1. 1 ECON 671 – International Economics Portfolio Balance Models

2. 2 Asset Market Approach to Exchange Rates

3. 3 Asset Markets Approach Asset MarketsPortfolio Balance Asset Markets or Portfolio Balance approach focuses on capital flows due to changes in assets held by residents –assumes that financial markets to keep international demand for stocks of national assets equal to their supply. Foreign & domestic bonds are imperfect substitutes. Characterize asset-holdings of residents as: –Domestic money, implicit cost of interest rate i. –Domestic government bonds yielding interest rate i. –Foreign government bonds yielding i* + xa where xa is the expected % change in the exchange rate (UIPC).

4. 4 Domestic Money Market 1. Domestic Money Market Money Demand - - + + Money Demand - - + + L = m( i, i*+xa, Y, P)W –m( ) is the percent of Wealth, W, held as domestic money. –Signs of i and i*+xa reflect opp. cost of holding money. Money Supply Money Supply M s = M 0 –Assuming money stock set by domestic central bank. Equilibrium Equilibrium M 0 = m(i, i*+xa, Y, P)W= L –Assuming only domestic residents hold domestic money.

5. 5 Domestic Bond Market 2. Domestic Bond Market Bond Demand + - - - Bond Demand + - - - B d = b( i, i*+xa, Y, P)W –b( ) is the percent of Wealth, W, held as domestic bonds. –Signs of Y and P reflect transaction demand for money. Bond Supply Bond Supply B s = B 0 –Assuming bond stock set by domestic government. Equilibrium Equilibrium B 0 = b(i, i*+xa, Y, P)W= B d

6. 6 Foreign Bond Market 3. Foreign Bond Market Bond Demand - + - - Bond Demand - + - - B* d = b*( i, i*+xa, Y, P)W –b*( ) is the percent of Wealth, W, held as foreign bonds. Bond Supply Bond Supply B* s = eB* 0 –Assuming bond stock set by foreign government. –Must multiply B* by e to convert into domestic currency. Equilibrium Equilibrium eB* 0 = b*(i, i*+xa, Y, P)W= B* d –Assuming domestic residents do not hold foreign money.

7. 7 Overall Asset Markets Model ¬ Domestic Money, (MM Curve) M 0 = m(i, i*+xa, Y, P)W ­ Domestic Bonds, (BB Curve) B 0 = b(i, i*+xa, Y, P)W ® Foreign Bonds, (FF Curve) eB* 0 = b*(i, i*+xa, Y, P)W ¯ Wealth Identities W = M + B + eB* 0 and m() + b() + b*() = 1

8. 8 Asset Markets Approach Features of the Model Features of the Model –Wealth identity ensures that equilibrium in two of the markets implies third market is also in equilibrium. –Wealth share identity means that changes in desire to hold one asset imply adjustments in one or both of the others. Asset Markets Approach Diagrams Asset Markets Approach Diagrams –Begin by looking at interactions between the three markets induced by policy events. –Then derive single diagram that summarizes the three markets equilibrium. Relate shifts in individual markets to shifts in market curves (MM, BB, FF) on this single diagram.

9. 9 Increase in Domestic Bond Supply

10. 10 3. 3. Rise in W raises B* d, capital outflows but rise in i lowers B* d. Effect on e uncertain. ? Increase in Domestic Bonds i M Ms0Ms0 Md0Md0 B Domestic Money Market Foreign Bond Market Domestic Bond Market B* P B = 1/i BdBd B s 0 P* B = 1/(i*+xa) B* s Increase in Domestic Bonds B s 1 1. 1. Supply of Domestic Bonds rises, P B falls. Wealth increases by amount of new bonds Direct Effects (Curve Shifts) B* d 0 i0i0 2. 2. Rise in W raises M d. Domestic i rises. Indirect Effects (Adjustments) i1i1 Md1Md1 4.1. 4. Rise in W raises B d partly offsets 1.

11. 11 Deriving Portfolio Balance Diagram Working with the three markets directly is cumbersome and hides the dependence of the markets through the Wealth identity. Portfolio Balance Diagram Portfolio Balance Diagram (Axes are e and i) –Derive relationship between e and i in each market. o Note that as e rises, eB* rises, and so wealth, W, rises. –Money Market, MM Curve M 0 = m(i, i*+xa, Y, P)W o Rise in e, leads to rise in W, which raises M d. To keep M s = M d requires rise in i. MM curve is upward-sloping in e-i diagram. –Domestic Bond Market, BB Curve B 0 = b(i, i*+xa, Y, P)W o Rise in e, leads to rise in W, which raises B d. To keep B s = B d requires rise in P B i.e. i falls. BB curve is downward-sloping in e-i diagram. –Foreign Bond Market, FF Curve eB* 0 = b*(i, i*+xa, Y, P)W o Fall in i, leads to rise in B* d. To keep B* s = B* d requires rise e. FF curve is downward-sloping in e-i diagram. o We are assuming expected future spot exchange rate is constant throughout.

