Investment and the Cost of Capital
Interest Rate Endogeneity & Robustness
Investment and the Cost of Capital
New Evidence from the Corporate Bond Market
Simon Gilchrist
1
Egon Zakrajˇsek
2
1
Department of Economics
Boston University and NBER
2
Division of Monetary Affairs
Federal Reserve Board
Fakulteta za Matematiko in Fiziko
Univerza v Ljubljani
December 2007
Interest Rate Endogeneity & Robustness
Investment and the Cost of Capital
Monetary policy:
Policymakers use leverage over short-term market interest rates to influence the cost of capital
Changes in the cost of capital affect interest-sensitive components of aggregate demand
Fiscal policy:
Elasticity of investment demand w.r.t. user cost of capital is the key parameter determining the costs and benefits of alternative corporate tax policies
Interest Rate Endogeneity & Robustness
Investment and the Cost of Capital
Monetary policy:
Policymakers use leverage over short-term market interest rates to influence the cost of capital
Changes in the cost of capital affect interest-sensitive components of aggregate demand
Fiscal policy:
Elasticity of investment demand w.r.t. user cost of capital is the key parameter determining the costs and benefits of alternative corporate tax policies
Interest Rate Endogeneity & Robustness
Investment and the Cost of Capital
Monetary policy:
Policymakers use leverage over short-term market interest rates to influence the cost of capital
Changes in the cost of capital affect interest-sensitive components of aggregate demand
Fiscal policy:
Elasticity of investment demand w.r.t. user cost of capital is the key parameter determining the costs and benefits of alternative corporate tax policies
Interest Rate Endogeneity & Robustness
Investment and the Cost of Capital
Monetary policy:
Policymakers use leverage over short-term market interest rates to influence the cost of capital
Changes in the cost of capital affect interest-sensitive components of aggregate demand
Fiscal policy:
Elasticity of investment demand w.r.t. user cost of capital is the key parameter determining the costs and benefits of alternative corporate tax policies
Interest Rate Endogeneity & Robustness
Investment and the Cost of Capital
Monetary policy:
Policymakers use leverage over short-term market interest rates to influence the cost of capital
Changes in the cost of capital affect interest-sensitive components of aggregate demand
Fiscal policy:
Elasticity of investment demand w.r.t. user cost of capital is the key parameter determining the costs and benefits of alternative corporate tax policies
Interest Rate Endogeneity & Robustness
Investment and the Cost of Capital
Monetary policy:
Policymakers use leverage over short-term market interest rates to influence the cost of capital
Changes in the cost of capital affect interest-sensitive components of aggregate demand
Fiscal policy:
Elasticity of investment demand w.r.t. user cost of capital is the key parameter determining the costs and benefits of alternative corporate tax policies
Interest Rate Endogeneity & Robustness
User Cost of Capital
Key components of the user cost of capital:
Price of capital relative to the price of output
Tax treatment of capital purchases and capital income.
(corporate tax rate, PDV of depreciation allowances, ITC)
Expected gains associated with capital purchases
The rate at which capital depreciates
Required real rate of return on financial assets
Interest Rate Endogeneity & Robustness
User Cost of Capital
Key components of the user cost of capital:
Price of capital relative to the price of output
Tax treatment of capital purchases and capital income.
(corporate tax rate, PDV of depreciation allowances, ITC)
Expected gains associated with capital purchases
The rate at which capital depreciates
Required real rate of return on financial assets
Interest Rate Endogeneity & Robustness
User Cost of Capital
Key components of the user cost of capital:
Price of capital relative to the price of output
Tax treatment of capital purchases and capital income.
(corporate tax rate, PDV of depreciation allowances, ITC)
Expected gains associated with capital purchases
The rate at which capital depreciates
Required real rate of return on financial assets
Interest Rate Endogeneity & Robustness
User Cost of Capital
Key components of the user cost of capital:
Price of capital relative to the price of output
Tax treatment of capital purchases and capital income.
(corporate tax rate, PDV of depreciation allowances, ITC)
Expected gains associated with capital purchases
The rate at which capital depreciates
Required real rate of return on financial assets
Interest Rate Endogeneity & Robustness
User Cost of Capital
Key components of the user cost of capital:
Price of capital relative to the price of output
Tax treatment of capital purchases and capital income.
(corporate tax rate, PDV of depreciation allowances, ITC)
Expected gains associated with capital purchases
The rate at which capital depreciates
Required real rate of return on financial assets
Interest Rate Endogeneity & Robustness
User Cost of Capital
Key components of the user cost of capital:
Price of capital relative to the price of output
Tax treatment of capital purchases and capital income.
(corporate tax rate, PDV of depreciation allowances, ITC)
Expected gains associated with capital purchases
The rate at which capital depreciates
Required real rate of return on financial assets
Interest Rate Endogeneity & Robustness
User Cost of Capital
Key components of the user cost of capital:
Price of capital relative to the price of output
Tax treatment of capital purchases and capital income.
(corporate tax rate, PDV of depreciation allowances, ITC)
Expected gains associated with capital purchases
The rate at which capital depreciates
Required real rate of return on financial assets
Interest Rate Endogeneity & Robustness
Summary of Empirical Evidence
What is the elasticity of investment demand w.r.t. user cost?
Published estimates range from 0 to -2
Interest rates play a minor role as determinants of investment spending
“Accelerator” variables (e.g., output, cash flow) have a much larger economic impact on capital spending than the user cost of capital
Interest Rate Endogeneity & Robustness
Summary of Empirical Evidence
What is the elasticity of investment demand w.r.t. user cost?
Published estimates range from 0 to -2
Interest rates play a minor role as determinants of investment spending
“Accelerator” variables (e.g., output, cash flow) have a much larger economic impact on capital spending than the user cost of capital
Interest Rate Endogeneity & Robustness
Summary of Empirical Evidence
What is the elasticity of investment demand w.r.t. user cost?
Published estimates range from 0 to -2
Interest rates play a minor role as determinants of investment spending
“Accelerator” variables (e.g., output, cash flow) have a much larger economic impact on capital spending than the user cost of capital
Interest Rate Endogeneity & Robustness
Summary of Empirical Evidence
What is the elasticity of investment demand w.r.t. user cost?
Published estimates range from 0 to -2
Interest rates play a minor role as determinants of investment spending
“Accelerator” variables (e.g., output, cash flow) have a much larger economic impact on capital spending than the user cost of capital
Interest Rate Endogeneity & Robustness
Summary of Empirical Evidence
What is the elasticity of investment demand w.r.t. user cost?
