International Monetary Equilibrium with Default

Transcription

1 International Monetary Equilibrium with Default M. Udara Peiris 1 Dimitrios P. Tsomocos 2 1 University College, 2 St. Edmund Hall Saïd Business School, University of 5th Annual Caress-Cowles Conference on General Equilibrium and its Applications April 19, 2009

2 Outline Motivation Model Propositions Numerical Example Comparative Statics Extensions

3 The Crisis of 1929 Speculation in housing and stock market so Fed tighetened money supply Figure: Why Money Matters, Friedman, WSJ, 17-Nov-06

4 The Crisis of 2007 In our view Procyclicality of Monetary Policy created conditions for crisis Leverage Cycle (Geanakoplos 2003) amplified severity

5 The Crisis of 2007: Tightening Liquidty

6 The Crisis of 2007: Supported by Capital Inflow

7 Analysis Transmission of crisis from a single sector of the UK to global economy demands relationship be understood in an international context. Orthodoxy in international finance literature primarily rested on studying transmission of domestic shocks via PPP (nominal or real frictions - Mundell-Fleming, Obstfeld Rogoff) and Current Account. No room to study liquidity or default as no nominal price effects (the classical dichotomy). Macroeconomic effects of asset accumulation, default and regulation are ad-hoc at best.

8 Analysis Transmission of crisis from a single sector of the UK to global economy demands relationship be understood in an international context. Orthodoxy in international finance literature primarily rested on studying transmission of domestic shocks via PPP (nominal or real frictions - Mundell-Fleming, Obstfeld Rogoff) and Current Account. No room to study liquidity or default as no nominal price effects (the classical dichotomy). Macroeconomic effects of asset accumulation, default and regulation are ad-hoc at best.

9 Analysis Transmission of crisis from a single sector of the UK to global economy demands relationship be understood in an international context. Orthodoxy in international finance literature primarily rested on studying transmission of domestic shocks via PPP (nominal or real frictions - Mundell-Fleming, Obstfeld Rogoff) and Current Account. No room to study liquidity or default as no nominal price effects (the classical dichotomy). Macroeconomic effects of asset accumulation, default and regulation are ad-hoc at best.

10 Analysis Transmission of crisis from a single sector of the UK to global economy demands relationship be understood in an international context. Orthodoxy in international finance literature primarily rested on studying transmission of domestic shocks via PPP (nominal or real frictions - Mundell-Fleming, Obstfeld Rogoff) and Current Account. No room to study liquidity or default as no nominal price effects (the classical dichotomy). Macroeconomic effects of asset accumulation, default and regulation are ad-hoc at best.

11 The Crisis and IMED The predictions of IMED consistent with recent financial events without any ad-hoc assumptions to supplement the model. Lower short term rates transmit to lower long term yields domestically, higher leverage globally, and when short term rates rise, higher default. Predictions of terms of trade moving against home country, higher asset prices and subsequently higher default globally are consistent with stylized facts.

12 IMED Has non-trivial 1) QTM, 2) Term Structure, 3) Fisher Effect, 4) PPP, 5) UIP and 6) Default propositions. IMED provides coherent framework to analyse international effects of monetary policy and hence liquidity, prices and hence trade, default and hence regulation. Captures foundations of full-bodied monetary general equilibrium model of agent optimisation, rational expectations, market clearing and positive nominal interest rates and value for money (and hence nominal determinacy). In IMED monetary policy affects interest rates, that in turn affects the cost of repayment and hence default rates, that then affect the relative attractiveness of assets.

13 IMED Has non-trivial 1) QTM, 2) Term Structure, 3) Fisher Effect, 4) PPP, 5) UIP and 6) Default propositions. IMED provides coherent framework to analyse international effects of monetary policy and hence liquidity, prices and hence trade, default and hence regulation. Captures foundations of full-bodied monetary general equilibrium model of agent optimisation, rational expectations, market clearing and positive nominal interest rates and value for money (and hence nominal determinacy). In IMED monetary policy affects interest rates, that in turn affects the cost of repayment and hence default rates, that then affect the relative attractiveness of assets.

14 IMED Has non-trivial 1) QTM, 2) Term Structure, 3) Fisher Effect, 4) PPP, 5) UIP and 6) Default propositions. IMED provides coherent framework to analyse international effects of monetary policy and hence liquidity, prices and hence trade, default and hence regulation. Captures foundations of full-bodied monetary general equilibrium model of agent optimisation, rational expectations, market clearing and positive nominal interest rates and value for money (and hence nominal determinacy). In IMED monetary policy affects interest rates, that in turn affects the cost of repayment and hence default rates, that then affect the relative attractiveness of assets.

15 IMED Extends Geanakoplos and Tsomocos (2002) to uncertainty, incomplete markets and endogeneous default (Shubik and Wilson, 1977 and Dubey et al., 2005) and as a result combines international trade with asset pricing and finance. Cash-in-advance monetary economy consistent with modelling approach of Dreze and Polemarchakis (2000 and 2001), and Bloise and Polemarchakis (2006) (but with outside money). Easily computable and readily adapted to allow for institutional realism by allowing for an explicit banking system (Tsomocos, 2003, and Goodhart et al., 2006), fiscal policy, government budget constraints or regional trade blocs.

16 IMED Extends Geanakoplos and Tsomocos (2002) to uncertainty, incomplete markets and endogeneous default (Shubik and Wilson, 1977 and Dubey et al., 2005) and as a result combines international trade with asset pricing and finance. Cash-in-advance monetary economy consistent with modelling approach of Dreze and Polemarchakis (2000 and 2001), and Bloise and Polemarchakis (2006) (but with outside money). Easily computable and readily adapted to allow for institutional realism by allowing for an explicit banking system (Tsomocos, 2003, and Goodhart et al., 2006), fiscal policy, government budget constraints or regional trade blocs.

