Bond Finance, Bank Credit, and Aggregate Fluctuations in an Open Economy

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Bond Finance, Bank Credit, and Aggregate Fluctuations in an Open Economy

Roberto Chang Andr´es Fernandez Adam Gulan

Rutgers University, Inter-American Development Bank, Bank of Finland

ONB, Vienna, July 2015¨ Extremely preliminary

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Motivation

In recent years, a considerable increase in external financing by the corporate sector in emerging market economies.

This trend accelerated during the period of low global interest rates following the global crisis.

Both direct loans as well as direct bond issuance.

The latter has been the one witnessing the largest increase. Shin (2013): new phase in global liquidity, with a broader change in the way private corporations fund themselves, where traditional bank financing is substituted with increased

funding through capital markets.

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Motivation

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Motivation

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Motivation

The latter has been the one witnessing the largest increase.

Shin (2013): new phase in global liquidity, with a broader change in the way private corporations fund themselves, where traditional bank financing is substituted with increased

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Motivation

The latter has been the one witnessing the largest increase.

Shin (2013): new phase in global liquidity, with a broader change in the way private corporations fund themselves, where traditional bank financing is substituted with increased

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Corporate debt in Latin America, bln USD

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Corporate debt in Latin America relative to GDP

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Some Questions

How can one rationalize this rise of corporate debt issuance in an environment where firms in a small open economy can access both direct or indirect finance?

What is the role of net worth (both of firms and of financial intermediaries)?

How does the observed growing reliance on debt issuance interact with the business cycle?

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Some Questions

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Some Questions

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This Paper

Builds a model where firms can borrow directly (bond issuance) or with the participation of intermediaries (bank finance) in world capital markets.

Extends the static, partial equilibrium framework of Holmstr¨om-Tirole (1997), into a dynamic stochastic small open economy framework.

We then use this framework to study the dynamic behavior of both direct and indirect finance when unexpected shocks occur.

Particularly, a large and persistent drop in world interest rates.

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This Paper

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This Paper

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This Paper

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Main Results (for now)

The model can generate an increase in both direct and indirect finance following a drop in world interest rates.

A key driver: evolution of net worth.

As their net worth builds up, firms are able to access more (cheaper) direct finance.

Access to (more costly) indirect finance also increases because some firms, that were previously absent from the market due to their low net worth, now have enough equity to participate in credit markets.

As in HT, the net worth of banks can substitute for the net worth of firms, and its evolution is critical for dynamics.

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Main Results (for now)

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Main Results (for now)

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Main Results (for now)

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Main Results (for now)

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The Model

Infinite horizon small open economy

A single traded final good (numeraire) produced with capital and labor

The economy is inhabited by:

Final good producers Households

Financial intermediaries (banks) Foreigners

Holdings of investment good producers

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The Model

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The Model

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The Model

Final good producers

Households

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The Model

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The Model

Financial intermediaries (banks)

Foreigners

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The Model

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The Model

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Final Good Producers

Usual, competitive sector, with production function Y_t =A_tK_t^αH_t¹⁻^α

Cost minimization:

αYt = r_t^KKt

(1−α)Yt = wtHt

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Households

Households own productive factors, including capital Capital accumulation is subject to adjustment costs:

K_t+1 = (1−δ)K_t+X_t− ^ϕ 2K_t

Kt+1

K_t −1 2

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Households

Budget constraint:

C_t+Q_tX_t+B_t₊₁=w_tH_t+r_t^KK_t+_Ψ_tR_t^∗B_t where

Ψt =_Ψ−φ(e^B^¯⁻^B −1)

Note that the price of investment goods (new capital), Qt, is variable

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Optimal Labor Supply

Preferences are GHH

Labor supply only depends on the wage:

w_t =κH_t^τ⁻¹

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Optimal Savings

The FOC for savings is standard:

λ^c_t = β^hEt(λ^c_t₊₁Ψt+1R_t^∗₊₁) with

λ^c_t =

C_t−κH^τ τ

−σ

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Optimal capital accumulation

Capital accumulation is given by the Euler equation

Q_t

1+ϕ K_t+1

K_t −1

= β^hE_tλ^c_t₊₁

λ^c_t [r_t^K₊₁+Q_t+1(1−δ) + ϕ

K_t+2

K_t₊₁ −1 K_t+2

K_t₊₁ − ^ϕ 2

K_t+2

K_t₊₁ −1 2

] This would be a standard model if Q_t ≡1

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Modeling the Supply of Capital Goods

“Holding companies”, each of which with a continuum of capital producing firms.

