Chapter 18 – IS-MP Analysis: Linking Interest Rates and Output

Aggregate Expenditure and Short-Run Fluctuations

• Aggregate expenditure (AE): total desired spending in the economy.
  • Formula: $AE = C + I + G + NX$
  • Components:
  • $C$ – Consumption
  • $I$ – Planned (private) investment
  • $G$ – Government purchases of goods & services
  • $NX$ – Net exports (exports − imports)
• Peloton example
  • Pandemic demand surge → over-production → $1.5\text{ billion USD}$ of unsold inventory.
  • Lesson: in the short run, spending (demand) drives output.
• Macroeconomic equilibrium
  • Condition: $Y = AE$ where $Y$ is actual (real) GDP.
  • If Y>AE → unplanned inventory build-up → firms cut production.
  • If Y<AE → inventory draw-down / back-orders → firms raise production.
• Inventory based adjustment mechanism continually pushes $Y$ toward equilibrium.
• Demand-driven short run vs. supply-driven long run
  • Short run: year-to-year business-cycle fluctuations explained by shifts in AE.
  • Long run: potential output $Y^*$ determined by full employment of resources.
• Output gap
  • Definition: $\text{Output gap}=\dfrac{Y - Y^<em>}{Y^</em>} \times 100\%$
  • "Too cold" (negative gap), "Too hot" (positive gap), "Just right" (gap = 0).
  • Actual $Y$ often deviates widely from $Y^*$ because AE fluctuates.
• Distinguish
  • Equilibrium output: resting point where $Y=AE$.
  • Potential output $Y^*$: highest sustainable level; where Goldilocks wants the economy.

The IS Curve – Output & the Real Interest Rate

• Goal: link Main-Street spending to the real interest rate $r$.
• Real interest rate $r$
  • $r = i - \pi^e$ where $i$ is nominal interest rate, $\pi^e$ expected inflation.
  • Interpreted as the opportunity cost of spending now versus saving.
• Why $r$ matters
  • Lower $r$ ↓ opportunity cost → ↑ spending → ↑ output.
  • Policymakers (Fed) manipulate $r$ to stabilise the economy.
• Effects of a lower real rate on AE components
  • Consumption: households substitute toward present spending and away from saving.
  • Investment: more capital projects pass the cost–benefit test; firms undertake them.
  • Government purchases: interest savings free fiscal space (though governments might repay debt instead).
  • Net exports: cheaper U.S. dollar (capital outflow) → ↑ exports, ↓ imports.
• Aggregate effect: falling $r$ shifts each component upward → AE curve shifts up → higher $Y$.
• IS curve characteristics
  • Axes: vertical $r$ ("price"), horizontal output gap $Y! -!Y^*$ ("quantity").
  • Downward-sloping: $\downarrow r \;\Rightarrow\; \uparrow AE \Rightarrow \uparrow Y$.
  • Movement along IS: CAUSED by a change in $r$.
  • Shift of IS: CAUSED by anything (other than $r$) that changes AE at every $r$.
• Historical illustration – Volcker disinflation (1980–82)
  • Fed pushed nominal $i$ ≈ $20\%$; with $\pi$ ≈ $10\%$ ⇒ $r\approx10\%$.
  • High $r$ → AE collapse → deepest post-war slump at that time.

The MP Curve – What Determines the Real Interest Rate

• Decomposition: $r = r_{\text{risk-free}} + \text{Risk premium}$.
  • $r_{\text{risk-free}}$ set by the Federal Reserve via the federal funds rate.
  • Risk premium determined in financial markets.
• Federal Reserve & monetary policy
  • Eight FOMC meetings per year; chooses target for the federal funds rate.
  • Sets nominal $i<em>{\text{ff}}$ ⇒ indirectly sets $r</em>{\text{risk-free}}$ because $r = i - \pi^e$.
  • Decisions ripple to other interest rates (savings, credit cards, mortgages…).
• Risk premium
  • Compensation to lenders for default, liquidity, interest-rate, and other risks.
  • Varies with borrower characteristics and macro/financial conditions (risk appetite).
  • Example: car loan < personal loan rate because collateralisable car lowers default risk.
• MP curve
  • Graphical device showing the current real rate given prevailing monetary policy and risk premium.
  • Shifts up (higher $r$) if the Fed tightens or risk premium rises; shifts down if the opposite.

