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IN

DEGREE PROJECT

MATHEMATICS,

SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2020

An Empirical Study on the

Reversal Interest Rate

PONTUS BERGLUND

DANIEL KAMANGAR

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ENGINEERING SCIENCES

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An Empirical Study on the

Reversal Interest Rate

PONTUS BERGLUND

DANIEL KAMANGAR

Degree Projects in Financial Mathematics (30 ECTS credits) Master's Programme in Applied and Computational Mathematics KTH Royal Institute of Technology year 2020

Supervisors at Sveriges Riksbank: Jens Iversen Supervisor at KTH: Boualem Djehiche

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TRITA-SCI-GRU 2020:049 MAT-E 2020:015

Royal Institute of Technology

School of Engineering Sciences

KTH SCI

SE-100 44 Stockholm, Sweden URL: www.kth.se/sci

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Abstract

Previous research suggests that a policy interest rate cut below the reversal interest rate reverses the intended effect of monetary policy and becomes contractionary for lending. This paper is an empirical investigation into whether the reversal interest rate was breached in the Swedish negative interest rate environment between February 2015 and July 2016. We find that banks with a greater reliance on deposit funding were adversely affected by the negative interest rate environment, relative to other banks. This is because deposit rates are constrained by a zero lower bound, since banks are reluctant to introduce negative deposit rates for fear of deposit withdrawals. We show with a difference-in-differences approach that the most affected banks reduced loans to households and raised 5 year mortgage lending rates, as compared to the less affected banks, in the negative interest rate environment. These banks also experienced a drop in profitability, suggesting that the zero lower bound on deposits caused the lending spread of banks to be squeezed. However, we do not find evidence that the reversal rate has been breached. Keywords: reversal interest rate, effective lower bound, negative interest rates, monetary policy transmission, interest rate pass-through, bank lending

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En empirisk studie p˚

a brytpunktsr¨

antan

Sammanfattning

Tidigare forskning menar att en s¨ankning av styrr¨antan under brytpunktsr¨antan g¨or att pen-ningpolitiken f˚ar motsatt effekt och blir ˚atstramande f¨or utl˚aning. Denna rapport ¨ar en empirisk studie av huruvida brytpunktsr¨antan passerades i det negativa r¨antel¨aget mellan februari 2015 och juli 2016 i Sverige. V˚ara resultat pekar p˚a att banker vars finansiering till st¨orre del be-stod av inl˚aning p˚averkades negativt av den negativa styrr¨antan, relativt till andra banker. Detta beror p˚a att inl˚aningsr¨antor ¨ar begr¨ansade av en l¨agre nedre gr¨ans p˚a noll procent. Banker ¨ar ovilliga att introducera negativa inl˚aningsr¨antor f¨or att undvika att kunder tar ut sina ins¨attningar och h˚aller kontanter ist¨allet. Vi visar med en ”difference-in-differences”-analys att de mest p˚averkade bankerna minskade l˚an till hush˚all och h¨ojde bol˚aner¨antor med 5-˚ariga l¨optider, relativt till mindre p˚averkade banker, som konsekvens av den negativa styrr¨antan. Dessa banker upplevde ¨aven en minskning av l¨onsamhet, vilket indikerar att noll som en nedre gr¨ans p˚a inl˚aningsr¨antor bidrog till att bankernas r¨antemarginaler minskade. Vi hittar dock inga bevis p˚a att brytpunktsr¨antan har passerats.

Nyckelord: brytpunktsr¨antan, styrr¨antans nedre gr¨ans, repor¨anta, negativa r¨antor, penning-spolitikens genomslag, bankers utl˚aning

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Acknowledgements

We are indebted to Dr. Jens Iversen for the wonderful opportunity to write our thesis at the Riksbank, and for introducing us to this fascinating topic. His kindness, support, and construct-ive advice throughout this project has been very much appreciated.

We are grateful to Professor Boualem Djehiche for his valuable remarks during the planning and development of this thesis.

Our sincere thanks are due to Jamie Rinder, for providing expert feedback on the structure, style, and language throughout this paper.

Many thanks to Dr. Gustaf Lundgren, Jan Alsterlind, Henrik Erikson, Amanda Nordstr¨om, Dr. Tommy von Br¨omsen, and Dr. Ana Maria Ceh; for all the good times and interesting discussions.

Finally, we wish to thank Associate Professor Anja Janssen for her assistance in keeping our progress according to schedule.

Stockholm, May 2020

Pontus Berglund & Daniel Kamangar1

1The views expressed in this paper are the sole responsibility of the authors and should not be interpreted as the

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Contents

1 Introduction 6

2 Literature Review 8

2.1 Theoretical Literature . . . 8

2.2 Empirical Literature . . . 8

2.3 Contribution to the Literature . . . 10

3 The Swedish Context 11 4 The Reversal Interest Rate: Framework 12 5 Theory 14 5.1 Difference-in-Differences . . . 14

5.1.1 Regression Model. . . 14

5.1.2 Assumptions . . . 15

5.1.3 Robustness . . . 15

5.2 Multiple Linear Regression . . . 16

5.3 Multicollinearity . . . 16 5.4 Heteroscedasticity . . . 17 5.5 Fixed Effects . . . 17 6 Data 18 7 Methodology 20 7.1 Empirical Strategy . . . 20 7.2 Regression Model . . . 21 7.3 Assumptions . . . 22 7.4 Placebo Tests . . . 22 8 Results 24 8.1 Bank Lending Volumes. . . 24

8.1.1 Robustness Checks . . . 26

8.2 Bank Profitability . . . 28

8.2.1 Robustness Checks . . . 28

8.3 Bank Lending Rates . . . 30

8.3.1 Robustness Checks . . . 30

9 Extensions 32 9.1 Tier 1 Capital Ratio . . . 32

9.2 Multiple Time Periods . . . 35

9.3 Continuous Deposit Ratio . . . 38

10 Discussion 39 10.1 Interpretation of Results . . . 39

10.2 Policy Implications and Future Research . . . 40

11 Conclusion 41

Appendices 44

A Parallel Trends Graphs 44

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1

Introduction

The 2010s represent an important chapter in central bank history. After decades of decreasing global interest rates, several central banks around the world made the unconventional decision to lower their policy interest rates below zero. Negative policy rates had previously only been studied as a theory, whereas since their implementation in the 2010s it has been empirically possible to study their dynamics and effect on the real economy.

Negative policy interest rates are the result of expansionary monetary policy. In a negative interest rate environment, banks have to pay the central bank interest for holding their excess reserves. This incentivises banks to reduce their central bank reserves by investing in other assets, or by lending to households and companies. In addition, negative (or low) policy rates generally lead to low mar-ket lending rates, which makes it increasingly attractive for households and companies to borrow money. Fundamentally, the purpose of negative policy rates is to stimulate lending and economic growth, and to ensure that the inflation target is reached. For instance, negative policy rates were introduced in Denmark in July 2012 to stabilise the Danish krone after sizable capital inflows to Denmark (Jørgensen and Risbjerg2012), whereas they were introduced in Sweden in February 2015 to reach the inflation target (Sveriges Riksbank2015).

The implementation of negative policy rates calls into question the existence of an effective lower bound on monetary policy. It was long assumed that the effective lower bound is at zero, because the return on cash is zero. However, this assumption was repeatedly challenged when negative policy rates were introduced by Danmarks Nationalbank in July 2012, the European Central Bank in June 2014, the Swiss National Bank in December 2014, and the Swedish Riksbank in February 2015.2,3 How low, then, can the policy rate be cut before the stimulating effects on the economy begin to reverse? When the Swedish Riksbank announced the decision to cut the policy rate below zero in February 2015, they wrote in the corresponding monetary policy report that ”there is uncertainty as to how negative the repo rate can be before the transmission mechanism weakens” (Sveriges Riksbank 2015). Moreover, Riksbank governor Stefan Ingves stated more recently: “I think there actually is a lower bound for the policy rate,” further stating that he finds it difficult to envisage a policy rate of −5% (Financial Times2020).

