Three essays in international finance and macroeconomics

(1)

Three Essays in International Finance and

Macroeconomics

Thèse

Simplice Aimé Nono

Doctorat en économique Philosophiæ doctor (Ph.D.)

Québec, Canada

(2)

Three Essays in International Finance and

Macroeconomics

Thèse

Simplice Aimé Nono

Sous la direction de:

(3)

Résumé

Cette thèse examine l’effet de l’information sur la prévision macroéconomique. De façon spéci-fique, l’emphase est d’abord mise sur l’impact des frictions d’information en économie ouverte sur la prévision du taux de change bilatéral et ensuite sur le rôle de l’information issue des données d’enquêtes de conjoncture dans la prévision de l’activité économique réelle. Issu du paradigme de la nouvelle macroéconomie ouverte (NOEM), le premier essai intègre des fric-tions d’informafric-tions et des rigidités nominales dans un modèle d’équilibre général dynamique stochastique (DSGE) en économie ouverte. Il présente ensuite une analyse comparative des résultats de la prévision du taux de change obtenu en utilisant le modèle avec et sans ces frictions d’information. Tandis que le premier essai développe un modèle macroéconomique structurel de type DSGE pour analyser l’effet de la transmission des choc en information incomplète sur la dynamique du taux de change entre deux économies, le deuxième et troi-sième essais utilisent les modèles factorielles dynamiques avec ciblage pour mettre en exergue la contribution de l’information contenu dans les données d’enquêtes de confiance (soit au niveau de l’économie nationale que internationale) sur la prévision conjoncturelle de l’activité économique réelle.

« The Forward Premium Puzzle : a Learning-based Explanation » (Essai 1) est une contribu-tion à la littérature sur la prévision du taux de change. Cet essai a comme point de départ le résultat théorique selon lequel lorsque les taux d’intérêt sont plus élevés localement qu’ils le sont à l’étranger, cela annonce une dépréciation future de la monnaie locale. Cependant, les résultats empiriques obtenus sont généralement en contradiction avec cette intuition et cette contradiction a été baptisée l’énigme de la parité des taux d’intérêt non-couverte ou encore « énigme de la prime des contrats à terme ». L’essai propose une explication de cette énigme basée sur le mécanisme d’apprentissage des agents économiques. Sous l’hypothèse que les chocs de politique monétaire et de technologie peuvent être soit de type persistant et soit de type transitoire, le problème d’information survient lorsque les agents économiques ne sont pas en mesure d’observer directement le type de choc et doivent plutôt utiliser un mécanisme de filtrage de l’information pour inférer la nature du choc. Nous simulons le modèle en présence de ces frictions informationnelles, et ensuite en les éliminant, et nous vérifions si les données artificielles générées par les simulations présentent les symptômes de l’énigme de la prime des contrats à terme. Notre explication à l’énigme est validée si et seulement si seules les données

(4)

générées par le modèle avec les frictions informationnelles répliquent l’énigme.

« Using Confidence Data to Forecast the Canadian Business Cycle » (Essai 2) s’appuie sur l’observation selon laquelle la confiance des agents économiques figure désormais parmi les principaux indicateurs de la dynamique conjoncturelle. Cet essai analyse la qualité et la quantité d’information contenu dans les données d’enquêtes mesurant la confiance des agents économiques. A cet effet, il évalue la contribution des données de confiance dans la prévision des points de retournement (« turning points ») dans l’évolution de l’économie canadienne. Un cadre d’analyse avec des modèles de type probit à facteurs est spécifié et appliqué à un indicateur de l’état du cycle économique canadien produit par l’OCDE. Les variables explicatives comprennent toutes les données canadiennes disponibles sur la confiance des agents (qui proviennent de quatre enquêtes différentes) ainsi que diverses données macroéconomiques et financières. Le modèle est estimé par le maximum de vraisemblance et les données de confiance sont introduites dans les différents modèles sous la forme de variables individuelles, de moyennes simples (des « indices de confiance ») et de « facteurs de confiance » extraits d’un ensemble de données plus grand dans lequel toutes les données de confiance disponibles ont été regroupées via la méthode des composantes principales,. Nos résultats indiquent que le plein potentiel des données sur la confiance pour la prévision des cycles économiques canadiens est obtenu lorsque toutes les données sont utilisées et que les modèles factoriels sont utilisés. « Forecasting with Many Predictors: How Useful are National and International Confidence Data? » (Essai 3) est basé sur le fait que dans un environnement où les sources de données sont multiples, l’information est susceptible de devenir redondante d’une variable à l’autre et qu’une sélection serrée devient nécessaire pour identifier les principaux déterminants de la prévision. Cet essai analyse les conditions selon lesquelles les données de confiance constituent un des déterminants majeurs de la prévision de l’activité économique dans un tel environnement. La modélisation factorielle dynamique ciblée est utilisé pour évaluer le pouvoir prédictif des données des enquêtes nationales et internationales sur la confiance dans la prévision de la croissance du PIB Canadien. Nous considérons les données d’enquêtes de confiance désagrégées dans un environnement riche en données (c’est-à-dire contenant plus d’un millier de séries macro-économiques et financières) et évaluons leur contenu informatif au-delà de celui contenu dans les variables macroéconomiques et financières. De bout en bout, nous étudions le pouvoir prédictif des données de confiance en produisant des prévisions du PIB avec des modèles à facteurs dynamiques où les facteurs sont dérivés avec et sans données de confiance. Les résultats montrent que la capacité de prévision est améliorée de façon robuste lorsqu’on prend en compte l’information contenue dans les données nationales sur la confiance. En revanche, les données internationales de confiance ne sont utiles que lorsqu’elles sont combinées dans le même ensemble avec celles issues des enquêtes nationales. En outre, les gains les plus pertinents dans l’amelioration des prévisions sont obtenus à court terme (jusqu’à trois trimestres en avant).

(5)

Abstract

This thesis examines the effect of information on macroeconomic forecasting. Specifically, the emphasis is firstly on the impact of information frictions in open economy in forecast-ing the bilateral exchange rate and then on the role of information from confidence survey data in forecasting real economic activity. Based on the new open-economy macroeconomics paradigm (NOEM), the first chapter incorporates information frictions and nominal rigidities in a stochastic dynamic general equilibrium (DSGE) model in open economy. Then, it presents a comparative analysis of the results of the exchange rate forecast obtained using the model with and without these information frictions. While the first chapter develops a structural macroeconomic model of DSGE type to analyze the effect of shock transmission in incomplete information on exchange rate dynamics between two economies, the second and third chapters use static and dynamic factor models with targeting to highlight the contribution of informa-tion contained in confidence-based survey data (either at the nainforma-tional or internainforma-tional level) in forecasting real economic activity.

The first chapter is entitled The Forward Premium Puzzle: a Learning-based Explanation and is a contribution to the exchange rate forecasting literature. When interest rates are higher in one’s home country than abroad, economic intuition suggests this signals the home currency will depreciate in the future. However, empirical evidence has been found to be at odds with this intuition: this is the "forward premium puzzle." I propose a learning-based explanation for this puzzle. To do so, I embed an information problem in a two-country open-economy model with nominal rigidities. The information friction arises because economic agents do not directly observe whether shocks are transitory or permanent and must infer their nature using a filtering mechanism each period. We simulate the model with and without this informational friction and test whether the generated artificial data exhibits the symptoms of the forward premium puzzle. Our leaning-based explanation is validated as only the data generated with the active informational friction replicates the puzzle.

