Where There’s Smoke, There’s FireAn Analysis of the Riksbank’s Interest Setting Policy

Mehdi Lahlou and Sebastian Sandstedt

Supervisor: Roine Vestman

EC6902 Bachelor Thesis

Department of Economics

Stockholm University

Autumn 2016

Abstract

We analyse the Swedish central bank, the Riksbank’s, interest setting policy in a Taylor

rule framework. In particular, we examine whether or not the Riksbank has reacted to

fluctuations in asset prices during the period 1995:Q1 to 2016:Q2. This is done by esti-

mating a forward-looking Taylor rule with interest rate smoothing, augmented with stock

prices, house prices and the real exchange rate, using IV GMM. In general, we find that the

Riksbank’s interest setting policy is well described by a forward-looking Taylor rule with

interest rate smoothing and that the use of factors as instruments, derived from a PCA,

serves to alleviate the weak-identification problem that tend to plague GMM. Moreover,

apart from finding evidence that the Riksbank exhibit a substantial degree of policy rate

inertia and has acted so as to stabilize inflation and the real economy, we also find evidence

that the Riksbank has been reacting to fluctuations in stock prices, house prices, and the

real exchange rate.

Keywords: Riksbank, Taylor Rule, Asset Prices, Instrumental Variables General Method

of Moments (IV GMM), Principal Component Analysis (PCA), Factor GMM.

Contents

List of Tables 2

List of Figures 2

1 Introduction 1

2 Theory and Previous Studies 3

2.1 Original Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Forward Looking Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Interest Rate Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4 Augmented Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.5 Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Econometric Theory 6

3.1 General Methods of Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2 Instrument Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Data 9

4.1 Policy Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.2 Baseline Target Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.2.1 Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.2.2 Output Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.3 Additional Target Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3.1 Real Exchange Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3.2 House Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.3.3 Stock Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.4 Unit Root Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5 Empirical Models 17

5.1 Baseline Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.2 Augmented Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.3 Making a Weak Instrument Set Stronger . . . . . . . . . . . . . . . . . . . . . . 19

6 Results 19

6.1 Original Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.2 Baseline Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6.3 Augmented Taylor Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

7 Conclusions 24

8 Suggestions for Future Research 25

9 Acknowledgements 25

10 References 26

11 Appendices 29

List of Tables

1 Unit Root Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 Estimation Results for the Taylor Rules . . . . . . . . . . . . . . . . . . . . . . 23

3 Variables in the Principal Component Analysis . . . . . . . . . . . . . . . . . . 29

List of Figures

1 Riksbank’s Repo Rate in Percent . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Inflation Rates in Annual Percentage Change . . . . . . . . . . . . . . . . . . . 11

3 Output Gaps in Percent of Potential Output . . . . . . . . . . . . . . . . . . . 13

4 Exchange Rates in Annual Percentage Change . . . . . . . . . . . . . . . . . . 14

5 House Prices in Annual Percentage Change . . . . . . . . . . . . . . . . . . . . 15

6 Stock Prices in Annual Percentage Change . . . . . . . . . . . . . . . . . . . . . 16

7 Actual Policy Rate vs. Model Policy Rates . . . . . . . . . . . . . . . . . . . . 20

8 Actual Policy Rate vs. Model Policy Rates . . . . . . . . . . . . . . . . . . . . 21

9 Actual Policy Rate vs. Model Policy Rates . . . . . . . . . . . . . . . . . . . . 22

1 Introduction

In a response to the high macroeconomic volatility in the 1970’s, most developed economies

abandoned the discretionary policies that was perceived to be the cause, and instead adopted

rule-based policies. In particular, the monetary policy of inflation targeting, which primarily

can be characterized by the announcement of an explicit numerical inflation target, and inde-

pendent central banks’ were instantiated. In practice, however, inflation targeting tended to

be “flexible” rather than “strict”, in the sense that central banks’ not only aimed at stabiliz-

ing inflation around the inflation target but also gave weight to stabilizing a given measure of

the real economy, for example resource utilization (Svensson, 2010). This ”flexible” inflation

targeting regime, together with a more rule-based fiscal policy and structural changes in the

economy, is believed to have contributed to the period starting in the mid-1980’s and ending

with the financial crisis of 2007-2008, called ”the Great Moderation” which was characterized

by a high degree of macroeconomic stability (Bernanke, 2004).

The monetary policy doctrine during the Great Moderation, most notably defended in Bernanke

and Gertler (1999), held to the notion that central banks’ should consider asset prices, such

as stock prices and house prices, only to the extent that they contain information regarding

inflation and the real economy. However, the financial crisis and the current environment of his-

torically low interest rates, asset price booms and spiraling household debts, have given rise to

a debate, not least in Sweden, on whether central banks’ should react to asset prices explicitly,

not only with macroprudential tools, but also with the policy rate, in order to increase financial

stability (Svensson, 2010). In addition, it has been suggested, that small-open economies may

benefit in terms of stability from pursuing some form of exchange rate targeting as a part of

its flexible inflation targeting (Taylor, 2001).

In Sweden, this debate over monetary policy, culminated in 2013 with Lars EO Svensson’s

resignment as deputy governor at the Riksbank after not having managed to gain support

in the executive board for a more expansionary monetary policy that he believed would lead

to a better target fulfilment as defined by the mandate given to the Riksbank (Riksbank, 2013).1

Since then, in a number of papers, columns, blog posts and public speeches, Svensson has

continued to issue loud criticism against the Riksbank’s monetary policy of “leaning-against-

1According to the Riksbank Act, the Riksbank’s objective is to ”maintain price stability”, which the Riksbankhas interpreted to mean a ”low and stable rate of inflation”. More specifically, an inflation target which is definedsuch that inflation, measured as the annual change in the consumer price index (CPI), should be 2 percent.Furthermore, it is also stated that the Riksbank shall, as a second-order objective, support the objective ofthe ”general economic policy with the aim of achieving sustainable growth and high employment”, meaningthat in addition to stabilizing inflation around the inflation target the Riksbank is set to ”stabilize output andemployment around long-term sustainable levels”. Lastly, the Riksbank has also been given the objective topromote a ”safe and efficient payment mechanism”, meaning that the Riksbank shall act to ”promote stabilityin the Swedish financial system as a whole” (Riksbank, 2011).

1

the-wind”, claiming that the costs of a tighter monetary policy than necessary in order to

stabilize inflation and the real economy with the goal of improving financial stability, exceed

the potential benefits (Svensson, 2016).

In light of the above discussion, a crucial question is whether the Riksbank, in fact, has re-

acted to fluctuations in asset prices as suggested by Svensson’s comments, the recent years’

Monetary Policy- and Financial Stability Report’s2, and the three independent evaluations of

the Riksbank’s monetary policy conducted by Giavazzi and Mishkin (2006), Goodhart and Ro-

chet (2011) and Goodfriend and King (2015). However, despite the question’s relevance to the

policy discussion, little has been done to answer it. In fact, the literature on the topic is lim-

ited to two studies by Sutherland (2015) and Pronin (2015), which come to different conclusions.