17 IMED Extends Geanakoplos and Tsomocos (2002) to uncertainty, incomplete markets and endogeneous default (Shubik and Wilson, 1977 and Dubey et al., 2005) and as a result combines international trade with asset pricing and finance. Cash-in-advance monetary economy consistent with modelling approach of Dreze and Polemarchakis (2000 and 2001), and Bloise and Polemarchakis (2006) (but with outside money). Easily computable and readily adapted to allow for institutional realism by allowing for an explicit banking system (Tsomocos, 2003, and Goodhart et al., 2006), fiscal policy, government budget constraints or regional trade blocs.

18 International Monetary Economy t T = {0, 1} time horizon. s S = {1,.., S} states of nature. State 0 occurs in period 0, while in period 1 nature chooses s S states of nature. s S = 0 S Countries c C = {1, 2,..., C}. Where α C we denote another country as β C α. γ C set of governments. 1 h H set of agents in the international monetary economy. 2 Each agent h H = α C Hα belongs to a country. 1 l L = {1, 2,..., L} perishable commodities exist in the international economy and cannot be inventoried between periods. 2 We also associate each commodity with a single country, and we write for example l L α. 3 The commodity space can be viewed as R S L + whose axes are indexed by S L.

19 International Monetary Economy t T = {0, 1} time horizon. s S = {1,.., S} states of nature. State 0 occurs in period 0, while in period 1 nature chooses s S states of nature. s S = 0 S Countries c C = {1, 2,..., C}. Where α C we denote another country as β C α. γ C set of governments. 1 h H set of agents in the international monetary economy. 2 Each agent h H = α C Hα belongs to a country. 1 l L = {1, 2,..., L} perishable commodities exist in the international economy and cannot be inventoried between periods. 2 We also associate each commodity with a single country, and we write for example l L α. 3 The commodity space can be viewed as R S L + whose axes are indexed by S L.

20 International Monetary Economy t T = {0, 1} time horizon. s S = {1,.., S} states of nature. State 0 occurs in period 0, while in period 1 nature chooses s S states of nature. s S = 0 S Countries c C = {1, 2,..., C}. Where α C we denote another country as β C α. γ C set of governments. 1 h H set of agents in the international monetary economy. 2 Each agent h H = α C Hα belongs to a country. 1 l L = {1, 2,..., L} perishable commodities exist in the international economy and cannot be inventoried between periods. 2 We also associate each commodity with a single country, and we write for example l L α. 3 The commodity space can be viewed as R S L + whose axes are indexed by S L.

21 International Monetary Economy t T = {0, 1} time horizon. s S = {1,.., S} states of nature. State 0 occurs in period 0, while in period 1 nature chooses s S states of nature. s S = 0 S Countries c C = {1, 2,..., C}. Where α C we denote another country as β C α. γ C set of governments. 1 h H set of agents in the international monetary economy. 2 Each agent h H = α C Hα belongs to a country. 1 l L = {1, 2,..., L} perishable commodities exist in the international economy and cannot be inventoried between periods. 2 We also associate each commodity with a single country, and we write for example l L α. 3 The commodity space can be viewed as R S L + whose axes are indexed by S L.

22 International Monetary Economy t T = {0, 1} time horizon. s S = {1,.., S} states of nature. State 0 occurs in period 0, while in period 1 nature chooses s S states of nature. s S = 0 S Countries c C = {1, 2,..., C}. Where α C we denote another country as β C α. γ C set of governments. 1 h H set of agents in the international monetary economy. 2 Each agent h H = α C Hα belongs to a country. 1 l L = {1, 2,..., L} perishable commodities exist in the international economy and cannot be inventoried between periods. 2 We also associate each commodity with a single country, and we write for example l L α. 3 The commodity space can be viewed as R S L + whose axes are indexed by S L.

23 International Monetary Economy e h s = e h sl R S L + endowment vector for agent h H α in state s. Each asset A j for j J = {1,..., J} is an (A, λ, Q) triple and is an (L + C) S dimensional vector whose sth components (A j 1,..., Aj L,..., Aj α,..., A j C ) represents the amount Aj sl of commodity l L and the money of country α C, A j sα, due in state s S. The private monetary endowment from Country α in state s S belonging to agent h is m h sα. u h : R S L + R utility function of agent h H. s S λ hj s [φ hj A j sα Dhj sα ]+ U h (w h ) = u h (x) j J p s v s to each agent of his optimising decisions.. This is the final payoff

24 International Monetary Economy e h s = e h sl R S L + endowment vector for agent h H α in state s. Each asset A j for j J = {1,..., J} is an (A, λ, Q) triple and is an (L + C) S dimensional vector whose sth components (A j 1,..., Aj L,..., Aj α,..., A j C ) represents the amount Aj sl of commodity l L and the money of country α C, A j sα, due in state s S. The private monetary endowment from Country α in state s S belonging to agent h is m h sα. u h : R S L + R utility function of agent h H. s S λ hj s [φ hj A j sα Dhj sα ]+ U h (w h ) = u h (x) j J p s v s to each agent of his optimising decisions.. This is the final payoff