The second chapter uses dynamic factor models to highlight the contribution of the infor-mation contained in Canadian confidence survey data for forecasting the Canadian business cycle: Using Confidence Data to Forecast the Canadian Business Cycle is based on the fact that confidence (or sentiment) is one key indicators of economic momentum. The chapter

(6)

assesses the contribution of confidence -or sentiment-data in predicting Canadian economic slowdowns. A probit framework is applied to an indicator on the status of the Canadian business cycle produced by the OECD. Explanatory variables include all available Canadian data on sentiment (which arise from four different surveys) as well as various macroeconomic and financial data. Sentiment data are introduced either as individual variables, as simple averages (such as confidence indices) and as confidence factors extracted, via principal com-ponents’ decomposition, from a larger dataset in which all available sentiment data have been collected. Our findings indicate that the full potential of sentiment data for forecasting future business cycles in Canada is attained when all data are used through the use of factor models. The third chapter uses dynamic factor models to highlight the contribution of the information contained in confidence survey data (either in Canadian or International surveys) for forecast-ing the Canadian economic activity. This chapter entitled Forecastforecast-ing with Many Predictors: How Useful are National and International Confidence Data? is based on the fact that in a data-rich environment, information may become redundant so that a selection of forecast-ing determinants based on the quality of information is required. The chapter investigates whether in such an environment; confidence data can constitute a major determinant of eco-nomic activity forecasting. To do so, a targeted dynamic factor model is used to evaluate the performance of national and international confidence survey data in predicting Canadian GDP growth. We first examine the relationship between Canadian GDP and confidence and assess whether Canadian and international (US) improve forecasting accuracy after controlling for classical predictors. We next consider dis-aggregated confidence survey data in a data-rich environment (i.e. containing more than a thousand macroeconomic and financial series) and assess their information content in excess of that contained in macroeconomic and financial variables. Throughout, we investigate the predictive power of confidence data by producing GDP forecasts with dynamic factor models where the factors are derived with and without confidence data. We find that forecasting ability is consistently improved by considering infor-mation from national confidence data; by contrast, the international counterpart are helpful only when combined in the same set with national confidence. Moreover most relevant gains in the forecast performance come in short-horizon (up to three-quarters-ahead).

(7)

(8)

List of Tables

1.1 Baseline estimates for the UIP regression under Complete information . . . 19

1.2 Baseline estimates for the UIP regression under Incomplete information . . . . 19

1.3 Nominal UIP regression estimates under Complete information . . . 21

1.4 Nominal UIP regression estimates Incomplete information . . . 21

1.5 Real UIP regression estimates - Complete information . . . 22

1.6 Real UIP regression estimates - Incomplete information . . . 22

1.7 Fisher effect test . . . 23

1.8 Nominal UIP regression estimates with variation of φ₁ . . . 25

1.9 Real UIP regression estimates with variation of φ1 . . . 25

2.1 Single-predictor Probit: Classical predictors and Confidence indices . . . 71

2.2 Single-predictor Probit: Individual Sentiment Variables . . . 72

2.3 Single-predictor Probit: Factors . . . 73

2.4 Probit with Multiple predictors: In-Sample Results . . . 74

2.5 Probit with Multiple Predictors: Longer Forecasting Horizons . . . 75

2.6 Probit with Multiple Predictors: Earlier Sample (2002Q3 - 2010Q1) . . . 76

2.7 An Out-of-Sample Experiment (2010Q2 to 2014Q1). . . 77

3.1 Different subsets of national and international data . . . 93

3.2 The Forecasting Experiment (2010Q1 - 2015Q4) . . . 93

3.3 Forecasting Performance with no targeting . . . 100

3.4 Forecasting Performance with Targeting I: Hard-Thresholding with t?= 1.28 . 101 3.5 Forecasting Performance with Targeting II: Hard-Thresholding with t? = 1.65 . 101 3.6 Forecasting Performance with Targeting I: Hard-Thresholding with t?= 2.58 . 102 3.7 Forecasting Performance with Predictor Soft-thresholding . . . 103

3.8 Forecasting Performance with Factor Targeting . . . 104

B.1 Chronology of the Canadian Business Cycle Since 1961 . . . 116

(12)

List of Figures

1.1 Responses to a transitory monetary policy shock I . . . 27

1.2 Responses to a transitory monetary policy shock II . . . 28

1.3 Responses to a transitory monetary policy shock III . . . 29

1.4 Responses to a persistent technological shock I . . . 30

1.5 Responses to a persistent technological shock II . . . 31

1.6 Responses to a persistent technological shock III . . . 32

1.7 Responses to a monetary policy shift I . . . 33

1.8 Responses to a monetary policy shift II . . . 34

1.9 Responses to a monetary policy shift III . . . 35

1.10 Monetary policy shift: Complete vs Incomplete Information I . . . 36

1.11 Monetary policy shift: Complete vs Incomplete Information II. . . 37

1.12 Monetary policy shift: Complete vs Incomplete Information III . . . 38

1.13 Monetary policy shift: Complete vs Incomplete Information IV . . . 39

1.14 UIP test with monetary policy regime shifts: Complete Information. . . 40

1.15 UIP test with monetary policy regime shifts: Incomplete Information . . . 41

1.16 UIP test with monetary policy shifts and shocks: Complete Information . . . . 42

1.17 UIP test with monetary policy shifts and shocks: Incomplete Information . . . 43

1.18 UIP test with frequent monetary policy regime shifts: Complete Information . 44 1.19 UIP test with frequent monetary policy regime shifts: Incomplete Information . 45 1.20 UIP test with persistent and transitory technology shocks: Complete Information 46 1.21 UIP test with persistent and transitory technology shocks: Incomplete Infor-mation. . . 47

1.22 Monetary policy shift: Incomplete Information-φ₁ = 0.95 vs φ1= 0.75 . . . 48

1.23 Monetary policy shift: Incomplete Information-φ1 = 0.95 vs φ1= 0.75 . . . 49

1.24 Monetary policy shift: Incomplete Information-φ1 = 0.95 vs φ1= 0.75 . . . 50

2.1 Canadian Recessions: OECD and C.D. Howe . . . 59

2.2 Estimated Probability of Slowdown: Confidence Indices and Confidence Factors 67 3.1 Confidence data and GDP growth: Conference Board Data . . . 88

3.2 Confidence data and GDP growth: Bank of Canada Data . . . 90

3.3 US confidence data and Canadian GDP growth . . . 91

(13)

List of Abbreviations

AIC Akaike Information Criterion

BCI Business Confidence Index

BIC Bayesian Information Criterion

BOS Business Outlook Survey

C.D. Howe Clarence Decatur Howe Institute

CCI Consumer Confidence Index

CEA Canadian Economic Association

CIP Covered interest rate parity

CML Cost-weighted Misclassification Losses

CPI consumer price index

CRS constant returns to scale

CSI Canada’s Short-Term Indicator

DM Diebold and Mariano (1995) test

DSGE Dynamic Stochastic General Equilibrium Model

FRED-MD Federal Reserve Economic Data - Monthly Database

GDP Gross Domestic Product

GW Giacomini and White (2006) test

ICE Index of Consumer Expectation

ICS Index of Consumer Sentiment

ISM Institute of Supply Management

KPSS Kwiatkowski-Phillips-Schmidt-Shin tests

LARS-EN Least Angle Regression Selection with Elastic Net

MSFE Mean Squared Forecast Error

NBER National Bureau of Economic Research

NIPA National Income and Product Accounts

NOEM New-Open Economy Macroeconomics

OECD Organisation for Economic Co-operation and Development

PC Principal Component

PCA Principal Component Analysis

(14)

QPS Quadratic Probability Score

SCSE Société Canadienne de Sciences Économiques

SLO Senior Loan Officers

SP/TSX Standard and Poor’s/Toronto Stock Exchange index

SPF Survey of Professional Forecasters

UIP Uncovered Interest Parity

UK United-Kingdom

US United-States

(15)

(16)

To the loving memory of my grandmother Jouego Luise.