To the best of our knowledge, the most comprehensive theoretical framework on the effective lower bound is that by Brunnermeier and Koby (2019). They introduce the reversal interest rate as a framework for defining the effective lower bound. The reversal rate is the rate at which monetary policy reverses its intended effect and becomes contractionary for lending (Brunnermeier and Koby 2019). When the policy rate is cut, banks generally respond by lowering lending rates. A policy rate cut below zero, however, narrows bank lending spreads (the difference between the lending rate and the deposit rate) due to the reluctance of banks to introduce negative deposit rates. Bank deposit rates are ”sticky” around zero because banks fear that customers would withdraw their money and hold cash if negative interest rates were charged on deposits. Thus, the lending spread is squeezed and bank profitability is reduced. At a certain point, the reversal interest rate is breached, causing banks to raise lending rates to protect their profitability. This would depress rather than stimulate the economy, and is the exact opposite of the intended effects of a policy rate cut.

Assuming that the reversal rate exists, the question arises as to where it is located. Brunnermeier and Koby (2019) find in a DSGE calibration that the reversal rate is at −1% for banks in the euro area. However, their result is purely theoretical. Empirical studies on the pass-through and impact of negative policy rates remain scarce, and those studies that exist show inconsistent results. For example, Eggertsson et al. (2019) find that negative policy rates have been contractionary for the credit growth and 5 year mortgage lending rates of the most affected banks in Sweden, as compared

2The Riksbank introduced negative policy rates on bank reserves in 2009, but only for a short period of time. 3The technical aspects of the implementations of negative policy rates vary depending on the central bank (Bech

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to the less affected banks. On the other hand, Erikson and Vestin (2019) show that negative policy rates have had an overall expansionary effect on Swedish bank lending rates, indicating that the reversal rate has not been breached.

In this paper, we empirically study if the reversal interest rate has been breached in Sweden, by measuring the impact of negative policy interest rates on bank lending behavior. With inspiration from Tan (2019), we employ a difference-in-differences approach to examine the lending behavior of banks that are most affected by the negative interest rate environment. Our main contribution to the literature is to present a comprehensive analysis on the transmission of negative policy rates to Swedish bank lending volumes. Understanding the transmission of negative policy rates is crucial for enabling monetary policymakers to make more effective decisions in the future. Furthermore, more empirical evidence surrounding the reversal interest rate makes it possible to test the validity of the framework as defined by Brunnermeier and Koby (2019).

In brief, our results suggest that the negative interest rate environment in Sweden caused the most affected banks to reduce household lending relative to the less affected banks. In addition, we find that negative policy rates have been contractionary for the 5 year mortgage lending rates of the most affected banks, as compared to the less affected banks, which is consistent with the findings of Eggertsson et al. (2019). Our results also suggest that the profitability of the most affected banks was hurt by the negative interest rate environment. However, we do not find evidence that the reversal rate has been breached.

The remainder of this paper is structured as follows. Section 2 provides a review of the related theoretical and empirical literature. Section3describes the Swedish context for negative policy rates. Section 4 provides an in-depth description of the reversal rate framework. Section 5 outlines the mathematical concepts that forms the basis of our methodology. Section6documents the data used in our analysis. Section7 describes our empirical strategy, regression model and robustness checks. Section 8 presents the results. Section 9 presents some additional results from three extensions. Section10interprets the results and discusses implications for the future. Section11concludes.

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2

Literature Review

2.1

Theoretical Literature

The literature on the reversal rate is closely related to the literature on the bank lending channel. In the bank lending channel, conceptualised by Bernanke and Blinder (1988), the transmission of monetary policy to the real economy is measured via the effect on banks’ assets (loans) and liabilities (deposits). Policy rate cuts lead to a greater supply of bank deposit funding, which are eventually translated to increases in bank credit supply (Bernanke and Blinder1988).

The limitations and possible detrimental effects of negative interest rates is discussed by Bernanke (2020). Bernanke (2020) states that banks benefit by revaluation gains on their assets when the policy rate declines. However, Bernanke (2020) further states that there is a risk that the lending capacity of banks will be impaired by negative policy rates since bank deposit rates are bounded by zero. Ulate (2019) adopts a similar reasoning, and theoretically demonstrates that the efficiency of monetary policy when the policy rate is negative is between 60% and 90% of its value when it is positive. Furthermore, Bernanke (2020) acknowledges that the existence of a reversal rate as conceptualised by Brunnermeier and Koby (2019) is possible.4

Sims and Wu (2019) present a quantitative theoretical study on unconventional monetary policy tools. According to Sims and Wu (2019), negative policy rates are passed through to the real economy via two channels that work in opposite directions: the forward guidance channel and the banking channel. The forward guidance channel suggests that negative interest rates have a similar impact on the economy as forward guidance; since negative policy rates signal the intent of the central bank to lower short term rates in the future, which is likely to be stimulating for long term market rates. In contrast, the banking channel (similar to the bank lending channel introduced by Bernanke and Blinder (1988)) represents the transmission mechanism by which negative policy rates reduce bank net worth and tighten credit conditions as deposit funding declines. Thus, a policy rate cut into negative territory could be contractionary if the contractionary effects of the banking channel outweighs the expansionary effects of the forward guidance channel.

2.2

Empirical Literature

Eggertsson et al. (2019) study the effects of negative policy interest rates on the Swedish economy between 2014 and 2016. Using monthly bank level data, they show that the policy rate transmission via the bank lending channel was weakened as the policy rate turned negative. Their results suggest that when deposit rates reach the zero lower bound, lending rates become unresponsive to further policy rate cuts. Their results indicate that a one percentage point decrease in the policy rate leads to an increase in 5 year fixed-rate mortgage rates by between 0.03 and 0.31 percentage points, which is evidence that negative policy rates have been contractionary. Furthermore, Eggertsson et al. (2019) analyse the impact of negative policy rates on bank lending volumes with a simple difference-in-differences model. Banks are categorised as either high deposit or low deposit, based on each banks’ reliance on deposit financing. They show that negative policy rates are associated with a reduction in credit growth for high deposit banks, as compared to low deposit banks. Their results suggest that high deposit banks had four percentage points lower growth of lending volumes compared to low deposit banks, in the negative interest rate environment. These results are an indication that negat-ive policy rates have been contractionary for the lending behavior of the most affected Swedish banks. Erikson and Vestin (2019) state that 3 month rates are best suited for illustrating the transmission from policy rates to bank lending rates. They document the pass-through of the Swedish policy rate to aggregate bank 3 month lending rates to households and non-financial companies (NFCs). In contrast to Eggertsson et al. (2019), Erikson and Vestin (2019) show that negative policy rates have

4Bernanke (2020) refers to an earlier version of the paper by Brunnermeier and Koby (2019). However, the

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had an overall expansionary effect on Swedish bank lending rates between 2015 and 2018, indicating that the reversal rate has not been breached in Sweden.

Heider, Saidi and Schepens (2019) study the transmission of negative policy rates on bank lending in the euro-area from 2013 to 2015. They use granular bank-level balance sheet data, and lending data from the syndicated loans market, where two or more banks form a syndicate which then lends to firms. They document that no banks in their sample charge households with negative deposit rates when the policy rate turned negative, which they state is due to banks fearing deposit withdrawals. However, they also document that some banks charge NFCs with negative deposit rates. Heider, Saidi and Schepens (2019) argue that the zero lower bound on deposits does not apply for corporate deposits since it is easier for households to withdraw their deposits and hold cash than it is for companies. This phenomenon is explored in more detail by Altavilla et al. (2019); they show that euro area banks’ with sound balance sheets are able to offer negative interest rates on the deposits of NFCs while experiencing an increase in lending volume at the same time.

