Financial Intermediation and Capital Reallocation
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1 Financial Intermediation and Capital Reallocation Hengjie Ai, Kai Li, and Fang Yang NBER Summer Institute, Asset Pricing July 09, / 19 Financial Intermediation and Capital Reallocation
2 Motivation Introduction Motivation Empirical Evidence Summary of the Paper How nancial intermediation a ects macroeconomic uctuations and asset returns 2 / 19 Financial Intermediation and Capital Reallocation
3 Motivation Empirical Evidence Summary of the Paper Motivation How nancial intermediation a ects macroeconomic uctuations and asset returns Majority of previous literature: focus on the formation of new capital 2 / 19 Financial Intermediation and Capital Reallocation
4 Motivation Empirical Evidence Summary of the Paper Motivation How nancial intermediation a ects macroeconomic uctuations and asset returns Majority of previous literature: focus on the formation of new capital When intermediaries are constrained, I drops =) K goes down =) Y = AK α N 1 α goes down 2 / 19 Financial Intermediation and Capital Reallocation
5 Motivation Introduction Motivation Empirical Evidence Summary of the Paper How nancial intermediation a ects macroeconomic uctuations and asset returns Majority of previous literature: focus on the formation of new capital When intermediaries are constrained, I drops =) K goes down =) Y = AK α N 1 α goes down Financial intermediation a ects the formation of new capital 2 / 19 Financial Intermediation and Capital Reallocation
6 Motivation Introduction Motivation Empirical Evidence Summary of the Paper How nancial intermediation a ects macroeconomic uctuations and asset returns Majority of previous literature: focus on the formation of new capital When intermediaries are constrained, I drops =) K goes down =) Y = AK α N 1 α goes down Financial intermediation a ects the formation of new capital This paper: the deployment of existing capital 2 / 19 Financial Intermediation and Capital Reallocation
7 Motivation Introduction Motivation Empirical Evidence Summary of the Paper How nancial intermediation a ects macroeconomic uctuations and asset returns Majority of previous literature: focus on the formation of new capital When intermediaries are constrained, I drops =) K goes down =) Y = AK α N 1 α goes down Financial intermediation a ects the formation of new capital This paper: the deployment of existing capital When intermediaries are constrained, capital cannot ow from low to high productivity rms 2 / 19 Financial Intermediation and Capital Reallocation
8 Motivation Introduction Motivation Empirical Evidence Summary of the Paper How nancial intermediation a ects macroeconomic uctuations and asset returns Majority of previous literature: focus on the formation of new capital When intermediaries are constrained, I drops =) K goes down =) Y = AK α N 1 α goes down Financial intermediation a ects the formation of new capital This paper: the deployment of existing capital When intermediaries are constrained, capital cannot ow from low to high productivity rms Reallocation or redeployment of existing capital 2 / 19 Financial Intermediation and Capital Reallocation
9 Motivation Empirical Evidence Summary of the Paper Empirical Evidence Measuring Misallocation (Hsieh and Klenow 2009) Misallocation, dispersion in the marginal product of capital 3 / 19 Financial Intermediation and Capital Reallocation
10 Empirical Evidence Introduction Measuring Misallocation (Hsieh and Klenow 2009) Motivation Empirical Evidence Summary of the Paper Misallocation, dispersion in the marginal product of capital Monopolistically competitive market and DS technology: Y = EF AK α L 1 α, ( R η a j MPKj α where EF = ( R a j MPKj α 1 di ) η η 1 +α 1 1 MPK di j η 1 ) α 3 / 19 Financial Intermediation and Capital Reallocation
