Three essays on Inflation Expectations
Thèse
Rolande Carine Baï Kpekou Tossou
Doctorat en économique
Philosophiæ doctor (Ph. D.)
Three Essays on Inflation Expectations
Thèse
Rolande Carine B. Kpekou Tossou
Sous la direction de:
Kevin Moran, directeur de recherche Charles Bellemare, codirecteur de recherche
Résumé
Cette thèse, organisée en trois chapitres, analyse comment différents types d’agents (les ex-perts, les ménages) forment leurs attentes à propos de l’inflation, une des questions les plus importantes en macroéconomie.
Le premier chapitre évalue les implications d’un comportement stratégique de la part des experts dont les opinions constituent la base des enquêtes comme "Survey of Professional Forecasters". Nous posons l’existence d’un désir de conformisme de la part de ces répondants et montrons que sa présence affecte la qualité des signaux envoyés aux autorités monétaires à propos de l’inflation future.
Le deuxième chapitre utilise les données de deux enquêtes récemment établies sur les attentes des consommateurs : l’Enquête américaine sur les attentes des consommateurs (Fed de New York) et l’Enquête canadienne sur les attentes des consommateurs (Banque du Canada), pour comparer le processus de formations et de mise à jour des attentes inflationnistes aux Etats-Unis et au Canada. Nos résultats mettent en évidence certaines différences entre les deux pays qui s’expliqueraient probablement par des différences dans leur régime de politique monétaire et dans la conception des enquêtes.
Le troisième chapitre présente des résultats descriptifs pour caractériser les attentes inflation-nistes des ménages canadiens et tester certains résultats obtenus sur les données américaines. Il étudie le lien entre les attentes inflationnistes et les perceptions de l’inflation passée, ainsi que leur évolution et leur biais. La plupart des résultats sont cohérents avec ceux obtenus avec les données américaines. Nous documentons également le lien entre les attentes inflationnistes et les attentes à propos de certaines variables économiques clées telles que les dépenses, le taux d’intérêt et le taux de croissance des salaires.
Abstract
This thesis, organized in three chapters, analyzes how a variety of economic agents (professional forecasters and households) form their expectations about future expectations, one of the most important questions in macroeconomics.
The first chapter investigates the implications of strategic behaviour among professional fore-casters whose opinions form the basis of surveys like the Survey of Professional Forefore-casters. We posit the existence of a conformism impulse among the survey respondents and show that its presence affects the signal about future inflation that monetary authorities extract from survey responses.
The second chapter uses data from two recently-established surveys on consumer expectations: the US Survey of Consumers Expectations (New York Fed) and the Canadian Survey of Consumers Expectations (Bank of Canada), to compare how consumers formulate and update inflation expectations in the US and Canada. Our results highlight some differences between the two countries which are likely explained by differences in their monetary policy framework and the surveys design.
The third chapter presents some descriptive results to characterize households’ inflation ex-pectations in Canada, and test some results that have been obtained on US data. It studies the link between inflation expectations and inflation perceptions, as well as change and bias in both. Most of results are consistent with those obtained with US data. We also document the link between inflation expectations and expectations about key economic variables such as spending, interest rate and wage growth.
Table des matières
Résumé iii
Abstract iv
Table des matières v
Liste des tableaux vii
Liste des figures viii
Remerciements xi
Avant-propos xiii
Introduction 1
1 Conformism and Inflation Expectations Surveys 4
1.1 Résumé . . . 4 1.2 Abstract . . . 5 1.3 Introduction. . . 6 1.4 The Model . . . 8 1.5 Empirical evidence . . . 13 1.6 Conclusion . . . 18 1.7 Bibliographie . . . 20
2 The Determinants of Consumers’Inflation Expectations : Evidence from the US and Canada 22 2.1 Résumé . . . 22
2.2 Abstract . . . 23
2.3 Introduction. . . 24
2.4 Data and descriptive analysis . . . 26
2.5 The determinants of consumers’ inflation expectations in the US and in Canada . . . 34
2.6 Benchmark Results . . . 37
2.7 Sensitivity analysis . . . 45
2.8 Conclusion . . . 49
2.9 Bibliographie . . . 50
3.1 Résumé . . . 52
3.2 Abstract . . . 53
3.3 Introduction. . . 54
3.4 Data . . . 56
3.5 Inflation expectations and inflation perceptions . . . 57
3.6 Inflation expectations and expectations about key economic variables . . . . 66
3.7 Conclusion . . . 74
3.8 Bibliographie . . . 76
Conclusion 79
A Appendix for Chapter 1 81
B Appendix for Chapter 2 85
Liste des tableaux
1.1 Forecast errors . . . 17
1.2 Maximization of posterior distribution . . . 18
2.1 Heterogeneity in inflation expectations . . . 32
2.2 Distribution of estimated parameters . . . 38
2.3 Weights on realized inflation and lagged expectations : Cross-section heteroge-neity . . . 39
2.4 Weights on public signal and individual volatility : Cross-section heterogeneity 41 2.5 Heterogeneity in estimated gain γi,s . . . 44
2.6 Distribution of estimated parameters : Alternative specification . . . 46
2.7 Distribution of estimated parameters : impact of survey frequency . . . 47
2.8 Distribution of estimated parameters : Changes in gas price . . . 48
2.9 Distribution of estimated parameters : Changes in food price . . . 48
3.1 Link between inflation expectations and inflation perceptions. . . 61
3.2 Bias in inflation expectations and perceptions . . . 64
3.3 Determinants of changes in inflation expectations . . . 67
3.4 Euler equation without control . . . 70
3.5 Excess sensitivity to expected income growth without control . . . 71
3.6 Inflation expectations and expectations about wage growth and interest rates . 73 B.1 Weights on realized inflation and lagged expectations : Alternative Specification 85 B.2 Weights on public signal and individual volatility : Alternative Specification . . 86
B.3 Heterogeneity in estimated gain γi,s : Alternative specification . . . 87
B.4 Weights on realized inflation and lagged expectations : Changes in gasoline price 88 B.5 Weights on public signal and individual volatility : Changes in gasoline price . 89 B.6 Weights on realized inflation and lagged expectations : Changes in food price . 90 B.7 Weights on public signal and individual volatility : Changes in food price . . . 91
C.1 Determinants of inflation perceptions . . . 93
C.2 Bias in inflation expectations and perceptions by socio-economic characteristics 94 C.3 Determinants of changes in inflation perceptions . . . 95
C.4 Subjective inter-temporal by employment situation . . . 96
C.5 Subjective inter-temporal by the number of working hours . . . 97
C.6 Subjective inter-temporal by type of work . . . 98
C.7 Subjective inter-temporal by financial situation . . . 99
Liste des figures
1.1 Median and Standard Deviation (“Disagreement”) in Reported Forecasts for the
Inflation Rate : SPF and Livingstone Surveys . . . 15
2.1 One-year ahead inflation expectations vs realized inflation . . . 29
2.2 Distribution of Inflation Expectations . . . 30
2.3 Disagreement in Inflation Expectations : Interquartile Range . . . 31
2.4 Average change in one-year-ahead inflation expectations . . . 33
2.5 Median change in one-year-ahead inflation expectations . . . 34
2.6 Estimated volatility . . . 42
2.7 Estimated gain parameters, by quantiles . . . 43
3.1 Consumers’ perceptions and expectations are above actual CPI inflation . . . . 58
3.2 Half of the values of inflation perceptions and expectations are within 1-3 range. 59 3.3 Inflation perceptions and inflation expectations are positively related . . . 59
3.4 Changes in inflation perceptions and changes in inflation expectations are po-sitively related . . . 66
B.1 Estimated gain parameters, by quantiles : Alternative specification . . . 86
A mon père Paulin, mon amour Antoine et ma fille Exaucée.