(17)

Economics has then as its purpose firstly to acquire knowledge for its own sake, and secondly to throw light on practical issues.

(18)

Acknowledgments

I owe a debt of gratitude to several people for the realization of this thesis, but first of all, I am grateful to the Almighty God for giving me the opportunity to pursue my doctoral studies and for providing me with health and the needed resources to complete this thesis. I would like to extend my deepest gratitude to all individuals and organizations that have provided me help and support throughout the whole period of my doctoral studies.

I express my gratitude first and foremost to my thesis advisor Prof. Kevin Moran for mentoring me over the course of my thesis. He provided me with essential tools in macroeconomic modeling and gave a clear direction to my research when leaving me a full autonomy. His professional breadth throughout this research guided me to improve its technical aspects and his experience led to this original proposal that analyzes a topical issue of social sciences in a more innovative way.

I also thank Dr. Imad Rherrad who accepted to act as my supervisor during my three years at the Quebec Ministry of Finance as a PhD research fellow. He patiently guided me with his precious comments and suggestions. His insight in economic research and analysis shaped this document; may he find in these words my gratitude for all I have learned from him and for his continuous support.

I would additionally like to thank Prof. Benoît Carmichael who has taught me in my doctoral coursework in Macroeconomics and Prof. Stephen Gordon who has taught me in my doctoral coursework in Econometrics and both accepted to be part of my thesis committee. I also thank Prof. John W. Galbraith from McGill University who accepted to serve as the external reviewer of this thesis. Their cogent comments and suggestions have improved the quality of this document.

I would also like to thank the Department of Economics of Université Laval and all its faculty members for the quality of training I have received and for their availability and assistance over the course of my studies. In particular, I thank Prof. Sylvain Dessy, who, as Chair of Graduate Studies in 2011, accepted my application to the PhD program and for his continuous support, encouragement and discussions over the last five years. His mentorship has been crucial in my academic success and my journey in the program.

(19)

I also thank The Honourable Prof. Jean-Yves Duclos, who, as Chair of the Department of Economics offer me my first contract as lecturer and after him, Prof. Guy Lacroix for giving me the same trust and support for the same job. I also thank Prof. Philippe Barla and Prof. Stephen Gordon, who, as chair of Graduate Studies successively, provided me timeliness support and assistance in renewing my immigration documents. I am grateful to Prof. Carlos Ordas Criado, who has taught me in my doctoral coursework in Econometrics, for his support and advice.

I am also grateful to all the professors of the Department of Economics, who helped improved the quality of my work with their comments and guidance on how to communicate and write efficiently a scientific document by attending my presentations at the Department. I am also grateful to all the administrative staff of the Department of Economics and its research center CIRPÉE for their kind collaboration and support.

I would like to thank conference participants at Laval University, Canadian Economics As-sociation Conference, Congrès annuel de la société canadienne de science économique, and discussants of my work at conferences. I am also grateful to all my macroeconomist colleagues at the Ministry of Finance of Quebec for their advice and assistance, a special thanks to Daniel Floréa and Raymond Fournier.

I would like to thank all the professors of the Department of Statistics at Padua University and the Department of Mathematics at the University of Yaoundé I, where I obtained my Bachelor and Master’s degrees. These undergraduate years in discovering Economics and learning quantitative tools were decisive in my PhD journey. A special thanks to Prof. Massimiliano Caporin, Prof. Nunzio Cappuccio, Prof. Efrem Castelnuovo, Prof. Guglielmo Weber, Prof. Ottorino Chillemi and Prof. Giovanni Battista Di Masi.

I would also like to express my appreciation to my colleagues of the Department of Economics for their (and non-) academic discussions, patience, assistance and friendship over the last five years. In particular, I am grateful to André-Marie Taptué for his time and support. I also express my gratitude to my elders Legrand Kana, Bouba Housseini, Alexendre Kopoin, Habib Some, Jerome Gagnon-April, Aboudrahim Savadogo and Rokaya Ndiaye for their advice. I also thank my close friends and colleagues for their crucial support and continuous encour-agement throughout the whole period of my PhD studies. Many thanks to Gilles Koumou, Jean-Armand, Ali, Setou, Isaora, Mbea, Abdhalla, Elfried, Marie-Albertine, Bodel, Carolle for giving me crucial support and assistance.

I also extend my deepest gratitude to my family, in particular, to my late grandmother Louise, who set the path for all possible knowledge in my life. To my mother and siblings, my friends in Quebec, Italy and Cameroon and all the persons who have always been there for me, physically or in thoughts. For their love, encouragement and continuous guidance to pursue

(20)

my PhD studies, may all of these persons find in these words my deepest gratitude.

Finally, I gratefully acknowledge logistical and financial support from: the Department of economics of Université Laval; the Faculty of Social Sciences of Université Laval, the Centre Interuniversitaire sur le Risque, les Politiques Économiques et l’Emploi (CIRPÉE) and the Quebec Ministry of Finance. I would also like to thank them for their logistical and financial support, including the sponsoring of my participation to various academic conferences and internship. These activities have hugely boosted my research skills and interest in the areas of macroeconomic modeling, economic analysis and forecasting.

(21)

(22)

Avant-propos

Cette thèse s’articule autour de trois chapitres indépendants qui s’inscrivent dans les champs de la macroéconomie, de la finance internationale et de prévision économique. Les trois chapitres constituent des articles soumis ou à soumettre à des revues scientifiques avec comité de lecture. Je suis le principal auteur de chacun de ces trois articles.

Le premier chapitre est un article réalisé avec mon directeur de thèse, Kevin Moran. Il fait l’objet de quelques révisions pour être soumis à une revue scientifique avec comité de lecture. Le deuxième chapitre est un article réalisé avec mon directeur de thèse, Kevin Moran, et mon co-auteur, Imad Rherrad. Cet article, dont je suis le principal auteur, a été soumis pour publication à une revue scientifique avec comité de lecture.

Le troisième chapitre est un article réalisé sous la direction de mon directeur de thèse, Kevin Moran, et avec la collaboration de mon co-auteur Imad Rherrad. Cet article a été soumis pour publication à une revue scientifique avec comité de lecture.

(23)

(24)

Chapter 1

The Forward Premium Puzzle: a

Learning-based Explanation

Abstract

When interest rates are higher in one’s home country than they are abroad, standard arbi-trage arguments suggest this signals that the home currency will depreciate in the future. However, empirical evidence has regularly been found to be strongly at odds with this intuition. This is the “forward premium puzzle”. This paper proposes a learning-based explanation for this puzzle. We embed an information problem in the two-country New-Open Economy Macroeconomics(NOEM) model with nominal rigidities. The information friction arises because the shocks affecting the model economy can be of either persistent or transitory types and economic agents do not directly observe the shocks’ types; instead they must infer their nature using a filtering mechanism. We simulate the model with and without this informational friction and test whether the generated artificial data exhibits the symptoms of the forward premium puzzle. Our leaning-based explanation is validated if only the data generated with the active informational friction replicates the puzzle.