The IS–MP Framework

• Combines demand side (IS) with interest-rate determination (MP).
• Equilibrium: intersection of IS and MP ⇒ simultaneously determines
  • Output gap (horizontal coordinate).
  • Real interest rate (vertical coordinate).
• Booms and busts
  • Optimistic expectations → IS rightward → boom (positive gap).
  • Pessimistic expectations → IS leftward → bust (negative gap).
  • Both are equilibria; Keynes: slumps can persist without intervention.

Policy Analysis within IS–MP

• Monetary policy (Fed)
  • Cuts $r_{\text{risk-free}}$ → MP shifts down → lower $r$ → movement along IS → ↑ output.
  • Example: From deep recession (point A) to higher but still below-potential output (point B).
• Fiscal policy
  • Government changes $G$ or taxes → direct effect on AE plus multiplier.
  • Multiplier definition: $\Delta GDP = \Delta Spending \times \text{Multiplier}$.
  • IS shifts horizontally by $\Delta G \times \text{Multiplier}$.
  • Example: $\Delta G = 150\text{ billion}, \text{Multiplier}=2 \Rightarrow \Delta Y=300\text{ billion}$.
  • Interest rate unchanged (movement is horizontal) when MP stays put.

Macroeconomic Shocks

• Classification
  1. Spending (demand) shocks → shift IS.
  2. Financial shocks → shift MP.
• Spending-shock sources & direction
  • Consumption: ↑ wealth, ↑ consumer confidence, ↑ transfers, ↓ taxes, ↓ inequality.
  • Investment: ↑ GDP growth prospects, ↑ business confidence, ↑ investment tax credits, easier lending, ↓ uncertainty.
  • Government purchases: stimulus bills, automatic stabilisers (not transfers directly).
  • Net exports: ↑ foreign GDP, ↓ dollar, ↓ foreign trade barriers, ↑ foreign barriers against U.S. protection.
• Financial-shock sources & direction
  • Fed actions: ↑ (↓) $r_{\text{risk-free}}$.
  • Market sentiment: ↑ (↓) risk premium due to default, liquidity, interest-rate risk, or risk aversion.
• Examples
  • China tariff on U.S. exports → IS left → ↓ GDP, $r$ unchanged.
  • Surge in auto-sector investment → IS right → ↑ GDP.
  • Fed rate hike to fight inflation → MP up → ↑ $r$, ↓ GDP.
  • Fall in default fears → MP down → ↓ $r$, ↑ GDP.
• Three-step forecasting checklist
  1. Identify shock type (spending or financial).
  2. Direction & magnitude of IS or MP shift.
  3. Deduce new equilibrium $r$ and output gap.

Case Study: Covid-19 Recession & Recovery

• 03 Mar 2020 – Fed emergency rate cut
  • Financial shock ↓ $r_{\text{risk-free}}$ → MP down → ↑ output.
• 13 Mar 2020 – Sudden drop in consumption
  • Spending shock (C) → IS left → ↓ output (gap widens).
• 18 Mar 2020 – Market panic raises risk premium
  • Financial shock ↑ risk premium → MP up → ↑ $r$, ↓ output.
• 23 Mar 2020 – Fed backstops credit markets
  • Financial shock ↓ risk premium → MP down → ↓ $r$, ↑ output.
• 27 Mar 2020 – CARES Act transfers & UI boost
  • Spending shock (C, G) → IS right → ↑ output, $r$ unchanged.

Recap & Key Take-Aways

• Short-run business-cycle fluctuations originate from aggregate expenditure.
• Real interest rate is both a driver of spending and a policy lever.
• $r = r_{\text{risk-free}} + \text{Risk premium}$
  • Fed controls $r_{\text{risk-free}}$ via the federal funds rate.
  • Financial markets set the premium.
• IS–MP equilibrium summarises macroeconomic conditions.
  • MP shifts ↔ monetary policy & financial shocks.
  • IS shifts ↔ fiscal policy & other spending shocks.
• Use the three-step method to forecast effects of any shock on the output gap and $r$.