"Current economic outcomes are determined by what people think the future will be, not necessarily by what the future will actually be"
Jean Boivin, Deputy-governor bank of Canada (2010-2012)
Remerciements
Je suis très chanceuse d’avoir travaillé avec trois professeurs ayant des domaines d’expertise très différents, c’est ce qui fait la richesse de ma thèse. Leurs conseils et orientations multiformes m’ont permis d’aller au bout de ce long cheminement. Qu’il me soit permis de leur exprimer ma profonde gratitude.
— Je remercie très sincèrement mon directeur de thèse Kevin Moran pour sa confiance, son soutien, sa disponibilité, sa bonne humueur, et pour tout le temps passé à lire et commenter mon travail. Merci de m’avoir accompagnée aussi bien dans ma thèse que sur le marché du travail et de m’avoir appuyée pour mon stage à la banque du Canada. J’ai aussi été honorée d’avoir été associée au projet BCEAO, j’ai beaucoup appris de ton expertise. Merci pour tout Kevin !
— J’exprime également ma profonde gratitude à mon co-directeur Charles Bellemare pour son accompagnement, sa disponibilité et ses belles idées et suggestions qui ont permis le meilleur avancement possible de cette thèse. Merci de m’avoir proposé de travailler sur les enquêtes sur les anticipations des ménages. Merci également pour le financement dont j’ai bénéficié durant ma thèse.
— Je tiens à remercier Vincent Boucher pour le dévouement et l’enthousiasme dont il a fait preuve sur mon premier projet. Il s’est toujours montré disponible quelque soit les circonstances. Merci pour ta volonté extraordinaire d’aider ses étudiants.
Ma reconnaissance va à l’endroit de tout le corps professoral du département d’économique de l’Université Laval pour tout ce que j’ai appris d’eux. Plus particulièrement, je remercie les professeurs Benôit Carmichael, Stephen Gordon et Bernard Fortin pour leur précieux commen-taires. Je remercie également le personnel administratif du département pour leur disponibilité sans cesse renouvellée. Un merci spécial à Josée Desgagnés et Martine Guay.
Je remercie très particulièrement le sous-gouverneur de la banque du Canada Larry Schem-bri pour m’avoir permis d’effectuer ce stage très bénéfique à la banque du Canada et pour toutes les discussions très enrichissantes que nous avons eues. Je remercie Patrick Sabourin de m’avoir acceuillie très charleuresement dans la division "Price, Labour and Housing" et m’avoir permis d’avoir un accès spécial aux données de l’Enquête Canadienne sur les attentes des ménages. Je n’oublie pas toutes les merveilleuses personnes que j’ai rencontrées durant
mon stage. Je remercie particulièrement Katsiaryna Katarshova, Olena Kostyshyna, Meh Cé-saire, Sharon Kozicki, Bruno Feunou, Rodrigo Sekkel, Willy Chetwin, Alexander Ueberfeldt Natasha Laponce et Dmitry Matveev.
Faire mon doctorat au Canada, et plus particulièrement à l’université Laval, était le seul moyen pour moi de retrouver Antoine, mon amour. Je suis contente d’avoir fait cette thèse pour toi. Je suis profondément reconnaissante du soutien inconditionnel que j’ai reçu de toi tout au long de mon doctorat. Merci pour tout chéri !
Mes chaleureux remerciements vont à l’endroit de mes collègues et amis, Élysée A. Hounde-toungan, Jean-Louis Bago, Daouda Belem, Morvan Nongni, Ibrahima Sarr, Ibrahima Diallo, Marius Sossou, Koffi Akakpo et Blanchard Conombo pour les discussions instructives et les bons moments passés ensembles.
Enfin, j’exprime ma gratitude à mes parents, Paulin et Romaine pour tous les sacrifices consen-tis pour mon éducation, merci pour votre soutien. Je remercie ma soeur Bélinda et son époux Marius, ma soeur Lucresse et mes frères Pacôme et Gorges pour leur soutien. Je n’oublie pas mes grands-parents Gabriel et Bernadette pour leurs bénédictions.
Ce cheminement n’aurait pas été possible sans le soutien financier du Département d’écono-mique de l’Université Laval, de mon co-directeur Charles Bellemare, du Centre de Recherche sur les Risques, les Enjux Economiques et les Politiques Publiques (CRREP), du Fonds de Recherche du Québec Société et Culture (FRQSC) et la Faculté des Sciences Sociales que je remercie ici.
Avant-propos
Cette thèse s’articule autour de trois chapitres indépendants qui s’inscrivent dans la littéra-ture sur le processus de formation des anticipations en Macroéconomie. Les trois chapitres constituent des articles à soumettre à des revues scientifiques avec comité de lecture. Je suis la principale auteure de chacun de ces trois articles. Le premier chapitre est un article réalisé avec mon directeur de thèse, Kevin Moran et Vincent Boucher. Le deuxième chapitre est un article réalisé avec mes co-directeurs de thèse, Kevin Moran et Charles Bellemare. Le troi-sième chapitre est un article réalisé avec Olena Kostyshyna, économiste séniore à la banque du Canada.
Introduction
Inflation expectations are one of the most important variables in macroeconomics and finance. For businesses, inflation expectations influence how workers and firms set prices and wages ; for households, inflation expectations have an impact on consumption and savings decisions. They also determine the level of real interest rates ; and, especially over longer horizons, provide an indication of the central banks’ inflation targeting credibility. It is therefore critical to carefully measure and interpret the signals sent by a variety of economic agents through inflation expectations.
There are two main ways to measure inflation expectations : survey-based measures and market-based measures. Market-based inflation expectations can be computed by comparing nominal interest rates to their inflation protected counterparts. As discussed Cunningham et
al. (2010), there are advantages and disadvantages to each type of measure.
In recent decades, survey-based inflation expectations are increasingly being subject to both empirical and theoretical analysis because they have a large breadth of coverage, including professional forecasters (also known as experts), firms and households. These categories of agents can differ considerably in their reported expectations as well as in their incentive when responding to the survey. Depending on the context central banks decide whose expectations it should care about.Coibion et al. (2018)document a number of dimensions along with inflation expectations of these different types of agents differ. This thesis contributes to the growing literature on inflation expectations formation process by focusing on professional forecasters and households’ expectations.
