Lecture 8. The IS–LM Model and the IS–LM–BP Model
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1. Limitations of earlier models
2. The IS–LM model
3. The IS–LM–BP model
1. Limitations of earlier models
⑴ Limitation 1. Even when analyzing demand-side factors, earlier frameworks did not consider the role of the interest rate determined in the money market.
① In the Keynesian model, when analyzing the goods market, the interest rate was treated as given.
② In the Keynesian model, when analyzing the money market, total output (income) was treated as given.
③ In reality, the goods market and the money market affect each other through the interest rate as an intermediary variable.
④ The IS–LM model achieves simultaneous equilibrium in the goods market and the money market.
⑵ Limitation 2. They emphasized demand-side factors only and did not analyze supply-side factors.
① The IS–LM model also does not analyze supply-side factors.
② Later, the AD–AS model considers supply-side factors as well.
2. The IS–LM model
⑴ Overview
① Aggregate demand side of GDP: goods market, money market, foreign exchange market
② Aggregate supply side of GDP: labor market
③ Assumption 1. Assume a small open economy.○ Most countries participate as price-takers.
○ Under this assumption, the foreign exchange market can be ignored.④ Assumption 2. In the IS–LM model, price changes are not considered.
○ A constant price level means the market has a horizontal demand curve.
○ Since the price level does not change, there is no need to distinguish between the real interest rate and the nominal interest rate.⑤ Since there are two endogenous variables (unknowns), Y and r, we use two equations: goods-market equilibrium and money-market equilibrium.
⑵ Step 1. Goods-market equilibrium: derive the IS curve (via the loanable-funds market perspective)
① Basic assumption: the supply of consumption/investment, etc., is automatically met.
○ In equation (1), the left-hand side is total supply, and the right-hand side is total demand.
○ Total supply: for aggregate demand level E, E = Y
○ Total demand: for aggregate demand level E, E = C + I + G + (X - Q)
○ In the IS–LM model, equilibrium national income is effectively aggregate demand.
○ In the AD–AS model, we begin to consider aggregate supply explicitly.○ Another interpretation: goods-market equilibrium is achieved as the equality of investment (injection) and saving (leakage).
○ b: interest-rate elasticity of investment○ Classical view: b ≫ 1
○ Keynesian view: b = 0
○ (Reference) Accelerator principle: investment and income are positively correlated.
② Goods-market equilibrium
Figure 1. Goods-market equilibrium and derivation of the IS curve
○ IS curve: the set of (Y, r) combinations that bring equilibrium in the goods market, plotted in the (Y, r) plane.
③ Interpretation: when government spending increases/decreases, the IS curve shifts right/left.
⑶ Step 2. Asset-market equilibrium: derive the LM curve (money market)
① Asset-market equilibrium
○ Asset choice between two perfectly substitutable financial assets: money and bonds
○ Asset-market equilibrium conditions○ Md: demand for money
○ Bd: demand for bonds
○ Ms: supply of money
○ Bs: supply of bonds○ If the money market is in equilibrium, the bond market is also in equilibrium.
○ Money-market equilibrium interest rate = bond-market equilibrium interest rate
○ Therefore, the LM curve introduced below focuses only on the money market.
② Real money demand (L, liquidity): based on liquidity preference theory
○ Transaction (precautionary) money demand: an increasing function of income. Dividing by P converts to real terms.
○ Speculative money demand: a decreasing function of the interest rate. Dividing by P converts to real terms.
○ (Reference) Why speculative demand exists: agents temporarily hold money while waiting for profitable investment opportunities in interest-bearing assets.
○ Supplement 1. Why bond prices rise when interest rates fall: by present-value logic, r appears in the denominator.
○ (Note) If interest rates rise, bond profitability rises (bond prices fall).
○ Supplement 2. Agents believe there is a “normal” interest rate and that the actual rate will revert to it (assumption).
○ Supplement 3. Classical economists do not recognize speculative money demand.
