INTEREST RATES. REAL INTEREST RATES Mishkin, P. 123-125.

INTEREST RATES

REAL INTEREST RATESMishkin, P. 123-125

Nominal and Real Interest Rates• Nominal return represents how much money you will

receive after 1 year for giving up 1 dollar of money today• Real return represents how many goods you can buy if

you give up the opportunity to buy 1 good today.• Nominal interest rate is money interest rate. Real interest

rate is goods interest rate.

Interest on a Simple Loan

• Interest rates are always measured in annual terms.

• Set T = # of years of a loan (may be fraction)

A simple loan implies a loan of principal and a single repayment which is the principal plus interest.

(1 )t Tt+T t tRepayment i Principal

• Imagine a 1 year loan [T =1]: The lender gives up some goods to make a loan and will buy goods in the future with the repayment.

• If the price of goods at time t is Pt, the foregone current goods are

• The goods value of the future repayment is

PrincipalP

1 t+1t

Repaymenti

Principal

Repayment

Real Interest Rate

t+1 t+1

t+1 tt

tt t t t

Repayment RepaymentP Principal

rPrincipal P

ir r i

• The real interest rate on the loan is defined as the future goods received relative to current goods foregone

Importance of the Real Interest Rate• Real interest rate is the intertemporal price of purchasing

power.• If you buy 1 unit of purchasing power today, you give up 1+r units

of future purchasing power. • It is the direct cost of credit for borrowers.

• An important determinant of the intertemporal allocation of demand.

Ex Ante Rate and the Fisher Effect

1EA FORECAST

t t ti r

• Savings and investment decisions must be made before future inflation is known so they must be made on the basis of an ex ante (predicted) real interest rate.

• Fisher Hypothesis: Ex ante real interest rate is determined by forces in the financial market. Money interest rate is just the real ex ante rate plus the market’s consensus forecast of inflation.

Great Inflation of the 1970’s

US Inflation Rates & Interest Rates

18.00M

Interest Rates

Inflation

Source: St. Louis Federal Reserve http://research.stlouisfed.org/fred2/

• We can also examine the ex post real return on a loan as the money interest rate less the actual outcome for inflation.

• The gap between actual and forecast inflation determines the gap between the ex post (actual) and ex ante (forecast) return.

Ex Ante vs. Ex post

1ExP ACTUAL

t t tr i

1 1ExP ExA FORECAST ACTUAL

t t t tr r

Unexpected Inflation Winners and Losers

• Higher than expected inflation means ex post real rates are lower than ex ante. Borrowers are winners/lenders are losers.

• Lower than expected inflation means ex post real rates are higher than ex ante. Lenders are losers/borrowers are winners.

Identifying the Ex Ante Rate• Calculating the ex post rate is straight-forward using

economic data. • Calculating the ex ante rate is harder since markets

expected inflation is not directly observable.• Option 1: Use survey data to elicit beliefs about inflation.

• Surveys of professional forecasters or perhaps consumers or corporate executives (better for short-term).

• Option 2: Use yields on inflation protected securities.• Many large countries treasuries issue bonds that guarantee a pay-

off in terms of purchasing power. The purchasing power yield that the market is will to accept should be similar to real yield on other assets (usually better for long-term).

• Banknotes do not pay interest. • The real interest rate on banknotes is

• If inflation is high, currency has sharply negative returns. People will avoid holding money leading to society losing the convenience of money transactions.

The Inflation Tax

Structure of Monetary Policy Implementation

Nominal Anchor

Variable used to pin down the value of

currency.

OperatingInstruments

ToolsDirect powers of the

Central bank.

Policy Feedback

Policy/Operating Instruments• “A variable that is very responsive to the central bank’s

tools and indicates the stance of monetary policy” • Developed economies and emerging markets typically

choose between using a short-term interest rate or an exchange rate as the instrument.

• Determines the implementation of monetary policy.

CHAPTER 16Interest Rate as the Policy Instrument

Interbank Market

• In conducting payments, banks may face a shortfall of reserves and be forced to borrow reserves from other banks or the central bank at the interbank rate.

• Demand: Each bank would like to keep a certain amount on reserve at any time to meet their own liquidity needs. Tradeoff for keeping stock of reserves is you cannot lend them to others. If the interbank rate IBR is high, they will want to lend their own balances to other banks and hold small reserves in their own account.

