Sources and References

Primary textbook — Mishkin, Frederic S. and Apostolos Serletis (2023). The Economics of Money, Banking, and Financial Markets, 8th Canadian Edition. Pearson Canada.

Supplementary texts — Mankiw, N. Gregory. Macroeconomics, 10th Edition. Worth Publishers. / Fabozzi, Frank J. Bond Markets, Analysis, and Strategies, 10th Edition. MIT Press. / Cecchetti, Stephen and Kermit Schoenholtz. Money, Banking, and Financial Markets, 6th Edition. McGraw-Hill.

Online resources — MIT OpenCourseWare 14.02 Principles of Macroeconomics; Federal Reserve Bank of St. Louis FRED database; Bank of Canada educational resources; BIS Working Papers on monetary economics.

---

Chapter 1: Why Study Money, Banking, and Financial Markets?

1.1 The Financial System and the Economy

The financial system performs the indispensable economic function of channeling funds from those who have saved a surplus of funds to those who have a shortage of funds and productive investment opportunities. Without well-functioning financial markets, an economy forfeits enormous amounts of potentially productive capital investment. A farmer who wishes to purchase additional land cannot borrow against next year’s harvest without some institutional mechanism for credible commitment; a startup company with a revolutionary idea cannot expand production without access to external finance.

Financial markets and financial intermediaries together constitute the financial system. Financial markets are markets where financial instruments—stocks, bonds, mortgages, and other claims—are bought and sold. Financial intermediaries are institutions such as banks, insurance companies, and pension funds that borrow funds from surplus units and lend them to deficit units, transforming the maturity, denomination, and risk characteristics of assets in the process.

1.2 Money and the Macroeconomy

Money — loosely defined as anything generally accepted in payment for goods and services or in repayment of debts — influences both the short-run behavior of output and employment and the long-run path of the price level. The empirical record shows tight correlations between money growth and nominal variables. Milton Friedman’s famous dictum — “inflation is always and everywhere a monetary phenomenon” — summarizes decades of evidence that sustained price-level increases trace to money supply growth in excess of real output growth.

Interest rates, another crucial variable studied in this course, affect the investment decisions of firms and the consumption decisions of households. High real interest rates discourage investment and dampen aggregate demand; low real rates stimulate borrowing and spending. Monetary policy works largely through its influence on interest rates, asset prices, exchange rates, and credit conditions.

1.3 Overview of the Canadian Financial System

Canada’s financial system is dominated by a small number of large, diversified chartered banks (the “Big Six”: Royal Bank, TD Bank, Bank of Nova Scotia, Bank of Montreal, CIBC, and National Bank), supplemented by credit unions, insurance companies, pension funds, investment dealers, and a growing fintech sector. The Bank of Canada, established by the Bank of Canada Act (1934), serves as the central bank, with a mandate to promote the economic and financial well-being of Canada.

Key regulatory bodies include the Office of the Superintendent of Financial Institutions (OSFI), the Canada Deposit Insurance Corporation (CDIC), and provincial securities commissions coordinated through the Canadian Securities Administrators (CSA).

---

Chapter 2: Financial Markets and Instruments

2.1 The Structure of Financial Markets

Financial markets can be classified along several dimensions:

Debt versus equity markets. Debt instruments (bonds, mortgages, commercial paper) involve a contractual obligation to make fixed payments at regular intervals and to repay principal at maturity. Equity instruments (common shares) represent residual ownership claims, entitling holders to dividends and capital gains but subordinating them to debt holders in bankruptcy.

Primary versus secondary markets. In primary markets, newly issued securities are sold to initial buyers; the proceeds flow to the issuing entity. In secondary markets, previously issued securities are resold among investors; no new funds flow to the issuer. Secondary market liquidity is critical because it makes primary market investors willing to buy new issues — they know they can exit.

Money markets versus capital markets. Money markets trade short-term debt instruments with maturities of one year or less (Treasury bills, commercial paper, bankers’ acceptances, overnight repurchase agreements). Capital markets trade longer-term instruments (Government of Canada bonds, corporate bonds, equities). Money market instruments are generally safer and more liquid; capital market instruments carry higher risk and offer higher expected returns.

Exchange-traded versus over-the-counter (OTC) markets. Exchanges such as the Toronto Stock Exchange (TSX) provide centralized, organized trading with standardized contracts and public price discovery. OTC markets are decentralized networks of dealers quoting bid and ask prices bilaterally; most bonds and foreign exchange trade OTC.

