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Jacopo Bonchi. Secular Stagnation and Rational Bubbles How Bubbles Postpone Low Interest Rates

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Jacopo Bonchi
La Sapienza Universita di Roma
Open seminar at Eesti Pank, 13 March 2018

Publicado en: Economía y finanzas
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Jacopo Bonchi. Secular Stagnation and Rational Bubbles How Bubbles Postpone Low Interest Rates

  1. 1. Intro Model Conclusions Secular Stagnation and Rational Bubbles How Bubbles Postpone Low Interest Rates Jacopo Bonchi La Sapienza Universit´a di Roma Eesti Pank, 13 March 2018 Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  2. 2. Intro Model Conclusions Secular Stagnation Definition Negative real interest rates are needed to equate saving and investment with full employment Specific Features 1 limited effectiveness of the standard monetary policy tools 2 trade-off between full employment, low inflation and financial stability Empirical Evidence The declining trend of the US real interest rates Figure 1 Benchmark Model Eggertsson et al. (2017) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  3. 3. Intro Model Conclusions Debate About SecStag Three theories: 1 Demand-Side View (Summers 2015) 2 Supply-Side View (Gordon 2015) 3 Saving Glut (Bernanke 2015) Even if a consensus has not emerged regarding the causes of low interest rates: many works point to demographic factors (e.g., Carvalho et al. 2016; Eggertsson et al., 2017) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  4. 4. Intro Model Conclusions Motivation The drivers of SecStag were already at work before the recent financial crisis Figure 2 HOWEVER the FED never hit the ZLB and the US did not experience low interest rates WHY? Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  5. 5. Intro Model Conclusions Motivation The drivers of SecStag were already at work before the recent financial crisis Figure 2 HOWEVER the FED never hit the ZLB and the US did not experience low interest rates WHY? Asset price bubbles counteracted the downward pressure on interest rates Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  6. 6. Intro Model Conclusions My Paper I augment the model of Eggertsson et al. (2017) with rational bubbles. In this way: Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  7. 7. Intro Model Conclusions My Paper I augment the model of Eggertsson et al. (2017) with rational bubbles. In this way: I account for the stylized facts of the US economy before the Great Recession (Looking Backward) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  8. 8. Intro Model Conclusions My Paper I augment the model of Eggertsson et al. (2017) with rational bubbles. In this way: I account for the stylized facts of the US economy before the Great Recession (Looking Backward) I study the mechanisms through which bubbles affect interest rates and their implications for the allocation of resources (Looking Forward) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  9. 9. Intro Model Conclusions Related Literature Debate on Secular Stagnation Summers (2014, 2015), Bernanke (2015), Gordon (2015) Rational Bubbles Tirole (1985), Kraay and Ventura (2007), Martin and Ventura (2011, 2012), Gal´ı (2014), Asriyan et al. (2016) Modelling Secular Stagnation Michau (2015), Teulings (2016), Eggertsson et al. (2017) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  10. 10. Intro Model Conclusions Setup OLG structure with population growth (gt > 0) Exogenous debt limit Dt No capital Perfectly competitive goods market Downward nominal wage Bubbly assets (they exist iff 1 + r < 1 + g) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  11. 11. Intro Model Conclusions About Bubbles Bubble creation and destruction Middle-aged households receive a fraction δ ∈ (0, 1) of a new bubbly asset and a portion δ of old bubbly assets loses value Bubble growth The quantity of bubbles grows at the same rate as population Bubbles as store of value Households can invest in bubbly assets or riskless bonds Bubbles as collateral Young households can pledge the bubbly assets they will receive the next period Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  12. 12. Intro Model Conclusions Household max C m t+1,C o t+2,ZB t+1|t+1−k Et lnCy t + βlnCm t+1 + β2 lnCo t+2) subject to: Cy t = By t Cm t+1 = Yt+1+δQB t+1|t+1−(1 + rt) By t −Bm t+1− ∞ k=0 QB t+1|t+1−kZB t+1|t+1−k Co t+2 = (1 + rt+1) Bm t+1+(1 − δ) (1 + gt) ∞ k=0 QB t+2|t+1−kZB t+1|t+1−k By t = Dt + δEtQB t+1|t+1 (1 + rt) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  13. 13. Intro Model Conclusions FOCs Euler equation: 1 Cm t = β (1 + rt) Et 1 Co t+1 Price of the bubbly asset: QB t|t−k = (1 − δ) (1 + gt) βEt Cm t Co t+1 QB t+1|t−k Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  14. 14. Intro Model Conclusions Firm Production function: Yt = Lα t Labor demand: Wt Pt = αLα−1 t Nominal Wage: Wt = max ˜Wt, Ptα¯Lα−1 where: ˜Wt = γWt−1 + (1 − γ) Ptα¯Lα−1 Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  15. 15. Intro Model Conclusions Monetary Policy Taylor rule: 1 + it = max 1, 1 + ¯i Πt Π φπ where: (1 + ¯i) = (1 + rf )Π HINT: it’s less likely to hit the ZLB with a high natural interest rate. This is crucial in a bubbly environment Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  16. 16. Intro Model Conclusions Bubbles Market Aggregate index for old bubbles: Bt = ˜Bt Nt−1 = δ ∞ k=1 (1 − δ)k QB t|t−k Aggregate bubble index (all bubbles): QB t = ˜QB t Nt−1 = δ ∞ k=0 (1 − δ)k QB t|t−k or: QB t = Ut + Bt = (1 + gt) βEt Cm t Co t+1 Bt+1 Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  17. 