A representative holding arrives to period t with equityK_t^f The holding’s equity is then split: a firm i is given equityAⁱ_t, according to some distribution Gt( ) =G(A;µt), so that K_t^f =R_∞

0 Aⁱ_tdGt Aⁱ_t

Each firm i is charged with financing and executing a project, which takesIt units of the final good as input, and returns a random amount of new capital goods.

The size of the investment project,I_t, is chosen by the manager of the holding and common to every firm.

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Modeling the Supply of Capital Goods

A representative holding arrives to period t with equityK_t^f

The holding’s equity is then split: a firm i is given equityAⁱ_t, according to some distribution Gt( ) =G(A;µt), so that K_t^f =R_∞

0 Aⁱ_tdGt Aⁱ_t

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Modeling the Supply of Capital Goods

0 Aⁱ_tdGt Aⁱ_t

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Modeling the Supply of Capital Goods

0 Aⁱ_tdGt Aⁱ_t

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Modeling the Supply of Capital Goods

0 Aⁱ_tdGt Aⁱ_t

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Firm distribution

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Typical Firms’s Problem

Follow HT (1997): consider a firm with Aⁱ_t <It

Need finance, but there is moral hazard problem

If project is executed, it returns RIt with probability p_H and zero otherwise

But, to gain a private benefit B, the firm can choose a ”bad” project that reduces success probability to p_L <p_H

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Typical Firms’s Problem

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Typical Firms’s Problem

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Typical Firms’s Problem

But, to gain a private benefit B, the firm can choose a ”bad”

project that reduces success probability to p_L <p_H

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Conditions for Direct Finance

Incentive Compatibility Constraint (ICC):

p_HR_t^f^,i ≥p_LR_t^f^,i+BI_t or, with ∆=p_H−p_L,R_t^f^,i ≥ ^BI_∆^t

Lenders’ Participation Constraint:

pH(QtRIt−R_t^f^,i)≥It−Aⁱ_t

Combining the two: Aⁱ_t ≥A^¯_t =I_t

1−p_H(Q_tR− ^B

∆)

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Conditions for Direct Finance

Combining the two: Aⁱ_t ≥A^¯_t =I_t

1−p_H(Q_tR− ^B

∆)

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Conditions for Direct Finance

Combining the two:

B

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Intermediated Finance

If a firm j does not have enough equity, it can seek the help of financial intermediaries or ”banks”

A bank can reduce the private benefit of the bad project to b <B at a costcI_t

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Intermediated Finance

If a firm j does not have enough equity, it can seek the help of financial intermediaries or ”banks”

A bank can reduce the private benefit of the bad project to b <B at a costcI_t

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Conditions for Bank Finance

ICC for firm j:

pHR_t^f^,j ≥pLR_t^f^,j+bIt

ICC for bank:

pHR_t^m,j −cIt ≥pLR_t^m,j so R_t^m,j ≡R_t^m

Outsiders’ participation constraint:

p_H(Q_tRI_t−R_t^f^,j−R_t^m,j)≥I_t−I_t^m,j−A^j_t Bank’s participation constraint:

pHR_t^m ≥ βtI_t^m,j so I_t^m,j ≡I_t^m

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Conditions for Bank Finance

ICC for firm j:

ICC for bank:

p_H(Q_tRI_t−R_t^f^,j−R_t^m,j)≥I_t−I_t^m,j−A^j_t Bank’s participation constraint:

pHR_t^m ≥ βtI_t^m,j so I_t^m,j ≡I_t^m

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Conditions for Bank Finance

ICC for firm j:

ICC for bank:

pH(QtRIt−R_t^f^,j−R_t^m,j)≥ It−I_t^m,j−A^j_t

Bank’s participation constraint: pHR_t^m ≥ βtI_t^m,j so I_t^m,j ≡I_t^m

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Conditions for Bank Finance

ICC for firm j:

