Estimating a DSGE model with Firm and Bank

Transcription

1 How Bad was Lehman Shock?: Esimaing a DSGE model wih Firm and Bank Balance Shees in a Daa-Rich Environmen* (wih H. Iiboshi, T. Masumae, and R. Namba) SWET Conference Augus 7, 2011 Shin-Ichi Nishiyama (Tohoku Universiy) * The views expressed in his presenaion are hose of he presener and does no necessarily reflec hose of ESRI or Cabine Office, Governmen of Japan. 1

2 Moivaion of his paper Recen financial i crisis i in U.S. which h was precipiaed i by so-called Lehman Shock has exemplified ha deerioraion of balance shee condiion, especially ha of financial secor, can cause a deep and long-lasing recession. As Alan Greenspan pus, We are in he mids of a once-in-a cenury credi sunami. (Tesimony made a he House of Represenaives, Oc. 23, 2008) Since wo years have pas since Lehman Shock, ime seems o be ripe in assessing he impac of he shock. How Bad was Lehman Shock? 2

3 Objecive of his paper In his paper, we quanify and assess he impac of Lehman Shock. We ask wo quesions: How large was he magniude of Lehman Shock? How large was he effec of Lehman Shock o he economy? Sraegy: We idenify Lehman Shock by banking secor ne worh shock. How Bad was Lehman Shock? 3

4 Conribuions of his paper We combine wo canonical financial fricion models. For corporae balance shee, we adop BGG (1999) For bank balance shee, we adop Gerler and Kiyoaki (2010) and Gerler and Karadi (2010) We need o model wo balance shees o idenify Lehman Shock Relaed work is Hirakaa, Sudo, and Ueda (2010) We adop Daa-Rich mehod proposed by Boivin i and Giannoni (2006) By uilizing muliple ime series informaion for each observable, we can expec an improved efficiency in esimaing parameers and srucural shocks. How Bad was Lehman Shock? 4

5 Model Descripion The idea is o embed corporae balance shee and bank balance shee o he sylized DSGE model. Includes sandard feaures: habi formaion, sicky price, sicky wage, invesmen-adjusmen cos, Taylor rule, ec. There are 8 srucural shocks: TFP shock, preference shock, labor supply shock, invesmen-specific echnology shock, gov. expendiure shock, moneary policy shock, enrepreneur ne worh shock, and bank ne worh shock How Bad was Lehman Shock? 5

6 Household Goods and Facor Inpus Flow Char τ Governmen c g Final Goods Mk. Labor Mk. Y Reailer i y(j) Enrepreneur j Capial Goods Mk. Capial Producer 6

7 Financial Flow Char Deposior Bankers Enrepreneurs b b_f be b_e b_e Q*K n_f Agency Cos (Moral Hazard/Cosly Enforcemen) Agency Cos (Cosly sae verificaion) n_e

8 Model Descripion

9 Model Descripion Represenaive Household s Problem E i= 0 i β χ c + i ( c + i hc + i c 1 σ 1 ) 1 σ c χ L + i 1+ ( l+ i ) 1+ σ σ L L R -1 div E F c b b - { + { = -1 τ + w { + Ξ { + Ξ { + Ξ { π consumpion deposi labor income dividend ne ransfer enreprene ur from ne ransfer from bankers

10 Model Descripion: Enrepreneur s Problem Faces sochasic survival rae, γ E +1 Each enering enrepreneur receives sar-up ransfer from he household. Toal sar-up ransfer is ξ E n E For exiing 1- γ E +1 enrepreneurs, hey ransfer heir exising ne worh back o household. o So, he ne ransfer ha household receive is (1- γ E +1- ξ E )n E

11 Model Descripion: Enrepreneur s Problem y α ( j ) = ω ( j ) A k ( j ) l ( j 12 3 idiosyncraictfp Shock Shock Producion Funcion: { Balance shee equaion is given by E E q k + 1 ( j ) = b ( j ) + n ( j ) Asse Liabiliy Ne Worh Income saemen equaion is given by n E ) 1 α E mc R 1 ( j) ) E ( j) = p ( j) y ( j) w { l b 1( j) + q (1 δ ) k ( j) π revenue labor cos resale value of capial borrowing cos How Bad was Lehman Shock? 11