With a difference-in-differences approach, Heider, Saidi and Schepens (2019) show that high deposit banks decrease lending and increase risk-taking, as compared to low deposit banks, in the negative interest rate environment. This could be an indication that negative policy rates have been contrac-tionary for lending in the euro area. However, the representatives of these results is questionable, since the data set is limited to the syndicated loan market, which does not necessarily reflect the loan market as a whole. For example, Eisenschmidt and Smets (2019) use highly representative bank-level balance sheet data, and show that the pass-through of the policy rate to bank lending rates and lending volumes remained unchanged when the policy rate turned negative in the euro area. Grandi and Guille (2019) conduct a study using granular and representative data on the French loan market. They find that negative policy rates induce high deposit banks to increase their lending relative to low deposit banks, which stands in contrast to the results by Heider, Saidi and Schepens (2019) for euro area banks. On the other hand, results by Grandi and Guille (2019) also suggest that high deposit banks increased their relative risk-taking in the negative policy rate environment, which is consistent with the results by Heider, Saidi and Schepens (2019) for banks in the euro area. Furthermore, Bubeck, Maddaloni and Peydr´o (2019) find similar results on risk-taking using a novel securities register for the 26 largest banking groups in the euro area.

Tan (2019) takes inspiration from the difference-in-differences methodology of Heider, Saidi and Schepens (2019), to analyse the impact of negative interest rates on bank credit supply, risk-taking, and profitability, in the euro-area between 2013 and 2015. Tan (2019) uses a granular data set comprising approximately 55 percent of the euro area banking system, making the sample more rep-resentative than that of Heider, Saidi and Schepens (2019). Tan (2019) documents that household deposit rates have a zero lower bound, whereas NFC deposit rates do not, which is an observation also made by Heider, Saidi and Schepens (2019). However, in contrast to Heider, Saidi and Schep-ens (2019), Tan (2019) finds that negative policy rates were expansionary for the credit supply of high deposit banks in relation to low deposit banks. Thus, the results of Tan (2019) indicate that negative policy rates have been expansionary in the euro area. In addition, Tan (2019) does not find a significant correlation between negative policy rates and bank risk-taking.

Bottero et al. (2019) study the case of Italy, and find that the introduction of negative policy rates in June 2014 had an expansionary effect on bank lending via the portfolio rebalancing channel. They provide evidence that policy rate cuts into negative territory induce a downward shift and flattening of the bond yield curve, which incentivises banks to rebalance their portfolios from liquid assets to lending. Moreover, Bottero et al. (2019) do not find evidence of a zero lower bound on bank deposit rates in Italy. They show that high deposit banks increase their loan volume relative to low deposit banks when the policy rate is negative, which is consistent with results by Grandi and Guille (2019) for French banks, and Tan (2019) for euro area banks. Thus, Bottero et al. (2019) find that negative policy rates have been expansionary in Italy. Furthermore, Bottero et al. (2019) show that banks

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preserved their margins and profitability in the negative interest rate environment by raising fees for deposit-related banking services.

Using confidential balance sheet data of 50 Swiss retail banks for the period July 2013 to June 2016, Basten and Mariathasan (2018) find that Swiss banks maintained their profitability when the policy rate turned negative by raising lending-related and overall fee income. Like Eggertsson et al. (2019) and Heider, Saidi and Schepens (2019), they document that household deposit rates are bounded by zero when the policy rate enters negative territory. Interestingly, Basten and Mariathasan (2018) exploit the fraction of central bank reserves in bank balance sheets as an identification strategy for exposure to negative policy rates, rather than using the fraction of deposits (deposit ratio), which is the most common strategy in the literature. Results show that negative policy rates have been expansionary in Switzerland: banks most exposed to negative policy rates rebalanced their portfo-lios by reducing their reserves and increasing mortgage lending, uncollateralized loans, and finanicial assets. In addition, their results also indicate that these banks increased their risk-taking.

Schelling and Towbin (2018) follow the methodology of Heider, Saidi and Schepens (2019) and use comprehensive confidential data on the lending of 20 Swiss banks to NFCs between July 2014 and July 2015. They find that negative policy rates lead to increased lending and risk-taking. Thus, they also show that negative policy rates have been expansionary in Switzerland. Furthermore, Schelling and Towbin (2018) show that the transmission of negative policy rates to lending rates are stronger for high deposit banks than for low deposit banks. In contrast to Basten and Mariathasan (2018), Schelling and Towbin (2018) find no evidence that banks raise their commissions in the negative policy rate environment.

In summary, the majority of the existing empirical studies on negative policy rates find that policy rate cuts to negative territory have been overall expansionary for the economy. In other words, most studies did not find evidence of the reversal rate having been breached. However, absence of evidence is not evidence of absence (Altman and Bland1995). Eggertsson et al. (2019) and Heider, Saidi and Schepens (2019) find that negative policy rates have been contractionary for high deposit banks, relative to low deposit banks, in Sweden and the euro area, respectively. These results suggest that high deposit banks are more adversely affected by negative policy rates than other banks.

2.3

Contribution to the Literature

There is limited empirical research surrounding the impact of negative policy rates on the lending behavior of Swedish banks. The pass-through phenomenon to lending rates has been addressed by Eggertsson et al. (2019), and Erikson and Vestin (2019). However, no studies to our knowledge have either addressed the pass-through to Swedish bank lending volumes or used bank-specific control variables and fixed effects in their analysis in the Swedish context.5

This degree project therefore focuses on Swedish bank lending volumes and has as its point of departure our understanding that the transmission mechanism between the policy rate and bank lending volumes is crucial in the framework presented by Brunnermeier and Koby (2019). We use not only the same source as Eggertsson et al. (2019) (Statistics Sweden) to collect data on bank-level lending volumes, but also data from Bloomberg on variables such as total equity, net interest margin, tier 1 capital ratio, and fees. Such a range of data sources enriches the data set, allows for a more comprehensive analysis, and forms the basis for a more data-rich and robust regression model that includes bank-specific control variables and fixed effects.

5Eggertsson et al. (2019) addressed the impact of negative policy rates on credit growth in Sweden. However, the

precision of their results is questionable since their model did not include control variables or fixed effects. In addition, they did not perform any robustness checks.

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3

The Swedish Context

Figure 1 shows the evolution of the Riksbank policy rate (the ”repo rate”) next to the aggregate deposit and lending rates of Swedish banks. The Riksbank cut the policy rate below zero for the first time in February 2015 (see Table 1). As Figure 1 shows, deposit rates have historically been lower than the policy rate. When the policy rate became negative, however, the relationship shifted, and bank deposit rates have been close to zero (above the policy rate) since February 2015. This is evidence that bank deposit rates are sticky around zero in Sweden. Furthermore, it is clear by visual inspection of Figure1that bank lending rates became less responsive to the policy rate when negative territory was entered. In other words, the pass through of the policy rate to bank lending rates appears to have been weakened as the policy rate became negative. This could be explained by that bank lending rates are squeezed when the policy rate is negative, as a result of the zero lower bound on deposit rates. In fact, the Riksbank raised this as a possible outcome when the decision to cut the policy rate below zero was announced in February 2015 (Sveriges Riksbank2015).

Figure 1: The Riksbank policy rate against aggregate overnight household, and NFC, deposit rates; and aggregate 3 month household, and NFC, lending rates. STIBOR is the Stockholm Interbank Offered Rate. Data on the Riksbank policy rate and STIBOR is retrieved from Sveriges Riksbank (2020b), and aggregate bank deposit rates and lending rates are retrieved from Statistics Sweden (2020a) and Statistics Sweden (2020b), respectively. The grey area represents the time period in the focus of our main analysis (September 2013 to July 2016).

Table 1: The Riksbank policy rate (implementation dates) between September 2013 and July 2016 (Sveriges Riksbank2020a), which is the time period of our main analysis.

Date New level (%)

2012-12-19 1 2013-12-18 0.75 2014-07-09 0.25 2014-10-29 0 2015-02-18 −0.1 2015-03-25 −0.25 2015-07-08 −0.35 2016-02-17 −0.5

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4

The Reversal Interest Rate: Framework

The reversal rate is the policy rate at which expansionary monetary policy reverses its effect and becomes contractionary for lending (Brunnermeier and Koby 2019). Figure 2 shows a stylised illustration of the dynamics by which the reversal rate is breached.

