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THE IMPACT of MONEY ILLUSION on CONSUMPTION an Empirical Investigation

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THE IMPACT of MONEY ILLUSION on CONSUMPTION an Empirical Investigation THE IMPACT OF MONEY ILLUSION ON CONSUMPTION An Empirical Investigation THESIS Presented to the Faculty of Economics and Social Sciences at the University of Fribourg (Switzerland), in fulfillment of the requirements for the degree of Doctor of Economics and Social Sciences by VINCENT POCHON from Dompierre (FR) Accepted by the Faculty of Economics and Social Sciences on February 23rd, 2015 at the proposal of Prof. Dr. Klaus Neusser (first advisor) and Prof. Dr. Volker Grossmann (second advisor) Fribourg (Switzerland), 2015 The Faculty of Economics and Social Sciences of the University of Fribourg (Switzer- land) does not intend either to approve or disapprove the opinions expressed in a thesis: they must be considered as the author’s own (decision of the Faculty Council of 23 January 1990). Acknowledgement First and foremost, I would like to express my sincere gratitude to my first advisor, Klaus Neusser. Not only did he immediately agree to become my new supervisor after the untimely death of Hans Wolfgang Brachinger, but he was also very acces- sible and supportive, and he provided highly valuable feedback that substantially improved my work. I would further like to thank Volker Grossmann, who agreed to be my second advisor and who gave me helpful comments. I also acknowledge Reiner Wolff for taking the role of the president of the defence jury. I owe particular credit to my former colleagues at the Chair of Statistics. I could always count on their support and a friendly atmosphere, even during the troubled period we had to go through. I think especially of Christoph Leuenberger, Michael Beer, Thomas Epper, Olivier “Silvio” Schöni, Daniel “the Queen” Suter, Severin “Sven” Bernhard and Helga Kahr, who all contributed in one way or another to this thesis. A special thank goes to my partner in crime, Lukas “Yolanda” Seger, who taught me that having the better odds in poker is not always sufficient to win. Further, I would like to thank all of my friends, who ceaselessly teased me with the same question: “Have you finished your thesis yet?” In fact, this trick question very often reinforced my motivation to persevere in my work. Finally, I am indebted to my family, and particularly my parents and brother, for their unwavering support and encouragement throughout the years. Most of all, my deepest thanks go to my wife Diana, for her unconditional love and faith in me. She was always there to hear my doubts and complaints, and she did everything she could to facilitate the completion of this thesis. You’re my first, my last, my everything! iii iv Table of Contents Acknowledgement iii List of Tables ix List of Figures xi 1 Introduction1 1.1 Motivation . .1 1.2 Outline . .2 2 Two Potential Benchmark Models5 2.1 Introduction . .6 2.2 The Rational Expectations–Permanent Income Hypothesis . .6 2.2.1 The Consumer’s Problem Under Uncertainty . .8 2.2.2 Definition of Permanent Income . 18 2.3 The Money in the Utility Function Model . 22 2.3.1 The Original Sidrauski Model . 23 2.3.2 Incorporating Money Illusion . 28 2.4 Conclusion . 31 3 Estimating a Money Illusion Consumption Function 33 3.1 Introduction . 34 3.1.1 Money Illusion in the Economic Literature . 35 3.1.2 Refining the Concept of Money Illusion . 38 3.2 A Simple Empirical Model for the U.S. 42 3.2.1 The Inflation-Augmented Random Walk Hypothesis . 42 3.2.2 Estimation Results Over the Whole Sample . 44 3.2.3 Estimations for High- and Low-Inflation Subperiods . 52 v 3.3 The Money Illusion Aggregate Consumption Function . 57 3.3.1 Liquidity Constraints and Habit Formation . 58 3.3.2 Real Interest Rate and Wealth . 60 3.3.3 An Error Correction Model Reformulation . 61 3.4 Estimation of the Money Illusion Consumption Function . 62 3.4.1 Extended Preferred Inflation-Augmented RW Models . 62 3.4.2 Finding the Best Aggregate Consumption Function . 65 3.5 Conclusion . 72 4 Money Illusion as a Signal Extraction Problem 75 4.1 Introduction . 76 4.2 Modeling Inflation as an Unobserved Variable . 77 4.2.1 Kalman Filter Estimation Results . 81 4.3 Modeling Inflation as an Observed Variable . 90 4.3.1 Kalman Filter Estimation Results . 91 4.4 Conclusion . 98 5 Seeking Robustness Against Money Illusion 101 5.1 Introduction . 102 5.2 Modeling Robust Control . 104 5.2.1 Robustness as Aversion Against Money Illusion . 104 5.2.2 A Static Robust Optimal Control Problem . 107 5.3 A Closed-Form Robust Permanent Income Hypothesis Model . 111 5.3.1 The Univariate REPIH Model . 111 5.3.2 Incorporating Robust Control . 114 5.3.3 Critical Evaluation of the RCPIH . 119 5.4 The Hansen et al.(1999) Robust Consumption Model . 128 5.4.1 The Robust Consumer’s Problem . 129 5.4.2 Estimation Results . 133 5.5 Conclusion . 138 References 141 A Data Description and Properties 155 A.1 U.S. Data Description . 155 A.2 Properties . 