In this thesis, we therefore aim to add to this literature by modeling the Riksbank’s inter-

est setting policy in a Taylor rule framework and examine whether or not the Riksbank has

reacted to asset prices such as stock prices, house prices and real exchange rates during the

period 1995:Q1 to 2016:Q2.3

To do this, we first introduce a smoothing parameter and augment a forward-looking Tay-

lor rule with stock prices, house prices and the real exchange rate. Second, in order to deal

with the non-linearity which is introduced by the smoothing parameter, and the potential en-

dogeneity and heteroskedasticity, we follow the approach of Clarida et al. (2000) in contrast

to Pronin (2015) and Sutherland (2015), and estimate the model with Instrumental Variables

General Method of Moments (IV GMM). Third, given the problem of weak-identification that

tend to plague GMM, we contribute to the previous literature by performing a Principal Com-

ponent Analysis (PCA) based on a large set of macroeconomic variables to derive stronger

instruments as suggested by for example Favero et al. (2005), Beyer et al. (2008) and Bernanke

and Boivin (2003).

In general, we find that the Riksbank’s interest setting policy is well described by a forward-

looking Taylor rule with interest rate smoothing and that the use of factors as instruments,

derived from a PCA, serves to alleviate the weak-identification problem. Moreover, apart from

finding evidence that the Riksbank exhibit a substantial degree of policy rate inertia and has

acted so as to stabilize inflation and the real economy, we also find evidence that the Riksbank

2The Monetary Policy Report is published by the Riksbank six times a year and describes the deliberationsmade by the Riksbank’s executive board following each repo rate decision. In contrast, the Financial StabilityReport is published two times a year and includes the Riksbank’s analyses and assessments of the stability ofthe financial system in Sweden.

3We limit ourselves to this period so as to exclude the collapse of the fixed exchange rate regime in 1992 andto cover the relatively consistent inflation targeting regime from 1995 and onwards. This, in turn, is done so asto limit the possibility of structural breaks in the coefficients of the Taylor rule.

2

has been reacting to fluctuations in stock prices, house prices, and the real exchange rate.

Lastly, we therefore suggest, in line with the recommendations of Giavazzi and Mishkin (2006),

Goodhart and Rochet (2011) and Goodfriend and King (2015), that the Riksbank Act should

be amended to further clarify the Riksbank’s mandate with regards to foreign exchange policy

and financial stability, in order to increase transparency, credibility, and prevent future clashes

between the board members. However, we do not stipulate what such an amendment would

consist of, in particular, whether it should come down on the side of Svensson or on the side of

the people that want the Riksbank to be more active with regards to financial stability.

The outline of the thesis is as follows. Section 2 presents the theoretical framework and previ-

ous studies. Section 3 reviews the econometric theory. Section 4 and 5 describe the data and

the empirical models, respectively. Section 6 summarizes the results. Section 7 then present

some conclusions whilst Section 8 provide suggestions for future research and Section 9 give

acknowledgements.

2 Theory and Previous Studies

In this section, the Taylor rule as originally formulated in Taylor (1993) is presented as well as

various augmentations of this rule reported in the literature, which form the theoretical basis of

our thesis. The section is concluded by a review of the previous studies on the topic of whether

central banks’ react to fluctuations in asset prices.

2.1 Original Taylor Rule

A monetary policy rule, or more specifically an instrument rule, expresses the target policy rate4

as an explicit and systematic function of the central bank’s information set.5 In particular, a

simple instrument rule is one where the target policy rate is expressed as a function of a small

subset of the central bank’s information set. The best-known example of a simple instrument

rule is the Taylor rule, according to which the target policy rate in period t is stated as a linear

function of the inflation gap and the output gap:

i∗t = i+ ψπ(πt − π∗) + ψxxt, (1)

where i is the nominal equilibrium policy rate at which inflation and output are at their targets,

(πt − π∗t ) is the ”inflation gap” where πt is the inflation rate in period t and π∗ is the inflation

target, xt ≡ log(yt)−log(yt) is the output gap where yt is output and yt is potential output in

period t, and (ψπ,ψx) are the respective response coefficients.

4The short nominal interest rate set by the central bank. For example, the federal funds rate in the case ofthe Federal Reserve (FED) in the United States and the repo rate in the case of the Riksbank in Sweden.

5In contrast to a targeting rule which is a first-order condition for optimal monetary policy (Svensson, 2010).

3

In his 1993 paper, Taylor assumed that the nominal equilibrium policy rate equal the sum

of the inflation rate and the equilibrium real interest rate (which was taken to be constant),

that the inflation target and the equilibrium real interest rate equal 2, and the response coeffi-

cients equal 0.5. Thus giving the original formulation of the Taylor rule:

i∗t = 2 + πt + 0.5(πt − 2) + 0.5xt = 1 + 1.5πt + 0.5xt. (2)

From a descriptive perspective, Taylor (1993) found that the Taylor rule presented a reasonably

good approximation of FED’s interest setting policy. Taylor (1999) later extended his earlier

work and introduced what is known as the ”Taylor principle” which states that in order to

achieve stabilization of inflation and equilibrium determinacy, the response of the policy rate to

inflation need to be larger than one-to-one, that is, the response coefficient on inflation needs

to exceed one.

Following Taylor’s seminal work, the Taylor rule, and its various augmentations, has continued

to provide a useful framework for the analysis of monetary policy, both in a descriptive- and

normative sense.

2.2 Forward Looking Taylor Rule

Given that central banks’ tend to be forward-looking and rely on forecasts, as documented in

for example Batini and Haldane (1999), we follow the approach of Clarida et al. (2000) and

formulate a modified Taylor rule which nest both backward- and forward-looking rules:

i∗t = i+ ψπ(E[πt+k|Ωt]− π∗) + ψxE[xt+q|Ωt], (3)

where i∗t is the target policy rate in period t and i is the nominal equilibrium policy rate,

E[πt+k|Ωt] and E[xt+q|Ωt] is the expected inflation rate in period t+ k and the expected out-

put gap in period t+q, respectively, conditional on the central bank’s information set in period

t (Ωt).

Apart from its empirical foundation as documented in for example Clarida et al. (2000), policy

rules such as (3) can be argued for on theoretical grounds as well since they can be shown to

be the optimal policy rule for a central bank with a quadratic loss function in the inflation-

and the output gap, assuming a New Keynesian sticky price model (Svensson, 1997).

4

2.3 Interest Rate Smoothing

Furthermore, to account for the fact that central banks’ seem to smooth changes in interest

rates over time (see eg. Goodfriend, 1987 and Woodford, 1999), and to allow for monetary

policy disturbances rather than a direct systematic relationship, we again follow Clarida et al.

