NMonetary reaction function: Forward-looking and Non-linear behaviours :Master's thesis - Major: Science Economics

Department of Economics

Professorship of Macroeconomics

Christian-Albrechts-University of Kiel

Monetary Reaction Function:

Forward-looking and Non-linear

Behaviours

Master’s thesis in Master of Science Economics

Supervisor: Prof. Dr. Kai Carstensen

WS 2016/2017

Abstract This paper investigates forward-looking and non-linear charac￾teristics of monetary reaction funciton using Fed’s data. By employing hybrid

New Keynesian with non-linear Phillips curve and asymmetric preferences of

Fed, a “hybrid-type” non-linear reaction function is derived. The estimation

results provide more empirical evidence for a non-linear monetary policy rule

in the period between 1983 and 2008, as well as a notable role of forward￾looking behavior of the policy rule toward output gap.

Name: Nguyen Thi Truc Ngan

Field of study: Economics

Semester: 8

E-mail: [email protected]

Deadline: 01.06.2017

Matriculation Number: 1020472

Contents

List of Abbreviation II

1 Introduction 1

2 Literature Review 2

2.1 Instrument rule and Targeting rule . . . . . . . . . . . . . . . . 2

2.2 Forward-looking behaviours . . . . . . . . . . . . . . . . . . . . 5

2.3 Non-linearity of the Reaction Function . . . . . . . . . . . . . . 6

2.3.1 Convex Aggregate Supply curve . . . . . . . . . . . . . 7

2.3.2 Asymmetric Preferences . . . . . . . . . . . . . . . . . . 8

2.4 Zero Lower Bound . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Monetary Reaction Function model 9

3.1 Case I: Linear Aggregate Supply (τ = 0) . . . . . . . . . . . . . 13

3.2 Case II: Quadratic Loss fucntion (γ → 0) . . . . . . . . . . . . 13

3.3 Case III: Linear Rule . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 With Zero Lower Bound . . . . . . . . . . . . . . . . . . . . . . 14

4 Estimation 14

4.1 Preliminary analysis . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1.1 Generated regressor . . . . . . . . . . . . . . . . . . . . 15

4.1.2 Measurement error . . . . . . . . . . . . . . . . . . . . . 16

4.1.3 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . 17

4.1.4 Inflation Target in the U.S . . . . . . . . . . . . . . . . 18

4.2 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Conclusion 21

Appendix III

A Monetary Reaction Function III

B Data appendix VII

References VIII

Affirmation XIII

I

List of Abbreviations

AS Aggregate Supply

ECB European Central Bank

FED Federal Reserve (U.S Central bank)

IPI Industrial Production Index

NAIRU Non-accelerating inflation rate of unemployment

NKPC New Keynesian Phillips Curve

ZLB Zero Lower Bound

II

1 Introduction

Literatures on monetary reaction function provide us learnings about charac￾teristics of policy as well as the priority target of the central bank. With the

introducting of New Keynesian model as the monetary transmission mecha￾nism (Clarida, Gali, and Gertler 1999) and inflation targeting (Svensson 1997,

Svensson 2003), the most used derivations of optimal rules is base on a linear￾quadratic framework. This framework involves the central bank minimizing its

quadratic-form objectives function subject to a linear structure of the econ￾omy. Derivations of this framework produce a linear reaction function, or

targeting rule (Svensson 1997, Svensson 2003).1

This linear reaction function means the Federal Reserve of the United

States’s adjustment of Federal fund rate is a straight line of inflation and out￾put. However, in recent literatures, this linear-quadratic framework has been

challenged, either by considering a non-linear Phillips curve (Orphanides and

Wieland 2000; Dolado, Marıa-Dolores, and Naveira 2005); or by abandoning

the quadratic loss function assumption and adopting asymmetric preferences

instead (Dolado and Pedrero 2002; Cukierman et al. 1999); or both (Surico

2003; Surico 2007; Dolado, Pedrero, and Ruge-Murcia 2004).

This paper studies the non-linearity of monetary reaction function com￾bining both channels: non-linear Phillips curve and asymmetric loss function

of central bank as conducted by Dolado, Pedrero, and Ruge-Murcia (2004).

We would like to engage in a quasi-convex Phillip curve as in Dolado et al.

(2004). Next, our asymmetric objective function suggested biased preference

in inflation only, output gap is also included, but in a quadratic form2

. This

setup will be discussed more in Section 3.

Several literatures using forward monetary policy rule augmenting purely

New Keynesian model have been conducted (Surico 2003; Clarida, Gali, and

Gertler 1999). Some of them have showed that a purely-forward looking

model may sometime misspecified due to the lack of history dependence (Gal´ı,

Gertler, and Lopez-Salido 2005). Thus, in this paper, the hybrid New Key￾nesian model, which covers both backward and forward-looking variables, is

employed instead.

1

In most papers, including this study, the term monetary policy rule, monetary reaction

function or Taylor rule are used interchargeable.

2This asymmetric loss function with the entering of output gap has also been mentioned

by Dolado, Pedrero, and Ruge-Murcia (2004), section 2.6, and a reaction function has been

derived. Nonetheless, in their studies, an empirical application based on this function was

not done.

1