25 International Monetary Economy e h s = e h sl R S L + endowment vector for agent h H α in state s. Each asset A j for j J = {1,..., J} is an (A, λ, Q) triple and is an (L + C) S dimensional vector whose sth components (A j 1,..., Aj L,..., Aj α,..., A j C ) represents the amount Aj sl of commodity l L and the money of country α C, A j sα, due in state s S. The private monetary endowment from Country α in state s S belonging to agent h is m h sα. u h : R S L + R utility function of agent h H. s S λ hj s [φ hj A j sα Dhj sα ]+ U h (w h ) = u h (x) j J p s v s to each agent of his optimising decisions.. This is the final payoff

26 International Monetary Economy e h s = e h sl R S L + endowment vector for agent h H α in state s. Each asset A j for j J = {1,..., J} is an (A, λ, Q) triple and is an (L + C) S dimensional vector whose sth components (A j 1,..., Aj L,..., Aj α,..., A j C ) represents the amount Aj sl of commodity l L and the money of country α C, A j sα, due in state s S. The private monetary endowment from Country α in state s S belonging to agent h is m h sα. u h : R S L + R utility function of agent h H. s S λ hj s [φ hj A j sα Dhj sα ]+ U h (w h ) = u h (x) j J p s v s to each agent of his optimising decisions.. This is the final payoff

27 International Monetary Economy e h s = e h sl R S L + endowment vector for agent h H α in state s. Each asset A j for j J = {1,..., J} is an (A, λ, Q) triple and is an (L + C) S dimensional vector whose sth components (A j 1,..., Aj L,..., Aj α,..., A j C ) represents the amount Aj sl of commodity l L and the money of country α C, A j sα, due in state s S. The private monetary endowment from Country α in state s S belonging to agent h is m h sα. u h : R S L + R utility function of agent h H. s S λ hj s [φ hj A j sα Dhj sα ]+ U h (w h ) = u h (x) j J p s v s to each agent of his optimising decisions.. This is the final payoff

28 Time Line

29 Definition of Equilibrium (η, (σ h ) h H ) is an International Monetary Equilibrium with Default (IMED) for the world economy E = ((u h, e h, m h ) h H, M γ, µ γ ) h H, γ C iff: 1 (σ h ) Argmax σ h B(η) U(x h ). Agents optimise 2 p sl h H α q h sl = h H bh sl + γ C Mγ sl. Goods market clears 3 π sαβ ( h H bh sαβ + γ C Mγ sαβ ) = h H bh sβα + γ C Mγ sβα. Currency market clears 4 h H µh sα + γ C µγ sα (1+r sα) = h H d α h + γ C Mγ sα. Money market clears 5 h H µh α + γ C µγ α (1+ r α) = d h h H α + M γ γ C α. 6 Bond market clears h H Dhj Ks j s + γ C Dγj s if = h H s φhj h H Aj sφ h j > 0 arbitrary if h H Aj sφ h. j = 0 Asset market clears for agents s S and γ C, α, β C, j J and h H.

30 Definition of Equilibrium (η, (σ h ) h H ) is an International Monetary Equilibrium with Default (IMED) for the world economy E = ((u h, e h, m h ) h H, M γ, µ γ ) h H, γ C iff: 1 (σ h ) Argmax σ h B(η) U(x h ). Agents optimise 2 p sl h H α q h sl = h H bh sl + γ C Mγ sl. Goods market clears 3 π sαβ ( h H bh sαβ + γ C Mγ sαβ ) = h H bh sβα + γ C Mγ sβα. Currency market clears 4 h H µh sα + γ C µγ sα (1+r sα) = h H d α h + γ C Mγ sα. Money market clears 5 h H µh α + γ C µγ α (1+ r α) = d h h H α + M γ γ C α. 6 Bond market clears h H Dhj Ks j s + γ C Dγj s if = h H s φhj h H Aj sφ h j > 0 arbitrary if h H Aj sφ h. j = 0 Asset market clears for agents s S and γ C, α, β C, j J and h H.

31 Definition of Equilibrium (η, (σ h ) h H ) is an International Monetary Equilibrium with Default (IMED) for the world economy E = ((u h, e h, m h ) h H, M γ, µ γ ) h H, γ C iff: 1 (σ h ) Argmax σ h B(η) U(x h ). Agents optimise 2 p sl h H α q h sl = h H bh sl + γ C Mγ sl. Goods market clears 3 π sαβ ( h H bh sαβ + γ C Mγ sαβ ) = h H bh sβα + γ C Mγ sβα. Currency market clears 4 h H µh sα + γ C µγ sα (1+r sα) = h H d α h + γ C Mγ sα. Money market clears 5 h H µh α + γ C µγ α (1+ r α) = d h h H α + M γ γ C α. 6 Bond market clears h H Dhj Ks j s + γ C Dγj s if = h H s φhj h H Aj sφ h j > 0 arbitrary if h H Aj sφ h. j = 0 Asset market clears for agents s S and γ C, α, β C, j J and h H.

32 Definition of Equilibrium (η, (σ h ) h H ) is an International Monetary Equilibrium with Default (IMED) for the world economy E = ((u h, e h, m h ) h H, M γ, µ γ ) h H, γ C iff: 1 (σ h ) Argmax σ h B(η) U(x h ). Agents optimise 2 p sl h H α q h sl = h H bh sl + γ C Mγ sl. Goods market clears 3 π sαβ ( h H bh sαβ + γ C Mγ sαβ ) = h H bh sβα + γ C Mγ sβα. Currency market clears 4 h H µh sα + γ C µγ sα (1+r sα) = h H d α h + γ C Mγ sα. Money market clears 5 h H µh α + γ C µγ α (1+ r α) = d h h H α + M γ γ C α. 6 Bond market clears h H Dhj Ks j s + γ C Dγj s if = h H s φhj h H Aj sφ h j > 0 arbitrary if h H Aj sφ h. j = 0 Asset market clears for agents s S and γ C, α, β C, j J and h H.