Central bank discussions and communications often focus on expectations by professional fo-recasters. Their expectations drives contemporaneous long-term interest rates and therefore provides a direct transmission mechanism of monetary policy actions to households’ and firms’ decisions (Coibion et al. 2018). However, professional forecasters may face various incentive when reporting expectations (Lamont, 2002 ; Laster et al., 1999 ; Ehrbeck and Waldmann, 1996), which may call into question the informativeness of their reported expectations. The first chapter analyzes the impact of a desire for conformism among professional forecasters on the signal about future inflation that central banks may extract from surveys. We use a game theory framework similar to those in Morris and Shin (2002) who study how private
and public signals may interact in games of strategic interaction between experts surveyed for their opinion and a monetary authority endowed with its own-in-house forecasting model. Specifically, we posit that survey participants receive both a private signal and a public one about future inflation and are then asked for a point forecast. They aim to report accurate but also consensual predictions, through a desire for conformism. We solve for the Bayesian Nash equilibrium the induced game and study the impact conformism for the accuracy of reported inflation predictions. Relative to Morris and Shin (2002), our emphasis on a desire for conformity is original and has important implications for how monetary authorities should incorporate survey data in their policy deliberations. We find that the experts’ average pre-diction constitutes an unbiased estimate of future inflation and that conformism reduces the variance of the experts’ predictions. As such, the presence of conformism may at first appear to improve the reliability of survey data as signals for future inflation. We also show that the presence of conformism, by increasing the desire of survey respondents to closely align toge-ther, may steer them to coordinate on the public signal and to dismiss potentially important information contained in their private ones. As such, a central bank suspecting a high level of conformism within surveyed experts should be very wary when experts’ average prediction differs even modestly from its Staff or the public forecast.
While a substantial body of empirical research has shown how professional forecasters form their inflation expectations and what characterize them (close to the inflation target on average with little cross-sectional variation, seeCoibion et al (2018), strategic behaviour, etc), there is no consensus on the best approach to model how household inflation expectations are formed. Especially in Canada, nothing is known about households’ inflation expectations, as a regular survey on consumers expectations did not exist until recently. Having a privileged access to the Canadian Survey of Consumers expectations, a new survey conducted by the Bank of Canada, we present first evidence on how Canadian households form their expectations about future inflation.
Specifically, we propose in the second chapter a model of household level inflation expectations that links individual consumers’ inflation expectations to their own lagged forecasts as well as proxies for the rational expectation forecasts. The model builds on the existing noisy infor-mation framework (Vellekoop and Wiederholt, 2019 ; Coibion and Gorodnichenko, 2015) and extends it in several dimensions. We explicitly model the expectations updating rule which consumers use to incorporate new information in their experience and take seriously hete-rogeneity in inflation expectations extensively documented in the literature. We exploit rich information present in the Survey of Consumer Expectations (New York Fed) and the Cana-dian Survey of Consumer Expectations (Bank of Canada) to estimate and compare findings for the US and Canada. Tackling this comparison had not been possible prior to this research because of the lack of data on Canadian households’ expectations. We find that inflation ex-pectations appear to correlate more strongly to measures of rational exex-pectations forecasts,
as a least-square learning forecast or the median response in the survey of professional fore-casters, in Canada than in the US, and conversely less to lagged expectations. The observed differences are likely explained by differences in the monetary policy framework in the two countries and in the survey design.
Finally, the third chapter presents some descriptive results to characterize households’ inflation expectations in Canada, and test some results that have been obtained on US data. We present evidence of the link between inflation expectations and inflation perceptions, as well as change and bias in both. Most of results are consistent with those obtained with US data. We also document the link between inflation expectations and expectations about key economic variables such as spending, interest rate and wage growth. We estimate Euler equation and find that the link between real spending growth expectations and inflation expectations is as expected by theory, with estimated intertemporal elasticity of substitution in the range between 0.6 and 0.9, consistent with findings in the literature.
Chapitre 1
Conformism and Inflation
Expectations Surveys
1.1
Résumé
Nous développons un modèle d’interaction stratégique entre les experts participant aux en-quêtes sur les attentes inflationnistes et étudions les implications d’un désir de conformisme sur les attentes rapportées dans ces enquêtes. Nous supposons que les experts reçoivent à la fois un signal privé et un signal public sur l’inflation future et sont ensuite invités à fournir des prévisions ponctuelles. Nous montrons que le désir de conformisme amène les experts à négliger leur signal privé et à coordonner leur prévision autour du signal public et donc réduit la variance des prévisions. Une banque centrale soupçonnant un degré élevé de conformisme dans ces sondages devrait donc prêter une attention particulière aux prévisions s’écartant même modestement du consensus.
Classification JEL : D82, E31, E37, E58
1.2
Abstract
We develop a model of strategic interaction between the experts participating in surveys about inflation expectations and study the implications of a desire for conformism on their reported expectations. We posit that experts receive both a private signal and a public one about future inflation and are then asked for a point forecast. We show that the desire for conformism leads them to de-emphasize their private signal about future inflation and coordinate their reported forecasts around the public ones, and then reduces the variance of the experts’ predictions. A Central Bank suspecting high degrees of such conformism in relevant surveys should therefore pay close attention to reported predictions departing even modestly from consensus.
JEL Codes : JEL Codes : D82, E31, E37, E58
1.3
Introduction
Survey data on the inflation expectations of businesses, consumers or investors have become important tools for central banks and policy makers worldwide. These data become available on a very timely manner and are not revised, two advantages that have contributed to their increased role in informing policy decisions. Considerable resources are thus employed by many organizations to develop, manage and study these surveys and the data they generate. This increased reliance on survey data has heightened interest for the incentives faced and ob-jectives pursued by survey participants. For instance, Croushore(1997) evokes the possibility that the experts participating in the Livingstone survey may report forecasts directed towards consensus in order to avoid unfavorable publicity if the forecasts are latter shown to be incor-rect. Alternatively,Lamont(2002) andLaster et al. (1999) argue that professional forecasters may report forecasts that aim at optimizing profits, reputation, shock value, or marketability, whileEhrbeck and Waldmann(1996) report evidence that they may bias forecasts in direction of the ablest forecasters. Relatedly, Clements (2015) posits the presence of a herding beha-viour among professional forecasters and presents evidence that such herding is present at the shortest forecast horizon (one quarter ahead), while also reporting that forecasters appear to exaggerate differences in their forecasts for the longer horizons.
This variety in the possible motives of survey participants calls into question the informati-veness of the signal about future inflation that central banks may extract from surveys. To study this issue, the present paper develops a model of strategic interaction between the ex-perts participating in a survey about inflation expectations and characterizes its implications. Specifically, we posit that survey participants receive both a private signal and a public one about future inflation and are then asked for a point forecast. We assume that the experts aim to report accurate but also consensual predictions, through a desire for conformism. This motivates each participant to alter their reported predictions such that they do not differ si-gnificantly one from the other. We solve for the Bayesian Nash equilibrium the induced game and study the impact conformism for the accuracy of reported inflation predictions.
