An Overview of the IS-LM Model

Transcription

1 Insde ECONOMICS Introducton to Macroeconomcs An Overvew of the IS-LM Model Introducton The IS-LM model shows the relatonshp between nterest rates and output n the goods market and money market. The IS-LM model was developed by Sr John Hck's and s essentally hs nterpretaton of some of the fundamental elements of Keynes' The General Theory of Employment, Interest, and Money (1936).The IS curve s the locus of all equlbra where C + I + G + NX s equal to an economes total output of GDP. The LM curve demonstrates equlbrum n the money market where the demand for money equals the money supply. Ths means that the LM curve shows the combnatons of nterest rates and real ncome are when the money market s n equlbrum. Therefore the ntersecton of the IS and LM curves represents a general equlbrum as the goods and money markets are both smultaneously n equlbrum. The IS-LM curve s a useful tool for n macroeconomcs as t provdes a way to examne the effects of fscal and monetary polcy on the nterest rate and output. Furthermore t s used to demonstrate how exogenous changes n the macro varables affect the goods and money markets. The IS-LM curve has been used to argue that an ncrease n fscal spendng to stmulate an economy crowds out the prvate nvestment as the government spendng wll push up the nterest rate make t less attractve for the non-government sector to borrow. Alternatvely Keynesans beleve that government spendng may cause crowdng n, where, f the government spendng s on nfrastructure and other output mprovng projects, the prvate sector s encouraged to nvest. However the ncrease n output from a fscal polcy s less than that whch would otherwse occurred f all the nvestment was prvate nvestment. However the degree of crowdng out s dependent on the shape of the LM Curve. Equlbrum n the Goods Market The IS (Investment and Savng) Curve The demand for domestc goods n a closed economy s the sum of consumpton C, nvestment I, Government spendng G. When we look at the open economy we must look at the net exports or exports mnus mports. Ths s because we have to take out the part of domestc demand for foregn goods. However we cannot just subtract foregn goods from domestc goods as mports are not n terms of domestc goods. Instead we put the foregn goods mported IM n terms of domestc goods by dvdng by the real exchange rate. Determnants of Demand = C + I + G + X M = C( T) + I(, r) + G + X( w, e) IM(, e) (+) (+, ) (+, ) (+, +) Consumpton depends postvely on dsposable ncome T Investment depends postvely on output, and negatvely on the nterest rate r Government spendng G s taken as a gven exogenous varable 1

2 Insde ECONOMICS Exports depends on postvely on rest of world ncome w and negatvely on the exchange rate e Imports depends postvely on domestc ncome and postvely on the exchange rate A Note on Imports IM e s the prce of domestc goods n terms of foregn goods. The value of mports n terms of foregn currency (n whch they are pad for) s IM P w. The value n terms of the domestc currency wll therefore be IM Pw where E s the nomnal exchange rate. IM Pw s the value of E EP foregn goods n terms of domestc goods. Therefore IM e s the quantty of mports tmes the relatve prce s the value of mports n terms of domestc goods. We usually just denote the value of mports n terms of the domestc good as IM. It should be noted that e (EP P w ) therefore e = E when we assume the domestc and foregn prce levels are fxed over the short. Ths means that because prces are fxed the real exchange rate and nomnal exchange rate wll move together and there s a one for one relatonshp between nomnal and real deprecaton. Wthout nflaton n the equaton the nomnal and real nterest rates are also the same. ths allows us to use the nomnal nterest rate n place of the real nterest rate r. For smplcty purposes t s often the case we use net exports rather than exports and mports as above. Net Exports s smply exports mnus mports. NX(, w, e) = X( w, e) IM(, e) e (, +, ) Net exports depends negatvely on ncome, postvely on world ncome and negatvely on the exchange rate. Knowng that e (EP P w ) enables us to equate e = E when we assume the domestc and foregn prce levels are fxed over the short. Ths means that because prces are fxed the real exchange rate and nomnal exchange rate wll move together and there s a one for one relatonshp between nomnal and real deprecaton. Wthout nflaton n the equaton the nomnal and real nterest rates are also the same. Ths allows us to use the nomnal nterest rate and nomnal exchange rate E n place of the real nterest rate r and real exchange rate e. From ths we can rewrte the equaton for equlbrum n the goods market as the followng. It s useful to remember that n an open economy an apprecaton (deprecaton) of the nterest rate leads to an ncrease (decrease) n the exchange rate. Both effects work n the same drecton wth respect to output. The IS Relatonshp (Equlbrum n the goods market) = C( T) + I(, ) + G + NX(, w, E) (+) (+, ) (, +, ) 2

