The IS-LM model in closed and open economy Michele Piffer∗ January 6, 2023 These notes follow the textbook by Olivier Blanchard, “Macroeconomics”, with a few minor modifications.1 1 IS-LM model in closed economy Relevant reading(s) from Blanchard, Macroeconomics, 7th edition: Chapter 5 (full chapter) 1. Combine the accounting equality Yd =C +I +G (1) with the following ‘theories’ for its components: C = C̄ + c · (Y − T ) I = I¯ − d · (i + f¯) G = Ḡ, T = T̄ (2) (3) (4) We get the IS curve in closed economy Y = Ā d − i m m (5) ∗ King’s Business School, King’s College London, UK. Email: michele.piffer@kcl.ac.uk, personal web page: https://sites.google.com/site/michelepiffereconomics/. These notes can be reproduced freely for educational and research purposes as long as they contain this notice and are retained for personal use or distributed for free. All errors are mine. Please get in touch if you find typos or mistakes. 1 For example, 1. we indicate foreign variables with levels; w rather than ∗ , using the latter to denote equilibrium 2. we do not assume that the function for investments is increasing in Y . 1 with Ā := C̄ − c · T̄ + I¯ − d · f¯ + Ḡ m := 1 − c (6) (7) Equivalently, the IS curve can be rewritten as i= Ā m − Y d d (8) The IS curve is a decreasing line in the space (i, Y ) with intercepts (i, Y ) = Ā ( Ād , 0) and (i, Y ) = (0, m ), and slope − md . The curve displays combinations of points in the space (i, Y ) such that the market of goods is in equilibrium. Points to the right (left) of the IS curve in the space (i, Y ) are interpreted as points for which the supply side of the economy is producing too much (too little) relative to aggregate demand, leading firms to adjust production downwards (upwards). The points along the IS curve are not equilibrium points for the full model, but only equilibrium points for the market of goods [see Figure 1]. 2. We do not formally model the money market, but assume that the central bank decides the nominal level of interest rate i = ī at which it wants the money market to clear. Hence, we treat ī as the choice variable of the central banker, assuming that the central bank can then adjust money supply to lead the interest rate to ī. This means that in the space (i, Y ), the LM curve is a horizontal line [see Figure 2]. 3. The equilibrium of the full model is pinned down by the central bank selecting the interest rate ī. This, in turn, implies an equilibrium level of the interest rate Ā − md ī: of i∗ = ī, which implies the equilibrium level of output equal to Y ∗ = m i∗ = ī Y∗ = (9) Ā d − ī m m (10) [see Figure 3] 4. Following a monetary expansion, the central bank decreases the interest rate from ī1 to ī2 , which increases output [see Figure 4]. To assess what happens to each component of the aggregate demand curve, remember the equilibrium condition Y = C(Y , T̄ ) + I( i , f¯) + G(Ḡ) (11) + − − − + The left hand side increases, hence the right hand side also increases. Closer inspection leads to note that 2 i Y C I G ↓ ↑ ↑ ↑ = We can summarize the effects discussed above as follows: i ↓→ I ↑→ Y d > Y s → Y ↑→ C ↑→ Y d > Y s → Y ↑→ C ↑→ ... (12) What is the model helping us understand about the real world? The model suggests that the unobserved transmission mechanism of monetary policy consists of at least two channels through which a decrease in the interest rate stimulates the economy: (a) the decrease in the interest rate increases investments, which contributes to the increase in equilibrium output (investment channel); (b) the increase in output increases consumption, which further increase output and contributes to the increase in equilibrium output (consumption channel). 5. A fiscal policy expansion via fiscal spending can be approximated in the model as an increase in Ḡ, holding T̄ constant. Assuming that the central bank leaves the interest rate unchanged, the fiscal expansion shifts the IS curve to the right, leading to a higher equilibrium level of output [see Figure 5]. The increase in G by ∆Ḡ leads to an equilibrium increase in output by 1 ∆G > ∆G (13) m due to c < 1, 1/m > 1: this implies a multiplicative effect. Starting from the equilibrium condition ∆Y ∗ = Y = C(Y , T̄ ) + I( i , f¯) + G(Ḡ) + − − − + (14) we find that a fiscal stimulus generated via an increase government spending leads to i Y C I G Surplus := T − G 3 = ↑ ↑ = ↑ ↓ We can summarize the effects discussed above as follows Ḡ ↑ Y d > Y s → Y ↑→ C ↑ Y d > Y s → Y ↑→ C ↑ .... (15) What is the model helping us understand about the real world? It helps us understand that, in principle, an increase in public spending does not need to increase output by the same amount as the increase in government spending, because it can generate an increase in output that feeds into an increase in consumption, which further feeds into an increase in output. Hence, there could be some multiplicative features that can be exploited to support the economy. Taking this line of thought to the extreme, the government could in principle spend ∆G in something completely useless, for instance digging holes in the ground. This could still increase equilibrium output. 