The Redistributive Effects of Quantitative Easing

Transcription

1 Te Redistributive Effects of Quantitative Easing Developing an illustrative model of te key mecanisms of Quantitative Easing By Mark van der Plaat * Abstract: Since te Financial crisis of , multiple central banks in te developed countries engaged in some kind of Quantitative Easing (QE), eiter large-scale asset purcases, improved central bank lending facilities or Operation Twist, to stimulate teir economies. Te current study develops an illustrative model tat investigates te effect of tese different types of QE-programmes on te distribution of income. All QE-policy discussed in te current study affect te income distribution by influencing te long-term and sort-term interest rates. Te initial effects of te different types of QE are ambiguous, owever, wen te economic agents react on te QE-policies income inequality increases unanimously. Tese results sow tat unconventional monetary policies, suc as QE, ave re-distributional side effects. Student number s Supervisor F. Bon, PD Institution Radboud University, Nijmegen Studies Masters in Economics, wit specialisation in: International Economics & Business Product Master s Tesis Economics Date 25 July 2016 * Please revert all correspondence to m.vanderplaat@student.ru.nl

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3 It would seem tat for every kind of capital-asset tere must be an analogue of te rate of interest on money (Keynes, 1936/2006)

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5 Table of Contents 1 Introduction Conventional and Unconventional Monetary Policy Conventional monetary policy Unconventional monetary policy Types of unconventional monetary policy Quantitative Easing (QE) QE and conventional monetary policy Te optimal coice of QE Tree policies of QE Two transmission cannels of QE Transmission cannel 1: Te portfolio-balancing cannel (Kimura & Small, 2006) Te setting of te paper Portfolio-balancing cannel in a CAPM-setting Policy 1: Large-scale asset purcases (Gertler & Karadi, 2013) Setting of te paper Te model Policy 1: Te basic illustrative model Te model set-up Te general solution Perturbation results Additions to te basic illustrative model Policy 2: Improved central bank lending facilities Policy 3: Operation twist Extension to policy 1: Cyclical securities Discussion and conclusion... 47

6 9 Bibliograpy Appendix A Policy 1: LSAPs of different central banks... I Te Federal Reserve... I Te Bank of England... I Te Bank of Japan... I Te European Central Bank... I Appendix B Appendix C Appendix D Transmission cannel 1: Re-writing te CAPM... II Transmission cannel 1.1: Derivation of te market variance... II Policy 1: Optimisation of ouseolds and banks in te basic illustrative model. III Houseolds... III Banks... V Appendix E Policy 1: Solution of te central bank cannels... VI Transmission cannel 1: Portfolio-balancing cannel... VI Transmission cannel 2: Signalling cannel... VII Appendix F Solution of te additions to te model... VIII Policy 2: Improved central bank lending facilities... VIII Policy 3: Operation twist... IX Allowing Pro-cyclical assets... XII Appendix G List of Symbols used... XVI

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8 Master s Tesis of Mark van der Plaat 1 Introduction On July Mario Dragi, te president of te European Central Bank (ECB), announced tat te ECB is ready to do watever it takes to preserve te euro and believe me, it will be enoug (ECB, 2012). In January 2015 te ECB put words into action and introduced te eurozone to te unconventional monetary policy tool of Quantitative Easing (QE), wic aimed to acieve te price stability witin its mandate (ECB, 2015a). QE is often regarded as a large-scale purcasing programme in wic te central bank purcases long-term assets on te secondary market to cutback te long-term interest rates and increase inflation (Joyce, Miles, Scott, & Vayanos, 2012). Te ECB was not te first central bank in te world to introduce suc a programme. As early as 2001, te Bank of Japan (BoJ) introduced QE to stem te continuous price decline in te country and create a basis for sustainable economic growt (Ugai, 2007). Since te financial crisis of , te Federal reserve of te US (te Fed) and te Bank of England (BoE) introduced QE as well. Because te national economies are different, central banks used different types of unconventional policies besides QE. Te current study identifies two oter unconventional policies tat are also a type of QE, namely improved central bank lending facilities and operation twist. Improved central bank lending facilities tend to decrease te long-term interest rate by improving te lending possibilities of banks at te central bank (Fawley & Neely, 2013; Joyce et al., 2012). Operation twist is very similar to te large-scale long-term asset purcasing programmes, but differs in te fact tat te central bank sells sort-term securities to fund te long-term securities purcases, ereby increasing te sort-term interest rates as well as decreasing te long-term interest rates (Fawley & Neely, 2013; Joyce et al., 2012). Te current study investigates te effects of tree QE-programmes on income inequality rater tan focussing on te interest rates. Since te publication of Piketty s bestseller Capital in te Twenty- First Century in 2014 te discussion about income inequality in te developed world as been reinvigorated. He sowed tat since te 1970s income inequality is rising in te US and in many European countries. Income inequality arises wen one as more resources earned from current and istoric income tan te oter as. Normally, te government can redistribute income by means of taxes, subsidies and oter social welfare measures. However, central banks redistribute income troug canges in asset prices and income flows (Brunnermeier & Sannikov, 2012). QE could ypotetically also ave an effect on te distribution of income. Te researc question of te current study is as follows: How does Quantitative Easing affect te distribution of income of private ouseolds? To study tese effects of QE, te current study introduces an illustrative model. Te basic illustrative model is based on te large-scale asset purcasing programmes, because tese are commonly used to acieve a QE-programme. Te illustrative model is furter extended to fit te oter two QE-policies. In te general setup of te illustrative model, te actors are ouseolds, banks and te central bank; ereby illustrating te direct effects and te indirect effects of QE on ouseolds. In tis way, ouseolds can directly invest in securities on te secondary market 1

9 Te Redistributive Effects of Quantitative Easing or can indirectly invest via banks. Te variations in asset valuations lead to mutations in te wealt of ouseolds and subsequent canges in income inequality. In summary, illustrative model suggests tat QE as a large-scale long-term asset purcasing programme as few effects on te interest rates and income inequality. Firstly, wen te central bank is credible, QE is able to decrease te sort-term interest rate. Secondly, wen te central bank purcases long-term securities, institutional investors are triggered to rebalance teir portfolios, wic increases te demand for long-term securities and decreases te long-term interest rates. Te decline in sort-term and long-term interest rates lead to an increase in security prices. If, and only if, te investing ouseolds, te bankers, are able to capitalise on te increased price of te long-term securities, income inequality increases. QE-policy 2, te improved central bank lending facilities, ave similar effects on te interest rates and income inequality, only not affecting te sort-term interest rates. QE-policy 3, operation twist, is somewat different, ere te long-term interest rates decrease, yet, te sort-term interest rates increase, leading to a decrease in income inequality at first but to an increase in income inequality wen ouseolds and banks react on te policy. Te following sections will discuss te results of te current study in more detail, starting wit a review of conventional and unconventional monetary policy, of wic QE is a part. Section 3 contains an in dept discussion of QE, wic elaborates on te tree different types of QE, wy QE is distinctly different from conventional monetary policy and introducing te two most important cannels of QE. Hereafter, te portfolio-balancing cannel, wic influences te long-term interest rates and is proposed by Kimura and Small (2006), is reviewed in section 4. Section 5 reviews and discusses te model of Gertler and Karadi (2013), wic will serve as te basis of te illustrative model. Based on te information gained in sections 3 troug 5, section 6 introduces te basic illustrative model. Tis model is based on QE as large-scale long-term asset purcasing programme. After te introduction of te basic illustrative model, section 6 furter discusses te results and te propositions based on te presented model. Te modified model including te two oter forms of QE, wic allows ouseolds and banks to invest in a greater variety of assets, is included in section 7. Finally, section 8 discusses and concludes te results of te current study. 2 Conventional and Unconventional Monetary Policy Tis section discusses te differences between conventional and unconventional monetary policy. Firstly, tis section discusses conventional monetary policy. Wat are te aims of tis policy, ow do central banks use conventional monetary policy and in wat is situation tis policy normally used. Secondly, unconventional monetary policy is discussed, including te difference in situation between conventional and unconventional monetary policy, te difference in aims and te difference in instruments. 2