2.2 Key Financial Instruments

Treasury bills (T-bills) are short-term, zero-coupon obligations of the federal government sold at a discount to face value. They are the safest and most liquid instruments in the money market.

Bankers’ acceptances (BAs) are drafts drawn on and accepted by a bank, guaranteeing payment at maturity. They are widely used in trade finance.

Commercial paper consists of unsecured short-term promissory notes issued by large, creditworthy corporations to fund working capital needs.

Mortgage-backed securities (MBS) pool mortgage loans and sell claims on the resulting cash flows to investors, transforming illiquid individual mortgages into tradable securities. The Canada Mortgage and Housing Corporation (CMHC) plays a central role in the Canadian MBS market.

2.3 The Role of Financial Intermediaries

Why do financial intermediaries exist? Three economic frictions make direct finance between savers and borrowers inefficient:

1. Transactions costs. Individual savers lack the expertise, time, and scale economies to evaluate and monitor individual borrowers. Banks and other intermediaries spread these costs over large loan portfolios.

2. Adverse selection. Before a transaction, borrowers know more about their own creditworthiness than lenders do. Intermediaries invest in screening technologies (credit scoring, loan officer expertise, collateral requirements) to separate good from bad borrowers.

3. Moral hazard. After a loan is made, borrowers may take on excessive risk, since they capture the upside while lenders bear the downside. Intermediaries monitor borrowers through covenants, periodic reporting, and relationship banking.

---

Chapter 3: What is Money?

3.1 Functions of Money

Money serves three classical functions:

1. Medium of exchange. Money eliminates the need for the “double coincidence of wants” that plagues barter economies. A carpenter can sell services for money and then use that money to buy groceries without first finding a grocer who needs carpentry services.

2. Unit of account. Money provides a common measuring rod for prices, wages, debts, and the values of assets. It reduces the number of prices in an economy: with \(n\) goods, barter requires \(\frac{n(n-1)}{2}\) relative prices, while a monetary economy requires only \(n-1\) prices in terms of money.

3. Store of value. Money allows purchasing power to be held over time. Other assets — real estate, stocks, bonds — also store value but may be less liquid. Inflation erodes money’s store-of-value function, which is why inflation control matters for monetary policy credibility.

3.2 Evolution of Money and the Payments System

The payments system has evolved from commodity money (gold, silver) to fiat money (government-decreed currency with no intrinsic value) to electronic payments. Key stages:

• Commodity money: Gold and silver coins whose value derived from the metal content. Subject to Gresham’s Law: “bad money drives out good” — when two coins have the same face value but different metal content, the more valuable coin is hoarded.
• Paper currency backed by gold (gold standard): Banknotes convertible to a fixed quantity of gold. Canada was on the gold standard until 1929; the Bretton Woods system maintained a modified gold standard until 1971.
• Fiat money: Current Canadian dollars are fiat money — they have value because the government declares them legal tender and because everyone expects others to accept them.
• Electronic payments: Debit cards, e-transfers, and real-time payment networks process the bulk of transactions by value. The Bank of Canada’s Lynx system (launched 2021) provides the high-value clearing and settlement infrastructure.

3.3 Measuring Money: The Monetary Aggregates

The Bank of Canada publishes several monetary aggregates that group assets by their degree of moneyness (liquidity and use in transactions):

\[ M1^+ = \text{Currency} + \text{Personal chequing deposits} + \text{Other demand deposits at chartered banks and trust companies} \]\[ M2 = M1 + \text{Personal savings deposits} + \text{Non-personal notice deposits} \]\[ M3 = M2 + \text{Non-personal fixed-term deposits} + \text{Foreign-currency deposits} \]

The Federal Reserve in the United States uses M1 and M2. The choice of aggregate matters for empirical work: the correlation between money growth and inflation is tighter for broader aggregates over long horizons.

---

Chapter 4: Understanding Interest Rates

4.1 Present Value and the Time Value of Money

The fundamental principle underlying interest rate theory is that a dollar received today is worth more than a dollar received in the future, because the present dollar can be invested to earn a return. The present value (PV) of a future cash flow \(C_t\) received \(t\) periods hence, discounted at interest rate \(i\), is:

\[ PV = \frac{C_t}{(1+i)^t} \]

For a stream of cash flows:

\[ PV = \sum_{t=1}^{T} \frac{C_t}{(1+i)^t} \]

4.2 Yield to Maturity

The yield to maturity (YTM) is the interest rate that equates the present value of all future payments from an instrument with its current market price. It is the most economically meaningful measure of the return on a debt instrument.