11 Empirical Evidence Introduction Measuring Misallocation (Hsieh and Klenow 2009) Motivation Empirical Evidence Summary of the Paper Misallocation, dispersion in the marginal product of capital Monopolistically competitive market and DS technology: Y = EF AK α L 1 α, ( R η a j MPKj α where EF = ( R a j MPKj α A rst order Taylor approximation: 1 di ) η η 1 +α 1 1 MPK di j η 1 ) α ln EF = 1 2 [α (η 1) + 1] αvar ln MPK j 3 / 19 Financial Intermediation and Capital Reallocation
12 Motivation Empirical Evidence Summary of the Paper Empirical Evidence_ Capital Misallocation and TFP Log TFP, Capital Utilization and Misallocation Measured in Log TFP Units Log TFP Log C apital U tiliz ation Misallocation (in Log TFP Units) / 19 Financial Intermediation and Capital Reallocation
13 Loan Change Capital M isallocation Empirical Evidence Bank Loan and Misallocation Introduction Motivation Empirical Evidence Summary of the Paper 50 Bank Loan Change and Capital Misallocation Bank Loan Change Capital Misallocation / 19 Financial Intermediation and Capital Reallocation
14 Summary of the Paper Introduction Motivation Empirical Evidence Summary of the Paper A GE model with capital reallocation and nancial intermediation 6 / 19 Financial Intermediation and Capital Reallocation
15 Summary of the Paper Introduction Motivation Empirical Evidence Summary of the Paper A GE model with capital reallocation and nancial intermediation Financial shocks generate variations in misallocation and account for a large fraction of macroeconomic uctuations 6 / 19 Financial Intermediation and Capital Reallocation
16 Summary of the Paper Introduction Motivation Empirical Evidence Summary of the Paper A GE model with capital reallocation and nancial intermediation Financial shocks generate variations in misallocation and account for a large fraction of macroeconomic uctuations Ampli cation is quantitatively small with TFP shocks only 6 / 19 Financial Intermediation and Capital Reallocation
17 Summary of the Paper Introduction Motivation Empirical Evidence Summary of the Paper A GE model with capital reallocation and nancial intermediation Financial shocks generate variations in misallocation and account for a large fraction of macroeconomic uctuations Ampli cation is quantitatively small with TFP shocks only Endogenous Counter-cyclical Volatility 6 / 19 Financial Intermediation and Capital Reallocation
18 Summary of the Paper Introduction Motivation Empirical Evidence Summary of the Paper A GE model with capital reallocation and nancial intermediation Financial shocks generate variations in misallocation and account for a large fraction of macroeconomic uctuations Ampli cation is quantitatively small with TFP shocks only Endogenous Counter-cyclical Volatility Counter-cyclical volatility at the aggregate level 6 / 19 Financial Intermediation and Capital Reallocation
19 Summary of the Paper Introduction Motivation Empirical Evidence Summary of the Paper A GE model with capital reallocation and nancial intermediation Financial shocks generate variations in misallocation and account for a large fraction of macroeconomic uctuations Ampli cation is quantitatively small with TFP shocks only Endogenous Counter-cyclical Volatility Counter-cyclical volatility at the aggregate level Counter-cyclical volatility in the cross-section 6 / 19 Financial Intermediation and Capital Reallocation
20 Summary of the Paper Introduction Motivation Empirical Evidence Summary of the Paper A GE model with capital reallocation and nancial intermediation Financial shocks generate variations in misallocation and account for a large fraction of macroeconomic uctuations Ampli cation is quantitatively small with TFP shocks only Endogenous Counter-cyclical Volatility Counter-cyclical volatility at the aggregate level Counter-cyclical volatility in the cross-section Recursive policy function iteration approach, global solution, crisis dynamics 6 / 19 Financial Intermediation and Capital Reallocation