10 Master s Tesis of Mark van der Plaat Table 1: Open market operations Central bank balance seet Assets 2.1 Conventional monetary policy Te current study defines conventional monetary policy as: te canges in te money supply of a specific country due to te creation or buying up of money by te central bank by means of open market transactions (Barro & Gordon, 1983; Blancard et al., 2010). Te two main aims of conventional monetary policy are to acieve low and stable inflation (Joyce et al., 2012, p. F271), and to manage liquidity in te money market and steer sort-term interest rates (De Haan, Oosterloo, & Scoenmaker, 2015, p. 123). In practice, tere are some differences among central banks. Te mandate of tree of te four biggest central banks, te ECB, te BoE and te BoJ only includes price stability. Te mandate of price stability of te ECB and te BoE are conditional to te union s and government s economic policy respectively (BoE, 2016; EU, 2008, p. 101), wereas te mandate of te BoJ does not ave suc a conditionality (BoJ, 2016a). Te fourt central bank, te Fed, goes a step furter and uses its monetary policy for te adjustment of unemployment and stable long-term interest rates (Fed, 2016a). Te common instrument of conventional monetary policy are open market transactions. Open market transactions are operations in wic central banks purcase i.e. expansionary policy or sell i.e. contractionary policy sort-term securities on te open market 1 (Mundell, 1963). Tis definition includes two important factors: securities and te open market. Securities are fungible, negotiable instruments representing financial value (De Haan et al., 2015, p. 156), tese can be categorised in debt and equity securities and are also known as assets 2. Open markets are markets in wic resellers can purcase and sell excess securities (Lee & Wang, 2002), meaning tat te original issuer of te securities is necessarily not involved. Liabilities Domestic securities Currency in circulation (+) Sort-term (+) Deposits eld by private banks Long-term Foreign securities Table 1 provides a scematic representation of a balance seet of a central bank and te effect of open market operations. Adapted from: Krugman, Obstfeld, and Melitz (2015). Wen te central bank engages in expansionary open market operations te sort-term securities on te asset-side of te balance seet increase by purcasing sort-term government securities. Simultaneously te currency in circulation on te liability-side of te balance seet increases by using new money to finance te securities. Open market operations are executed by central banks as follows: central banks purcase sortterm domestic securities on te open market in excange for money, tereby increasing te money supply. Te balance seet of central bank increases wen performing expansionary open market transactions (Table 1). On te assets side, te sort-term domestic securities increase and on te liability 1 Or secondary market 2 Debt securities are specifically known as bonds 3

11 Te Redistributive Effects of Quantitative Easing side, te currency in circulation increases, i.e. te money supply. Te purcases ave tree effects. Firstly, an increased money supply stimulates inflation in te economy. Secondly, open market purcases increase te demand of specific securities, increasing teir prices and, conversely, decreasing te respective yields. Tirdly, if investors are able to capitalise on te increased prices, e.g. sell te securities for iger prices tan bougt for, teir wealt can increase, possibly increasing income inequality if not all economic agents are able to invest on te secondary market. As will become apparent section 3, QE as a long-term asset-purcasing programme as some similarities wit open market transactions. Conventional monetary policy is usually conducted in an environment wit positive sort-term interest rates. In suc an environment, central banks are able to steer te interest rates and te corresponding inflation. Positive interest rate was previously assumed a necessary condition of monetary policy. Te interest rates were assumed to be bounded by zero because, at a zero interest rate, securities and money become almost perfectly substitutable, meaning tat money is more liquid tat securities. As a result, investors strictly prefer money to securities and invest in money. Tus wen te central bank engages in expansionary monetary policy, te increase in money supply as no effect on te interest rates, for investors would prefer money to securities, leaving te demand for securities and te interest rates uncanged. Te next subsection sows tat tis assumption did not old. 2.2 Unconventional monetary policy After te financial crisis of , conventional monetary policy proved to be inadequate. Conventional monetary policy could not deal wit two issues. Firstly, te Taylor-rule demanded negative or close to zero interest rates. Te Taylor-rule was introduced by Taylor (1993) and is a rule ow monetary policy can be applied in practice. In particular, te rule provides information on ow te policy rate would ave been set in te past in a particular country subjected to economic conditions (Gerlac-Kristen, 2003), wic could be useful for setting te current policy rates. Generally, te original Taylor rule is as follows: r t = ρ + π + K π (π t π ) + K y (y t y ), (1) were r t is te real interest rate at time t, π * is te inflation target, π t is te actual inflation, y t is te real output, y * is te ypotetical potential output, and K π and K y are weigt factors. It means tat te actual interest rate is cosen based on te baseline pat of te real interest (ρ + π ), te gap between te actual inflation and target inflation, and te output gap. Terefore, wen te actual inflation decreases below te inflation target, te optimal interest rate will decrease as well; a similar argument olds for te output gap. After te financial crisis of , for many developed countries te Taylor-rules indicated negative interest rates. Tis was mainly due to an increase in te output gap rater tan in te inflation gap (Blancard, Cerutti, & Summers, 2015; Nikolsko Rzevskyy & Papell, 2013). Te negative Taylorrule lead to te adoption of unconventional tools by central banks. 4

12 Master s Tesis of Mark van der Plaat Secondly, markets, wose bubbles ad burst during te financial crisis, became very illiquid and te solvency of te actors in tese markets sarply decreased (De Haan et al., 2015). Markets tat became illiquid during te financial crisis were, among oters, ousing markets and money markets (De Jong, 2011). Banks around te world ad used te process of securitisation to pool, repack and resell ousing loans to oter banks and investors in order to diversify risk 3 (De Haan et al., 2015). Wen te ousing bubble in te US burst, it became apparent tat tis risk was not diversified. Securitisation was supposed to sell te risky securities, but due to te bad credit rating and te complexity of te instrument, many risky securities remained on te balance seet of te banks (De Haan et al., 2015). Te result was tat money market liquidity dried up. Te money market provides sort-term loans to and from financial institutions. Te cras of te tese markets was te incentive for te Fed and oter central banks to provide liquidity to suc markets (De Haan et al., 2015). Central banks around te world reverted to unconventional monetary policy tools to re-liquidise te markets wit several measures, of wic QEpolicies are te best known. 2.3 Types of unconventional monetary policy Te previous subsection argued tat central banks ad to revert to unconventional tools to stimulate te economy. Tere are several forms of unconventional monetary policy tools, suc as negative policy rates, forward guidance and balance seet expansion. Te negative policy rates are relevant to discuss, because it leads to te situation in wic te central bank ad to revert to QE. Forward guidance is relevant, because its mecanisms of influencing te interest rates are similar to tese of QE. Balance seet expansion also known as QE and is discussed in dept in te next section. Te first commonly used unconventional monetary policy tool is negative policy rates. Tis tool, among oters, is used by te European Central Bank (ECB) and (Joyce et al., 2012) and by te Bank of Japan (BoJ). Negative policy interest rates by te central banks were designed to increase te incentive for banks to lend more money to oter parties and disincentives banks to make use of overnigt facilities of te central banks, wic are used by banks to stall excess liquidity overnigt. Furtermore, negative interest rates would also stimulate spending, because olding money would be less favourable. According to Bossone (2013/2016) critics argue, owever, tat negative interest rates would only lead to cas oarding and safe asset accumulation instead of increased expenditures. QE in Japan, te eurozone, te United States and te United Kingdom was introduced in a situation of near-to-zero interest rates, making te situation in wic QE was introduced unique. Anoter unconventional monetary policy tool is forward guidance. Forward guidance is wen a central bank communicates to old te policy interest rate at its current level for some time in te future and tereby olding te interest rates low (Bossone, 2013/2016; De Haan et al., 2015). Te mecanism 3 Credit defaults swaps were used in combination wit securitisation to furter diversify risk. Credit default swaps are instruments tat allows investors to take a position wen te counterparty defaults. 5

13 Te Redistributive Effects of Quantitative Easing Figure 1 Figure 1 provides a scematic representation of ow forward guidance affects te output and inflation in te AS-AD model, adapted from: (Blancard, Amigini, & Giavazzi, 2010). Wen central banks forward guidance is successful, it decreases te expectations of te interest rates, leading to a decrease in te interest rates. Te lower interest rates lead to more investments by private companies, sifting te AD-curve upward from AD to AD, increasing te national income and te inflation rate. beind forward guidance is tat wen te central bank communicates clearly to te market tat it is willing to old te interest rate on a certain level, market expectations will follow correspondingly. Especially at te zero-bound interest rates, a credible promise to old te policy interest rate low can stimulate current aggregate demand and economic growt (Campbell, Evans, Fiser, Justiniano, Calomiris, & Woodford, 2012, p. 2). Tis relation can be captured in te AS-AD framework (Blancard et al., 2010), wic explains te relationsip between output and inflation troug te equilibrium between te aggregate demand and supply. It is assumed tat forward guidance decreases te interest rates. Low interest rates make investments more attractive due to te lower interest costs. An increase in investment increases te aggregate demand or te AD-line 4 in figure 1 from AD to AD. To satisfy te increased demand, te suppliers of goods ave to increase production. Increased production decreases unemployment, wic increases te nominal wages. Te increased nominal wages lead to an increase in te prices set by te firms, i.e. inflation rises. Figure 1 illustrates tis as an increase along te AS-line 5. Tis framework does not specify if te interest rates are sort-term or long-term. A critical note toug, only partial empirical evidence was found for te effects of forward guidance (Bossone, 2013/2016). 4 AD: y = C(Y T) + I(Y, i) + g; M = YL(i) (Blancard et al., 2010) P 5 AS: P = P e (1 + μ)f(1 Y, z) (Blancard et al., 2010) L 6