17. Intro Model Conclusions Loan Market Market clearing condition: NtBy t = Nt−1Bm t Loan demand: Ld t = (1 + gt) (1 + rt) (Dt + EtUt+1) Loan supply: Ls t = β 1 + β (Yt − Dt−1 − Ut − Bt) − 1 1 + β (Bt + Ut) Equilibrium real interest rate: (1 + rt) = (1 + gt) (1 + β) (Dt + EtUt+1) β (Yt − Dt−1 − Ut − Bt) − (Bt + Ut) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  18. 18. Intro Model Conclusions How Bubbles Affect Interest Rates 2 Channels: 1 Saving Channel (effect a la Tirole) Bubbly assets divert savings away from riskless bonds Bubbles induce to save less by providing an income in the old age 2 Borrowing Channel (effect a la Martin and Ventura) Bubbly collateral increases the total amount of debt Higher debt implies less savings Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  19. 19. Intro Model Conclusions How Bubbles Affect Interest Rates 2 Channels: 1 Saving Channel (effect a la Tirole) Bubbly assets divert savings away from riskless bonds Bubbles induce to save less by providing an income in the old age 2 Borrowing Channel (effect a la Martin and Ventura) Bubbly collateral increases the total amount of debt Higher debt implies less savings SO: the real interest rate is higher in a bubbly economy than in a bubbleless one Figure 3 Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  20. 20. Intro Model Conclusions Saving Channel vs Borrowing Channel Saving channel > Borrowing channel Figure 4 The strength of the channels varies according to the size of the aggregate bubble: Borrowing channel: for small aggregate bubbles its effect is greater Saving channel: for large aggregate bubbles its effect is greater Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  21. 21. Intro Model Conclusions Aggregate Supply Vertical AS (Π ≥ 1): Yt = ¯Lα = Y f Upward sloping AS (Π < 1): γ Π = 1 − (1 − γ) Y Y f 1−α α AS kink: Π = 1 Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  22. 22. Intro Model Conclusions Aggregate Demand Downward sloping AD (i > 0): Y = D + 1 + β β (U + B) + 1 + β β (1 + g) Γ Πφπ−1 (D + U) Upward sloping AD (i = 0): Y = D + 1 + β β (U + B) + 1 + β β (1 + g) Π (D + U) where Γ = Π φπ−1 1 + rf )−1 AD kink: Πkink = 1 (1 + rf ) 1 φπ Π φπ−1 φπ Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  23. 23. Intro Model Conclusions Bubbleless and Bubbly SS Effects of bubbles: Lower AD kink it’s less likely to hit the ZLB for the CB Redistributive Bubbles The full employment E is unchanged, but resources are redistributed Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  24. 24. Intro Model Conclusions Redistributive Bubbles: Bubbleless FE SS (1 + r) = (1 + g) (1 + β) D β (Y f − D) By = D (1 + r) Bm = β 1 + β Y f − D Cy = By = 1 (1 + g) β 1 + β Y f − D Cm = 1 1 + β Y f − D Co = (1 + g) D Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  25. 25. Intro Model Conclusions Redistributive Bubbles: Bubbly FE SS (1 + r) = (1 + g) (1 + β) (D + U) β (Y f − D − U − B) − (U + B) By = D + U (1 + r) Bm = β 1 + β Y f − D − (U + B) Cy = By = 1 (1 + g) β 1 + β Y f − D − (U + B) Cm = 1 1 + β Y f − D Co = (1 + g) (D + U + B) Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  26. 26. Intro Model Conclusions Welfare Analysis Bubbles redistribute resources from young to old households Net effect on welfare: UB − UNB = ln 1 − (1 + β) (U + B) β (Y f − D) + β2 ln 1 + U + B D It depends on the parameters β and D, as well as the size of the aggregate bubble. β D Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  27. 27. Intro Model Conclusions Welfare Analysis Bubbles redistribute resources from young to old households Net effect on welfare: UB − UNB = ln 1 − (1 + β) (U + B) β (Y f − D) + β2 ln 1 + U + B D It depends on the parameters β and D, as well as the size of the aggregate bubble. β D Result: the representative agent is worse off Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  28. 28. Intro Model Conclusions Calibration Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  29. 29. Intro Model Conclusions How Bubbles Prevent SecStag The mechanism: Figure 5 Bubbles push the natural interest rate up As a consequence, demographic change does not lead to a negative natural interest rate The central bank can escape the ZLB and the economy does not reach the SecStag equilibrium Furthermore: the size of the bubble necessary to keep the natural interest rate positive is 5% of GDP Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  30. 30. Intro Model Conclusions Summing Up I have explained how speculative movements in asset prices postponed SecStag: bubbles redistribute resources across generations by serving as store of value (saving channel) and collateral (borrowing channel) this redistribution is welfare reducing and raise the natural interest rate avoiding SecStag Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  31. 31. US Natural and Real Interest Rates 1982-2015 Source: Laubach and Williams (2003), Federal Reserve Bank of Cleveland. Back Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  32. 32. US Life Expectancy and Population Growth Source: World Bank. Back Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  33. 33. Loan Market Equilibrium Back Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  34. 34. Saving Channel vs Borrowing Channel Back Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  35. 35. Welfare Analysis: Different Values of β Back Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  36. 36. Welfare Analysis: Different Values of D Back Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles
  37. 37. How Bubbles Prevent SecStag Back Jacopo Bonchi (La Sapienza) Secular Stagnation and Rational Bubbles

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