Module 3: Goods and Financial Markets - The IS-LM Model

Introduction to the IS-LM Model

• Joint Determination: The IS-LM model, originally formulated by John Hicks and Alvin Hansen, focuses on how the interest rate and the level of output are determined jointly in the short run by considering both the goods and financial markets simultaneously.

• Integration of Markets: Spending decisions in the economy depend on borrowing conditions, and borrowing conditions depend on income and policy. Income and the interest rate are determined by the interaction between these two spheres.

• Key Questions for Consideration:     * Why can a cut in the policy rate fail to raise demand during periods of financial stress?     * How can "risk" move the economy even if fiscal policy remains unchanged?     * What does the model predict about the optimal policy mix during a recession?

The Goods Market and the IS Relation

• Refining Investment: In simpler models, investment ($I$) is often assumed to be constant. In the IS relation, investment is redefined as being dependent on two main variables:     * Production/Sales ($Y$): High sales lead to higher investment.     * The Interest Rate ($i$): Higher interest rates make borrowing more expensive, reducing investment.

• The IS Equation: The equilibrium in the goods market is represented by:     * $Y = C(Y - T) + I(Y, i) + G$

• The IS Curve Profile:     * Derivation: An increase in the interest rate decreases the demand for goods at any given level of output, which leads to a decrease in the equilibrium level of output.     * Slope: The IS curve is downward sloping because higher interest rates correspond to lower equilibrium output in the goods market.

• Shifts in the IS Curve:     * Factors: Any change that decreases (or increases) the demand for goods, given a fixed interest rate, shifts the curve.     * Examples: An increase in taxes ($T$) reduces disposable income and demand, shifting the IS curve to the left. Increases in government spending ($G$) or consumer confidence shift it to the right.

Financial Markets and the LM Relation

• The Money Equilibrium: Derived from the relation $M = ext{£}Y L(i)$, where $M$ is nominal money supply and $L(i)$ is liquidity demand.

• The Real LM Relation: By dividing both sides by the price level ($P$), the relation becomes:     * $\frac{M}{P} = Y L(i)$

• Equilibrium Requirement: In equilibrium, the real money supply must equal the real money demand. Real money demand depends on real income ($Y$) and the interest rate ($i$).

• Central Bank Intervention: In modern practice, central banks (like the Bank of England with the "Bank Rate") choose the interest rate and then adjust the money supply to achieve that specific rate. This results in a horizontal LM curve at the chosen interest rate policy.

The Combined IS-LM Model

• Simultaneous Equilibrium: The IS and LM relations together determine output and the interest rate.     * IS relation: $Y = C(Y - T) + I(Y, i) + G$     * LM relation: $i = \bar{i}$

• Point A: Any point on the IS curve corresponds to goods market equilibrium. Any point on the horizontal LM curve corresponds to financial market equilibrium. Only the intersection (Point A) satisfies both equilibrium conditions.

• Policy Categorization:     * Fiscal Contraction/Consolidation: A decrease in $(G - T)$ (lower spending or higher taxes).     * Fiscal Expansion: An increase in $(G - T)$.     * Monetary Expansion: A decrease in the interest rate ($i$), achieved by increasing the money supply ($M$).     * Monetary Contraction/Tightening: An increase in the interest rate ($i$), achieved by decreasing the money supply ($M$).

Policy Impacts and the Policy Mix

• Analyzing Changes: To analyze changes in policy or exogenous variables, one must ask if the change shifts the IS curve, the LM curve, or both, and then identify how output and interest rates respond.

• Tax Increase Example: An increase in taxes shifts the IS curve to the left, which leads to a decrease in the equilibrium level of output while the interest rate (set by the LM curve) remains unchanged.

• Interest Rate Cut Example: A monetary expansion shifts the LM curve down, which leads to a higher level of output along the downward-sloping IS curve.

• The Policy Mix: This refers to the combination of monetary and fiscal policies.     * Recession Response: To increase output during a recession, a government can use fiscal expansion (shift IS right) and monetary expansion (shift LM down) simultaneously, both of which increase output.     * Deficit Reduction without Recession: A combined fiscal consolidation (IS shifts left) and monetary expansion (LM shifts down) can allow for a reduction in the budget deficit without triggering a recession.