14 Master s Tesis of Mark van der Plaat 3 Quantitative Easing (QE) Te term Quantitative Easing was created in Japan in te 2001 after a period of deflationary pressures and an upcoming recession (Joyce et al., 2012; Ugai, 2007). Te policy interest rates were near to zero and pused te BoJ to develop tis new measure to stimulate te economy (Spiegel, 2006). Tis section discusses te differences between QE and conventional monetary policy, wy central banks reverted to different QE-programmes, te tree types of QE-policies and two important QE-cannels. 3.1 QE and conventional monetary policy QE is used by central banks in special circumstances. It as different aims from conventional monetary policy and makes QE strictly distinguisable to conventional monetary policy. Firstly, QE aims to decrease te long-term interest rates, providing stimulus to te economy (Cristensen & Rudebusc, 2012). Secondly, QE aims to increase te amount of liquid assets in te economy (Den Haan, 2016), of wic an increase in te money supply is most desirable. Tirdly, central banks seek to stimulate te entire economy of te country, in contrast to a specific market. Wen central banks only seek to stimulate one market, e.g. stimulate markets tat are illiquid, tey engage in credit easing (Fawley & Neely, 2013; Sleifer & Visny, 2010). Besides te differences in aims, QE-policies also differ from conventional monetary policies. Te best-known form of QE are te large-scale long-term asset purcasing programmes (LSAPs). Te current study identifies two oter forms of unconventional policies used tat could also be classified as QE. Te first form are te improved lending facilities (ILFs) of te central bank, altoug tis form does not involve purcases of assets on te secondary market, it as te same aims as LSAPs. Te second form is operation twist, tis form is very similar LSAPs, owever, it does not increase te amount of liquid assets on te market by means of new money, but wit sort-term securities. Te LSAPs return as QE in te illustrative model of section 6, section 7 includes te oter types of QE in te illustrative model. Te LSAPs are cosen as te basis of te illustrative model because te two cannels of te policy are also applicable to oter types of QE-policies. 3.2 Te optimal coice of QE Te optimal form of a central bank s QE-programme depends on te structure of te financial system. Before proceeding to te discussion of tese tree forms, two types of financial systems, a bank-based and a market-based financial system are briefly discussed. In a bank-based system, financial intermediaries are important, wereas in a market-based system financial markets are important. Te main difference between tese two systems is tat financial intermediaries ave close business relationsips wit firms in wic tey invest, wereas investors in financial markets do not ave any business relationsips (Degryse & Van Cayseele, 2000). Tese business relationsips give financial intermediaries an information advantage, wic could constrain 7

15 Te Redistributive Effects of Quantitative Easing Table 2 Type of QE Policy 1: LSAP Policy 2: ILF Policy 3: Operation Twist Operation of te central bank Purcase long-term securities on te secondary market New long-term loans to Financial intermediaries Purcase long-term securities and sell sortterm securities on te secondary market investment projects of oter firms (Levine, 2002). However, te lack of business relations could lead to less investments in projects due to te less available information (Levine, 2002). Te Fed, te BoE, te BoJ and te ECB based teir use of different QE-programmes on respective te structure of teir financial systems. Tese central banks were cosen to investigate in te current study, because teir relative importance in te world economy. Based on GDP, te US and te eurozone ave two of te biggest economies in te world (based on OECD figures). And based on te global foreign excange market turnover, te four currencies of tese central banks were te most traded in te world in 2013 (BIS, 2013). Decreasing longterm interest Fulfilled Fulfilled Fulfilled Aims of QE Increase liquid assets in te market Fulfilled (money supply) Fulfilled (money supply) Fulfilled (sortterm securities) Macroeconomic stimulus Fulfilled Fulfilled Fulfilled Table 2 provides a representation of te types of QE, ow tey operate and if te fulfil te aims of QE. Altoug different in operation te LSAP and ILF fulfil all te aims of QE, making tem good instruments of QE. Operation twist is operational wise very similar to LSAP and only differs tat operation twist finances te purcases wit sort-term securities. Consequently, te money supply is not increased toug te sort-term securities are. Based on te amount of bank assets to GDP, Germany is considered to ave te most bankbased financial system and te US te most market-based financial system in te world (Levine, 1997). Generally, te ideal types do not exist and financial systems are often a combination of bank-based and market-based. To study tis, Kwok and Tadesse ave developed a continuous measure 6 tat sows if countries ave more bank-based or market-based financial systems. Teir results suggest tat, overall; te UK and te US are predominantly market-based. Japan is relatively bank-based. Te eurozone, 6 Teir measure is based on a variety of financial arcitecture indicators, wic can be split into tree variables (Kwok & Tadesse, 2006, pp ): i) te size of te stock markets relative to te size of te banking sector, ii) te activity of te stock markets relative to tat of banks and (iii) te relative efficiency of stock markets vis-àvis tat of te banks. 8

16 Master s Tesis of Mark van der Plaat Table 3: Policy 1 LSAPs Central bank balance seet Assets Liabilities Domestic securities Currency in circulation (+) Sort-term Deposits eld by private banks Long-term (+) Foreign securities Bank balance seet Assets Liabilities Reserves (+) Deposits accounts Loans Central bank loans Securities Sort-term Long-term ( ) Table 3 provides a scematic representation of te balance seet of a central bank and of a bank and te effects of largescale long-term asset purcases on tem, adapted from: (Blancard et al., 2010). Wen a central bank engages in largescale asset purcasing programmes, it augments te long-term domestic on te asset-side of te balance seet; at te same time te currency in circulation on te liability-side increases for te purcases are financed by new money. On te bank s balance seet someting different appens: te purcases of te central bank lead to a decrease of te long-term securities on te asset-side of te balance seet but to an increase in reserves te bank can use to finance new investments ereby increasing te national income. owever, is difficult to place in te scale according to tis measure. But based on te findings of Levine (1997), Levine (2002) and Kwok and Tadesse (2006), eurozone is relatively more bank-based. 3.3 Tree policies of QE Tere are tree different types of QE seen in te years after te financial crisis of Table 2 presents te tree different types of QE, ow tey operate and if te tree aims as described above are met. Te tree QE-policies are discussed in tis subsection Policy 1: Large-scale long-term asset purcases Te first QE-policy, QE as an LSAP, was first used by te BoJ (Ugai, 2007) and later used by te Fed, te BoE and te ECB in te aftermat of te financial crisis of (Fawley & Neely, 2013). Effectively, tis policy entails te purcase of safe long-term securities, including long-term government bonds and long-term mortgage-backed securities (MBS) (Krisnamurty & Vissing-Jorgensen, 2011), inflating te balance seet of te central bank and, as a result, increasing te money supply. Backed securities, including mortgage-backed securities, are distinctly different from oter securities in two ways: i) if a backed security defaults, investors can fall back on te underlying collateral pool and ii) banks are obliged to include te underlying collateral on teir balance seets (Scwarcz, 2011). Te central bank of te country as to pursue te goal of te programme, e.g. an inflation target, until te goal is completed for QE-policy 1 to effectively affect te expectations 9

17 Te Redistributive Effects of Quantitative Easing Notice tat in suc a QE-programme, te central bank purcases long-term as opposed to sortterm securities of te open market operations. A second distinction is te difference in scale between QE as described and open market operations. By te end of 2012 te Fed ad accumulated 3,152 trillion dollars in government, agency, and mortgage-backed securities (Fawley & Neely, 2013), wic corresponds approximately wit 20% of te GDP of te US in 2012 (according to te World Bank). Tis is in contrast wit te net open market purcases of te fed in 2011 and 2012, wic were 638 billion dollars and 34 billion dollars respectively (Fed, 2016b). If a central bank engages in QE-policy 1, te programme provides a stimulus for te economy in te following way: wen committed to QE, te long-term domestic securities of te central bank increases. Since tese securities are purcased wit money, te currency in circulation on te central banks liability side increases. Te long-term securities on te balance seet of te central bank consist of long-term government and ig-grade long-term private securities. Table 3 is a scematic representation of te balance seets of a central bank and banks. Note te difference between QE and open market operations tables 1 and 3. On te banks balance seets te following events occur: purcases of te central bank lead to a decrease in long-term securities on te banks balance seets. Te purcases of te central bank provide te banks wit new reserves in terms of money. Banks can use tese reserves to provide firms wit fres long-term loans or purcase long-term securities on te secondary market, effectively rebalancing teir portfolios and stimulating te economy. Central banks, toug, are not constraint by purcasing long-term securities from banks only. A QE-programme like tis can also purcase longterm assets from individual investors. Tis is similar to purcases from banks, namely tat individual investors sell part of teir long-term securities for money, wic tey use to purcase new securities, funding firms investments and terefore stimulating te economy. Tis tecnique is terefore suitable for every financial system. Even toug te financial systems of te US, te UK, Japan and te Eurozone are different, all central banks engaged in QE-policy 1. Te Fed and te BoE very quick in engaging in long-term asset purcases. Teir programmes started in 2008 and 2009 respectively. Bot largely focus on te purcase of government bonds on te secondary market (Fawley & Neely, 2013; Krisnamurty & Vissing- Jorgensen, 2011). In te beginning of te 2000s te BoJ combined improved central bank lending facilities and LSAP (Ugai, 2007). Te BoJ abandoned te programme in 2006 (Ugai, 2007) only to reinstate it in 2010 (BoJ, 2010a). Te ECB introduce LSAPs officially in 2015 (ECB, 2015a). During te course of all programme all central banks increased te amount wit wic tey purcased longterm securities. For more in dept information see appendix A Policy 2: Improved central bank lending facilities Improved central bank lending facilities (ILFs) are a second type of QE. Tis type of QE is essentially for bank-based financial systems, since te central bank provides long-term loans to banks in excange 10