Figure 2: Illustration of the relationship between the policy rate, and commercial bank lending and deposit rates. The lending spread (difference between lending rate and deposit rate) is squeezed when the policy rate is cut. Since deposit rates are constrained by the zero lower bound, banks will raise their lending rates when the policy rate breaches the reversal rate, to protect their profitability. Note: this graph is a simplification, as interest rates are not linear or perfectly parallel in reality. The reversal rate is a framework for conceptualising the policy rate at the effective lower bound. The framework provides a specific definition of the effective lower bound, which has testable implications. The reversal interest rate, iRR, is defined as the rate at which a cut in the current nominal policy rate, i, is stimulating for lending if and only if i > iRR (Brunnermeier and Koby 2019). More specifically: 1. i > iRRimplies dLdi∗ < 0; 2. i = iRRimplies dL∗ di = 0; 3. i < iRRimplies dL∗ di > 0,

where L is lending volume, i is the current nominal policy interest rate, and iRRis the reversal rate

(Brunnermeier and Koby2019). This is illustrated in Figure3.

Figure 3: Illustration of the relationship between the policy rate and bank lending volumes (credit supply). Lending declines when the reversal rate is breached. Note: this graph is a simplification.

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In the framework by Brunnermeier and Koby (2019), banks are assumed to be (ex-ante) identical, leading to a constant reversal rate across banks. Furthermore, bank balance sheets are simplified, where the asset side is composed of bank loans (Lt) and fixed-income assets (St), and the liability side

is composed of deposits (Dt) and equity (E0). Furthermore, banks are subject to capital constraints,

which capture economic and regulatory factors, of the form

ψLL + ψSS ≤ N1, (1)

where N1 is the nominal net worth of banks, and ψS, ψL ≥ 0 are risk weights (Brunnermeier and

Koby2019). In addition, banks face liquidity constraints, which capture the necessity of banks to have easily accessible funds to avoid risk, of the form

S ≥ ψDD, (2)

where ψD> 0 (Brunnermeier and Koby2019). Moreover, Brunnermeier and Koby (2019) state that

banks earn their profits from two sources: net interest income (NII) and capital gains (CG). NII is defined as N II = iL∗L∗+ iS∗ | {z } Interest income − iD∗D∗ | {z } Interest expenses , (3)

where iL∗ and iD∗ are the optimal interest rates on loans and deposits, respectively. CG is defined

as

CG = E0(i) − E0(io), (4)

which is the change in initial equity (retained earnings) caused by the surprise change in interest rates (Brunnermeier and Koby2019).

Brunnermeier and Koby (2019) calibrate a DSGE model and find that the reversal rate depends on four key determinants: 1) long-term fixed income assets held by banks, 2) the pass-through of monetary policy to bank deposit interest rates, 3) capital constraints faced by banks, and 4) ex ante bank capitalisation. When the policy rate is lowered, banks make capital gains on long-term fixed income assets (e.g. bonds). This dynamic mitigates credit losses and thus decreases the reversal rate. However, since deposit rates are constrained by a zero lower bound, a policy rate cut below zero also leads to a decrease in bank net interest income as the lending spread is squeezed, leading to a drop in profitability. As profit margins shrink, banks may increase their lending volume to protect profits. In addition, a drop in profitability due to rate cuts lowers banks’ net worth given the decrease in retained earnings. These two forces work in tandem until banks’ capital constraint binds and lending contracts. Also, the probability that the capital constraint becomes binding is a function of banks’ initial capitalisation, i.e. higher capitalised banks have a lower reversal rate. In this framework, the reversal rate is time varying, endogenous, and state-dependent. Furthermore, Brunnermeier and Koby (2019) state that the reversal rate has a ”creeping up” effect; meaning that it increases over time. The capital gains (asset revaluations) following a policy rate cut gradually cease as bank’s fixed-income holdings mature over time; enabling the reversal rate to creep up since the negative effects of the policy rate cut on net interest income cumulate. In addition, Brunner-meier and Koby (2019) state that the reversal rate is increased by quantitative easing; adding that it thus ”should only be employed after interest rate cuts are exhausted.” As central banks implement quantitative easing, the reversal rate increases since it removes long-term fixed income assets from banks’ balance sheets along with the capital gains stemming from asset revaluations.

In summary, the reversal rate is the rate at which the policy rate becomes contractionary for lending. When the policy rate breaches the reversal rate, banks will raise lending rates to protect their profitability (see Figure2), and reduce lending volumes (see Figure3). Our study investigates if the reversal rate was breached by the Riksbank during the time when the policy rate entered negative territory, between February 2015 and June 2016. We examine the impact that the negative interest rate environment had on bank lending volumes, bank profitability and bank lending rates.

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5

Theory

This section provides an overview of the mathematical concepts that lay the foundation of our methodology. Firstly, difference-in-differences estimation is described. Secondly, multiple linear regression is described. The section ends with some theory on multicollinearity, heteroscedasticity, and fixed effects. The reader that is familiar with these concepts can skip this section.

5.1

Difference-in-Differences

Difference-in-differences (or double difference) estimation is a method for impact evaluation, e.g. for measuring the effect of policy interventions (Fredriksson and Oliveira 2019). It is a research design that combines cross-sectional treatment-control methodology with before-after comparisons to achieve a more robust identification (Fredriksson and Oliveira2019). The simplest form of the difference-in-differences approach is a case with two groups in two periods, in which data is used from two groups, treatment and control group; and two periods, pre-treatment and post-treatment (Wing, Simon and Bello-Gomez2018). However, difference-in-differences estimation can also be used for more complex applications involving multiple groups and time periods (Wing, Simon and Bello-Gomez 2018). Our study uses the two groups in two periods application. The policy intervention is implemented between the pre-treatment and post-treatment periods, and the treatment group is subjected to the policy, whereas the control group is not (Fredriksson and Oliveira 2019). The difference-in-differences estimate is achieved by taking the difference between the dependent variable post-treatment and pre-treatment, for the control group; and deduct it from the same difference for the treatment group (Fredriksson and Oliveira 2019). The idea is to remove the effect of potential confounding factors on the treatment and control groups (Lechner2011). If there are time trends or other changes that occur between the post-treatment and post-treatment periods, that affect both the treatment group and control group, then these factors are controlled for when the post-treatment-pre-treatment difference in the dependent variable for the control group is netted out from the same difference for the treatment group (Fredriksson and Oliveira2019). In addition, if there are important characteristics that differ between the treatment and control groups, which are determinants of the dependent variable; their influence is eliminated by studying changes over time (Fredriksson and Oliveira2019). The difference-in-differences estimate is illustrated in Figure4.

Figure 4: Illustration of the difference-in-differences approach with two groups in two periods. Ygt

is the dependent variable of interest, where g = 1 (2) for the control (treatment) group and t = 1 (2) for the pre-treatment (post-treatment) period.

5.1.1 Regression Model

Regression analysis is required to determine the significance of the difference-in-differences estimate (Fredriksson and Oliveira2019). With an ordinary least squares method, the difference-in-differences

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estimate is obtained by computing the β3-coefficient of Equation (5) (Wing, Simon and Bello-Gomez 2018).

