**BIS Working Papers **

**No 699**

**Deflation expectations**

by Ryan Banerjee and Aaron Mehrotra

**Monetary and Economic Department **

February 2018

JEL classification: E31, E58

Keywords: deflation; inflation expectations; forecast disagreement; monetary policy

This publication is available on the BIS website (www.bis.org).

*© Bank for International Settlements 2017. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated.*

ISSN 1020-0959 (print)

ISSN 1682-7678 (online)

**Deflation expectations**

By Ryan Banerjee and Aaron Mehrotra

**Abstract **

We analyse the behaviour of inflation expectations during periods of deflation, using a large cross-country data set of individual professional forecasters’ expectations. We find some evidence that expectations become less well anchored during deflations. Deflations are associated with a downward shift in inflation expectations and a somewhat higher backward-lookingness of those expectations. We also find that deflations are correlated with greater forecast disagreement. Delving deeper into such disagreement, we find that deflations are associated with movements in the lefthand tail of the distribution. Econometric evidence indicates that such shifts may have consequences for real activity.

JEL classification: E31; E58

Keywords: deflation; inflation expectations; forecast disagreement; monetary policy

- Bank for International Settlements.
- Bank for International Settlements. Corresponding author’s email: [email protected]
- The views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank for International Settlements. Matthias Loerch provided excellent research assistance. We thank participants at the 49th Money, Macro and Finance Conference and at seminars held at the Bank for International Settlements and the Swiss National Bank. We also thank an anonymous referee, Marlene Amstad, Bill English, Andy Filardo, Petra Gerlach, Marco Lombardi, Gianni Lombardo, Roland Meeks, Elmar Mertens, Dubravko Mihaljek, Jouchi Nakajima, Maritta Paloviita and James Yetman for their helpful comments and suggestions.

**1. Introduction**

The widespread shift to a low inflation environment after the Great Financial Crisis (GFC) of 2008-09, and Japan's earlier experience, brought policymakers' concerns about deflation back to the fore. While the previous literature has proposed theoretical frameworks for the behaviour of inflation and inflation expectations during deflationary periods (Benhabib et al (2002) and Busetti et al (2014)), in general empirical research on inflation expectations has not focused explicitly on periods of falling prices. For example, Ehrmann (2015) and IMF (2016) cover episodes of low inflation but do not focus on periods of deflation.

Analysing the behaviour of inflation expectations during deflations is relevant for a number of reasons. Such expectations matter for wage and price setting and any second-round effects from falling prices. The degree of anchoring of expectations is thus likely to affect both the depth and duration of deflation (see eg Fuhrer (2017), Nishizaki et al (2014) and Williams (2009)). A downward drift in inflation expectations and risks thereof have been one rationale for the use of unconventional monetary policies in the euro area (eg Draghi (2015)). Avoiding deflation was also a significant factor behind the accommodative US monetary policy stance of the early 2000s (eg Greenspan (2004)).

There are divergent views on the dynamics of deflation, in part driven by historical evidence relating to deflationary spells before the Second World War.^{3} On the one hand, the deflationary spell experienced during the Great Depression suggests that economies could be at risk of adverse deflations, with aggregate demand deficiencies reflected in falling price levels and economic slack. On the other hand, the more benign deflationary experience of the latter part of the 19^{th} century provides less evidence that deflation leads to strong negative feedback loops with aggregate demand (Bordo and Filardo (2005) and Borio et al (2015)).^{4} This unsettled debate may also be evident in a wider dispersion of professional forecasts during deflations.

In this paper, we analyse the behaviour of inflation expectations during deflationary episodes. In particular, we investigate whether expectations become less well anchored. If expectations are well anchored, they should remain relatively stable at a given level over time, with only minor disagreements across forecasters.

We use surveys of professional forecasters from Consensus Economics at the forecaster level for headline inflation in the next calendar year. The data comprise forecasts for inflation in 43 advanced and emerging market economies. The global nature of the data set is highly relevant, as deflations have not been limited to advanced economies - 30 of the 47 deflationary episodes identified in our data set occur in emerging market economies (EMEs), mostly in Asia and central and eastern Europe. We first provide some stylised facts about the deflationary episodes themselves and the behaviour of professional forecasters' inflation expectations during periods of falling prices. Then, we formally examine whether there is evidence that deflation has affected the level of inflation expectations and forecast disagreement, ie two measures of the anchoring of inflation expectations.

We also examine how the monetary policy regime - as well as potential constraints in the form of the zero lower bound (ZLB) - influence inflation expectations during deflations. The behaviour of inflation expectations depends on the expected reaction (or lack) of monetary policy. For example, in inflation targeting (IT) regimes, monetary policy may be expected to address deflation concerns more aggressively than in regimes operating with less explicit inflation mandates. The distance of interest rates from the ZLB could also affect inflation expectations. For example, deflations occurring at times of near-zero short-term interest rates could have different dynamics from other deflations due to perceived constraints on monetary policy. Our paper provides evidence concerning these different dimensions.

We report a number of findings which, taken together, suggest that inflation expectations become less well anchored during deflations. First, deflations are associated with a downward shift in the level of inflation expectations. As we study relatively short-term inflation expectations, uncovering a level effect may not be surprising per se. However, we also find some evidence that deflation renders the levels of inflation expectations more dependent on lagged inflation rates, ie expectations become more backward-looking. Second, deflations lead to greater forecast disagreement. This effect remains after controlling for the deviation of inflation from the inflation target, and controlling for periods of low positive inflation, suggesting that deflation has an effect on disagreement which is over and above that caused by deviations from explicit central bank targets or simply low inflation. Whereas Mankiw et al (2004) document that the dispersion of inflation forecasts is increasing in the level of actual inflation outcomes, we uncover a U-shaped relationship when deflations are included: forecast disagreement rises with the absolute levels of both inflation and deflation outcomes. Third, greater forecast disagreement and level shifts in expectations do not only arise in the context of the ZLB, as their links with deflation also manifest themselves strongly when periods of near-zero interest rates are excluded from the analysis.

As we find stronger forecast disagreement to be a prominent feature of deflations, we delve deeper into the tails of the forecast distribution. Doing so, we find that deflations are associated with greater backward-lookingness in expectations especially in the left-hand tail of the forecast distribution. We investigate the macroeconomic impact of negative shifts in the left-hand tail with a panel vector autoregressive model. The results indicate that such shifts lead to greater disagreement over forecasts for GDP growth but also to temporarily lower output gap and inflation outcomes, suggesting that they have consequences for real activity.