12. 12 Portfolio Balance Diagram Exchange Rate, e Domestic Interest Rate, i MM FF BB i0i0 e0e0 1. 1. Increase in relative M s shifts MM back as i falls to raise M d. 2. 2. Increase in relative B s shifts BB out as i rises to raise B d. 3. 3. Increase in relative B* s shifts FF down as e falls to raise xa, and so B * d.

13. 13 Increase in Domestic Bonds Exchange Rate, e Domestic Interest Rate, i MM 0 FF 0 BB 0 i0i0 2. 2. Rise in Wealth shifts MM out & i up to keep M D equal to unchanged M S. MM 1 4. 4. Rise in wealth also partially offsets original shift in BB (not shown). 1. 1. Increase in domestic B s shifts BB out.. BB 1 e0e0 5.Results? 5. Results? Domestic i rises with certainty but effect on spot e not certain depends on shifts in FF. Likely FF shift is small so e falls i1i1 3. 3. FF shifts out as wealth up but i up may bring offsetting shift back. FF 1

14. 14 Open Market Operations

15. 15 Open Market Operations i M Ms0Ms0 MdMd B Domestic Money Market Foreign Bond Market Domestic Bond Market B* P B = 1/i BdBd B s 0 P* B = 1/(i*+xa) B* d (i 0 ) B* s Open Market Sale of Gov’t Bonds B s 1 1. 1. Supply of Domestic Bonds rises, P B falls. Direct Effects (Curve Shifts) 4. 4. Domestic currency appreciates, spot e falls, raising xa and return on foreign bonds. 3. 3. Rise in i lowers B* d. Capital inflows. Indirect Effects (Adjustments) B* d (i 1 ) Ms1Ms1 2. 2. Domestic Money Supply falls, i rises. i1i1 i0i0

16. 16 Open Market Operations Exchange Rate, e Domestic Interest Rate, i MM 0 FF BB 0 i0i0 e0e0 1. 1. Central bank does Open Market Sale of government bonds. Reduces M S. 2. 2. MM shifts out as i rises to keep M D equal to lower M S. MM 1 4. 4. No change in foreign B S or FF. 3. 3. BB shifts out as bonds supply increases, bond price (1/i) falls. BB 1 5. 5. Lower i leads to capital outflows. Result: e down, (foreign currency depreciates). Assumed i* fixed but outflows may cause i* to fall also. e1e1 i1i1

17. 17 Short Run vs. Long Run - Exchange Rate Overshooting

18. 18 Exchange Rate Overshooting Feature of FX markets is that exchange rates “overshoot” new equilibrium positions during adjustment to a market shock. Assume Home country is “small” relative to Rest of World and that capital is perfectly mobile. –UIPC holds, foreign & domestic assets are perfect substitutes. –Asset markets adjust more rapidly to external shocks than goods markets. Equilibrium involves both Asset market equilibrium and Goods market equilibrium simultaneously. Goods Market Equilibrium Goods Market Equilibrium (e = P/P* i.e. Relative PPP holds) –Higher P implies rise in e (depreciation) to keep Absolute PPP. Asset Market Equilibrium Asset Market Equilibrium (i = i* + xa i.e. UIPC holds) –Higher P, implies higher M d, which implies higher i, so i > i* + xa. –Capital flows in, strengthens e which raises xa leads to i = i* + xa.

19. 19 Overshooting in Monetary Model Interest rates M/P 0 L( i, Y 0 ) i0i0 RD 0 Spot Rate, e RF 0 e0e0 Domestic M S Domestic Money Market Perfect Capital Mobility M/P SR e SR i1i1 RD 1 M/P LR e LR RF 1 Rise in future price level, leads to expected future dep’n of currency. Shifts RF outwards in SR & LR.

20. 20 Dornbusch Overshooting Model Domestic Price level, P Spot EXR, e Absolute PPP e = P/P* P0P0 e0e0 UIPC i = i* + xa Higher P leads to higher M d which raises i > i* + xa. Must have fall in e (xa up) for UIPC.

21. 21 SR Overshooting of EXR Domestic Price level, P Spot EXR, e Absolute PPP e = P/P* UIPC 0 P0P0 e0e0 UIPC 1 1. 1. Increase in Domestic M s, lowers i, shifts out UIPC. (xa falls for UIPC) SR e SR 2. 2. Asset markets adjust quickly, P sticky. In SR, EXR rises to e SR. LR e LR P1P1 3. 3. Goods markets adjust slowly, P rises. Real M s falls, i rises in LR, EXR falls back to e LR. Exchange Rate Overshooting!!!

