an index of common inflation expectations that is otherwise unobservable.

One potential solution would be to transform the CIE index factor into a standard normal variable, which has a mean of zero and a standard deviation of one. (See Chart 2.) That would allow us to draw some simple conclusions from the general shape of the CIE index: inflation expectations were, on average, notably higher in the decade between 2004 and 2014 and have been notably lower since 2015, even dropping to a 20-year low in the early stages of the pandemic. But this is far from an ideal solution. The problem with the factor in this standard normal form is that it is impossible to interpret in terms of what it means for expectations specifically in relation to the Fed’s 2% PCE inflation target.

Chart 2: Standard Normal CIE Index

Source: CE

In their paper, the Fed staffers overcome this problem by projecting their factor on to the survey of professional forecasters expectations for PCE inflation in 10 years’ time. (See Chart 3.) Their index is essentially the fitted values generated by the model for that series. There rationale for doing so is that they think “professional forecasters’ inflation expectations might be more accurate than those of households”. As we noted above, however, we would argue that professional forecasters are predisposed to assume that central bank inflation targets are fully credible over the medium term.

Chart 3: CIE Factors Fitted to SPF 10-Year PCE Inflaton Expectations

Sources: Federal Reserve (see here), CE, Refinitiv

To compare our index with theirs, we can take the same approach. On that like-for-like basis, the Fed’s CIE factor is slightly more stable than ours, with a particularly big divergence opening in recent months, when our index rebounds more significantly. Some of that gap is explained by the Fed model’s quarterly periodicity which means, because their latest data point is for the fourth quarter of last year, it misses the big surge in financial market measures of inflation compensation this year, after the Georgia Senate run-offs cleared the path for the Democrats to pass another massive fiscal stimulus.

The choice of variables included in the competing datasets probably plays a role in that divergence too, however. Their dataset relies much more on surveys of professional forecasters, whereas we include more surveys of households and businesses and financial market measures. They Include the blue chip, consensus economics and the survey of professional forecasters, which means they are tripling down on the forecasts from the same relatively small pool of forecasters who, as we argued above, we think have an inbuilt bias to write down 2% automatically.

The other major drawback to that method of using the SPF 10-year ahead inflation expectations measure as an anchor for the CEI index is that the R2 value in our model for that variable is very low. (See Chart 22 in the Appendix.) In other words, our CIE factor doesn’t explain a lot of the movement in the SPF inflation expectations variable, which is mostly captured by idiosyncratic shocks instead. Given that Chart 3 suggests the Fed’s index doesn’t explain any more of the movement in the SPF expectations variable than our own index. The upshot is that, using the factor loadings to project either of these CIE factors on to that variable gives a potentially false sense of stability in inflation expectations.

As an alternative, we project our CIE index onto actual core PCE inflation, using a simple OLS regression. (See Chart 4.) The downside to this approach is that we may be over-stating the true variance in long-run inflation expectations. But the upside is that it makes it much easier to interpret our CIE index in terms of what it implies for actual inflation over the medium-term, particularly in relation to the Fed’s 2% target.

What we find is that, even though inflation expectations are still not quite at a level consistent with that target, they have rebounded significantly in recent months and now stand at a six-year high. We think this is a potentially important revelation because most Fed officials still seem to believe that inflation expectations are significantly lower than needed to hit the 2% PCE inflation target.

Chart 4: CIE Index Fitted to Actual Core PCE Inf. (%)

Sources: CE, Refinitiv

Conclusions

At a time when concerns about inflation are growing, inflation expectations are being more closely watched than ever. But with so many diverse measures of expectations available, it is hard to know what is really happening. That is why we developed our Common Inflation Expectations (CIE) index, to offer a single underlying measure of medium-term expectations. What we find is that, although expectations have been unusually muted for most of the past decade, they have rebounded markedly over the last 12 months.

Data Appendix

Chart 5: 5-Year Breakeven Inflation Compensation (%)

Chart 7: 20-Year Breakeven Inflation Compensation (%)

Chart 9: 1-Year Inflation Swap Rate (%)

Chart 11: 5-Year Inflation Swap Rate (%)

Chart 6: 10-Year Breakeven Inflation Compensation (%)

Chart 8: 5-Yr-5-Yr-Forward Inflation Compensation (%)

Chart 10: 3-Year Inflation Swap Rate (%)

Chart 12: 7-Year Inflation Swap Rate (%)

Sources: Refinitiv, CE

Data Appendix Contin’d

Chart 13: 10-Year Inflation Swap Rate (%)

Chart 15: 5-Year UoM Households’ Inflation Expect. (%)

Chart 17: 1-Year NY Fed Households Inf Exp (%)

Chart 19: 1-Year Atlanta Fed Businesses’ Inf Exp (%)

Chart 14: 1-Year UoM Households’ Inflation Exp (%)

Chart 16: 1-Year Conf. Board Households’ Inf Exp (%)

Chart 18: 3-Year NY Fed Households Inf Exp (%)

Chart 20: 5-10 Year Atlanta Fed Businesses’ Inf Exp (%)

Sources: Refinitiv, NY Fed, Atlanta Fed, CE

Data Appendix Contin’d

Chart 21: 1-Year Professional Forecasters CPI Inf Exp (%)

Chart 23: 5-Yr/5-Yr-Forw’d Prof. Fore. CPI Inf Exp (%)

Chart 25: 5-Yr Professional Forecasters PCE Inf Exp (%)

Chart 22: 5-Year Professional Forecasters CPI Inf Exp (%)

Chart 24: 10-Yr Professional Forecasters CPI Inf Exp (%)

Chart 26: 10-Yr Professional Forecasters PCE Inf Exp (%)

Sources: Refinitiv, CE


Paul Ashworth, Chief US Economist, paul.ashworth@capitaleconomics.com
Sepideh Dolatabadi, Econometrician, sepideh.dolatabadi@capitaleconomics.com