Our paper is related to different strands of literature. It adds to the vast and expanding literature that uses surveys to analyse the anchoring of expectations (eg Levin et al (2004), Kozicki and Tinsley (2012), Mehrotra and Yetman (2017) and Yetman (2017a)). It is also related to research on inflation forecast disagreement (eg Mankiw et al (2004), Capistran and Timmermann (2009), Dovern et al (2012) and Siklos. And it is related to papers that analyse the implications of price dispersion and forecast disagreement (eg Andrade et al (2015), Huizinga (1993) and Nakamura et al (2017)). Recently, Wiederholt (2015) has shown that heterogeneous inflation expectations render deflation spirals less severe at the ZLB but also reduce the effectiveness of forward guidance policies. Nakata (2017) finds that greater uncertainty regarding the effects of exogenous shocks at the zero lower bound exacerbates output declines during recessions.

Our paper is also related to research on the empirical behaviour of inflation expectations during the post-GFC period. Ehrmann (2015) analyses the anchoring of expectations when inflation is below the central bank's target while the IMF (2016) evaluates changes in anchoring both over time and conditional on monetary policy. Similarly, Blanchard et al (2015) and Blanchard (2016) document changes in the anchoring of expectations over long time periods, including in the post-GFC years. The Bank of Japan (2016) evaluates the behaviour of various measures of inflation expectations after the introduction of quantitative and qualitative monetary easing (QQE) in April 2013. Natoli and Sigalotti (2017a, 2017b) propose novel techniques based on the distribution of financial market data to examine the anchoring of inflation expectations during the post-GFC period. Buono and Formai (2016) use time-varying parameter regressions to examine whether long-term survey expectations react to short-term forecasts in major advanced economies, including in the aftermath of the GFC. And Kenny and Dovern (2017) use data from Surveys of Professional Forecasters to analyse how the distribution of long-run inflation expectations has changed in the euro area after the GFC. To our knowledge, no empirical study has previously focused explicitly on the behaviour of expectations during deflations in a large sample of countries.

This paper is structured as follows. The next section describes the data and presents some data-based stylised facts on inflation outcomes and expectations. Section 3 discusses the methodology used to examine the behaviour of expectations. This is followed in Section 4 by a formal investigation of how deflation affects the behaviour of inflation expectations. In the same section, we also analyse the macroeconomic effects of shifts in the tails of the forecast distribution. We consider various extensions and robustness tests in Section 5. Concluding comments are provided in Section 6.

We use surveys of professional forecasters from Consensus Economics. These data are available for a relatively long history and are collected in a comparable fashion across a large number of countries, both advanced and emerging. Having a global data set is essential for the analysis, given the large number of deflation episodes in emerging market economies. Regarding the favourable forecasting performance of subjective expectations, Faust and Wright (2013) find that survey measures of inflation expectations tend to improve the forecasts that come from a large number of different forecasting models.

Each month, Consensus Economics polls a panel of experts from public and private economic institutions, mostly investment banks and research institutions, about their predictions for the main macroeconomic variables for the current and next calendar year. Our analysis uses the fixed event forecasts for the next calendar year. Although our study focuses on relatively short-term expectations, changes in short-term inflation expectations may well spill over to those at longer horizons as Buono and Formai (2016) document for the euro area, potentially affecting the credibility of monetary policy. Moreover, for the setting of monetary policy, the most relevant horizon is arguably related to the frequency with which most prices and wages are adjusted, and hence has an important impact on inflation dynamics. Indeed, Fuhrer (2017) finds that short-term expectations play a quantitatively important role for actual inflation outcomes in estimated Phillips curves for Japan and the United States.^{6}

On the use of fixed event forecasts, we note that forecasts based on fixed horizons are often easier to use in empirical applications, and some studies approximate fixed-horizon forecasts with a weighted average of two fixed-event forecasts made for different periods (eg Dovern et al., 2012; Gerlach, 2007; Siklos, 2013). However, this approach results at times in significant approximation errors (see Yetman (2017b)), and Kortelainen et al (2011) note that the induced moving average process affects the properties of the data. Moreover, some central bank publications report fixed event inflation forecasts (see eg Bank of Canada (2017, p. 22).

Our data cover 43 economies, 12 advanced and 31 emerging. The length of the data set depends on the availability of inflation forecast data. For advanced economies, the data start earliest in 1990, yielding a maximum of 319 monthly observations per country (see Annex Table A1 for details). For emerging markets, the starting dates vary by region. For most countries in emerging Asia, the data start in late 1994; for Latin America in 2001; and for Central and Eastern Europe in 2007. The number of forecasters varies both across countries and within the same country across time. The average number of forecasters in the country-specific samples vary from 8 in Lithuania to 30 in the United Kingdom; in the full sample, the average number of forecasters per country is 15.

Our inflation data are for headline consumer price inflation (CPI, year on year).^{7} While developments in core inflation would also be interesting, expectations data are not widely available for this measure. Moreover, for some EMEs where volatile components such as food comprise a large share of the consumption basket, developments in core inflation may be less relevant than those in headline inflation (eg Anand et al (2015)).

We focus on deflation episodes characterised by negative headline inflation rates (year on year) for at least six consecutive months. Furthermore, a country is regarded as exiting the deflation episode only in the third consecutive month of positive inflation rates that follow deflation. This classification ensures that very short bouts of negative inflation rates do not count as individual deflation episodes. Moreover, it avoids longer deflation periods being classified as several shorter ones, if they are interrupted only by one or two months of positive inflation rates. In the empirical analysis, we also consider "persistent" deflation episodes that comprise a minimum of twelve consecutive months of negative headline inflation rates.

A partial exception is the United Kingdom, where inflation refers to retail price (RPIX) inflation until 2004 and CPI inflation thereafter.

The 47 deflation episodes identified in our sample are shown in Graph 1. Three periods with greater occurrence of deflations stand out. First, various Asian economies experienced deflation around the time of the Asian financial crisis: Hong Kong SAR, mainland China, Chinese Taipei, Singapore and Thailand. Japan also experienced a long spell of deflation as its domestic banking crisis occurred. The second, more global, bout of deflations took place during the GFC. The third relatively widespread period of falling prices occurred in 2014-15, affecting many European countries but also some emerging economies in Asia. Over time, deflations were increasingly associated with near-zero interest rates (blue lines in Graph 1).

Overall, the deflation periods are relatively widely dispersed across countries, as in 16 countries deflation episodes occurred only once. 17 deflation episodes took place in advanced economies and 30 in emerging markets, while 11 occurred in countries that were part (or later became part) of the euro area. Hong Kong SAR

experienced the lowest inflation outcome within a single deflation episode in the sample (-6.1%). On average the minimum inflation outcome across all the different deflation episodes was -1.7%. Annex Table A2 shows details of the identified deflations, including their length and the minimum inflation outcomes and levels of expectations during these time periods.