6. Can you think outside of the model? Here are some examples of things that the model does not explicitly account for, but which could well affect the conclusions drawn using the model: (a) for monetary policy, are we sure that the central bank can decrease the interest rate, or is the interest rate too close to zero? (zero lower bound) (b) for fiscal policy, are we sure that the increase in government debt associated with the increase in Ḡ given T̄ fixed has no relevant implications? What if agents see that the government is spending more and decide to save more, just in case the government will need to raise taxes in the future? (Ricardian Equivalence) (c) for fiscal policy, are we sure that an increase in borrowing from the government will not push interest rates up due to the higher demand for money, and hence lead to a higher cost of borrowing for firms, which in turn reduces investments? (crowding out) The above analysis assumes that economy does not have any trading or financial relation with the rest of the world. Let’s now extend the analysis to an open economy. 2 Intro to Open economy Relevant reading(s) from Blanchard, 7th edition: Chapter 17 (full chapter), Chapter 18 (only the discussion of the Marshall-Lerner condition, 18-4, “Depreciation, the trade balance, and output”) 4 7. There is no single definition of the nominal exchange rate, it’s a relative concept. Define Dc the currency of the domestic country, and F c the currency of the foreign economy: a) the indirect (or European) definition of the nominal exchange rate is: EF c,Dc = price of the domestic in terms of foreign = = number of foreign per 1 unit of domestic = #F c = 1Dc hence EF c,Dc ↑→ Dc appreciates; b) the direct (or American) definition of the nominal exchange rate is: EDc,F c = price of the foreign in terms of domestic = = number of domestic per 1 unit of foreign = #Dc = 1F c hence EDc,F c ↑→ Dc depreciates; Some books use the indirect definition (Blanchard, Mishkin), others the direct one (Carlin an Soskice, Delli Gatti, Williamson). We follow Blanchard and use the indirect (European) definition: E = EF c,Dc (16) which increases when Dc appreciates. 8. To understand what determines the nominal exchange rate E we need to understand who trades Dc for F c and vice versa, i.e. what drives their demand and supply on the Forex market (foreign exchange market,or currency market). The starting point is the Balance of Payments, which is an account that registers the transactions of the domestic economy with the rest of the world. Balance of Payment = Current Account + Capital Account BoP = CA + KA The current account consists of three components: the trade balance/net export (export X minus imports IM , both expressed in domestic currency, with X − IM = N X), the income balance (net payments on cross-country asset holdings, i · N F A) and net transfers (foreign aid, T r). The capital account includes the net capital inflows into the domestic economy for new investments (Kin − Kout , both expressed in domestic currency). Omitting net transfers for 5 simplicity, the following equation clarifies which of the above items generate a demand of domestic versus foreign currency: BoP = CA + KA = DDc ,SF c = X DF c ,SDc DDc ,SF c DDc ,SF c DF c ,SDc − IM + i · N F A + Kin − Kout where I am assuming N F A > 0 for simplicity. 