(2000) and assume that the actual policy rate (it) adjust to the target policy rate (i∗t ) as implied

by equation (3), according to the following partial adjustment mechanism:

it = ρ(L)it−1 + [1− ρ]i∗t + εt, (4)

where εt is assumed to be an exogenous shock, ρ(L) = ρ1 + ρ2L +...+ ρnLn−1 is an n-lag

polynomial with L being the lag-operator, and ρ = ρ1 + ρ2 +...+ ρn is a smoothing parameter

which measure the degree of interest rate smoothing.

Substituting the target policy rate as implied by (3) into equation (4) then gives:

it = [1− ρ](i+ ψπ(E[πt+k|Ωt]− π∗) + ψxE[xt+q|Ωt]

)+ ρ(L)it−1 + εt. (5)

2.4 Augmented Taylor Rule

Moreover, to account for the fact that central banks’ may pursue other policies in addition to

stabilizing inflation and the real economy, one can augment equation (5) to include additional

target variables denoted by the variable vector wt+pwt+pwt+p. Doing this, we obtain:

it = [1− ρ](i+ ψπ(E[πt+k|Ωt]− π∗) + ψxE[xt+q|Ωt] +ψwψwψwE[wt+pwt+pwt+p|Ωt]

)+ ρ(L)it−1 + εt, (6)

where ψwψwψw is a parameter vector including the coefficients on the variables in wt+pwt+pwt+p.

In our thesis, we specifically aim to include various asset price measures such as stock prices,

house prices, and the real exchange rate, as additional target variables in order to test the

hypothesis that the Riksbank has reacted to fluctuations in asset prices during the sample

period.

2.5 Previous Studies

Following the influential work of Clarida et al. (2000), a number of studies have attempted to

answer the question of whether central banks’ react to asset price fluctuations by estimating

various augmented forward-looking Taylor rules with interest rate smoothing, such as equation

(6), using IV GMM in order to deal with the potential endogeneity problem that macroeco-

nomic research usually come up against.

5

The focus of these studies has often been limited to the larger developed economies such as the

United States (U.S.), the United Kingdom (U.K.), and the Euro-zone. For example Bernanke

and Gertler (1999) and Rigobon and Sack (2003) estimated a forward-looking Taylor rule with

interest rate smoothing, augmented with stock prices, for the U.S. Chadha et al. (2004) esti-

mated a forward-looking Taylor rule with interest rate smoothing, augmented with stock prices

and the real exchange rate, for the U.S., the U.K. and Japan. Gerdesmeier and Roffia (2004)

estimated a forward-looking Taylor rule with interest rate smoothing, augmented with stock

prices, the real exchange rate and money supply growth, for the Euro-zone. The evidence from

these studies and others alike seem to suggest that central banks’ in fact do react to fluctuations

in asset prices.

Studies performed on the Swedish economy and the Riksbank, is limited to Sutherland (2015)

and Pronin (2015). Sutherland (2015) estimated a forward-looking Taylor rule with interest rate

smoothing, augmented with stock prices, house prices, and the nominal exchange rate, using

Two-Stage Least Squares (TSLS) and the method of Limited Information Maximum Likeli-

hood (LIML). The result of this study suggest that the Riksbank did not respond to asset price

fluctuations during the period 1995:Q1 to 2014:Q4. In contrast to Sutherland (2015), Pronin

(2015) estimated a forward-looking Taylor rule augmented with house prices in the context of

a Dynamic Stochastic General Equilibrium (DSGE) model with Bayesian methods, and found

evidence for the proposition that the Riksbank responded to house price fluctuations during

the period 1995:Q1 to 2013:Q4.

However, as pointed out by Mavroeidis (2010), studies such as Clarida et al. (2000) and Suther-

land (2015) which uses GMM and TSLS, tend to suffer from the presence of weak instruments,

resulting in weak-identification and invalid statistical inferences. In order to derive stronger

instruments, several authors such as Favero et al. (2005), Beyer et al. (2008) and Bernanke and

Boivin (2003) have used the method of PCA on a large set of macroeconomic variables in order

to derive stronger instruments. The result of which has shown to be promising in terms of alle-

viating the weak-identification problem and increasing the precision of the parameter estimates.

This has in turn stimulated theoretical research on the finite sample and asymptotic properties

of IV GMM estimators with factor instruments (Factor GMM), such as Kapetanio and Mar-

cellino (2010) and Bai and Ng (2010), showing that Factor GMM outperforms weak-instrument

IV GMM.

3 Econometric Theory

In this section we will briefly review the econometric theory that serve as the basis for our

thesis. That is, we will cover the basics of GMM, in general, and IV GMM, in particular.

6

We stress, however, that whilst other, more complex estimation methods, can be used and

has been used in the literature in order to answer the question of whether central banks’ react

to asset price fluctuations, we restrict ourselves to IV GMM mainly out of availability and

simplicity.

3.1 General Methods of Moments

The General Method of Moments (GMM) is a general class of estimators, that makes use of

so-called population orthogonality conditions, which subsumes many standard estimators such

as Ordinary Least Squares (OLS) and Two-Stage Least Squares (TSLS) (Hansen, 1982). Of

specific interest to our thesis is the special class of estimators referred to as IV GMM estimators.

In order to illustrate the basic idea we consider the simple case of linear IV GMM. The model

of interest, in matrix notation, is:

yyy = βββXXX + uuu, (7)

with the row:

yyyt = βββXXXt + uuut, (8)

where T is the number of observations, uuu is an error term and XXX is a K×T dimensional matrix

of endogenous regressors, so that E[XXXtuuut] 6= 0. Furthermore, let ZZZ be a L × T dimensional

matrix of exogenous instrumental variables (instruments), so that E[ZZZtuuut] = 0. This gives us

a set of L population moments:

gggt(βββ) = ZZZtuuut= ZZZt(yyyt − βββXXXt). (9)

Moreover, the exogeneity of the instruments implies a set of L population moment (orthogo-

nality) conditions:

E[gggt(βββ)

]= 0, (10)

which are satisfied at the true value of βββ.

The sample analogs of the population moments in equation (9) for some given estimator βββ

are given by:

ggg(βββ) =1

T

T∑t=1

gggt(βββ). (11)

The GMM estimator, in general, and the IV GMM estimator, in particular, for the parameter

vector βββ is then defined as the estimator that sets the sample analogs of the population mo-

ments as close to zero as possible.

7

Furthermore, a necessary condition for identification of the model parameters is the so-called

order condition which states that the number of moment conditions needs to be atleast as many

as the number of parameters (L ≥ K). That is, in order for the order condition to hold, the

model needs to be either exactly identified (L = K) or over-identified (L > K).