22. 22 Short Run vs. Long Run - Asset Market Model

23. 23 Real Side of the Economy So far have examined only asset market conditions. –All these quantities are in nominal terms, i.e. W = M + B D + eB F Focus now on real side of the economy, i.e. production and demand of goods & services in the economy. –Assume full domestic employment in prod’n of two types of goods. o Non-traded Goods, Y N (q) : produced & consumed in domestic economy. o Traded Goods, Y T (q) : produced domestically but consumed both domestically and abroad. Y T q > 0, Y N q < 0 –Relative Price of Traded vs. Non-traded goods: q = e/P N Price of Non-tradables = P N Price of tradables = P T = e –Overall Price Level: P = P N a e 1- a –Demand for goods by consumers o Non-traded goods, C N = C N (q, w) with C N q > 0, C N w > 0 o Traded goods, C T = C T (q, w) with C T q > 0, C T w > 0 –Real Wealth = W/P = (M + B + eB*)/P –Macro Identities o C = C N + C T Y D = Y N + Y T + (i*+ xa)eB*

24. 24 Deriving Real Side Diagram Real side of model has two equilibrium conditions: –Equilibrium in Production: How much of total prod’n goes to tradable good? –Equilibrium in Consumption: How much of total consump. is tradable good? Real Side Diagram Real Side Diagram (Axes are e and Y T, C T ) –Derive relationship between e and Y T or C T. –Production Equilibrium, YY Curve o Rise in e (currency depreciates), leads to rise in value of Tradable good, prod’n switches to Y T. YY curve slopes up. o YY curve shifts with changes in full employment GDP and P N –Consumption Equilibrium, CC Curve o Rise in e (currency depreciates), leads to rise in value of Tradable good, consumption switches away from Y T. CC curve slopes down. o CC curve shifts with changes in real wealth, w = W/P –Increase in real wealth shifts CC curve away from origin

25. 25 Real Side Diagram Exchange Rate, e Y T, C T YY CC Y T C T e0e0 1. 1. Increase in P N, price of Non-traded good shifts both curves.1.1. 2. 2. Increase in real wealth, shifts CC curve outwards.2.

26. 26 Linking Real & Asset Sides Asset markets and real economy are linked in two ways. –Exchange rate is determined/affects both parts of the economy –Level of real wealth is determined/affected by both parts also. 1. Interaction on exchange rate is captured by placing Asset market and real-side diagrams back-to-back. 2. Interaction with real wealth is more complicated. –Clearly asset market nominal supplies affect nominal & real wealth. –Less obvious is that real-side equilibrium affects real wealth o Assume consumers have a target level of real wealth, w*. o Their savings behavior is based on comparison of desired level with actual level of real wealth, S = b (w* - w), b > 0 o By definition Savings equals difference between total income Y D and total consumption C. Can show using identities that: S = (Y T – C T ) + (i* + xa)eB* –i.e national savings equals net exports plus income on foreign investments. Thus change in real wealth over time is related to current account position, which affects Asset market equilibrium.

27. 27 Linking Real & Asset Sides I Exchange Rate, e Domestic Interest Rate, i MM FF i0i0 e0e0 BB Y T, C T YY CC Y T C T

28. 28 Linking Real & Asset Sides Important to be clear about time frames in within which interactions occur between markets in the economy. Impact Period (Shifts in MM-BB-FF curves) Impact Period (Shifts in MM-BB-FF curves): –Instantaneous adjustment of Asset markets to shock in one or more of the Asset markets of the economy. Short Run (Price Changes through e affect YY-CC curves) Short Run (Price Changes through e affect YY-CC curves): –Prices change as a result of the asset market shock(s) and have effects on real quantities in the the model. Will cause a divergence between actual real wealth and desired real wealth, which in turn causes changes in savings behavior and current account. Long Run (Current account imbalance affects w & W) Long Run (Current account imbalance affects w & W): –Changes in flow of real savings cause accumulated changes in level of real & nominal wealth in the economy over longer periods. These flow accumulations lead the economy to new long run equilibrium in both Asset and real markets of the economy.

29. 29 Open Market Operation: Impact, Short Run & Long Run

30. 30 Open Market Operations: Impact Effects Exchange Rate, e Domestic Interest Rate, i FF 0 Y T, C T YY 0 CC 0 Y 0 T C 0 T MM 0 BB 0 i0i0 e0e0 BB I MM I iIiI eIeI Impact Current Account Surplus

31. 31 CC SR Open Market Operations: SR Effects Exchange Rate, e Domestic Interest Rate, i MM 1 FF 0 i1i1 e1e1 BB 1 Y T, C T YY 0 CC 0 Y0 T C0TY0 T C0T MM 0 BB 0 i0i0 e0e0 Short Run Current Account Surplus C T SR Y T SR

32. 32 CC SR Open Market Operations: LR Effects Exchange Rate, e Domestic Interest Rate, i MM 1 FF 0 i1i1 e SR BB 1 Y T, C T YY 0 CC 0 Y0 T C0TY0 T C0T MM 0 BB 0 i0i0 e0e0 C T SR Y T SR CC LR YY LR e LR LR Current Account Deficit