Simple loan. For a loan of principal \(L\) repaid with interest in one period at rate \(i\):

\[ L = \frac{L(1+i)}{1+i} \]

The yield to maturity equals the stated interest rate.

Coupon bond. A bond with face value \(F\), annual coupon \(C\), and \(n\) years to maturity has yield to maturity \(i\) solving:

\[ P = \sum_{t=1}^{n} \frac{C}{(1+i)^t} + \frac{F}{(1+i)^n} \]

When \(P = F\), the YTM equals the coupon rate. When \(P < F\) (bond trades at a discount), the YTM exceeds the coupon rate, and vice versa.

Consol (perpetuity). A bond paying coupon \(C\) forever has:

\[ P = \frac{C}{i} \implies i = \frac{C}{P} \]

Discount bond (Treasury bill). A zero-coupon instrument with face value \(F\) and current price \(P\):

\[ i = \frac{F - P}{P} \]

4.3 The Distinction Between Real and Nominal Interest Rates

The real interest rate measures the purchasing-power return on a loan. If the nominal rate is 5% and expected inflation is 3%, the expected real rate is approximately 2%. Lenders care about real rates; nominal rates reflect both the real return and compensation for expected inflation.

Ex ante versus ex post real rates. The ex ante real rate uses expected inflation (known at the time the loan is made). The ex post real rate uses actual realized inflation.

\[ r_{ex\ post} = i - \pi_{actual} \]

If inflation turns out higher than expected, the ex post real rate falls below the ex ante real rate, redistributing wealth from lenders to borrowers.

4.4 Distinction Between Interest Rates and Returns

The return on a bond held for one period differs from the yield to maturity unless the bond is held to maturity. The one-period return is:

\[ R = \frac{C + P_{t+1} - P_t}{P_t} = i_c + g \]

where \(i_c = C/P_t\) is the current yield and \(g = (P_{t+1} - P_t)/P_t\) is the capital gain rate. Because bond prices move inversely with interest rates, a rise in market interest rates produces capital losses on existing bonds, so the total return can be negative even when the coupon yield is positive.

---

Chapter 5: The Behavior of Interest Rates

5.1 Determinants of Asset Demand

The theory of portfolio choice identifies five factors influencing the quantity of an asset demanded:

1. Wealth. As wealth rises, the demand for all assets rises. The wealth elasticity of demand for a “luxury” asset exceeds one.
2. Expected return relative to alternatives. Investors demand more of an asset whose expected return rises relative to competing assets.
3. Risk relative to alternatives. Risk-averse investors demand less of a riskier asset, holding expected return constant.
4. Liquidity relative to alternatives. More liquid assets command greater demand; illiquid assets must offer a liquidity premium.
5. Information and transactions costs. Lower costs of acquiring information and transacting increase asset demand.

5.2 Supply and Demand in the Bond Market

Using a loanable funds framework: the bond market equilibrates the supply of bonds (borrowers demanding funds) with the demand for bonds (lenders supplying funds).

The demand curve for bonds slopes downward in \((Q, P)\) space (upward in \((Q, i)\) space, since higher prices mean lower yields and thus lower incentive to hold bonds).

The supply curve for bonds slopes upward in \((Q, P)\) space (lower interest rates make borrowing cheaper, increasing quantity supplied of bonds).

Equilibrium occurs where quantity demanded equals quantity supplied.

Factors shifting bond demand: changes in wealth, expected inflation, expected returns on alternatives, risk, and liquidity. Factors shifting bond supply: changes in expected profitability of investment, expected inflation, and government borrowing.

5.3 The Liquidity Preference Framework

Keynes’s alternative framework analyzes the market for money directly. People hold their wealth either as money (liquid but zero nominal return) or bonds (illiquid but pays interest). Given a fixed wealth level, excess demand for money implies excess supply of bonds, and vice versa.

Money demand slopes downward in \((M, i)\) space: higher interest rates raise the opportunity cost of holding money, reducing money demand.

Money supply is determined by the central bank; in the simple model it is a vertical line.

Equilibrium interest rate equates money demand and supply. An increase in money supply shifts the money supply curve right, lowering the equilibrium interest rate — the liquidity effect of monetary policy.