• Supply: Central bank controls the supply reserves.

Interbank Market: Basics

Reserve Accounts

Equilibrium• Excess Supply: If iIBR > i* , banks will have funds in

reserve accounts in excess of that required to meet their own liquidity needs. They will offer funds at competitive rates pushing rates down.

• Excess Demand: If iIBR < i*, banks will tend to hold on to reserves rather than lend them at unattractive rates. Banks facing shortfalls must offer better rates

• Policy Instrument: Target for interbank lending rate• US Fed: Fed Funds Rate; • Bank of Japan: Uncollateralized Call Money Rate

Interbank Rate

Tools: Open Market Operations• Open Market Purchase: Central bank buys short-term

government bills from commercial banks. Credits counter-parties with additional funds in reserve accounts.

• Open Market Sale: Central bank sells bills to commercial banks. Debits counterparties reserve accounts.

Sets supply of reserves

Central Bank Balance Sheets

Assets Liabilities

Monetary Liabilities• Currency• Reserves

Non-monetary Liabilities• Long-term “Stabilization Bonds• Government Fiscal Reserves

• Government Bills• Foreign Reserves

• Unconventional Assets

T-Accounts• T-Accounts are a handy tool for examining the effects that

any transaction has on balance sheets.• A bank transaction will change both liabilities and assets

(and possibly net worth). The total change in liabilities plus net worth must always equal the total change in assets.

Open Market Purchase: Central Bank Purchases $100 of T-Bills from Bank A

• Fed credits the reserve accounts of Bank A which increases its liabilities and takes possession of an equal value of securities as assets.

• Bank A gets an extra amount of reserves and loses an equal amount of securities.

Assets Liabilities

+100 T-Bills + 100 Reserves

Assets Liabilities

+100 Reserves-100 T-Bills

Fed Balance Sheet

Bank A Balance Sheet

OMO’s usually implemented with repo operations.

Repurchase Agreements:

Repo • Central bank purchases

quantity of government securities from commercial bank.

• Central bank simultaneously contracts to sell securities back to the bank at some future date (typically 1 to 13 days) at a slightly higher price.

• Equivalent to perfectly collateralized loan with interest

Reverse Repo

• Central bank sells quantity of government securities to commercial bank.

• Central bank simultaneously contracts to buy securities from the bank at some future date (typically 1 to 13 days) at a slightly higher price.

• Equivalent to perfectly collateralized deposit with interest

Tools: Standing Facilities• Loan Facility: Commercial banks can borrow reserves

overnight at a loan facility rate. • Deposit Facility: Commercial banks can deposit reserves

overnight at a deposit facility rate.

These opportunities keep interbank rate within narrow band of the policy rate.

For historical reasons, standing facilities are called the discount window.

Interbank Market: Basics

Reserve Accounts

Facility: Supply and Demand• If the interbank rate rises above the lending facility rate,

then banks can borrow as much as they want from the central bank through the discount window. Supply becomes perfectly elastic at iLF.

• If the interbank rate rises above the deposit facility rate, banks can lend as much to the central bank as they want through the window. Demand for reserves is perfectly elastic at iDF.

POLICY RATE

Criterion for Operating Instruments

1. Controllable

2. Observable

3. Linked to Goals

Operating Instruments are the Targets that central banks set in day to day operations.

Why short-term rates as policy instrument?

1. Controllable: Central bank controls liquidity conditions in certain market

2. Easily Observable: changes send clear signal of changes in policy

3. Helps to Achieve GoalsA. Financial Stability: avoid fluctuating interest rates

B. Predictable Effects: transmission mechanism from changes in interest rate to economy are relatively well understood

Operating Instruments: Target Interest Rates• In this chapter, we examine the monetary policy of banks that use asset transactions to control the level of an interest rate in interbank market

Fed Federal Funds Rate

BoJ Uncollateralized Call Money Rate

ECB Main Refinancing Rate

BoK Base Rate

UK Official Bank Rate

Policy Rate Implementation

• Monetary policy committee announces policy rate.

• At regular intervals, central bank holds a reverse auction, offering to “lend”* banks as much reserves as they want to hold at policy rate.• Ex. Bank of Korea has weekly auction with 7 day rp

agreements

• Banks take up enough to fill demand. • By setting an interest rate, supply of reserves respond to demand.