3 Insde ECONOMICS The IS Curve IS 0 0 The above dagram llustrates the relatonshp between nterest rate and the goods market. The IS curve s downward slopng as an ncrease n nterest rates wll drectly and ndrectly (exchange rate) decrease demand and decrease output. It s clear that as nterest rates decrease the level of output ncreases and vce versa. If any of the determnants of demand change t wll move the IS curve. For nstance an ncrease n government spendng wll shft the IS curve up and to the rght resultng n hgher output and hgher nterest rates. The slope of the IS curve s determned by the level of mpact nterest rates have on output. So t the IS curve s flat t would be hghly senstve to changes n the money market and shfts n the LM curve would greatly mpact output. It s mportant to remember that the IS curve s a locus of equlbra n the goods market or real (non-fnancal) economy. Examples of IS Shfts An Increase Government spendng G A Decrease n Investment I A Decrease n Net Exports NX An Increase n Consumpton C

4 Insde ECONOMICS Equlbrum n the Fnancal Market The LM (Lqudty preference and Money Supply Equlbrum) M P = L(, ) Equlbrum n the money market commands that money demanded s equal to money supply. Money demand s smply a preference for lqudty whch s the preference to hold cash nstead of securtes. The money supply s determned by the central bank. In the above equaton we have P the prce level and M the money supply. By dvdng the money supply by the prce level t gves us the real supply of money as opposed to just the nomnal money supply. The level of transacton s bascally real output as determned by the opportunty cost of holdng money rather than bonds whch s just the nomnal nterest rate on bonds. The preference for lqudty (money demand) s determned by two elements 1. wllngness to hold cash for transacton purposes where transacton demand s postvely related to the level of output (consdered exogenous n ths equaton) 2. Speculatve demand for money as an nvestment as oppose to bonds where the opportunty cost of holdng cash rses as nterest rates ncrease. In an open economy we must examne the money supply and subsequently the demand and supply of domestc and foregn bonds. To have equlbrum n the market for domestc and foregn bonds t must be the case that both have equal expected rates of return otherwse nvestors would only be wllng to hold one type of bond. If domestc nterest rates ncreases ts nterest rates nvestors wll sell the bonds they are holdng and purchase the bond wth a greater return. In dong ths the nvestor must sell ther foregn bonds and exchange the money to purchase the domestc bonds. Ths mples that there s an equlbrum n the foregn exchange market. The ntal apprecaton of the domestc currency must be accordng to the expected future deprecaton whch compensates for the ncrease n the domestc nterest rate. Ths means that nvestors wll become ndfferent between domestc and foregn bonds. Ths relatonshp s known as nterest rate party. 4

5 Insde ECONOMICS Example: Interest Rate Party Imagne that the UK one year nterest rate and the Australan 1 year nterest rate are equal at 5%. Then suppose that the UK nterest rate ncreases by 4% to 9%. If the expected exchange rate over the duraton of the nterest perod (1 year) does not change then the UK pound wll apprecate by approxmately 4% today (or exactly 3.67%). Ths s because that f the UK pound apprecates by 4% today and nvestors don't change ther expectaton of the exchange rate one year ahead the pound wll deprecate by 4% over the comng year. Therefore the Australan dollar s expected to apprecate by approxmately 4% over the next year so holdng Australan bond wll return approxmately 9% wth 5% from the Australan dollar return on the Australan bond and then 4% from the apprecaton of the Australan dollar over the UK pound. Holdng ether Australan or UK bonds wll yeld an expected rate of return of approxmately 9%. t domestc nterest rate (UK) t foregn Interest rate (Australan) E e expected future exchange rate e E t+1 E t expected rate of apprecaton of domestc currency E t E t = (1 + t) (1 + t ) Ee The nterest rate party condton By modfyng the nterest rate party condton we can show the above (1 + t ) 1 + 5% 1 + t = 1 + E e = 1 + 9% = t+1 E t % = 1.09 E t Usng an approxmate verson of the above equaton t t E e t+1 E t = 9% = 5% ( 4%) E t Every pont on the LM curve s the ntersecton between the preference for lqudty (demand for money) and the money supply functons gven the level of ncome. The LM curve s postvely sloped because as an ncrease n output rases the preference for lqudty and therefore rases the nterest rate. Example of Shfts n the LM Curve (Monetary Contracton) Monetary Contracton M 1 LM 2 LM