If the model is exactly identified it is possible to find a unique estimator for βββ that solves

ggg(βββ) = 0 analytically. However, if the model is over-identified this is not the case. Instead, the

GMM estimator for βββ is defined as the estimator that minimizes the so called GMM objective

function, J(βββ), with respect to βββ:

βGMMβGMMβGMM ≡ arg minβββ

J(βββ) = Tggg(βββ)′WWWggg(βββ), (12)

where WWW is a symmetric, L×L, weighting matrix. Assuming that the orthogonality conditions

and the stationarity assumption are valid, then the GMM estimator in equation (12) is con-

sistent for any positive definite weighting matrix, WWW , but not necessarily efficient. Thus, the

estimator in (12) is known as the possibly inefficient GMM estimator. In contrast, an efficient

GMM estimator (βEGMMβEGMMβEGMM ) is a GMM estimator with an optimal weighting matrix, WWW , which

minimizes the asymptotic variance of the estimator. Specific examples is the Two-step Feasi-

ble Efficient GMM estimator, the Iterated GMM estimator, the Continuously-Updating GMM

(CUE) estimator, and the Limited Information Maximum Likelihood (LIML) estimator, which

all can be made heteroskedastic- and autocorrelation-consistent (HAC) using for example the

Newey-West weighting matrix.

In additon, whilst CUE and LIML provide no asymptotic gains over the rest, it has been

shown that their finite-sample performance is superior. In particular, in the presence of weak

instruments, it has been shown that CUE GMM and LIML outperform TSLS, two-step feasible

efficient GMM and the iterated GMM. However, CUE GMM is often preferred over LIML given

that LIML requires stronger distributional assumptions (Baum et al., 2007).

3.2 Instrument Diagnostics

Apart from the order condition, in order for the IV GMM estimator to be identified and produce

valid statistical inferences, two additional conditions are necessary. First, the instruments needs

to be exogenous, that is independent of the error term, so that the orthogonality conditions are

valid. Second, the instruments need not only be correlated with the endogeneous regressors,

but be sufficiently correlated to not be considered ”weak” (Baum et al., 2007).

8

Given that the model is over-identified, it is possible to test the plausibility of the instrument

exogeneity condition by testing the null hypothesis that the orthogonality conditions for the

over-identifying restrictions (L −K) are valid. In the IV GMM-context, such a test is known

as the Hansen test or J-test and is based on the GMM objective function evaluated at the

efficient GMM estimator. If the J-statistic is significantly greater than zero, we can reject the

null hypothesis and conclude that at least one of the orthogonality conditions are invalid or

that the model is mis-specified (Baum et al., 2007).

Given the assumption of independent- and identically-distributed (i.i.d.) errors, a test of the

null hypothesis that the instruments are weak, can be based on the Cragg-Donald Wald F-

statistic which reduces to the familiar first-stage F-statistic in the case of a single endogeneous

regressor. In contrast, the Wald F-statistic based on the Kleibergen–Paap rk statistic is robust

to non-i.i.d. errors. For the former, Stock and Yogo (2005) has tabulated critical values, derived

under the assumption of i.i.d. errors. Despite this, Baum et al. (2007) suggest that the use of

the latter, with Stock and Yogo (2005)’s critical values or simply using the rule of thumb which

states that if F < 10 then the instruments are weak, is preferable to the former in the case of

non-i.i.d. errors.

4 Data

In this section, we present the data on the main variables used in our thesis. For the data-set

used in the PCA, we refer to the Appendix, Table 3. In general, the data used is in quarterly

frequencies and the sample period is 1995:Q1 to 2016:Q2, if not stated otherwise. In addition,

due to time-constraints, we make use of so-called ex-post data rather than real-time data6,

which is in contrast to the recommendations of Orphanides (2001) and could potentially bias

our results.

4.1 Policy Rate

As a measure of the policy rate, we use the Riksbank’s repo rate7 given that it has been the

main policy instrument of the Riksbank to perform monetary policy since 1994 when it replaced

the so-called marginal rate.

The repo rate was obtained in quarterly averages from the Riksbank’s own database. In Figure

1, we can observe that the repo rate has had a clear negative trend during the sample period.

6Real-time data is defined as the data that was available at every given policy rate decision.7The repo rate is the rate of interest at which private banks can borrow or deposit funds at the Riksbank

for a period of seven days.

9

However, we find it likely that the negative trend that we observe is the result of two structural

breaks. First, the price-setting behavior is believed to have changed in the Swedish economy

in the mid-to-late 90’s, in part due to a more credible fiscal policy following the creation of a

new budget-framework in Sweden which reduced the ability to enact unmotivated expansionary

policies (Riksbank, 1997). This, in turn, allowed the Riksbank to sharply cut in rates in 1996.

Second, the financial crisis of 2007-2008, which caused the Riksbank to aggressively cut rates

in 2008, is believed to have impacted the world’s financial markets, in particular the money

markets, to the extent that the effectiveness of traditional monetary policy instruments has

diminished (Svensson, 2010).

Figure 1: Riksbank’s Repo Rate in Percent

4.2 Baseline Target Variables

4.2.1 Inflation

Although the Riksbank’s inflation target is expressed in terms of the CPI, the Riksbank often

uses different measures of so-called underlying inflation8 in its analyses and communication.

Until 2008, a measure of underlying inflation called the CPIX9 held a special status as a mea-

sure that adjusts for the direct effects of the Riksbank’s repo rate changes. However, the usage

of the CPIX was based on the assumption that the average long-term CPI- and CPIX-inflation

was the same, so focusing on the latter ensured that the target of the former was achieved.

Since 2008, however, the Riksbank started to phase out the CPIX measure, in part because the

8Underlying inflation measures the more permanent inflation pressures, in contrast to the CPI inflation whichtend to fluctuate following temporary shocks.

9The CPIX is the CPI with household mortgage interest expenditures, indirect taxes and subsidies heldconstant.

10

CPI- and CPIX-inflation was expected to differ in the future, but also due to issues with the

way it was calculated (Riksbank, 2008). The Riksbank, therefore, introduced the CPIF10, in

place of the CPIX, which they believed could better adjust for the direct effects of its policy.

The Riksbank, however, emphasized that the CPIF would not hold the same special status

as the previous measure, instead the CPI and other alternative measures of underlying infla-

tion would receive relatively higher weights in its analyses and communication (Riksbank, 2008).

In light of the special status that the CPIX measure has been given by the Riksbank and

that its publication stopped at the start of 2016, we will instead be using the so-called CPIF-

CT11 as our inflation measure, given that they are shown to be highly correlated. However, we

stress that the phasing out of the CPIX and the introduction of the CPIF, could potentially

bias our results.

The data on the various inflation measures was obtained from Statistic Sweden (SCB) in

monthly frequencies, which we then transformed into quarterly frequencies by taking the 3-

month average. In Figure 2, we can observe the evolution of the different inflation measures,

expressed in annual percentage change, during the sample period. In addition to the fact that

the underlying inflation measures (CPIX, CPIF-CT, and CPIF) are shown to be more stable

relative to the CPI, we can also see that the Riksbank has failed to reach its inflation target of

2% since 2010.

Figure 2: Inflation Rates in Annual Percentage Change

10The CPIF is the CPI with only household mortgage rates held constant.11The CPIF-CT is the CPI with household mortgage rates, indirect taxes and subsidies held constant.