Our findings are as follows. First, we show that the experts’ average prediction constitutes an unbiased estimate of future inflation and that conformism reduces the variance of the experts’ predictions. As such, the presence of conformism may at first appear to improve the reliability of survey data as signals for future inflation. However, we also show that this variance decrease may be misleading : as it stems from the desire to not report outlier forecasts, it may be discarding valuable information. Second, we derive how a central bank should formally incorporate the signals received from surveys, by computing the Bayesian posterior predictor of future inflation when the prior is the central bank’s Staff or public forecast. We show that the presence of conformism, by increasing the desire of survey respondents to closely align together, may steer them to coordinate on the public signal and to dismiss potentially
important information contained in their private ones. As such, a central bank suspecting a high level of conformism within surveyed experts should be very wary when experts’ average prediction differs even modestly from its Staff or the public forecast. Third, we show through an empirical application using recent inflation history that the best historical forecast for inflation is obtained by a central bank assuming a low-to-negligible degree of conformism. This suggests that the recent inflation experience has not included any significantly-volatile episode for the private signals received by experts to contain crucial signals about upcoming accelerations in inflation.
A significant literature has studied the statistical properties of inflation forecasts drawn from surveys, assessing whether they are unbiased, efficient, or characterizing the heterogeneity across participants they contain. Exemplified by contributions such as Roberts (1997), Tho-mas (1999),Mehra(2002),Mankiw et al. (2003) orJain(2018), this literature has motivated researchers to reevaluate the relevance of rational expectations as the key building blocks of macroeconomic modelling (Coibion et al.,2018). Our paper contributes to this literature by showing how a desire for conformism may affect the properties of reported inflation expecta-tions.
Our paper also recalls the literature, exemplified by Morris and Shin (2002), studying how private and public signals may interact in games of strategic interactions between experts surveyed for their opinions and a monetary authority endowed with its own in-house forecasting model. Relative toMorris and Shin(2002), our emphasis on a desire for conformity is original and has important implications for how monetary authorities should incorporate survey data in their policy deliberations.
Our paper also contributes more generally to the literature on conformism e.g. Blume et al. (2015), Boucher (2016) and Patacchini and Zenou (2009). In particular Blume et al. (2015) present a model of conformism with imperfect information and quadratic preferences. In their setting, individuals have privately known tastes but want to conform their behaviour. In our setting however, individuals (i.e. the forecasters) have private information about the unknown inflation rate and want to conform with the predictions of their peers. We show that we still obtain a unique Bayesian Nash equilibrium, which can only be expressed analytically by imposing parametric assumptions on the distribution of the inflation rate and the forecasters’ private signals.
The remaining of the paper is structured as follows. In Section 1.4, we present our conformism model and derive the main theoretical results. Section1.5presents the data and our empirical application. We conclude in Section 1.6.
1.4
The Model
We present a model where a finite number of experts are asked to make point predictions about the rate of inflation. Experts are concerned about reporting accurate but also consensual predictions. The timing of events is as follows :
1. At each period t, Nature chooses next period’s inflation rate st+1 from the distribution
S.
2. Each expert independently receives a private signal θi,t about next period’s inflation,
from a distribution Θ(st+1) such that Eθi,t= st+1.
3. Experts are simultaneously asked to provide a point prediction pi,t of st+1 given their
private information θi,t.
The distribution S represents the prior information about the inflation rate, is common know-ledge and in practice can be a function of the current and past inflation rates as well as any other economic variable, to accommodate various time series properties found in actual infla-tion processes.1In addition, Eθi,t = st+1implies that we assume private signals to be unbiased
indicators of future inflation. We also restrict the experts’ message space to a single point pre-diction pi,t because this matches the practice of most surveys about inflation expectations
and to abstract from strategic concerns between the principal and the expert (Ottaviani and Sørensen,2006).2
We assume that the experts’ expected utility is given by : U (pi,t, p−i,t, θi,t) = EsEθ−i
−(1 − α) 2 [pi,t(θi,t) − st+1] 2 + −α 2(n − 1) X j6=i
[pi,t(θi,t) − pj,t(θj,t)]2|θi,t
(1.1) for α ∈ [0, 1]. Similar utility functions have been used in the literature, e.g. Morris and Shin (2002) or Patacchini and Zenou(2009).
The utility function is a convex combination of two different costs. The first one is an accuracy cost : experts loose utility if their prediction pi,t is far from the realized inflation rate st+1. The second one is a conformity cost : experts loose utility if their prediction is far from the other experts’ predictions.
A central feature of our model is that experts do not observe the other experts’ predictions, nor do they observe their private signals. Each expert must therefore use their private signal (and the public signal) in order to predict the true inflation rate as well as the other experts’
1. Note that we are abstracting from feedback loops wherein expectations may feed into actual future inflation rates, for instance via the decisions of price-setters in New Keynesian models. Our set-up remains valid as long as the expectations of the experts in the survey are not perfectly correlated with the aggregate expectations about future inflation rates entering the feedback loop.
2. The more recently established Survey of Consumer Expectations at the New York Federal Reserve Bank elicits information about the distribution of variables of interests, in addition to point predictions
predictions. This approach, similar to the one used by Blume et al. (2015), leads to a static Bayesian game with the following characteristics.3
Proposition 1 Suppose that S, Θ(), and {pi,t()}i are in L2, then :
1. If α = 1, there is an infinity of Bayesian Nash equilibria. In particular, any solution of the form pi,t(θi,t) = pj,t(θj,t) = p∗ for all i, j is an equilibrium.
2. If α ∈ [0, 1), there exists a unique Bayesian Nash equilibrium. Moreover, it is symmetric in the sense that p∗i(θi,t) = p∗(θi,t) for all i and such that :
p∗t(θi,t) = (1 − α)Est+1|θi,t+ αEp∗t(θj,t)|θi,t (1.2)
The technical assumption in Proposition 1 ensures that the utility function is always well defined.
If α = 1, there is no accuracy cost and experts only want to match the predictions of the other experts. In that case, any prediction, when simultaneously reported by all experts, is an equilibrium. By contrast, when α ∈ [1, 0), the accuracy cost acts as a coordination mechanism that helps direct the experts’ reported prediction towards the expectation of the inflation rate. In such a case, the equilibrium is unique and given by (1.2), which shows that the optimal prediction is a convex combination between the expected inflation rate and the expected prediction of the other experts. Note that since the equilibrium is symmetric, the number or identity of the other experts is not important : from a given expert’s point of view, all the other experts are identical.
The general expression in (1.2) does not admit closed-form solutions (but see Section 1.4.1 below for a closed-form expression obtained by assuming normally distributed shocks). Impor-tant properties of the equilibrium can be derived even without those assumptions, however. Formally :
Proposition 2 Suppose that (1.2) holds, then 1. Ep∗(θi,t) = Est+1
2. V ar(p∗(θi,t)) ≤ V ar(Est+1|θi,t)
Here, the expectations are taken with respect to the private signals. The first part of Propo-sition 2 says that ex ante, the expected prediction is equal to the expected inflation rate. As
such, conformism does not bias the average prediction. This is typical of conformism games and is featured for instance in Boucher(2016), Patacchini and Zenou(2009), and Morris and Shin (2002).4 We show in Section 1.5.2 that this has an important impact on our ability to identify the level of conformism α from the data.
The second part of Proposition 2 is also typical of conformism games : conformism reduces the variance of the predictions. We will see that this has important implication for the infor-mativeness of the experts’ prediction for the central Bank as the distribution of predictions are unlikely to contain extreme values when conformism is high.
Finally, it is worth noting that the inequality in this second part of Proposition2 is generally strict, i.e. whenever α ∈ (0, 1) and the distribution of θi,t is informative about st and not
degenerate.