18 Master s Tesis of Mark van der Plaat Table 4: Policy 2 ILFs Central bank balance seet Assets Liabilities Domestic securities Currency in circulation (+) Sort-term Deposits eld by private banks Long-term (+) Foreign securities Bank balance seet Assets Liabilities Reserves (+) Deposits accounts Loans Central bank loans (+) Securities Sort-term Long-term Table 4 provides a scematic representation of te balance seet of a central bank and of a bank wit respect to te effects of Improved central bank lending facilities, adapted from: (Blancard, 2010). Wen te central bank improves its lending facilities it effectively augments te long-term domestic assets on te asset-side of te balance seet by providing more loans to banks, erewit increasing te currency in circulation on te liability-side of te balance seet. On te banks balance seet on te asset-side te reserves increase, wic can be used for new investments and te central bank loans on te liability-side of te balance seet increase as well keep in mind tat tese are long-term loans. Table 5: Policy 3 Operation twist Central bank balance seet Assets Liabilities Domestic securities Currency in circulation Sort-term ( ) Deposits eld by private banks Long-term (+) Foreign securities Bank balance seet Assets Liabilities Reserves Deposits accounts Loans Central bank loans Securities Sort-term (+) Long-term ( ) Table 5 provides a scematic representation of te balance seet of a central bank and of a bank wit respect to operation twist, adapted from: (Blancard et al., 2010). Te central bank purcases long-term securities financed by selling of sortterm securities ereby increasing te long-term domestic securities and decreasing te sort-term domestic securities on te asset-side of te balance seet. On te banks balance seet te opposite appens, namely te sort-term securities increase and te long-term securities decrease on te asset-side ereby twisting te yield-curve. for a greater variety of eligible collateral (Fawley & Neely, 2013; Joyce et al., 2012). As a result, banks will be able to receive more long-term loans of te central banks on less collateral, increasing te lending facilities of banks (Fawley & Neely, 2013; Joyce et al., 2012). How tis form of QE works, is explained in table 4. Here, te central bank does not purcase long-term securities, but obtains tem by lending to 11

19 Te Redistributive Effects of Quantitative Easing banks; tis increases te long-term domestic securities and te money supply. On te banks balance seets, te liabilities increase wit te amount tey borrow from central banks and te assets increases wit te amount of money supply gained from te policy. Te idea is tat te banks will now lend out teir newly gained reserves to private firms or consumers, wo, in turn, use tis money to invest. Te interest rates on te loans decrease, due to an increased supply of loans (Fawley & Neely, 2013). Tis means tat te more fres loans are created, te iger te market liquidity. Te problem of QE-policy 2 is tat it inges on te willingness of banks to provide loans; in a crisis, banks may be less willing to lend money. Te ECB, before it committed to te in QE purcasing programmes, it engaged in ILFs. Tis measure is called te fixed-rate tender, full allotment (FRFA) programme. An FRFA involves repurcasing operations (repos) by te ECB for an increased amount of eligible collateral or assets (Joyce et al., 2012). A repo operation is wen a central bank sells assets wile obtaining te rigt and obligation to repurcase it at a specific time and at a specific price (De Haan et al., 2015, p. 162). Tis effectively means tat banks could borrow money from te central bank more easily at a fixed rate. Te BoJ as introduced tis type of QE in Te goal of tis was to cange te main operating target for money market operations from te uncollateralized overnigt call rate to te outstanding current account balances (CABs) eld by financial institutions at te BOJ, and provide ample liquidity to realize a CAB target substantially in excess of te required reserves (Ugai, 2007, p. 2) Policy 3: Operation twist QE-policy 3 is a variation on te QE purcasing programme. Te Fed used tis strategy and is known as operation Twist (Joyce et al., 2012), and as of yet no oter central bank as used tis tecnique (Fawley & Neely, 2013). Te total operation ad a size of $667 billion in total by te end of 2012 (Fed, 2013). Altoug operation twist does not increase te money in te market, it does increase te amount of liquid assets by selling sort-term securities for long-term securities. Te Fed designed it to ave an effect on te long-term and sort-term interest rates and was not aimed at a specific market (Joyce et al., 2012). Operation twist is terefore not a pure form of QE, but since te effects were meant to be economy-wide, tis study regards it as a form of QE. Wen engaged in operation twist, central banks sell sort-term bonds in order to purcase long-term bonds (Joyce et al., 2012) (Table 5). Tis tecnique will twist te yield-curve by decreasing te long-term interest rates relative to te sort-term interest rates. Similar to te asset-purcasing QE, tis form of QE is suitable for bot bank-based and marketbased financial systems. 3.4 Two transmission cannels of QE As discussed in section 3.3.1, from tis subsection onward QE is considered as an LSAP, considering all big central banks ave used suc a QE-programme (Fawley & Neely, 2013; Joyce et al., 2012). Tis makes it te most widely used and most known QE-policy. Te cannels discussed in tis subsection 12

20 Master s Tesis of Mark van der Plaat return in te illustrative model in section 6. In section 7, te oter two policies are separately entered into te basic illustrative model. Hereafter, section 7 discusses te effects of eac policy on te economy and income inequality. QE affects te long-term and sort-term interest rates in several ways. Te current section introduces te two most important cannels making QE-policy 1 possible. were r b t+i Generally te nominal yield of a n-year bond is as follows (Fawley & Neely, 2013): r b t+i b = r t+i + τ t+i,n, (2) is te expected nominal interest rate at time t + i on a long-term bond and r t+i is te average b expected overnigt (sort-term) nominal interest rate over te following n-years at time t + i, τ t+i,n te term-premium on a bond of n-years at time t + i. Tis equation illustrates tat tere are two possible cannels for QE to affect real bond yields, namely: i) te term premium may fall (te portfolio-balancing cannel) and ii) te expected pat 7 of te policy interest rates may fall (te signalling cannel). is Cannel 1: Te portfolio-balancing cannel Te first cannel, te portfolio-balancing cannel, affects te term-premium on long-term assets, because te central bank purcases long-term securities on te market. As will be explained in more detail in section 4, tese purcases lead to a lower supply of securities in te market, decreasing te term-premium on long-term assets, leading to a decrease in only te long term interest rate (Joyce et al., 2012; Kimura & Small, 2006). A term-premium is te mark-up on te interest on a specific medium- or long-term asset to compensate investors for te duration risk tey are exposed to. Duration risk relates to te lengt of a loan (Boquist, Racette, & Sclarbaum, 1975): te longer te loan, te furter away te final payment, te iger te risk of default. Investors will demand more return wen te duration risk is iger, wic is captured in te term-premium. Te key assumption of tis cannel lies in te idea of imperfect asset substitutability (Joyce, Tong, & Woods, 2011/2016). Under perfect asset substitutability, all assets can replace any oter asset irrespectively of te caracteristics of te assets suc as duration or te organisation tat issued it. Meaning tat if long-term securities are substitutable te purcase of one type of long-term security decreases te interest rate of anoter type as well. A second important element is te assumption of a balanced portfolio of institutional investors 8. A balanced portfolio means tat institutional investors require a well-diversified portfolio of investments. Tis means tat investors create portfolios wit te igest possible return subjected to te lowest risk possible by investing in multiple assets (Brealey, 7 An interest rate pat is evolution of a certain interest rate troug time. Wen te expected pat fall interest rates will decrease. 8 Institutional investors pool money of many individuals to invest for a specific goal or in a specific manner e.g. mutual funds, insurance companies and pension funds. All over te developed world institutional investors are important in te financial markets and ave a portfolio wit a large amount of assets (Ferreira & Matos, 2008). 13

21 Te Redistributive Effects of Quantitative Easing Myers, & Allen, 2011). Tis implies tat institutional investors ave a preferred abitat, meaning tat investors ave specific preferences for assets of specific maturities (Krisnamurty & Vissing- Jorgensen, 2011). If te portfolio is unbalanced, institutional investors will try to rebalance teir portfolios. Weter te preferred abitat demand is broad or narrow depends on te substitutability of te assets. Wen assets are igly substitutable, te preferred abitat is broad and vice versa. QE transforms a part of te portfolio of institutional investors from long-term government bonds and long-term backed private securities into money. Institutional investors now ave more liquidity, but on te oter and ave an unbalanced portfolio because money is an imperfect substitute to long-term government bonds. Tey use te newly acquired liquidity to rebalance teir portfolios, e.g. purcase long-term securities, until teir portfolios are balanced again. Te rebalancing of portfolios and QE itself lead to an increased demand in long-term assets (Joyce et al., 2011/2016), wic will cause te investors to demand less compensation for te duration risk (Fawley & Neely, 2013; Kimura & Small, 2006). In te illustrative model in section 6, tis cannel is responsible for te decrease in te long-term interest rates. Tere is some evidence for te portfolio-balancing cannel. For example, Cristensen and Rudebusc (2012) found tat te portfolio-balancing cannel dominated te signalling cannel in te UK. Tey used te announcements of QE in te UK as events tat triggered canges in te yields in gilts (government bonds from te UK). Tey found tat, overall, te yields on te long-term gilts decreased more tan te sort-term gilts. Tis was confirmed wen tey decomposed te response of te term structure of te instantaneous forward rates into forecasted future spot rates and instantaneous forward term premiums. Te effect sown by Cristensen and Rudebusc (2012) was also found by Joyce et al. (2012) and Ugai (2007) for te US and UK, and Japan respectively. Based on te evidence, te portfolio-balancing cannel returns in te basic illustrative model, because it is an important driver of te decrease in long-term interest rates. Because tis cannel is relatively compreensive and important for QE as an LSAP, it is discussed in more detail in section 4 using te paper of Kimura and Small (2006). Te studies discussed ere use te approac of decomposing te yield curves and ten extract te effect of te signalling. In suc an approac, te researcers split te total movements of te interest rates into several factors tat influence te movement of te interest rate. Te upside of suc a metod is tat specific factors can be isolated so tey can be studied separately. Te downside is tat splitting te interest rate movements into several factors is often by construct, in oter words: te influencing factors are dependent. Tis means tat splitting te yield-curve into specific factors is often difficult and ambiguous. Te results of tis tecniques are terefore ambiguous, as tey can be created by construct or be te real effect. 14