11

4.2.2 Output Gap

The output gap gives a measure of the resource utilization in the economy, and is defined as the

difference between actual and potential output in percent of potential output, where potential

output in turn is defined as the level of output that is consistent with a sustainable long-run

level of output and a constant rate of inflation. A positive output gap signals that the economy

is overworking its resources, causing the economy to overheat and putting an upward pressure

on inflation. A negative output gap, in contrast, signals that the economy is underworking its

resources, implying a slack and sluggish economy, putting a downward pressure on inflation.

However, given that potential output is unobservable, to obtain a measure of the output gap,

one must first estimate potential output. Several methods are available, ranging from sim-

ple univariate methods such as the Hodrick-Prescott (HP)-filter which is a purely statistical

approach, to more complex multivariate methods such as the ”hybrid” Production Function

Approach (PFA), Structural VAR (SVAR) models, Unobserved Components (UC) models, and

Dynamic Stochastic General Equilibrium (DSGE) models, which all to varying degrees, incor-

porates structural relationships from economic theory (Hjelm and Jonsson, 2010).

The Riksbank has previously been using the HP-filter and the PFA in order to estimate the

output gap (Hjelm and Jonsson, 2010). However, since the Riksbank’s own measure of the

output gap only extend back to 2000:Q1, we will instead be using the Swedish Institute of

Economic Research (NIER)’s output gap measure as they are shown to be highly correlated

with each other.

The data on the Riksbank’s output gap measure was obtained from the Riksbank’s own database

while NIER’s output gap measure was collected from NIER’s Swedish Economy Report, both in

quarterly frequencies. In Figure 3, we can observe that both measures of the output gap evolve

pretty much in unison during the sample period and thus tell a similar story. A story, that

starts in the wake of the financial crisis that hit Sweden in the early-to-mid 1990’s. From this

point, after a series of reforms to its fiscal- and monetary policy, the Swedish economy steadily

improved and reached its potential by year 2000. Following, during much of the early 2000’s,

the Swedish economy oscillated around its potential but started to rapidly climb running up

to the financial crisis of 2007-2008 which set Sweden, like the rest of the world, into a com-

plete turmoil. The Swedish economy, however, recovered relatively quickly in an international

comparison just in order to be catapulted back into a sluggish state following the uncertainty

created by the Euro-crisis. Since then, the Swedish economy has steadily climbed back towards

its potential which it, as of now, has reached and surpassed.

12

Figure 3: Output Gaps in Percent of Potential Output

4.3 Additional Target Variables

In addition to our baseline target variables in our baseline model, we consider three additional

target variables for the augmented model, namely the real exchange rate, house prices, and

stock prices. In general, all three target variables were transformed by taking the 4-quarter log-

difference in order to obtain the annual percentage change, but also to make them stationary,

following previous studies such as Chadha et al. (2004) and Lubik and Schorfheide (2007).

4.3.1 Real Exchange Rate

In general, the choice of using the real exchange rate, rather than the nominal exchange rate, is

based on the fact that it is the real exchange rate that enters the Riksbank’s forecasting models

(see e.g. Adolfson et al., 2013). Thus, as a measure of the real exchange rate, we have chosen

to use the so called real KIX-index, where the KIX-index is a so-called effective exchange rate12

that aggregates a total of 32 bilateral exchange rates that are important to Sweden (Erlandsson

and Markowski, 2006).

The choice of using the real KIX-index, in particular, was based on the fact that it has been

of major focus in the Riksbank’s international analysis as of 2012. Before 2012, however, the

Riksbank’s international analysis was largely based on the so-called TCW-index. The difference

12In general, an effective exchange rate index is defined as a weighted average of multiple bilateral exchangerates, where the weights are set to give the relative significance of the bilateral exchange rate’s for the country(Erlandsson and Markowski, 2006).

13

being that the KIX-index places a greater weight on emerging markets than does the TCW-

index. Whilst the two measures have developed differently in nominal terms, the difference

in real terms is relatively small (Riksbank, 2012). The results should therefore, largely, be

unaffected by our choice of KIX instead of TCW.

The data on the real- and nominal KIX-index was collected from NIER’s Swedish Economy

Report in quarterly frequencies. In Figure 4, we can observe that the annual percentage change

in the real- and nominal KIX-index developed similarly during the sample period. Given that

the nominal KIX-index is expressed in SEK per foreign currency unit, it follows that an increase

in the index value represent a real depreciation of the Swedish krona. In contrast, a decrease

in the index value represent a real appreciation of the Swedish krona.

Figure 4: Exchange Rates in Annual Percentage Change

4.3.2 House Prices

As a measure for house prices, we chose a real-estate price index for one- and two-dwelling

buildings for permanent living which we collected from SCB in quarterly frequencies. Even

though this index does not cover the whole of the Swedish housing market, it has been frequently

used by the Riksbank as a proxy in their Monetary Policy- and Financial Stability Reports’.

As of late, the Riksbank has started to report on another index named the Valueguard-KTH

Housing Index Sweden, which cover a relatively larger part of the Swedish housing market.

However, given that this index only extends back to 2005, we found it preferable to use the

former, rather than the latter, in order to obtain a larger sample.

14

In addition, another issue is whether to use nominal- or real house prices. However, as can

be observed in Figure 5, which reports the annual percentage change of nominal- and real

house prices13 as measured by SCB’s real-estate price index, the difference is rather small and

shouldn’t have a large effect on our results. For comparison, we thus follow Pronin (2015) and

use real-, rather than, nominal house prices.

Figure 5: House Prices in Annual Percentage Change

4.3.3 Stock Prices

As a measure for stock prices, we chose the OMXS30, which is an index that consists of the 30

most-traded stocks on the Stockholm Stock Exchange, given that it has been one of the indexes

that has been used by the Riksbank to monitor the development of the Swedish stock market.

Another measure, also frequently used by the Riksbank, is the OMXS, which in contrast to the

OMXS30, consider all stocks that trade on the Stockholm Stock Exchange. The decision to

use OMXS30, instead of OMXS, is purely arbitrary but shouldn’t affect our results given their

high degree of correlation.

The data on OMXS30 and OMXS was collected in daily frequencies from Nasdaq OMX Nordic,

which we transformed into quarterly frequencies by taking the 3-month average. In Figure 6,

we can observe the evolution of the annual percentage change in stock prices as measured by

the OMXS30 and OMXS, respectively, during the sample period.

13Nominal house prices deflated with the CPI.

15

Figure 6: Stock Prices in Annual Percentage Change

4.4 Unit Root Tests

Lastly, as the GMM estimator requires that the time-series’ are stationary, we conduct a battery

of unit-root tests. However, given the low power of the commonly used augmented Dickey-Fuller

(DF) and the Phillips-Perron (PP) tests against the alternative hypothesis of no unit root when

the time series is near-integrated of order 1 (see e.g. Perron and Qu, 2007), we have chosen

to use the modified Phillips-Perron test given in Perron and Qu (2007), together with the

Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test, as these have shown to perform better.