---

Chapter 6: The Risk and Term Structure of Interest Rates

6.1 The Risk Structure of Interest Rates

Bonds that are identical in maturity but differ in issuer quality command different yields. The default risk premium (also called the credit spread) compensates investors for the probability that an issuer will fail to make promised payments.

\[ i_{corporate} = i_{government} + \text{default risk premium} + \text{liquidity premium} \]

Bond rating agencies (Moody’s, Standard & Poor’s, DBRS Morningstar in Canada) assign credit ratings from AAA/Aaa (highest quality) to D/C (default). Higher-rated bonds carry lower yields. Credit spreads widen during recessions (when default risk rises) and narrow during expansions.

Liquidity premium. Even for bonds with identical default risk, the less liquid bond commands a higher yield. Government bonds are the most liquid; certain corporate bonds are thinly traded.

Tax treatment. In Canada, interest income is taxed as ordinary income while capital gains receive preferential treatment, affecting after-tax yields.

6.2 The Term Structure of Interest Rates and the Yield Curve

The term structure of interest rates describes the relationship between yields and maturities for bonds that are otherwise comparable (same issuer, same default risk, same liquidity). The graphical representation is the yield curve.

Three competing theories explain the shape of the yield curve:

6.2.1 The Expectations Theory

The yield on a long-term bond equals the average of expected short-term rates over the bond’s life. Formally, for a two-period bond with yield \(i_{2t}\):

\[ (1 + i_{2t})^2 = (1 + i_{1t})(1 + i^e_{1t+1}) \]

Taking logarithms (approximation):

\[ i_{2t} \approx \frac{i_{1t} + i^e_{1t+1}}{2} \]

Under this theory, a steeply upward-sloping yield curve signals market expectations that short-term rates will rise in the future. A flat yield curve implies rates are expected to remain unchanged; an inverted yield curve predicts rate declines.

6.2.2 The Segmented Markets Theory

Investors have strong habitat preferences for particular maturities (e.g., pension funds prefer long bonds to match long-duration liabilities; money market funds prefer very short instruments). Markets for different maturities are therefore largely separate — “segmented” — and yields are determined independently in each segment by supply and demand within that segment.

This theory explains the typical upward slope by positing that investors generally prefer short-term bonds (less interest rate risk), so long-term bonds must offer higher yields to attract buyers.

6.2.3 The Liquidity Premium (Preferred Habitat) Theory

This theory combines the two above. Long-term yields include a liquidity premium \(l_{nt}\) over the average of expected future short rates:

\[ i_{nt} = \frac{i_{1t} + i^e_{1t+1} + \cdots + i^e_{1t+n-1}}{n} + l_{nt} \]

where \(l_{nt} > 0\) and typically increases with maturity (investors demand compensation for bearing interest rate risk). This theory is most consistent with empirical evidence:

• The yield curve normally slopes upward even when rates are not expected to rise (liquidity premium effect).
• Inverted yield curves, which require the expectations component to dominate, reliably signal recessions.

---

Chapter 7: The Stock Market, Rational Expectations, and the Efficient Market Hypothesis

7.1 Stock Valuation: The Gordon Growth Model

A share of common stock entitles its holder to the firm’s future dividends. The Dividend Discount Model prices the stock as the present value of all expected future dividends:

\[ P_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1+k_e)^t} \]

where \(k_e\) is the required return on equity. For a firm with dividends growing at constant rate \(g\):

\[ P_0 = \frac{D_1}{k_e - g} \]

This is the Gordon Growth Model (Gordon 1962). It implies that stock prices rise when dividends are expected to grow faster, when required returns fall (e.g., due to lower interest rates), or when the discount rate for equity risk falls.

7.2 The Theory of Rational Expectations

The rational expectations hypothesis has profound implications for macroeconomics and finance. Under rational expectations, purely anticipated monetary policy cannot systematically affect real output (the Policy Ineffectiveness Proposition of Lucas and Sargent). For financial markets, rational expectations underpin the efficient markets hypothesis.

7.3 The Efficient Markets Hypothesis

The Efficient Markets Hypothesis (EMH), developed by Eugene Fama (1970), states that financial asset prices fully reflect all available information. Three forms are typically distinguished:

Weak-form efficiency. Prices reflect all past price and volume information. Technical analysis — predicting future price movements from historical patterns — cannot generate abnormal profits.