Keywords: monetary policy, learning, exchange rate, forward premium puzzle, open-economy, UIP, DSGE.

(25)

1.1 Introduction

Research in international finance has documented the presence of several empirical regularities that pose significant challenges to standard open-economy models and arguments. These regularities, often described as “anomalies” or “puzzles”, are the subject of much active research. One important such anomaly is the forward premium puzzle. This puzzle arises because simple theories of international finance suggest that observing a premium between the domestic interest rate and its foreign counterpart signals that the home currency will depreciate in the future. However, data on interest rates and realized exchange rate depreciations have strongly and consistently refuted the implication of these theories.1

This paper proposes a learning-based explanation for the forward premium puzzle. To do so, we first embed an information friction in the New-Open Economy Macroeconomics (NOEM henceforth) model with nominal rigidities.2 Specifically, we assume that monetary policy and technology shocks can each either be of a persistent or a transitory type, but that economic agents do not observe the type directly and must instead infer its nature using a filtering mechanism. We then simulate the model repeatedly, with and without this informational friction, and assess the generated artificial data to see if they exhibit the signs of the forward premium puzzle. Validation for our leaning-based explanation for the puzzle arises in the event that only the data generated with the active informational friction can replicate the puzzle. The simulations undertaken with our model lead to these findings: the forward premium puzzle arises in an environment where investors face an information bias about the relevant nature of each shock hitting the economy. As the time-horizon increases the puzzle lessens and subsequently disappears in the medium-term of about two or three years. Only under incomplete information, we document a strong consistency with the regularities emerging from most empirical studies in literature, namely the negative correlation between the interest rate differential and the foreign exchange rate changes overtime (the negative slope coefficient in theFama [1984] regression).

The rest of this paper is organized as follows. Section 2 presents a short literature review that discusses the forward premium puzzle and the literature that analyses it and attempts to ra-tionalize it. Section 3 presents our model economy. Section 4 describe the information friction that we embed in the NOEM model and the filtering mechanism used to distinguish between persistent and transitory shocks. Section 5 presents our simulation results and discusses them, while Section 6 concludes.

1_{The existence of this puzzle was documented in early contributions such as}_{Hansen and Hodrick}_[₁₉₈₀_]

and Fama[1984] and confirmed since by several subsequent studies [Froot and Thaler,1990,Gourinchas and Tornell,2004,Engel,2014].

2_{The NOEM framework originates from}_{Obstfeld and Rogoff}_[₁₉₉₅_{] and is an open-economy extension of}

the New Keynesian model. SeeLane[2001] andCorsetti[2008] for surveys on the NOEM andCorsetti et al.

(26)

1.2 Review of literature

According to the efficient-market hypothesis, prices integrate all the information available to market participants and there is no possibility for a trader to earn excess returns. One implication of this hypothesis is that in foreign exchange markets, the covered interest rate parity condition (CIP) holds:

ft− et= it− i∗t , (1.1)

where i_t and i∗_t are the returns on comparable domestic and foreign assets, respectively, be-tween time t and t + 1, ft denotes the logarithm of the forward exchange rate (the rate for

foreign exchange delivered next period) and et is the spot exchange rate (the price of foreign

currency in units of domestic currency). Equation (1.1) represents a no-arbitrage condition because all the variables are known at time t. Several empirical analyses have confirmed the validity of the CIP condition using a large variety of currencies.3

The empirical evidence has not been as supportive of the uncovered interest parity condition, however. This condition arises by taking (1.1), assuming further that agents are risk neutral so that no risk premium is required by an agent choosing between a risky and a risk-free asset, that they have rational expectations and that forward rates equal expected future rates, so that

Et(et+1− et) ≈ it− i∗t , (1.2)

where E_t(et+1) is the rational expectation of the future spot exchange rate et+1. Since by

definition et+1= Et(et+1) + ξt+1with ξt+1∼ i.i.d N (0, σ), condition (1.2) can be rewritten as

et+1− et= it− i∗t+ ξt+1. (1.3)

The empirical validity of this condition is usually assessed by running the following regression in nominal terms:

et+1− et= α0+ α1(it− i∗t) + ξt+1, (1.4)

or in real terms:

st+1− st= α0+ α1(rt− r∗t) + ξt+1, (1.5)

where the real rate s_t = et∗ Pt/Pt∗ and testing the unbiasedness hypothesis H0 : α0 =

0 , α1 = 1. Under this null hypothesis, realized changes in the spot exchange rates should

therefore have a one to one correlation with the interest rate differential. However, results from the literature reject H₀ decisively, with estimatesα_b06= 0,αb1 1 and many instances of negative estimates for α1.4 Such frequent rejection of H0 is referred to as the forward premium

3_See_{Sarno and Taylor}_[₂₀₀₂_{], Chap. 2, for a detailed description and analysis of the CIP.}

4_{As indicated above, several authors report such evidence; among them,}_{Froot and Thaler}_[₁₉₉₀_],_Backus

et al.[1993],Lewis[1995],Bansal and Dahlquist[2000],Moore and Roche[2002,2008],Gourinchas and Tornell

(27)

puzzle. Froot and Thaler [1990], for example, survey more than 70 empirical contributions that analyse the puzzle and report that the average estimate of α₁ is −0.88.

A large literature has proposed various explanations to rationalize the forward premium puzzle, among them, Bacchetta and Van Wincoop[2006],Kearns[2007],Benigno and Benigno[2008],

Chakraborty and Evans [2008],Burnside et al.[2007],Evans [2010],Snaith et al. [2013],Hall et al.[2011],Martin[2011],Ilut[2012],Coudert and Mignon[2013],Yu[2013],Djeutem[2014]

and Londono and Zhou [2015]. This literature and contributions have proposed two main

approaches to explain the puzzle.

The first such approach originates in Fama [1984] and focuses on the existence of a risk premium. This premium, when introduced either in capital asset pricing, portfolio balance, if both highly volatile and positively correlated with the interest rate differential it− i∗t could

affect the estimation of (1.4) and help induce a small or even negative estimate for α₁. Macklem

[1991], Engel [1992] andBekaert [1994] show that such class of models can indeed generate a risk premium, but that the quantitative magnitude of this premium is not sufficient to account for the high volatility in the data. This occurs because the implied variability in the inter-temporal marginal rate of substitution of the agents is too low. Using a general equilibrium, open-economy model similar to the one used here but with incomplete markets, Leduc[2002] shows that it can generate at best a degree volatility in the risk premium that is 30% of what would be necessary to rationalize the findings in the empirical literature.

Alternatively, Froot and Frankel [1989] propose to decompose the predictable excess returns (a fact closely associated to the presence of the foward premium puzzle) into currency risk premium and expectation error components, using survey data to measure expectations. They show that the forward premium puzzle is mostly associated with the expectation error com-ponent. Accordingly, the conclude that models based on risk premia may have less potential to provide an explanation to the puzzle.