33 Definition of Equilibrium (η, (σ h ) h H ) is an International Monetary Equilibrium with Default (IMED) for the world economy E = ((u h, e h, m h ) h H, M γ, µ γ ) h H, γ C iff: 1 (σ h ) Argmax σ h B(η) U(x h ). Agents optimise 2 p sl h H α q h sl = h H bh sl + γ C Mγ sl. Goods market clears 3 π sαβ ( h H bh sαβ + γ C Mγ sαβ ) = h H bh sβα + γ C Mγ sβα. Currency market clears 4 h H µh sα + γ C µγ sα (1+r sα) = h H d α h + γ C Mγ sα. Money market clears 5 h H µh α + γ C µγ α (1+ r α) = d h h H α + M γ γ C α. 6 Bond market clears h H Dhj Ks j s + γ C Dγj s if = h H s φhj h H Aj sφ h j > 0 arbitrary if h H Aj sφ h. j = 0 Asset market clears for agents s S and γ C, α, β C, j J and h H.

34 Definition of Equilibrium (η, (σ h ) h H ) is an International Monetary Equilibrium with Default (IMED) for the world economy E = ((u h, e h, m h ) h H, M γ, µ γ ) h H, γ C iff: 1 (σ h ) Argmax σ h B(η) U(x h ). Agents optimise 2 p sl h H α q h sl = h H bh sl + γ C Mγ sl. Goods market clears 3 π sαβ ( h H bh sαβ + γ C Mγ sαβ ) = h H bh sβα + γ C Mγ sβα. Currency market clears 4 h H µh sα + γ C µγ sα (1+r sα) = h H d α h + γ C Mγ sα. Money market clears 5 h H µh α + γ C µγ α (1+ r α) = d h h H α + M γ γ C α. 6 Bond market clears h H Dhj Ks j s + γ C Dγj s if = h H s φhj h H Aj sφ h j > 0 arbitrary if h H Aj sφ h. j = 0 Asset market clears for agents s S and γ C, α, β C, j J and h H.

35 Existence of Equilibrium Theorem There always exists an IMED of E(M, λ, ) provided 1 Gains-to-trade and Inactive Market Hypothesis holds 2 M, λ>0.

36 Quantity Theory of Money Period 0 h H l L α p 0l q h 0l M 0α + m 0α Period 1 h H l L α p sl q h sl M sα + m sα + ˆm sα

37 Term Structure of Interest Rates At any IMED, for all s S and for all α C, Period 0 d 0α (1 + r 0α )+ µ 0α + b 0 α + µα + ψ j φ j + ˆm sα 1 + r 0α 1 + r α j J α = d 0α + µ 0α + b 0α + d α + j J α ψ j θ j + b 0 + m 0α Period 1 d sα(1 + r sα)+ µsα + b s α r d α(1 + r α) + θ j KsA j j s sα j J α = d sα + µ sα + b sα + µ sα + j J α D j s + b s + m sα + ˆm sα The RHS represents the money flowing into the system, and the LHS represents the money flowing out of the system. If all government expenditures and transfers are zero and there is no private money in the economy then interest rates are not determined endogeneously and are zero.

38 Term Structure of Interest Rates At any IMED, for all s S and for all α C, Period 0 d 0α (1 + r 0α )+ µ 0α + b 0 α + µα + ψ j φ j + ˆm sα 1 + r 0α 1 + r α j J α = d 0α + µ 0α + b 0α + d α + j J α ψ j θ j + b 0 + m 0α Period 1 d sα(1 + r sα)+ µsα + b s α r d α(1 + r α) + θ j KsA j j s sα j J α = d sα + µ sα + b sα + µ sα + j J α D j s + b s + m sα + ˆm sα The RHS represents the money flowing into the system, and the LHS represents the money flowing out of the system. If all government expenditures and transfers are zero and there is no private money in the economy then interest rates are not determined endogeneously and are zero.

39 Term Structure of Interest Rates Corollary: At any IMED for all s S and γ C, 1 + r 0γ M 0γ + m 0γ M 0γ 1 + r sγ Msγ + msγ + ˆmsγ M sγ Clearly if the government spends too much money without expanding the money supply, then interest rates will rise and trade will come to a complete halt. Through this we can see how fiscal policy, monetary policy and (when it is allowed in the money market) default are connected in a financial economy.

40 Term Structure of Interest Rates Corollary: At any IMED for all s S and γ C, 1 + r 0γ M 0γ + m 0γ M 0γ 1 + r sγ Msγ + msγ + ˆmsγ M sγ Clearly if the government spends too much money without expanding the money supply, then interest rates will rise and trade will come to a complete halt. Through this we can see how fiscal policy, monetary policy and (when it is allowed in the money market) default are connected in a financial economy.

41 Term Structure of Interest Rates Corollary: At any IMED for all s S and γ C, 1 + r 0γ M 0γ + m 0γ M 0γ 1 + r sγ Msγ + msγ + ˆmsγ M sγ Clearly if the government spends too much money without expanding the money supply, then interest rates will rise and trade will come to a complete halt. Through this we can see how fiscal policy, monetary policy and (when it is allowed in the money market) default are connected in a financial economy.