Semi-strong-form efficiency. Prices reflect all publicly available information (earnings announcements, economic data, news). Fundamental analysis based only on public information cannot systematically earn abnormal returns.

Strong-form efficiency. Prices reflect all information, including insider information. Even corporate insiders with privileged information cannot earn abnormal profits.

7.3.1 Formal Statement

In an informationally efficient market, the price \(P_t\) of an asset evolves according to:

\[ P_{t+1} = P_t (1 + r_t) + \varepsilon_{t+1} \]

where \(r_t\) is the required return (which may vary with risk) and \(\varepsilon_{t+1}\) is white noise with \(E[\varepsilon_{t+1} | \Omega_t] = 0\), where \(\Omega_t\) is all available information at time \(t\). Equivalently, price changes are unpredictable given current information — the random walk hypothesis.

7.3.2 Evidence and Anomalies

Substantial evidence supports weak-form and semi-strong-form efficiency in major markets. Prices react quickly to earnings announcements, central bank decisions, and other public news. However, several anomalies have been documented:

• The January effect: Stock returns tend to be higher in January, particularly for small firms — possibly due to tax-loss selling in December.
• The value premium: Stocks with low price-to-book ratios earn higher average returns than growth stocks, inconsistently with simple risk adjustments.
• Momentum: Stocks with high recent returns tend to continue outperforming over the next 3–12 months.
• Excess volatility: Stock price volatility appears too large relative to the volatility of dividends, a puzzle noted by Shiller (1981).

---

Chapter 8: Central Banking and the Bank of Canada

8.1 The Origins and Functions of Central Banks

Central banks emerged gradually from commercial banking history. The Bank of England (1694) was originally a private institution that lent to the government; it gradually assumed regulatory and monetary policy functions. The Bank of Canada was established in 1934, initially as a private institution, and nationalized in 1938.

Core functions of a modern central bank:

1. Issuer of currency. The Bank of Canada has the exclusive right to issue Bank of Canada notes.
2. Banker to chartered banks. Banks hold settlement balances (deposits) at the Bank of Canada and access overnight credit through the Bank Rate.
3. Banker to the federal government. The government of Canada maintains its deposits at the Bank; the Bank manages the national debt auction calendar.
4. Lender of last resort. In a financial panic, solvent but illiquid banks can borrow from the central bank to prevent contagion. Walter Bagehot’s (1873) classical prescription: lend freely, at a penalty rate, against good collateral.
5. Monetary policy. The Bank of Canada sets the overnight rate target to achieve its 2% inflation target (the mid-point of a 1–3% range, renewed through agreements with the federal government).
6. Financial stability. The Bank monitors systemic risk and contributes to macro-prudential policy alongside OSFI and CDIC.

8.2 The Structure of the Bank of Canada

The Bank of Canada is governed by a Board of Directors, but monetary policy is set by the Governing Council, comprising the Governor, Senior Deputy Governor, and four Deputy Governors. The Governor is appointed for a seven-year term. The Minister of Finance can formally direct the Bank under Section 14 of the Bank of Canada Act after public consultation, but this power has never been used, preserving de facto independence.

Goal independence versus instrument independence. The Bank of Canada has high instrument independence (it chooses its policy rate without government approval) but limited goal independence (the inflation target is jointly agreed with the federal government). Most economists regard this arrangement as appropriate: elected governments set the objective; technocrats implement it.

---

Chapter 9: The Money Supply Process

9.1 The Simple Deposit Multiplier

Commercial banks create money through the lending process. When a bank receives a deposit, it need hold only a fraction in reserve (either required reserves under regulation or desired reserves for liquidity management). The remainder can be lent out, creating new deposits elsewhere in the banking system.

Starting from an initial deposit \(\Delta D_0\), with required reserve ratio \(rr\):

\[ \Delta \text{Deposits (total)} = \frac{1}{rr} \times \Delta D_0 \]

This is the simple deposit multiplier. With a 10% reserve ratio, a $100 initial deposit ultimately supports $1,000 in total deposits.

9.2 The Money Multiplier with Currency

Let \(c = C/D\) be the currency-to-deposit ratio (determined by public preferences) and \(e = ER/D\) be the excess reserve ratio (determined by banks’ liquidity preferences). Total high-powered money (monetary base) \(H = C + R\), where \(R = rr \cdot D + ER\). Then:

\[ M = \frac{1+c}{rr + e + c} \times H \]

This is the money multiplier \(m\), so \(M = m \times H\).