* Implemented by Reverse Auction

Main Refinancing Operation

Reserve Accounts

Fine tuning operations• On a day-to-day, minute-to-minute basis the willingness of

banks to hold reserves will change creating intra-refinancing period volatility in the market interbank rate for reserves.

• Standing facility creates a corridor for fluctuations in the interbank rate but this is only a backstop.Ex. Bank of Korea• Lending facility is policy rate +100 bps• Deposit facility is policy rate -100bs.

• Central bank conducts ad hoc OMSs to match fluctuations in demand for reserves with supply in order to stabilize interbank rate (ex. BoK stabilizes overnight call money rate) near policy rate.

Increase in Demand for Reserves matched by fine tuning

OMO purchase to keep interbank rate from rising.

Reserve Accounts

BoK Monetary Policy Report

Operating Instrument in Euroland• The Governing Council (Monetary Policy committee)

decides a rate of interest for these repos, the main financing rate, as the policy interest rate.

• Every week, the ECB engages in 1-week repurchase agreements with banks in member countries at policy rate providing reserves in exchange for securities.

• Auctions are decentralized and done through • In between periods, The ECB intermittently conducts

fine-tuning operations to make sure , the interbank interest rate called EURIBOR, stays near the target.

Operating Instrument• In USA & Japan, all OMO’s are ad hoc.• No main refinancing operation.

What shifts the demand for reserves?

• Demand for Broad Money – When households want to hold liquid assets, they hold liquid bank deposits. When bank deposits go up, demand for bank reserves go up.

• Reserve Requirements – When regulations require banks to hold a high share of reserves relative to deposits, demand for reserves goes up.

• Liquidity Risk – When the financial institutions want to hold liquidity, demand for liquidity goes up.

Changing the Target• After a decision has been made to change the target, the central bank’s traders kick into action and conduct active open market operations.• To lower the target interest rate, the central bank will

conduct open market purchases, making reserves more plentiful and reducing the cost of borrowing them.

• To raise the target interest rate, the central bank will conduct open market sales, making reserves less plentiful and raising the cost of borrowing them.

Cutting Policy Rates: OM Purchase

Reserve Accounts

Key point

• Monetary policy decisions focus on expected future inflation.• Inflation expectations drive the real interest rate given

choice of the policy instrument, so the policy instrument must respond to expectations.

• Policy changes affect the economy only with a lag, so only helpful in responding to future inflation threats

Principles

Interbank Rates and the Money Market• Money market: Debt markets w/ maturity less than 1 year: CP,

T-bills, NCDs, repos.

• Interbank rates steer rates in the broader money market through arbitrage.

• If iIB < iMM, borrow in interbank market, lend in money market;

• if iIB > iMM, then reverse.

Money Market• Market for debt instruments with initial maturity less than 1

year• Treasury Bills• Commercial Paper: Corporate debt• NCD’s

Korean Money Market

Call Money Rate

KIBOR 1 week

6 Month KIBOR

1 Year Treasury

3 Month NCD

3 Month Commercial Paper

Source: CEIC Database

Policy Rate: Month End: Overnight Policy Rate (Malaysia) Base Lending Rate: Period Average: Commercial Banks (Malaysia)

Interbank Rate: Weighted Average: Overnight (Malaysia)

10.000

11.000

12.000

13.000

“..the pass-through from the overnight policy rate (OPR) to other interbank rates and retail market rates has remained high since April 2004 and has increased significantly during the most recent increases in the OPR … As the level of competitiveness in the banking system has increased over the past decade, long-run interest rate pass-through has also increased and has generally remained high,” Ooi Sang Kuang, Deputy Governor, Bank Negara Malaysia Link

Monetary Policy Transmission Mechanisms in Pacific Islands Countries

Open Market OperationsEligible Securities• U.S. Fed only uses T-bills and T-bonds for repurchase• ECB and BoJ use some private securities including

collateralized bonds and high quality commercial paper.

