How To Calculate The World Interest Rate

Transcription

1 International Debt Deleveraging Luca Fornaro CREI and Universitat Pompeu Fabra 12 th Macroeconomic Policy Research Workshop Budapest, September 213 1

2 Motivating facts: Household debt/gdp Household debt/gdp (percent) Ireland Un. Kingdom Portugal United States Spain 2

3 Motivating facts: Current account/gdp Current account/gdp (percent) Euro core Japan United Kingdom United States Euro periphery

4 Motivating facts: GDP Real GDP (index, 27=1) United States Euro core Japan United Kingdom Euro periphery

5 Research questions What happens when a group of financially integrated countries enters a process of debt deleveraging? What role does the exchange rate regime play? 5

6 This paper Provides a framework for understanding debt deleveraging in a group of financially integrated countries Key result: monetary unions are particularly prone to enter a liquidity trap during deleveraging 6

7 Overview of the framework World featuring a continuum of small open economies Foreign borrowing/lending is used to smooth the impact of idiosyncratic productivity shocks on consumption The deleveraging process is triggered by an unexpected permanent decrease in the (exogenous) borrowing limit 7

8 Overview of the results An unexpected drop in the borrowing limit generates a fall in the world interest rate With flexible exchange rates, production shifts toward high debt countries In a monetary union with nominal wage rigidities The fall in the interest rate is amplified Liquidity trap is associated with deep recession, especially in high-debt countries 8

9 Related literature Exchange rate regime and crises: Cespedes, Chang and Velasco (24), Christiano, Gust and Roldos (24), Gertler, Gilchrist and Natalucci (27), Schmitt-Grohe and Uribe (211) Deleveraging and liquidity traps: Eggertsson and Krugman (21), Guerrieri and Lorenzoni (21), Benigno and Romei (212) 9

10 Outline A model of international deleveraging Deleveraging with flexible wages Deleveraging in a monetary union with nominal wage rigidities The zero lower bound Policy experiments 1

11 Outline A model of international deleveraging Deleveraging with flexible wages Deleveraging in a monetary union with nominal wage rigidities The zero lower bound Policy experiments 11

12 Model World composed of a continuum of small open economies Each economy is inhabited by a continuum of measure 1 of households and by a large number of firms 12

13 Household Expected lifetime utility in country i Budget constraint E [ t= C T i,t + p N i,tc N i,t + B i,t+1 R t Borrowing constraint β t U ( C T i,t, C N i,t, L i,t ) ] B i,t+1 κ = w i,t L i,t + B i,t + Π i,t Optimality conditions 13

14 Firms Tradable sector ( ) Yi,t T = A T i,t L T αt i,t A T i,t is a country-specific productivity shock Non-tradable sector Yi,t N = A ( ) N L N αn i,t 14

15 Market clearing Tradable consumption good Ci,t T = Yi,t T B i,t+1 + B i,t R t Non-tradable consumption good Labor World market clearing 1 C T i,t di = Ci,t N = Yi,t N L i,t = L T i,t + L N i,t 1 Y T i,t di 1 B i,t+1 di = 15

16 Some useful definitions The stock of net foreign assets owned by country i at the end of period t is NFA i,t = B i,t+1 R t Current account ( NFA i,t NFA i,t 1 = CA i,t = Yi,t C T i,t+b T i,t 1 1 ) R t 1 16

17 Functional forms Preferences U ( C T, C N, L ) = C 1 γ 1 γ L1+ψ 1 + ψ Productivity shock C = ( C T ) ω ( C N ) 1 ω A T i,t = ρa T i,t 1 + ɛ i,t 17

18 Parameters Table 1: Parameters (annual) Value Source/Target Risk aversion γ = 4 Standard value Discount factor β =.9756 R = 1.25 Frisch elasticity of labor supply 1/ψ = 1 Kimball and Shapiro (28) Labor share in trad. sector α T =.65 Standard value Labor share in non-trad. sector α N =.65 Standard value Share of trad. in consumption ω =.5 Stockman and Tesar (1995) TFP process σ ɛ =.194 Benigno and Thoenissen (28) ρ =.84 Initial borrowing limit κ =.9 Debt/GDP= 2% 18