Factors reducing the money multiplier:

• Higher currency-to-deposit ratio \(c\) (public holds more cash)
• Higher excess reserve ratio \(e\) (banks hold more precautionary reserves)
• Higher required reserve ratio \(rr\)

9.3 The Monetary Base and the Bank of Canada’s Balance Sheet

The Bank of Canada controls the monetary base through its balance sheet operations. Simplified Bank of Canada balance sheet:

Assets	Liabilities
Government of Canada securities	Bank notes outstanding
Advances to banks	Settlement balances (deposits of chartered banks)
Foreign exchange reserves	Government of Canada deposits

When the Bank buys government securities (open market purchase), it credits the seller’s bank account, expanding settlement balances and thus the monetary base. When it sells securities (open market sale), it debits bank accounts, contracting the base.

---

Chapter 10: Tools of Monetary Policy

10.1 The Target for the Overnight Rate

The Bank of Canada’s primary policy instrument is the target for the overnight rate — the interest rate at which major financial institutions borrow and lend one-day funds among themselves in the Large Value Transfer System (now Lynx). The Bank implements this target by:

• Setting a Bank Rate (lending rate) equal to target + 25 basis points (the ceiling on overnight rates).
• Paying interest on settlement balances at target − 25 basis points (the floor on overnight rates).
• These create an operating band of 50 basis points around the target, within which the overnight rate fluctuates.

The Bank announces policy rate decisions eight times per year on fixed dates.

10.2 Open Market Operations

Open market operations (OMOs) involve the Bank buying or selling Government of Canada Treasury bills and bonds in the secondary market to add or drain settlement balances, thereby influencing short-term interest rates.

• Expansionary OMO (purchase): Bank buys securities → settlement balances increase → overnight rate falls (banks have more reserves to lend)
• Contractionary OMO (sale): Bank sells securities → settlement balances decrease → overnight rate rises

In Canada, the Bank also conducts Special Purchase and Resale Agreements (SPRAs) and Sale and Repurchase Agreements (SRAs) at the Bank Rate to maintain the overnight rate within the operating band on a daily basis.

10.3 The Discount Rate (Bank Rate) and Lending Facilities

The Bank Rate is the interest rate charged by the Bank of Canada on advances (loans) to chartered banks. In Canada, the Bank Rate serves as the ceiling of the overnight rate operating band. Discount window borrowing in the US context is analogous; in Canada the Bank’s standing lending facility (SLF) provides overnight loans at the Bank Rate to any participant in the payment system.

10.4 Reserve Requirements

Canada eliminated formal reserve requirements in 1992 (the Bank Act amendments). Banks now manage their settlement balance levels based on operational needs and the interest on excess reserves (the deposit rate at the floor of the operating band). This is the corridor system; many central banks, including the Fed after 2008, moved to a “floor system” where large excess reserve holdings are remunerative.

10.5 Unconventional Monetary Policy

When the policy rate approaches the effective lower bound (ELB) — approximately zero, given technological lower limits on negative rates — conventional policy is constrained. Unconventional tools include:

• Forward guidance: Explicit communication about the future path of the policy rate to influence longer-term rates and expectations.
• Quantitative easing (QE): Large-scale asset purchases that expand the central bank’s balance sheet, pushing down long-term yields and the term premium.
• Yield curve control (YCC): Direct targeting of yields on specific maturities (used by the Bank of Japan).
• Negative interest rates: Charging banks for holding excess reserves (used by ECB, Riksbank, SNB).

The Bank of Canada deployed a form of QE during the COVID-19 pandemic (2020–21), purchasing Government of Canada bonds and provincial bonds to maintain market functioning and ease financial conditions.

---

Chapter 11: Monetary Theory and the Quantity Theory of Money

11.1 The Equation of Exchange

Irving Fisher formalized the relationship between money and prices in the equation of exchange:

\[ M \times V = P \times Y \]

where \(M\) is the money supply, \(V\) is the velocity of money (average number of times each dollar changes hands in transactions), \(P\) is the price level, and \(Y\) is real output. This is an accounting identity by definition: total spending \(P \times Y\) must equal money times its velocity.

11.2 The Quantity Theory of Money

The quantity theory of money converts Fisher’s identity into a theory by assuming that \(V\) and \(Y\) are determined independently of \(M\) in the long run (velocity by institutional factors and payments technology; output by real factors — labor, capital, technology). Then:

\[ \Delta M \% \approx \Delta P \% \]

That is, proportional changes in the money supply lead to proportional changes in the price level. The quantity theory predicts that money growth drives inflation in the long run.