9. Except for small statistical discrepancies, the Balance of Payments must ‘balance’, which means BoP = CA + KA = 0 BoP = CA + KA = ∆IR flexible exchange rate fixed exchange rate with IR the stock of international reserves, or foreign reserves. In general BoP > 0 → DDc > SDc → if flexible exchange rate: Dc appreciates → if fixed exchange rate: buy F c, ∆IR > 0 & M s ↑= SDc ↑ BoP < 0 → DDc < SDc → if flexible exchange rate: Dc depreciates → if fixed exchange rate: sell F c, ∆IR < 0 & M s ↓= SDc ↓ Some interesting lessons: (a) Under a flexible exchange rate, a negative CA requires borrowing from the rest of the world and ensuring Kin > Kout . But this increases the total level of debt versus the rest of the world (NFA ↓), which further reduces CA via the income balance. Things can get out of hand, and at some point the country needs to accept to improve its net exports by cutting imports/increasing exports. But that’s easier said than done; (b) Under a fixed exchange rate, if the domestic central bank must fight against a depreciation, it had better have enough international reserves! The tendency of an appreciation, instead, implies that the country can accumulate international reserves, i.e. foreign reserves. Since ∆IR = ∆M , committments on E imply that M cannot be set freely. This also constrains the central banker’s ability to set i. 6 10. Later, we will introduce the simplifying assumption that, in a flexible exchange rate regime, the nominal exchange rate is mainly driven by the KA. In fact, while KA= - CA (unless we are in a fixed exchange rate regime), the absolute transactions in the CA are usually much lower than in KA, i.e. Kin +Kout >>> X + IM + r · N SA. Building on this, we postulate that E is pinned down by the uncovered interest rate parity (UIP) between domestic and foreign interest rate: Et (17) (1 + it ) = (1 + iw t ) e Et+1 What is the idea behind the UIP? A domestic investor might well find it optimal to invest abroad even if the foreign nominal interest rate is lower than the domestic one (iw t < it ) if he expects the domestic currency to depreciate over time EEe t > 1. In fact, a domestic investor who invests one unit of domestic t+1 currency abroad at time t will effectively invest Et units of foreign currency c ). At time t + 1, this delivers a gross return (remember, we are using E = #F 1Dc w of (1 + it )Et units, which is still denominated in foreign currency, which is equivalent to (1 + iw t )Et /Et+1 units of domestic currency, given Et+1 the future exchange rate (which is unknown at time t + 1). Hence, if the investor expects e the currency to depreciate enough, then Et /Et+1 > 1, offsetting (1 + it ) > w (1 + it ). The UIP is an equilibrium condition, i.e. an equality that must hold for a certain condition to be satisfied (which, for the UIP, is a no arbitrage condition between investing domestically and investing abroad). An equilibrium condition is conceptually very different from a causal mechanism, i.e. a force that drives variables up and down. Later in these notes, we will argue that given an e unchanged (iw , Et+1 ), an increase in it generates a capital inflow, which leads the domestic economy to appreciate, Et ↑. This line of thought ‘makes sense’: as capital flows into the economy, more agents demand for the domestic currency which hence appreciates. Yet, it’s an argument that hints at a causal mechanism, and has nothing to do with an equilibrium condition. It does not even strictly require the UIP to hold. Still, it’s useful to note that it is cone sistent with the UIP: within the UIP, since we are treating Et+1 as fixed, the appreciation generates the expectation of a depreciation, which makes foreign investment more profitable in terms of the domestic currency, hence allowing for it > iw t to hold in equilibrium. The expected depreciation of the domestic currency guarantees that the return for a domestic investor from investing abroad is not as low as iw t . 11. The above point summarizes a ‘theory’ for the determinants of the KA, or at least an equilibrium condition affecting 2 variables (i, iw ) which play an important role for KA. We now need a ‘theory’ for what drives CA, especially net exports, because net exports are part of aggregate demand, and we want to 7 use the model to study what drives aggregate output and how economic policy can affect it. We defined X as exports denominated in the domestic currency. We now need to distinguish between IM , the value of imports expressed in domestic currency, and IMF c , the value of the same imports expressed in foreign currency. We assume X = X(E ) and IMF c = IMF c (Y , E ). It then holds that − + + IM = IMF c /E. Hence, in principle, the effect of E on NX is not clear, since IMF c (Y , E ) + N X = X − IM = X(E ) − + E − (18) However, we assume that the Marshall-Lerner condition holds: we assume that in response to a depreciation, the direct effect of E on (X, IMF c ) is stronger than the revaluation effect that increases the value of IMF c . Or even more, we assume