42 Purchasing Power Parity For agent h H who buys good α from Country α and purchases good β from country β α who faces exchange rate π sαβ which is foreign currency per unit of home currency we have: u (c h sα) u (c h sβ ) = π sαβp sα p sβ u (csα) h u (csβ h ) = π sαβp sα (1 + r sα)p sβ

43 Fisher Effect Suppose that some agent h in Country α who sells a bond domestically and in Country α and chooses b h 0α > 0 and b h sα > 0 for state both state 1 and state 2 and has some Country α money left over when long loans come due in period 1, then at IME we must have: u (c0α h ) p 0α s S θh u (csα h ) s p sα = 1 + r α u (c h 0α ) p 0α s S (1 + rsα)θh u (csα h ) s p sα = 1 + r α where α C and θ h is the subjective belief of agents.

44 Fisher Effect Rearranging the above and taking logarithms allows us to interpret the above as the nominal rate of interest being equal to the real rate of interest plus (expected) inflation plus risk premium term. log( u (c0α) h u (c1α h ) ) + log( p 1α ) + p 0α log( θ1 h u (c1α h ) p 1α ) log(θ1) h s S θh u (csα h ) s p sα r α From here we can see that the nominal interest rate is approximately the real interest rate plus the rate of inflation plus a risk premium term

45 Uncovered Interest Rate Parity Suppose in period 0 agent h has one unit of country α money. He can either deposit the money domestically and convert it to country β money in the future or he can convert it to country β money immediately and invest the money there. These two strategies will have the same value in expectation. That is, we must have: π 0αβ (1 + r β ) = π 1αβ θ βs 1 + r α s S = E θ β [π 1 αβ] That is, the UIP proposition gives the future exchange rate (the exchange rate in period 1 is given by π 1 αβ) under the risk neutral measure ( θ β )

46 Untraded Assets On-the-verge Condition (1 + r sα)u (c h sα) = λ Paper has two examples that highlight the importance on the decision to trade assets of 1 different monetary policy regimes 2 different regulatory regimes in determining which assets are traded and by which agents.

47 World Economy 2 countries, home is US, foreign is UK. Representative agent in each country endowed with a single good each. 2 periods, 2 states of the world in second period. Single risky bond in each country. Agents borrow in bond market at home and purchase bonds abroad. Agents can only participate in domestic money market. Symmetric data in each country. Central Bank in each country willing to offer money for loan in money market.

48 World Economy 2 countries, home is US, foreign is UK. Representative agent in each country endowed with a single good each. 2 periods, 2 states of the world in second period. Single risky bond in each country. Agents borrow in bond market at home and purchase bonds abroad. Agents can only participate in domestic money market. Symmetric data in each country. Central Bank in each country willing to offer money for loan in money market.

49 World Economy 2 countries, home is US, foreign is UK. Representative agent in each country endowed with a single good each. 2 periods, 2 states of the world in second period. Single risky bond in each country. Agents borrow in bond market at home and purchase bonds abroad. Agents can only participate in domestic money market. Symmetric data in each country. Central Bank in each country willing to offer money for loan in money market.

50 World Economy 2 countries, home is US, foreign is UK. Representative agent in each country endowed with a single good each. 2 periods, 2 states of the world in second period. Single risky bond in each country. Agents borrow in bond market at home and purchase bonds abroad. Agents can only participate in domestic money market. Symmetric data in each country. Central Bank in each country willing to offer money for loan in money market.

51 Data of World Economy Agent h α Agent h β Agent h α Agent h β Outside Money in State 0,1,2 Endowments of Goods 1,2 in State 0,1,2 m 0α α, mβ 0β e 01, e m 1α α, mβ 1β e 11, e m 1α α, mβ 2β e 21, e Preferences for home good Subjective Probabilities for State 1 h α, h β θ 1 α, θhβ Money Supply in States 0,1,2 CRRA Risk Aversion US UK ρα, ρ β M 01, M Default Penalty M 11, M US UK M 21, M λ α,λ β Table: Parameters of Initial Equilibrium

52 Equilibrium Micro Variables Agent h α Agent h β Agent h α Agent h β Consumption of Good 1 in State 0,1,2 Consumption of Good 2 in State 0,1,2 c 01 α, cβ c 02 α, cβ c 11 α, cβ c 12 α, cβ c 21 α, cβ c 22 α, cβ Money Offered for Goods 1, 2 Money Offered to Foreign Exchange Market in State 0,1,2 in State 0,1,2 b 02 α, bβ b 012 α, bβ b 12 α, bβ b 112 α, bβ b 22 α, bβ b 212 α, bβ Amount Repaid to Short-Term Lending/Borrowing in Country α Money Market in State 0,1,2 Long Term Bond Market µ α 0α, µβ 0β µ α 1α, µβ 1β µ α 2α, µβ 2β µ α 1, d β Lending/Borrowing in Country β Long Term Bond Market Utility of Agents dα, µ β 2 2 U α,u β Table: Endogenous Variables of Economy

53 Equilibrium Macro Variables US UK US UK Price of Goods 1,2 in States 0,1,2 Short Term interest Rates in States 0,1,2 p 01, p r 0α, r 0β 8.3% 8.3% p 11, p r 1α, r 1β 13.3% 13.3% p 21, p r 2α, r 2β 10.0% 10.0% Sales of Goods 1,2 in States 0,1,2 Long Term interest Rate q 01, q Rα, R β 12.1% 12.1% q 11, q Delivery Rate q 21, q K 11, K % 73.9% US Nominal Trade Balance in States 0,1,2 Exchange Rates in States 0,1,2 TB0α TB1α TB2α π 0αβ π 1αβ π 2αβ Table: Macroeconomic Variables of Economy

54 Initial Equilibrium Money enters the economy through the money markets in IMED and, in equilibrium, the demand for money will meet the money supply at a price of the short term interest rates. Lower the interest rate efficient trade (Dubey and Geanakoplos, 1992 and Espinoza et al., 2009). Micro table shows a bias toward home consumption due to the financing cost creating an inefficiency in purchasing foreign goods. Macro table shows price level depends on the quantity of money offered to the goods market depends on money supply. In period 0 only fraction of the money used in goods market while in period 1 all money available used. Liquidity in the currency markets also dependent on the quantity of money available money offered to FX but currency demand depends on relative demand for assets and goods FX rate not simply ratio of money supplies.