ICC for bank:

pH(QtRIt−R_t^f^,j−R_t^m,j)≥ It−I_t^m,j−A^j_t Bank’s participation constraint:

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Conditions for Bank Finance

Combining, firmj will have access to bank finance if it has enough equity: A^j_t ≥A_t, where

A_t =It

1−p_H c

∆βt

−p_H

QtR−^b+c

∆

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Project Size

The holding’s manager choosesIt to maximize profits:

Π^ft = pHQtRIt[1−Gt(A_t)] +

Z _A_t

0

Aⁱ_tdGt Aⁱ_t

−

Z∞ A¯t

It−Aⁱ_t

dG Aⁱ_t

−

Z A¯t

At

It−pH

cIt

∆βt

−Aⁱ_t

dG Aⁱ_t

−p_HcI_t

∆ [G(A^¯_t)−G(A_t)]

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Distribution

We have assumed thatGt(A) =G(A;µt)for some parameter µt. In particular, if

Aⁱ_t =K_t^fz_tⁱ

wherez_tⁱ is i.i.d. across agents and time, with cdfF(z), mean one, and some variance

Gt(A) =Pr

Aⁱ_t ≤A =Pr n

K_t^fz_tⁱ ≤A o

=F A

K_t^f

≡G(A;µt) ForG_t(.)to be lognormal with mean µt and varianceσ_G²,

µt =logK_t^f −^σ

2 G

2

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Holding’s optimality conditions

The FOC’s are:

(pHQtR−1) [1−Gt(A_t)]−pH

c

∆βt

(βt−1)[G(A^¯t)−G(A_t)]

= λ¹_t

1−p_H(Q_tR− ^B

∆)

+λ²_t

1−p_H c

∆βt

−p_H

Q_tR− ^b+c

∆

with

λ¹_t =gt(A^¯t)ItpH

c

∆βt

(βt−1)

λ²_t =gt(A_t)It

p_HQtR−1−p_H c

∆βt

(βt−1)

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Temporary Equilibrium

βt adjusts to equate demand for bank equity to its supply:

K_t^m =pH

cIt

∆βt

[G(A^¯t;µt)−G(A_t;µt)]

The price of new capital,Qt, adjusts to clear the new capital market:

X_t =p_HRI_t[1−G(A_t;µt)]

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Temporary Equilibrium

βt adjusts to equate demand for bank equity to its supply:

K_t^m =pH

cIt

∆βt

[G(A^¯t;µt)−G(A_t;µt)]

The price of new capital,Qt, adjusts to clear the new capital market:

X_t =p_HRI_t[1−G(A_t;µt)]

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Dynamics of Equity

Banks’ equity:

K_t^m₊₁ =θ^mp_HcI_t

∆ [G(A^¯_t;µt)−G(A_t;µt)]

Holding’s (capital producers’) equity: K_t^f₊₁ = θ^fΠ^ft

= θ^f{K_t^f + (p_HQ_tR−1)I_t[1−G(A_t;µt)]

−p_H cI_t

∆βt

(βt−1) [G(A^¯_t;µt)−G(A_t;µt)]}

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Dynamics of Equity

Banks’ equity:

K_t^m₊₁ =θ^mp_HcI_t

∆ [G(A^¯_t;µt)−G(A_t;µt)]

Holding’s (capital producers’) equity:

K_t^f₊₁ = θ^fΠ^f_t

= θ^f{K_t^f + (p_HQ_tR−1)I_t[1−G(A_t;µt)]

−p_H cI_t

∆βt

(βt−1) [G(A^¯_t;µt)−G(A_t;µt)]}

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Calibration

An important aspect of the parameterization concerns the distribution of equity supply which is assumed to be

G(A;µ) = 0.4 G(A;^¯ µ) = 0.8

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Calibration

Parameter Description Value ϕ Cost of capital adjustment 4.602 Ψ˜ Risk premium elasticity 0.001 β Rate of return to bank equity 1.042 p_H High prob. of project success 0.99 p_L Low prob. of project success 0.96 α Cobb-Douglas capital share 0.3 K/Y Capital-to-output ratio 20

β^h Household’s discount factor 0.99

δ Depreciation rate 0.05

A TFP 1

H Hours 0.33

C/Y Consumption-to-output ratio 0.7

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