○ (Note) Money is a liquid asset, whereas bonds are not—hence “liquidity preference.”○ Real money demand = transaction money demand + speculative money demand
○ k: income elasticity of money demand (classical: large; Keynesian: small)
○ h: interest-rate elasticity of money demand (classical: small; Keynesian: large)
○ Remaining term: autonomous money demand
○ (Note) Unlike classical economists, Keynes emphasized the interest-rate elasticity h.
③ Money supply (M, money)
○ If the monetary base is exogenously determined: independent of the interest rate.
○ When the currency-deposit ratio and required reserve ratio are stable, the monetary base set by the central bank determines money supply.
○ The money stock is determined as a money-multiplier multiple of the monetary base: it is also independent of the interest rate.
○ H: monetary base (high-powered money) supplied by the central bank
○ C: currency created through deposit creation
○ D: deposit money supplied by commercial banks (also called demand deposits)
○ E: loans provided by banks to the private sector
○ η: fraction of currency held by the public out of the money stock (C + D), 0 < η < 1
○ θ: fraction of deposits (D) held as required reserves, 0 < θ < 1
○ 1 / (η + θ(1 - η)) : money multiplier (or credit multiplier)
○ Deposit money creation process: loans flow back into currency and deposits.
Table 1. Deposit money creation process
○ The following expression is also useful:
○ k: currency-deposit ratio (C / D)
○ z: required reserve ratio (R / D)
④ Money-market equilibrium
Figure 2. Money-market equilibrium and derivation of the LM curve
○ LM curve: the set of (Y, r) combinations that bring equilibrium in the money market, plotted in the (Y, r) plane.
○ L stands for money demand or liquidity preference.
○ M stands for money supply.○ Formulation: the IS–LM model does not consider price changes. Dividing by P converts to real terms.
⑤ Interpretation
○ If real money supply increases/decreases, the LM curve shifts right/left.
○ If real money demand decreases/increases, the LM curve shifts right/left.
⑷ Step 3. The intersection of IS and LM: simultaneous equilibrium in the goods market and money market
① Equilibrium national income
② Government spending multiplier
③ For the IS curve: left of the curve (excess demand → pressure to move right). On the curve (no left-right movement). Right of the curve (excess supply → pressure to move left).
④ For the LM curve: above the curve (downward movement pressure). On the curve (no up-down movement). Below the curve (upward movement pressure).
⑤ In disequilibrium: the sum of the movement components in (③) and (④) appears. (Note) It can feel like rotating counterclockwise.
⑸ Applications
① Multiplier effects
○ The larger the injections (c, i), the larger the multiplier.
○ The smaller the leakages (s, t, m), the larger the multiplier.② Crowding-out
○ Definition: when government spending increases, output Y does not rise by the full multiplier amount.
○ Mechanism: G ↑ → Y ↑ (by ΔG × multiplier) → Ld ↑ → r ↑ → I ↓ → Y ↓
○ Classical and monetarist views: crowding-out is large.
○ Keynesian view: crowding-out is small.③ Fiscal policy and monetary (financial) policy
○ Fiscal policy: government policy through shifts in the IS curve
○ Monetary policy: government policy through shifts in the LM curve
○ Tip 1. The flatter the IS curve: fiscal policy becomes less effective; monetary policy becomes more effective.
○ Tip 2. The flatter the LM curve: fiscal policy becomes more effective; monetary policy becomes less effective.
○ (Note) To understand these tips, consider multiplier effects and crowding-out.④ Liquidity trap
○ Definition: when the nominal interest rate is extremely low, everyone expects interest rates to rise soon.
○ (Reference) People hold cash now and plan to buy bonds later, expecting rates to rise.
○ Speculative money demand rises without bound (h → ∞) → liquidity becomes “trapped.”
○ Money demand is absorbed into speculative demand; transaction demand does not rise, so income does not change.
○ A horizontal LM curve: even if monetary policy shifts LM rightward, the curve does not effectively change.
○ Assumption used in the Keynesian model.○ Pigou effect
○ Even in a liquidity trap, monetary policy may be effective.
○ Consumption function includes the real value of wealth.
○ Goods-market equilibrium includes the real value of wealth.
○ Case 1. Money supply increases or P falls → real wealth (A/P) rises → consumption rises → aggregate demand rises (IS shifts right).