55 Initial Equilibrium Money enters the economy through the money markets in IMED and, in equilibrium, the demand for money will meet the money supply at a price of the short term interest rates. Lower the interest rate efficient trade (Dubey and Geanakoplos, 1992 and Espinoza et al., 2009). Micro table shows a bias toward home consumption due to the financing cost creating an inefficiency in purchasing foreign goods. Macro table shows price level depends on the quantity of money offered to the goods market depends on money supply. In period 0 only fraction of the money used in goods market while in period 1 all money available used. Liquidity in the currency markets also dependent on the quantity of money available money offered to FX but currency demand depends on relative demand for assets and goods FX rate not simply ratio of money supplies.

56 Initial Equilibrium Money enters the economy through the money markets in IMED and, in equilibrium, the demand for money will meet the money supply at a price of the short term interest rates. Lower the interest rate efficient trade (Dubey and Geanakoplos, 1992 and Espinoza et al., 2009). Micro table shows a bias toward home consumption due to the financing cost creating an inefficiency in purchasing foreign goods. Macro table shows price level depends on the quantity of money offered to the goods market depends on money supply. In period 0 only fraction of the money used in goods market while in period 1 all money available used. Liquidity in the currency markets also dependent on the quantity of money available money offered to FX but currency demand depends on relative demand for assets and goods FX rate not simply ratio of money supplies.

57 Initial Equilibrium Money enters the economy through the money markets in IMED and, in equilibrium, the demand for money will meet the money supply at a price of the short term interest rates. Lower the interest rate efficient trade (Dubey and Geanakoplos, 1992 and Espinoza et al., 2009). Micro table shows a bias toward home consumption due to the financing cost creating an inefficiency in purchasing foreign goods. Macro table shows price level depends on the quantity of money offered to the goods market depends on money supply. In period 0 only fraction of the money used in goods market while in period 1 all money available used. Liquidity in the currency markets also dependent on the quantity of money available money offered to FX but currency demand depends on relative demand for assets and goods FX rate not simply ratio of money supplies.

58 Initial Equilibrium Money enters the economy through the money markets in IMED and, in equilibrium, the demand for money will meet the money supply at a price of the short term interest rates. Lower the interest rate efficient trade (Dubey and Geanakoplos, 1992 and Espinoza et al., 2009). Micro table shows a bias toward home consumption due to the financing cost creating an inefficiency in purchasing foreign goods. Macro table shows price level depends on the quantity of money offered to the goods market depends on money supply. In period 0 only fraction of the money used in goods market while in period 1 all money available used. Liquidity in the currency markets also dependent on the quantity of money available money offered to FX but currency demand depends on relative demand for assets and goods FX rate not simply ratio of money supplies.

59 Initial Equilibrium Money enters the economy through the money markets in IMED and, in equilibrium, the demand for money will meet the money supply at a price of the short term interest rates. Lower the interest rate efficient trade (Dubey and Geanakoplos, 1992 and Espinoza et al., 2009). Micro table shows a bias toward home consumption due to the financing cost creating an inefficiency in purchasing foreign goods. Macro table shows price level depends on the quantity of money offered to the goods market depends on money supply. In period 0 only fraction of the money used in goods market while in period 1 all money available used. Liquidity in the currency markets also dependent on the quantity of money available money offered to FX but currency demand depends on relative demand for assets and goods FX rate not simply ratio of money supplies.

60 Initial Equilibrium In period 1 agents weigh the marginal rate of substitution (MRS) of repayment of the loan with that of the default punishment. As there is a real default penalty, the price level does not enter into the decision. Rather it is the interest rate. The higher the interest rate, the higher will be MRS of the agent with respect to the penalty and hence higher default. The higher spot rate of %13.3 in state 1 means that agents will find it optimal to default, and given the default penalty imposed there is only default in state 1.

61 Initial Equilibrium In period 1 agents weigh the marginal rate of substitution (MRS) of repayment of the loan with that of the default punishment. As there is a real default penalty, the price level does not enter into the decision. Rather it is the interest rate. The higher the interest rate, the higher will be MRS of the agent with respect to the penalty and hence higher default. The higher spot rate of %13.3 in state 1 means that agents will find it optimal to default, and given the default penalty imposed there is only default in state 1.

62 Initial Equilibrium In period 1 agents weigh the marginal rate of substitution (MRS) of repayment of the loan with that of the default punishment. As there is a real default penalty, the price level does not enter into the decision. Rather it is the interest rate. The higher the interest rate, the higher will be MRS of the agent with respect to the penalty and hence higher default. The higher spot rate of %13.3 in state 1 means that agents will find it optimal to default, and given the default penalty imposed there is only default in state 1.