Published estimates range from 0 to -2
Interest rates play a minor role as determinants of investment spending
“Accelerator” variables (e.g., output, cash flow) have a much larger economic impact on capital spending than the user cost of capital
Interest Rate Endogeneity & Robustness
Empirical Challenges
Econometric issues:
Simultaneity between interest rates and investment demand
Price of capital and depreciation rates have little cyclical variation
Many tax changes are transitory and/or anticipated
Interest Rate Endogeneity & Robustness
Empirical Challenges
Econometric issues:
Simultaneity between interest rates and investment demand
Price of capital and depreciation rates have little cyclical variation
Many tax changes are transitory and/or anticipated
Interest Rate Endogeneity & Robustness
Empirical Challenges
Econometric issues:
Simultaneity between interest rates and investment demand
Price of capital and depreciation rates have little cyclical variation
Many tax changes are transitory and/or anticipated
Interest Rate Endogeneity & Robustness
Empirical Challenges
Econometric issues:
Simultaneity between interest rates and investment demand
Price of capital and depreciation rates have little cyclical variation
Many tax changes are transitory and/or anticipated
Interest Rate Endogeneity & Robustness
Empirical Challenges
Econometric issues:
Simultaneity between interest rates and investment demand
Price of capital and depreciation rates have little cyclical variation
Many tax changes are transitory and/or anticipated
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Our Approach
Estimate the relationship between firm-level investment decisions and firm-specific estimates of the user cost of capital:
Measure the marginal cost of external finance with prices of outstanding senior unsecured bonds traded in the secondary market
Cross-sectional heterogeneity in interest rates:
Differences in default risk
Differences in risk factors
Differences in liquidity premiums
Related literature:
Guiso, Kashyap, Panetta & Terlizzese (2002)
Philippon (2007)
Interest Rate Endogeneity & Robustness
Neclassical Investment Model
CES production in capital ( K ) and variable inputs ( L ) :
Y = ( aK
σ
+ bL
σ
)
1
σ
FOC for the firm’s desired capital ( K
∗
) :
1 − σ a
Y
K ∗
= C K
C K = user cost of capital
Partial adjustment between K and K
∗
:
∆ ln K = η + λ ln
Y
K
−
1
1 − σ ln C K
0 < λ < 1 = speed of adjustment
1 / (1 − σ ) = L-R elasticity of capital w.r.t. the user cost
Interest Rate Endogeneity & Robustness
Neclassical Investment Model
CES production in capital ( K ) and variable inputs ( L ) :
Y = ( aK
σ
+ bL
σ
)
1
σ
FOC for the firm’s desired capital ( K
∗
) :
1 − σ a
Y
K ∗
= C K
C K = user cost of capital
Partial adjustment between K and K
∗
:
∆ ln K = η + λ ln
Y
K
−
1
1 − σ ln C K
0 < λ < 1 = speed of adjustment
1 / (1 − σ ) = L-R elasticity of capital w.r.t. the user cost
Interest Rate Endogeneity & Robustness
Neclassical Investment Model
CES production in capital ( K ) and variable inputs ( L ) :
Y = ( aK
σ
+ bL
σ
)
1
σ
FOC for the firm’s desired capital ( K
∗
) :
1 − σ a
Y
K ∗
= C K
C K = user cost of capital
Partial adjustment between K and K
∗
:
∆ ln K = η + λ ln
Y
K
−
1
1 − σ ln C K
0 < λ < 1 = speed of adjustment
1 / (1 − σ ) = L-R elasticity of capital w.r.t. the user cost
Interest Rate Endogeneity & Robustness
Neclassical Investment Model
CES production in capital ( K ) and variable inputs ( L ) :
Y = ( aK
σ
+ bL
σ
)
1
σ
FOC for the firm’s desired capital ( K
∗
) :
1 − σ a
Y
K ∗
= C K
C K = user cost of capital
Partial adjustment between K and K
∗
:
∆ ln K = η + λ ln
Y
K
−
1
1 − σ ln C K
0 < λ < 1 = speed of adjustment
1 / (1 − σ ) = L-R elasticity of capital w.r.t. the user cost
Interest Rate Endogeneity & Robustness
Neclassical Investment Model
CES production in capital ( K ) and variable inputs ( L ) :
Y = ( aK
σ
+ bL
σ
)
1
σ
FOC for the firm’s desired capital ( K
∗
) :
1 − σ a
Y
K ∗
= C K
C K = user cost of capital
Partial adjustment between K and K
∗
:
∆ ln K = η + λ ln
Y
K
−
1
1 − σ ln C K
0 < λ < 1 = speed of adjustment
1 / (1 − σ ) = L-R elasticity of capital w.r.t. the user cost
Interest Rate Endogeneity & Robustness
Neclassical Investment Model
CES production in capital ( K ) and variable inputs ( L ) :
Y = ( aK
σ
+ bL
σ
)
1
σ
FOC for the firm’s desired capital ( K
∗
) :
1 − σ a
Y
K ∗
= C K
C K = user cost of capital
Partial adjustment between K and K
∗
:
∆ ln K = η + λ ln
Y
K
−
1
1 − σ ln C K
0 < λ < 1 = speed of adjustment
1 / (1 − σ ) = L-R elasticity of capital w.r.t. the user cost
Interest Rate Endogeneity & Robustness
Empirical Implementation
Regression specification:
∆ ln K t
= η + η y ln ( Y t
/K t − 1
) + η c ln C t
K + ε t
ε t
= random error term
−
η c
η y
=
1
1 − σ
= L-R elasticity of capital w.r.t. user cost
Cobb-Douglas production function ⇒ σ = 0
Interest Rate Endogeneity & Robustness
Empirical Implementation
Regression specification:
∆ ln K t
= η + η y ln ( Y t
/K t − 1
) + η c ln C t
K + ε t
ε t
= random error term
−
η c
η y
=
1
1 − σ
= L-R elasticity of capital w.r.t. user cost
Cobb-Douglas production function ⇒ σ = 0
Interest Rate Endogeneity & Robustness
Empirical Implementation
Regression specification:
∆ ln K t
= η + η y ln ( Y t
/K t − 1
) + η c ln C t
K + ε t
ε t
= random error term
−
η c
η y
=
1
1 − σ
= L-R elasticity of capital w.r.t. user cost
Cobb-Douglas production function ⇒ σ = 0
Interest Rate Endogeneity & Robustness
Empirical Implementation
Regression specification:
∆ ln K t
= η + η y ln ( Y t
/K t − 1
) + η c ln C t
K + ε t
ε t
= random error term
−
η c
η y
=
1
1 − σ
= L-R elasticity of capital w.r.t. user cost
Cobb-Douglas production function ⇒ σ = 0
Interest Rate Endogeneity & Robustness
Empirical Implementation
Regression specification:
∆ ln K t
= η + η y ln ( Y t
/K t − 1
) + η c ln C t
K + ε t
ε t
= random error term
−
η c
η y
=
1
1 − σ
= L-R elasticity of capital w.r.t. user cost
Cobb-Douglas production function ⇒ σ = 0
Interest Rate Endogeneity & Robustness
Key Results
Investment spending is highly sensitive to user cost of capital:
1 pp. increase in the user cost implies a 50–75 bps. decline in the investment rate
Economic impact of the user cost is as large as that of “economic fundamentals”
Long-run elasticity of capital is unity
Interest Rate Endogeneity & Robustness
Key Results
Investment spending is highly sensitive to user cost of capital:
1 pp. increase in the user cost implies a 50–75 bps. decline in the investment rate
Economic impact of the user cost is as large as that of “economic fundamentals”
Long-run elasticity of capital is unity
Interest Rate Endogeneity & Robustness
Key Results
Investment spending is highly sensitive to user cost of capital:
1 pp. increase in the user cost implies a 50–75 bps. decline in the investment rate
Economic impact of the user cost is as large as that of “economic fundamentals”
