2.3. IS-LM model (open economy) without international capital flows Blanchard: Macroeconomics

IS-LM model: aasumptions Model of income and interest rates determination Assumptions Public sector Goods and services market –Goods sector Money market – Money sector Open economy (only goods and services flows (no capital flows) Fixed prices Therefore, two sectors and two key relationships: For any level of output Y, the IS curve shows the real interest rate r for which the goods market is in equilibrium … IS curve or the IS relation For any level of output Y, the LM curve shows the real interest rate r for which the monetary sector is in equilibrium -… LM curve or the LM relation IS-LM equilibrium … is the joint equilibrium in both commodities and financial (bonds) markets Blanchard: Macroeconomics

Goods and services market and the IS curve (i) From the basic keynesian model, we can derive the IS curve: For any level of output Y, the IS curve shows the real interest rate r for which the goods market is in equilibrium. We assume that firms adopt only those investment projects with a positive Net Present Value. Clearly, if the interest rate is lower, there is a greater chance that a particular project will the pass the test and the investment will be made. Mathematically, we will assume that the investment function is linear: being b a positive parameter which captures the sensitivity of investment to interest rates Blanchard: Macroeconomics

Goods and services market and the IS curve (ii) Investment function r Better expectations of investment I0<I1 I=I0-br I=I1-br I0 I1 I Blanchard: Macroeconomics

Goods and services market and the IS curve (iii) TWO EXTREME CASES Low Sensitivity I to r (b=0) High Sensitivity I to r (b=) r r I=I0-br I=I0-br I I Blanchard: Macroeconomics

Goods and services market and the IS curve IS (iv) We carry over the assumptions from the Simple Keynesian Model and include the following: We assume that firms adopt only those investment projects with a positive Net Present Value. Clearly, if the interest rate is lower, there is a greater chance that a particular project will the pass the test and the investment will be made.   Model: Substituting C, I, G and XN in the AD function: Blanchard: Macroeconomics

Goods and services market and the IS curve (v)   In compact form: Now, any increase in the interest rate will lead a decrease in the aggregate demand, since will lead a lowe level of investment. Blanchard: Macroeconomics

The IS curve A0-br ADo=Ao-br+[c(1-t)-m]Y E Graphically…. AD 45o line Eqiollibrium: Y = AD Y0 Y Blanchard: Macroeconomics

The IS curve (ii) The IS curve (or relation) shows for any level of output Y, the real interest rate r for which the goods market is in equilibrium. Therefore, the IS consists of the set of pairs (interest rates, income levels in equilibrium) . Formally : IS: Income=spending Investment=savings Remember that in equilibrium AD=Y, that is, Production=Spending=Income Blanchard: Macroeconomics

Derivation of the IS curve AD 45o line AD1=Ao-br1+[c(1-t)-m]Y E1 ADo=Ao-br0+[c(1-t)-m]Y r1<r0 A0-br1 E0 Panel a: GOODS AND SERVICES MARKET A0-br0 Y0 Y1 Y r r0 E0 Panel b: IS CURVE E1 r1 IS CURVE: {(Y,r) SUCH THAT Y=AD} Y0 Y1 Y Blanchard: Macroeconomics

Mathematically   Then, in compact form: Blanchard: Macroeconomics

The IS curve: two extreme cases IS perfectly inelastic IS perfectly elastic b=0 b= r r Investment trap IS (A0) IS(A0) Y Y Blanchard: Macroeconomics

What causes shifts in the IS curve What causes shifts in the IS curve? Not only changes in A, but also in α Increase A0 decrease A0 r r A1>A0 IS(A0) A1<A0 IS(A1) IS(A1) IS(A0) α A0 αA1 Y Y Blanchard: Macroeconomics