The results of the modified PP-test and the KPSS-test are reported in Table 1. The modi-

fied PP-test reject the presence of a unit-root for all variables but the policy rate. In addition,

the KPSS-test fails to reject the null hypothesis of stationarity for all variables but the policy

rate. Thus, the only variable that show signs of the presence of a unit root is the policy rate.

However, since we expect that the policy rate has been subject to structural breaks which

would tend to induce bias towards the presence of a unit root in the unit-root tests, we perform

the so-called Clemente-Montanes-Reyes (CMR) test which allow for structural breaks (Perron,

2006). The result of the CMR-test is also reported in Table 1, which show that the CMR-test

rejects the presence of a unit-root for the policy rate, allowing for structural breaks. Thus, we

find it safe to assume that all variables are stationary.

16

Table 1: Unit Root Tests

Policy Rate Inflation Rate Output Gap Real Exchange Rate House Prices Stock Prices

PP-testa -2.774 -3.104** -2.671* -3.569*** -2.668* -3.117**

KPSS-testb 1.07*** .31 .211 .0433 .103 .114CMR-testc -6.063**Note: ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. The decision of whether to include a trend or not was based ontheoretical expectations and through observing the graphs of the respective variables.aH0 : Unit Root.bH0 : Stationarity.cH0 : Unit Root.

5 Empirical Models

In this section, we review the empirical models. In general, following Clarida et al. (2000),

the models will be estimated using IV GMM in order to deal with the non-linearity which is

introduced by the smoothing parameter, the potential endogeneity problem and heteroskedastic

policy shocks.

5.1 Baseline Taylor Rule

Initially, for estimation purposes, we rewrite equation (5) as follows:

it = [1− ρ](α+ ψπE[πt+k|Ωt] + ψxE[xt+q|Ωt]

)+ ρ(L)it−1 + εt, (13)

where α = i− ψππ∗. Moreover, based on statements from the Riksbank that it focuses on the

forecast of inflation twelve to twenty-four months ahead, we follow Berg et al. (2004) and pick 8

quarters (k = 8) as the forecast horizon for inflation. However, the choice of the forecast horizon

for the output gap is less obvious but given the standard view of the monetary transmission

mechanism, it seems reasonable to assume that q < k (see e.g. Clarida et al., 2000). Absent any

further information, we thus follow the approach of Clarida et al. (2000) and Berg et al. (2004)

by setting q = 0 as in the original Taylor rule. Hence, our baseline forward-looking Taylor rule

with interest rate smoothing (assuming a single lagged policy rate) can be written as:

it = [1− ρ](α+ ψπE[πt+8|Ωt] + ψxE[xt|Ωt]

)+ ρit−1 + εt. (14)

However, to estimate equation (14), we first replace the expectations with realized variables

which gives:

it = [1− ρ](α+ ψππt+8 + ψxxt

)+ ρit−1 + vt, (15)

17

where vt ≡ εt − [1 − ρ](ψπ(πt+8 - E[πt+8|Ωt]) + ψx(xt - E[xt|Ωt])

)is a sum of the assumed

exogenous shock and a linear combination of the forecast errors which are orthogonal to any

current and past variables in the central bank’s information set assuming rational expectations.

Second, let ZtZtZt be a vector of exogenous instruments within the central bank’s information

set in period t.14 Generally, in the case of q such instruments, we have the following set of q

orthogonality conditions:

E[ZtZtZt

(it − [1− ρ](α+ ψππt+8 + ψxxt)− ρit−1

)]= 0. (16)

Equation (16) then allow us to estimate the parameter vector [ψπ, ψx, α, ρ] using the Two-

Step Feasible GMM estimator with a Newey-West weighting matrix in order to take the moving

average (MA) component in vt into account.

5.2 Augmented Taylor Rule

The baseline forward-looking Taylor rule with interest rate smoothing in equation (14) does

not consider the role of stock prices, house prices and the real exchange rate as target variables

explicitly. To account for this and to control for the potential endogeneity that would otherwise

result, we therefore augment equation (14) with stock prices (st+v), house prices (ht+m) and

the real exchange rate (et+n). As in Bernanke and Gertler (1999) and Chadha et al. (2004), in

contrast to for example Sutherland (2015), we assume that the targets are constants and hence

become subsumed in the intercept. Additionally, following Bernanke and Gertler (1999) and

Chadha et al. (2004), the Riksbank is assumed to only intervene when stock prices has been

observed to deviate from target rather than anticipating future misalignments, thus having

stock prices enter with a one-period lag. With regards to house prices and the real exchange

rate, we assume that the Riksbank is forward-looking given that it de facto produces forecasts

of these variables but without any a-priori expectation of the forecasting horizon we further

assume that q = m = n = 0.15 These considerations give rise to the following augmented

forward-looking Taylor rule with interest rate smoothing (again assuming a single lagged policy

rate):

it = [1−ρ](α+ψπE[πt+8|Ωt]+ψxE[xt|Ωt]+ψsE[st−1|Ωt]+ψhE[ht|Ωt]+ψeE[et|Ωt]

)+ρit−1+εt. (17)

As in the baseline case, we can replace the expectations with realized variables giving:

it = [1− ρ](α+ ψππt+8 + ψxxt + ψsst−1 + ψhht + ψeet

)+ ρit−1 + vt, (18)

14Similar to Clarida et al. (2000), we consider four lags of inflation, output gap and the policy rate for IVGMM Baseline, and four lags of the five factors for the Factor GMM Baseline and Factor GMM Augmented.For further information, see Table 2.

15As a robustness test, we consider q = m = n = 4.

18

which again allow us to estimate the parameter vector [ψπ, ψx, ψs, ψh, ψe, α, ρ] using the

Two-Step Feasible Efficient GMM estimator with a Newey-West weighting matrix.16

Our theoretical expectation of the signs of the coefficients stem from the fact that the cen-

tral bank act to stabilize inflation if the response coefficient on inflation exceed one, and act

to stabilize output, stock prices, house prices, and the real exchange rate, if the respective

response coefficients exceed zero (Chadha et al., 2004).

5.3 Making a Weak Instrument Set Stronger

In order to alleviate the problem of weak-identification resulting from the presence of weak-

instruments mentioned in Mavroeidis (2010), we follow the approach of Favero et al. (2005),

Beyer et al. (2008) and Bernanke and Boivin (2003). That is, we estimate the models us-

ing, as instruments, the estimated factors obtained from a PCA17 on a data-set containing 52

macroeconomic variables which has been chosen so as to provide a proxy for the Riksbank’s

information set.18

However, whilst there exist no general agreement on a specific method to determine the optimal

number of factors, several different methods are available. One such method is the minimiza-

tion of a given information criteria such as the Akaike information criterion (AIC) and the

Bayesian information criterion (BIC). However, these criteria only considers the cross-sectional

dimension of the data, result being that they tend to over-estimate the true number of factors.