Long-run elasticity of capital is unity
Interest Rate Endogeneity & Robustness
Key Results
Investment spending is highly sensitive to user cost of capital:
1 pp. increase in the user cost implies a 50–75 bps. decline in the investment rate
Economic impact of the user cost is as large as that of “economic fundamentals”
Long-run elasticity of capital is unity
Interest Rate Endogeneity & Robustness
Key Results
Investment spending is highly sensitive to user cost of capital:
1 pp. increase in the user cost implies a 50–75 bps. decline in the investment rate
Economic impact of the user cost is as large as that of “economic fundamentals”
Long-run elasticity of capital is unity
Robustness
Interest Rate Endogeneity & Robustness
Results are robust to:
Different production sectors and time periods
Controlling for endogeneity of interest rates
Additional explanatory variables (default risk, Tobin’s Q)
Robustness
Interest Rate Endogeneity & Robustness
Results are robust to:
Different production sectors and time periods
Controlling for endogeneity of interest rates
Additional explanatory variables (default risk, Tobin’s Q)
Robustness
Interest Rate Endogeneity & Robustness
Results are robust to:
Different production sectors and time periods
Controlling for endogeneity of interest rates
Additional explanatory variables (default risk, Tobin’s Q)
Robustness
Interest Rate Endogeneity & Robustness
Results are robust to:
Different production sectors and time periods
Controlling for endogeneity of interest rates
Additional explanatory variables (default risk, Tobin’s Q)
Interest Rate Endogeneity & Robustness
Data Sources
Lehman/Warga & Merrill Lynch : prices of outstanding corporate bonds traded in the secondary market:
(Jan1973–Dec2005, month-end)
U.S. nonfarm, nonfinancial issuers only
Senior unsecured issues only
Option-adjusted yields
Term-premium adjustment for each bond on each day
Compustat : firm-level income and balance sheet data
(1973–2005, fiscal year-end)
Panel Dimensions : 5,800 bonds issued by 926 firms
Interest Rate Endogeneity & Robustness
Data Sources
Lehman/Warga & Merrill Lynch : prices of outstanding corporate bonds traded in the secondary market:
(Jan1973–Dec2005, month-end)
U.S. nonfarm, nonfinancial issuers only
Senior unsecured issues only
Option-adjusted yields
Term-premium adjustment for each bond on each day
Compustat : firm-level income and balance sheet data
(1973–2005, fiscal year-end)
Panel Dimensions : 5,800 bonds issued by 926 firms
Interest Rate Endogeneity & Robustness
Data Sources
Lehman/Warga & Merrill Lynch : prices of outstanding corporate bonds traded in the secondary market:
(Jan1973–Dec2005, month-end)
U.S. nonfarm, nonfinancial issuers only
Senior unsecured issues only
Option-adjusted yields
Term-premium adjustment for each bond on each day
Compustat : firm-level income and balance sheet data
(1973–2005, fiscal year-end)
Panel Dimensions : 5,800 bonds issued by 926 firms
Interest Rate Endogeneity & Robustness
Data Sources
Lehman/Warga & Merrill Lynch : prices of outstanding corporate bonds traded in the secondary market:
(Jan1973–Dec2005, month-end)
U.S. nonfarm, nonfinancial issuers only
Senior unsecured issues only
Option-adjusted yields
Term-premium adjustment for each bond on each day
Compustat : firm-level income and balance sheet data
(1973–2005, fiscal year-end)
Panel Dimensions : 5,800 bonds issued by 926 firms
Interest Rate Endogeneity & Robustness
Data Sources
Lehman/Warga & Merrill Lynch : prices of outstanding corporate bonds traded in the secondary market:
(Jan1973–Dec2005, month-end)
U.S. nonfarm, nonfinancial issuers only
Senior unsecured issues only
Option-adjusted yields
Term-premium adjustment for each bond on each day
Compustat : firm-level income and balance sheet data
(1973–2005, fiscal year-end)
Panel Dimensions : 5,800 bonds issued by 926 firms
Interest Rate Endogeneity & Robustness
Data Sources
Lehman/Warga & Merrill Lynch : prices of outstanding corporate bonds traded in the secondary market:
(Jan1973–Dec2005, month-end)
U.S. nonfarm, nonfinancial issuers only
Senior unsecured issues only
Option-adjusted yields
Term-premium adjustment for each bond on each day
Compustat : firm-level income and balance sheet data
(1973–2005, fiscal year-end)
Panel Dimensions : 5,800 bonds issued by 926 firms
Interest Rate Endogeneity & Robustness
Data Sources
Lehman/Warga & Merrill Lynch : prices of outstanding corporate bonds traded in the secondary market:
(Jan1973–Dec2005, month-end)
U.S. nonfarm, nonfinancial issuers only
Senior unsecured issues only
Option-adjusted yields
Term-premium adjustment for each bond on each day
Compustat : firm-level income and balance sheet data
(1973–2005, fiscal year-end)
Panel Dimensions : 5,800 bonds issued by 926 firms
Interest Rate Endogeneity & Robustness
Data Sources
Lehman/Warga & Merrill Lynch : prices of outstanding corporate bonds traded in the secondary market:
(Jan1973–Dec2005, month-end)
U.S. nonfarm, nonfinancial issuers only
Senior unsecured issues only
Option-adjusted yields
Term-premium adjustment for each bond on each day
Compustat : firm-level income and balance sheet data
(1973–2005, fiscal year-end)
Panel Dimensions : 5,800 bonds issued by 926 firms
Interest Rate Endogeneity & Robustness
Bond Characteristics
Variable Mean
# of bonds per firm/month 3.39
Mkt. Value of Issue ($mil.) 285.3
Maturity at Issue (years)
Duration (years)
S&P Credit Rating
14.1
6.41
-
Coupon Rate (pct)
Nominal Yield (pct)
Real Yield (pct)
Credit Spread (bps)
7.67
8.00
4.83
149
StdDev
4.16
322.5
9.5
2.91
-
2.13
2.44
1.81
135
Min
1.00
1.21
2.0
0.01
D
0.00
1.39
-3.47
0
Median
2.00
210.5
10.0
6.03
A3
7.42
7.67
4.71
105
Panel Dimensions
Obs.
= 316 , 984 N = 5 , 800 bonds
Min. Tenure = 1 Median Tenure = 45 Max. Tenure = 229
Max
57.00
6,771.1
50.0
29.5
AAA
16.63
24.06
15.27
1000
Interest Rate Endogeneity & Robustness
The Evolution of Corporate Bond Yields
Percent
Median
Baa
P95−P5
Monthly
1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003
Interest Rate Endogeneity & Robustness
Comparing Data with Broader Aggregates
60
Percent
40
Sample Aggregate
NIPA
20
Annual
0
−20
1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004
Interest Rate Endogeneity & Robustness
Neoclassical User Cost of Capital
User cost of capital for firm j in period t :
C K jt
=
P I st
P Q st
1 −
1
τ
− t
τ z t st
| {z
Relative Price
} |
(1 − τ t
) i jt
+ δ st
− E t
{z
Financial Cost
∆ P K s,t +1
P K st
}
P I st
/P Q st
= relative price of capital goods in industry s
(1 − τ t
) i jt
= after-tax nominal bond yield for firm j
τ t
= corporate income tax rate
δ st
= depreciation rate in industry s z t
= PDV of depreciation allowances in industry s
Interest Rate Endogeneity & Robustness
Neoclassical User Cost of Capital
User cost of capital for firm j in period t :
C K jt
=
P I st
P Q st
1 −
1
τ
− t
τ z t st
| {z
Relative Price