Similarly to deflations, we also classify periods of relatively high inflation in the analysis. We define an economy to have high inflation if the headline inflation rate is above four per cent for at least six consecutive months.^{[1]} Furthermore, the country only exits a high inflation episode in the third consecutive month of below-four- percent inflation rates. In our analysis, we omit as outliers all observations with inflation rates exceeding 10%.

Graph 2 shows simple graphical evidence about the relationship between inflation outcomes and the level of forecasts. We divide the sample into twenty buckets based on inflation outcomes and show the average level of next year's forecast within each bucket. Furthermore, we distinguish by colour the different inflation environments using the definitions specified above: deflations, high inflations and other periods.

Not surprisingly, Graph 2 suggests that deflations are associated with lower levels of expectations than other environments. Yet, the average expectation for the next calendar year remains positive for all inflation buckets during deflation periods (see also Annex Table A2 for evidence on individual deflation episodes). This contrasts with high inflation periods where the forecasts appear to track inflation outcomes more closely. The relatively limited downward shift of expectations during deflations is consistent with Blanchard et al (2015) and Blanchard (2016) who find that well- anchored expectations helped avoid outright deflation spirals in post-GFC years despite large unemployment gaps. Coibion and Gorodnichenko (2015) argue that a rise in commodity prices during 2009-11 raised inflation expectations and helped avoid major disinflation despite the marked slowdown in activity.

In Graph 3, we plot inflation outcomes together with a measure of forecast disagreement, the interquartile range of next year forecasts. We use a generalised additive model to illustrate the relationship between the variables, shown as the blue line. The generalised additive model fits locally linear regressions, where smoothing is achieved by cubic basis splines (see Hastie and Tibshirani (1990) for more details).

Graph 3 suggests that the relationship between inflation outcomes and forecast disagreement is U-shaped. At low and positive inflation rates of around 1-2%, the interquartile range obtains its lowest value, of around 0.5%. The upward-sloping part of the curve during positive inflation rates has been documented in previous research, see eg Mankiw et al (2004). Our results suggest a similar relationship during deflation.

In particular, once inflation passes the zero mark and enters negative territory, the interquartile range rises. At an inflation rate of -1.7%, corresponding to the average minimum inflation outcome across the deflation episodes, forecast disagreement is at a similar level as with a positive inflation rate of 6%.

**3. Empirical strategy**

We formally investigate the behaviour of expectations during deflations by examining the level and dispersion of expectations over time. Both are relevant for the anchoring of expectations. If expectations are well anchored, they should remain relatively stable at a given level over time, with only a small dispersion across forecasters (forecast disagreement; see eg Dovern et al (2012)).^{10}

In the analysis of level effects, we follow the approach of papers such as Ball and Sheridan (2004) and Levin et al (2004) to examine whether deflation affects the dependence of the level of expectations on past inflation outcomes, and whether deflation leads to shifts in the level of inflation expectations. Recently, Ehrmann (2015) has used the approach to evaluate whether periods of below and above target inflation affect the anchoring of inflation expectations in ten advanced economies. Lyziak and Paloviita (2017) estimate a similar model to investigate whether the GFC affected the behaviour of inflation expectations in the euro area. Similarly, Blanchard (2016) investigates the dependence of inflation expectations on inflation outcomes in order to examine changes in anchoring over several decades.

Our survey expectations pertain to the relatively short run whereby some effects of currently observed shocks may persist in the forecast horizon. Thus, we effectively test whether deflation makes inflation expectations *more* dependent on past inflation outcomes and/or leads to a *lower* level of expectations than would be the case during periods of positive inflation rates.

We consider a panel fixed effects regression of the type:

where *E _{i}*

is a similarly specified dummy variable for high inflation periods. *X _{c}*

In the framework described by (1) above, evaluating whether deflation increases the dependence of expectations on past inflation outcomes amounts to testing whether the coefficient *p _{3}* on the interaction variable between deflation and lagged inflation is positive and statistically significant. Similarly, if high inflation renders expectations more dependent on lagged inflation outcomes, the coefficient

Equation (1) is estimated by ordinary least squares. We use heteroscedasticity- consistent standard errors clustered both by time and by forecaster, using the estimator for linear models with multi-dimensional fixed effects proposed by Correia

Thus, we relax the assumption that the errors are independently distributed within these two dimensions and allow the residuals to be correlated both within the same forecaster over time and across forecasters during the same time period.^{14}

The second approach to evaluate the behaviour of inflation expectations focuses on forecast disagreement, ie how much forecasters disagree about the same future inflation outcome. Forecast disagreement has been extensively studied in previous inflation literature, eg Mankiw et al (2004); Capistran and Timmermann (2009); Dovern et al (2012); Siklos (2013); Ehrmann (2015); but not in the context of deflations.

There are various reasons why forecast disagreement could rise during deflation. First, forecasters may be uncertain about the macroeconomic implications of deflation, including its potential interaction with debt. As prices fall, real debt burdens rise, which could lead to lower spending and even defaults (Fisher (1933); see also Borio et al (2015)). Such a dynamic could further exacerbate consumer price deflation dynamics.

Second, and relatedly, forecasters may view the historical evidence of deflations as unsettled. On the one hand, the experience of deflation during the Great Depression suggests that economies may be at risk of adverse deflations with aggregate demand deficiencies reflected in falling price levels and economic slack. On the other hand, the more benign experience of deflation in the latter part of the 19th century provides less evidence that deflation has strong negative feedback loops with aggregate demand (Bordo and Filardo (2005); Borio et al (2015); see, however, Eichengreen et al (2017)).

Third, asymmetries in individual forecasters' costs of over and under predicting inflation could be at play. The model by Capistran and Timmermann (2009) suggests that due to such factors, inflation forecast disagreement varies over time reflecting the level and variance of current inflation.

The estimated equation for forecast disagreement is of the type:

In (2), *disp _{ct}(n_{ct+h})* denotes the dispersion (disagreement) of next calendar year forecasts, for forecasts formed at period

In an equation similar to (2), Ehrmann (2015) includes the level of inflation expectations, to allow for the fact that higher inflation tends to be more volatile and therefore might be subject to more disagreement. We modify this by including *E _{ct}(abs(n_{ct+h})),* ie the absolute level of median expected inflation in the next calendar year in country c, with the expectation formed in period

The vector of lagged control variables *X*_{ct}__{1} in (2) comprises the output gap yf“^, deviations from the inflation target *infl gap _{c t}__{4}* and its squared term, the policy interest rate

as only a fraction of forecasters update their information sets in each period, giving rise to an endogenous rise in forecast dispersion when the economy faces large shocks affecting prices. The inclusion of squared change in the policy rate is also consistent with the empirical study by Dovern et al (2012) for G-7 countries, where the latter variable is used as a proxy for variation in monetary policy.

