Monetary Economics (HBE 223): Comprehensive Study Guide on IS-LM, Transmission Mechanisms, Phillips Curve, and Quantitative Easing

TOPIC 5: THE IS-LM FRAMEWORK AND MONETARY POLICY ANALYSIS

5.1 Deriving the IS Curve: Goods Market Equilibrium

• Definition: The IS curve represents all combinations of interest rates ($i$) and output ($Y$) at which the goods market is in equilibrium.

• Equilibrium Condition: In the goods market, aggregate demand must equal aggregate supply (output). Total aggregate demand is calculated using the formula:

$Y = C + I + G + (X - M)$

  Where:

• $Y$ is output.

• $C$ is consumption.

• $I$ is investment.

• $G$ is government spending.

• $X$ is exports.

• $M$ is imports.

  • Deriving the Relationship:

• Investment Sensitivity: Investment ($I$) is the key component that depends on interest rates ($i$). Higher interest rates increase the cost of borrowing, which reduces investment. Firms postpone projects that have lower expected returns.

• Consumption Sensitivity: Consumption may decline with higher interest rates due to the intertemporal substitution effect.

• Functionality: Investment is a decreasing function of the interest rate: $I = I(i)$, where \frac{dI}{di} < 0.

• Mechanism: When the interest rate increases, investment falls. This decline in investment reduces aggregate demand, requiring output to fall to maintain equilibrium (because when output falls, saving must fall to equal the lower investment levels).

• Slope: There is a negative relationship between interest rate ($i$) and output ($Y$); thus, the IS curve slopes downward.

  • The Multiplier:

• The magnitude of the output response to changes in investment depends on the multiplier.

• Formula: If autonomous investment falls by $\Delta I$, output falls by $\frac{1}{s} \times \Delta I$.

• $s$ represents the marginal propensity to save, which is calculated as $1 - c$ (where $c$ is the marginal propensity to consume).

  • IS Curve Characteristics:

• Steep IS Curve: Indicates that output changes very little when interest rates change. This occurs if (1) investment is insensitive to interest rates, or (2) the multiplier is small (resulting from a high savings rate).

• Flat IS Curve: Indicates that investment is highly sensitive to interest rates and/or the multiplier is large (resulting from a low savings rate and high consumption response).

5.2 Deriving the LM Curve: Money Market Equilibrium

• Definition: The LM curve represents all combinations of interest rates and output at which the money market is in equilibrium.

• Equilibrium Condition: The quantity of money supplied must equal the quantity demanded:

$\frac{M}{P} = Md(Y, i)$

  Where:

• $\frac{M}{P}$ is the real money supply (nominal money supply deflated by price level).

• $Md$ is money demand, which is a function of income ($Y$) and interest rate ($i$).

  • Money Demand Dynamics:

• Income Influence: Money demand increases with income ($Y$) because higher income leads to more transactions, which require more money.

• Interest Rate Influence: Money demand decreases as interest rates ($i$) rise because the opportunity cost of holding money increases.

  • Deriving the Relationship:

• Assuming the real money supply is fixed ($\frac{M}{P} = \frac{\bar{M}}{P}$), at higher levels of output, money demand is higher.

• To maintain equilibrium (so that demand equals the fixed supply), the interest rate must rise to make people willing to hold only the existing supply despite their higher income.

• This creates a positive relationship between $Y$ and $i$, meaning the LM curve slopes upward.

  • LM Curve Characteristics:

• Steep LM Curve: Means that changes in output significantly affect interest rates, suggesting money demand is highly sensitive to income levels.

• Flat LM Curve: Means that changes in output have very little effect on interest rates.

• Shifts of the LM Curve: If the central bank increases the money supply, the LM curve shifts to the right. At any given output level, the interest rate is lower because the increased availability of money eliminates the need for high rates to clear the market.

5.3 Equilibrium and Monetary Policy Effects in the IS-LM Framework

• General Equilibrium: The macroeconomy reaches equilibrium at the intersection of the IS and LM curves. At this point, both the goods market (output equals aggregate demand) and the money market (money demand equals money supply) are in equilibrium.

• Expansionary Monetary Policy (CBK Context):

  • When the Central Bank of Kenya (CBK) increases the money supply, the LM curve shifts to the right.

  • At the original interest rate, money supply now exceeds money demand. Individuals try to eliminate excess money by purchasing bonds and other assets, which drives interest rates down.

  • As interest rates fall, investment increases because borrowing costs are lower, and aggregate demand increases.

  • The economy moves along the IS curve to a new equilibrium defined by lower interest rates and higher output ($Y$).

• Effectiveness Factors:

  • Slope of the IS Curve: If the IS curve is steep (investment is insensitive to rates), monetary policy is less effective. Interest rates must fall significantly to stimulate even a modest increase in output.