22 Master s Tesis of Mark van der Plaat Figure 2 Figure 2 provides a scematic representation of te spot-rate curve. Here te spot-rate curve represents all interest rates on all assets of different maturities from sort-term to long-term. Wen te signalling cannel functions properly, te sort-term interest rate decreases. Referring to equation (2) wen te sort-term interest decreases te long-term interest rate decreases similarly leading to an equal decrease over te entire spot-rate curve, decreasing te sport-rate curve to spot-rate Cannel 1: Te signalling cannel Te second cannel troug wic QE affects long-term interest rates on securities is te signalling cannel. As can be seen in equation (3), tis cannel works troug te expectations of future interest rates of te market. Rewritten, te expectations about te interest rate are te following (Rudebusc, 1995): n 1 r d t = 1 n [r t + E t r t+j ], (3) j=1 were r t d is te average expected overnigt nominal interest rate at time t, r t is te nominal interest rate n 1 D at time t and E t+i j=1 r t+i+j are te expectations of all nominal interest rates in te future over n 1 periods. Equation (3) states tat if economic agents expect lower interest rates in te future, te nominal sort-term interest rates today will decrease accordingly. Weter te agents believe a low interest rate to persevere depends on te credibility of QE and te communication of te QE-programme by te central bank. Announcements of central banks give economic agents (or te market) information about te future state of te economy and policy pat of te central bank (Cristensen & Rudebusc, 2012). Using tis information, tey can infer weter te interest rates will decrease or increase. In many teoretical models, a central bank is credible and te announcements are credible wen te central banks attains a iger expected utility by following te announcement compared to wen te central bank 15

23 Te Redistributive Effects of Quantitative Easing reneges (Blinder, 1999). Tis cannel resembles forward guidance in tat it influences te interest rates troug te expectations of economic agents. Figure 2 sows te nominal spot-rate curve of securities wit several maturities. Te figure sows tat wen te time to maturity of a security increases te corresponding interest rates increases as well. In figure 2 a decrease in te sort-term interest rate is a downward sift of te spot-rate curve to spot-rate. In oter words, te nominal interest rate decreases for all maturities. For Japan Ugai (2007) presented some confirming evidence for te signalling cannel in multiple studies. All te papers discussed by Ugai ave found a lowering effect on te yield curve by te signalling effect of te BoJ during te first period of QE (as described above). Furtermore, te majority of te papers discussed by Ugai found a larger decrease in te yield curve under QE tan under te prior zero-interest rate policy. Te results presented ere suggest downward pressure on te yield curve of te Japanese government bonds in te period due to QE, even more so tan te zerointerest rate policy could acieve. A similar story emerges for te QE1 and QE2-programme of te Fed (see Appendix A). Krisnamurty and Vissing-Jorgensen (2011) found tat yields significantly declined several times during te QE1 programme for most maturities of te treasury bonds and MBSs, and all of te agency bonds. Tey use similar tecniques as te papers discussed in Ugai (2007). Wen tese declines were split into te several cannels, tey found tat te signalling effect on treasury bonds wit a maturity of five to ten years is associated wit a 20 to 40 basis points decrease. Te autors found similar evidence for te QE2 period, wit a sligtly less strong downward pressure on te yield curve tan during QE1. Based on te evidence of te signalling cannel in Japan and te US, one can assume tat tis cannel may be salient during times of QE and is an important factor in te decrease of long-term interest rates in multiple countries. Tis cannel will terefore return in te basic illustrative model in section 6. 4 Transmission cannel 1: Te portfolio-balancing cannel (Kimura & Small, 2006) Te portfolio-balancing cannel is one of te two cannels tat is used in te basic illustrative model in section 6. Te framework of te basic illustrative model is based on te paper of Gertler and Karadi (2013), in wic tis cannel togeter wit te signalling cannel is introduced. Tis section discusses te portfolio-balancing cannel based on Kimura and Small (2006). Firstly, te researc topic of te paper is introduced. Secondly, a model of te portfolio-balancing cannel in a CAPM-setting is discussed. 4.1 Te setting of te paper Kimura and Small (2006) study te effects of te portfolio-balancing cannel during te period of QE in Japan tat started in Marc 2001 wit a formal model and empirically. According te autors, some 16

24 Master s Tesis of Mark van der Plaat believe te portfolio-balancing cannel did not function properly during te QE-period, because te capital position of financial intermediaries ad been impaired due accumulation of non-performing loans 9. Tis lead to a fall in asset prices and a subsequent recession. As a result, financial intermediaries were less willing to take on portfolio risks by purcasing risky securities. Tus, te QE-programme of te BoJ was seen as ineffective, because te financial intermediaries and institutional investors were reluctant to purcase new assets wit te increased reserves. Te autors argue oterwise. Tey argue tat financial intermediaries and institutional investors in a crisis are willing to rebalance teir portfolios, ereby decreasing te long-term interest rate, because tey are averse to business cycle risks. Business cycle risks are te variations in return on securities due to te economic cycle (Perez Quiros & Timmermann, 2000). Tis means tat te iger te correlation of securities wit te business cycle, te more te returns will decrease during an economic crisis. Te underlying mecanism argued by te autors is as follows: wen in an economic downturn, investors 10 invest more in safe assets, suc as government bonds, wic are negatively correlated wit business cycles. Te QE-policy 1 transforms government bond-oldings of all investors into money, wic leads to a more pro-cyclical portfolio of te financial intermediaries and institutional investors. In turn, tese investors will rebalance teir portfolio in order to create a more counter-cyclical portfolio. Tis rebalancing beaviour increases te demand for counter-cyclical securities and decreases te demand for pro-cyclical securities. As a result, interest rates on cyclical securities equities and low-grade private debt securities will rise and interest rates on counter-cyclical securities government bonds and ig-grade private debt securities will decrease. Beside te model, te autors empirically test teir ypotesis tat QE leads to more portfolio rebalancing and tus a decrease in long-term interest rates. Te autors find two effects of te portfoliobalancing cannel. Firstly, te QE-policy increased te demand for counter-cyclical assets tat are substitutes for te long-term Japanese government bonds, decreasing teir interest rates. Conversely, tis lead to a decline in demand for pro-cyclical assets, increasing teir risk-premiums. Te effect on pro-cyclical assets is small but significant and is conditional on close to zero policy interest rates. Namely, in above-zero interest rates situations te central bank can alter te policy interest rate downward to create a similar effect. Secondly, te QE-policy of te BoJ leads to a decrease in volatility and in corresponding returns in some asset markets, decreasing te overall market risk. In addition to te evidence provided in section 3.4.1, te evidence provided by Kimura and Small (2006) indicate tat te portfolio-balancing cannel is important for te functioning of QE. 9 Are loans were te borrower defaults on te payments. 10 Eiter institutional investors or financial intermediaries. 17

25 Te Redistributive Effects of Quantitative Easing 4.2 Portfolio-balancing cannel in a CAPM-setting Kimura and Small (2006) propose a portfolio balancing model based on te CAPM 11. Te model is built around te premise tat some financial asset prices rose wile oters fell. If te signalling cannel were te driver of te canges in assets prices, one would expect every asset price to decrease. Te autors use te CAPM to define te asset pricing and enter a measure of te market return as a function of business cycles into te model to illustrate te effects of te portfolio-balancing cannel. Kimura and Small (2006) define te asset pricing according to te CAPM as follows: E[r j f t r t ] = m j E[r m t r f Cov[rt, r t ] t ] Var[r m, (4) t ] were r t j is te return on asset j, r t m is te return on te market portfolio, r t f is te risk free rate of return, E[r t j r t f ] is te risk-premium on asset j, E[rt m r t f ] is te risk-premium on te market portfolio, Cov[r t m, r t f ] is te covariance of te return on te market portfolio and te risk free rate of return, Var[r m t ] is te variance of te return on te market portfolio and E[r t m f r t ] is te market price of risk. Var[r t m ] Assumed is tat te market portfolio comprises of several types of assets, j, suc as money, equities, government bonds and different types of corporate bonds. In a few steps, te autors rewrite equation (5) as (see appendix B for more details): E[r t j r t f ] = kρ[rt m, r t j ] Var[r t j ] Var[r t m ], (5) were k is constant and equal to te market price of risk, E[r t m f r t ] and Cov[r m t, r f t ] is split into te Var[r t m ] correlation coefficient and te variances. Equation (5) expresses tat te excess return on asset j, defined as te risk-premium on top of te risk free rate of return, depends on te volatility of te market and te correlation between asset j and te market, wic means tat if eiter cange, te risk-premium on asset j canges as well. To define te asset returns and to model te economic situation, i.e. an economic recession and low policy rates, in wic te BoJ engaged in long-term asset purcases, te autors introduce a measure of business cycle downturns. For an expositional case, te autors assume tat te ex post returns are governed by: r t j = λ 0 j + λ 1 j Z t + ε t j, (6) were Z t is te variable for business cycles and ε t j captures te specific return of asset j. Te autors assume tat Z t < 0, meaning tat tere is a business cycle downturn. Equation (6) sows tat te economic situation of a country affects te return on asset j. Te autors furter assume tat 11 Original notation is used in tis section, see appendix G for all symbols 18