The next subsection makes additional distributional assumptions in order to obtain closed-form solutions and some additional insights.
1.4.1 A Parametric Specification with Normal Disturbances
Let xt be a series of observable variables at time t and st = {sτ}t
τ =−∞ be the history of
previous inflation rates. Let the inflation rate at time t be given by
st+1= φ (st, xt) + εt+1 (1.3)
where
εt+1∼ N (0, σε2).
Then, at each period Nature chooses the inflation rate according to S = N (φ (st, xt) , σε2)
and (1.3) is the common-knowledge data generating process for st+1. We refer to φ (st, xt) as
the “public signal” as it represents an ex-ante unbiased estimate of the inflation rate and is a commonly known quantity. In practice, one may think of φ as a state-of-the-art forecasting model for inflation based on easily accessible public data, such as the factor models assessed inStock and Watson (1999).
We assume that the experts’ private signals are given by
θi,t= st+1+ νi,t (1.4)
where νi,t ∼ N (0, σν2), so Θ(st+1) = N (st+1, σ2ν). As such, all signals have the same precision
but every expert observes a different signal.
The use of normal distributions is convenient since conjugate normal distributions result in a normally distributed posterior distribution (see the Appendix for details and technical deriva-tions).
Moreover, these assumptions allow us to solve for the experts’ prediction as an explicit function of the model’s fundamentals. Using a “guess and verify” approach, described in detailed in the Appendix, we find that an expert’s prediction can be expressed as a convex combination between his private signal and the public signal. Specifically :
p∗(θi,t) = w(σ2ε, σν2, α) φ (st, xt) + [1 − w(σ2ε, σν2, α)] θi,t, (1.5)
where the weight on the public signal is w(σ2ε, σν2, α) = σ
2 ν
σ2
ε(1 − α) + σ2ν
. Straightforward computations show that ∂w∂α(·) > 0, ∂σ∂w2
ν(·) > 0, and ∂w ∂σ2
ε(·) < 0. When confor-mism increases, the accuracy cost is reduced and so the experts have greater incentives to coordinate. This lead them to put more weight on the public signal and leads to ∂w∂α(·) > 0. A similar reasoning applies when σν2 increases : since the private signal is less precise relative to the public one, the accuracy cost of conforming to the public signal is reduced. This leads experts to put more weight on the public signal. A symmetric argument applies if σ2ε increases and leads to ∂σ∂w2
ε(·) < 0.
Finally, we can also show that ∂α∂σ∂2w2
ν(·) > 0, or ∂2w ∂α∂σ2 ε(·) < 0, if α < (σ 2 ε− σν2)/σε2. Note that
this last condition is greater than 0 iff the private signal is more informative than the public signal. Then, for small levels of conformism, increasing conformism strengthens the effects of the variations of σ2ε and σν. However, for high levels of conformism, increasing conformism
weakens them.
Now, since (1.5) is valid for all experts, we can also derive the expression for the variance of the predictions, which is :
V ar(p∗(θi,t)) = (1 − α)σε2 σ2 ν+ (1 − α)σ2ε 2 σν2 (1.6)
We already know, from Proposition 2, that the variance is lower with than without confor-mism. The expression (1.6) provides additional information. First, V ar(p∗(θi,t)) is strictly
decreasing in α ∈ (0, 1) : the variance of the predictions decreases as conformism increase. Second, V ar(p∗(θi,t)) is strictly increasing in σε2 : if the public signal is less precise, so are the
predictions. Third, we can show that V ar(p∗(θi,t)) is strictly increasing in σν2iff (1−α)σε2 > σν2.
This implies that when the private signal is very precise and experts accordingly put signi-ficant weight on it, any loss in precision is transmitted to the predictions. However, further losses in the private signal’s precision when it was low to start with only convince the experts to coordinate more fully on the public signal, which reduces the variance of the predictions. Finally, we can also show that ∂2V ar(p
∗(θ i,t)) ∂α∂σ2
ε < 0 : In periods of high volatility (σ 2
ε is large),
the impact of conformism on the variance is stronger.
Those effects on the experts’ predictions have important implication for the informativeness of those predictions. We now derive the Central Bank’s posterior beliefs about future inflation, conditional on having observed the experts’ predictions.
1.4.2 The Central Bank’s Posterior Beliefs
Consider a monetary authority with access to the public signal φ (st, xt), either via a Staff
forecast or through a public model. How should it include and embed the information received from the survey of experts into its outlook for future inflation ? We study this question by computing the authority’s posterior beliefs.
Since we already assumed that the true distribution of inflation is commonly known among experts, we also assume that it is common knowledge for the experts and the Bank. As such the Bank’s a priori belief about future inflation is therefore given by a normal distribution with mean φ(st, xt) and variance σ2ε.
Since the experts’ predictions are also normally distributed, we can obtain the Bank’s pos-terior in closed form. Specifically, the Appendix shows that the pospos-terior distribution of the inflation rate, given the experts’ predictions {pi,t}i and assuming a known conformism level
α, is normally distributed with mean µst+1 = N σε2θ + σ¯ 2νφ(st, xt) N σ2 ε+ σ2ν (1.7) and variance σs2t+1 = σ 2 νσε2 N σ2 ε+ σ2ν
Here, since we assumed that the Bank knows the level of conformism α, it can infer θi,t from
pi,t, using (1.5). In reality, the Bank cannot know the level of conformism with certainty
but this analysis nonetheless allows us to discuss the impacts of conformism for the Bank’s beliefs. Indeed, using (1.5) and substituting in (1.7), we find that the posterior belief is the following simple combination of the public signal and the average of the forecasts reported by the experts : µst+1 = φ(st, xt) + N(1 − α)σ2 ε+ σ2ν (1 − α)(N σ2 ε + σν2) . ¯pt− φ(st, xt) (1.8) Specifically, the posterior mean depends on the difference between the average prediction of experts and the public signal (¯pt− φ(st, xt)). When this difference is positive (negative), the
posterior mean is higher (lower) than the public signal. Note that this holds even for α = 0 and allows to understand the informativeness of the experts’ prediction for the Bank. Since the Bank also knows the true distribution of the inflation, the additional information provided by the experts arises from their private signals, information that is not already encoded in φ(st, xt).
The usefulness of the experts’ predictions may therefore be impaired by conformism. From (1.8), we see that the level of conformism α impacts how much the Bank should weight the difference between the average experts’ prediction and the public signal. When conformism is high, small differences between ¯p and φ(st, xt) are more important. Indeed, conformism
reduces the probability of observing predictions by experts that differ greatly from the public signal. Then, when the average prediction does differ from the public signal, it implies that some of the experts received extreme private signals. If the Central Bank suspects a high level of conformism within surveyed experts, it should be pay particular attention to episodes when the experts’ average reported forecast differs from their in-house or Staff prediction, even by small amounts.
1.5
Empirical evidence
This section describes an empirical application using the insights drawn from our model of strategic interactions between surveyed experts. We first start by describing the data we use, then discuss our estimation and identification strategy.
