Applications of the IS-LM Model

Shocks and Monetary Policy

Today's discussion continues the analysis of the IS-LM model, focusing on:

1. Shocks and monetary policy: Determining the optimal monetary policy in response to shocks in the goods or money markets.
2. The Taylor rule: Understanding how monetary policy is conducted and integrating this into the IS-LM model.
3. IS-LM model with banks: Analyzing the macroeconomic impacts of the 2008 financial crisis.

Shocks in the IS-LM Model

• Policies can cause fluctuations in output and interest rates by changing the equilibrium.
• Economies encounter unexpected changes, known as shocks, which drive the business cycle.
• The IS-LM framework can be used to analyze short-run fluctuations in output.
• Monetary policy can be employed to stabilize these short-run economic fluctuations.

Economic Shocks

• Shocks: Unexpected exogenous events with economic consequences. These explain business cycles, including booms and recessions.
• Types of shocks:
  1. Real shocks: Affect the IS curve.
     • Negative shock: IS curve shifts left.
     • Positive shock: IS curve shifts right.
  2. Monetary shocks: Affect the LM curve (money demand shocks).
     • Negative shock: LM curve shifts left.
     • Positive shock: LM curve shifts right.

Monetary Policy

Central banks have two types of policy to choose from:

1. Money targeting: Setting $M$ and allowing $r$ to adjust.
   • $ΔM$ leads to excess demand/supply of money, causing bond prices to adjust, which changes $r$ (Theory of Liquidity Preference).
2. Interest rate targeting: Setting $r$ and adjusting $M$ to maintain the chosen $r$.

Monetary Policy Choice

• Central banks commit to a monetary policy type before economic shocks occur.
• Policymakers must decide on a policy without knowing the type, timing, or direction of future shocks.
• Assumption: Policymakers want real output stability.
• The most desirable policy is the one that minimizes the expected variability of real income.

Interest Targeting with Real Shocks

• A real shock shifts the IS curve right for positive shocks and left for negative shocks.
• With interest rate targeting, the central bank adjusts the money supply to maintain the initial interest rate.
  • Positive real shock: Money supply increases.
  • Negative real shock: Money supply decreases.
• This leads to a larger expected variability of real income, which is undesirable.

Money Targeting with Real Shocks

• With money targeting, the central bank keeps the money supply constant, regardless of real shocks.
• This results in less variability of real income, which is desirable.

Optimal Policy for Real Shocks

If the central bank anticipates future real shocks and must commit to a policy rule, money targeting is better. This involves keeping the money supply fixed while allowing the market interest rate to change, reducing the expected output variability due to real shocks.

Interest Rate Targeting with Monetary Shocks

• A monetary shock shifts the LM curve to the right if positive and to the left if negative.
• With interest rate targeting, the central bank adjusts the money supply to maintain the initial interest rate.
  • Positive monetary shock: Money supply decreases.
  • Negative monetary shock: Money supply increases.
• This results in zero expected variability of real income, which is desirable.

Money Targeting with Monetary Shocks

• With money targeting, the central bank does not intervene after a monetary shock.
• Consequences:
  • Positive monetary shock: Real output increases.
  • Negative monetary shock: Real output decreases.
• This leads to larger variability of real income, which is undesirable.

Optimal Policy for Monetary Shocks

If the central bank believes monetary shocks are more likely, committing to interest rate targeting is better. This stabilizes output in the event of monetary shocks.

Real-World Application

Most central banks, like the Bank of England and the Fed, use interest rate targeting, suggesting they believe monetary shocks are more common than real shocks.

Conducting Monetary Policy

• Central banks control interest rates using the money supply by targeting the overnight interest rate, which is the rate banks charge each other for overnight loans.
  • In the US, this is the Federal Funds Rate; in the UK, the Bank Rate.
• This official rate influences other interest rates, such as for mortgages and business loans.

Updating the IS-LM Model

• Since most central banks use interest rate targeting, the money supply is endogenous.
• The LM curve was originally derived assuming an exogenous money supply.

The Taylor Rule

• Central banks use interest rates to stabilize output and inflation.
• John Taylor proposed the Taylor Rule, which aligns with observed Fed behavior:
  $i = ρ + ϕπ(π − π∗) + ϕY (Y − Y∗)$
• The central bank targets an interest rate based on changes in inflation and real output.

Components of the Taylor Rule

$i = ρ + ϕπ(π − π∗) + ϕY (Y − Y∗)$

• $\pi$: Inflation
• $\pi^*$: Inflation target
• $Y^*$: Natural level of real output (target)
• $\rho$: Natural nominal interest rate when ($Y = Y^*$)
• $\phi_{\pi} > 0$: Central bank's concern about inflation deviations.
• $\phi_Y > 0$: Central bank's concern about real output deviations.

Taylor Rule Scenarios

• $\pi < \pi^<em>$ & $Y < Y^</em>$: Recession → Reduce $i$
• $\pi > \pi^<em>$ & $Y > Y^</em>$: Boom → Increase $i$
• $\pi > \pi^<em>$ & $Y < Y^</em>$: Stagflation → Depends on relative size of $\phi<em>{\pi}$ and $\phi</em>Y$
• $\pi < \pi^<em>$ & $Y > Y^</em>$: Depends on relative size of $\phi<em>{\pi}$ and $\phi</em>Y$

IS-TR Model

• Incorporates the Taylor rule into the IS-LM framework.
• In the short run, prices are fixed, so $\pi = 0$. The Taylor Rule simplifies to:
  $i = r^* + \phi_Y(Y - Y^*)$
• Monetary policy is passive, with the Taylor Rule dictating the target interest rate, and the central bank adjusts $M$ accordingly.

IS-TR Model: Fiscal Policy

• When government spending increases ($G \uparrow$):
  • The outcome is similar to the IS-LM model, with $r \uparrow$ and $Y \uparrow$, but the mechanism differs.
  • IS-LM model: The interest rate increases due to changes in the money market (Theory of Liquidity Preference).
  • IS-TR model: The interest rate increases due to the Taylor rule.

Differences Between IS-LM and IS-TR Models

• The new equilibrium after a given $G \uparrow$ is not typically the same in the IS-LM and IS-TR models due to the different underlying mechanisms.

IS-LM Model: Credit Crunch

• The 2008 financial crisis led to a credit crunch, where banks stopped lending, reducing credit availability.
• This can be analyzed using the IS-LM model by introducing banks.

IS-LM Model with Banks

Banks' balance sheets include:

• Assets: Loans, other assets

• Liabilities: Capital (equity and debt), deposits

• Leverage ratio: $Leverage = \frac{Assets}{Equity}$

  • A higher leverage ratio indicates a riskier but potentially more profitable bank.

Impact of Banks on the IS Curve

• Businesses borrow from banks at a rate higher than what savers receive:
  $\rho = i + x$
• The IS curve is now:
  $I(\rho)$
• $x$ is determined by bank equity: If equity decreases, leverage increases, lending decreases, and $x$ increases.

Financial Crisis Impact

A crash leads to:

• Bank capital decreasing.
• Lending decreasing.
• $x$ increasing.
• Investment decreasing.

Policy Responses

Policies to overcome the recession:

• Fiscal policy: Increasing $G$ or decreasing $T$ shifts the IS curve outward.

• Monetary policy: Increasing $M$ shifts the LM curve outward.

• However, a liquidity trap may prevent returning to the original output level with a positive interest rate.