} |
(1 − τ t
) i jt
+ δ st
− E t
{z
Financial Cost
∆ P K s,t +1
P K st
}
P I st
/P Q st
= relative price of capital goods in industry s
(1 − τ t
) i jt
= after-tax nominal bond yield for firm j
τ t
= corporate income tax rate
δ st
= depreciation rate in industry s z t
= PDV of depreciation allowances in industry s
Interest Rate Endogeneity & Robustness
Neoclassical User Cost of Capital
User cost of capital for firm j in period t :
C K jt
=
P I st
P Q st
1 −
1
τ
− t
τ z t st
| {z
Relative Price
} |
(1 − τ t
) i jt
+ δ st
− E t
{z
Financial Cost
∆ P K s,t +1
P K st
}
P I st
/P Q st
= relative price of capital goods in industry s
(1 − τ t
) i jt
= after-tax nominal bond yield for firm j
τ t
= corporate income tax rate
δ st
= depreciation rate in industry s z t
= PDV of depreciation allowances in industry s
Interest Rate Endogeneity & Robustness
Neoclassical User Cost of Capital
User cost of capital for firm j in period t :
C K jt
=
P I st
P Q st
1 −
1
τ
− t
τ z t st
| {z
Relative Price
} |
(1 − τ t
) i jt
+ δ st
− E t
{z
Financial Cost
∆ P K s,t +1
P K st
}
P I st
/P Q st
= relative price of capital goods in industry s
(1 − τ t
) i jt
= after-tax nominal bond yield for firm j
τ t
= corporate income tax rate
δ st
= depreciation rate in industry s z t
= PDV of depreciation allowances in industry s
Interest Rate Endogeneity & Robustness
Neoclassical User Cost of Capital
User cost of capital for firm j in period t :
C K jt
=
P I st
P Q st
1 −
1
τ
− t
τ z t st
| {z
Relative Price
} |
(1 − τ t
) i jt
+ δ st
− E t
{z
Financial Cost
∆ P K s,t +1
P K st
}
P I st
/P Q st
= relative price of capital goods in industry s
(1 − τ t
) i jt
= after-tax nominal bond yield for firm j
τ t
= corporate income tax rate
δ st
= depreciation rate in industry s z t
= PDV of depreciation allowances in industry s
Interest Rate Endogeneity & Robustness
Neoclassical User Cost of Capital
User cost of capital for firm j in period t :
C K jt
=
P I st
P Q st
1 −
1
τ
− t
τ z t st
| {z
Relative Price
} |
(1 − τ t
) i jt
+ δ st
− E t
{z
Financial Cost
∆ P K s,t +1
P K st
}
P I st
/P Q st
= relative price of capital goods in industry s
(1 − τ t
) i jt
= after-tax nominal bond yield for firm j
τ t
= corporate income tax rate
δ st
= depreciation rate in industry s z t
= PDV of depreciation allowances in industry s
Interest Rate Endogeneity & Robustness
Neoclassical User Cost of Capital
User cost of capital for firm j in period t :
C K jt
=
P I st
P Q st
1 −
1
τ
− t
τ z t st
| {z
Relative Price
} |
(1 − τ t
) i jt
+ δ st
− E t
{z
Financial Cost
∆ P K s,t +1
P K st
}
P I st
/P Q st
= relative price of capital goods in industry s
(1 − τ t
) i jt
= after-tax nominal bond yield for firm j
τ t
= corporate income tax rate
δ st
= depreciation rate in industry s z t
= PDV of depreciation allowances in industry s
Interest Rate Endogeneity & Robustness
Firm Characteristics
Variable
Sales ($bil.)
Mkt. Capitalization ($bil.)
Par Value to L-T Debt
Investment to Capital
Sales to Capital
Profits to Capital
Tobin’s Q
User Cost of Capital
Mean StdDev
9.34
5.89
0.45
0.18
3.50
0.47
1.62
0.15
18.80
12.46
0.25
0.12
3.23
0.39
0.85
0.05
Min
< .
01
< .
01
< .
01
0.01
0.17
-0.46
0.44
0.04
Median
3.89
1.89
0.42
0.15
2.65
0.36
1.37
0.15
Panel Dimensions
Obs.
= 6 , 398 N = 896 firms
Min. Tenure = 1 Median Tenure = 6 Max. Tenure = 19
Max
275.8
172.5
1.00
1.00
25.0
2.99
15.3
0.35
Interest Rate Endogeneity & Robustness
Econometric Methodology
Investment regression specifications:
Semi-log:
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
Log-log: ln
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
The marginal product of capital (MPK):
MPK S = sales-based measure of MPK
(proportional to [ S/K ] jt
)
MPK Π = profits-based measure of MPK
(proportional to [Π /K ] jt
)
Interest Rate Endogeneity & Robustness
Econometric Methodology
Investment regression specifications:
Semi-log:
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
Log-log: ln
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
The marginal product of capital (MPK):
MPK S = sales-based measure of MPK
(proportional to [ S/K ] jt
)
MPK Π = profits-based measure of MPK
(proportional to [Π /K ] jt
)
Interest Rate Endogeneity & Robustness
Econometric Methodology
Investment regression specifications:
Semi-log:
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
Log-log: ln
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
The marginal product of capital (MPK):
MPK S = sales-based measure of MPK
(proportional to [ S/K ] jt
)
MPK Π = profits-based measure of MPK
(proportional to [Π /K ] jt
)
Interest Rate Endogeneity & Robustness
Econometric Methodology
Investment regression specifications:
Semi-log:
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
Log-log: ln
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
The marginal product of capital (MPK):
MPK S = sales-based measure of MPK
(proportional to [ S/K ] jt
)
MPK Π = profits-based measure of MPK
(proportional to [Π /K ] jt
)
Interest Rate Endogeneity & Robustness
Econometric Methodology
Investment regression specifications:
Semi-log:
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
Log-log: ln
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
The marginal product of capital (MPK):
MPK S = sales-based measure of MPK
(proportional to [ S/K ] jt
)
MPK Π = profits-based measure of MPK
(proportional to [Π /K ] jt
)
Interest Rate Endogeneity & Robustness
Econometric Methodology
Investment regression specifications:
Semi-log:
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
Log-log: ln
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
The marginal product of capital (MPK):
MPK S = sales-based measure of MPK
(proportional to [ S/K ] jt
)
MPK Π = profits-based measure of MPK
(proportional to [Π /K ] jt
)
Interest Rate Endogeneity & Robustness
Econometric Methodology
Investment regression specifications:
Semi-log:
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
Log-log: ln
I
K jt
= β
1 ln MPK jt
+ β
2 ln C K jt
+ µ j
+ λ t
+ ε jt
The marginal product of capital (MPK):
MPK S = sales-based measure of MPK
(proportional to [ S/K ] jt
)
MPK Π = profits-based measure of MPK
(proportional to [Π /K ] jt
)
Interest Rate Endogeneity & Robustness
Static Specification (OLS/Within)
Log-Log Specification
Variable ln MPK S jt ln MPK
Π jt ln C K jt
Relative Price
Financial Cost
L-R Elasticity
Pr > F
R
2
(within)
(1)
0.746
(0.039)
-
-0.729
(0.078)
-
-
-1.023
(0.116)
-
0.308
(2)
0.748
(0.039)
-
-
-0.758
(0.114)
-0.686
(0.089)
-
0.605
0.308
(3)
0.747
(0.039)
-
-
-0.761
(0.114)
-0.222
(0.154)
-
0.004
0.293
(4)
-
0.511
(0.029)
-0.477
(0.072)
-
-
-1.072
(0.177)
-
0.244
(5)
-
(6)
-
0.512
0.520
(0.029) (0.029)
-
-0.488
-0.488
(0.095) (0.096)
-0.459
0.045
(0.100) (0.126)
-
0.827
0.244
0.001
0.237
Interest Rate Endogeneity & Robustness
Dynamic Specification (GMM/Orthogonal Deviations)
Variable ln MPK