that IM = IM (Y , E ), i.e. we assume that the increase in imports + + following an appreciation of the domestic currency is stronger than the reevaluation effect (via 1/E) of having to convert foreign denominated imports into the domestic currency at an appreciated exchange rate. In short, we assume that N X(E , Y ) = X(E ) − IM (Y , E ) (19) − − − + + hence, that a depreciation of Dc increases NX. We will assume the functional form N X = X̄ − x · E − z · Y (20) 12. In principle, import and export decisions depend on the real exchange rate , not on the nominal exchange rate E, with = E·P Pw (21) However, we only use the model to study the short term, in which we are comfortable to assume fixed prices. Hence, we can just apply the normalization P w = P = 1, which implies =E (22) We will stick to E rather than , but it’s good to appreciate the distinction. 3 IS-LM model in open economy Relevant reading(s) from Blanchard, Macroeconomics, 7th edition: Chapter 19 (full chapter), Chapter 20 (only 20-2, “Exchange rate crisis under fixed exchange rate”) 8 Let’s see how the lessons draws from the model in Section 1 change when the model is made a bit more realistic by allowing the economy to interact with other economies. 13. Combine the accounting equality Y d = C + I + G + NX (23) with the following ‘theories’ for its components: C = C̄ + c · (Y − T ), I = I¯ − d · (i + f¯), G = Ḡ, T = T̄ N X = X̄ − x · E − z · Y (24) (25) (26) (27) We get the IS curve in open economy Y = Ā d x − i− E m m m (28) with Ā := C̄ − c · T̄ + I¯ − d · f¯ + Ḡ + X̄ m := 1 − c + z (29) (30) The IS curve is a decreasing curve in the space (i, Y ) with intercepts (i, Y ) = Ā x −m · E), and slope − md . It shifts rightwards ( Ād − xd · E, 0) and (i, Y ) = (0, m when the domestic currency depreciates (lower E), hence there is an entire set of IS curves, each one associated with a value of E.2 [see Figure 6] We should think of the IS curve in different ways depending on whether we are in a fixed or a flexible exchange rate regime. In a fixed exchange rate regime, E = Ē, = ¯, hence the IS curve is an equilibrium condition in two endogenous variables: (Y, i). By contrast, in a flexible exchange rate the IS curve is an equilibrium condition in three endogenous variables: (Y, i, E). Again, the IS curve captures the equilibrium condition for the market of goods, not the equilibrium of the full model. 3.1 Flexible exchange rate regime 14. Under a flexible exchange rate, the central bank has no commitment on the equilibrium value of E, international reserves do not adjust to balance the 2 Blanchard substitutes E in the IS curve right away, hence the IS curve is not a function of E anymore. I do not follow this approach, but the solution of course does not change. 9 balance of payments, hence the central bank can set i freely, say at the desired level ī. Given that we use the UIP to determine E, the model is pinned down by three equations, Ā d x − i− E m m m i = ī E (1 + i) = (1 + iw ) e E+1 Y = (31) (32) (33) in three unknowns, (Y, i, E). Rewrite the UIP as 1 + iw i= ·E−1 e E+1 (34) w This is a positively sloped line in the space (i, E) with slope 1+i e , crossing E+1 w e i = i for E = E+1 . Alternatively, we can rewrite the UIP to highlight the equilibrium exchange rate given the interest rate, E= 1+i e · E+1 1 + iw (35) [see Figure 7] We can solve the model recursively as follows: The central bank sets i = ī, 1+ī e which pins down E ∗ = 1+i w · E+1 . Last, the solution for E pins down a single IS curve, which crosses i = ī in the equilibrium value of output [see Figure 8]. This gives the analytical solution i∗ = ī (36) 1 + ī e · E+1 1 + iw d x 1 + ī Ā e − ī − · E+1 Y∗ = m m m 1 + iw E∗ = (37) (38) 15. Let’s study what happens if the central bank expands monetary policy. From the solution, we see that a monetary expansion consists of a decrease in the interest rate, which leads to a depreciation of the domestic currency and an increase in output. To understand what is going on, assume that the economy e is initially in the following equilibrium: i∗1 = ī1 = iw and E1∗ = E+1 . As the ∗ w central bank now sets the new interest rate i2 < i , capital outflows depreciate the domestic currency, leading to E2∗ < E1∗ , generating an expectation of a future appreciation that allows for i < iw to co-exist. Last, the IS curve shifts to the right, leading to Y2∗ > Y1∗ due to both an investment effect and an external channel effect [see Figure 9]. 