Factors that Shift the IS Curve Changes in A0 Changes in autonomous consumer expenditure Changes in planned investment spending unrelated to the interest rate (Autonomous investment) Changes in government spending Changes in autonomous component of the net exports Changes in transfers Changes in the multiplier (in this case not only de intercept but also the slope will be affected) Changes in taxes Changes in the marginal propensity to import Changes in the marginal propensity to consume

Money market and the LM curve For any level of output Y, the LM curve shows the real interest rate r for which the monetary sector is in equilibrium. Then, the LM curve is defined as: Where L is the money demand and M/P is the money supply. To this end, the money supply M/P is assumed to be exogenously determined by the central Bank: M/P=(M0/P0 ) Blanchard: Macroeconomics

Money supply To this end, the money supply M/P is assumed to be exogenously determined by the central Bank: M/P=(M0/P0 )

The liquidity preference or demand for money The demand for money – or as Keynes called it – the liquidity preference – is a function of the level of income and the interest rate. Three motives have been identified for holding liquid balances (money) in preference to other assets: Transactions motive – people need money to engage in daily transactions. Thus the demand for liquidity will be some proportion of total national income. Precautionary motive – at times major events occur that need to be resolved through transactions – for example, maintaining a cash balance to pay for engine repairs on a car. This motive also tends to vary with national income as the higher is the level of economic activity, the higher are the overall transactions. ce will be lower.

The liquidity preference Speculative motive – Keynes contribution, was to highlight that money is not simply a means of exchange. People used money in times of uncertainty over movements in interest rates. They have a choice between holding money which earns no interest return or purchasing an interest-bearing asset, which has less liquidity. Keynes juxtaposed the decision to hold money or bonds. If the interest rate is expected to rise, the price of bonds falls and capital losses would be expected. So at lower interest rates more people would prefer to hold money than take a chance that they would lose should they invest in bonds. Alternatively, if the interest rate falls, the price of bonds rises and capital gains would be enjoyed. At higher interest rates, more people will form the view that rates will fall rather than rise and the liquidity preference will be lower THEREFORE, The demand for money – or as Keynes called it – the liquidity preference – is a function of the level of income and the interest rate. Where k , and h, are two positive parameters, which capture the sensitivity of the money demand to changes in the income level and in the interest rates, respectively.

Analytically Let us derive analytically the LM curve applying the money market equilibrium condition (demand of money = money supply). Then the equation of the LM curve is given by: Blanchard: Macroeconomics

Deriving the LM curve r r L(Y1) L(Y0) L, M/P Y Panel a: MONEY MARKET Panel b: the lm curve r r LM: {(Y,r) such that L=M/P} E1 E1 r1 r1 E0 r0 E0 r0 L(Y1) Y1>Y0 L(Y0) M/P L, M/P Y0 Y1 Y Blanchard: Macroeconomics

THE LM CURVE: EXTREME CASES LM perfectly inelastic LM perfectly elastic Case 1: Money demand completely insensitive to the interest rate r (h=0) Case 1: Money demand is extremely sensitive to the interest rate (h=) Case 2: Liquidity preference is extremely sensitive to shifts in income (Y) (k=)i Case 2: Money demand completely insensitive to cahnges in the income level Y (k=0) r r LM(M/P)0 Liquidity trap LM(M/P)0 Y Y Blanchard: Macroeconomics

Shifts in the LM curve r r Y Y LM(M0/P) LM(M1/P) LM(M1/P) LM(M0/P) Expansionary Monetary policy Contractionary monetary policy r r LM(M0/P) LM(M1/P) LM(M1/P) LM(M0/P) M1>M0 M1<M0 Y Y Blanchard: Macroeconomics