63 Money Supply M 0α M 1α M 2α M 0α M 1α M 2α c 01 α r 01 - = = c 11 α = - = r 11 = - = c 21 α =/- - + r 21 = = - c 02 α r 02 = = = c 12 α = = = r 12 = = = c 22 α =/- - + r 22 = = = c β rα c β 11 = + = r β c β 21 =/+ + - π 0αβ - = = c β π 1αβ = - = c β 12 = = = π 2αβ =/+ + - c β 22 =/+ + - TB(01) =/- - + Utility α - =/- =/+ TB(11) = + = Utility β + =/+ =/- TB(21) Table: Comparative Statics For (Non-Cooperative) Monetary Expansion in US

64 Money Supply M 0α M 1α M 2α M 0α M 1α M 2α µ α + = = dα µ α = + = µ µ α = = + dβ µ β 02 = = = µ β µ β 12 = = = K µ β 22 = = = K 12 =/- - + p 01 + =/- - q p 11 = + = q 11 = + = p 21 =/- - + q 21 =/+ + - p 02 - =/- - q p 12 = = = q 12 = = = p 22 =/+ + - q 22 =/- - + b 02 α b 012 α + = = b 12 α = = = b 112 α b 22 α = = = b 212 α b β =/+ b β 021 = = = b β 11 = + = b β b β 21 = = + b β Table: Comparative Statics For (Non-Cooperative) Monetary Expansion in US

65 Unanticipated Increase in Money Supply Mundell Flemming Model: policy will depreciate exchange rate, reduce global interest rates and a beggar-thy-neighbor effect on output. The Obstfeld Rogoff model: world interest rates fall, domestic current account surplus, increase in world demand leading to symmetric welfare gains both at home and abroad. IMED: Able to analyse the effect of this through multiple channels and prices and we find vastly different results.

66 Unanticipated Increase in Money Supply Mundell Flemming Model: policy will depreciate exchange rate, reduce global interest rates and a beggar-thy-neighbor effect on output. The Obstfeld Rogoff model: world interest rates fall, domestic current account surplus, increase in world demand leading to symmetric welfare gains both at home and abroad. IMED: Able to analyse the effect of this through multiple channels and prices and we find vastly different results.

67 Unanticipated Increase in Money Supply Mundell Flemming Model: policy will depreciate exchange rate, reduce global interest rates and a beggar-thy-neighbor effect on output. The Obstfeld Rogoff model: world interest rates fall, domestic current account surplus, increase in world demand leading to symmetric welfare gains both at home and abroad. IMED: Able to analyse the effect of this through multiple channels and prices and we find vastly different results.

68 PPP effects From term structure of interest rates (TS) - expansion in domestic (US) money supply lowers the money market interest rate there. interest rate cost of purchasing imports. From purchasing power parity (PPP) US then imports and demand for Pounds to purchase UK goods depreciates Dollar. Stronger UK Pound British imports and financed by an exports and debt increase in the volume of global trade and a (slight) deterioration in the US nominal trade balance. From UIP, expect (slight) improvement in US nominal trade balance in future. Compatible with predictions of Mundell-Fleming but extend analysis to intertemporal optimisation.

69 PPP effects From term structure of interest rates (TS) - expansion in domestic (US) money supply lowers the money market interest rate there. interest rate cost of purchasing imports. From purchasing power parity (PPP) US then imports and demand for Pounds to purchase UK goods depreciates Dollar. Stronger UK Pound British imports and financed by an exports and debt increase in the volume of global trade and a (slight) deterioration in the US nominal trade balance. From UIP, expect (slight) improvement in US nominal trade balance in future. Compatible with predictions of Mundell-Fleming but extend analysis to intertemporal optimisation.

70 PPP effects From term structure of interest rates (TS) - expansion in domestic (US) money supply lowers the money market interest rate there. interest rate cost of purchasing imports. From purchasing power parity (PPP) US then imports and demand for Pounds to purchase UK goods depreciates Dollar. Stronger UK Pound British imports and financed by an exports and debt increase in the volume of global trade and a (slight) deterioration in the US nominal trade balance. From UIP, expect (slight) improvement in US nominal trade balance in future. Compatible with predictions of Mundell-Fleming but extend analysis to intertemporal optimisation.

71 PPP effects From term structure of interest rates (TS) - expansion in domestic (US) money supply lowers the money market interest rate there. interest rate cost of purchasing imports. From purchasing power parity (PPP) US then imports and demand for Pounds to purchase UK goods depreciates Dollar. Stronger UK Pound British imports and financed by an exports and debt increase in the volume of global trade and a (slight) deterioration in the US nominal trade balance. From UIP, expect (slight) improvement in US nominal trade balance in future. Compatible with predictions of Mundell-Fleming but extend analysis to intertemporal optimisation.

72 PPP effects From term structure of interest rates (TS) - expansion in domestic (US) money supply lowers the money market interest rate there. interest rate cost of purchasing imports. From purchasing power parity (PPP) US then imports and demand for Pounds to purchase UK goods depreciates Dollar. Stronger UK Pound British imports and financed by an exports and debt increase in the volume of global trade and a (slight) deterioration in the US nominal trade balance. From UIP, expect (slight) improvement in US nominal trade balance in future. Compatible with predictions of Mundell-Fleming but extend analysis to intertemporal optimisation.

73 PPP effects From term structure of interest rates (TS) - expansion in domestic (US) money supply lowers the money market interest rate there. interest rate cost of purchasing imports. From purchasing power parity (PPP) US then imports and demand for Pounds to purchase UK goods depreciates Dollar. Stronger UK Pound British imports and financed by an exports and debt increase in the volume of global trade and a (slight) deterioration in the US nominal trade balance. From UIP, expect (slight) improvement in US nominal trade balance in future. Compatible with predictions of Mundell-Fleming but extend analysis to intertemporal optimisation.