12 Model Descripion: Enrepreneur s Problem Capial demand equaion is given by E mc R + (1 ( j) p + 1( j) mpk + 1( j) δ ) q + 1 E = E π + 14 q expeced corporae real borrowing rae expeced marginal reurn of capial invesmen Deb conrac beween enrepreneur and banker Exis informaion asymmery: cosly sae verificaion E k 1( ) R ( ) { = q j + F ( ) ( j) s j s E E R 1( m) = exernal premium finance n j s ( j) risk-adjused leverage raio lending rae How Bad was Lehman Shock? 12

13 Model Descripion: Enrepreneur s Problem Aggregaion Thanks o consan-reurn-o-scale producion echnology and risk-neuraliy of enrepreneur, marginal cos, MPL, MPK, and leverage raio are he same across enrepreneurs. Aggregae ne worh ransiion n E E E k E E E + 1 = γ + 1 [ r + 1 q k + 1 b ] + ξ n 4243 π 12 3 realized gross reurn sar-up ransfer from capial deb repaymen from household Noice ha sochasic survival rae ac like an aggregae ne worh shock in corporae secor R 13

14 Model Descripion: Banker s Problem Faces sochasic survival rae, γ F +1 Each enering banker receives sar-up ransfer from he household. Toal sar-up ransfer is ξ F n F For exiing 1- γ F +1 bankers, hey ransfer heir exising ne worh back o he household. o So, he ne ransfer ha household receive is (1- γ F +1- ξ F )n F

15 Model Descripion: Banker s Problem Balance shee equaion is given by E F F b ( m ) = b ( m ) + n ( m ) banker's asse liabiliy banker' s ne banker's worh Noice ha banker s asse becomes enrepreneur s liabiliy Income saemen equaion is given by n F R + 1 ( m ) E R F ( m) = b ( m) b ( m π + 1 π F + 1 ) gross reurn from lending deb repaymen 15

16 Model Descripion: Banker s Problem Banker s objecive funcion is given by F i F F F V ( m ) = E β (1 γ + 1) γ + 1, + 1+ i n + 1+ i i= ne presen value of banking business Moral hazard / cosly enforcemen problem Banker has a echnology o diver fracion λ of his asse Incenive consrain for a banker o remain in business becomes V F E ( m) λb ( m ) reservaion reained by banker value 16

17 Model Descripion: Banker s Problem Imposing his consrain, Gerler and Kiyoaki (2010) shows he NPV of banking business o be V F E F ( m) =ν b ( m) + η n ( m) Also, hey show bank leverage raio o be consrained by E b ( m ) F n ( m) 123 bank leverage raio φ η λ ν Noice he similariy wih Basel Regulaion How Bad was Lehman Shock? 17

18 Model Descripion: Banker s Problem Aggregaion Gerler and Kiyoaki (2010) shows ha ν, η, and φ o be equal across bankers which makes he aggregaion very simple. Also given ha E R F (m) is equal across m, we can obain he following aggregae ransiion of banking secor ne worh. Aggregae ne worh ransiion of banking secor n F F F R 1 E R F F F = γ [ b b ] ξ n π π sar-up ransfer aggregae gross aggregae gross from household reurn from lending deb repaymen Noice ha sochasic survival rae ac like an aggregae ne worh shock in banking secor. How Bad was Lehman Shock? 18

19 Model Descripion: Recap of Ineres Raes There are wo ypes of ineres rae spreads in his model Exernal finance premium Profi margin of bank lending rae E R > { R > { R exernal finance premium F profi margin of bank klending rae Semming from agency problem beween enrepreneur and banker: Cosly sae verificaion How Bad was Lehman Shock? Semming from agency problem beween banker and deposior: Moral lhazard d/ cosly enforcemen 19