6 Insde ECONOMICS From the above dagrams we can see than a decrease n the money supply wll push nterest rates upwards. At ths pont t s probably useful to combne both curves and determne the effects of changes n the determnng factors. Combnng the Goods Market and the Fnancal Market 1. = C( T) + I(, ) + G + NX(, w, E) 2. M P = L(, ) 3. = 0 (Monetary polcy s set by the central bank choosng a partcular nterest rate) 4. E t = (1+ t) (1+ t ) Ee These four equatons determne the level of output, the nterest rate, money supply and the exchange rate. It s easy to smplfy these three equatons nto three equatons by substtutng the exchange rate nto the expresson for the IS Curve. 1. = C( T) + I(, ) + G + NX(, w, (1+ t ) (1+ t ) Ee ) 2. M P = L(, ) 3. = 0 Now the IS curve has multple mpacts from a change n the nterest rate. One effect s the drect effect on nvestment whch occurs n both a closed and open economy. The second effect occurs only n the open economy where the nterest rate has a negatve mpact on the net exports. For nstance f the nterest rate ncreases t causes the domestc currency to apprecate and ths wll result n a decreases next exports. The decrease n net exports decreases output. The nterest rate has a negatve relatonshp on both nvestment and net exports. Ths means that as the nterest rate ncreases nvestment and net exports decrease. The IS curve s downward slopng because an ncrease n the nterest rates leads to a decrease n output. The LM curve s upward slopng because an ncrease n ncome ncreases the demand for money whch n turn requres an ncrease n the market clearng nterest rate. Essentally for a fxed value of money stock M, an ncrease n GDP leads to an ncrease n the demand for P money whch therefore means the equlbrum nterest rate must ncrease. The money supply M s an endogenous varable n the model whch adjusts so for any gven level of output, the money market s n equlbrum at the nterest rate set by the central bank. It s also worth notng that gven the expected future expected exchange rate and the foregn nterest rate the domestc nterest rate determnes the exchange rate through the nterest party relaton. The nterest party relaton s upward slopng because as nterest rates rse the exchange rate ncreases. 6

7 Insde ECONOMICS IS-LM Interest Rate Party Relaton LM 1 A E 0 Example 1 Expansonary Fscal Polcy (Increase n Government Spendng) Suppose that the government s operatng a balanced budget and decde to ncrease government spendng on nfrastructure. The government decdes to nvest n nfrastructure wthout rases taxes so t borrows and pulls the budget nto defct. As government spendng s part of the IS equaton the IS curve wll shft up and to the rght and output wll ncrease. The amount of ncrease n output wll depend on whether the central bank decdes to change nterest rates or not. Government spendng does not enter the LM equaton so ths curve does not change. IS-LM Interest Rate Party Relaton LM 1 1 A 1 1 A 1 0 A 0 A 2 0 A E 0 E 1 G 0 IS 2 E 0 A 2 G 1 IS 1 E 1 A 1 If the central bank does not respond to the ncrease n output the nterest rate s unchanged. By not changng the nterest rate output ends up at 2. Ths level of output s hgher than what would have occurred f the nterest rate s ncreased. If the central bank beleves there s nflatonary pressure t may decde to ncrease nterest rates to cool the economy. Ths means that the nterest rate s rased and set at 1 whch results n a level of output of 1. Ths level of output s lower than when the central bank does not change nterest rates. The adjustment of nterest rates wll affect the LM curve as now the For llustratve purposes we have not shown the change n the LM curve n the above dagram. However the LM curve wll move up and to the left. If we are to nclude all curves the two scenaros of the IS-LM dagram would look lke the followng. 7

8 Insde ECONOMICS IS-LM Dagram IS-LM Dagram LM 1 LM 2 LM 1 & LM 3 LM The Interest Rate s ncreased Interest Rate s Unchanged In the case where the nterest rate s unchanged the LM curve wll move to the left and downwards as ncome has ncreased and therefore there s a greater demand for money. Remember that output/ncome has a postve relatonshp wth the demand for money. In addton the nterest rate has a negatve mpact on the demand for money. When the nterest rate s ncreased as a response to nflatonary pressure the LM curve moves twce. The ntal ncrease n output moves the LM curve to LM 2 however once the nterest rate ncrease to 1 ths moves the LM curve up and to the left to LM 3 because ths decreases the demand for money as bonds become more attractve at hgher nterest rates. It s usually the case that as output ncreases the nterest rate s ncreased as a means to control nflaton so t s much more lkely that the nterest rate wll ncrease. Summary of the Components of Demand = C + I + G + X M = C( T) + I(, r) + G + X( w, e) IM(, e) (+) (+, ) (+, ) (+, +) = C +I? +G +X M It s usually the case that as output ncreases the nterest rate s ncreased as a means to control nflaton so t s much more lkely that the nterest rate wll ncrease. Consumpton wll ncrease due to hgher levels of dsposable ncome gven that taxes are unchanged. The mpact on nvestment s uncertan as the ncrease n output and nterest rates have opposng effects. Also the nterest rate ncrease rases the demand for bonds and the domestc currency apprecates whch means that the exchange rate ncreases and mports rse and exports fall. Furthermore the ncrease n output wll ncrease the level of mports as hgher levels of ncome result n a level of consumpton on foregn goods. Example 2: Expansonary Monetary Polcy (A decrease n Interest Rates) Suppose that the central bank feels that the economy s enterng nto a recesson and n the absence of an nflatonary threat decde to lower the nterest rate. In ths case the nterest rate s set to at a lower level so that 0 >