26 Master s Tesis of Mark van der Plaat Cov[Z, ε t j ] = 0, j. Wit te specification of te asset returns (equation (7)), te autors define te return on te market portfolio: r m t = λ 0,m + λ 1,m Z t + ε m,t = j j λ j 0 + w j λ j 1 Z t N j=1 N j=1 N j + w j ε t j=1, (7) were w j is te sare of asset j in te market portfolio and λ 1,m is a measure of cyclicality of te portfolio. Assumed is tat te market portfolio is pro-cyclical λ 1,m > 0. As argued before, interest rates of pro-cyclical and counter-cyclical securities could be different. In te model, tis means tat λ 1 j differs between asset classes. For government bonds λ 1 N < 0 (for wic j = N), meaning tat tese are counter-cyclical securities. Investors are more inclined to invest in tese safe government bonds in an economic crisis. Investment beaviour like tis is associated wit a lower interest rate and capital gains in economic downturns due to te increased demand. Equities are more pro-cyclical tan government bonds, implying tat λ 1 j > λ 1 N and λ 1 j > 0. Te autors suggest tat iggrade private debt securities beave like similar to government bonds and low-grade government bonds like equities. Te following analysis assumes tat government bonds and ig-grade private debt securities are strictly negative, and equities and low-grade private debt securities are strictly positive. Te autors substitute equation (7) in equation (5) and ereby illustrate te effect of QE a decrease in w N on te variance of te market portfolio and te covariance of asset j and te market, tereby illustrating te effect te workings of te portfolio-balancing cannel Transmission cannel 1.1: Canges in variance Te variance of te market portfolio is (see appendix C for te derivation): N var[r m j t ] = ( w j λ 1 j=1 ) 2 N var[z t ] + w 2 j j var[ε t ], (8) j=1 were bot variances of te business cycle, var[z t ], and te asset specific return, var[ε t j ], are positive. Differentiating var[r t m ] wit respect to w N yields: var[r t m ] w N N j = 2 ( w j λ 1 j=1 ) λ 1 N var[z t ] + 2w N var[ε t N ]. (9) It means tat te first term on te rigt-and side is negative due to te assumption of λ 1 N < 0 and te N j second term is positive. Tere could be situations in wic 2( j=1 w j λ 1 )λ N 1 var[z t ] > 2w N var[ε N t ], wic means tat te variance of te market portfolio of financial intermediaries and institutional investors increase if te central bank engages in QE. Returning to equation (5). An increase in te market variance due to QE leads to a lower risk-premium in te market portfolio of financial intermediaries and institutional investors, creating an incentive to invest in new long-term or iger risk assets because te 19

27 Te Redistributive Effects of Quantitative Easing Table 6 Affected part of te CAPM Variance of te market portfolio Covariance of te market portfolio financial intermediaries and institutional investors are business cycle risk averse, decreasing te termpremium long-term assets as defined in equation (2). Effect of LSAPs Counter-cyclical securities Pro-cyclical securities If 2( N j=1 j w j λ 1 )λ N 1 var[z t ] > 2w N var[ε N t ], tan variance of te market portfolio increases for bot counter-cyclical and pro-cyclical securities, leading to a decrease in te termpremium. Decreases for counter-cyclical securities, leading to a decrease in te term-premium. Increases for pro-cyclical securities, leading to an increases in te termpremium. Table 6 provides a summary of te findings of te paper of Kimura and Small (2006). LSAPs ave an effect on te variance and te covariance of a portfolio of an investor. Wen te variance decrease due to LSAPs, te term-premium on countercyclical and pro-cyclical securities decreases. Te covariance of te market portfolio decreases for counter-cyclical and increases for pro-cyclical securities leading to a respective decrease and increase of te term-premium Transmission cannel 1.2: Canges in covariance Te second result of te model are te canges in covariance. Te autors give te covariance as follows: Cov[r t m, r t j ] = λ 1 j λ 1,m Var[Z t ] + w j Var[ε t j ]. (10) Wen differentiating Cov[r t m, r t j ] wit respect to w N te first-order conditions are: Cov[r t m, r t j ] w N = (λ 1 N λ 1 N + λ 1,m )Var[Z t ] + w j Var[ε t N ] > 0, j = N (11) Cov[r m t, r j t ] = λ j w 1 λ N 1 Var[Z t ] > N < 0 as λ j > 1 < 0, j N (12) Equation (11) states tat outrigt purcases of long-term government bonds of te central bank will decrease te covariance of te market portfolio and government bonds, because λ 1 N < 0. Tis decreases te risk-premium in equation (5). Te covariance of te market portfolio and ig-grade private debt securities sow a similar reaction (λ 1 j < 0), owever te effect of te covariance of te market portfolio and purcases of ig-grade private debt is less strong. Te outrigt purcases of long-term government bonds will increase te covariance between te cyclical assets and te market portfolio (λ 1 j > 0), see equation (12). Tis will increase te risk premium in equation (5). In conclusion, te model of Kimura and Small (2006) suggests two effects of QE as outrigt purcases of government bonds in a situation wen tere is a business cycle downturn and near-to-zero interest rates. Firstly, te variance of te portfolio of financial institutions or investors could increase, suggesting 20

28 Master s Tesis of Mark van der Plaat an increase in cyclicality of te portfolio. Tis will lead to portfolio rebalancing beaviour of tese private agents and a subsequent decrease of te risk-premium on government bonds. Secondly, QE decreases te covariance between te market return and return on government bonds, meaning tat te risk premium on government bonds will decrease. Hig-grade private debt securities sow similar beaviour, albeit less strong. Equities and low-grade private debt securities, owever, sow opposite beaviour: purcases of government bonds lead to an increase in te risk-premium because investors seek to rebalance teir portfolio wit counter-cyclical assets. Table 6 presents a summary of te findings of te model of Kimura and Small (2006). 5 Policy 1: Large-scale asset purcases (Gertler & Karadi, 2013) Tis section discusses te paper of Gertler and Karadi (2013), wic serves as te basis for te basic illustrative model in te next section. Te autors setup a DSGE-model, in wic banks are able to invest in private securities and government bonds in order to model an LSAP as a monetary policy tool witin a macroeconomic environment. Tis section only discusses te relevant matematical setup of te model. 5.1 Setting of te paper Gertler and Karadi (2013) propose QE as an LSAP and teir model is based on te tree periods of QE te Fed as initiated see Appendix A. Te purpose of teir paper is to develop a macroeconomic model tat presents a unified approac to analysing [QE] as a monetary policy tool (Gertler & Karadi, 2013, p. 7). Teir DSGE model presents a compreensive economy wit many actors. Te most important actors are banks, te central bank and ouseolds. Te illustrative model proposed in te current study only considers te important actors, meaning tat te oter actors are not presented. As a result only te important actors are discussed in more detail. Tere are two reasons for omitting tese actors. Firstly, including tese actors does not provide more information as to ow te central bank affects te excess returns, and consequently te banks and ouseolds in tis model. Secondly, tese actors are included by Gertler and Karadi (2013) to create a general equilibrium. However, te current study is not concerned wit investigating te general equilibrium, but wit te basic mecanisms of QE. Te first actor is te central bank. In contrast to common believe, te autors argue tat in a situation of economic crisis te central bank replaces part of te banks intermediation to decrease te excess return tat ave occurred due to te crisis. Te excess returns are defined as te difference between te rate of return in market wit arbitrage friction and markets wit frictionless arbitrage. Wen tere is frictionless arbitrage, banks and ouseolds are able to fully capture te excess returns on te market, meaning tat tere are no suc excess returns occur on te market. Te intermediation of te central bank leads to a decline in excess returns. Te central bank intermediation is as follows: te central bank sells sort-term government debt and wit te proceeds purcases private securities and 21