155 vi B Estimations of the Inflation-Augmented RW Model 157 C Description of the Kalman Filter 171 D Solving the Robust Dynamic Programming Problem 173 D.1 Derivation of the Value Function . 173 D.2 Derivation of C .............................. 178 D.3 The Robust Consumption Function and Consumption Growth . 180 D.4 Proof that F < 1 ............................. 181 E Estimation Results for the Hansen et al.(1999) Model 183 vii viii List of Tables 3.1 Impact of Inflation on Consumption – Linear Model . 49 3.2 Impact of Inflation on Consumption – Nonlinear Model . 50 3.3 Re-Estimation of the Preferred Inflation-Augmented RW Models . 64 3.4 Money Illusion Consumption Function – High-Inflation Period . 67 3.5 Money Illusion Consumption Function – Low-Inflation Period . 68 4.1 Inflation Unobserved: Estimations for a Single Correlation . 84 4.2 Inflation Unobserved: Estimations for Two Correlations . 85 4.3 Estimation Results When Inflation Is Observed . 93 5.1 Estimates of β in the Selected Subperidos . 135 A.1 Unit Root Tests of Selected U.S. Time Series . 156 B.1 Linear IPD-Inflation Effect – Whole Sample . 158 B.2 Linear CPI-Inflation Effect – Whole Sample . 159 B.3 Linear IPD-Inflation Effect – High-Inflation Subperiod . 160 B.4 Linear CPI-Inflation Effect – High-Inflation Subperiod . 161 B.5 Linear IPD-Inflation Effect – Low-Inflation Subperiod . 162 B.6 Linear CPI-Inflation Effect – Low-Inflation Subperiod . 163 B.7 Nonlinear IPD-Inflation Effect – Whole Sample . 164 B.8 Nonlinear CPI-Inflation Effect – Whole Sample . 165 B.9 Nonlinear IPD-Inflation Effect – High-Inflation Subperiod . 166 B.10 Nonlinear CPI-Inflation Effect – High-Inflation Subperiod . 167 B.11 Nonlinear IPD-Inflation Effect – Low-Inflation Subperiod . 168 B.12 Nonlinear CPI-Inflation Effect – Low-Inflation Subperiod . 169 E.1 Estimation of the Robust Consumption Model of Hansen et al.(1999) 184 ix x List of Figures 3.1 Evolution of U.S. IPD and CPI Quarterly Inflation . 53 3.2 LR F-Statistic Series . 54 4.1 Predicted and Actual CPI Inflation (demeaned) . 88 4.2 Innovations to Consumption Growth and Real Income Growth . 97 5.1 Ambiguity Circle . 106 5.2 The Impact of Robustness on the Response of ct+1 to εt+1 ...... 122 5.3 Impulse Response Functions of ct+1 to εt+1 .............. 125 5.4 Impulse Response Function of Consumption to Income Shocks . 136 xi xii Chapter 1 Introduction Does money illusion have an impact on aggregate consumption? Every well-educated economist should answer this question in the negative, with the argument that the representative consumer is rational and, therefore, perfectly knows the difference between nominal and real values. In consequence, consumption should remain un- affected by variations in the general price level, such that the neutrality of money prevails. By theoretically and empirically unveiling a short- to medium-term impact of inflation on consumption, the present dissertation shows that the answer to this question is – contrary to the typical assumption – far from evident. 1.1 Motivation The idea of analyzing the effect of money illusion on aggregate consumption is motivated by two observations: First, people typically present some degree of money illusion, and, second, aggregate consumption models completely leave out inflation from their analysis. Money Illusion Exists at the Individual Level With the success of behavioral economics in the 1990s, there has been a renewed in- terest in money illusion as a departure from the pure rationality assumption. Money illusion argues that consumers rely not only on real values, as assumed by the tradi- tional models, but also partly on nominal values. As a result, money illusion reveals that inflation is a potentially significant determinant of consumption. In fact, money illusion need not be the reflection of an intrinsic irrationality or a foible on the part of the individuals; rather, it is equally consistent with the widely assumed rational- 1 2 Chapter 1. Introduction ity assumption. Following the literature on rational inattention (see, for example, Sims, 2003; Mankiw and Reis, 2002), this dissertation considers money illusion as pertaining to the fact that the consumer is constrained in her ability or willingness to collect and process information about inflation. Although surveys and experimen- tal studies show that people are confused between nominal and real values (see, in particular, Shafir et al., 1997; Fehr and Tyran, 2001), there is no certainty whether they really behave in an illusioned way and, consequently, whether this confusion has a real impact on aggregate values. The present thesis addresses this question by investigating whether inflation has a significant impact on real consumption and whether this impact can be attributed to money illusion. Traditional Consumption Models Exclude any Role for Inflation Inflation is typically defined as a purely monetary phenomenon, influencing nominal values but leaving real values unchanged, upon which most macroeconomic models rely.
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