Yigt= β0+ β1Tg+ β2Pt+ β3(Tg× Pt) + igt (5)

Here, an individual is indexed by i, and the group is indexed by g, equaling 1 for control group and 2 for treatment group. Time is indexed by t, equaling 1 for pre-treatment and 2 for post-treatment (Wing, Simon and Bello-Gomez2018). Tg is a dummy variable that identifies observations on the

treatment group, i.e. Tg=2 = 1 and Tg=1 = 0 (Wing, Simon and Bello-Gomez 2018). Group

membership is time invariant, which is why Tg does not have a time subscript (Wing, Simon and

Bello-Gomez2018). Ptis a dummy variable that identifies observations from the treatment period,

i.e. Pt=2= 1 and Pt=1= 0 (Wing, Simon and Bello-Gomez2018). Pthas no group subscript because

the time period is the same across the groups (Wing, Simon and Bello-Gomez2018). Tg× Ptis the

interaction term between Tg and Pt, Y is the dependent variable, and  is the error term (Lan and

Yin2017). Furthermore, β0, β1, β2, and β3 are coefficients to be estimated. More specifically, β0

is a constant term. β1captures the time-invariant difference in the dependent variable between the

two groups, and β2captures the combined effects of any unmeasured covariates that change between

the two periods but affect the dependent variable the same way in both groups (Wing, Simon and Bello-Gomez 2018). In essence, β1 is the group effect and β2 the time trend. β3 represents the

difference-in-differences estimate, also called the average treatment effect for the treatet (ATT), and is defined as:

β3= ( ¯Yg=2,t=2− ¯Yg=2,t=1) − ( ¯Yg=1,t=2− ¯Yg=1,t=1), (6)

where ¯Yg=2,t=2 and ¯Yg=2,t=1 are the mean outcome for the treatment group in period t = 2

(post-treatment) and t = 1 (pre-(post-treatment); and ¯Yg=2,t=1 and ¯Yg=1,t=1 are the corresponding values for

the control group (Fredriksson and Oliveira2019; Lan and Yin2017). 5.1.2 Assumptions

The difference-in-differences relies on three key assumptions (Fredriksson and Oliveira 2019). The first assumption is the parallel trends assumption, which states that the treatment group would have followed the same trend as the control group had it not been subjected to the policy intervention (for the dependent variable) (Fredriksson and Oliveira2019). In other words, the average outcomes of the treatment and control groups would follow parallel trends in the absence of treatment (Lan and Yin2017). This means that the difference in outcome between the treatment and control group would have remained constant in absence of treatment. Second, the Stable Unit Treatment Assump-tion (SUTVA) must hold, which states that there should be no relevant interacAssump-tions between group members (Lechner2011), and treatment applied to one member (or group) should not influence the outcome of another member (or group) (Fredriksson and Oliveira 2019). Third, control variables should be exogenous, i.e. unaffected by the treatment, to avoid bias in the difference-in-differences estimate (Fredriksson and Oliveira2019).

In addition to the assumptions mentioned above, the five major assumptions in multiple linear regression, listed in Section 5.2, are also required to obtain an unbiased difference-in-differences estimator.

5.1.3 Robustness

A common approach for evaluating the robustness of a difference-in-differences model is to perform a placebo test, in which the model is tried for a treatment intervention that logically should not have a significant effect on the dependent variable (Strumpf, Harper and Kaufman2017).

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5.2

Multiple Linear Regression

In matrix notation, the general multiple linear regression model with k independent variables is written as below (Montgomery, Peck and Vining2012):

y = Xβ + , (7) where y =      y1 y2 .. . yn      , X =      1 x11 x12 . . . x1k 1 x21 x22 . . . x2k .. . ... ... ... 1 xn1 xn2 . . . xnk      , β =      β0 β1 .. . βk      ,  =      1 2 .. . n      (8)

Here, y is a n × 1 vector of the observations, X is a n × p matrix of the levels of the independent variables, β is a p×1 vector of the coefficients, and  is a n×1 vector of random errors (Montgomery, Peck and Vining2012). ˆβ is the vector of least squares estimators that minimizes

S(β) =

n

X

i=1

2i = 0 = (y − Xβ)0(y − Xβ), (9)

which can also be expressed as

S(β) = y0y − 2β0X0y + β0X0Xβ, (10) since β0X0y is a 1×1 matrix (or a scalar) and its transpose (β0X0y)0is the same scalar (Montgomery, Peck and Vining2012). From Montgomery, Peck and Vining (2012), we further have that the least squares estimators, ˆβ, must satisfy

∂S ∂β|βˆ= −2X 0y + 2X0X ˆβ = 0, (11) which gives: X0X ˆβ = X0y (12) ˆ β = (X0X)−1X0y (13)

Regression analysis relies on five major assumptions:

1. The relationship between the dependent variable and the independent variables is linear, at least approximately;

2. The error term  has zero mean;

3. The error term  has constant variance σ2;

4. The errors are uncorrelated; and

5. The errors are normally distributed (Montgomery, Peck and Vining 2012).

5.3

Multicollinearity

Multicollinearity implies near-linear dependence among the independent variables in a regression model, which can negatively impact the ability to estimate regression coefficients (Montgomery, Peck and Vining2012).

Variance inflation factors (VIF) are useful for detecting multicollinearity (Montgomery, Peck and Vining2012). For each term in the regression model, the VIF measures the combined effect of the dependencies among the independent variables on the variance of that term (Montgomery, Peck and Vining 2012). Depending on the model, a VIF-value that exceeds 5, or 10, is an indication that the concerned regression variables are poorly estimated because of multicollinearity (Montgomery, Peck and Vining 2012). Methods for dealing with multicollinearity include, but are not limited to, collecting additional data, model respecification, and ridge regression (Montgomery, Peck and Vining2012).

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5.4

Heteroscedasticity

Regression errors whose variances change across observations are heteroscedastic (Greene 2012). Thus, heteroscedasticity is a violation of the third of the major assumptions for OLS regression listed in Section5.2. Regression coefficients are still unbiased in the presence of heteroscedasticity; however, heteroscedasticity could cause inaccurate inferences and standard errors (Greene2012). The Breusch-Pagan Lagrange multiplier test is designed to detect heteroscedasticity in OLS models (Greene 2012). The test statistic, a Lagrange Multiplier measure, has a chi-squared distribution under the null hypothesis of homoscedasticity (constant error variances), and is rejected if the p-value is below the selected threshold (Greene 2012). One possible remedy for heteroscedasticity is to reformulate the regression model, for example by transforming variables or changing control variables (Lang2016).

5.5

Fixed Effects

When analysing panel data, the basic regression model is of the form:

yit= x0itβ + z0iα + it, (14)

where there are K regressors in x0it, not including a constant term (Greene 2012). z0iα is the

heterogenity, or individual effect, where the elements of z0i are a constant term and a set of

group-specific variables that are observable, such as sex, location, or size, etc., or unobservable, such as entity specific characteristics, individual heterogenity in skill or preferences, etc., all of which are taken to be constant over time (Greene2012). In a fixed effects model, Equation (14) becomes:

yit= x0itβ + αi+ it, (15)

where αi= z0iα embodies all observable effects and specifies an estimable conditional mean (Greene 2012). In other words, αi is a fixed effects variable: a group-specific constant term in the regression

model (Greene2012). The name ”fixed” effects stems from the fact that αi does not vary over time

(Greene2012). This model can be extended by adding the time effect, γt, which yields in Equation

(16) below (Greene2012).

yit= x0itβ + αi+ γt+ it (16)

Least squares estimates of the slopes, i.e. β, are obtained by regression of

y∗it= yit− ¯yi∗− ¯yt∗+ ¯y¯ (17) on x∗it= xit− ¯xi∗− ¯xt∗+ ¯x,¯ (18) where ¯ yi∗ = 1 T T X t=1 yit, ¯yt∗= 1 n n X i=1 yit, and ¯y =¯ 1 nT n X i=1 T X t=1 yit, (19)

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6

Data

All the data used in this study is collected from public sources. Bank balance sheet data is retrieved from Statistics Sweden (2020c). The original sample is comprised of 55 monetary financial insti-tutions (MFIs)6, with balance sheet items observed monthly for the time period December 2012 to July 2016.7 Balance sheet items include total assets, total loans, loans to households, loans to non-financial corporations (NFCs), total deposits, household deposits, NFC deposits, and securities holdings (retrieved as bonds and other interest bearing securities). Total loans comprise of all lend-ing activities, includlend-ing loans to other MFIs, houslend-ing credit institutions, and funds, etc; and total deposits include deposits from all entities. 34 MFIs are excluded from the sample because of lack of data for the time period of interest. We also remove foreign branches operating in Sweden (2 MFIs), since branches are often aided by the foreign parent company (which is not affected by Swedish monetary policy). For the remaining 19 MFIs, we check for historically large ups and downs in total assets. Like Tan (2019), we define large jumps as a monthly growth rate of total assets above the 99th percentile, and MFIs with five our more large jumps are considered unrepresentative. Never-theless, there are no MFIs in our data set with more than two large jumps in total assets.