The equilibrium in the IS-LM model(i) Tras analizar por separado la curva de equilibrio del mercado de bienes y servicios –curva IS- y la curva de equilibrio del mercado de activos –curva LM- estamos en disposición de interrelacionar ambas curvas, cosa que podemos hacer gracias a que ambas están dispuestas en el mismo plano, el plano r-Y. De la intersección de ambas curvas de equilibrio, surgirá una combinación de tipo de interés y nivel de renta para la cual, el mercado de bienes y servicios estará en equilibrio -al pertenecer a la IS- y el mercado de activos también lo estará -al pertenecer a la LM-. Por tanto, el par (r*, Y*) representa el equilibrio conjunto de todos los mercados existentes en la economía. Blanchard: Macroeconomics

The equilibrium in the IS-LM model(ii) Y* Y Blanchard: Macroeconomics

Deriving the equilibrium in the IS-LM model (i) The equilibrium will be the solution of the system of equations Para hallar de forma analítica la intersección de la IS con la LM, tan solo tendremos que hallar la solución del sistema formado por las ecuaciones de ambas curvas: Al resolver dicho sistema, obtenemos la expresiones de la renta y el tipo de interés de equilibrio: Blanchard: Macroeconomics

Puntos situados fuera de la curva IS DA Línea 45o DA1=Ao-br1+[c(1-t)-m]Y E1 DAo=Ao-br0+[c(1-t)-m]Y B r1<r0 A0-br1 A A0-br0 E0 Y0 Y1 Y r E0 Puntos a la derecha de la IS (Punto A): Exceso de oferta de bienes y servicios r0 A Puntos a la izquierda de la IS (Punto B): Exceso de demanda de bienes y servicios B E1 r1 Curva IS: {(Y,r) tales que Y=DA} Y0 Y1 Y Blanchard: Macroeconomics

Puntos situados fuera de la curva LM Curva LM: {(Y,r) tales que L=M/P} C E1 C E1 r1 r1 E0 D r0 E0 r0 D L(Y1) Y1>Y0 L(Y0) M/P L, M/P Y0 Y1 Y Puntos a la izquierda de la LM (Punto C): Exceso de oferta de dinero Exceso de demanda de bonos Puntos a la derecha de la LM (Punto D): Exceso de demanda de dinero Exceso de oferta de bonos Blanchard: Macroeconomics

IS – LM: Equilibrium and non-equilibrium points Excess supply of goods and services Excess supply of money E r* Excess demand of goods and services Excess supply of money Excess supply of goods and services Excess demand of money Excess demand of goods and services Excess demand of money IS Y* Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Si quisiéramos saber cómo cambia el equilibrio ante un cambio en cualquiera de los parámetros del modelo, basta diferenciar las expresiones de la renta y el tipo de interés de equilibrio: A partir de: Si diferenciamos: Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Política fiscal expansiva: Efecto sobre la renta y el tipo de interés de un aumento del gasto público… Teniendo en cuenta que si se produce un aumento del gasto público, dA0=dG0 Vemos cómo tanto el tipo de interés como la renta aumentan, al aumentar el gasto público. Gráficamente, al variar el gasto público, varía la demanda agregada y, por tanto, la curva IS se desplaza a la derecha Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Política fiscal expansiva: Efecto sobre la renta y el tipo de interés de un aumento del gasto público… r LM (M0/P) dG0>0 [1] [2] [3] Efecto expulsión (EE)=[1]-[2] E2 r1 E0 E1 r0 IS’ (A0+dG0) IS (A0) Y0 Y2 Y1 Y [1] [2] [3] Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Crowding-out effect Podemos ver como esta política fiscal expansiva tiene un primer efecto expansivo sobre la renta que se ve parcialmente compensado por el efecto negativo que sobre la renta tiene la disminución de la inversión privada provocada por la subida de tipos. Se dice, pues, que el gasto público desplaza a la inversión privada. Blanchard: Macroeconomics

Comparative Statics in the IS-LM model CONTRACTIONARY MONEATARY POLICY… If the money supply decreases: Hence: As a result, income will decrease and the interest rate will increase. Graphically, in the next slide, a decrease in the real money supply decreases shifts the LM curve leftward. Blanchard: Macroeconomics