In this section, we analyse formally whether deflation has affected inflation expectations. First, we investigate whether there is evidence of unanchoring of inflation expectations, both in terms of the level of expected inflation and forecast disagreement. Second, we evaluate the role of the monetary policy framework and policy constraints posed by the zero lower bound. Finally, we go deeper to the tails of the forecast distribution and analyse the macroeconomic implications of shifts in the left-hand tail of forecast distribution.

First, we analyse whether deflation affects the level of inflation expectations. The level regressions are estimated using panels of forecaster-level data, yielding over 120,000 observations. We use forecaster and time fixed effects, clustering the standard errors both by forecaster and time period. Periods of inflation rates above 10% are excluded from all estimations in the paper.^{15}

The estimates in Table 1 suggest that deflation does affect the level of inflation expectations. Column (1) shows that expectations are somewhat backward-looking in our sample - the coefficient on the lagged inflation term is 0.310. Column (2) adds dummy variables for deflation and high inflation periods, respectively, while Column (3) additionally considers interaction terms of lagged inflation with deflation and high inflation dummy variables, respectively. Thus, the two models examine whether inflation expectations dynamics differ in periods of deflation and high inflation. These estimations suggest that deflations are associated with a downward level shift in expected inflation, by around 0.15 percentage points, as shown by the statistically significant negative coefficients on D^^{6}^. The interaction term between the deflation dummy variable with lagged inflation in Column (3) is positive and economically significant, yet only weakly significant in a statistical sense. The estimates imply that the coefficient on lagged inflation increases by 50% during deflations.^{16} Statistical significance is stronger for the interaction between high inflation and lagged inflation.

Results for longer deflations are broadly similar to the shorter ones. Columns (4) and (5) in Table 1 re-estimate Equation (1) using our second definition of deflationary episodes, where negative inflation rates persist for a minimum of twelve consecutive months. Persistent deflations are associated with an economically and statistically significant decline in the level of inflation expectations, by around 0.3 percentage points. At the same time, the interaction between the deflation dummy and lagged inflation is no longer statistically significant. Taken together, our results indicate that deflations affect the level of inflation expectations mainly through level shifts, with somewhat weaker evidence for increased backward-lookingness. These results suggest that deflations make it more difficult to return inflation to target.

The control variables in Columns (1) to (5) obtain coefficients with the expected signs. More positive output gaps are associated with higher levels of expected inflation, with highly statistically significant coefficients. While a faster rate of effective exchange rate appreciation and higher policy rates are associated with a decline in expected inflation, the coefficients are not significantly different from zero.

These results are robust to excluding the period of the GFC (September 2008- December 2009), as shown in Annex Table A4. In particular, when the GFC is excluded, the statistical significance of deflation-induced level shifts and greater backward- lookingness in expectations actually rises (Column (3)).

Our estimates show that deflation is also associated with greater forecast disagreement (Table 2). Using the interquartile range as the benchmark measure for disagreement, the coefficient on the deflation dummy in Column (1) is economically and statistically significant even in the presence of a battery of control variables - forecast dispersion rises by around 0.15 percentage points during deflation, compared to other periods. In contrast, high inflation does not lead to a further rise in forecast disagreement, beyond that already captured by a higher level of expected inflation. Indeed, Column (1) shows that when the absolute level of next year's forecast is higher, forecast disagreement is larger.^{18}

Does higher forecast disagreement during deflations simply reflect the fact that inflation is below the central bank's target? We include in Column (2) as further control variables the absolute deviation of inflation from the inflation target (the inflation gap in absolute terms) and the squared value of the gap. For countries that specify target ranges, the deviation refers to the distance of inflation from the midpoint of the target range. For economies that do not pursue IT, and for current inflation targeters prior to the adoption of IT, we use the deviation of inflation outcomes from a Hodrick-Prescott filtered trend, with a smoothing parameter of 14,400. We find that the coefficient on the deflation dummy remains robust to the inclusion of such variables, suggesting that deflations affect forecast disagreement beyond the impact of inflation gaps. Column (3) displays results for deflation periods that last a minimum of twelve months. They show that forecast disagreement rises also during the more persistent deflation periods, with a similarly sized coefficient estimate, albeit somewhat weaker statistical significance.

The other control variables in Table 2 obtain the expected signs and are in some cases highly statistically significant. Forecast disagreement rises in response to large changes in policy rates, and is also greater when changes in exchange rates are larger. The response is consistent with a framework where expectations are adjusted infrequently and there are costs to acquire and process inflation, such as a sticky information or rational inattention models.^{19} Moreover, forecast disagreement increases as the output gap falls, with the coefficient significant at the 1% level. The sign on the output gap is consistent with the results of Dovern et al (2012) for the G-7 economies. Our results are again robust to excluding the GFC; in this case, the rise in disagreement during persistent deflations becomes statistically significant at 5% level (Column (3) in Annex Table A5).

Does the monetary policy regime affect the relationship between deflation and inflation expectations? The behaviour of inflation expectations depends on the expected reaction (or lack) of monetary policy. For example, in IT regimes, monetary policy may be expected to address deflation concerns more aggressively than in regimes operating with less explicit inflation mandates, perhaps in order to maintain credibility of the announced targets. We investigate this by dividing the sample into IT economies and those pursuing other regimes, following the classification of countries in the working paper version of Mehrotra and Yetman (2017). We consider both the level of expectations (Table 3) and forecast disagreement (Table 4).

We find little systematic evidence that the monetary policy regime matters for the relationship between deflation and the level of inflation expectations. On the one hand, the negative coefficient on the deflation dummy variable is only (weakly) significant in a statistical sense for IT economies when all deflations are included (Table 3, Columns (1) and (2)). On the other hand, inflation expectations are more backward-looking in non-IT countries during deflations. During persistent deflations (Columns (3) and (4)), the deflation dummy variable is statistically significant for both inflation targeters and the non-inflation targeters (Table 3, Columns (3) and (4)).

Being an inflation targeter does make a difference in terms of forecast disagreement. For IT economies, deflations are not associated with a statistically significant increase in forecast disagreement, neither during all deflations nor when only persistent deflations are considered (Table 4, Columns (1) and (3)). This is in contrast to non-inflation targeters that see a greater rise in disagreement both during all deflations and during persistent deflations only (Table 4, Columns (2) and (4)).

Another factor affecting the behaviour of expectations during deflation is the possibility that conventional interest rate policy is constrained. Forecast dynamics and the macroeconomic implications of deflations may be expected to be more adverse if monetary policy is perceived to lack the tools to return inflation to target. In order to examine to what extent interest rates close to zero are affecting the results, we exclude periods with policy interest rates at levels of 0.5% or below from the level regressions (last two columns in Table 3) and from the regressions of forecast disagreement (last two columns in Table 4).