11.3 The Cambridge Cash Balance Approach

Alfred Marshall and Arthur Cecil Pigou reformulated the quantity theory by focusing on money demand. The Cambridge approach states:

\[ M^d = k \times P \times Y \]

where \(k = 1/V\) is the Cambridge \(k\) — the fraction of nominal income people wish to hold as money. In equilibrium \(M = M^d\), so \(MV = PY\) as before, but the Cambridge approach emphasizes the behavioral determinants of money demand (portfolio choice, convenience), paving the way for Keynes’s liquidity preference theory.

11.4 Keynes’s Liquidity Preference Theory of Money Demand

Keynes (1936) argued that money demand depends not only on income but also on the interest rate (the opportunity cost of holding money). He identified three motives for money demand:

1. Transactions motive: Households and firms hold money to finance everyday purchases (proportional to income).
2. Precautionary motive: Holding money as a buffer against unforeseen expenditures.
3. Speculative motive: Holding money when bond prices are expected to fall (interest rates expected to rise), to avoid capital losses.

\[ L = f(Y, i) \quad \frac{\partial L}{\partial Y} > 0, \quad \frac{\partial L}{\partial i} < 0 \]

11.5 The Baumol-Tobin Transactions Demand Model

Baumol (1952) and Tobin (1956) modeled money demand as an inventory problem. An individual receives income \(Y\) and makes \(T\) trips to the “bank” each period. Each trip costs \(b\) (brokerage or transactions cost). The average money balance held is \(Y/(2T)\). The opportunity cost of holding money is \(i \times Y/(2T)\) and total transactions costs are \(bT\). Minimizing total cost with respect to \(T\):

\[ M^* = \sqrt{\frac{b \cdot Y}{2i}} \]

This implies that money demand has an income elasticity of 0.5 and an interest rate elasticity of −0.5, both below unity — economies of scale in money holding (“square-root rule”).

---

Chapter 12: The IS-LM-AD-AS Framework and Monetary Policy Transmission

12.1 Aggregate Demand

The IS curve describes goods market equilibrium: combinations of output \(Y\) and interest rate \(i\) for which planned spending equals output. It slopes downward: lower interest rates stimulate investment and (via the exchange rate and wealth effects) consumption, increasing equilibrium output.

The LM curve (in its traditional form) describes money market equilibrium: for a given money supply, higher output increases money demand, requiring a higher interest rate to restore equilibrium. It slopes upward.

Together, IS and LM determine the short-run equilibrium \((Y^*, i^*)\). Monetary easing shifts LM right (or, in modern terms, lowers the policy rate), stimulating aggregate demand.

The aggregate demand (AD) curve plots equilibrium output from the IS-LM model as a function of the price level. When the price level falls, real money supply rises (for given nominal \(M\)), shifting LM right and raising equilibrium output — so AD slopes downward.

12.2 Aggregate Supply

The short-run aggregate supply (SRAS) curve slopes upward: firms produce more when the price level is unexpectedly high (because input costs are slow to adjust). Shifting factors include wages, input prices, and productivity.

The long-run aggregate supply (LRAS) curve is vertical at potential output \(Y^*\) — determined by labor, capital, and technology. In the long run, prices and wages adjust fully, and output returns to potential.

12.3 Monetary Policy Transmission Channels

The channels through which monetary policy affects the economy:

1. Interest rate channel. Policy rate → short-term market rates → long-term rates (via expectations) → investment and consumption spending → aggregate demand.

2. Exchange rate channel. Lower domestic interest rates → capital outflows → depreciation of the Canadian dollar → higher net exports.

3. Asset price channel. Lower interest rates → higher equity and real estate prices → higher household wealth → higher consumption (the wealth effect).

4. Credit channel (bank lending channel). Tighter monetary policy reduces bank reserves, constraining bank lending capacity, especially to bank-dependent small firms.

5. Balance sheet channel. Higher interest rates reduce firm cash flows and collateral values, worsening credit conditions (the financial accelerator mechanism of Bernanke, Gertler, and Gilchrist 1999).