20 Daa-Rich Esimaion The idea of Boivin and Giannoni s (2006) Daa-Rich mehod is o exrac a common facor from muliple ime series daa and o mach ha wih each observable variable in he model. One-o-one maching (sandard Bayesian esimaion) One-o-many maching (Daa-Rich esimaion) A meri of his approach is ha we can expec improved efficiency in esimaing parameers and srucural shocks. Why Daa-Rich esimaion in his paper? Since our focus is o obain a reliable esimae of he impac of Lehman Shock, Daa-Rich esimaion is vial. How Bad was Lehman Shock? 20

21 Daa-Rich Esimaion DSGE model in sae-space form s = Φ{ s 1 + Γ{ u (opimal sae ransiion eq.) { { { ( N 1) ( N N ) ( N 1) ( N J ) ( J 1) x = Λ s + (measuremen equaion) e { { { { 1) ( M N ) ( N 1) ( M 1) ( M The idea is o increase he dimension of X (i.e., larger M) by supplying muliple ime series, while keeping he dimension of Φ, Γ, s, and u consan. Can expec efficiency gain in esimaing srucural parameers, smoohing saes and srucural shocks. How Bad was Lehman Shock? 21

22 Daa-Rich Esimaion: Measuremen Eq. Case A se-up: (Sandard Bayesian esimaion) oupu daa #1 1 = inflaion daa #1 0 M M 0 1 M L L O s + e Case B se-up: (Daa-Rich esimaion) oupu daa #1 1 0 oupu daa #2 λ y2 0 M M M oupu daa # n y λyn 0 inflaion daa #1 = 0 1 inflaion daa #2 0 λ π 2 M M M inflaion daa #nπ 0 λ π n M M M L L M L L L M L M 0 0 M 0 0 s + e 0 M 0 M 22

23 Daa Se Sample Period: 1985Q2 o 2010Q2 Case A Daa Se (11 daa series) 1. real GDP, 2. personal consumpion expendiure, 3. business fixed invesmen, 4. GDP deflaor, 5. real wage, 6. hours worked, 7. Fed Funds rae, 8. Moody s Baa corporae bond index, 9. business leverage raio, 10. commercial bank leverage raio, 11. charge-off raes (all financial insiuion) Case B Daa Se (21 daa series) In addiion o Case A daa se 12. Personal consumpion expendiure (non-durable), 13. Privae domesic invesmen, 14. Price deflaor (PCE), 15. Core CPI (ex. food and energy), 16. Civilian labor force, 17. Employees (oal non- farm), 18. Core capial leverage raio, 19. Domesically charered commercial banks leverage raio, 20. Charge-off rae (all loans and leases), 21. Charge-off rae (all loans) How Bad was Lehman Shock? 23

24 Esimaion Resuls: Esimaed IRF bank ne worh shock corporae ne worh shock 24

25 Esimaion Resuls: Smoohed Observables Acual Daa Smoohed (Case A) How Bad was Lehman Shock? 25

26 Esimaion Resuls: Smoohed Observables Acual Daa Smoohed (Case A) Smoohed (Case B) How Bad was Lehman Shock? 26

27 Esimaion Resuls: Esimaed Shocks Es. Shock (Case A) How Bad was Lehman Shock? 27

28 Esimaion Resuls: Esimaed Shocks Es. Shock (Case A) Es. Shock (Case B) How Bad was Lehman Shock? 28

29 Esimaion Resuls: Bank Ne Worh Shock Es. Shock (Case A) How Bad was Lehman Shock? 29

30 Esimaion Resuls: Bank Ne Worh Shock Es. Shock (Case A) Es. Shock (Case B) How Bad was Lehman Shock? 30

31 Hisorical Decomposiion: Oupu (Case A) TFP Shock Enrepreneur Ne Worh Shock Governmen Spending Shock Labor Supply Shock Oupu Preference Shock Banking Secor Ne Worh Shock Invesmen SpecificTechnology Shock Moneary Policy Shock Smoohed (Oupu) How Bad was Lehman Shock? 31