The data from Statistics Sweden lacks some variables of interest, and is therefore complemented with data from Bloomberg for the same time period. Five variables are retrieved from Bloomberg: total equity, net interest margin8, fee and commission income, fee and commission expense, and tier 1 capital ratio9. Moreover, additional data on total equity is retrieved from the annual reports of some MFIs to offset missing data points in the Bloomberg data. Nevertheless, two MFIs are excluded because of insufficient data on total equity. In addition, the Bloomberg data is in varying frequen-cies depending on the MFI (either quarterly, semi-annually or annually). Thus, we use quadratic spline interpolation to give monthly frequency to the whole data set and to fill absent observations. However, the data on fee and commission income, fee and commission expense, and tier 1 capital ratio is only interpolated for 10 MFIs because of missing data points. For the same reason, data on net interest margin is only interpolated for 9 MFIs. Note that we remove one additional MFI from the samples for net interest margin, fee and commission income, and fee and commission expense, respectively, because it is an outlier that violates the parallel trends assumption.

We create a variable for net fee margin, computed as the difference between fee and commission income, and fee and commission expense, as a percentage of total assets. In addition, we create a variable for fee income, computed as fee and commission income as a percentage of total assets. High (low) deposit banks are defined as banks with a total deposit ratio above (below) the median in January 2015 (one month before the policy rate became negative). One MFI is excluded because it switches between being a high and low deposit bank during the time period (it cannot be classified as neither high nor low deposit). Thus, our final sample consists of 16 MFIs, of which 8 are high deposit and 8 are low deposit. The total assets of these 16 MFIs amounted to 11 600 billion SEK in January 2015, equivalent of 82% of the total assets of all Swedish MFIs (14 107 billion SEK) (Statistics Sweden2020c). Table2provides an overview of the primary data, prior to interpolation. Mortgage lending rates are retrieved from Macrobond for 8 Swedish MFIs, for the time period December 2012 to July 2016. The Macrobond data is reported daily, and we average it to monthly observations. Two MFIs are excluded from this sample because of missing data points. Thus, the mortgage lending rates sample is comprised of 6 banks. Because of missing data points for some lending rates, the data set is restricted to loans of five different maturities: 3 month, 1 year, 2 year, 3 year, and 5 year. Monthly data on policy rates is retrieved from Sveriges Riksbank (2020b).

6In this paper, we also refer to MFIs as banks.

7This time interval comprises of our main analysis (September 2013 to July 2016), and the placebo tests specified

in Equation (22) (September 2013 to July 2016) and Equation (23) (December 2012 to September 2014).

8The difference between interest income, and interest expenses, as a percentage of interest earning assets. 9Tier 1 capital as a percentage of total risk-weighted assets.

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Table 2: Summary statistics for Swedish banks. The data shown is restricted to between September 2013 and July 2016, which is the time period in the focus of our main analysis.

September 2013 to July 2016

Assets N Mean Median St. Dev. p5 p95

Total assets (in million SEK)

All MFIs 560 682468 216531 769918 25627 2242863 High deposit 280 767860 118414 938052 23569 2320093 Low deposit 280 597075 363428 541382 54162 1712803 Total loans (% total assets)

All MFIs 560 69.89 69.77 21.15 32.03 97.46 High deposit 280 60.49 61.63 14.07 33.34 82.79 Low deposit 280 79.28 90.46 22.83 31.28 97.66 Loans to households (% total assets)

All MFIs 560 34.80 21.20 28.16 2.16 8.07 High deposit 280 20.15 19.92 15.58 2.16 34.97 Low deposit 280 49.45 60.84 30.25 2.15 81.76 Loans to NFCs (% total assets)

All MFIs 560 11.40 10.47 8.57 0.13 26.12 High deposit 280 8.41 4.87 8.51 0.00 25.35 Low deposit 280 14.39 13.27 7.54 4.14 27.02 Loans to MFIs (% total assets)

All MFIs 560 9.46 4.28 11.94 0.19 39.57 High deposit 280 11.98 4.21 13.99 0.23 41.69 Low deposit 280 6.94 4.34 8.79 0.06 30.25 Securities holdings (% total assets)

All MFIs 560 7.32 8.87 8.99 0.00 27.53 High deposit 280 9.84 7.39 9.14 0.00 31.71 Low deposit 280 4.81 0.00 8.09 0.00 25.37 Liabilities

Total deposits ratio (% total assets)

All MFIs 560 49.22 45.70 18.32 19.97 78.69 High deposit 280 64.67 65.68 9.98 46.36 82.96 Low deposit 280 33.76 34.60 9.69 16.69 45.58 Household deposits ratio (% total assets)

All MFIs 560 14.60 9.90 17.42 0.00 52.19 High deposit 280 24.22 20.35 18.23 0.00 51.89 Low deposit 280 4.97 0.00 9.46 0.00 28.86 NFC deposits ratio (% total assets)

All MFIs 560 3.18 1.01 3.51 0.00 8.75 High deposit 280 4.56 5.21 3.24 0.02 9.04 Low deposit 280 1.80 0.00 3.23 0.00 7.95 MFI deposits ratio (% total assets)

All MFIs 560 16.05 7.61 18.02 0.04 67.98 High deposit 280 11.56 3.02 21.92 0.03 68.92 Low deposit 280 20.55 24.40 11.37 1.16 34.73 Total equity (in million SEK)

All MFIs 141 40372 12386 48607 1618 128607 High deposit 81 56509 11679 58400 1618 131928 Low deposit 60 18587 13771 11897 4852 36991 Tier 1 capital ratio (%)

All MFIs 96 24.14 21.55 11.53 14.18 42.52 High deposit 55 20.35 21.10 3.84 14.20 25.96 Low deposit 41 29.24 22.90 15.79 9.50 44.00 Profitability

Net interest margin (%)

All MFIs 87 1.01 1.00 24.96 64.26 13.90 High deposit 45 11.67 12.23 21.33 78.51 14.09 Low deposit 42 83.68 81.01 15.53 60.92 10.57 Fee and commission income (in million SEK)

All MFIs 93 1712 922 2029 1 5726

High deposit 48 3124 3232 1963 312 5781

Low deposit 45 268 12 433 1 1016

Fee and commission expense (in million SEK)

All MFIs 93 508 351 504 32 14

High deposit 48 866 753 471 369 1484

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7

Methodology

7.1

Empirical Strategy

There are several econometric challenges associated with analysing the reversal rate. One of the main challenges stem from the fact that the level of the reversal rate varies across banks and time. For example, some banks have stronger balance sheets, and are therefore more able to maintain lend-ing volumes and low lendlend-ing rates when profits are hit by the negative interest rate environment. Another challenge is to avoid confounding factors; in other words, to determine the true cause of the changes that banks experience during the negative interest rate environment. Furthermore, it is difficult to precisely asses every single variable that could influence the variable of interest when analysing real world economic data; thus, the problem of omitted variables needs to be accounted for. It is also probable that banks have different characteristics and strategies affecting their lending behaviour, which are hard to specify and measure. In addition, the variables in the time series data could be non-stationary, stemming from time trends such as loan demand, GDP growth, etc. These things considered, our empirical strategy and regression model is therefore based on a difference-in-differences framework, and is inspired by the methodology of Tan (2019). As mentioned in Section

2.2, various takes on the difference-in-differences approach have been employed by Heider, Saidi and Schepens (2019), Eggertsson et al. (2019), Bottero et al. (2019), Basten and Mariathasan (2018), and Schelling and Towbin (2018). The difference-in-differences estimate is convenient because it measures the unbiased causal effect of a policy intervention (e.g. negative policy rates). As Section

5.1describes, the difference-in-differences approach is designed to remove confounding factors since it differences out omitted variables that are constant for the control and treatment group. Moreover, we combine the difference-in-differences research design with a twoways fixed effects model, to ac-count for bank and time fixed effects.