S jt ln MPK
Π jt ln C K jt
[ I/K ] j,t − 1
L-R Elasticity
Semi-Log Specification Log-Log Specification
(1)
0.102
(0.016)
-
-0.105
(0.032)
0.311
(0.039)
-0.970
(0.286)
(2)
-
0.094
(0.018)
-0.076
(0.031)
0.342
(0.037)
-1.237
(0.558)
(3)
0.576
(0.075)
-
-0.513
(0.142)
0.450
(0.035)
-1.122
(0.294)
(4)
-
0.547
(0.081)
-0.400
(0.137)
0.472
(0.035)
-1.368
(0.475)
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Interest Rate Endogeneity
Components of corporate bond yields:
General level of interest rates
Probability of default
Expected recovery rate
Risk and liquidity premiums
Simultaneity bias:
Expected default is a function of leverage and hence endogenous to firm’s financial policy:
If financial policy and investment policy are linked this may create bias
Liquidity premium is exogenous to the firm’s investment policy
Interest Rate Endogeneity & Robustness
Some Theory
Bond pricing equation:
SPREAD jt
= (1 − R ) × P jt
× Λ t
× U jt
P jt
= expected probability of default
R = recovery rate
Λ t
= price of default risk
U jt
= liquidity premium
Interest Rate Endogeneity & Robustness
Some Theory
Bond pricing equation:
SPREAD jt
= (1 − R ) × P jt
× Λ t
× U jt
P jt
= expected probability of default
R = recovery rate
Λ t
= price of default risk
U jt
= liquidity premium
Interest Rate Endogeneity & Robustness
Some Theory
Bond pricing equation:
SPREAD jt
= (1 − R ) × P jt
× Λ t
× U jt
P jt
= expected probability of default
R = recovery rate
Λ t
= price of default risk
U jt
= liquidity premium
Interest Rate Endogeneity & Robustness
Some Theory
Bond pricing equation:
SPREAD jt
= (1 − R ) × P jt
× Λ t
× U jt
P jt
= expected probability of default
R = recovery rate
Λ t
= price of default risk
U jt
= liquidity premium
Interest Rate Endogeneity & Robustness
Some Theory
Bond pricing equation:
SPREAD jt
= (1 − R ) × P jt
× Λ t
× U jt
P jt
= expected probability of default
R = recovery rate
Λ t
= price of default risk
U jt
= liquidity premium
Interest Rate Endogeneity & Robustness
Some Theory
Bond pricing equation:
SPREAD jt
= (1 − R ) × P jt
× Λ t
× U jt
P jt
= expected probability of default
R = recovery rate
Λ t
= price of default risk
U jt
= liquidity premium
Interest Rate Endogeneity & Robustness
Identifying the Liquidity Premium
Monthly panel regression: ln SPREAD jt
= θ
1 ln EDF j,t − 1
+ θ
0
2 c jt
+ λ t
+ u jt
SPREAD jt
= credit spread in month t
EDF j,t − 1
= expected year-ahead default frequency in month t − 1
λ t
= price of default risk c jt
= vector of controls for individual firm’s (S&P) credit rating and industry (3-digit NAICS) u jt
= liquidity shock in month t
Interest Rate Endogeneity & Robustness
Identifying the Liquidity Premium
Monthly panel regression: ln SPREAD jt
= θ
1 ln EDF j,t − 1
+ θ
0
2 c jt
+ λ t
+ u jt
SPREAD jt
= credit spread in month t
EDF j,t − 1
= expected year-ahead default frequency in month t − 1
λ t
= price of default risk c jt
= vector of controls for individual firm’s (S&P) credit rating and industry (3-digit NAICS) u jt
= liquidity shock in month t
Interest Rate Endogeneity & Robustness
Identifying the Liquidity Premium
Monthly panel regression: ln SPREAD jt
= θ
1 ln EDF j,t − 1
+ θ
0
2 c jt
+ λ t
+ u jt
SPREAD jt
= credit spread in month t
EDF j,t − 1
= expected year-ahead default frequency in month t − 1
λ t
= price of default risk c jt
= vector of controls for individual firm’s (S&P) credit rating and industry (3-digit NAICS) u jt
= liquidity shock in month t
Interest Rate Endogeneity & Robustness
Identifying the Liquidity Premium
Monthly panel regression: ln SPREAD jt
= θ
1 ln EDF j,t − 1
+ θ
0
2 c jt
+ λ t
+ u jt
SPREAD jt
= credit spread in month t
EDF j,t − 1
= expected year-ahead default frequency in month t − 1
λ t
= price of default risk c jt
= vector of controls for individual firm’s (S&P) credit rating and industry (3-digit NAICS) u jt
= liquidity shock in month t
Interest Rate Endogeneity & Robustness
Identifying the Liquidity Premium
Monthly panel regression: ln SPREAD jt
= θ
1 ln EDF j,t − 1
+ θ
0
2 c jt
+ λ t
+ u jt
SPREAD jt
= credit spread in month t
EDF j,t − 1
= expected year-ahead default frequency in month t − 1
λ t
= price of default risk c jt
= vector of controls for individual firm’s (S&P) credit rating and industry (3-digit NAICS) u jt
= liquidity shock in month t
Interest Rate Endogeneity & Robustness
Identifying the Liquidity Premium
Monthly panel regression: ln SPREAD jt
= θ
1 ln EDF j,t − 1
+ θ
0
2 c jt
+ λ t
+ u jt
SPREAD jt
= credit spread in month t
EDF j,t − 1
= expected year-ahead default frequency in month t − 1
λ t
= price of default risk c jt
= vector of controls for individual firm’s (S&P) credit rating and industry (3-digit NAICS) u jt
= liquidity shock in month t
Interest Rate Endogeneity & Robustness
Identifying the Liquidity Premium
Monthly panel regression: ln SPREAD jt
= θ
1 ln EDF j,t − 1
+ θ
0
2 c jt
+ λ t
+ u jt
SPREAD jt
= credit spread in month t
EDF j,t − 1
= expected year-ahead default frequency in month t − 1
λ t
= price of default risk c jt
= vector of controls for individual firm’s (S&P) credit rating and industry (3-digit NAICS) u jt
= liquidity shock in month t
Interest Rate Endogeneity & Robustness
Credit Spreads and Default Risk
Specification
Variable
Constant ln EDF j,t − 1
Industry Effects
Time Effects
Ratings Effects
R
2
(1) (2)
3.662
3.737
(0.028) (0.084)
0.393
0.386
(0.007) (0.007) no yes no
(0.000) no no no
0.483
0.509
(3)
4.207
(0.091)
0.359
(0.008) yes
(0.000) yes
(0.000) no
0.576
(4)
5.776
(0.088)
0.119
(0.007) yes
(0.000) yes
(0.000) yes
(0.000)
0.755
Interest Rate Endogeneity & Robustness
Credit Rating Effects
80
40
0
−40
−80
−120
−160
−200
200
Basis Points
160
120
C
CC
CCC3CCC2CCC1
B3 B2 B1 BB3 BB2 BB1
BBB3 BBB2 BBB1
Credit Rating (S&P)
A3 A2 A1 AA3 AA2 AA1 AAA
Interest Rate Endogeneity & Robustness
Investment, Cost of Capital, and Liquidity Shocks
Variable ln MPK
S jt ln MPK
Π jt ln C K jt
[ I/K ] j,t − 1
L-R Elasticity
Semi-Log Specification Log-Log Specification
(1)
0.153
(0.025)
-
-0.204
(0.054)
0.276
(0.051)
-0.747
(0.193)
(2)
-
0.132
(0.022)
-0.148
(0.046)
0.329
(0.050)
-0.890
(0.302)
(3)
0.671
(0.126)
-
-0.749
(0.226)
0.439
(0.043)
-0.895
(0.209)
(4)
-
0.432
(0.111)
-0.405
(0.180)
0.444
(0.048)
-1.065
(0.433)
Interest Rate Endogeneity & Robustness
Investment, Cost of Capital, and Other Factors
Log-Log Specification
Variable ln MPK Π jt ln C
K jt ln Q AVG jt ln Q KMV jt ln EDF j,t − 1
R
2
(within)
(1)
0.539
(0.036)
-0.511
(0.093)
-
-
-
0.268
(2) (3)
0.440
0.460
(0.042) (0.048)
-0.464
-0.479
(0.092) (0.121)
0.491
-
(0.056)
-
-
0.368
(0.051)
-
(4)
0.500
(0.041)
-0.450
(0.102)
-
0.311
0.324
-0.096
(0.014)
0.305
(5)
0.442
(0.048)
-0.417
(0.121)
-
0.246
(0.059)
-0.069
(0.017)
0.335
Summary
Interest Rate Endogeneity & Robustness
Investment is highly sensitive to interest rates through a user-cost of capital formulation when interest rates reflect firm-level bond prices.