The second general approach thus relies on expectation errors. Froot and Frankel[1989],Lewis

[1988, 1993], De Long et al. [1990] and Gourinchas and Tornell [1996] argue that the puzzle may be due to systematic expectational errors on the part of investors. In addition, they point out that the presence of market speculators create informational heterogeneity between traders, which can lead to inefficient expectation errors, of that rational expectation errors may emerge from regime shifts and so called peso problems.5

The present paper contributes to this literature by investigates whether a general equilibrium, two-country model with rational and risk-averse agents can explain the forward premium puz-zle, in the information environment is such that agents cannot directly observe the persistence 5_{Yet another line of inquiry into the forward premium puzzle involves assuming and showing that}

sub-stantial non-linearities affect the regression (1.4). Mark and Moh[2002] illustrate that transaction costs and central bank interventions can indeed lead to a non-linear variance of the innovation term in (1.4). See also

(28)

of a given shock but must instead use a filtering mechanism to ascertain that persistence. Our methodological approach thus followsLewis[1988,1995] andAndolfatto et al.[2008] and repeatedly simulates the economy with and without the information friction and then running the classic econometric tests of coefficients in the Fama (1984) regression, reporting the value of each coefficient and the frequency at which the null hypothesis of unbiasedness is rejected.

1.3 The model economy

This section describes our two-country model economy. The model is part of the New Open-Economy Macroeconomics (NOEM) literature exemplified by Corsetti [2008] and Corsetti

et al. [2010]. As indicated above, this model is drawn from the New Keynesian paradigmn

with monopolistic competition and nominal rigidities, extended to a two-country world. The world economy consists of two countries of equal size, denoted H(Home) and F (Foreign). Each country specializes in one type of traded good produced in a number of varieties (or brands) defined over a continuum of unit mass. Brands of tradable goods are indexed by h ∈ [0, 1] in the Home country and f ∈ [0, 1] in the Foreign country. Firms producing the goods are monopolistic suppliers of one brand only and use labor as the only input to production. These firms set nominal prices in local currency units and in staggered fashion, à la Calvo [1983]. Finally, international asset markets are complete.6

1.3.1 Preferences

We describe the structure of the Home country, with the understanding that similar expressions characterize the Foreign country economy with obvious notational changes. We consider a cashless economy in which the representative household (or Home agent) maximizes expected lifetime utility : W0= E0 ∞ X t=0 βtU [Ct, Lt], (1.6)

where instantaneous utility U is a function of the consumption index Ctand of leisure (1 − Lt),

as follows: U [Ct, Lt] = C_t1−σ 1 − σ + κ (1 − Lt)1+η 1 + η , σ > 0. (1.7)

Households consume both domestically-produced and imported goods, aggregated in the bas-kets CH,t and CF,t respectively. We define Ct(h) as Home’s consumption of Home good h,

and similarly, Ct(f ) as Home’s consumption of imported Foreign good f . Each good h (or f )

is an imperfect substitute for other varieties so that the baskets C_H,t and C_F,t are: CH,t≡ Z 1 0 Ct(h) θ θ−1_dh , CF,t≡ Z 1 0 Ct(f ) θ θ−1_df , (1.8)

(29)

with the constant elasticity of substitution θ > 1 common across baskets. The full consump-tion basket C_t aggregates both domestic and foreign baskets according to the following CES function: Ct≡ a1/φ_H C φ−1 φ H,t + a 1/φ F C φ−1 φ F,t _φ−1φ , φ > 0, (1.9)

where aH and aF are the weights of home and foreign goods in total Home consumption,

respectively, and φ is the elasticity of substitution between CH,t and CF,t. As in Corsetti

et al. [2010], the utility-based CPI associated with the consumption basket C_t is the result

minimizing total expenses in order to purchase one unit of Ctand entails

Pt=

h

aHP_H,t1−θ+ aFP_F,t1−θ

i_1−θ1

, (1.10)

where sub-indices P_H,t and P_F,t of home and foreign composites are

PH,t= Z 1 0 Pt(h)1−θdh _1−θ1 ; PF,t= Z 1 0 Pt(f )1−θdf _1−θ1 . (1.11)

1.3.2 Assets market and budget constraint

In each time period t, Home households purchase Bt+1 units of contingent claims at the price

pbt,t+1. These assets represent a promise to pay one unit of local currency the next period for

each possible realization of the state of nature. Domestic households also derive income from work, WtLt, from their ownership of domestic firms, Π(h), with h ∈ [0, 1] and from bonds

holdings B_t. Home’s disposable income is used to consume both home and foreign produced goods or invested to transfer wealth in the next period. The budget constraint for the Home’s is therefore PH,tCH,t+ PF,tCF,t+ Z s pbt,t+1Bt+1 ≤ WtLt+ Bt+ Z 1 0 Π(h) dh. (1.12)

Home household’s optimization problem can therefore be explicitly defined as

maxE0 ∞ X t=0 βt C 1−σ t 1 − σ + k (1 − Lt)1+η 1 + η , subject to (1.12).

Foreign households face a similar maximization problem, as in

maxE0 ∞ X t=0 βt C ∗1−σ t 1 − σ + k (1 − L∗_t)1+η 1 + η , subject to P_H,t∗ C_H,t∗ + P_F,t∗ C_F,t∗ + Z s p∗_bt,t+1B_t+1∗ ≤ W_t∗L∗_t + B∗_t + Z 1 0 Π(f ) df,

(30)

1.3.3 Firms

Three different types of firms are present in the home and foreign country, each producing a specific type of good.

1.3.3.1 Domestic final goods

Domestic final good assemblers operate in a perfectly competitive environment and use the following CRS production function:

Dt= a 1 φ HD φ−1 φ H,t + a 1 φ FD φ−1 φ F,t _φ−1φ ,

where DH,t represents inputs of home-produced goods and DF,t inputs of foreign-produced

goods, respectively, with φ the elasticity of substitution between home and foreing goods in production. Profit maximisation for these firms entails

max

DH,t;DF,t

[PtDt− PH,tDH,t− PF,tDF,t] ,

with the optimality conditions leading to input-demand functions D_H,t = Dt

_P H,t Pt and DF,t= Dt _P F,t Pt

. Further, imposing the zero-profit condition leads to equation (1.10).

1.3.3.2 Domestic composite goods

Domestic composite good assemblers operate under perfect competition, using the following CRS technology: DH,t= Z 1 0 Dt(h) θ−1 θ dh _θ−1θ ,

where Dt(h) represents their input demand for each of the differentiated domestic goods h.

Their profit maximization problem is therefore as such:

max Dt(h) PH,tDH,t− Z 1 0 Pt(h)Dt(h) dh .

and from the optimality conditions and the zero-profit condition, one can derive

Dt(h) = DH,t Pt(h) PH,t (1.13) and PH,t= Z 1 0 Pt(h)1−θdh _1−θ1 . (1.14)

For assemblers of the foreign composite good, similar expressions obtain:

max Dt(f ) PF,tDF,t− Z 1 0 Pt(f )Dt(f ) df s.t. DF,t= Z 1 0 Dt(f ) θ−1 θ df _θ−1θ ,

(31)

with Dt(f ) = DF,t Pt(f ) PF,t , (1.15) and PF,t= Z 1 0 Pt(f )1−θdf _1−θ1 .

1.3.3.3 Domestic basic goods

Domestic producers of basic goods operate under monopolistic competition and employ do-mestic labor to produce a differentiated good h using the following linear production function:

Yt(h) = ZtLt(h), (1.16)

where Lt(h) is the demand for labor by the producer of good h and Ztis a technology shock

common to all producers in the domestic country, which follows a statistical process to be specified below.