○ Case 2. Quantitative easing → direct injection of liquidity → real wealth (A/P) rises.○ Ultimately, the IS–LM intersection shifts right: the liquidity-trap problem is alleviated.
○ Case 3. Domestic stock prices rise → real wealth (A/P) rises.
○ (Reference) Higher stock prices can raise investment via Tobin’s q theory. ○ Effects
○ Money supply increases or P falls → aggregate demand rises → the AD curve becomes flatter.
○ Consumption may increase more than income.○ Quantitative easing (QE)
○ The central bank purchases government bonds and certain private assets to directly inject liquidity (money) into the market.
○ In other words, it supplies short-term liquidity directly where funding is needed, not only through government bonds.
○ Effect 1. Credit creation via an increased monetary base: stimulates consumption and investment.
○ Effect 2. Increases real wealth by injecting abundant liquidity.
○ Effect 3. Depreciates the domestic currency, increasing net exports.
○ Effect 4. Raises expected inflation, encouraging current consumption and increasing overall consumption.
○ Shifts the IS curve.
○ Japan has pursued QE under the name “Abenomics” to escape a liquidity trap.
3. The IS–LM–BP model
BP comes from the first letters of balance of payments.
⑴ Exchange rate (exchange rate)
① Overview
○ Definition: the exchange ratio between two countries’ currencies (e.g., how many won per 1 dollar).
○ An increase/decrease in the exchange rate means the domestic currency value falls/rises.② Exchange rate determination theory 1: Purchasing power parity (PPP)
○ Definition: exchange rates are determined by the ratio of purchasing power (i.e., the ratio of price levels) across countries.
○ Equilibrium exchange rate: prevents arbitrage between foreign and domestic goods.○ e: equilibrium exchange rate
○ P, Pf: domestic and foreign price levels (not the price of an individual good)
○ If ePf > P: imports fall, exports rise → FX supply increases → exchange rate falls.
○ If ePf < P: imports rise, exports fall → FX demand increases → exchange rate rises.
○ Premise: the law of one price holds and trade is active.
○ Limits: trade barriers (tariffs), transaction costs, heterogeneous goods, existence of non-tradables.
○ Evidence: among advanced economies with low trade barriers and low transaction costs, PPP tends to hold in the long run.③ Exchange rate determination theory 2: Interest rate parity (IRP) (proposed by Dornbusch)
○ Definition: focusing on the capital account, the exchange rate is determined at the level that equalizes investment returns across countries.
○ IRP curve: when the interest rate or exchange rate changes, the point moves; when the expected future exchange rate changes, the curve shifts.
Figure 3. IRP curve
○ r: domestic real interest rate
○ rf: foreign real interest rate
○ et: current exchange rate
○ eᵉ_{t+1}: expected exchange rate one year ahead
○ 1 + r: future value of 1 unit of domestic currency
○ (eᵉ_{t+1} / et) × (1 + rf): future value if 1 unit is converted into dollars now
○ Δeᵉ / e: expected rate of exchange-rate change; equals the nominal interest-rate differential○ Taking logs yields the following approximation.
○ Capital movement: since asset prices and interest rates are generally inversely related, capital tends to move toward higher interest rates.○ If (LHS) > (RHS): demand and price of domestic financial assets rise → domestic interest rate falls; domestic money demand rises → exchange rate falls.
○ If (LHS) < (RHS): demand and price of foreign financial assets rise → foreign interest rate falls; foreign money demand rises → exchange rate rises.○ (Reference) Covered interest parity
○ Definition: the expected exchange rate is a contracted forward exchange rate.
○ No exposure to investment-loss risk.○ Evidence: works well among countries with free capital mobility and financial products of similar risk.
○ 1960s–1970s: international capital mobility was directly controlled; exchange-rate changes were mainly driven by current-account changes.
○ Since the 1980s: cross-border capital flows expanded → the capital account plays a larger role in exchange-rate movements.④ (Reference) Exchange rate determination theory 3: Current-account theory
○ The exchange rate is determined where FX demand and supply intersect.
○ If the current account improves, FX supply increases (supply curve shifts right).
○ The equilibrium exchange rate falls, i.e., the domestic currency appreciates.