• Historical Focus: The recessesions in France and Germany (2001–2002) illustrated these dynamics, with fluctuating GDP growth rates, government expenditure shifts, and ECB interbank rate adjustments.

Model Dynamics and Empirical Facts

• Adjustment Lag: In reality, output does not adjust instantly. Dynamics must be considered:     * Consumers take time to adjust consumption following changes in disposable income.     * Firms take time to adjust investment spending following changes in sales or interest rates.     * Firms take time to adjust production levels to match changes in sales.

• Monetary Policy Shocks: Research by Miranda-Agrippino & Ricco (2021) shows that contractionary monetary policy reduces industrial production and raises unemployment, with effects typically peaking after 6 months.

• Inflation Behavior: The Consumer Price Index (CPI) declines gradually following shocks, a phenomenon consistent with nominal rigidities and delayed price adjustment.

Nominal versus Real Interest Rates

• Definitions:     * Nominal Interest Rate ($i$): The return expressed in terms of currency (e.g., pounds).     * Real Interest Rate ($r$): The return expressed in terms of purchasing power.

• The Fisher Equation:     * $(1 + r_t) = \frac{1 + i_t}{1 + \pi^e_{t+1}}$     * Where $\pi^e_{t+1}$ is expected inflation between time $t$ and $t+1$.

• Approximation: For moderate rates, the relation is simplified to:     * $r \approx i - \pi^e$

• Implications for IS-LM:     * Spending decisions depend on the real interest rate. The IS relation becomes: $Y = C(Y - T) + I(Y, r) + G$.     * The central bank sets the nominal rate ($i$), but demand responds to $r = i - \pi^e$.     * If expected inflation ($\pi^e$) increases, the real rate ($r$) falls for a given nominal rate, which increases demand.     * Ex-ante vs. Ex-post: The real rate based on expected inflation is the ex-ante interest rate; the realized rate is the ex-post interest rate.     * Zero Lower Bound (ZLB): The nominal interest rate cannot fall below zero. This implies the real interest rate cannot be lower than the negative of inflation.

Risk and Financial Intermediation

• Risk Premium ($x$): Bond holders require a premium to compensate for risk, determined by the probability of default ($p$) and the degree of risk aversion.

• Calculating the Premium: To equalize expected returns between a riskless bond ($i$) and a risky bond ($i + x$):     * $(1 + i) = (1 - p)(1 + i + x) + (p)(0)$     * Solving for $x$: $x = \frac{(1 + i)p}{1 - p}$

• Financial Intermediaries: Most borrowing happens through banks which borrow short-term and lend long-term. Their capital and liquidity levels affect lending capacity.

• Extended IS Relation: The model is updated to reflect the borrowing rate as the sum of the real policy rate ($r$) and the risk premium ($x$):     * $Y = C(Y - T) + I(Y, r + x) + G$     * $r = \bar{r}$

• Financial Shocks: An increase in the risk premium ($x$) shifts the IS curve to the left, decreasing equilibrium output. While a decrease in the policy rate ($r$) can offset this in principle, the ZLB may limit the central bank's ability to respond.

Case Study: The 2008 Financial Crisis

• Genesis: Excessive leverage and risky lending led to financial fragility.

• The Mechanism: When house prices (which rose from 2000 to 2006) crashed, banks faced losses and credit tightened. Borrowing costs rose, and consumer/business confidence plummeted (bottoming in early 2009).

• IS-LM Interpretation: Credit tightening and lower confidence shifted the IS curve sharply to the left.

• Policy Response:     * Monetary: Policy rates were reduced toward the zero lower bound; central banks employed unconventional policies like Quantitative Easing (QE) and liquidity provision (shifting LM down).     * Fiscal: Temporary tax cuts and increased public spending were implemented (shifting IS back to the right).

• Limits: Despite these interventions, the ZLB constraint limited the extent of monetary policy effectiveness, resulting only in a partial shift back toward original output levels.