29 Te Redistributive Effects of Quantitative Easing government bonds in te secondary market. Central bank intermediation is less efficient tan bank intermediation, te autors posit. Te sort-term debt te central bank issues is very safe and creates a way for te central bank to elastically obtain funds 12. Banks are intermediaries in te model and are, in contrast to te central bank, unable to elastically obtain funds from te market due to an agency problem. Banks divert a portion of teir netequity to te owners of te banks, te bankers. However, te owners of te deposits, te workers, do not want tese practices, because it increases te cance of te bank going bankrupt. If te bank goes bankrupt, te depositors lose teir money. Tat is wy te workers witdraw part of teir deposits if te banks divert money to te bankers. Tis means tat te bankers are only able to divert a specific amount of money from te bank before te workers punis te banks by witdrawing a part of te deposits. Houseolds ave multiple functions in te model. Firstly, ouseolds supply money in te form of deposits to banks and in te form of sort-term government debt to te central bank. Tis ensures tat te central bank and te banks are able to function as intermediates. Secondly, ouseolds are able to directly invest into private securities and government bonds albeit not as efficiently as banks. Tirdly, ouseolds are owner of te banks and are willing to divert funds of te bank to te ouseolds. Te autors make a distinction between ouseolds tat are owners of te banks, bankers, and tose wo do not, workers. In general, te autors argue tat government bond purcases are less efficient tan purcases of private debt securities because te limits to arbitrage are weaker in te markets for government bonds tan in markets for private debt securities. Reason being tat te liquidity in te market for government bonds is greater tan tat of te private securities markets. Wen a market is liquid, transactions are abundant and do not affect te prices of te assets (Brunnermeier & Pedersen, 2009). Notice tat ere te purcases of government bonds are less efficient due to te greater market liquidity, wereas Kimura and Small (2006) argue tat tese purcases are more efficient due to te counter-cyclicality of te longterm government bonds. In conclusion, te autors find tat te transmission to real output and inflation of QE is very similar to conventional monetary policy. Unlike conventional monetary policy, QE is useful at te zerobound interest rates. In addition, te autors find tat QE is effective in decreasing te long-term interest rates. Besides te reduction in long-term interest rates, sort-term interest rates are less like to rise over a specific time-period due to te expectations of low interest rates. Te remainder of tis section reviews eac of te tree actors in more detail. 5.2 Te model Before reverting to te players in te model, te private securities and te government bonds in te market are discussed, in wic ouseolds, banks and te central bank invest in. Private securities are 12 Tis means tat te supply of sort-term government debt is always met by te demand for it. 22

30 Master s Tesis of Mark van der Plaat loans to non-financial private companies tat use it for investing in teir own production process. Te government issues government bonds in order to finance its deficit. Bot are longer tan one period and are terefore defined long-term securities. Note tat all te signs used ere are tose used in te paper of Gertler and Karadi (2013). Te total supply of bot private securities and government bonds is as follows: S t = S pt + S t + S gt (13) B t = B pt + S t + S gt (14) were S pt and B pt are te total amount of private securities and government bonds tat are intermediated by banks, S t and B t are te total amount of private securities and government bonds eld by ouseolds and S gt and B gt are te total amount of private securities and government bonds eld by te central bank Houseolds All ouseolds consume, save and supply labour. Te ouseolds save by lending funds to banks or to te central bank. More importantly, a ouseold can be two types, eiter worker or banker. Workers earn labour income, wereas bankers manage banks and transfer any earnings to te ouseolds. At any time, tere are 1 f members of te ouseold workers and f bankers; bot types of members can switc occupation troug time. Tere is a probability of σ tat te banker will stay banker next period wit an average survival time of 1. Te model as a finite orizon to prevent bankers from cumulating 1 σ enoug resources to fund all investments wit teir own capital. Te ouseold provides new bankers wit a start-up fund equal to X (1 σ)f. Te autors use tis as a scematic representation of ow ouseolds evolve trougout time; since in reality less-endowed ouseolds gain wealt and wellendowed ouseolds lose wealt. Te utility of te ouseolds is a follows: u t = E t β i [ln(c t+i C t+i 1 ) χ 1 + φ L t+i i= φ ], (15) were te utility of te ouseold, u t, consists of te current consumption, C t+i, minus te discounted consumption of te previous period, C t+i 1, and te labour time weigted by a factor of relative preference to work, χ L 1+φ 1+φ t+i. Here is χ te relative risk aversion of ouseolds and φ te inverse elasticity of work effort wic is te sum of te substitution elasticity and a measure of people s willingness to trade work for consumption over time (Reicling & Walen, 2012). Furtermore, E t is te expectance operator and β i is te subjective discount rate. Te ouseold utility function states tat te utility of te ouseolds increase wen present consumption relative to past consumption increase, but decreases wen te ouseolds provide more labour. Te ouseold budget constraint is as follows:

31 Te Redistributive Effects of Quantitative Easing C t = W t L t + Π t X + T t + R t D t 1 D t, (16) were te consumption, C t, consist of te labour income, W t L t, te transfers from banks to ouseolds, Π t, te total transfer for ouseold members to become banker, X, te lump-sum tax from te government to te ouseold, T t, te gross real return on deposits from te period t 1, R t D t 1, and te total quantity of sort-term debt te ouseolds acquire, D t. Te sort-term debt of te ouseolds consists of deposits eld at te bank and sort-term government debt. Bot te deposits and sort-term government bonds are one period assets. Because te budget constraint in equations (16) does not allow for direct investment into securities, ouseolds ave to use intermediaries to invest teir money into securities. In te next step, te autors allow ouseolds to purcase securities directly witout intermediation of banks. Adding te possibility to invest directly into securities gives: C t + D t + Q t [S t k(s t S ) 2 ] + q t [B t k(b t B ) 2 ] = W t L t + Π t X + T t + R t D t 1 + R kt S t 1 + R bt B t 1, (17) were te olding costs for private securities and government bonds are 1 k(s 2 t S ) 2 and 1 k(b 2 t B ) 2 respectively, te return from period t 1 for private securities and government bonds are R kt S t 1 and R bt B t 1 respectively, and te investments in new securities of bot types are Q t S t and q t B t containing te respective market price and te amount invested at time t. Te costs are introduced to prevent te ouseolds to engage in frictionless arbitrage, owever, tere are certain amounts of assets te ouseolds can old costless. Te autors argue tat tis cost structure is a simple representation of te limited participation in asset markets tat lead to incomplete arbitrage. Finally, te discount rate of te budget constraint of te ouseolds is equal to te marginal rate of substitution of te ouseolds. Te first-order conditions are as follows maximised to C t, L t, D t, S t and B t : uc t W t = χl t φ ; (18) E t Λ t,t+1 R t+1 = 1, Λ t,t+1 = β uc t+1 uc t ; (19) S t = S + E tλ t,t+1 (R kt+1 R t+1 ); k (20) B t = B + E tλ t,t+1 (R bt+1 R t+1 ). k (21) Equation (18) states te coice of te ouseolds to supply labour, equation (19) specifies te preferences of te ouseolds for deposits. In equation (18) wen te wage rate, W t, increases, ouseolds are more inclined to provide more labour. If te expected safe sort-term interest rate in equation (19), R t+1, increases, ouseolds are more inclined to old deposits. Equations (20) and (21) state tat te demand for eac asset above its frictionless capacity level is increasing wen te excess returns are ig conditional to te marginal costs. Important to note is tat Λ t,t+1, is te marginal rate of substitution of ouseolds, tis is used as a discount rate for te ouseolds as well as for banks. 24

32 Master s Tesis of Mark van der Plaat Especially equation (20) and (21) are interesting for te workings of QE. Te equations state tat ouseolds will invest an amount into securities tat is at least equal to te frictionless amount. Investment above tis amount depends on two aspects, te first is te excess returns on te specific securities and te second are te marginal costs. If te excess returns on securities will increase, ouseolds are more inclined to invest in te specific securities. Te ouseolds are less willing to invest in securities if te marginal costs of investment increase Banks Banks are able to fully participate in financial markets and ave an intermediary function. Te banks are constraint in ow muc money tey can obtain from ouseolds due to te agency problem as aforementioned. Te autors set up te optimisation problem for a single bank before aggregating banks. Tis section does not mention te aggregation of te banks, because it does not cange te argument of te paper. First, te single bank s utility function is a function of te net income of te bank and of an agency problem. Te utility function is given by V t = E t (1 σ)σ i 1 Λ t,t+i n t+i, (22) i=1 were σ is te probability tat te banker stays a banker in te next period and n t+i is te total amount of equity of te bank at time t+i. Te discount rate of te bank, Λ t,t+i, is equal to te marginal rate of substitution of te ouseolds. Te bank s utility function says tat if te cances of remaining a banker increase or te expected discounted wealt increases, te utility increases. Tere are two constraints to wic te utility function of te bank is constraint, te balance seet constraint and te incentive constraint. Tese are: Q t s t + q t b t = n t + d t, (23) were n t = R kt Q t 1 s t 1 + R bt q t 1 b t 1 R t d t 1, and (24) V t θq t s t + Δθq t b t. (25) Were s t and b t are te amounts te bank invest in private securities and government bonds respectively, n t is te net amount of equity of a bank at time t, d t are te amount of deposits obtained from ouseolds, θ is te amount of funds te bank can divert of te private securities and Δθ is te amount of funds te bank can divert from te government bonds; 0 Δ < 1. Te autors define te diversion of funds like tis, because te autors argue banks can more easily divert funds from teir private loan portfolio because ouseolds ave more difficulties in monitoring tem tan government bonds. Equations (23) and (24) are te bank s balance seet constraint, stating tat te bank s investments are constraint by te balance seet of te bank and cannot invest unlimitedly. Te left side of equation (25) depicts te total assets of a bank consisting of total investment in private securities and government bonds and te rigt side are te liabilities of a bank consisting of te net wort in equity of te bank and te total amount of 25