○ (Note) This does not seem to be a major concept here.
⑵ When interest rate parity holds
① (Reference) Goods-market equilibrium
② (Reference) Money-market equilibrium
③ Foreign exchange market equilibrium (IRP curve)
Figure 4. IRP curve
④ IS–LM–IRP system
○ (Note) This is much simpler than the IS–LM–BP system below.
○ If the expected exchange rate is constant: not very different from standard IS–LM; the nominal exchange rate is determined afterward.
○ If the expected exchange rate changes: the IRP curve shifts and first affects investment, net exports, etc.⑤ Floating exchange rate regime
○ Floating exchange rate regime (see below)
○ Expansionary monetary policy○ 1st. LM shifts right due to higher real money supply.
○ 2nd. Real income rises; the interest rate falls.
○ 3rd. As the interest rate falls, the point moves along IRP → the nominal exchange rate rises.
○ 4th. As the nominal exchange rate rises, exports increase and imports decrease: movement along the IS curve.○ Expansionary fiscal policy
○ 1st. IS shifts right.
○ 2nd. Real income rises; the interest rate rises.
○ 3rd. As the interest rate rises, the point moves along IRP → the nominal exchange rate falls.
○ 4th. As the nominal exchange rate falls, exports decrease and imports increase: movement along the LM curve.⑤ Fixed exchange rate regime
○ Fixed exchange rate regime (see below)
○ Expansionary monetary policy
○ Expansionary fiscal policy
⑶ When interest rate parity does not hold
① Factor 1: PPP
○ An increasing function of the real exchange rate: a lower domestic currency value boosts exports and suppresses imports.
○ An increasing function of foreign income (Yf): exports rise with foreign income.
○ A decreasing function of domestic income (Y): imports rise with domestic income.② Factor 2: IRP
○ Under IRP, net capital inflows are determined by the domestic–foreign interest-rate differential and expected exchange-rate changes.
○ For simplicity, the expected rate of exchange-rate change is often set to 0. (Note) That is, IRP is not explicitly considered.
○ In other words, next period’s exchange rate is expected to equal the current period’s actual exchange rate.③ (Reference) Goods-market equilibrium
④ (Reference) Money-market equilibrium
⑤ Foreign exchange market equilibrium (BP curve): combinations of national income (Y) and interest rate (r) that yield balance-of-payments equilibrium
○ Formulation
○ NX: the part of net exports determined as an increasing function of the real exchange rate (ePf / P) and foreign income
○ NX - qY: net exports
○ rp: risk premium
○ F(r - rf - rp): net capital inflow
○ BP > 0: balance-of-payments surplus
○ BP < 0: balance-of-payments deficit
Figure 5. BP curve with imperfect vs. perfect capital mobility
○ Case 1. BP curve under perfect capital mobility
○ Capital inflows and outflows are completely free.
○ A horizontal BP curve: capital moves so sensitively to the interest-rate differential that a sustained differential cannot exist.
○ Since (r - rf) is approximately the expected rate of exchange-rate change, expected exchange-rate change is near 0.○ Case 2. BP curve under imperfect capital mobility
○ Capital flows occur at a limited level (transaction costs, etc.).
○ An upward-sloping BP curve: higher income worsens the current account → to keep BP = 0, the interest rate must rise.
○ If the exchange rate rises, the BP curve shifts right.
○ (Reference) In the 1980s, global capital mobility was not fully free.○ Case 3. BP curve under extreme capital controls
○ Since total output is fixed, it appears as a vertical line.
○ If the exchange rate rises, the BP curve shifts right.