19 Policy functions.4 Current account Labor High TFP Low TFP Wealth at the start of the period: B t Wealth at the start of the period: B t 19

20 Distribution of net foreign assets/gdp.8.6 Fraction Net foreign assets/gdp 2

21 Deleveraging shock Start from steady state with κ = κ H Unexpected permanent drop to κ = κ L < κ H I set κ L =.75κ H (in the final steady state world debt/gdp is 15 percent) graph 21

22 Outline A model of international deleveraging Deleveraging with flexible wages Deleveraging in a monetary union with nominal wage rigidities The zero lower bound Policy experiments 22

23 Transitional dynamics.9 Borrowing limit 21 World debt/gdp.8.7 percent percent Interest rate years % dev. from initial ss World output years Tradable good Non-tradable good 23

24 Impact response across the NFA distribution change from initial steady state Current account/gdp 2th p er c. 5t h p er c. % deviation from initial ss Output of tradables 2t h p er c. 5t h p er c. B < k Wealth at the start of the transition : B Wealth at the start of the transition : B % deviation from initial ss 5 5 Consumption of tradables 2th p er c. 5t h p er c. % deviation from initial ss 5 5 2t h p er c. Real wage 5t h p er c Wealth at the start of the transition : B Wealth at the start of the transition : B Current account equation 24

25 Wage rigidities and the nominal exchange rate Nominal wages adjust slowly to shocks Movements in the nominal exchange rate can act as a substitute for nominal wage flexibility Equations Proposition From the perspective of a single country the flexible wage equilibrium attains the constrained optimum. 25

26 Outline A model of international deleveraging Deleveraging with flexible wages Deleveraging in a monetary union with nominal wage rigidities The zero lower bound Policy experiments 26

27 A monetary union Budget constraint in terms of currency P T t C T i,t + P N i,tc N i,t + B i,t+1 R N t = W i,t L i,t + B i,t + Π i,t Bonds are denominated in units of currency Borrowing limit B i,t+1 P T t+1 κ 27

28 Central bank There is a single central bank that uses R N as its policy instrument Start by considering a central bank that targets zero inflation in the tradable sector P T t+1 = P T t 28

29 Nominal wage rigidities Nominal wages are fixed in the short run (period ) From period t = 1 wages are fully flexible 29

30 Transitional dynamics in a monetary union.9 Borrowing limit 21 2 World debt/gdp.8 percent percent Interest rate 4 Monetary union Flex. wage years % dev. from initial ss World output Tradable good Non-tradable good years 3

31 Impact response across the NFA distribution change from initial steady state Current account/gdp 2th p er c. 5t h p er c. % deviation from initial ss Output of tradables 2t h p er c. 5t h p er c. B < k Wealth at the start of the transition : B Wealth at the start of the transition : B % deviation from initial ss Consumption of tradables 2th p er c. 5t h p er c. % deviation from initial ss Output of non-tradables 2t h p er c. 5t h p er c Wealth at the start of the transition : B Wealth at the start of the transition : B Production of non-tradables 31

32 Outline A model of international deleveraging Deleveraging with flexible wages Deleveraging in a monetary union with nominal wage rigidities The zero lower bound Policy experiments 32

33 The zero lower bound Define ˆR t N as the nominal interest rate consistent with the inflation target Now monetary policy is given by R N t = MAX ( ) ˆRN t, 1 During period, the price of the tradable good has to fall to guarantee market clearing Two effects Employment in the tradable sector decreases Fisher s debt-deflation: the real debt burden increases 33

34 Transitional dynamics in a liquidity trap.9 Borrowing limit 21 World debt/gdp.8.7 percent 2 19 percent Interest rate years % dev. from initial ss World output 2 Tradable good Non-tradable good years 34