In contrast, the criteria proposed by Bai and Ng (2002) considers both the cross-sectional and

the time-series dimension of the data, and therefore tend to outperform the AIC and BIC.

However, for simplicity and availability, we consider the so-called Scree test, introduced by

Cattell (1966). In our case, such a test suggest the use of five factors.

6 Results

6.1 Original Taylor Rule

First, as a point of comparison, we estimate the original Taylor rule given in equation (1) by

OLS. The result of which is reported in Table 2, Column 1. The estimated response coefficient

on inflation is shown to be statistically significant, positive and above one as per the Taylor

principle.

16As a robustness test, we consider the CUE GMM given the relatively poor finite-sample performance ofTwo-Step Feasible Efficient GMM.

17PCA is a general way of reducing a large data set into a few latent factors which is assumed to drive thesystematic variation.

18A detailed description of the data-set can be found in the Appendix, Table 3.

19

The estimated response coefficient on the output gap is in contrast not statistically significant

at conventional levels of significance and, in fact, wrongly signed in terms of theoretical expec-

tations.

These results would thus imply that whilst the Riksbank has responded strongly to devia-

tions of inflation from the target, it has not responded to fluctuations in the output gap during

the sample period. However, these result should be interpreted with reservation given the po-

tential problem of endogeneity.

Moreover, as can be observed in Figure 7, both the Taylor rule with Taylor (1993)’s pro-

posed parametrization and the estimated version show very poor fits compared to the actual

repo rate.

Figure 7: Actual Policy Rate vs. Model Policy Rates

6.2 Baseline Taylor Rule

Next we estimate the baseline forward-looking Taylor rule with interest rate smoothing given

in equation (15) with IV GMM and Factor GMM. The result of which is reported in Table 2,

Column 2 and 3, respectively. In contrast to the OLS estimation of equation (1), IV GMM

estimates of the response coefficients on inflation and the output gap are statistically signifi-

cant at the 10 and 1 percent significance level, respectively, and exhibit the expected positive

signs. In addition, the large difference in the estimates between the estimations indicates that

the OLS-estimation suffer from endogeneity problems. Moreover, the Factor GMM estimation

is shown to yield substantially lower standard errors and hence higher precision of the estimates.

20

Thus, in the Factor GMM estimation, estimates of the response coefficients on inflation and

the output gap are both statistically significant at the 1 percent level and exhibit the expected

positive signs. These results would thus imply that the Riksbank has responded strongly to

deviations of inflation from the target and fluctuations in the output gap during sample period.

Furthermore, both estimations show signs of a substantial degree of policy rate inertia given

the high estimate of the smoothing parameter.

In comparison to the OLS estimation of equation (1), both estimations exhibit a very good

fit vis-a-vis the actual repo rate given the high R-squares (0.9540 and 0.9571, respectively), as

can be observed in Figure 8. Moreover, high values of the J-statistic in both estimations implies

that the null hypothesis cannot be rejected and thus that the over-identifying restrictions are

valid. Lastly, the Wald F-statistic based on the Kleibergen–Paap rk statistic, is substantially

higher in the Factor GMM estimation than in the IV GMM estimation, suggesting that the

weak-identification problem is less severe in the former than in the latter.

Figure 8: Actual Policy Rate vs. Model Policy Rates

6.3 Augmented Taylor Rule

Given that the Factor GMM model outperform the IV GMM model, we restrict ourselves to

the factor case. The result of the Factor GMM estimation of the augmented forward-looking

Taylor rule with interest rate smoothing in equation (18) is reported in Table 2, Column 4.

The estimated response coefficients are all statistically significant at the 1 percent significance

level and exhibit the expected positive signs. In addition, the large difference in the estimates

21

between the Factor GMM estimation of the baseline model and the Factor GMM estimation of

the augmented model suggest that the baseline model suffer from endogeneity problems as it

does not consider stock prices, house prices, and the real exchange rate as target variables.

These results hence provide evidence to the proposition that the Riksbank has responded,

not only to deviations of inflation from the target and fluctuations in the output gap, but also

to stock price inflation, house price inflation and real appreciations. In particular, the evidence

suggest that higher stock prices and house prices has led the Riksbank to raise rates and real

appreciations has led them to cut rates during the sample period. That is, the Riksbank has

so-called ”leaned-against-the-wind”. Moreover, the augmented model confirms the conclusion

drawn from the baseline model that the Riksbank exhibit a substantial degree of policy rate

inertia given the high estimate of the smoothing parameter.

Given that the additional target variables are significant it follows that the Factor GMM es-

timation of the augmented model exhibit a higher R-square than the Factor GMM estimation

of the baseline model which can be observed in Figure 9. Furthermore, high values of the

J-statistic implies that the null hypothesis cannot be rejected and thus that the overidentifying

restrictions are valid. Lastly, the Wald F-statistic based on the Kleibergen–Paap rk statistic,

is again shown to be relatively high suggesting that the weak-identification problem is less of a

problem.

Figure 9: Actual Policy Rate vs. Model Policy Rates

22

Finally, in order to strengthen the internal validity of our result, we conduct two robustness

tests. First, we estimate equation (18) with Factor GMM, using a different set of forecasting

horizons for the output gap, house prices and the real exchange rate, given that we lacked any a-

priori expectations. The result of which are given in Table 2, Column 5, and shown to be similar

across the estimation since the confidence intervals overlap. Second, we estimate equation (18)

with CUE GMM instead of Two-Step Feasible Efficient GMM, in order to confirm that the

result is not driven by the relatively poor finite-sample performance of the latter. Again, the

result is shown to be similar across the estimations, thus lending considerable support to our

result.19

Table 2: Estimation Results for the Taylor Rules

OLS IV GMM Factor GMM Factor GMM Factor GMMOriginala Baselineb Baselinec Augmentedd Augmentede

Constant (α) .324 1.218 1.119*** .544*** .556***(.469) (1.147) (.138) (.122) (.105)

Inflation Rate (ψπ) 1.440*** 1.103* 1.156*** 1.618*** 1.651***(.274) (.626) (.072) (.075) (.069)

Output Gap (ψx) -.155 .704*** .813*** .766*** .808***(.106) (.105) (.024) (.036) (.029)

Smoothing Parameter (ρ) .882*** .894*** .895*** .895***(.012) (.003) (.004) (.003)

Stock Prices (ψs) .042*** .054***(.003) (.003)

House Prices (ψh) .092*** .121***(.020) (.012)

Real Exchange Rate (ψe) .140*** .153***(.014) (.013)

R2 .2839 .954 .957 .963 0.966J − statistic 7.441 4.933 5.154 4.681F − statistic 3.952 126.064 109.411 76.500Note: HAC standard errors in parenthesis. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01.a Estimating equation (1) by OLS.b Estimating equation (15) by Two-Step Feasible Efficient GMM with Newey-West weighting ma-trix. The instrument set include four lags of inflation, output gap and the repo rate.c Estimating equation (15) by Two-Step Feasible Efficient GMM with Newey-West weighting ma-trix. The instrument set include four lags of the five factors.d Estimating equation (18) by Two-Step Feasible Efficient GMM with Newey-West weighting ma-trix. The instrument set include four lags of the five factors. q = m = n = 0.e Estimating equation (18) by Two-Step Feasible Efficient GMM with Newey-West weighting ma-trix. The instrument set include four lags of the five factors. q = m = n = 4.