74 QTM and FE From the quantity theory of money (QTM), money supply in US price level. In the UK, from the QTM we can see that trade in goods in the price level. Stronger Pound British purchase more American bonds and as there is expected deflation in US so from Fisher Effect (FE) nominal yields. in expected UK inflation nominal yield in the UK.

75 QTM and FE From the quantity theory of money (QTM), money supply in US price level. In the UK, from the QTM we can see that trade in goods in the price level. Stronger Pound British purchase more American bonds and as there is expected deflation in US so from Fisher Effect (FE) nominal yields. in expected UK inflation nominal yield in the UK.

76 QTM and FE From the quantity theory of money (QTM), money supply in US price level. In the UK, from the QTM we can see that trade in goods in the price level. Stronger Pound British purchase more American bonds and as there is expected deflation in US so from Fisher Effect (FE) nominal yields. in expected UK inflation nominal yield in the UK.

77 QTM and FE From the quantity theory of money (QTM), money supply in US price level. In the UK, from the QTM we can see that trade in goods in the price level. Stronger Pound British purchase more American bonds and as there is expected deflation in US so from Fisher Effect (FE) nominal yields. in expected UK inflation nominal yield in the UK.

78 Default nominal yield in the US results in American debt while the higher yields in the UK induce in US purchases of UK assets. That is, lower US interest rates global economy becoming more leveraged. Higher debt levels in the future need to be repaid in the presence of liquidity constraints. If the government does not commit to expanding money supply in the future, then from the on-the-verge (OTV) condition we know that in the state of the world where we expect default, the marginal cost of repayment > default penalty.

79 Default nominal yield in the US results in American debt while the higher yields in the UK induce in US purchases of UK assets. That is, lower US interest rates global economy becoming more leveraged. Higher debt levels in the future need to be repaid in the presence of liquidity constraints. If the government does not commit to expanding money supply in the future, then from the on-the-verge (OTV) condition we know that in the state of the world where we expect default, the marginal cost of repayment > default penalty.

80 Default Agents default as marginal cost of repayment > marginal cost of default delivery rates in both countries fall. In good state, agents have a higher MRS domestically than abroad where they have asset returns. From PPP agents send less money abroad and liquidity in the currency market.

81 Default Agents default as marginal cost of repayment > marginal cost of default delivery rates in both countries fall. In good state, agents have a higher MRS domestically than abroad where they have asset returns. From PPP agents send less money abroad and liquidity in the currency market.

82 Summary welfare for the US while for the UK. In a setting with default we need to analyse both the allocation and the deadweight loss associated with the penalty imposed on default. Allocationally US imports in period 0 while in every other state in UK consumption. First order effect in the model is change in the short term interest rate in the US. Prompts a large expenditure from home good towards imports in the US and from the future to the present. As the UK responds to price effects, they do not accomodate American consumption demands and trade in a mutually beneficial way as would be possible in a closed economy setting but rather the UK benefits from the inefficient intertemporal re-allocation for American. Prices and quantities have limited response due to default penalty. Main welfare results through intertemporal transmission. welfare for British, for American.

83 Summary welfare for the US while for the UK. In a setting with default we need to analyse both the allocation and the deadweight loss associated with the penalty imposed on default. Allocationally US imports in period 0 while in every other state in UK consumption. First order effect in the model is change in the short term interest rate in the US. Prompts a large expenditure from home good towards imports in the US and from the future to the present. As the UK responds to price effects, they do not accomodate American consumption demands and trade in a mutually beneficial way as would be possible in a closed economy setting but rather the UK benefits from the inefficient intertemporal re-allocation for American. Prices and quantities have limited response due to default penalty. Main welfare results through intertemporal transmission. welfare for British, for American.

84 Summary welfare for the US while for the UK. In a setting with default we need to analyse both the allocation and the deadweight loss associated with the penalty imposed on default. Allocationally US imports in period 0 while in every other state in UK consumption. First order effect in the model is change in the short term interest rate in the US. Prompts a large expenditure from home good towards imports in the US and from the future to the present. As the UK responds to price effects, they do not accomodate American consumption demands and trade in a mutually beneficial way as would be possible in a closed economy setting but rather the UK benefits from the inefficient intertemporal re-allocation for American. Prices and quantities have limited response due to default penalty. Main welfare results through intertemporal transmission. welfare for British, for American.

85 Summary welfare for the US while for the UK. In a setting with default we need to analyse both the allocation and the deadweight loss associated with the penalty imposed on default. Allocationally US imports in period 0 while in every other state in UK consumption. First order effect in the model is change in the short term interest rate in the US. Prompts a large expenditure from home good towards imports in the US and from the future to the present. As the UK responds to price effects, they do not accomodate American consumption demands and trade in a mutually beneficial way as would be possible in a closed economy setting but rather the UK benefits from the inefficient intertemporal re-allocation for American. Prices and quantities have limited response due to default penalty. Main welfare results through intertemporal transmission. welfare for British, for American.

86 Summary welfare for the US while for the UK. In a setting with default we need to analyse both the allocation and the deadweight loss associated with the penalty imposed on default. Allocationally US imports in period 0 while in every other state in UK consumption. First order effect in the model is change in the short term interest rate in the US. Prompts a large expenditure from home good towards imports in the US and from the future to the present. As the UK responds to price effects, they do not accomodate American consumption demands and trade in a mutually beneficial way as would be possible in a closed economy setting but rather the UK benefits from the inefficient intertemporal re-allocation for American. Prices and quantities have limited response due to default penalty. Main welfare results through intertemporal transmission. welfare for British, for American.

87 Extensions Banking Sector (Goodhart et al., 2006) Production Infinite Horizon (eg. Bewley, 1980)