Comparative Statics in the IS-LM model CONTRACTIONARY MONETARY POLICY… r LM’ (M1/P) LM (M0/P) E1 r1 r0 E0 dM<0 IS (A0) Y1 Y0 Y Blanchard: Macroeconomics

The effectiveness of fiscal, monetary and trade policy in stimulating economic activity Podemos ver cómo las pendientes de las curvas IS y LM inciden sobre la efectividad o inefectividad de una determinada política. Por efectividad de una política entendemos el grado de acercamiento al objetivo pretendido. Por ejemplo, una política expansiva pretende que aumente la producción y el empleo. Si como consecuencia de una política expansiva, la producción no varía diremos que tal política es completamente inefectiva. A modo de ejemplo, veremos dos casos: Política fiscal expansiva cuando h Política monetaria expansiva cuando b Blanchard: Macroeconomics

The effectiveness of fiscal, monetary and trade policy in stimulating economic activity Expansionary fiscal policy Demanda de saldos reales muy sensible a cambios en los tipos de interés (h) Como hemos visto, en este caso la LM es completamente elástica Analíticamente, el efecto sobre la renta y el tipo de interés se puede calcular igual que anteriormente, pero teniendo además en cuenta que ahora h . Para resolver la indeterminación, Blanchard: Macroeconomics

The effectiveness of fiscal, monetary and trade policy in stimulating economic activity Expansionary fiscal policy Demanda de saldos reales muy sensible a cambios en los tipos de interés (h) Por tanto, Que como podemos observar, coincide con lo que aumentaría la renta tras una política fiscal expansiva en el modelo keynesiano básico. Diremos pues que la política en este caso es plenamente efectiva y el efecto expulsión es nulo. Con respecto a la variación del tipo de interés: Blanchard: Macroeconomics

The effectiveness of fiscal, monetary and trade policy in stimulating economic activity Expansionary fiscal policy when h= r dA0>0 Completely effective policy Crowding out effect= null E0 E1 r0=r1 LM (M0/P) IS’ (A0+dA0) IS (A0) Y0 Y1 Y Blanchard: Macroeconomics

The effectiveness of fiscal, monetary and trade policy in stimulating economic activity Expansionary monetary policy Investment highly sensitive to the interest rate (b=) Como hemos visto, en este caso la IS es completamente elástica Analíticamente, el efecto sobre la renta y el tipo de interés se puede calcular igual que anteriormente, pero teniendo además en cuenta que ahora b . Para resolver la indeterminación, Blanchard: Macroeconomics

The effectiveness of fiscal, monetary and trade policy in stimulating economic activity Expansionary monetary policy INVESTMENT SPENDING HIGHLY SENSITIVE TO THE INTEREST RATE (b=) Hence, And the variation of the interest rate is: Then, income level will increase while interest rate will remain constant. Monetary policy will be effective. Blanchard: Macroeconomics

The effectiveness of fiscal, monetary and trade policy in stimulating economic activity Expansionary monetary policy when b= r dM>0 LM (M0/P) LM’ (M1/P) E0 E1 r0=r1 IS (A0) Completely effective policy Y0 Y1 Y Blanchard: Macroeconomics

IS-LM model without capital flows Blanchard: Macroeconomics

Comparative Statics in the IS-LM model EFFECT OF AN INCREASE IN AUTONOMOUS CONSUMPTION…. r LM (M0/P) E2 dC0>0 r1 E0 E1 r0 IS’ (A0+dC0) IS (A0) Y0 Y2 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model A FAVOURABLE EFFECT ON INVESTMENT EXPECTATIONS… r LM (M0/P) E2 dI0>0 r1 E0 E1 r0 IS’ (A0+dI0) IS (A0) Y0 Y2 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model EXPANSIONARY FISCAL POLICY (FISAL STIMULUS): AN INCREASE IN THE GOVERNMENT SPENDING… r LM (M0/P) dG0>0 [1] [2] [3] CROWDING OUT=[1]-[2] E2 r1 E0 E1 r0 IS’ (A0+dG0) IS (A0) Y0 Y2 Y1 Y [1] [2] [3] Blanchard: Macroeconomics