⑥ IS–LM–BP system (also called the Mundell–Fleming model)
○ Domestic interest rate: at the intersection of the IS and LM curves
○ International interest rate: on the BP curve○ Rightward shift of IS: increase in autonomous investment, fiscal deficits and overconsumption, yuan appreciation, tax cuts, higher unemployment benefits
○ Leftward shift of IS: decline in corporate equipment investment, recession, downturn in advanced economies, excessive household debt, North Korea nuclear crisis, deteriorating investor sentiment
○ Rightward shift of LM: central bank open-market purchases of government bonds, lower required reserve ratio, development of money substitutes
○ Leftward shift of LM: central bank open-market sales of government bonds, higher required reserve ratio, interest-rate hikes
○ Upward shift of BP: higher world interest rates, higher risk premium due to sovereign credit downgrade
○ Downward shift of BP: lower world interest rates, lower risk premium due to sovereign credit upgrade
○ Rightward shift of BP: higher exchange rate, higher foreign income
○ Leftward shift of BP: (not specified)
⑦ Floating exchange rate regime and the BP curve (PPP)
○ Floating exchange rate regime
○ A regime in which the exchange rate is freely determined at the level that equalizes FX demand and supply, without central bank intervention.
○ If there is no government intervention at all, it is a free float; otherwise it is a managed float.
○ Under a floating regime, FX-market equilibrium is a necessary and sufficient condition for balance-of-payments equilibrium, because the exchange rate adjusts flexibly.○ Case 1. Domestic interest rate > world interest rate
○ 1st. Net capital inflow, BOP surplus
○ 2nd. Exchange rate falls
○ 3rd. Current account worsens: exports fall
○ 4th. IS shifts left○ Case 2. Domestic interest rate < world interest rate
○ 1st. Net capital outflow, BOP deficit
○ 2nd. Exchange rate rises
○ 3rd. Current account improves: exports rise
○ 4th. IS shifts right○ Higher government spending or tax cuts
○ Shifts IS right, but capital inflow → exchange rate fall → net exports fall → IS returns toward its original position.
○ As a result, a fiscal deficit (lower tax revenue) and a current-account deficit occur; this is called the twin deficits.○ Monetary policy
○ Under a floating regime, the freer capital mobility is, the larger the income-expansion effect.
○ It frees the economy from the burden of maintaining a fixed exchange rate and blocks the leakage of monetary-policy effects abroad.○ Fiscal policy
○ Under a floating regime, the freer capital mobility is, the smaller the income-expansion effect.
⑧ Fixed exchange rate regime and the BP curve (PPP)
○ Fixed exchange rate regime
○ Raising (lowering) the fixed exchange rate level implies a depreciation (appreciation) of the domestic currency.
○ Examples: Argentina; the Eurozone (giving up the national currency)○ Case 1. Domestic interest rate > world interest rate
○ 1st. Net capital inflow, BOP surplus
○ 2nd. Pressure for the exchange rate to fall (domestic currency appreciates)
○ 3rd. The central bank intervenes: sells domestic currency and buys foreign currency
○ 4th. Domestic money supply increases
○ 5th. LM shifts right○ Case 2. Domestic interest rate < world interest rate
○ 1st. Net capital outflow, BOP deficit
○ 2nd. Pressure for the exchange rate to rise (domestic currency depreciates)
○ 3rd. The central bank intervenes: buys domestic currency and sells foreign currency
○ 4th. Domestic money supply decreases
○ 5th. LM shifts left○ Devaluation and revaluation
○ Devaluation: lower the domestic currency value by raising the fixed exchange rate level, increasing net exports
○ Upvaluation (revaluation)○ Sterilization policy
○ Definition: to offset money-supply changes caused as a byproduct of a fixed exchange rate regime, the central bank conducts open-market operations in the opposite direction of FX intervention.
○ If the central bank sells domestic currency and buys FX (Case 1), it sells competing domestic bonds in the open market.
○ This can create the illusion of no change in money supply, temporarily generating IS–LM–BP imbalance.
○ In general, sterilization cannot last long.
○ In particular, if FX is sold, reserves fall and speculation may occur in anticipation of that limit.
⑷ Applications
① J-curve effect
○ Definition: after raising the exchange rate, the current account may worsen in the short run even though it improves in the long run.
○ Reason: prices change immediately, but export and import quantities adjust only with a lag.② Overshooting theory
○ Definition: because the price level is sticky in the short run, the exchange rate can deviate substantially from its long-run equilibrium.
③ Impossible trinity (trilemma)
○ Definition: free capital mobility, a fixed exchange rate, and an independent monetary policy cannot all coexist simultaneously.
Entered: 2020.10.03 13:45