The level shifts in expectations and greater forecast disagreement during deflations do not appear to hinge on the zero interest rate floor. Regarding level shifts, while the coefficient on the deflation dummy does fall in statistical significance when periods of near-zero interest rates are excluded (Column (5) in Table 3), the absolute point estimate actually rises. There is also a large increase in the absolute value of the coefficient on persistent deflation periods ((Column (6) in Table 3).

Similarly, for forecast disagreement, the point estimates on the deflation dummy variables are somewhat higher when periods of near-zero interest rates are excluded from the analysis (Columns (5) and (6) in Table 4). This suggests that disagreement regarding future inflation - potentially reflecting diverging views about the persistence of deflation pressure and its macroeconomic implications - does not arise due to perceived lack of potency of monetary policy.

As we find a larger forecast disagreement to be a prominent feature of deflations, we further investigate changes in the forecast distribution by focusing on the tails of the distribution. Table 5 evaluates the effects on deflation on both the left and right tails, ie the 10th and 90th percentiles, respectively. In these estimations, the empirical specification follows the one used in the level regressions (Equation (1)).

The results suggest that deflations affect the left-hand tail of the distribution more than that in the right. The interaction between the deflation dummy and lagged inflation is significant at the 10th percentile (Columns (2) and (4)), especially during persistent deflations, but never at the 90th percentile (Columns (5) to (8)). Thus, expectations at the lower tail become more backward-looking during deflations. Similar results are obtained if the 25th and 75th percentiles are used instead; deflation episodes affect expectations in the left-hand tail, but not those in the right (Annex Table A6).

Contrasting with behaviour at the lower tail, expectations at the 90th percentile obtain an economically and statistically significant coefficient on the interaction between high inflation and lagged inflation (Table 5, Columns (6) and (8)). An identical result is obtained at the 75th percentile (Annex Table A6).

Do these shifts in forecast distributions have macroeconomic implications? Regarding forecast disagreement more generally, the primary cost of inflation in a New Keynesian model arises from price dispersion. If inflation forecast disagreement leads to firms setting prices too high or too low, there are costs due to an inefficient allocation of resources. Similarly, if inflation forecast disagreement reflects inflation uncertainty, the signals provided by prices could become blurred and hurt activity. Huizinga (2016) argues that inflation uncertainty could affect investment by increasing uncertainty about the real net present value of capital expenditures. Siklos (2016) suggests that the increase in forecast disagreement could negatively affect the credibility of the central bank. At the same time, greater dispersion does not necessary entail a slower convergence to an inflation target: this is the case if inflation forecasts are broadly centred at the central bank's target, and these mean forecasts are close to those used for price and wage setting, for example.

However, in order to examine the macroeconomic implications of forecast behaviour during deflations, one cannot simply examine the effects of greater inflation forecast disagreement. As the relationship between inflation outcomes and forecast dispersion is U-shaped, deflation periods cannot be identified through forecast disagreement alone. Instead, we use the result that there are changes in the left-hand tail of the forecast distribution during deflations which do not affect the right-hand tail. In particular, the higher backward-lookingness in the left-hand tail, even if only weakly statistically significant, can partly account for the higher forecast disagreement during deflations. Moreover, during persistent deflations, backward- lookingness increases only at the left-hand tail of the forecast distribution and not for the entire sample. This can be seen by comparing the interaction coefficients between persistent deflation and inflation outcomes, in particular Column 4 of Table 5 (which is positive and significant even at the 1% level), with Column 5 of Table 1 (which is not significantly different from zero). Thus, in what follows we use shifts in the left- hand tail that are not mirrored by the median, to examine the macroeconomic implications of forecast behaviour during deflations.

There are various economic reasons why shifts in the tails of the forecast distribution could be relevant. One possibility is that some forecasters in the tails are particularly sensitive to incoming information. Taking shifts in their expectations into account could then help policymakers anticipate future inflation. Another issue is that some states of the world - such as deflation and the ZLB - may be particularly costly and monitoring shifts in forecast tails can help avoid their realisation (Evans et al Andrade et al (2015) develop a measure called "Inflation-at-Risk" that is associated with the left- and right-hand tails and estimated based on surveys. They find that changes in inflation risks help predict future inflation in the United States and affect changes in the Fed Funds rate. Relatedly, Christensen et al (2012) measure deflation probabilities in the United States using yields on nominal and real Treasury bonds.

To examine the macroeconomic implications of shifts in the left-hand tail, we use a panel vector autoregression with fixed effects, as follows:

where *y _{c t}* is a vector of

The model incorporates monthly data for country *c* for the output gap, inflation, the policy interest rate, median inflation expectations, the left-hand tail (10th percentile) of the inflation forecast distribution and GDP growth forecast disagreement (the interquartile range), in the same order. All expectations variables refer to the next calendar year. The vector of exogenous variables is comprised of month dummy variables, each obtaining the value of one during a particular month and zero otherwise, to account for the changing forecast horizon over the calendar year. The model is estimated by generalised method of moments (GMM) for an identical sample as the panel regressions in the earlier part of the paper, again excluding observations with inflation rates exceeding 10% or policy rates in excess of 100%. Three lags are included in the VAR. The panel-specific fixed effects are removed through forward orthogonal deviation, with the lags of the transformed variables

instrumented by lags of the untransformed variables (see Abrigo and Love (2015) for details).

The usefulness of the VAR in this context hinges on the possibility to identify largely "exogenous" shocks to the lower tail of the inflation forecast distribution and trace their impact on the other variables in the system. For this purpose, after the estimation of the reduced form VAR, we use impulse response analysis and identify the shocks using a recursive identification scheme and a Cholesky decomposition of the variance-covariance matrix. The first three variables in the system form a block of macro variables, and their ordering follows conventional monetary VARs with interest rates ordered last. The slow responsiveness of output to shocks can be justified by rigidities such as predetermined expenditure plans, as in Rotemberg and Woodford (1997), and investment adjustment costs, as in Christiano et al (2005); that of inflation could result from costs of price adjustment, as in Rotemberg (1982). In contrast, we allow changes in professional forecasters' expectations to occur with a shorter delay. However, we restrict the contemporaneous impact of the left-hand tail shock on the median forecast to be zero. Given these assumptions, we can consider the shock to the lower tail a news shock that only affects a fraction of the forecasters instantaneously and does not have real economy implications during the month of the shock. 90% confidence intervals are used to illustrate parameter uncertainty, obtained with 1,000 Monte Carlo draws.