10 To assess what happens to each component of the aggregate demand curve, remember the equilibrium condition Y = C(Y , T̄ ) + I( i , f¯) + G(Ḡ) + X(E ) − IM (Y , E ) + − − − − + + + (39) The left hand side increases, hence the right hand side also increases. Closer inspection leads to note that under the flexible exchange rate, a monetary expansion generates i E Y C I G X IM NX ↓ ↓ ↑ ↑ ↑ = ↑ undetermined undetermined We can summarize the effects discussed above as follows: i ↓ → Y d > Y s → Y ↑→ C ↑→ .. d s → E ↓→ X ↑→ Y > Y → Y ↑ C ↑→ .. (40) (41) What is the model helping us understand about the real world? According to the model, the unobserved transmission of monetary policy in the real world may consist of several channels that occur at the same time: (a) the decrease in the interest rate increases investments, which contributes to the increase in equilibrium output (investment channel); (b) the increase in output increases consumption, which further increase output and contributes to the increase in equilibrium output (consumption channel); (c) the depreciation of the domestic currency increases exports, which further contributes to increasing equilibrium output (the export channel); (d) the increase in output increases imports, which lowers domestic aggregate demand, hence attenuating the effect of the monetary expansion. The effect of output on imports might offset the opposite effect exerted on imports by the depreciation of the domestic currency, leaving the effect on imports undetermined. 11 16. Let us now use the model to guide our understanding of how the economy responds to a fiscal expansion. Let’s consider the case of an increase in government spending that does not affect taxes, and that is hence funded by government debt. Start again from an equilibrium of i∗1 = ī1 = iw and e . An increase in Ḡ from Ḡ1 to Ḡ2 does not affect (i, E), hence E1∗ = E+1 ∗ ∗ ∗ i2 = i1 , E2 = E1∗ . The IS curve shifts to the right due to G ↑. Equilibrium output hence increases [see Figure 10]. Let us inspect the transmission mechanism of the fiscal expansion by studying how each component of aggregate demand changes. As before, we start from the equilibrium condition Y = C(Y , T̄ ) + I( i , f¯) + G(Ḡ) + X(E ) − IM (Y , E ) + − − − + − + + (42) The left hand side increases, hence the right hand side also increases. Closer inspection leads to note that under the flexible exchange rate, a fiscal expansion generates i E Y C I G X IM NX = = ↑ ↑ = ↑ = ↑ ↓ We can summarize the effects discussed above as follows Ḡ ↑ Y d > Y s → Y ↑ → C ↑→ Y d > Y s → Y ↑→ C ↑ .... → IM ↑→ Y d ↓ (43) (44) What is the model helping us understand about the real world? The model is suggesting that in an open economy with a flexible exchange rate, a fiscal expansion can indeed increase output, but the effect will be partially offset by an increase in imports. Hence, the decrease in net exports partially crowds out the increase in fiscal spending. 3.2 Fixed exchange rate regime 17. Let us now move to the case of a fixed exchange rate. Suppose the central bank commits to the fixed exchange rate Ē. It hence commits to intervening 12 on the Forex (Foreign Exchange) market to ensure that the market clears at E = Ē. The IS curve now simplifies to Ā d x − i − Ē (45) m m m hence, there is now only one IS curve in the space (i, Y ), rather than an entire set, as long as the exchange rate remains at Ē. Assume that the exchange e = Ē, which implies i = iw via the UIP. rate regime is credible, hence E+1 The central bank is not free to set the interest rate at any desired level ī. The equilibrium is then given by [see Figure 11] Y = E ∗ = Ē i∗ = iw Y∗ = d x Ā − iw − Ē m m m (46) (47) (48) 18. Can the central bank expand monetary policy under a fixed exchange rates? Suppose the central bank tries to lower the interest rate in order to increase e = Ē, the UIP shows that the decrease in i requires output. Assuming E+1 a lower value of E, i.e. an immediate depreciation: this depreciation of the domestic currency can be interpreted as the result of capital outflows that are triggered by the now lowered domestic interest rate. But it violates the fixed exchange rate agreement! This is equivalent to the central banker trying to move along the IS curve and then having to revert back to the initial equilibrium [see Figure 12]. We can summarize the effects discussed above as follows: i ↓→ Kout ↑→ E ↓→ i ↑ (49) What is the model helping us understand about the real world? One monetary policy tool (the interest rate) cannot be used both as an independent tool for monetary policy and as a tool to ensure the fixed exchange rate regime. If the country decides to fix its exchange rate, it must accept the fact that monetary policy will not be available any more for economic policy. 