9 Insde ECONOMICS IS-LM Interest Rate Party Relaton LM 1 LM A A E 1 E 0 At a gven level of output a decrease n the nterest rate requres that the central bank through open market operatons shft the LM curve down from LM 1 to LM 2. The central bank wll acheve a lower nterest rate by ncreasng the money supply. Decreasng the nterest rate ncreases the level of output from 0 to 1.. Ths wll change the equlbrum from A 0 to A 1. The monetary expanson decreases the nterest rate whch leads to an ncrease n output and a deprecaton of the domestc currency. The domestc currency deprecates because the lower nterest rates makes bonds less attractve. The hgher nterest rate wll ncrease nvestment. The effect on net exports s ambguous because the deprecaton of the domestc currency ncreases exports and decreases mports but at the same tme the level of output ncreases the level of mports. Therefore the we can see that exports wll defntely ncrease from the deprecaton but mports may ncrease or decrease. M LM E A 1 A Mathematcal Example of IS-LM Analyss n a Closed Economy (Lnear Models) Ths secton explans how of lnear algebra can be used so solve for equlbrum between the IS and LM relatons. Frstly to make ths system of lnear equatons clear we must study the lnear verson of IS-LM model. Therefore we wll ntroduce some new terms to show how the system works. IS Relaton: = C( T) + I(, ) + G + NX(, w, (1+ t ) (1+ t ) Ee ) LM Relaton: M P = L(, ) C = b Consumpton s a functon of output and the margnal propensty to consume b s = 1 b s s the Margnal propensty to save I = I 0 ar Investment s decreasng functon of the nterest rate and the margnal effcency of captal = C + I + G = by + (I 0 ar) + G IS relatonshp s + ar = I 0 + G 9

10 Insde ECONOMICS M s money supply M d money demand M dt component of money demand based on transacton requrements M ds component of money demand based on speculatve demand M dt = m as ncome rses so does the demand for money M ds = M 0 hr the demand for speculatve money decreases as the nterest rate rses LM relatonshp M s = m + M 0 hr System of Lnear Equatons IS relatonshp s + ar = I 0 + G LM relatonshp M s = m + M 0 hr The equlbrum ncome/output and nterest rates r are solutons to the system of lnear equatons. The ncome. As there are two equatons for a soluton there cannot be more than two unknowns. When solvng ths system all the other varables wll have values and the nterest rate and output solve the system so they each sde equate. The solutons depend on the gven polcy parameters of G and M s all the other factors are behavoural. The advantage of usng a system of equatons to descrbe the equlbrum s that you can see how the solutons to the system change as the parameters change. Suppose we have the followng s = I 0 ar + G = 0.4 = r M s = m + M 0 hr = 300 = r Hnt: We can rewrte these equatons to make t easer to put them nto matrx form. To order the matrx correctly smply vertcally algn lke varables. In ths case we have the varables n lne then followed by the nterest rate varables r then the constants r = r = 550 The left hand sde of the equaton wll be the coeffcent matrx and the rght hand sde wll be the vector of constants. When convertng nto the matrx we remove the and r and put them nto a soluton vector because these two varables are the soluton for the system Coeffcent Matrx A = , Soluton Vector X = y, r Vector of Constants B = Wrtng the system of equatons n matrx form = 400 r

11 Insde ECONOMICS Now we use the Inverse Matrx Method to solve the system of equatons. Snce A 1 exsts the soluton x can be found by X = A 1 B A 1 = 1 A AdjA The determnant of A equals, A = 0.4 ( 111) = adj = Therefore, A 1 = 1 A AdjA = Now we can solve the system, X = A 1 B 111 X = = Therefore we have = and r = = It s mportant to note that ths s just a smple example and we should not take the nterest rate lterally as we have not specfed unts. It could be the case that we are usng bass ponts whch would make the nterest rate 3.47%.The same logc apples to the output. From the gven nputs we can solve for the market equlbrum where IS-LM curves ntersect and the goods and fnancal markets are also n equlbrum. 11