Monetary Transmission Mechanism

Interbank Interest Rate

Money Market Rates

Economy

Stock P

t Rate

Principles of Monetary Policy Strategy, Pt. III

Managing the Future

4. Expectations are critical to monetary policy outcomes;

5. Taylor Principle is necessary for price stability

Expectations, Policy Credibility, and Transparency53

Mishkin, Monetary Policy Strategy After the Crisis

4. Why are expectations so important?

• Economic decisions such as price-setting, hiring, wage contracting, investment are made only intermittently.

• Rational actors will take future conditions into account when making decisions, since they know they will live with them for a while. • Ex. If workers think inflation will be high in the

future, they will only sign contracts today that allow for high wage growth to maintain living standards.

Principles

TERM STRUCTUREChapter 6: The Term Structure of Interest Rates

Term Structure of Interest Rates

• Bonds of different maturities typically have different interest rates.

• Typically, bonds of longer maturity pay higher yields over their lifetime.

• Segmented Market Theory: Long-term bonds have greater interest rate risk and less liquidity. This explains why long-term bonds have greater yields on average.

Average Yield Curve: Korea Yield Curve

Call 1 Year 3 Year 5 Year 10 Year0

Average Korean Yields 2001-2014 by Ma-turity

Expectations Theory

• Portfolio holders are indifferent between long and short-term bonds.

• Yield to maturity over the life of a long-term bond must be equal to average yields on repeated rollovers of short-term bond holdings during the same period.

• Consider two strategies which should have the same expected pay-off. Starting with $1.

1. Buy a two year discount bond and hold it for two years. Payoff:

2. Buy a 1 year bond. After 1 year, invest pay-off in another 1 year bond. Payoff:

22 21)21()1( iiii

eeee iiiiiiii 1,111,111,111,11 1)(1)1()1(

Two Strategies

• Arbitrage between markets implies equal returns on equal assets.

• Equal pay-offs imply that yield on a two year bond is equal to the expected average yield of 1 year bonds over the next two years.

21 1, 1 2(1 ) (1 ) (1 )ei i i

• In general, if the pay-off for investing in an n period bond should be the same as the pay-off from rolling over 1 year bonds for n periods:

• Then a n period bond yield is (approximately) equal to the average expected yield on 1 period bonds between today and date n.

)1(...)1()1()1()1( 1,12,11,11e

n iiiii

n1,12,11,11 ...

Preferred Habitat Theory

• Bonds have some differences in risk and liquidity characteristics. Regardless, they are close substitutes and the expectation theory well describes the connection between bonds of different yields.

• Yields of bonds of period n are represented as the

• The maturity premium hn tends to increase in n.

1,12,11,11 ...

Forecasting with the Term Structure

• If the expectations theory holds, long-term interest rates can be used to infer market expectations of future interest rates.

• Steep yield curve indicates low short-term rates and high future interest rates.

• Inverted yield curve indicates high short-term rates and low future interest rates.

Short Rates More Volatile than Long

Korea Yield

Overnight 1 Year 3 Year 5 Year 10 Year

Monetary Expansion Means Steep Yield Curve

5Year - Overnight

What drives policy changes• Nominal anchor and monetary policy framework

determine necessary changes. • In inflation targeting framework, central bank must

announce inflation target and publish

• Real interest rate impacts demand for goods.• Real interest rate is rt = it - E[πt+1]

• When E[πt+1] rises, central bank should increase it

more than 1-for-1 to raise real interest rate, limit demand and limit inflation.

• When E[πt+1] falls, central bank should reduce it

more than 1-for-1 to drop real interest rate, raise demand and avoid deflation.

5. Economics of the Policy Mechanism Taylor Principle

Zero Lower Bound• One constraint on using the interbank interest rate as an operating target: nominal interest rates cannot go below zero.

• As inflation drops, the central bank can purchase government securities to lower interest rates only up to the lower bound.

• Once, that point has been reached banks will no longer lend out their excess reserves preferring to keep them rather than accept a negative interest rate.

• A bank that sets a ZIRP, zero interest rate policy must also target a level of reserves

Zero Lower Bound

• Taylor Principle suggests that when inflation expectations fall, the policy rate should be brought down on a more than 1-for-1 basis.

• But interest rates cannot be brought down below zero: no one will lend money with a negative interest rate since money always pays a 0% interest rate.