This finding contrasts sharply with macroeconomic literature which has a difficult time finding a robust negative effect of the user-cost on investment.
Results are robust to sample period, alternative specifications, and endogeneity concerns.
Are these facts consistent with standard financial contracting models?
Summary
Interest Rate Endogeneity & Robustness
Investment is highly sensitive to interest rates through a user-cost of capital formulation when interest rates reflect firm-level bond prices.
This finding contrasts sharply with macroeconomic literature which has a difficult time finding a robust negative effect of the user-cost on investment.
Results are robust to sample period, alternative specifications, and endogeneity concerns.
Are these facts consistent with standard financial contracting models?
Summary
Interest Rate Endogeneity & Robustness
Investment is highly sensitive to interest rates through a user-cost of capital formulation when interest rates reflect firm-level bond prices.
This finding contrasts sharply with macroeconomic literature which has a difficult time finding a robust negative effect of the user-cost on investment.
Results are robust to sample period, alternative specifications, and endogeneity concerns.
Are these facts consistent with standard financial contracting models?
Summary
Interest Rate Endogeneity & Robustness
Investment is highly sensitive to interest rates through a user-cost of capital formulation when interest rates reflect firm-level bond prices.
This finding contrasts sharply with macroeconomic literature which has a difficult time finding a robust negative effect of the user-cost on investment.
Results are robust to sample period, alternative specifications, and endogeneity concerns.
Are these facts consistent with standard financial contracting models?
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Gilchrist, Sim & Zakrajˇsek (2007)
Specify firm’s investment problem with endogenous default and investment subject to adjustment costs :
In the absence of adjustment costs, the firm’s net worth is the state variable of the firm’s decision problem
(Cooley & Quadrini ( AER 2001)).
With adjustment costs, both capital and debt are state variables in the firm’s decision problem
Sources of financial market imperfections:
Verification costs—CSV framework
Limited enforceability—debt renegotiation
Can such a model replicate key stylized facts?
Positive relationship between credit spreads, default probabilities, and leverage
Negative relationship between investment and credit spreads
Interest Rate Endogeneity & Robustness
Technology and Product Markets
Technology :
Cobb-Douglas production function in capital ( K ) and labor ( L ) .
Technology shock Z ∈ Z ⊆ transition probability Q ( Z, Z
0
R
+
) .
, follows a Markov process with
Capital accumulation: K
0
= (1 − δ ) K + I
Convex investment adjustment costs: c ( I, K )
( c ( · , · ) is homogeneous of degree 0 in ( I, K ) )
Product markets :
Monopolistic competition (demand elasticity ξ > 1 ).
Revenue function :
R ( Z, K, N ) = Z
(1 − α
K
− α
N
)
K
α
K N
α
N
α
K
≡ α (1 − 1 /ξ ) and α
N
≡ (1 − α )(1 − 1 /ξ )
Interest Rate Endogeneity & Robustness
Technology and Product Markets
Technology :
Cobb-Douglas production function in capital ( K ) and labor ( L ) .
Technology shock Z ∈ Z ⊆ transition probability Q ( Z, Z
0
R
+
) .
, follows a Markov process with
Capital accumulation: K
0
= (1 − δ ) K + I
Convex investment adjustment costs: c ( I, K )
( c ( · , · ) is homogeneous of degree 0 in ( I, K ) )
Product markets :
Monopolistic competition (demand elasticity ξ > 1 ).
Revenue function :
R ( Z, K, N ) = Z
(1 − α
K
− α
N
)
K
α
K N
α
N
α
K
≡ α (1 − 1 /ξ ) and α
N
≡ (1 − α )(1 − 1 /ξ )
Interest Rate Endogeneity & Robustness
Technology and Product Markets
Technology :
Cobb-Douglas production function in capital ( K ) and labor ( L ) .
Technology shock Z ∈ Z ⊆ transition probability Q ( Z, Z
0
R
+
) .
, follows a Markov process with
Capital accumulation: K
0
= (1 − δ ) K + I
Convex investment adjustment costs: c ( I, K )
( c ( · , · ) is homogeneous of degree 0 in ( I, K ) )
Product markets :
Monopolistic competition (demand elasticity ξ > 1 ).
Revenue function :
R ( Z, K, N ) = Z
(1 − α
K
− α
N
)
K
α
K N
α
N
α
K
≡ α (1 − 1 /ξ ) and α
N
≡ (1 − α )(1 − 1 /ξ )
Interest Rate Endogeneity & Robustness
Technology and Product Markets
Technology :
Cobb-Douglas production function in capital ( K ) and labor ( L ) .
Technology shock Z ∈ Z ⊆ transition probability Q ( Z, Z
0
R
+
) .
, follows a Markov process with
Capital accumulation: K
0
= (1 − δ ) K + I
Convex investment adjustment costs: c ( I, K )
( c ( · , · ) is homogeneous of degree 0 in ( I, K ) )
Product markets :
Monopolistic competition (demand elasticity ξ > 1 ).
Revenue function :
R ( Z, K, N ) = Z
(1 − α
K
− α
N
)
K
α
K N
α
N
α
K
≡ α (1 − 1 /ξ ) and α
N
≡ (1 − α )(1 − 1 /ξ )
Interest Rate Endogeneity & Robustness
Technology and Product Markets
Technology :
Cobb-Douglas production function in capital ( K ) and labor ( L ) .
Technology shock Z ∈ Z ⊆ transition probability Q ( Z, Z
0
R
+
) .
, follows a Markov process with
Capital accumulation: K
0
= (1 − δ ) K + I
Convex investment adjustment costs: c ( I, K )
( c ( · , · ) is homogeneous of degree 0 in ( I, K ) )
Product markets :
Monopolistic competition (demand elasticity ξ > 1 ).
Revenue function :
R ( Z, K, N ) = Z
(1 − α
K
− α
N
)
K
α
K N
α
N
α
K
≡ α (1 − 1 /ξ ) and α
N
≡ (1 − α )(1 − 1 /ξ )
Interest Rate Endogeneity & Robustness
Technology and Product Markets
Technology :
Cobb-Douglas production function in capital ( K ) and labor ( L ) .
Technology shock Z ∈ Z ⊆ transition probability Q ( Z, Z
0
R
+
) .
, follows a Markov process with
Capital accumulation: K
0
= (1 − δ ) K + I
Convex investment adjustment costs: c ( I, K )
( c ( · , · ) is homogeneous of degree 0 in ( I, K ) )
Product markets :
Monopolistic competition (demand elasticity ξ > 1 ).
Revenue function :
R ( Z, K, N ) = Z
(1 − α
K
− α
N
)
K
α
K N
α
N
α
K
≡ α (1 − 1 /ξ ) and α
N
≡ (1 − α )(1 − 1 /ξ )
Interest Rate Endogeneity & Robustness
Technology and Product Markets
Technology :
Cobb-Douglas production function in capital ( K ) and labor ( L ) .
Technology shock Z ∈ Z ⊆ transition probability Q ( Z, Z
0
R
+
) .