19. Consider now the unfortunate case in which the central bank commits to the exchange rate Ē but loses its credibility, and markets start to expect E+e < Ē. The loss of credibility leads investors to invest abroad, which is consistent with the UIP rotating to the left. If the central bank leaves the interest rate at iw , the equilibrium exchange rate will indeed decrease, breaking the commitment of the central bank. Hence, the central bank should increase the interest rate to i∗2 , which is the level that ensures an equilibrium exchange rate of Ē. Note 13 that to avoid the depreciation in the domestic currency, the central bank must buy domestic currency from the Forex market, which in turn decreases money supply (an effect consistent with the increase in the interest rate) and requires selling foreign reserves. If the central bank does not have a sufficient amount of foreign reserves, this plan might be infeasible. In addition, it implies a decrease in output, as seen from the movement along the IS curve [see Figure 13]. Starting from Y = C(Y , T̄ ) + I( i , f¯) + G(Ḡ) + X(E ) − IM (Y , E ) + − − − + − + + (50) the left hand side decreases, hence the right hand side also decreases. Closer inspection leads to note that a sudden loss of credibility of the fixed exchange rate regime might require i E Y C I G X IM NX ↑ = ↓ ↓ ↓ = = ↓ ↑ We can summarize the effects discussed above as follows E+e ↓→ Kout ↑→ i ↑→ I ↓→ Y d < Y s → Y ↓ (51) What is the model helping us understand about the real world? The model suggests that if the fixed exchange rate is not considered credible any more by financial markets, the central bank must fight back by increasing the interest rate and offsetting capital outflow by selling foreign currency and lowering the amount of domestic money available for trade in the Forex market. This can generate a fall in output, further exacerbated by the fall in consumption, investment, and net exports. Alternatively, the country must accept that the fixed exchange rate is not feasible any more and abandon it. 20. The effects of a fiscal expansion are the same when comparing fixed and flexible exchange rate, at least within the specific formulation of the IS-LM model considered here. This is because in our setting, the fiscal expansion generates no pressure on the exchange rate, hence there is no difference whether we are in a fixed or a flexible exchange rate regime. 14 21. Can you think outside of the model? Here is one example of what the model does not explicitly account for, but which could well affect the conclusions drawn using the model. In this model, does an increase in investments have a positive effect in the future production possibility of the economy? Not really, because it is a demand-side model: aggregate supply is simply assumed to follow demand. Yet, an increase in aggregate demand driven by investments should also generate a second round effect on the potential level of output. The model does not formally include this, hence it might underestimate the positive effects associated with an increase in aggregate investments. 4 Exchange rate regimes Relevant reading(s) from Blanchard, Macroeconomics, 7th edition: Chapter 20 (only 20-4, “Choosing between exchange rate regimes”) 22. As discussed, adopting a fixed exchange rate regime does not improve the effectiveness of fiscal policy, and it implies that monetary policy is lost as an independent tool for economic policy. Then, why should a country agree to a fixed exchange rate regime? The general consensus is that a flexible exchange rate regime is better, except for two cases: (a) if two or more countries are very integrated, a fixed exchange rate (or even more, a common currency) can lower transaction costs, improve competition across countries, facilitate a stronger political integration. However, the more dissimilar are the shocks that hit the different countries, the more costly it will be to have given up on monetary policy as an independent tool; (b) if a country struggles to build credibility on how it uses money, then it can be optimal to tie the hands of the central bank and of the politicians. This can convince foreign investors to invest in the countries. An extreme version of the hard peg is the dollarization. 15