Japanese Monetary Policy

CALL MONEY RATE

Six Strategies for Dealing w/ Zero Lower Bound

(i) expanding the central bank’s balance sheet beyond level required

(ii) targeted asset purchases: altering the central bank’s balance sheet to change the relative supplies of securities in the market

(iii) managing interest-rate expectations : lower long-term rates;

(iv) Increase inflation target

(v) Price level target

(vi) Negative Interest Rates

i. Expanding Balance Sheets

• In 2001, Bank of Japan implemented a sharp increase of OM purchases to expand bank reserves referred to as Quantitative Easing.

• Banks mostly held extra reserves on their balance sheets and did not increase lending or deposit creation.

• In 2013, Japan begins asset purchases again.

Japan: Quantitative Easing…2 rounds73

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

Two Rounds of Quantitative Easing

BoJ Assets M2/10

USA: Quantitative Easing

Challenges to Monetary Policy Effectiveness 74

BASEM2/10

ii. Targeted Asset PurchasesB o J, "Quantitative and Qualitative Monetary Easing "

Bank of Japan announcement April 4, 2013 -- “An increase in JGB purchases and their maturity extension by a unanimous vote -- With a view to encouraging a further decline in interest rates across the yield curve, the Bank will purchase JGBs so that their amount outstanding will increase at an annual pace of about 50 trillion yen.”

“In addition, JGBs with all maturities including 40-year bonds will be made eligible for purchase, and the average remaining maturity of the Bank's JGB purchases will be extended from slightly less than three years at present to about seven years…” Link

LT interest rates fell76

QE Large-Scale Asset Purchase Program77

iii. Interest Rate Expectations Management

• Ueda (2005) argues that Japan QE was part of a strategy to indicate a BoJ commitment to pushing down long-term interest rates.

• In 2009 financial crisis, Bank of Canada was more explicit…

Did reversal of first QE reduce credibility?

…With monetary policy now operating at the effective lower

bound for the overnight policy rate, it is appropriate to

provide more explicit guidance than is usual regarding its future

path so as to influence rates at longer maturities. Conditional

on the outlook for inflation, the target overnight rate can be

expected to remain at its current level until the end of

the second quarter of 2010 in order to achieve the inflation

target. ……Bank of Canada Website

• Fed offers FOMC forecasts of policy

iv. Raise Inflation Target• Cost of borrowing (in terms of purchasing power) is the interest

rate adjusted by the inflation rate between the time a loan is made and the time is repaid.

1t t t tr i E With zero interest rates, real borrowing rates will fall when inflation rises.

Inflation Target83

The newly-introduced "price stability target" is the inflation rate that the Bank judges to be consistent with price stability on a sustainable basis. … Based on this recognition, the Bank sets the "price stability target" at 2 percent in terms of the year-on-year rate of change in the consumer price index (CPI) -- a main price index.

Interest Rate Management and Inflation Targeting• Ben Bernanke (1999) – “In particular, a target in the 3-4% range for inflation, to be maintained for a number of years, would confirm not only that the BOJ is intent on moving safely away from a deflationary regime, but also that it intends to make up some of the “price-level gap” created by eight years of zero or negative inflation.”

Make-up inflation target sometimes referred to as price-level targeting

v. Price Level Targeting

• Level targeting is a backward looking form of inflation target in which central bank responsible for fixing past mistakes.

• If there is a large negative shock to inflation that drives interest rate to zero, central bank commits to raising future inflation.

Price Level Targeting vs. Inflation Targeting USA

Challenges to Monetary Policy Effectiveness

Price level would be 40% higher if previous trends had continued

Japan CPI (in Natural Logs)

vi. Negative Interest Rates Euro• Deposit facility puts tax on deposits.

2012-2 2012-3 2012-4 2013-1 2013-2 2013-3 2013-4 2014-1 2014-2 2014-3

Eurozone Rate, ECB Data

Deposit Facility Refinancing Rate Lending Facility

Negative Rates

• In a deflationary slump, banks hold large stocks of excess reserves rather than make loans. • When interest rates are zero, this is costless.• When interest rates are negative, taxes penalize this

behavior, stimulating lending (hopefully).

Prevention: Making Liquidity Traps Less Likely

• Central banks have targeted inflation near 2% which has kept short-term interest rates low on average

• Running a higher inflation target might give more cushion to cut rates.

INTEREST RATES. REAL INTEREST RATES Mishkin, P. 123-125.

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