1.5.1 Data
We analyze two sources of data on inflation expectations : the Livingston Survey and the Sur-vey of Professional Forecasters (SPF), both conducted and managed by the Federal Reserve of Philadelphia. The Livingston Survey was initiated by Joseph Livingston in June 1946, and reports forecasts for 18 different variables describing national output, prices, unemployment, and other macroeconomic variables. The survey is populated by economists working in sectors such as Nonfinancial Businesses, Investment Banking, Academic Institution, Insurance compa-nies, or Government. We focus on inflation expectations at the 12-month-ahead horizon. The SPF is similar to the Livingston Survey. Its specificity comes from the fact that respondents are economists for whom forecasting is a major part of their job. the SPF was begun in 1968 but questions about CPI inflation were added to the questionnaire at the 3rdquarter of 1981. The Livingston survey is conducted twice a year, in June and December. The questionnaires are sent to the forecasters in May and November, after the release of CPI data for April and October, respectively, and are due back early June and early December before the May and November CPI releases. As forecasters do not yet know CPI numbers for May (June survey) and November (December survey), we consider, following Carlson (1977), that they base their forecasts on information available through April and October. This assumption implies that forecasts cover a fourteen-month span, from May of the year in which the survey is conducted to June of the following year (November to December in the subsequent year for the November survey). As such, even if the forecast is denoted as twelve-months-ahead, they really cover fourteen months. In the questionnaire, participants are requested to forecast CPI level rather than inflation rates. We use the CPI answers to compute the implied 12 months forecast (see Appendix for details).
The SPF is conducted quarterly and questionnaires go out at the end of the first month of each quarter after the government’s release of quarterly data. Unlike its Livingston counterpart, the
SPF directly asks for a forecast of CPI inflation instead of the CPI level. Forecasters know the value of the inflation rate for the quarter prior to current one when the survey is conducted and they submit their projections. They are asked to forecast the inflation rate for the current quarter (the one during which the survey is conducted) and for the four following quarters. This means that their provide forecasts for five different and subsequent quarters. Using this information, we compute the implied 12 months forecasts (see Appendix for details).
Panels A and C in Figure1.1present time series of the realized and median expected inflation rates for SPF and the Livingston survey.5 The horizontal axis refers to the endpoint of the relevant forecast horizon rather than the time the forecast was made. We observe that both the SPF and the Livingston survey appear to predict inflation reasonably well, although they often fail to match periods of low inflation. The difference between realized and forecast inflation is fairly persistent for two series. Panels B and D show the disagreement within respondents for our inflation expectations series. Disagreement is measured as in Coibion and Gorodnichenko (2012) by the standard deviation in the answers. The extent of disagreement within each of these surveys varies substantially over time.
Forecast disagreement is high at the beginning of the sample for SPF participants (between 1982 and 1985), and becomes low by 1992, but it stays relatively the same for the rest of sample. The level of disagreement is higher for the Livingston survey than SPF. This may be due to the cross-sectional heterogeneity in Livingston survey participants. The participants of Livingston survey are composed of all categories of economist (banking, government, academic) ; while the SPF participants are economists for whom forecasting is major part of their job. Then, SPF respondents are more homogeneous.
Figure 1.1 – Median and Standard Deviation (“Disagreement”) in Reported Forecasts for the Inflation Rate : SPF and Livingstone Surveys
−3 −1 1 3 5 7 9 11 13 15 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 Inf altion r ate , % Expected Inflation Realized Inflation
Panel A: SPF, inflation rate
−3 −1 1 3 5 7 9 11 13 15 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 2017 Inf altion r ate , % Expected Inflation Realized Inflation
Panel C: Livingston Survey, inflation rate
0.0 0.5 1.0 1.5 2.0 2.5 3.0 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 Disagreement Panel B: SPF, disagreement 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007 2012 2017 Disagreement
Panel D: Livingston Survey, disagreement
Notes : This figure plots median inflation expectations over time from the SPF (panel A) and the Livingston survey (panel B) as well as the realized inflation rate for a sample period from 1981 to 2016 for SPF and from 1954 to 2015.
In the next section, we discuss how we can use this data in order to gain some insight about the usefulness of those inflation expectation surveys.
1.5.2 Empirical Strategy
In this section, we discuss two empirical questions :
1. Is it possible to identify and estimate the true level of conformism ?
2. Has conformism impaired the Bank’s ability to forecast the inflation in recent historical episodes ?
The first question refers to our ability to infer conformism from the experts’ predictions. The second question is conceptually different. From our analysis in the previous section, we
know that conformism reduced the likelihood of observing (potentially informative) extreme predictions. Whether of not this is important strongly depends on the volatility of the inflation rate.
Consider the first question. Since the signals are normally distributed and the mean equal to the true inflation rate (see Proposition2), the only source of variation comes from the variance of the predictions : V ar(p∗) = (1 − α)σε2 σ2 ν + (1 − α)σ2ε 2 σ2ν
Since σε2 can be estimated from the realized inflation rates using (1.3), we have two unknown parameters (σ2
ν and α), but only one moment (V ar(p∗)). Thus, it is not possible to identify α
without any additional assumption,
This identification failure highlights the difference between our model and the previous litera-ture. For example, Clements(2015) assume that experts conform to the consensus, defined as the previous period’s average prediction, a (generally) biased estimate of the current inflation rate. The difference between the average prediction and the true inflation state provides an additional moment.
Since we have shown in our setting that experts conform with the public signal (an unbiased estimator of the true inflation rate) the average prediction is also unbiased, as per Proposition 2. It is therefore impossible to distinguish conformism from the precision of the experts’ private signals looking only at the variance of the predictions.
Given the identification failure, we therefore concentrate on the second question and maximize the likelihood based on Bank’s posterior belief, assuming that it knows the true conformism level. The likelihood function is :
L(s1, . . . , sT, α, σν) = − T 2 log(2πσ 2 st+1) − 1 2σ2 st+1 T X t (st+1− µst+1) 2, (1.9) where µst+1 = Nt(1 − α)ˆσ2ε,t+ σν2 [¯pt− φ(st, xt)] (1 − α)(N ˆσ2ε,t+ σ2 ν) + φ(st, xt) and : σ2st+1 = σ 2 νσˆ2ε,t Ntσˆ2ε,t+ σ2ν
We therefore seek to find the assumed level of conformism α that maximizes the ability of the bank to forecast inflation.
Note that σε2 has been replaced by ˆσ2ε,t in the likelihood function. This is due to the fact that we use the Bank’s best estimate of the variance at time t in order to compute the belief function. The precise estimation procedure is described in the next section.
1.5.3 Estimation and Results
We first describe the estimation of (1.3), which allows us to compute φ(st, xt) as well as ˆσε,t2 . Stock and Watson (2008) distinguishes four groups of single-equation inflation forecasting models : (1) forecasts based solely on past inflation ; (2) forecasts based on activity measures (Phillips curve forecasts) ; (3) forecasts based on the forecasts of others ; and (4) forecasts based on other predictors. They show that the performance of these forecasting models is episodic, each of them does sometimes better than and sometimes worse than others. To illustrate our theoretical model, we will focus on the first group, especially ARIMA models which are generalizations of the simple auto regressive (AR). We compute out-of-sample forecasts using the whole set of ARIMA models with AR lags ranging from 1 to 4 and MA terms ranging from 0 to 4. The criteria to select the models are Bayesian Information Criteria (BIC). Ljung-Box autocorrelation test for ARIMA residuals is done to ensure that residuals are independent. The question about CPI inflation was introduced in the SPF in 3rd 1981. We then suppose that the Bank, and the experts, observe past inflation rate until Q3 1981 when forming their forecast in Q3 1981. The first estimation sample starts in Q1 1960 and ends in Q3 1981 in order to produce forecasts for Q3 19826, as in the survey. The next estimation sample is extended for one quarter up to Q4 1981 in order forecast for Q4 1982. This rolling procedure continues until the last observation of the survey. We do the same thing with the Livingston Survey by using monthly data.