The objective of our analysis is to measure the impact of negative policy rates on three outcomes of interest. The first and most important outcome of interest is bank lending volumes. By quantifying the impact of negative policy rates on bank lending volumes, we measure the transmission of negat-ive policy rates via the bank lending channel. The second outcome of interest is bank profitability, which measures if negative policy rates reduce bank profits. Third, we examine the pass-through of negative policy rates to bank lending rates. By measuring the effect of negative policy rates on these outcomes of interest, we can get an overall picture of whether the negative interest rate envir-onment has been stimulating or depressing for the economy. To reduce the influence of confounding factors, we focus our analysis to the time period between September 2013 and July 2016 (35 months). As mentioned in Section 4, the framework by Brunnermeier and Koby (2019) assumes that the reversal rate is constant across banks. However, that is not the case in reality, since banks are different with respect to relevant characteristics, e.g. the composition of their balance sheets. High deposit banks, whose loan funding is dominated by deposits, should be most affected by negative policy rates. This is because the zero lower bound on deposits squeezes bank lending spreads when the policy rate is negative (see Figure2), inducing affected banks to raise lending rates to protect their profitability. On the other hand, low deposit banks are less reliant on deposits to fund their lending, which means that they are less affected by the zero lower bound on deposits caused by the negative interest rate environment. In essence, our difference-in-differences approach is based on the identification that low deposit banks (the control group) represent the counterfactual outcome for high deposit banks (the treatment group) in absence of negative policy rates (the treatment). Since the treatment group is only observed as treated, the true counterfactual scenario cannot be observed. Ultimately, the difference-in-differences approach makes it possible to study the impact of negative policy rates on the lending behavior of the most affected (high deposit) banks, relative to the impact on the lending behavior of the less affected (low deposit) banks.

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7.2

Regression Model

Our basic regression model is constructed as follows:10

Yigt= α + βDeposit ratiog× Af ter(02/2015)t+ igt (20)

Yigt is the dependent variable for bank i in group g for time t. For our analysis on bank lending

volumes, the dependent variable is defined as the log of lending of bank i in month t. We perform separate regressions on the log of total lending, lending to households, lending to NFCs, and lending to other MFIs. For the analysis on bank profitability, we run separate regressions with Yigt defined

as net interest margin, net fee margin, and fee income, respectively. For the analysis on bank lending rates, Yigt is defined as mortgage lending rates with the respective maturities 3 month, 1 year, 2

year, 3 year and 5 year. Table 3provides an overview of the representativeness of our data on the different dependent variables.

Moreover, Af ter(02/2015)tis a treatment intervention dummy variable that equals one if the policy

rate is negative, and zero otherwise. Deposit ratiog is a dummy variable that indicates if a bank

is in the treatment group or the control group: it equals one for above median deposit ratio (high deposit), and zero for below median deposit ratio (low deposit) in January 2015 (one month before negative policy rates were implemented by the Riksbank). Furthermore, α is a constant, igt is the

error term, and β is the difference-in-differences estimate that measures the treatment effect of the negative interest rate environment starting in February 2015. A positive (negative) β indicates that the dependent variable increased (decreased) for high deposit banks relative to low deposit banks. For example, if lending is the dependent variable, a negative β would mean that the negative interest rate environment has been contractionary for high deposit banks relative to low deposit banks. Table 3: Overview of the samples used in the separate regressions. For each dependent variable, the table shows the number of banks for which observations are made, the representativeness of the sample, and the distribution of high and low deposit banks. The representativeness of each sample is computed as the sum total assets of the banks in January 2015, as a percentage of the total assets of all Swedish banks, which amounted to 14 107 billion SEK in January 2015 (Statistics Sweden 2020c). Since we have more sufficient data for some variables than others, the representativeness differs across the dependent variables (see Section6).

Dependent variable Number of banks Representativeness High (low) deposit

Total lending 16 82% 8 (8)

Household lending 16 82% 8 (8)

NFC lending 16 82% 8 (8)

MFI lending 16 82% 8 (8)

Fee income 9 66% 4 (5)

Net fee margin 9 66% 4 (5)

Net interest margin 8 63% 4 (4)

3 month lending rates 6 52% 3 (3)

1 year lending rates 6 52% 3 (3)

2 year lending rates 6 52% 3 (3)

3 year lending rates 6 52% 3 (3)

5 year lending rates 6 52% 3 (3)

The basic regression model in Equation (20) does not account for the possibility that changes to the dependent variable could have been caused by factors other than the negative interest rate envir-onment. For example, there exists a possibility for both observable and intrinsic key characteristics

10Note that Equation (20) does not include Deposit ratio

g and Af ter(02/2015)t as separate terms such as in

Equation (5). This is because these terms would become colinear with the fixed effects that are added to the model in Equation (21).

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that differ between the banks, and that are determinants of the dependent variables (Fredriksson and Oliveira2019). In addition, the dependent variables could be influenced by time trends that are the same for all banks, such as the demand on loans or the GDP. Therefore, we make the regression model more robust and stationary by sequentially adding bank fixed effects, time fixed effects, and bank-specific control variables. This yields in the final regression model:

Yigt= α + βDeposit ratiog× Af ter(02/2015)t+ γxi,t−1+ δi+ ηt+ igt (21)

xi,t−1 are bank-specific control variables: size (defined as log of total assets), capital ratio (total

equity as % of total assets), and securities ratio (securities holdings as % of total assets). Following the lead of Tan (2019), the control variables are lagged one month to solve endogeneity problems. Furthermore, γ is a coefficient, and δi and ηt are bank fixed effects and time fixed effects,

respect-ively.11

We check for multicollinearity in all regressions by computing the VIF-value for each of the inde-pendent variables. A VIF-value that exceeds 5 indicates multicollinearity. Furthermore, we also check for heteroscedasticity by performing the Breush-Pagan test. Heteroscedasticity is assumed if the resulting p-value from the test is below 0.05.

7.3

Assumptions

The first and most important assumption is the parallel trends assumption (see section5.1.2). Par-allel trends graphs are presented in Appendix A for each of the dependent variables. With visual inspection, we can confirm that the dependent variables followed the same trends for high deposit banks and low deposit banks, before the February 2015 rate cut.

Second, we must address the Stable Unit Treatment Value Assumption (SUTVA). According to Hersche and Moor (2018), SUTVA cannot be tested. It could be argued that SUTVA does not hold because there is a possibility that there are spillover effects between the banks in our sample. For example, interbank lending before and during the treatment period is highly probable. Nevertheless, we argue that the spillover effects between banks is sufficiently small with respect to our selection of dependent variables, with the exception of MFI lending. For instance, it is unlikely that the household or NFC lending of one bank has a significant impact on that of another bank. Even if one assumes that there are spillover effects with respect to MFI lending or another dependent variable, the impact of these effects is possibly negligible in relation to the impact of the treatment (negative policy rates). In addition, SUTVA has not been addressed in any of the previous studies mentioned in Section2.2that also employ a difference-in-differences approach. These things considered, we are confident that SUTVA can be relaxed for our analysis.

Third, following the lead of Tan (2019), we account for the endogeneity assumption by lagging the control variables by one month. This shifts the eventual effects of the treatment on the control variables. Fourth, also inspired by Tan (2019), we assume that the decision by the Riksbank to cut the policy rate below zero in February 2015 came as a ”surprise” to commercial banks. Thus, we assume that banks did not incorporate expectations of negative policy rates in their lending behaviour in the months prior to the treatment period.