For a typical such producer, output satisfies a domestic and a foreign demand in that:

Yt(h) = Dt(h) + Dt∗(h) (1.17)

where Dt(h) is the domestic demand for the good, expressed above in equation (1.14) and

D∗_t(h) is the foreign demand for the same good. Total real revenues for this firm are therefore: Pt(h)Dt(h) + EtPt∗(h)D∗t(h)

Pt

,

where E_t is the nominal exchange rate i.e. the price of the domestic currency in terms of the foreign one (increases in Etthus represent domestic depreciations). Firms are subject to

nom-inal rigidities `a la Calvo. Every period t, some firms receive a signal indicating they can set a new price. Each firm receiving this signal chooses its domestic and foreign-currency prices Pt(h) and Pt∗(h) knowing the same prices continue to apply in future periods with

proba-bility α, while their real production cost will be mc_t(Dt(h) + D∗t(h)). 7 The intertemporal

maximization problem is then:

max P (h),P∗_(h)Et ( _∞ X k=0 (αβ)kµt+k µt 1 Pt+kPt(h)Dt+k(h) + EtP ∗ t(h)Dt+k∗ (h) − M Ct+k Pt+k Dt+k(h) + D ∗ t+k(h) !) (1.18) where µt+1

µt is the firm’s stochastic nominal discount factor between t and t + k.

8 _{By the}

first order condition of the producer’s problem, the optimal price P_t(h) in domestic currency charged to domestic customers is:

Pt(h) = θ θ − 1 Et P∞ k=0(αβ)kµt+kmct+kPH,t+kθ CH,t+k Et P∞ k=0(αβ)kµt+kPH,t+kθ CH,t+k Pt+k , (1.19)

7_{This specification of the production assumes that when firms update their prices, they do so simultaneously}

in the Home and in the Foreign market and in the respective currencies.

8

(32)

similarly, the optimal price P_t∗(h) in domestic currency charged to foreign customers is: P_t∗(h) = θ θ − 1 EtP∞_k=0(αβ)kµ_t+k∗ mc∗_t+kP_H,t+k∗θ C_H,t+k∗ EtP∞_k=0(αβ)kµ∗_t+kP_H,t+k∗θ C_H,t+k∗ P_t+k∗ .

Since all the producers allowed to set new prices in period t make the same choices ePt(h) = ePt,

we obtain the following equation for P_H,tand P_H,t∗ :

P_H,t1−θ = αP_H,t−11−θ + (1 − α) ePt(h)1−θ,

P_H,t∗1−θ= αP_H,t−1∗1−θ + (1 − α) eP_t∗(h)1−θ, (1.20) and we note that similar relations is applicable for the Foreign firms f .

For the goods market clearing condition in the Home economy, it follows that :

Dt= Ct, DH,t= CH,t, DF,t= CF,t.

We obtain dual relations in the Foreign economy.

1.3.4 Monetary policy

We complete the model by adding a policy rule for the domestic interest rate, which represents the behavior of the monetary authority. Let i_t and π_t denote the (net) nominal interest rate and the (net) inflation rate and let it , respectively. Further, let ¯r and ¯yt denote the steady

state value of the real interest rate and the natural rate of real GDP.9 The rule is then:

it= ρit−1+ (1 − ρ) [¯r + ¯πt+ ψπ(πt− ¯πt) + ψy(yt− ¯y)] + t. (1.21)

In (1.21), ¯πt denotes the monetary authority’s date t ’s inflation target and t denotes an

exogenous monetary policy shock. We consider that the target ¯πt varies occasionally because

of infrequent shifts in targeted or mandated inflation. The parameter ρ ∈ [0, 1) represents the degree of interest rate smoothing. According to (1.21), therefore, the central bank gradually adjusts its interest rate instrument in response to domestic inflation and output gaps. We consider that the monetary authority in the foreign economy follows a similar policy rule.

1.4 Information frictions and filtering mechanism

This section describes how shocks affecting this economy, to the technology in production and to the monetary policy rule, both have persistent and transitory types. It also details how agents, who cannot directly observe the persistence of these shocks, instead use a filtering mechanism (the Kalman filter) to disentangle both components.

(33)

1.4.1 Technology shocks

We consider first the shock to multi-factor productivity Zt. We assume that Zt is affected by

a persistent and by a transitory component, so that we have:

logZt= logZtp+ logZtτ , (1.22)

where Z_tp is the persistent component and Z_tτ the transitory component. We assume further that these components evolve according to:

" logZ_t+1p logZ_t+1τ # = " λp 0 0 λτ # . " logZ_tp logZ_tτ # + " ν_t+1p ν_t+1τ # , (1.23)

where λpand λτ represent the serial correlation of each component of the shock with λp >> λτ

and ν_t+1p and ν_t+1τ follow iid zero-mean processes with standard deviations σνp and σντ. Taken

together, (1.22) and (1.23) form a state-space system integral to our model solution.

1.4.2 Monetary policy shocks

For the shocks in monetary policy, the transitory component t is imputable to the reaction

of the monetary authority to various unexpected economic developments and is assumed to follow the process:

t= φ1t−1+ et, (1.24)

with 0 ≤ |φ1| 1 and et∼ N (0, σ2e).

FollowingAndolfatto et al.[2008], let the persistent component of the monetary policy shocks arise from regime shifts to the inflation target ¯πt. Let at ≡ ¯πt− ¯π denote an occasional

deviation of the current target of monetary authorities ¯πt from its very long run mean ¯π. The

monetary regime shift at can be attributed to a new insight (revolutionary vision) about the

economy or to preference changes with the monetary authority. We assume that at has the

following dynamic process:

at=

(

at−1 with prob. φ2

gt with prob. (1 − φ2) and gt∼ N 0, σ2g

(1.25)

where φ₂ reflects the persistence of any given regime in terms of duration and σ2 g is the

importance of regime shifts in terms of size, when they do occur. Using the definition of a_t, the policy rule (1.21) can be rewritten:

it= ρit−1+ (1 − ρ) [¯r + ¯π + ψπ(πt− ¯π) + ψy(yt− ¯y)] + ut, (1.26)

where

(34)

The observed shock to monetary policy u_tis thus a combination of the transitory component t and the persistent component at . In our complete information environment, agents can

observe separately atand tso that the rule is effectively as written in (1.21). The state-space

system for monetary policy shocks is therefore: " at+1 t+1 # = " φ2 0 0 φ1 # . " at t # + " ea_t+1 e_t+1 # , (1.27) and ut= [(1 − ρ)(1 − ψ) 1] " at t # , (1.28) with ea t+1 defined as: ea_t+1= ( (1 − φ2)at with prob. φ2 gt+1− φ2at with prob. (1 − φ2) .