The forecasts obtained from this procedure allow us to compute φ(st, xt) as well as ˆσ2ε,t for
the entire time series. We also compute two measures of forecast accuracy : the square root of the average squared error (RMSE) and the mean absolute error (MAE). Table 1.1reports the accuracy of the median expectations in each survey, both over their maximal samples, and for a common sample (1982-2015). It also reports the RMSE and MAE of forecasts from the previous estimations. Inflation expectations are relatively accurate in the two surveys compare to the ARIMA model. As expected, for the common sample, SPF forecasts are the most accurate.
Table 1.1 – Forecast errors
SPF Livingston survey ARIMA
1982-2015 1982-2015 1955-2016 1982-2015
RMSE 1.26 1.28 1.63 1.76
MAE 0.96 1.03 1.2 1.26
Notes : The table reports two measures of forecast accuracy for the SPF and the Livingston Survey, compared to the ARIMA predictions
6. We use real data from Federal Reserve of St Louis : Consumer Price Index : Total All Items , Growth Rate Same Period Previous Year, Quarterly, Not Seasonally Adjusted
Using the estimated values for φ(st, xt) and ˆσ2
ε,t, we can now maximize (1.9)7. The results for
level of conformism α and the variance of experts’ public signal that maximize the performance of bank posterior distribution using the SPF and the Livingston survey are displayed in Table 1.2.
The reported values for σε2 represent the residuals variance obtained from the last estimation of the rolling procedure, which is interpreted as the variance of public signal. For the SPF, this variance is larger than the variance of experts’ private signal σν2, meaning that the professional private signal is more informative than the public one. This is not the case for the Livingston survey where σ2ν > σ2ε. Also note that, the private signal of professional is more precise than those of Livingston participants, which is anticipated.
Table 1.2 – Maximization of posterior distribution SPF Livingston survey α 0.000 0.000 (0.000) (0.000) σν2 0.280∗∗∗ 0.570∗∗∗ (0.002) (0.002) n 134 111 σε2 0.28 0.29
Notes : The table reports results of the maximization of (1.9). ∗ ∗ ∗p<0.01.
Importantly, note that the estimated value for α close to zero. This does not mean that there is no conformism. Indeed, as discussed at the beginning of this section, it is not possible to identify conformism without additional (strong) assumptions. What it does mean however, is that the past variations of the inflation rate were largely anticipated (given the historical distribution of inflation) so that conformism had a negligible impact on the Bank’s beliefs. Indeed, the informativeness of the experts’ prediction is in revealing information that is not present in the data. As seen from Figure 1.1 and Table 1.1, the experts’ predictions (which partly include the public signal) do only slightly better than the public signal alone. This therefore limits the negative impact of conformism.
1.6
Conclusion
A crucial aspect of monetary policy is managing inflation expectations. Despite the resurgent focus on the nature of expectation formation process, there is no consensus among economists on how economic agents form their inflation expectations. This paper, focusing on inflation expectations by professional forecasters (SPF) and economists in general (Livingston survey), attempts to contribute to this literature by addressing a new aspect of inflation expectation :
7. We are aware that inference from the maximization might be affected by the variability of ˆσ2
ε,tcoming
the behaviour of respondents. We investigate the implications of conformism among forecasters for the evaluation and use of inflation expectations data in static bayesian game framework. We find that the experts’ reported predictions are a convex combination of the public signal and their private one, with degree of conformism leading to increases in the weight of the pu-blic signal in reported predictions. We also find that conformism does not affect the mean of experts’ predictions, but it reduces their variance. This means that the presence of conformism leads to forecasts with lower mean-squared deviations. Computing the central bank posterior distribution about inflation, we show that conformism reduces probability of receiving predic-tions that differ too much from the public signal. Then, when the average prediction do differs from the public signal, it implies that some of the experts received extreme private signals.
1.7
Bibliographie
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Chapitre 2
The Determinants of
Consumers’Inflation Expectations :
Evidence from the US and Canada
2.1
Résumé
Nous proposons et estimons un modèle d’attente inflationniste qui relie les anticipations in-dividuelles des ménages à leurs propres valeurs passées ainsi qu’à des mesures d’anticipation rationnelle. Le modèle se base sur le cadre du "noisy information" existant et l’étend de plu-sieurs manières. Nous modélisons explicitement la règle de mise à jour des attentes utilisées par les ménages pour incorporer de nouvelles informations dans leur expérience et prenons au sérieux l’hétérogénéité des attentes inflationnistes largement documentée dans la littéra-ture. Nous estimons le modèle à l’aide des données de l’Enquête américaine sur les attentes des consommateurs de la Fed de New York et de l’Enquête canadienne sur les attentes des consom-mateurs de la Banque du Canada. Nous montrons que les attentes inflationnistes semblent corrélées plus fortement aux mesures d’anticipation rationnelle au Canada qu’aux États-Unis, et inversement moins aux valeurs retardées. Plus précisément, le répondant médian attribue des pondérations globales d’environ 75 % aux mesures d’anticipation rationnelles et de 25 % aux valeurs retardée au Canada, tandis que ces pondérations sont d’environ 50/50 pour les États-Unis. Nous montrons que ces différences de poids ne s’expliquent pas par des différences dans les caractéristiques des ménages dans chaque pays. Compte tenu de ce résultat, une ex-plication possible pourrait être liée à l’objectif d’inflation explicite au Canada comparé au double mandat aux États-Unis.
Classification JEL :C33, D83, D84, E31
2.2
Abstract
We propose and estimate a model of inflation expectations that links individual consumers’ inflation expectations to their own lagged forecasts as well as proxies for the rational expec-tation forecasts. The model builds on the existing noisy information framework and extends it in several dimensions. We explicitly model the expectations updating rule which consumers use to incorporate new information in their experience and take seriously heterogeneity in inflation expectations extensively documented in the literature. We estimate the model using data from the New York Fed’s US Survey of Consumer expectations and the Bank of Cana-da’s Canadian Survey of Consumer Expectations. We find that inflation expectations appear to correlate more strongly to measures of rational expectations forecasts in Canada than in the US, and conversely less to lagged expectations. More specifically, the median respondent assigns overall weights of roughly 75% to proxies for the rational expectation forecasts and 25% to lagged expectations in Canada while these weights are around 50-50 for the US. We show that these differences in weights are not explained by differences in the characteristics of their stand-in consumers. Given this finding, one candidate explanation could be related to the explicit inflation target in Canada in comparison to the dual mandate in the US.