Comparative Statics in the IS-LM model EXPANSIONARY FISCAL POLICY: INCREASE IN TRANSFERS… r LM (M0/P) dTR0>0 [1] [2] [3] Crowding out(EE)=[1]-[2] E2 r1 E0 E1 r0 IS’ (A0+cdTR0) IS (A0) Y0 Y2 Y1 Y [1] [2] [3] Blanchard: Macroeconomics

Comparative Statics in the IS-LM model CONTRACTIONARY MONETARY POLICY… r LM’ (M1/P) LM (M0/P) E1 r1 r0 E0 dM<0 IS (A0) Y1 Y0 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model EXPANSIONARY TRADE POLICY… r LM (M0/P) E2 dXN0>0 r1 E0 E1 r0 IS’ (A0+dXN0) IS (A0) Y0 Y2 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary Fiscal policyb= r dA0>0 LM (M0/P) E0 r0=r1 IS (A0)= IS’ (A0+dA0) E1 Fiscal policy completely (totally) ineffective Crowding out effect neutralizes discretionary fiscal policy (the expansionary effect of the fiscal stimulus is offset by the crowding out effect) Y0=Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary Fiscal policy when h= r dA0>0 Ficsl policy totally effective Crowding out =0 E0 E1 r0=r1 LM (M0/P) IS’ (A0+dA0) IS (A0) Y0 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary fiscal policy when k0 r dA0>0 Ficsl policy totally effective Crowding out =0 E0 E1 r0=r1 LM (M0/P) IS’ (A0+dA0) IS (A0) Y0 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary policy when b=0 IS (A0) IS’ (A0+dA0) r dA0>0 LM (M0/P) E1 r1 E0 r0 Ficsl policy totally effective Crowding out =0 Y0 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary fiscal policy when h=0 LM (M0/P) r dA0>0 E1 Fiscal policy completely (totally) ineffective Crowding out effect neutralizes discretionary fiscal policy (offset the fiscal stimulus) FULL CROWDING OUT r1 E0 r0 IS’ (A0+dA0) IS (A0) Y0=Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary fiscal policy when k= LM (M0/P) r dA0>0 E1 Fiscal policy completely (totally) ineffective Crowding out effect neutralizes discretionary fiscal policy (the expansionary effect of the fiscal stimulus is offset by the crowding out effect) FULL CROWDING OUT r1 E0 r0 IS’ (A0+dA0) IS (A0) Y0=Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary monetary policy when b r dM>0 LM (M0/P) LM’ (M1/P) Monetary policy completely effective E0 E1 r0=r1 IS (A0) Y0 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary Monetary policy when h= r dM>0 Ineffective monetary policy E0 r0=r1 LM (M0/P)=LM’ (M1/P) E1 IS (A0) Y0=Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary monetary policy when k=0 r dM>0 Monetary policy completely effective E0 r0 LM (M0/P) E1 r1 LM’ (M1/P) IS (A0) Y0 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary monetary policy when b=0 LM (M0/P) IS (A0) r dM>0 LM’ (M1/P) E0 r0 Ineffective monetary policy E1 r1 Y0=Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model Expansionary Monetary policy when h=0 LM (M0/P) LM’ (M1/P) r dM>0 Monetary policy completely effective E0 r0 E1 r1 IS (A0) Y0 Y1 Y Blanchard: Macroeconomics

Comparative Statics in the IS-LM model EXPANSIONARY MONETARY POLICY WHEN k= LM (M0/P)=LM’ (M1/P) r dM>0 Ineffective monetary policy E0 r0=r1 E1 IS (A0) Y0=Y1 Y Blanchard: Macroeconomics