, follows a Markov process with
Capital accumulation: K
0
= (1 − δ ) K + I
Convex investment adjustment costs: c ( I, K )
( c ( · , · ) is homogeneous of degree 0 in ( I, K ) )
Product markets :
Monopolistic competition (demand elasticity ξ > 1 ).
Revenue function :
R ( Z, K, N ) = Z
(1 − α
K
− α
N
)
K
α
K N
α
N
α
K
≡ α (1 − 1 /ξ ) and α
N
≡ (1 − α )(1 − 1 /ξ )
Interest Rate Endogeneity & Robustness
Technology and Product Markets
Technology :
Cobb-Douglas production function in capital ( K ) and labor ( L ) .
Technology shock Z ∈ Z ⊆ transition probability Q ( Z, Z
0
R
+
) .
, follows a Markov process with
Capital accumulation: K
0
= (1 − δ ) K + I
Convex investment adjustment costs: c ( I, K )
( c ( · , · ) is homogeneous of degree 0 in ( I, K ) )
Product markets :
Monopolistic competition (demand elasticity ξ > 1 ).
Revenue function :
R ( Z, K, N ) = Z
(1 − α
K
− α
N
)
K
α
K N
α
N
α
K
≡ α (1 − 1 /ξ ) and α
N
≡ (1 − α )(1 − 1 /ξ )
Interest Rate Endogeneity & Robustness
Firm’s Decision Problem
Financing :
Firm issues a one-period discount bond
Value of the firm :
V ( K, B, Z ) = max
I,N,B
0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B + q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
W ( K
0
, B
0
, Z
0
) Q ( Z, dZ
0
)
) s.t.
K
0
= (1 − δ ) K + I q ( B
0
, K
0
, Z ) = price of the one-period discount bond
µ/ (1 + r ) = firm’s discount factor (0 < µ < 1)
Interest Rate Endogeneity & Robustness
Firm’s Decision Problem
Financing :
Firm issues a one-period discount bond
Value of the firm :
V ( K, B, Z ) = max
I,N,B
0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B + q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
W ( K
0
, B
0
, Z
0
) Q ( Z, dZ
0
)
) s.t.
K
0
= (1 − δ ) K + I q ( B
0
, K
0
, Z ) = price of the one-period discount bond
µ/ (1 + r ) = firm’s discount factor (0 < µ < 1)
Interest Rate Endogeneity & Robustness
Firm’s Decision Problem
Financing :
Firm issues a one-period discount bond
Value of the firm :
V ( K, B, Z ) = max
I,N,B
0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B + q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
W ( K
0
, B
0
, Z
0
) Q ( Z, dZ
0
)
) s.t.
K
0
= (1 − δ ) K + I q ( B
0
, K
0
, Z ) = price of the one-period discount bond
µ/ (1 + r ) = firm’s discount factor (0 < µ < 1)
Interest Rate Endogeneity & Robustness
Firm’s Decision Problem
Financing :
Firm issues a one-period discount bond
Value of the firm :
V ( K, B, Z ) = max
I,N,B
0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B + q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
W ( K
0
, B
0
, Z
0
) Q ( Z, dZ
0
)
) s.t.
K
0
= (1 − δ ) K + I q ( B
0
, K
0
, Z ) = price of the one-period discount bond
µ/ (1 + r ) = firm’s discount factor (0 < µ < 1)
Interest Rate Endogeneity & Robustness
Firm’s Decision Problem
Financing :
Firm issues a one-period discount bond
Value of the firm :
V ( K, B, Z ) = max
I,N,B
0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B + q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
W ( K
0
, B
0
, Z
0
) Q ( Z, dZ
0
)
) s.t.
K
0
= (1 − δ ) K + I q ( B
0
, K
0
, Z ) = price of the one-period discount bond
µ/ (1 + r ) = firm’s discount factor (0 < µ < 1)
Interest Rate Endogeneity & Robustness
Firm’s Decision Problem
Financing :
Firm issues a one-period discount bond
Value of the firm :
V ( K, B, Z ) = max
I,N,B
0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B + q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
W ( K
0
, B
0
, Z
0
) Q ( Z, dZ
0
)
) s.t.
K
0
= (1 − δ ) K + I q ( B
0
, K
0
, Z ) = price of the one-period discount bond
µ/ (1 + r ) = firm’s discount factor (0 < µ < 1)
Interest Rate Endogeneity & Robustness
Default Decision
Endogenous default :
At the beginning of the period, the entrepreneur decides whether or not to default.
Continuation value :
W ( K, B, Z ) = max V ( K, B, Z ) , V d
( K ))
V d
( K ) = entrepreneur’s outside option (i.e., default value)
V d
( K ) = v d
K ; v d
> 0
Entrepreneur cannot expropriate the level of technology embodied in the project (i.e., V d does not depend on Z ).
(Thomas & Worrall ( ReStud 1994); Albuquerque & Hopenhayn
( ReStud 2004); Cooley, Marimon & Quadrini ( JPE 2004))
Interest Rate Endogeneity & Robustness
Default Decision
Endogenous default :
At the beginning of the period, the entrepreneur decides whether or not to default.
Continuation value :
W ( K, B, Z ) = max V ( K, B, Z ) , V d
( K ))
V d
( K ) = entrepreneur’s outside option (i.e., default value)
V d
( K ) = v d
K ; v d
> 0
Entrepreneur cannot expropriate the level of technology embodied in the project (i.e., V d does not depend on Z ).
(Thomas & Worrall ( ReStud 1994); Albuquerque & Hopenhayn
( ReStud 2004); Cooley, Marimon & Quadrini ( JPE 2004))
Interest Rate Endogeneity & Robustness
Default Decision
Endogenous default :
At the beginning of the period, the entrepreneur decides whether or not to default.
Continuation value :
W ( K, B, Z ) = max V ( K, B, Z ) , V d
( K ))
V d
( K ) = entrepreneur’s outside option (i.e., default value)
V d
( K ) = v d
K ; v d
> 0
Entrepreneur cannot expropriate the level of technology embodied in the project (i.e., V d does not depend on Z ).
(Thomas & Worrall ( ReStud 1994); Albuquerque & Hopenhayn
( ReStud 2004); Cooley, Marimon & Quadrini ( JPE 2004))
Interest Rate Endogeneity & Robustness
Default Decision
Endogenous default :
At the beginning of the period, the entrepreneur decides whether or not to default.
Continuation value :
W ( K, B, Z ) = max V ( K, B, Z ) , V d
( K ))
V d
( K ) = entrepreneur’s outside option (i.e., default value)
V d
( K ) = v d
K ; v d
> 0
Entrepreneur cannot expropriate the level of technology embodied in the project (i.e., V d does not depend on Z ).
(Thomas & Worrall ( ReStud 1994); Albuquerque & Hopenhayn
( ReStud 2004); Cooley, Marimon & Quadrini ( JPE 2004))
Interest Rate Endogeneity & Robustness
Default Decision
Endogenous default :
At the beginning of the period, the entrepreneur decides whether or not to default.
Continuation value :
W ( K, B, Z ) = max V ( K, B, Z ) , V d
( K ))
V d
( K ) = entrepreneur’s outside option (i.e., default value)
V d
( K ) = v d
K ; v d
> 0
Entrepreneur cannot expropriate the level of technology embodied in the project (i.e., V d does not depend on Z ).
(Thomas & Worrall ( ReStud 1994); Albuquerque & Hopenhayn
( ReStud 2004); Cooley, Marimon & Quadrini ( JPE 2004))
Interest Rate Endogeneity & Robustness
Default Decision
Endogenous default :
At the beginning of the period, the entrepreneur decides whether or not to default.