JEL Codes : C33, D83, D84, E31
2.3
Introduction
Expectations about future inflation are of central importance for public policy and monetary authorities. The inflation expectations of consumers, in particular, influence economic choices related to wage negotiations, consumption or saving and, in turn, influence pricing decisions of firms and aggregate price changes. Monitoring and analyzing the inflation expectations of consumers thus represent important aspects of monetary policy practice.
Considerable resources are therefore allocated to the production and the analysis of data about consumer expectations. Two recently-established surveys are of particular interest : the Survey of Consumers Expectations (SCE), conducted by the Federal Reserve Bank of New York, and the Canadian Survey of Consumers Expectations (CSCE), under the responsibility of the Bank of Canada. They are both nationally representative, internet-based surveys and follow rotating panels of more than 1,000 household heads. These respondents provide their expectations about future inflation but are also queried for their forecasts for other variables, such as future labour market outcomes or real estate prices. Importantly, participation in those surveys is repeated (up to one year) and a rich set of socio-economic characteristics for the participants is available, allowing analysis of the heterogeneity and updating processes for inflation expectations.
In this context, the present paper uses these data to compare how consumers form and update their expectations about future inflation in the US and Canada, two large economies with dif-ferent monetary policy regimes. Canada adopted an inflation target in 1991, with a symmetric target around 2%. In contrast, the US did not have a specific numerical target for inflation before 2012. The federal Reserve Bank also differs from the Bank of Canada in that it has a dual mandate, price stability and maximum sustainable employment. In contrast, the Bank of Canada has a single mandate, price stability, which is simpler, more transparent and easier for market participants and the general public to understand. In addition, the Federal Reserve target is specified in term of the Personal Consumption Expenditure (PCE) deflator, not in Consumer Price Index (CPI), as is the case for the Bank of Canada. It is therefore important to investigate how consumers form their expectations about future inflation in these different situations1. This comparison has been done using inflation expectations from professional fo-recasters inYetman(2017). He fits inflation forecasts by professional forecasters in Canada and the US using a parsimonious parametric model and finds that, over time, Canadian inflation forecasts have become strongly anchored at the target level of 2%, with very small deviations from this level for forecasts horizons above one year.
In this paper, we use an approach inspired by the ‘noisy signal’ literature exemplified by work like Coibion and Gorodnichenko (2015a) and recently Vellekoop and Wiederholt (2019) to
1. While inflation expectations of consumers in the US have been largely studied using the Michigan survey, nothing is known about consumers’ inflation expectations in Canada due to a lack of data.
study the process by which American an Canadian consumers form their expectations about inflation. We assume that reported inflation expectations are related to the lagged expectation of the survey participants and to proxies for the rational expectations forecasts, represented by the experience of realized inflation rates during household’s tenure in the survey or a publicly-available signals about future inflation. Our model allows parameters to depend on the socio-economic characteristics of the participants and we utilize the panel aspect of the surveys to assess how consumers update their expectations and incorporate new information received during their survey tenure.
Our results are as follow. First, inflation expectations appear to correlate more strongly to measures of rational expectations forecasts in Canada than in the US, and conversely less to lagged expectations. More specifically, the median respondent assigns overall weights of roughly 75% to proxies for the rational expectation forecasts and 25% to lagged expectations in Canada while these weights are around 50-50 for the US. This finding is likely explained by the explicit inflation target in Canada in comparison to the dual mandate in the US, and the differences in the surveys’ design. Second, the degree at which new information is incorporated in the respondents’ experience during their tenure in the survey decreases as they become familiar with the survey, but it decreases faster in the US and becomes essentially zero after five months of repeated participation. This may suggest that US respondents, after they have been surveyed four or five months, stop incorporating new values in their updating rule. Third substantial socio-economic heterogeneity is present in the parameters related to inflation experience, to past expectations and to the public signal. Finally, using gasoline-price or food-price inflation instead of information from the survey of professional forecasters as the public signal does not change results.
There as been a lot of research on the inflation expectations of consumers. Notably, several researchers have documented significant correlations between expectations and demographic characteristics such as gender, age, income and education levels and others (Bryan and Ven-katu,2001;Souleles,2004;Bruine de Bruin et al.,2010;Malmendier and Nagel,2015;Madeira and Zafar, 2015). In addition, it has been shown that one’s outlook influences forecasting success, with pessimistic consumers having less accurate inflation forecasts (Ehrmann et al., 2017), that the personal experience of respondents as consumers of specific goods influences their reported expectations (Bruine de Bruin et al., 2011), and that news reports about in-flation (Carroll,2003) or increases in the price of gasoline or supermarket groceries (Cavallo et al.,2017) impact expectations. This paper presents novel results in that dimension, by ap-plying these questions to important new surveys, while the literature has concentrated on the Michigan Survey.
How consumers update their inflation expectations has also been an important part of this literature.Ehrmann et al. (2017) investigate whether some household groups in the Michigan survey update their expectations more often than others and find that the financial situation
of participants has a bearing on the frequency of update. Using data from the Michigan Survey as well, Coibion and Gorodnichenko (2015c) show that the impact of high oil prices in 2009-2011 might explain how consumer expectations became disassociated with those of the experts participating in the Professional Forecasters’ survey, while Dräger and Lamla(2012) provide evidence that inflation expectations are quantitatively adjusted relatively frequently, whereas the qualitative assessment changes less often. Using a survey with an embedded information experiment,Armantier et al.(2016) investigate how consumers’ inflation expectations respond to new information. They find that respondents, on average, are not fully informed about past as well as future macroeconomic measures, and when provided with new inflation-relevant in-formation, they do update their inflation expectations, but in highly-heterogeneous manners. Earlier contributions byCarroll(2003) andMankiw and Reis(2002) estimate that consumers update their inflation expectations roughly once a year. Coibion and Gorodnichenko (2012) investigate the responsiveness of expectations to macroeconomic shocks, and find the pre-sence of imperfect information not only for consumers, but also more broadly for professional forecasters, firms, central bankers and financial market participants. Finally, papers closely related to ours, by Malmendier and Nagel (2015) and Madeira and Zafar (2015) once again use Michigan Survey data to estimate formal models taking into account both cross-section characteristics and repeated participation.
The data from the SCE and the CSCE are ideally suited to study the factors governing how consumers update their inflation expectations, because of the relatively high number of (consecutive) participation periods of the various respondents. In addition, the fact that the two surveys differ importantly on that dimension (monthly in the US and quarterly in Canada) allows us to ascertain which consumers adapt their expectations, how fast they do it, and how that process depends on the survey’s structure.
The remainder of the paper is structured as follows. Section 2 describes the data contained in the SCE and the CSCE and provides a descriptive analysis of the heterogeneity that these data contain. Section 3 then develops our model of expectation formation and the econometric approach we employ to assess it quantitatively. Section 4 reports and discusses our benchmark results while Section 5 explores the robustness of these results through various sensitivity analyses. Section 6 then summarizes our results and concludes.
2.4
Data and descriptive analysis
2.4.1 Data
Our data are drawn from the Survey of Consumer Expectations (SCE), conducted by the Federal Reserve Bank of New York, and the Canadian Survey of Consumer Expectations (CSCE), which is undertaken by the Bank of Canada. Both surveys are nationally represen-tative, internet-based queries of rotating panels of more than 1000 household heads. The SCE