Graph 4 shows the response of all endogenous variables to a negative one standard deviation shock in the left-hand tail of the forecast distribution, until 40 months have passed from the shock. The shock to the left-hand tail is temporary and peters out slowly (upper left-hand panel). The median inflation forecast follows the tail and adjusts downward with a lag. Notably, the shock to the lower tail leads to a temporary increase in GDP forecast disagreement, with the largest effect occurring contemporaneously. Both the output gap and inflation fall. We also consider an alternative ordering of the endogenous variables, reversing the order of the last two: the left-hand tail of the inflation forecast distribution and GDP forecast disagreement. In these estimates as well, GDP forecast disagreement rises in response to a negative shock in the lower tail of inflation forecasts, with a statistically significant impact, after the contemporaneous (imposed) zero response.^{22}

The rise in GDP forecast dispersion, together with actual falls in the output gap and inflation, suggests that movement in the left-hand tail of the inflation forecast distribution could have real effects.^{23} Various papers document a link between forecast dispersion - or another closely-related proxy for uncertainty - and real activity. Using forecast disagreement measures based on Blue Chip surveys, Ferderer (1993) finds that uncertainty depresses investment activity. Similarly, Guiso and Parigi (1999) use firm-specific uncertainty measures from Italian manufacturing surveys and find that greater uncertainty weakens the response of investment to demand. Banerjee et al (2015) document that increases in GDP forecast disagreement, taken as proxy for demand uncertainty, have a negative effect on business investment in G-7 economies.

**5. Extensions and further robustness tests**

In this section, we consider various extensions and further robustness tests. We distinguish between periods of low inflation and deflation; examine the importance of the macroeconomic context in which the deflation occurs; evaluate common global trends in expectations; and use alternative measures for some of the explanatory variables.

One question is whether our results are indeed driven by deflation, or if they reflect the effect of low inflation on inflation expectations more broadly. Indeed, Ehrmann (2015) finds that below-target inflation weakens the anchoring of inflation expectations. To address this issue, we construct low inflation and persistent low inflation dummy variables similarly to their deflation counterparts, but using a threshold of 1% instead of zero inflation. The identified low inflation periods are thus a superset of the deflation episodes in the sample. We then include both the low inflation and deflation dummy variables in the level and disagreement regressions.

The results in Table 6 indicate that deflation has a significant effect on inflation expectations, beyond that of low inflation alone. In the level regressions, when all episodes of low inflations and deflations are included, only deflation periods lead to statistically significant downward shifts in expected inflation and greater backward- lookingness (Column (1)). And when only persistent episodes of low inflation and deflation are considered, both low inflation and deflation are associated with statistically significant declines in expected inflation, with the deflation dummy obtaining a larger negative coefficient (Column (2)). Similar results are obtained in the disagreement regressions, as shown in Columns (3) and (4). In particular, the deflation dummy obtains larger coefficients than the low inflation dummy even as deviations of inflation from the target and squared deviations are controlled for. However, in thelast two columns, the coefficient on the deflation dummy variable is only statistically significant when all deflations are considered.

Next, we examine whether the macroeconomic environment in which deflations occur plays a role. As the first category we consider periods of negative output gaps in order to capture the possibility that demand falling short of supply is contributing to deflation.

We also include episodes of strong exchange rate appreciation in order to capture deflations that occur due to exchange rate pass-through. Exchange rate appreciations have played a role in several deflations, including those in China during the late 1990s-early 2000s (Ha et al (2003)), and in Switzerland in the 2010s (IMF (2012)).

As a third category we consider deflations that occur during or after credit booms. As prices fall, real debt burdens rise, which could lead to lower spending and even defaults (Fisher (1933); see also Borio et al (2015)). Several papers highlight the prominent contribution of credit growth to financial instability (eg Kaminsky and Reinhart (1999); Schularick and Taylor (2012)). Financial distress may further exacerbate consumer price deflation dynamics. Such episodes could represent what Bordo and Filardo (2005) label "bad deflations" - the cause of additional weakness in the economy rather than only a symptom of weak demand.

We classify a deflation episode as belonging to one or more of the different categories if either during the deflation episode or in the twelve months preceding it one or several of the following occurred: (i) the output gap was negative; (ii) the y-o- y change in the nominal effective exchange rate (NEER) was above the 90th percentile; (iii) the credit gap, measured as the deviation of total credit to GDP from its long-run trend, was above 2 percentage points. Previous research has demonstrated the favourable performance of the credit gap as an early warning indicator of financial crises (eg Borio and Drehmann (2009)).

Out of the months that fall within our identified deflation episodes, 52% are associated with high credit gaps, 49% with large exchange rate appreciations, and a total of 99% with negative output gaps. Moreover, given the high shares of months allocated to the various type of deflations, there is significant overlap between them. In particular, 35% of the deflation episode months are classified as both credit gap and NEER deflations; 49% as both NEER and output deflations; and 52% as both credit gap and output deflations.

All three deflation environments have effects on the level of inflation expectations (Table 7, Columns (1)-(3)). For all three categories, the coefficient on the deflation dummy variable and its interaction with lagged inflation is significant at least at 10% level, suggesting increased backward-lookingness in expectations. The coefficient estimates on the interaction variables are larger for deflations associated with high credit gaps and exchange rate appreciations than for deflations occurring at times of negative output gaps, but the difference is not statistically significant. The result for exchange rate deflations is consistent with IMF (2015) that finds that disinflationary pressure from external factors, such as an appreciating NEER, was feeding into two-year ahead inflation expectations in 2011-14 in European IT countries.

All three environments are also significant drivers of higher forecast disagreement (Columns (4)-(6)). Deflations associated with negative output gaps and high credit gaps have positive coefficients that are significant at the 5% level; exchange rate-related deflations are significant at the 10% level. Thus, uncertainty about the macroeconomic implications of deflations appears to occur more robustly during or after credit booms, possibly due to concerns of debt deflation, and during periods of demand falling short of supply.

Next, we consider the existence of common global deflationary trends in the behaviour of inflation expectations. Indeed, deflation episodes have often occurred simultaneously across economies (Graph 1), and several studies find an important common component in inflation (eg Ciccarelli and Mojon (2010); Mumtaz and Surico (2012)). To do this, we plot in Graph 5 the estimated time fixed effects from the level regression (Column (3) of Table 1) as the orange line, as well as from the regression for forecast disagreement (Column (2) of Table 2) as the blue line.

Graph 5 shows that the time fixed effect from the level regression declined notably over the sample. It dips during the Asian financial crisis and then again during the "deflation scare" of the early 2000s. Another drop occurs during the GFC and then a more modest decline in 2014-15 when many economies are simultaneously experiencing deflations. Thus, there appears to be a global deflationary tendency in expectations during parts of the sample. Moreover, the time fixed effects from the level and disagreement regressions are negatively correlated during some time periods when many countries are experiencing very low inflation or deflation. In particular, the fixed effect from the disagreement regression surges as the fixed effect from the levels regression drops, both in the late 1990s and during the GFC.