21 Motivation Empirical Evidence Summary of the Paper Literature Credit market frictions/ nancial intermediation Bernake and Gertler (1989), Kiyotaki and Moore (1997), Rampini and Vishwanathan (2015). Gertler and Kiyotaki (2010), He and Krishnamurthy (2014), Brunnermeier and Sannikov (2014). Capital Reallocation Eisfeldt and Rampini (2006), Hsieh and Klenow (2009), Cui (2014). Kurlat (2013), Fuchs, Green and Papanikoloau (2014), Whited and Li (2014). Financial Shocks: Jermann and Quadrini (2012) Asset pricing: Bansal and Yaron (2004), Corhay, Kung and Schmid (2015). 7 / 19 Financial Intermediation and Capital Reallocation
22 Final Goods Producers A nal good producer: Y = R η 1 η η 1 η y j dj 8 / 19 Financial Intermediation and Capital Reallocation
23 Final Goods Producers A nal good producer: Y = R η 1 η η 1 η y j dj A continuum of islands. A representative rm on each island: α y j = Aa j kj α l1 j ; a j 2 fa H, a L g 8 / 19 Financial Intermediation and Capital Reallocation
24 Final Goods Producers A nal good producer: Y = R η 1 η η 1 η y j dj A continuum of islands. A representative rm on each island: α y j = Aa j kj α l1 j ; a j 2 fa H, a L g A representative bank on each island 8 / 19 Financial Intermediation and Capital Reallocation
25 Final Goods Producers A nal good producer: Y = R η 1 η η 1 η y j dj A continuum of islands. A representative rm on each island: α y j = Aa j kj α l1 j ; a j 2 fa H, a L g A representative bank on each island Supply capital to local rms 8 / 19 Financial Intermediation and Capital Reallocation
26 Final Goods Producers A nal good producer: Y = R η 1 η η 1 η y j dj A continuum of islands. A representative rm on each island: α y j = Aa j kj α l1 j ; a j 2 fa H, a L g A representative bank on each island Supply capital to local rms Intermediate capial reallocation across islands 8 / 19 Financial Intermediation and Capital Reallocation
27 Final Goods Producers A nal good producer: Y = R η 1 η η 1 η y j dj A continuum of islands. A representative rm on each island: α y j = Aa j kj α l1 j ; a j 2 fa H, a L g A representative bank on each island Supply capital to local rms Intermediate capial reallocation across islands Productivity shocks are islands speci c and capital do not move freely across islands. 8 / 19 Financial Intermediation and Capital Reallocation
28 Aggregation Notation: φ = K η 1 H ah ; ˆφ = K L a L 9 / 19 Financial Intermediation and Capital Reallocation
29 Aggregation Notation: Aggregate output φ = K η 1 H ah ; ˆφ = K L a L Y = EF AK α L 1 α, 9 / 19 Financial Intermediation and Capital Reallocation
30 Aggregation Notation: Aggregate output φ = K η 1 H ah ; ˆφ = K L a L Y = EF AK α L 1 α, The e ciency margin given by π ˆφ 1 ξ α φ ξ ξ + 1 π EF = uf (φ) = u (πφ + 1 π) α π ˆφ + 1 π α ξ α 9 / 19 Financial Intermediation and Capital Reallocation
31 _ Timeline of Decisions 10 / 19 Financial Intermediation and Capital Reallocation
32 Limited Enforcement The limited enforcement constraint: Q H (A) [K 1 + RA H (A)] Q (A) RA H (A) R f B f θq H (A) [K 1 + RA H (A)] 11 / 19 Financial Intermediation and Capital Reallocation
33 Limited Enforcement The limited enforcement constraint: Q H (A) [K 1 + RA H (A)] Q (A) RA H (A) R f B f θq H (A) [K 1 + RA H (A)] This can be simpli ed: (1 θ) Q H A 0, φ 0 (1 ω) Q (u 0 ) (1 θ) Q H (A 0, φ 0 ) u 0 φ 0 πφ π 1 s 0, where s 0 = R f B f K 0 11 / 19 Financial Intermediation and Capital Reallocation
34 Implications of the Model The Main Theorem Proposition There exists functions ŝ (A), s (A) and s (A), such that If s 0 ŝ (A 0 ), then rst best achieves 12 / 19 Financial Intermediation and Capital Reallocation
35 Implications of the Model The Main Theorem Proposition There exists functions ŝ (A), s (A) and s (A), such that If s 0 ŝ (A 0 ), then rst best achieves If ŝ (A 0 ) < s 0 s (A 0 ), then the limited enforcement constraint on high productivity islands binds 12 / 19 Financial Intermediation and Capital Reallocation