1.4.3 Incomplete information and Kalman filter

The overall state-space representation for the two shocks affecting the economy is:       logZ_t+1p logZ_t+1τ at+1 t+1       =       λp 0 0 0 0 λτ 0 0 0 0 φ2 0 0 0 0 φ1       .       logZ_tp logZ_tτ at t       +       ν_t+1p ν_t+1τ ea_t+1 e_t+1       (1.29) and " logZt ut # = " 1 1 0 0 0 0 (1 − ρ)(1 − ψ) 1 #       logZ_tp logZ_tτ at t       . (1.30)

Under complete information, agents know all structural parameters and directly observe the two components of each shock. Under incomplete information, by contrast, agents know all structural parameters but cannot distinguish between the two components of each shock. In this case, we apply the Kalman filter to the state-space system (1.29) and (1.30) to determine the expectations of the variables logZ_t+1p , logZτ

t+1, at+1and t+1, conditional to the set of

infor-mation available at time t. These forecasts illustrate how agents learn to use new inforinfor-mation available in the economy to infer the probable future values of shocks. The filter produces estimates for the unobserved variables logZ_tp, logZ_tτ, a_t and _t, by updating sequentially as every new information become available, as in the following:

(35)

      EtlogZtp EtlogZtτ Etat Ett       =       Et−1logZt−1p Et−1logZt−1τ Et−1at−1 Et−1t−1       + Kt " logZt ut # − E_t−1 " logZt−1 ut−1 #!

where Kt is the Kalman gain.10 Thus, using (1.29) and (1.30) we compute the expectations

of unobserved variables:       EtlogZ_t+1p EtlogZt+1τ Etat+1 Ett+1       =       λp 0 0 0 0 λτ 0 0 0 0 φ2 0 0 0 0 φ1       .       EtlogZtp EtlogZtτ Etat Ett       and Et " logZt+1 ut+1 # = " 1 1 0 0 0 0 (1 − ρ)(1 − φπ) 1 #       EtlogZ_t+1p EtlogZt+1τ Etat+1 Ett+1       .

1.5 Results

This section presents our results. First, we discuss how key model parameters are assigned numerical values (ie. calibrated). Second, we report a series of standard impulse response experiments studying the economy’s evolution, under full information, following three types of shocks: the transitory monetary policy shock, the persistent technology shock, and the persistent shift in the monetary authorities’ target for inflation. This is undertaken in order to develop intuition about the model and verify that its implications are consistent with similar contributions in the literature. Third, we then report the reaction of the economy following the monetary policy shift when we compare responses under full information and incomplete information. This illustrates how gradual learning about the persistence of a given shock can modify the responses of key variables and entail departures from UIP in realized paths for interest rates differentials and exchange rate depreciations. Fourth, we describe the procedure whereby regressions are ran on simulated data and analyzed, to assess if they can reproduce results from UIP tests conducted on actual data in the literature. Finally, we present a section with a sensitivity analysis of our main results.

1.5.1 Parameter calibration

We parametrize the model to a quarterly frequency. We thus assume β = 0.99, which implies a real annualized return on assets of about 4% in the steady state. We set the elasticity

(36)

of substitution between the brands, θ, to be 6, which implies a markup over the marginal cost equal to 20% at the steady state. The parameter α, governing the frequency of price changes, is equal to 0.75, which implies an average of four periods (one year) between two price adjustments. We set the parameter governing the curvature on labor disutility η, to be equal to 1.5 and the parameter κ such that the hours worked are 1/3 of available time at the steady state. Finally we assume an import share in consumption equal to aF = 0.4,

corresponding to the import/GDP ratio in Canada.11

The calibration of the monetary policy rule (1.21) is adapted from Andolfatto et al. [2008]. First, we set the coefficient governing the response to inflation deviations from target, ψπ,

to 1.8 and the coefficient governing the inertia in interest rate, ρ, to 0.1. The calibration of the shock processes, which play a decisive role in the model, is next. To this end, note that φ2 characterizes the mean duration of a given regime shift in monetary authorities’ inflation

target and σg the standard deviation of the distribution governing the magnitude of such

regime shifts when they do occur. Following Andolfatto et al. [2008], we set φ₁ = 0.0 and φ2 = 0.975, σg = 0.01 and σ= 0.005; these values entail Kalman filter gains that are similar to

those used byErceg and Levin[2003] andSchorfheide[2005]. Note that these parameter values imply that monetary policy shifts occur infrequently (on average once every 40 quarters, or 10 years) and that when they do occur their magnitude is relatively high, changing the inflation target by a typical 4 points of percentage on an annualized basis (0.01·4). For the technological shocks, we similarly set λ_τ = 0.0 and λp = 0.95, as well as στ = 0.005 and σp = 0.0025. We

use a similar calibration for the foreign economy’s monetary policy.

1.5.2 Impulse response functions: Complete information

This subsection presents the impulse response functions of our model economy, under complete information, following the three major types of shocks affecting the economy. Figures 1.1

-1.3 first report the effect of a one percent (positive) transitory monetary policy shock (e_t). Recall that such a shock represents a transitory positive displacement to (1.21), the domestic monetary policy rule. Real activity variables are displayed in Figure 1.1 while Figure 1.2

-1.3 report nominal and financial variables (interest rates, inflation, nominal exchange rate depreciation) or their real counterparts (the real ex-ante interest rate, the real exchange rate, realized real depreciation, etc.). All responses are computed assuming complete information in order to compare these results to other contributions in the NOEM literature. Finally, note the presence of the UIP errors in the graphs: this simply refers to the difference between interest rate differentials and realized depreciations, as in (1.4) and (1.5) under H0.

Next, Figures1.4-1.6record the responses following a favorable one percent persistent produc-tivity shock. Finally, Figures 1.7-1.9 display the dynamic properties of the economy arising 11_{These values are similar to those used in}_{Corsetti et al.}_[₂₀₁₀_{], apart from the import share (which they}

(37)

from of a one percent negative persistent monetary policy shift. Recall that this entails a decline in a_tfrom (1.25) and thus such a shift implies that monetary authorities have lowered their target rate for inflation πtand that this decline will be persistent.

Monetary Policy Shocks

Figures 1.1-1.3depict the economy’s response to a one percent (positive) transitory monetary policy shock (e_t). This represents a tightening of monetary policy in the domestic country; said otherwise, domestic monetary authorities choose a more aggressive stance than their usual rule (1.21). Recall however that this aggressive stance will be short-lived, as we have set the autocorrelation of monetary policy shocks φ1 to 0. Note also that when describing

the responses of the economy to the shock, both endogenous and exogenous aspects to the monetary policy rule (1.21) come into play: whereas the positive shock to (e_t) implies a tighter monetary policy, all things equal, the actual interest rate will continue to depend on inflation and the output gap through the endogenous coefficient ψ_π.

The aggressive stance of the domestic monetary authorities increases both the domestic nom-inal interest rate, Figure 1.2, and the domestic real rate, Figure1.3, because of the rigidities in the evolution of prices. Through its impact on consumption decisions, the increase in the real ex-ante rate depresses domestic economic activity and thus labour demand, so that do-mestic consumption, hours worked and GDP decline on impact (Figure1.1). Note that in this economy monetary policy shocks can have real economic impacts only because of the price rigidities’ presence. It is therefore not surprising that natural output, consumption and hours worked do not react to the shock (Figure 1.1).12 Finally, note that as expected, the domestic monetary tightening results in decreases in domestic inflation and the opening of a negative output gap (Figure 1.2).

So far, the responses discussed are common to complete- and open-economy versions of the New Keynesian model. We now discuss the transmission of the shock to international variables. The increase in domestic interest rates implies that all things equal, they will be higher than their international counterparts. Because UIP holds in the economy, this can only occur if an expected path of currency depreciation opens up. Indeed positive interest rate differentials (between domestic rates and their foreign counterparts) manifest themselves, both measured in nominal terms (Figure 1.2) and in real terms (Figure 1.3). Further, these interest rate differentials are accompanied by expected depreciations for the nominal and real exchange rate.13

12_{Recall that natural variables are computed by simulating responses from a “parallel” economy where}

nominal rigidities are absent.