**6. Conclusion**

In this paper, we analyse the behaviour of inflation expectations during periods of deflation, using a large cross-country data set of Consensus forecasts. We find some evidence of an unanchoring of expectations. Deflations are associated with a downward shift in the level of inflation expectations, somewhat higher backward- lookingness and greater forecast disagreement.

Whereas previous research has documented that forecast disagreement is increasing in the level of actual inflation outcomes, we uncover a U-shaped relationship when deflations are included, such that forecast disagreement rises with the absolute levels of both inflation and deflation outcomes. The increase in disagreement occurs over and above that caused by low positive inflation rates or deviations of inflation from the central bank's target. Our data suggest that the magnitude of forecast disagreement at an inflation rate of -1.7%, the lowest inflation outcome on average during deflation episodes, is similar to that observed when inflation rates are around 6%.

Delving deeper into the forecast distribution, we find that deflations are associated with movements in the left-hand tail rather than in the right-hand one. Such shifts appear to have macroeconomic implications: in addition to temporarily affecting output and inflation outcomes, negative shocks to the lower tail of inflation forecasts also lead to stronger disagreement about output forecasts.

While the paper provides the first systematic attempt to analyse forecast behaviour during deflation periods in a large number of economies, it leaves a number of questions open. For instance, it would be interesting to analyse which theoretical model could describe the behaviour of inflation expectations during deflations. While the dynamics of forecast disagreement appear to be partly consistent with sticky information model or rational inattention models, there are questions as to what extent such frameworks can be used to describe the behaviour of professional forecasters during deflations. Relatedly, one may wish to explore how forecast disagreement changes over time as the economy moves through deflation and eventually escapes from it. Finally, the costs of inflation forecast disagreement deserve further study, potentially by conducting a systematic analysis of the relationship between forecast dispersion and a large number of macroeconomic indicators.

**References**

Abrigo, M and I Love (2015): "Estimation of panel vector autoregression in Stata: a package of programs", *University of Hawaii Working Paper.*

Anand, R, E Prasad, B Zhang (2015): "What measure of inflation should a developing country central bank target?", *Journal of Monetary Economics* 74, pp. 102-116.

Andrade, P, E Ghysels and J Idier (2015): "Tails of inflation forecasts and tales of monetary policy", mimeo.

Ball, L and N Sheridan (2004): "Does inflation targeting matter?", In: B Bernanke and M Woodford (eds.), The inflation-targeting debate. University of Chicago Press.

Ballantyne, A, Gillitzer, C, Jacobs, D and E Rankin (2016): "Disagreement about inflation expectations", *Reserve Bank of Australia Research Discussion Paper* RDP 2016-02.

Banca d'ltalia (2017a): Box: Private sector contract renewals in 2016. *Economic Bulletin *No 1/2017.

Banerjee, R, J Kearns and M Lombardi (2015): "(Why) Is investment weak?", *BIS Quarterly Review,* March.

Bank of Canada (2017): Monetary policy report - October 2017.

Bank of Japan (2017): "Development in inflation expectations over the three years since the introduction of quantitative and qualitative monetary easing (QQE)", October.

Benhabib, J, S Schmitt-Grohe and M Uribe (2002): "Avoiding liquidity traps", *Journal of Political Economy* 110(3), pp. 535-63.

Blanchard, O (2016): "The Phillips Curve: Back to the '60s?", *American Economic Review *106(5), pp. 31-34.

Blanchard, O, E Cerutti and L Summers (2015): "Inflation and activity - two explorations and their monetary policy implications", *IMF Working Paper* 15/230.

Bordo, M and A Filardo (2005): "Deflation and monetary policy in a historical perspective: remembering the past or being condemned to repeat it?", *Economic Policy,* October, pp. 799-844.

Borio, C and M Drehmann (2009): "Assessing the risk of banking crises - revisited", *BIS Quarterly Review,* March.

Borio, C, A Filardo and B Hofmann (2015): "The costs of deflations: a historical perspective", *BIS Quarterly Review,* March.

Breach, T, S D'Amico and A Orphanides (2016): "The term structure and inflation uncertainty", *Federal Reserve Bank of Chicago Working Paper* 2016-22.

Buono I and S Formai (2016): "The evolution of the anchoring of inflation expectations", *Bank of Italy Occasional Paper* no 321.

Burdekin, R and P Siklos (eds) (2010): *Deflation. Current and historical perspectives. *Cambridge University Press.

Busetti, F, G Ferrero, A Gerali and A Locarno (2014): "Deflationary shocks and deanchoring of inflation expectations", *Occasional Paper* no. 252, Banca d'Italia.

Capistran, C and A Timmermann (2009): "Disagreement and biases in inflation expectations", *Journal of Money, Credit and Banking* 41(2-3), pp. 365-96.

Christensen, J, J Lopez and G Rudebusch (2012): "Extracting deflation probability forecasts from Treasury yields", *International Journal of Central Banking* 8(4),pp. 21-60.

Christiano, L J, M Eichenbaum and C L Evans (2005): "Nominal rigidities and the dynamic effects of a shock to monetary policy", *Journal of Political Economy* 113(1), pp. 1-45.

Ciccarelli, M and B Mojon (2010): "Global inflation", *Review of Economics and Statistics *92(3), pp. 524-535.

Coibion, O and Y Gorodnichenko (2015): "Is the Phillips curve alive and well after all? Inflation expectations and the missing disinflation", *American Economic Journal: Macroeconomics* 7(1), pp. 197-232.

Correia, S (2014): "reghdfe: Stata module to perform linear or instrumental-variable regression absorbing any number of high-dimensional fixed effects", *Statistical Software Components* s457874, Boston College Department of Economics, revised 25 July 2015

Dovern, J, U Fritsche and J Slacalek (2012): "Disagreement among forecasters in G7 countries", *The Review of Economics and Statistics* 94(4), pp. 1081-1096.

Draghi, M (2015): "Introductory statement to the press conference", Frankfurt am Main, 22 January.

Ehrmann, M (2015): "Targeting inflation from below: how do inflation expectations behave?", *International Journal of Central Banking* 11(S1), pp. 213-249.

Eichengreen, B, D Park and K Shin (2017): "Should the dangers of deflation be dismissed?", *Journal of Macroeconomics* 52, pp. 287-307.

Erceg, C and A Levin (2003): "Imperfect credibility and inflation persistence", *Journal of Monetary Economics* 15, pp. 915-944.

Evans, C, J Fisher, F Gourio and S Krane (2015): "Risk management for monetary policy near the zero lower bound", *Brookings Papers on Economic Activity,* Spring, pp. 141-196.

Faust, J and J Wright (2013): "Forecasting inflation", *Handbook of Economic Forecasting 2A,* 2-56, G Elliott and A Timmermann (eds), Elsevier, Amsterdam

Ferderer, J (1993): "Does uncertainty affect investment spending?", *Journal of Post Keynesian Economics* 16(1), pp. 19-35.