36 Implications of the Model The Main Theorem Proposition There exists functions ŝ (A), s (A) and s (A), such that If s 0 ŝ (A 0 ), then rst best achieves If ŝ (A 0 ) < s 0 s (A 0 ), then the limited enforcement constraint on high productivity islands binds If s (A 0 ) < s 0 s (A 0 ), then the limited commitment constraint for all banks bind 12 / 19 Financial Intermediation and Capital Reallocation
37 Implications of the Model The Main Theorem Proposition There exists functions ŝ (A), s (A) and s (A), such that If s 0 ŝ (A 0 ), then rst best achieves If ŝ (A 0 ) < s 0 s (A 0 ), then the limited enforcement constraint on high productivity islands binds If s (A 0 ) < s 0 s (A 0 ), then the limited commitment constraint for all banks bind The cuto levels, ŝ (A 0 ) and s (A 0 ) are all increasing functions of A 0 12 / 19 Financial Intermediation and Capital Reallocation
38 Implications of the Model The Limited Enforcement Constraint 13 / 19 Financial Intermediation and Capital Reallocation
39 Normalized investment Normalized consumption Normalized output Implications of the Model_ Misallocation and Capital Utilization Normalized net worth Normalized net worth Normalized net worth
40 Interest spread Price of consumption claim Price of capital Implications of the Model Production and Market Clearing Normalized net worth Normalized net worth Normalized net worth
41 Marginal value of n Capital utilization Capital reallocation Price Implications of the Model Production and Market Clearing Normalized net worth Normalized net worth Normalized net worth Normalized net worth
42 Implications of the Model Calibration: Macroeconomic Moments Moments Data TFP Shocks Financial Corr [ ln Y, Var ( ln Y )] Var [ uf h (φ)] /Var [ TFP] i 11% 96% Corr ln gtfp, ln RA h i Corr ln gtfp, Var (ln MPK ) h i Corr ln gtfp, ln u / 19 Financial Intermediation and Capital Reallocation
43 Implications of the Model Calibration: Crisis Dynamics Moments Non-Recession Periods Recession Periods Data Model Data Model Vol [ ln Y ] 3.53% 3.2% 4.18% 5.96% Vol [ ln C ] 2.32% 1.28% 3.42% 2.28% Vol [ ln I ] 9.07% 14.08% 9.86% 13.92% E [u] 81.1% 81.12% 78.41% 73.23% Vol [u] 3.87% 2.87% 5.27% 4.8% E [ln R I ln R f ] 0.56% 0.84% 0.98% 1.62% Vol [ln R I ln R f ] 0.36% 0.17% 0.59% 0.23% 18 / 19 Financial Intermediation and Capital Reallocation
44 and Extension Agency frictions in nancial intermediation can have large impact on the real economy 19 / 19 Financial Intermediation and Capital Reallocation
45 and Extension Agency frictions in nancial intermediation can have large impact on the real economy Capital reallocation quantitatively important 19 / 19 Financial Intermediation and Capital Reallocation
46 and Extension Agency frictions in nancial intermediation can have large impact on the real economy Capital reallocation quantitatively important A model of endogenous time variations in aggregate and idiosyncratic volatility 19 / 19 Financial Intermediation and Capital Reallocation
47 and Extension Agency frictions in nancial intermediation can have large impact on the real economy Capital reallocation quantitatively important A model of endogenous time variations in aggregate and idiosyncratic volatility Recursive policy function iteration can be applied to other GE models with agency frictions 19 / 19 Financial Intermediation and Capital Reallocation
48 and Extension Agency frictions in nancial intermediation can have large impact on the real economy Capital reallocation quantitatively important A model of endogenous time variations in aggregate and idiosyncratic volatility Recursive policy function iteration can be applied to other GE models with agency frictions Extensions: asset pricing, policy issues. 19 / 19 Financial Intermediation and Capital Reallocation
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