35 Impact response across the NFA distribution change from initial steady state Current account/gdp 2th p er c. 5t h p er c. % deviation from initial ss Output of tradables 2t h p er c. 5t h p er c. B < k % deviation from initial ss Wealth at the start of the transition : B Consumption of tradables 2th p er c. 5t h p er c Wealth at the start of the transition : B % deviation from initial ss Wealth at the start of the transition : B Output of non-tradables 2t h p er c. 5t h p er c Wealth at the start of the transition : B 35

36 Outline A model of international deleveraging Deleveraging with flexible wages Deleveraging in a monetary union with nominal wage rigidities The zero lower bound Policy experiments 36

37 Policy experiments One period is a quarter Persistent nominal wage rigidities Gradual tightening of the borrowing limit 37

38 Transitional dynamics index (t 1 =1) Borrowing limit Consumer price index quarters percent percent (annualized) World debt/gdp Real interest rate quarters percent (annualized) % deviation from initial ss Nominal interest rate World output 6 Trad. Non-trad quarters 38

39 Changing the inflation target percent percent (annualized) World debt/gdp Real interest rate quarters percent (annualized) % deviation from initial ss Nominal interest rate World output - tradables quarters index (t 1 =1) % deviation from initial ss Consumer price index World output - non-trad. 6 inf. target = 2% inf. target = 4% quarters 39

40 Soft landing index (t 1 =1) Borrowing limit Consumer price index quarters percent % deviation from initial ss World debt/gdp World output - tradables quarters percent (annualized) % deviation from initial ss Nominal interest rate World output - non-trad. 6 baseline soft landing quarters 4

41 Conclusion Main message: monetary unions are particularly prone to enter a liquidity trap during deleveraging Other policy tools Fiscal transfers and debt relief policies (Fornaro 213) 41

42 Thank you 42

43 Household s optimality conditions p N i,t = U C N i,t U C T i,t U Li,t = w i,t U C T i,t U C T i,t R t = βe t [ U C T i,t+1 ] + µ i,t B i,t+1 κ, with equality if µ i,t >, Back 43

44 Nominal wage rigidities and the exchange rate Define S i as country i nominal exchange rate against the key international currency P T i,t = S i,t P T t Normalize P T = 1, firms labor demand implies ( L T i,t = α T A T i,t S i,t W i,t ) 1 1 α T Back 44

45 The current account Back ( CA i,t = Yi,t T Ci,t T + B i,t 1 1 ) R t 1 45

46 Real exchange rate and production of non-tradables Real exchange rate P N i,t = 1 ω ω Ci,t T P T Ci,t N t Equilibrium labor in the non-tradable sector L N i,t = ( α N A P N ) 1 N 1 α N i,t W i,t Back 46

47 Motivating facts: Household debt/gdp Household debt/gdp (percent) Ireland Un. Kingdom Portugal United States Spain 47

48 Motivating facts: Current account/gdp Current account/gdp (percent) Euro core Japan United Kingdom United States Euro periphery

49 Motivating facts: CA deficits and unemployment Current account/gdp in DEU NLD JPN FIN AUT BEL FRA ITA GBR USA PRT IRL GRC Change in unemployment rate - 27/211 ESP 49

50 Eurozone: net debtors NFA/GDP Eurozone - net debtors NFA/GDP percent year Source: data from Milesi-Ferretti and Lane (29) Back 5

51 A model with interest rate spreads Suppose households in country i are charged the interest rate R i,t U C T i,t ] = R i,t βe t [U C T i,t+1 Assuming the borrowing constraint in the main text R [ ] t U C T i,t = 1 µ i,t R t βe t U C T i,t+1 U C T i,t The two models are isomorphic if R i,t = R t 1 µ i,t R t U C T i,t and if the spread R i,t R t is rebated to households in country i through lump-sum transfers 51