  • Slope of the LM Curve: If the LM curve is steep (money demand is very sensitive to income), monetary policy is less effective. The rightward shift of the LM curve results in only small interest rate decreases because the new money is quickly absorbed by rising money demand as output grows.

  • The Liquidity Trap: In extreme cases where interest rates are near zero and expected to rise, the LM curve becomes nearly horizontal. Monetary policy is ineffective here because rates cannot fall further.

• Contractionary Monetary Policy:

  • When the CBK decreases the money supply (by raising the CBR), the LM curve shifts left.

  • Interest rates rise, causing investment to fall and output to decrease as the economy moves down the IS curve.

TOPIC 6: THE MONETARY TRANSMISSION MECHANISM - COMPREHENSIVE ANALYSIS

6.1 How Monetary Policy Affects the Real Economy: The Five Channels

• Channel 1: The Interest Rate Channel (Traditional):

  • Mechanism: CBK raises CBR $\rightarrow$ Interest rates rise $\rightarrow$ Investment falls $\rightarrow$ Aggregate demand falls $\rightarrow$ Output falls.

  • Process:

  1. CBK raises the policy rate (CBR).

  2. Commercial banks increase lending rates to customers.

  3. Higher rates reduce the present value of investment projects, leading firms to cancel or postpone them.

  4. Higher deposit rates increase the opportunity cost of consumption, encouraging households to increase savings and reduce spending.

  5. AD declines, firms reduce production, output falls, and unemployment rises.

  • Time Lag: This channel operates with a lag of 6-12 months. In Months 1-2, decisions are based on old expectations. By Months 3-6, investment responses begin. By Month 12, most adjustment has finished.

  • Kenya Context: Operates through the impact of CBR changes on bank lending rates.

• Channel 2: The Credit Channel:

  • Focuses on the availability of credit rather than the cost.

  • Mechanism: CBK raises CBR $\rightarrow$ Bank borrowing costs rise and reserves fall $\rightarrow$ Banks become cautious $\rightarrow$ Loan availability drops $\rightarrow$ Firms cannot borrow even at high rates $\rightarrow$ Investment falls.

  • Bank Balance Sheet Channel: Higher rates shrink net interest margins (banks pay more on deposits but hold fixed-rate loans), leading to reduced lending.

  • Collateral Channel: Rates rise $\rightarrow$ Asset prices (stocks, real estate) fall $\rightarrow$ Collateral value used for loans decreases $\rightarrow$ Banks reduce lending.

  • Historical Note: During the 2008 financial crisis, the Fed cut rates, but credit remained restricted because banks feared insolvency.

• Channel 3: The Asset Price Channel:

  • Mechanism: Higher interest rates increase the discount rate for future dividends/rents, reducing the present value and stock/real estate prices.

  • Wealth Effects: Lower asset prices reduce household wealth. People feel poorer, reducing consumption and increasing saving.

  • Quantitative Metric: A $10\%$ decline in stock market wealth may reduce consumption by $0.5\%$ to $1\%$. In large economies, this is a substantial impact.

  • Kenya Context: The Nairobi Stock Exchange and real estate markets are key. Fluctuating property values significantly affect Kenyan household consumption.

• Channel 4: The Exchange Rate Channel:

  • Mechanism (Contractionary): CBK raises CBR $\rightarrow$ Kenyan assets more attractive to foreign investors $\rightarrow$ Shilling demand increases $\rightarrow$ Shilling appreciates $\rightarrow$ Exports more expensive $\rightarrow$ Net exports decline $\rightarrow$ Output falls.

  • Mechanism (Expansionary): CBK lowers CBR $\rightarrow$ Rates fall $\rightarrow$ Foreign investors withdraw $\rightarrow$ Shilling demand falls $\rightarrow$ Shilling depreciates $\rightarrow$ Exports cheaper $\rightarrow$ Output increases.

  • Kenya Context: Kenya exports coffee, tea, and cut flowers. A strong shilling makes these less competitive. While depreciation helps exports, it hurts import-competing industries and increases costs for imports like oil and manufactured goods.

• Channel 5: The Expectations Channel:

  • Mechanism: Based on central bank credibility. If the CBK is trusted to maintain price stability, policy works via expectations.

  • Process: CBK commits to target ($5\% \pm 2.5\%$) $\rightarrow$ Public believes inflation will stay on target $\rightarrow$ Expectations remain anchored even with expansion $\rightarrow$ Nominal wages don't surge $\rightarrow$ Real interest rates fall significantly $\rightarrow$ Strong investment stimulus.