12.4 Monetary Policy Rules and the Taylor Rule

Rather than responding discretionarily, most central banks follow systematic reaction functions. John Taylor (1993) proposed:

\[ i_t = r^* + \pi_t + \frac{1}{2}(\pi_t - \pi^*) + \frac{1}{2}(Y_t - Y^*_t) \]

where \(r^*\) is the neutral real rate, \(\pi^*\) is the inflation target, and \(Y_t - Y^*_t\) is the output gap. The Taylor rule calls for raising the policy rate more than one-for-one with inflation (the Taylor principle, ensuring a positive real rate response), stabilizing both inflation and output.

12.5 Monetary Policy Goals and Strategy

The Bank of Canada’s primary objective is price stability, operationalized as keeping CPI inflation within a 1–3% control range, with a 2% midpoint. Secondary objectives include contributing to maximum sustainable employment and financial stability, though the Bank’s mandate does not specify the employment objective as explicitly as the Fed’s dual mandate.

Inflation targeting regime. Canada adopted inflation targeting in 1991, one of the first countries to do so. Key features: (1) a numerical target announced publicly; (2) the operating instrument is the overnight rate; (3) policy horizon is approximately 18–24 months (the time for policy to affect inflation); (4) the Bank publishes a quarterly Monetary Policy Report explaining its outlook.

Empirical evidence strongly supports the view that explicit inflation targeting has anchored inflation expectations, reducing the sacrifice ratio (the output cost of disinflating) and improving macroeconomic stability in Canada compared to the pre-targeting era.

---

Chapter 13: Monetary Theory Synthesis — The Classical versus Keynesian Debate

13.1 Classical Dichotomy and Money Neutrality

The classical dichotomy asserts that real variables (output, relative prices, employment) are determined by real factors (technology, preferences, endowments) and are unaffected by the nominal money supply. Money affects only the price level. This is the basis for long-run money neutrality:

\[ \frac{d\ln Y}{d\ln M} = 0 \quad \text{(long run)} \]

In the short run, however, prices and wages may be sticky (because of menu costs, wage contracts, imperfect information), allowing monetary policy to affect real output transiently.

13.2 The Neutrality Debate in Context

Superneutrality is a stronger claim: permanent changes in the growth rate of money affect only the inflation rate and not even the level of real output or capital stock. Whether superneutrality holds depends on the Tobin effect (higher inflation reduces the real return on money, shifting portfolios toward capital, increasing the capital stock) and the reverse Tobin effect.

Short-run non-neutrality is broadly accepted: monetary policy surprises move output and employment. The debate concerns the size and persistence of these effects and the appropriate policy response. New Keynesian models (covered in ECON 406) provide the modern synthesis: short-run non-neutrality arising from nominal rigidities, long-run neutrality through price adjustment.

13.3 Inflation, Unemployment, and the Phillips Curve

The Phillips curve (Phillips 1958) documented an empirical inverse relationship between unemployment and wage (later price) inflation in the UK. In the short run:

\[ \pi_t = \pi^e_t - \alpha(u_t - u^*) + \varepsilon_t \]

where \(\pi^e_t\) is expected inflation, \(u^*\) is the natural rate of unemployment, and \(\alpha > 0\). A central bank can temporarily reduce unemployment below \(u^*\) by generating surprise inflation, but rational agents adjust expectations upward, shifting the short-run Phillips curve up until unemployment returns to \(u^*\) at a higher inflation rate.

Long-run Phillips curve is vertical at \(u^*\): there is no permanent output-inflation tradeoff. This is consistent with long-run money neutrality. The implication for monetary policy: attempts to peg unemployment below the natural rate cause accelerating inflation (the Friedman-Phelps “accelerationist” hypothesis).

---

Summary Reference: Key Equations

The following equations synthesize the core technical content of the course:

\[ PV = \frac{C}{(1+i)^t} \]\[ i \approx r + \pi^e \]\[ P = \sum_{t=1}^{n} \frac{C}{(1+i)^t} + \frac{F}{(1+i)^n} \]\[ P_0 = \frac{D_1}{k_e - g} \]\[ i_{nt} = \frac{1}{n}\sum_{k=0}^{n-1} i^e_{1,t+k} + l_{nt} \]\[ MV = PY \]\[ M = \frac{1+c}{rr+e+c} \times H \]\[ M^* = \sqrt{\frac{bY}{2i}} \]\[ i_t = r^* + \pi_t + \frac{1}{2}(\pi_t - \pi^*) + \frac{1}{2}(Y_t - Y_t^*) \]\[ \pi_t = \pi^e_t - \alpha(u_t - u^*) + \varepsilon_t \]