7.4

Placebo Tests

The treatment effect measured by the difference-in-differences estimate incorporates not only the effect of the negative interest rate environment, but also the effect of the policy rate cuts. We there-fore check the robustness of our results by performing two placebo tests, to ensure that our results

11Note that Tan (2019), Heider, Saidi and Schepens (2019), Eggertsson et al. (2019), Bottero et al. (2019), and

Schelling and Towbin (2018) all use bank-level clustered standard errors to remedy serial correlation, whereas we do not. We argue that our sample of 16 banks is too small to motivate the usage of clustered standard errors. Our perspective is based on the recommendations in Cameron and Miller (2015), in which a minimum amount of 20-50 clusters is proposed.

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only stem from the negative interest rate environment. For each regression that yields in significant results, we perform one placebo test `a la Tan (2019) and one placebo test of our own design. In the placebo test `a la Tan (2019), the interaction term Deposit ratiog× Af ter(07/2014)tis added

to Equation (21), which yields in Equation (22).12 This analysis is performed on the same time period as the main regression (September 2013 to July 2016).

Yigt= α + βDeposit ratiog× Af ter(02/2015)t (22)

+ θDeposit ratiog× Af ter(07/2014)t+ γxi,t−1+ δi+ ηt+ igt

Here, Af ter(07/2014)tis a treatment intervention dummy variable that equals one after the policy

rate cut in July 2014, and zero otherwise. Deposit ratiogis a dummy variable that indicates if a bank

is in the treatment group or the control group: it equals one for above median deposit ratio (high deposit), and zero for below median deposit ratio (low deposit) in January 2015 (one month before the policy rate became negative). θ captures the effect of the interest rate environment between July 2014 and July 2016; which, as Table1and Figure 1shows, is a time period that comprises of both a positive and a negative interest rate environment. On the other hand, β captures the effect of the interest rate environment between February 2015 and July 2016, which is a time period during which the interest rate environment is negative from beginning to end.

The significance and the signs of β and θ provide insight to whether or not policy rate cuts into negative territory are ”special”, or if they have the same effect as policy rate cuts in positive interest rate environments. If both β and θ are significant and of the same sign, it is evidence that it is the policy rate cut, and not the negative interest rate environment, that causes the differences in outcomes between high and low deposit banks. However, if β is significant, and θ is not; or if β and θ are both significant but of different signs, it is evidence that the differences in outcomes are due to the negative interest rate environment.

In the placebo test of our own design, we construct the model as below. In this placebo test, we restrict the analysis to the time period between December 2012 and September 2014 (21 months), during which the policy rate was positive from beginning to end.

Yigt= α + φDeposit ratiog× Af ter(12/2013)t+ γxi,t−1+ δi+ ηt+ igt (23)

Here, Af ter(12/2013)tequals one after the policy rate cut in December 2013 from 1% to 0.75%, and

zero otherwise; and Deposit ratiog equals one (zero) if a bank is high (low) deposit in November

2013 (one month before the policy rate cut). By comparing the significance and sign of φ in our placebo test with the significance and sign of β in our main analysis specified in Equation (21), similar conclusions can be drawn as those by comparing β and θ in the placebo test `a la Tan (2019) in Equation (22).

12Note that Tan (2019) takes inspiration from Heider, Saidi and Schepens (2019) when constructing the placebo

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8

Results

This sections presents the results. The section begins with our findings on bank lending volumes, with separate results for total lending, lending to households, lending to NFCs, and MFI lending. Second, we show our findings on bank profitability, with separate results for net interest margin, net fee margin, and fee income. Third, we show our results for bank mortgage lending rates, with separate results for loans of maturities 3 month, 1 year, 2 year, 3 year, and 5 year.

8.1

Bank Lending Volumes

Table 4 shows the results of the regressions on the log of total lending. Column (1) shows the outcome of the basic regression model in Equation (20), which incorporates neither control variables nor fixed effects. In Columns (2)-(8), fixed (bank and time) effects and control variables are sub-sequently added to the model, yielding in the regression model in Equation (21), which is our final and preferred specification. This stepwise approach shows that the significance of the difference-in-differences estimate is gradually improved as control variables and fixed effects are added to the model. In addition, saturating the model with control variables and fixed effects increases the ex-planatory power of the model (the R-squared is only 0.059 in Column (1), whereas it is 0.729 in Column (8)). This adds further confidence to the validity of the model specification. However, the R-squared estimates in Columns (5)-(6) are higher than those in Columns (7)-(8), which implies that the latter models capture less of the variability of the data observed for total lending. This loss of variability could be attributed to the addition of bank fixed effects. Nevertheless, the significance of the difference-in-differences estimate is improved as bank fixed effects is added in Columns (7)-(8), and the R-squared estimate is still high at 0.729 in Column (8). Thus, the specification in Equation (21) still remain as our final and preferred specification.

The control variables in Columns (5)-(8) are consistently significant and of the same sign. The interpretation is that, ceteris paribus, an increase in capital or size, or a decrease in securities, cor-responds to increased lending. These results are intuitive. Better capitalised banks have stronger balance sheets, and they are therefore more able to maintain or increase lending in the negative in-terest rate environment. The positive correlation between size and lending can be explained by that larger banks lend more than smaller banks. The negative and significant effect of securities could be due to the fact that banks either invest in securities or lending, i.e. banks with more securities lend less and vice versa. Additionally, banks fund some of their loans through the liquidation of securities. In other words, a decrease in securities (liquidation) is equivalent of increased lending. Column (8) shows that for the final regression model, the difference-in-differences estimate is −0.020 and significant. This is equivalent of a decrease by approximately 2% ((e−0.02− 1) × 100) in total lending for the treatment group (high deposit banks) relative to the control group (low deposit banks). Put differently, banks most affected by the negative interest rate environment reduced lend-ing by 2% relative to less affected banks.

Table5 presents our results on more granular forms of lending, next to the results on total lending (for reference). Columns (2)-(4) show the results for the log of household lending, NFC lending, and MFI lending, respectively. Loans to households is the only granular form of lending for which banks experienced a significant impact following the rate cut in February 2015. As Column (2) shows, the estimate for household lending equals −0.045 and is highly significant. This corresponds to a decrease of 4.4% ((e−0.045− 1) × 100) in household lending for high deposit banks relative to low deposit banks during the negative interest rate environment. It should be noted, however, that the R-squared of this result is low (0.065), meaning that the model does not capture the variability in household lending particularly well.

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25

Table 4: Results on total lending. September 2013 to July 2016

Dependent variable: log(Total lending)

(1) (2) (3) (4) (5) (6) (7) (8)

Deposit ratio × Af ter(02/2015) 0.011 0.011 0.011 0.011 −0.044 −0.044 −0.020∗ −0.020∗∗

(0.279) (0.019) (0.288) (0.019) (0.044) (0.045) (0.010) (0.010) Capital ratio 5.843∗∗∗ 5.838∗∗∗ 3.961∗∗∗ 4.132∗∗∗ (0.447) (0.453) (0.624) (0.701) Securities ratio −1.387∗∗∗ −1.387∗∗∗ −0.266∗∗ −0.275∗∗ (0.138) (0.140) (0.114) (0.118) Size 1.070∗∗∗ 1.070∗∗∗ 0.976∗∗∗ 0.997∗∗∗ (0.008) (0.008) (0.031) (0.034) Constant 12.459∗∗∗ −1.326∗∗∗ (0.142) (0.104) Observations 560 560 560 560 560 560 560 560 R2 0.059 0.146 0.058 0.001 0.977 0.977 0.765 0.729 Adjusted R2 0.054 0.119 −0.007 −0.097 0.977 0.976 0.756 0.700

Bank FE No Yes No Yes No No Yes Yes

Time FE No No Yes Yes No Yes No Yes

Controls No No No No Yes Yes Yes Yes

Note: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01

References

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