  • Contrast: A low-credibility bank triggers immediate inflation expectations and nominal wage demands, resulting in little output stimulus and high inflation.

TOPIC 7: THE PHILLIPS CURVE AND INFLATION-UNEMPLOYMENT TRADE-OFF

7.1 Historical Development and Modern Understanding

• Original Phillips Curve: Proposed by A.W. Phillips in 1958 based on UK data (1861-1957). He found a negative relationship between wage inflation and unemployment.

• Logic: Low unemployment leads to tight labor markets where firms must raise wages to attract staff, pushing up costs and prices. High unemployment makes labor plentiful, so wages do not rise.

• Policy Menu: Policymakers in the 1960s (e.g., in the U.S. during the Vietnam War and Great Society) used the curve as a menu to choose preferred inflation-unemployment combinations.

• The Breakdown: In the 1970s, many nations hit stagflation (high inflation and high unemployment). Friedman and Phelps argued the curve shifted outward as workers revised inflation expectations upward.

7.2 The Expectations-Augmented Phillips Curve

• Modern Formula:

$\pi = \pi^e - a(u - u^*)$

  Where:

• $\pi$ is actual inflation.

• $\pi^e$ is expected inflation.

• $u$ is unemployment.

• $u^*$ is the natural rate of unemployment.

• $a$ is a positive constant measuring inflation responsiveness to the unemployment gap.

  • The Natural Rate ($u^*$): The unemployment rate consistent with stable inflation. It is determined by structural factors like sectoral composition, labor market frictions, search times, and geographic mobility.

  • Short-Run Trade-off: Exists for 6-12 months before expectations adjust. Policymakers can temporarily lower unemployment below $u^*$ by accepting higher inflation.

  • Long-Run Phillips Curve: The curve is vertical at the natural rate. Expectations eventually adjust to actual inflation, meaning unemployment cannot stay below $u^*$ permanently without ever-accelerating inflation.

  • Dynamics of Inflation Example: Start at natural rate with $\pi = \pi^e = 5\%$.

• Months 1-6: Expansion pushes u < u^*; inflation rises to $7\%$.

• Months 6-12: Agents observe $7\%$ inflation and revise expectations upward.

• Months 12-24: The Phillips Curve shifts outward; keeping u < u^* requires inflation to rise to $8-9\%$.

• Long Run: Unemployment returns to $u^*$ but inflation is trapped at a higher level.

  • Credibility: CBK's inflation targeting framework ($5\% \pm 2.5\%$) has built credibility over 15+ years, anchoring expectations and making the policy trade-off less severe.

TOPIC 8: QUANTITATIVE EASING WHEN CONVENTIONAL POLICY FAILS

8.1 The Lower Bound on Nominal Interest Rates and the Liquidity Trap

• Zero Lower Bound (ZLB): Nominal interest rates cannot fall significantly below zero because people can always hold cash (which pays $0\%$). If bank rates are negative, people withdraw cash, removing the bank's capacity to pay negative rates.

• Liquidity Trap: Occurs when interest rates reach the ZLB and conventional policy cannot stimulate the economy. Increased money supply is simply held as excess reserves. Examples include Japan's "Lost Decade" and the U.S./Europe post-2008.

8.2 What is Quantitative Easing and How Does it Work?

• Definition: Large-scale asset purchases (long-term bonds and mortgage-backed securities) by central banks when conventional rate policy is exhausted.

• Mechanisms:

  1. Liquidity Effect: Banks selling securities gain reserves, increasing the supply of loanable funds.

  2. Portfolio Balance Effect: Central bank purchases reduce the supply of long-term bonds, pushing prices up and yields (interest rates) down to stimulate investment.

  3. Signal/Expectations Effect: Large purchases signal commitment to maintaining low rates for an extended period, encouraging long-term borrowing (e.g., mortgages).

  4. Asset Price Effect: Increased demand for assets raises prices of stocks and real estate, increasing household wealth and consumption.

8.3 Limitations, Risks, and Challenges

• Limitations: QE is less effective if the financial system is frozen, confidence has collapsed, there is a debt overhang (households focusing on deleveraging), or a global recession occurs.

• Risks:

  1. Inflation: Large money supply could trigger inflation during recovery; exiting (unwinding) is technically and politically difficult.

  2. Asset Bubbles: Artificially low rates create speculative bubbles in stocks, commodities, and real estate.

  3. Inequality: QE benefits asset owners over wage earners, exacerbating wealth inequality.

  4. Exit Difficulty: Selling assets to withdraw liquidity can crash prices and signal future tightening, pushing rates up sharply.

• Kenya Context: CBK has not implemented large-scale QE due to normal interest rate ranges, though it applied targeted liquidity measures during the COVID-19 pandemic.