Fisher, I (1933): "The debt-deflation theory of great depressions", *Econometrica* 1(4), pp. 337-57.

Fuhrer, J (2017): "Japanese and U.S. inflation dynamics in the 21^{st} century", *IMES Discussion Paper* No. 2017-E-5.

Gerlach, S (2007): "Interest rate setting by the ECB, 1999-2006: Words and deeds", *International Journal of Central Banking* 3(3), 1-45.

Gerlach, S and P Kugler (2007): "Deflation and relative prices: Evidence from Japan and Hong Kong", *WWZ Working Paper* no 08/07.

Greenspan, A (2004): "Risk and uncertainty in monetary policy", Remarks at the meetings of the American Economic Association, San Diego, 3 January.

Guiso, L and G Parigi (1999): "Investment and demand uncertainty", *The Quarterly Journal of Economics*, 114(1), pp. 185-227.

Gurkaynak, R, A Levin and E Swanson (2010): "Does inflation targeting anchor long- run inflation expectations? Evidence from the US, UK, and Sweden", *Journal of the European Economic Association* 8(6), pp. 1208-1242.

Ha, J, K Fan and C Shu (2003): "The causes of inflation and deflation in mainland China", *Hong Kong Monetary Authority Quarterly Bulletin,* September, pp. 23-31

Hastie, T and R Tibshirani (1990): "Generalized Additive Models", *Monographs on Statistics and Applied Probability* 43, Chapman & Hall.

Huizinga, J (1993): "Inflation uncertainty, relatively price uncertainty, and investment in U.S. manufacturing", *Journal of Money, Credit and Banking* 25(3), pp. 521-549.

International Monetary Fund (2012): *Switzerland Article IV Report*, 2012.

International Monetary Fund (2015): "Cross-country report on inflation", *IMF Country Report* no. 15/184.

International Monetary Fund (2016): "Global disinflation in an era of constrained monetary policy", *World Economic Outlook,* Chapter 3, October, pp. 121-70.

Kaminsky, G and C Reinhart (1999): "The twin crises: the causes of banking and balance-of-payments problems", *American Economic Review* 89(3), pp. 473-500.

Kearns, J (2016): "Global inflation forecasts", *BIS Working Paper* no. 582.

Kenny, G and J Dovern (2017): "The long-term distribution of expected inflation in the euro area: what has changed since the great recession?", *ECB Working Paper* no. 1999.

Kortelainen, M, M Paloviita and M Viren (2011): "Observed inflation forecasts and the new Keynesian macro model", *Economics Letters* 112(1), pp. 88-90.

Kozicki, S and P A Tinsley (2012): "Effective use of survey inflation in estimating the evolution of expected inflation", *Journal of Money, Credit and Banking* 44(1), pp. 145-169.

Krippner, L (2016): "Documentation for measures of monetary policy", available at https://www.rbnz.govt.nz/- /media/ReserveBank/Files/Publications/Research/Additional%20research/Leo%20Kri ppner/5892888.pdf?la=en

Levin, A, F Natalucci and J Piger (2004): "The macroeconomic effects of inflation targeting", *Federal Reserve Bank of St. Louis Review*, 86(4), pp. 51-80.

Lyziak, T and M Paloviita (2016): "Anchoring of inflation expectations in the euro area: recent evidence based on survey data", *European Journal of Political Economy* 46, pp. 52-73.

Mankiw, N G and R Reis (2002): "Sticky information versus sticky prices: A proposal to replace the New Keynesian Phillips curve", *The Quarterly Journal of Economics* 117(4), pp. 1295-1328.

Mankiw, N G, R Reis and J Wolfers (2004): "Disagreement about inflation expectations", in: M Gertler and K Rogoff (eds), *NBER Macroeconomics Annual 2003, *pp. 209-48.

Mehrotra, A and J Yetman (2017): "Decaying expectations: what inflation forecasts tell us about the anchoring of inflation expectations", *International Journal of Central Banking*, forthcoming.

Mumtaz, H and P Surico (2012): "Evolving international inflation dynamics: world and country-specific factors", *Journal of the European Economic Association* 10(4), pp. 716-34.

Nakamura, E, J Steinsson, P Sun and D Villar (2017): "The elusive costs of inflation: price dispersion during the U.S. great inflation", *The Quarterly Journal of Economics, *forthcoming.

Nakata, T (2017): "Uncertainty at the zero lower bound", *American Economic Journal: Macroeconomics* 9(3), pp. 186-221.

Natoli, F and L Sigalotti (2017a): "A new indicator of inflation expectations anchoring", *ECB Working Paper* no. 1996.

Natoli, F and L Sigalotti (2017b): "Tail co-movement in inflation expectations as an indicator of anchoring", *International Journal of Central Banking,* forthcoming.

Nishizaki, K, T Sekine and Y Ueno (2014): "Chronic deflation in Japan", *Asian Economic Policy Review* 9(1), pp. 20-39.

Orphanides, A and J Williams (2005): "Imperfect knowledge, inflation expectations, and monetary policy", In The Inflation-Targeting Debate, edited by B Bernanke and M Woodford, Chicago: University of Chicago Press, pp. 201-234.

Rotemberg, J (1982), "Sticky Prices in the United States", *Journal of Political Economy, *90, pp. 1187-1211

Rotemberg, J and M Woodford (1997): "An optimization-based econometric framework for the evaluation of monetary policy" In NBER Macroeconomics Annual 1997, edited by B Bernanke and J Rotemberg. Cambridge, MA: MIT Press.

Schularick, M. and A Taylor (2012): "Credit booms gone bust: Monetary policy, leverage cycles, and financial crises, 1870-2008", *American Economic Review* 102(2), pp. 1029-61.

Siklos, P (2013): "Sources of disagreement in inflation forecasts: An international empirical investigation", *Journal of International Economics* 90(1), pp. 218-31.

Siklos, P (2016): "Forecast disagreement and inflation outlook: New international evidence", *IMES Discussion Paper* 2016-E-3.

Smith, G (2006): "The spectre of deflation: A review of empirical evidence", *Canadian Journal of Economics* 39(4), pp. 1041-72.

Wiederholt, M (2015): "Empirical properties of inflation expectations and the zero lower bound", mimeo.

Williams, J C (2009): "The risk of deflation", *FRBSF Economic Letter* 2009-12, Federal Reserve Bank of San Francisco.

Yetman, J (2017a): "The evolution of inflation expectations in Canada and the US", *Canadian Journal of Economics* 50(3), pp. 711-37.

Yetman, J (2017b): "The perils of approximating fixed horizon inflation forecasts with fixed event forecasts", mimeo.