33 Te Redistributive Effects of Quantitative Easing received deposits. Te equity of te bank evolves as equation (24) suggests te sum of te total return on private securities and government bonds of te previous period minus te cost of te deposits of te previous period. Equation (25) is te incentive constraint and effectively says tat tat banker can gain a specific sum equal to te rigt-and side but wen doing so loses in francise value (te left-and side). Te effect of te incentive constraint can be seen in te following equations maximized wit respect to R kt+1, R bt+1 and R t+1 : E t Λ t,t+1 (R kt+1 R t+1 ) = λ t 1 + λ t θ, Λ t,t+1 Λ t,t+1 Ω t+1 ; (26) λ t E t Λ t,t+1 (R bt+1 R t+1 ) = Δ θ; (27) 1 + λ t were te expected excess returns on private securities and government bonds are E t Λ t,t+1 (R kt+1 R t+1 ) and E t Λ t,t+1 (R bt+1 R t+1 ) respectively, λ t is te lagrangian multiplier of te incentive constraint (equation (26)) and te Λ t,t+1 is te augmented stocastic discount factor of te bank Ω t+1 is te sadow value of a unit of net wort to te bank at time t+1. If te incentive constraint is binding or not, as two interpretations. First, wen te incentive constraint is not binding, i.e. λ t = 0, t, banks acquire assets to te point were te discounted return on eac asset equals te discounted costs of tese assets. A QE-programme of te central bank would in tis situation only lead to a displacement of intermediation from banks and ouseolds to te central bank witout any effect on te asset prices. Second, wen te incentive constraint is binding, limits to arbitrage will emerge tat could lead to positive excess returns in equilibrium, meaning tat a QE programme in suc a situation increases te demand for securities and tereby decrease te excess returns. Moreover, notice tat te effect of QE on te excess returns of government bonds are smaller tan te effect on te excess returns of private securities due to te definition of Δ Central Bank Te last agent, te central bank can purcase eiter safe private securities, S gt, or long-term government bonds, B gt eac for its respective market price. To finance tese purcases te central bank issues riskless sort-term debt securities. Contrary to banks, te central bank does not ave an agency problem for it onours its debt. Te balance seet constraint of te central bank is: Q t S gt + q t B gt = D gt. (28) Equation (28) states tat te central bank can expand its investments in securities equal to te expansion of sort-term government debt. Here te autors assume tat if te central bank makes any profits it is transferred to te treasury and money transfers from te treasury cover any losses. Lastly, te autors note tat arbitrage is weaker for government bonds and tat QE sould move te yield on government bonds less tan te yields on private securities, tis can be depicted as: 26

34 Master s Tesis of Mark van der Plaat E t Λ t,t+1 (R kt+1 R t+1 ) = ΔE t Λ t,t+1 (R bt+1 R t+1 ). (29) Equation (29) means tat wen te expected discounted excess returns on private securities decrease, te excess returns on government bonds only decrease by a fraction of it. Tis is contrary to te idea of Kimura and Small (2006), wo argue tat te effect of purcasing of government bonds is more effect due to te ig counter-cyclicality of tese securities. In conclusion, Gertler and Karadi (2013) present a model in wic actors interact wit eac oter. Te most important actors for te current study are ouseolds, banks and te central bank. Te most important notions of te model are: i) in a financial crisis te excess returns on assets increases, ii) te central bank replaces part of te intermediation of banks in a crisis situation, decreasing te excess returns, iii) te ouseolds are able to participate in te financial market but not efficiently, iv) ouseolds are eiter workers or banks, meaning tat different effects on bot types of ouseold members could occur and v) te central bank is able to elastically obtain funds from ouseolds, wo supply funds to te financial intermediaries and te central bank. Te general mecanism of te model is wen excess returns of assets in te economy are ig due to a financial crisis and banks are unable to fully capture tese excess returns te central bank can decrease te excess returns in te economy by pursuing QE effectively increasing te demand on tese assets. Consequently, a decrease in te excess returns sould lead to a decrease of investments in securities by te ouseolds and te banks. Te autors, owever, do not elaborate on te mecanism of ow asset-purcases affect te excess returns, tis is important for te basic illustrative model and will terefore be added. 6 Policy 1: Te basic illustrative model Tis section introduces te illustrative model. Te model of Gertler and Karadi (2013) is taken as a departure. Te illustrative model proposed in te current study adds two transmission cannels, te portfolio-balancing cannel, see section 4, and te signalling cannel, see section 3. Te portfoliobalancing cannel is especially interesting, because it clearly illustrates te effects of QE-policy 1 and QE-policy 3 on te long-term interest rates. Te signalling cannel is interesting in te illustrative model, for it demonstrates te effect of QE-policy 1 on te sort-term interest rates, an aspect tat is missing in te model of Gertler and Karadi (2013). Te model of Gertler and Karadi (2013) is simplified for a tree reasons. Firstly, te current study is not interested in investigating a general equilibrium, but solely to te workings of QE. A simplification of teir model terefore suffices to illustrate te effects of QE. Tis means tat only te ouseolds, banks and te central bank are used in te current study. As a result, some variables presented in te previous section eiter are simplified or drop out entirely. Secondly, including more actors tan te tree aforementioned to te model probably does not lead to different results. Te current study is interested in te transmission of QE to ouseolds. However, banks are added because tey directly affect te ouseolds and are directly affected by QE. Tirdly, 27

35 Te Redistributive Effects of Quantitative Easing te additions of te two transmission cannels require different mecanics tan present in te model of Gertler and Karadi (2013). As a result, some mecanics unique to teir model are omitted or canged to serve te two transmission cannels. Te notation is, were possible, equal to tat in section 4 and 5, see appendix G for a description of te notation used. Besides simplification, tere are a few canges to te basic framework of Gertler and Karadi (2013). Firstly, te definition of te excess returns of Gertler and Karadi (2013) differs. As argued in section 3.4, QE sould ave an effect on te term-premium (Fawley & Neely, 2013) and not on te difference between te frictionless interest rate and te interest rate on a market wit market frictions. Te results may be very similar, toug in te remainder of te study te excess returns are defined as te difference between te long-term interest rate and te sort-term interest rate. Tis as te additional effect tat te agency problem of banks is ineffective in affecting te excess returns and tis terefore omitted from te model. Secondly, te framework of Gertler and Karadi (2013) does not elaborate on te mecanisms of QE and only argues tat te central bank increases te total market demand in assets. To illustrate te effects of QE in more dept, te balance portfolio cannel and te signalling cannel are added to te model separately, meaning tat te central bank is not defined as a player wit an optimisation problem but enters exogenously as two separate cannels. Consequently, an additional assumption is made, namely te central bank in unconstraint and te funding of te central bank does not return in tis model; due to te new assumption, ouseolds only old bank deposits. Tirdly, te long-term government bonds and te long-term ig-grade private securities of te model of Gertler and Karadi (2013) are combined for reasons of parsimony and are encefort called counter-cyclical securities. Notice tat ouseolds and banks can only invest in tese securities. Section 7.3 allows ouseolds and banks to investment in pro-cyclical securities. Fourtly, tere are two types of interest rates, a sort-term interest rate on deposits and long-term interest rate on counter-cyclical securities. Te remainder of te section is set up as follows. Firstly, te model setup is presented. Tereafter, te general results are presented. Lastly, te perturbation results are presented, ere te results of te QE-policy are perturbed to ceck te effect of QE on te interest rates. Tese canges are ten linked to te results of te ouseolds and banks leading to four propositions. 6.1 Te model set-up Te model setup is divided in to te timing of te events, ouseolds, banks and te central bank. 28

36 Master s Tesis of Mark van der Plaat Figure 3 Figure 3 provides a timing of events of te model. Te time span of te model is to infinity. For te analysis tree moments are of special interest. At time is t ouseolds and banks optimise teir relative optimisation problems, after tis te central bank engages in QE, leading to te primary effects i.e. before te ouseolds are able to react on te policy. At time t + 1 ouseolds and banks are able to react on te policy by re-optimising teir respective optimisation problems. Te corresponding analysis is as follows: firstly te first-order conditions are calculated, secondly, te QE-variables are perturbed and ten te first-order conditions tat are affect by te perturbation is discussed Timing of events Unique to tis illustrative model is te timing of events. Te definition of te timing of te events is important for understanding te four propositions tat follow in section 6.3. Te model as an infinite time orizon of wic tree events are specifically important for te analysis. Figure 3 provides a scematic illustration of te timing of te events. At time is t, ouseolds and banks optimise teir respective optimisation problems. Houseolds coose teir optimum level of labour, deposits and investments in counter-cyclical securities, wereas banks only coose teir optimal level of countercyclical securities. After ouseolds and banks ave optimised, te central bank commences te QEpolicy. Important to notice is tat at tis point in time ouseolds and banks cannot react on te policy, meaning tat te perturbation results of te QE-policy on te original equilibrium at time is t lead to te primary effects. After te central bank engages in QE, ouseolds and banks are able to react on te policy at time is t + 1. At tis time ouseolds and banks re-optimise teir respective portfolios based on te perturbation due to QE, leading to secondary effects of QE. 29