19The result from the CUE GMM can be provided upon contacting the authors.

23

7 Conclusions

The aim with this thesis was to model the Riksbank’s interest setting policy in a Taylor rule

framework and examine whether or not the Riksbank has reacted to asset prices during the

period 1995:Q1 to 2016:Q2. This was done, in general, by estimating a forward-looking Taylor

rule with interest rate smoothing, augmented with stock prices, house prices and the real ex-

change rate, using IV GMM.

In general, we find that the Riksbank’s interest setting policy is well described by a forward-

looking Taylor rule with interest rate smoothing and that the Riksbank exhibit a substantial

degree of policy rate inertia given the high value of the estimated smoothing parameter. In

addition, we find that the use of factors as instruments, derived from a PCA, serves to al-

leviate the weak-identification problem that tend to plague GMM and result in a significant

improvement of the model. More importantly, we find that the response coefficient on inflation

is above one for all estimations, thus indicating that the Riksbank has followed the Taylor

principle during the sample period. Moreover, given that the main objective of the Riksbank is

to obtain and maintain price stability whilst stabilization of the real economy is of secondary

order, the finding that the response coefficient on the output gap is positive but lower than

the response coefficient on inflation is expected. Lastly, the main result of our thesis is that

stock price inflation, house price inflation and real depreciation, all enter significantly and with

expected positive signs, thus giving evidence to the proposition that the Riksbank has reacted

to asset prices and ”leaned-against-the-wind” during the period 1995:Q1 to 2016:Q2. However,

it should be noted that the ”leaning-against-the-wind”-policy has not been performed in com-

plete disregard of the stabilization of inflation and the real economy.

Thus, our study seem to confirm the general result of previous studies based on IV GMM

such as Clarida et al. (2000), Bernanke and Gertler (1999) and Rigobon and Sack (2003) for

the U.S., Chadha et al. (2004) for the U.S., the U.K. and Japan, and Gerdesmeier and Roffia

(2004) for the Euro-zone, that central banks’ react to fluctuations in asset prices. Our findings

are also consistent with and serves to validate the work of Pronin (2015), which provided evi-

dence in favor of the proposition that the Riksbank has responded to house price fluctuations,

rather than the work of Sutherland (2015) whose result suggested the opposite. One potential

reason for the conflicting results between our study and Sutherland (2015), could be that our

study, to a greater degree, manage to alleviate the weak-identification problem.

24

Given our main result which indicates that the Riksbank has reacted to fluctuations in asset

prices, we agree with the conclusion of Giavazzi and Mishkin (2006), Goodhart and Rochet

(2011) and Goodfriend and King (2015), that the Riksbank Act is too vague and admit to

several mutually inconsistent interpretations. We therefore echo their recommendation that

the Riksbank Act should be amended to further clarify the Riksbank’s mandate relating to

foreign exchange policy and financial stability, in order to increase transparency, credibility,

and prevent future clashes between the board members. However, we do not stipulate what

such an amendment would consist of, in particular, whether it should come down on the side

of Svensson or on the side of the people that want the Riksbank to be more active with regards

to financial stability.

8 Suggestions for Future Research

One potential source of bias in our study is the use of ex-post rather than real-time data as

pointed out in Orphanides (2001). In addition, our result might depend upon the specific

number of factors used. Thus, for future research, in the context of IV- and Factor GMM, we

suggest that one construct a real-time data set and use the method of Bai and Ng (2002) to

determine the number of factors.

We further suggest the use of more complex models which allow for time-varying response

coefficients, time-varying targets, stochastic intercepts, and non-linearities, in order to corrob-

orate or overthrow our results.

9 Acknowledgements

We would specifically like to thank Emre Unlu at the Riksbank, who gave us recommendations

in the early stage of writing this thesis, and to our supervisor Roine Vestman for his valuable

comments and advice throughout.

25

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11 Appendices

In Table 3, we list the variables used in the PCA, with their respective sources and the given

transformations applied so as to assure stationarity of both the time series’ and the resulting

factors.

Table 3: Variables in the Principal Component Analysis

Number Variables Transformation Source

1 Real GDP 2 OECD2 Trade Balance 2 OECD3 Current Account 2 OECD4 Industrial Production Index 2 OECD5 Construction Production Index 2 OECD6 Industrial Capacity Utilization 0 OECD7 New Order Intakes 2 OECD8 Retail Sales Index 2 OECD9 Started Housing Projects, Index 2 OECD10 Composite Leading Indicator 0 OECD11 Household Consumer Indicator 0 OECD12 Industry Consumer Indicator 0 OECD13 CPI, all items 2 SCB14 CPIF, all items 2 SCB15 CPIF-CT, all items 2 SCB16 Wage Index 2 IMF17 Disposable Income 2 IMF18 Export Prices 2 OECD19 Import Prices 2 OECD20 Producer Prices 2 OECD21 World Commodity Price Index 2 IMF22 Nominal House Price Index 2 SCB23 Real House Price Index 2 SCB∗

24 Repo Rate 1 Riksbank25 3M T-Bill 1 Riksbank26 10Y Government Bond 1 Riksbank27 Long-Short Spread 1 Riksbank28 2Y Mortgage Bond 1 Riksbank29 5Y Mortgage Bond 1 Riksbank30 User Cost Short Rate 1 Riksbank31 User Cost Long Rate 1 Riksbank32 M3 Money Supply 2 OECD33 OMXS30 2 Yahoo Finance34 Euro Stoxx 50 2 Yahoo Finance35 S&P 500 2 Yahoo Finance36 Nominal KIX Exchange Rate 2 NIER37 Real KIX Exchange Rate 2 NIER38 Population 2 NIER39 Labor Force 2 NIER40 Job Vacancy Rate 1 NIER41 Unemployment Rate 1 NIER42 Employment Rate 1 NIER43 Unit Labor Cost 1 OECD44 Labor Compensation 1 OECD45 GDP Per Employed 1 OECD46 GDP Gap 0 NIER47 Labor Market Gap 0 NIER48 Productivity Gap 0 NIER49 Equilibrium Unemployment 0 NIER50 KIX GDP 2 OECD and Riksbank∗

51 KIX CPI 2 OECD and Riksbank∗

52 KIX Short-Term Interest Rate 2 OECD and Riksbank∗

Note: Sample period is 1995:Q1 to 2016:Q2. All variables are in quarterly fre-quencies and seasonally adjusted. Transformation 0 refer to no transformation,1 refer to first-difference and 2 refer to first log-difference. ∗ denote our owncalculations.

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