32 Hisorical Decomposiion: Oupu (Case B) TFP Shock Enrepreneur Ne Worh Shock Governmen Spending Shock Labor Supply Shock Oupu Preference Shock Banking Secor Ne Worh Shock Invesmen SpecificTechnology Shock Moneary Policy Shock Smoohed (Oupu) How Bad was Lehman Shock? 32

33 Hisorical Decomposiion: Invesmen (Case A) TFP Shock Enrepreneur Ne Worh Shock Governmen Spending Shock Labor Supply Shock Invesmen Preference Shock Banking Secor Ne Worh Shock Invesmen SpecificTechnology Shock Moneary Policy Shock Smoohed (Invesmen) How Bad was Lehman Shock? 33

34 Hisorical Decomposiion: Invesmen (Case B) TFP Shock Enrepreneur Ne Worh Shock Governmen Spending Shock Labor Supply Shock Invesmen Preference Shock Banking Secor Ne Worh Shock Invesmen SpecificTechnology Shock Moneary Policy Shock Smoohed (Invesmen) How Bad was Lehman Shock? 34

35 Hisorical Decomposiion: Corporae Borrowing Rae (Case A) TFP Shock Enrepreneur Ne Worh Shock Governmen Spending Shock Labor Supply Shock Corporae Borrowing Rae Preference Shock Banking Secor Ne Worh Shock Invesmen SpecificTechnology Shock Moneary Policy Shock Smoohed (Corporae Borrowing Rae) How Bad was Lehman Shock? 35

36 Hisorical Decomposiion: Corporae Borrowing Rae (Case B) TFP Shock Enrepreneur Ne Worh Shock Governmen Spending Shock Labor Supply Shock Corporae Borrowing Rae Preference Shock Banking Secor Ne Worh Shock Invesmen SpecificTechnology Shock Moneary Policy Shock Smoohed (Corporae Borrowing Rae) How Bad was Lehman Shock? 36

37 Hisorical Decomposiion: Bank Leverage (Case A) TFP Shock Enrepreneur Ne Worh Shock Governmen Spending Shock Labor Supply Shock Bank Leverage Preference Shock Banking Secor Ne Worh Shock Invesmen SpecificTechnology Shock Moneary Policy Shock Smoohed (Bank Leverage) How Bad was Lehman Shock? 37

38 Hisorical Decomposiion: Bank Leverage (Case B) TFP Shock Enrepreneur Ne Worh Shock Governmen Spending Shock Labor Supply Shock Bank Leverage Preference Shock Banking Secor Ne Worh Shock Invesmen SpecificTechnology Shock Moneary Policy Shock Smoohed (Bank Leverage) How Bad was Lehman Shock? 38

39 Hisorical Conribuion of Bank Ne Worh Shock oupu inves. corp. borr. rae profi margin bank lev. his. con. bank nw shock (Case A) 39

40 Hisorical Conribuion of Bank Ne Worh Shock oupu inves. corp. borr. rae profi margin bank lev. How Bad was Lehman Shock? 40 his. con. bank nw shock (Case A) his. con. bank nw shock (Case B)

41 Conclusion: Conribuions of his paper Theoreical Conribuion: Combined wo canonical financial fricion models and embedded o he sylized DSGE model. Empirical i i l Conribuion: i Adoped Daa-Rich esimaion mehod in esimaing bank ne worh shock. How Bad was Lehman Shock? 41

42 Conclusion: So How Bad was Lehman Shock? How large was he magniude of Lehman Shock? Larges bank ne worh shock a leas in pas 25 years. Much larger han hose during S&L crisis. How large was is impac o he economy? Quie large. Lehman Shock may have suppressed invesmen by nearly 10%. Is i over? The shock seems o have been successfully counered by TARP and aggressive credi easing ha he recessionary effec direcly caused by Lehman Shock seems o be over. How Bad was Lehman Shock? 42