13_{Recall that our notation implies that an increase in the level of the exchange rate represents a depreciation}

(38)

Because our open economy is relatively highly-integrated (recall our calibration of a_F = 0.4) the shock also has important negative impacts on the foreign economy: Foreign GDP, hours worked, and inflation all decline and a negative output gap also opens in the foreign econ-omy. Considering that the interest rate rule followed by the foreign monetary authority is of the same form as (1.21), the foreign interest rate responds to these depressed conditions with a small decline. Finally, note that the real exchange rate appreciates on impact: this occurs because perfect risk sharing commands that this rate equal the ratio of domestic to foreign consumption, and domestic consumption has declined importantly. Said otherwise, the model rationalizes the fall in the foreign to domestic consumption ratio by increasing the relative price of domestic goods, ie. by appreciating the real exchange rate. As discussed above, this contemporaneous, real appreciation is expected to undo itself in future periods and the currency is thus expected to experience future depreciations. This pattern, whereby a contemporaneous real exchange rate appreciation is associated with future depreciations, real or nominal, is consistent with the classic Dornbush overshooting hypothesis and is discussed at length in Eichenbaum et al. [2017]. It will play a key role below when we discuss depar-tures from UIP under incomplete information. Here, under complete information, UIP holds exactly however so that the positive interest rate differentials are exactly matched with the subsequent depreciations and UIP errors are nil (Figure 1.2-Figure 1.3).

Technology Shocks

Next, Figures1.4-1.6report the impulse responses following a favourable shock to technology. Recall that such a shock is relatively persistent, as we calibrated λp to be 0.95. The shock

makes domestic goods cheaper to produce, so absent rigidities one would expect production and consumption of these goods to increase and their relative price to decrease. Indeed, Figure1.4

does report that natural output and consumption increase. However, the presence of nominal rigidities means that domestic prices cannot decrease fast enough to accommodate this change in the relative competitiveness of domestic goods: as a result, one expects economic activity to initially increase by less than this new potential. Indeed, Figure 1.5shows that a shortfall between realized and potential output opens up (ie. the domestic output gap is negative) in the first few periods immediately after the onset of the shock.

Domestic monetary policy can compensate somewhat for the lack of flexibility in prices, by boosting money supply and reducing interest rates: Figure 1.5 shows this occurs to some extent, as the nominal and real domestic interest rates decrease; however, this is not enough for the output gap to be eliminated. Finally, as the favourable shock renders domestic goods cheap compared to foreign counterparts, the real exchange rate depreciates (Figure 1.6): as such, it is up to the nominal exchange rate to make the necessary adjustments between the relative prices of domestic and foreign goods when actual money prices cannot change. Once

(39)

more, note that UIP continues to hold exactly: the negative differentials in interest rates are exactly matched by expected and realized depreciations and the UIP errors (Figure 1.5-1.6) are nil. Said otherwise, the contemporaneous real depreciation is associated with an expected path of future appreciations, a key negative correlation that is consistent with data [Burnside

et al.,2007] and that will imply departures from UIP under incomplete information, below.

Inflation Targets Shifts

Finally, Figure 1.7 through 1.9 display our open economy’s dynamic properties after a one percent (negative) persistent monetary policy shock, ie. a decline in the long term inflation target of domestic monetary authorities. The sudden occurrence of this shift implies that domestic monetary authorities are now aiming for lower inflation and therefore will judge current inflation in a more hawkish manner, tending to set higher interest rates, all things equal.14

In the short term this shift represents a tightening of domestic monetary policy and tends, all things equal, to create a transitory economic slowdown in the domestic economy.15 This occurs because of the monetary authority’s desire to have higher interest rates and the inflexibility of domestic prices. This is illustrated in Figure 1.8 which shows that nominal domestic rates decrease but less, in magnitude, than domestic inflation, so that domestic real rates increase (Figure 1.9). This tightening creates a transitory economic slowdown in domestic production and hours worked (Figure 1.7). The responses of the foreign monetary authorities are much more subdued, and a positive interest rate differential thus opens up when measured by the rate interest rate (Figure 1.9) and is associated with future expected (and realized) depreciations. Eventually however, the reality of a persistently lower rate of monetary expansion in the domestic country starts to have beneficial long-term impacts and the direction of the economy reverses itself. Domestic output and hours worked become positive and stay above steady-state for several periods.16 Finally, as was the case for the other two shocks analysed above, UIP continues to hold: the differentials in interest rates are exactly matched by expected and realized rates of appreciation or depreciation, so that the UIP errors in Figure1.8and Figure

1.9 are nil.

14_{Recall that the shift is destined to be ultimately transitory, because sooner or later a new regime shift will}

come to replace it; see (1.25). This creates a difficulty in graphing the impulse response function following the shift: how long should we make is persist? We solve this practical problem by producing the impulse response function using the expected duration of the shift, which is governed by the parameter φ2.

15_{Recall that both the shift to the target and the monetary policy shock materialize themselves as increases}

in the composite shock utin (1.28). As such, the shift is a persistent version of the monetary policy tightening

analyzed above in Figure 1.1-1.3.

(40)

1.5.3 Impulse response functions: Complete versus incomplete information

We now contrast our economy’s responses to shocks under complete and incomplete informa-tion. To this end, we once again study the monetary policy shift described above, but now introduce the incomplete information responses. These arise when agents can only observe the composite monetary policy tightening ut in (1.28), but have to ascertain whether it

oc-curred because of a temporary tightening (an increase in e_t) or because of a persistent decline in the inflation target (a decline in a_t). Under incomplete information, this learning occurs via a filtering mechanism; as such, agents will place positive probability weights on the event that the shift was transitory and will therefore be surprised, in subsequent periods, when the tightening persists. This surprise will then trigger departures from UIP.

Figure 1.10 - 1.12 report the impulse responses for both cases, where complete information is displayed in full lines and incomplete information is in dashed lines.17 The key difference between the two cases is the perceived persistence of the tightening: full-information agents know it will be persistent, and thus price-setting reacts to a larger extent than it does under incomplete information, when agents view the shock as likely transitory. As a result, the con-temporaneous decline in inflation is substantial under complete information and very modest under incomplete information.

This change of perception in turn modifies the rest of the economy’s responses. Since inflation has declined substantially under complete information, monetary authorities’ new hawkish preferences are satisfied and the nominal interest rates decreases (Figure 1.11) and the real rate increases only slightly (Figure 1.12). By contrast, the two figures show that under incom-plete information, monetary authorities react to the very mild decrease in inflation by further tightening: the nominal rate actually increases, and the rise in the real rate is now substantial (Figure 1.12). Looking further, the harsher tightening under incomplete information also has consequences for the real economy: domestic consumption does not adjust fully to the new reality of a persistently lower inflation target, so the decline under incomplete information is very small; this in turn implies that the real exchange rate (Figure 1.12), which should appreciate substantially, only does so modestly. The initial real exchange rate appreciation is expected to undo itself in subsequent periods, so agents expect future real depreciations, both under complete and incomplete information. On the nominal side, a similar story plays out: because of the price rigidities, the nominal rate does much of the adjusting and appre-ciates substantially (complete information) or just a little (incomplete information). Because the shock is expected to be very transitory under incomplete information, this appreciation is expected to undo itself and agents expect a nominal depreciation (a fact consistent with the positive nominal interest rate differential - Figure 1.11). Under complete information by contrast, agents know the shock will persist and the nominal exchange rate has already