Continuation value :
W ( K, B, Z ) = max V ( K, B, Z ) , V d
( K ))
V d
( K ) = entrepreneur’s outside option (i.e., default value)
V d
( K ) = v d
K ; v d
> 0
Entrepreneur cannot expropriate the level of technology embodied in the project (i.e., V d does not depend on Z ).
(Thomas & Worrall ( ReStud 1994); Albuquerque & Hopenhayn
( ReStud 2004); Cooley, Marimon & Quadrini ( JPE 2004))
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower
Contract specifies :
Face value of the bond and bond price (i.e., yield).
Renegotiated debt burden.
Debt renegotiation :
V ( K
0
,
¯
( K
0
, Z
0
) , Z
0
) = V d
( K
0
)
¯
( K 0 , Z 0 ) = level of debt that makes entrepreneur indifferent between defaulting and staying in business.
Default threat is credible because V d > 0 .
Facing the credible threat, bondholders agree to renegotiate the firm’s debt.
If the value function V is strictly decreasing in B :
¯
( K
0
, Z
0
) = V
− 1
V d
( K
0
); K
0
, Z
0
, for given K
0
, Z
0
Interest Rate Endogeneity & Robustness
Contract: The Borrower (contd.)
Continuation value with debt restructuring :
W ( K
0
, B
0
, Z
0
) = max V ( K
0
, B
0
, Z
0
) , V d
( K
0
)
= V K
0
, min { B
0
,
¯
( K
0
, Z
0
) } , Z
0
Value of the firm :
V ( K, B, Z ) = max
I,N,B 0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B +
0
, Z
0
) Q ( Z, dZ
0
)
) q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
V ( K
0
, s.t.
K
0
= (1 − δ ) K + I
0
= min B
0
,
¯
( K
0
, Z
0
)
Interest Rate Endogeneity & Robustness
Contract: The Borrower (contd.)
Continuation value with debt restructuring :
W ( K
0
, B
0
, Z
0
) = max V ( K
0
, B
0
, Z
0
) , V d
( K
0
)
= V K
0
, min { B
0
,
¯
( K
0
, Z
0
) } , Z
0
Value of the firm :
V ( K, B, Z ) = max
I,N,B 0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B +
0
, Z
0
) Q ( Z, dZ
0
)
) q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
V ( K
0
, s.t.
K
0
= (1 − δ ) K + I
0
= min B
0
,
¯
( K
0
, Z
0
)
Interest Rate Endogeneity & Robustness
Contract: The Borrower (contd.)
Continuation value with debt restructuring :
W ( K
0
, B
0
, Z
0
) = max V ( K
0
, B
0
, Z
0
) , V d
( K
0
)
= V K
0
, min { B
0
,
¯
( K
0
, Z
0
) } , Z
0
Value of the firm :
V ( K, B, Z ) = max
I,N,B 0
(
R ( Z, K, N ) − wN − I − c ( I, K ) K − B +
0
, Z
0
) Q ( Z, dZ
0
)
) q ( B
0
, K
0
, Z ) B
0
µ
+
1 + r
Z
Z
V ( K
0
, s.t.
K
0
= (1 − δ ) K + I
0
= min B
0
,
¯
( K
0
, Z
0
)
Interest Rate Endogeneity & Robustness
Contract: The Lender
Standard debt contract :
Default region: D = { Z ∈ Z | V ( K, B, Z ) ≤ V d
( K ) }
Verification costs: 0 < χ < 1
(Proportional to the size of the firm and paid by bondholders.)
If Z
0
∈ D ( K
0
, B
0
) , the firm’s debt is restructured to
¯
( K
0
, Z
0
)
Risk-neutral competitive bond market :
(1 + r ) B
0 q ( K
0
, B
0
, Z ) =
"
Z
¯
( K 0 ,B 0 )
B
0
Q ( Z, dZ
0
)
+
Z
D ( K
0
,B
0
)
¯
( K
0
, Z
0
) − χK
0
Q ( Z, dZ
0
)
#
Interest Rate Endogeneity & Robustness
Contract: The Lender
Standard debt contract :
Default region: D = { Z ∈ Z | V ( K, B, Z ) ≤ V d
( K ) }
Verification costs: 0 < χ < 1
(Proportional to the size of the firm and paid by bondholders.)
If Z
0
∈ D ( K
0
, B
0
) , the firm’s debt is restructured to
¯
( K
0
, Z
0
)
Risk-neutral competitive bond market :
(1 + r ) B
0 q ( K
0
, B
0
, Z ) =
"
Z
¯
( K 0 ,B 0 )
B
0
Q ( Z, dZ
0
)
+
Z
D ( K
0
,B
0
)
¯
( K
0
, Z
0
) − χK
0
Q ( Z, dZ
0
)
#
Interest Rate Endogeneity & Robustness
Contract: The Lender
Standard debt contract :
Default region: D = { Z ∈ Z | V ( K, B, Z ) ≤ V d
( K ) }
Verification costs: 0 < χ < 1
(Proportional to the size of the firm and paid by bondholders.)
If Z
0
∈ D ( K
0
, B
0
) , the firm’s debt is restructured to
¯
( K
0
, Z
0
)
Risk-neutral competitive bond market :
(1 + r ) B
0 q ( K
0
, B
0
, Z ) =
"
Z
¯
( K 0 ,B 0 )
B
0
Q ( Z, dZ
0
)
+
Z
D ( K
0
,B
0
)
¯
( K
0
, Z
0
) − χK
0
Q ( Z, dZ
0
)
#
Interest Rate Endogeneity & Robustness
Contract: The Lender
Standard debt contract :
Default region: D = { Z ∈ Z | V ( K, B, Z ) ≤ V d
( K ) }
Verification costs: 0 < χ < 1
(Proportional to the size of the firm and paid by bondholders.)
If Z
0
∈ D ( K
0
, B
0
) , the firm’s debt is restructured to
¯
( K
0
, Z
0
)
Risk-neutral competitive bond market :
(1 + r ) B
0 q ( K
0
, B
0
, Z ) =
"
Z
¯
( K 0 ,B 0 )
B
0
Q ( Z, dZ
0
)
+
Z
D ( K
0
,B
0
)
¯
( K
0
, Z
0
) − χK
0
Q ( Z, dZ
0
)
#
Interest Rate Endogeneity & Robustness
Contract: The Lender
Standard debt contract :
Default region: D = { Z ∈ Z | V ( K, B, Z ) ≤ V d
( K ) }
Verification costs: 0 < χ < 1
(Proportional to the size of the firm and paid by bondholders.)
If Z
0
∈ D ( K
0
, B
0
) , the firm’s debt is restructured to
¯
( K
0
, Z
0
)
Risk-neutral competitive bond market :
(1 + r ) B
0 q ( K
0
, B
0
, Z ) =
"
Z
¯
( K 0 ,B 0 )
B
0
Q ( Z, dZ
0
)
+
Z
D ( K
0
,B
0
)
¯
( K
0
, Z
0
) − χK
0
Q ( Z, dZ
0
)
#
Interest Rate Endogeneity & Robustness
Equilibrium Contract
Bond price/yield : q ( K
0
, B
0
, Z ) =
1
1 + r
"
1 −
Z
D ( K
0
,B
0
)
1 −
¯
( K
B
0
, Z
0
0
)
− χ
K
0
B 0
Q ( Z, dZ
0
)
Equilibrium class of contracts :
Contract bond yield depends on
¯
( K
0
, Z
0
)
Restrict attention to a class of contracts such that homogeneous of degree 1 in ( K, Z ) :
¯
( K 0 , Z 0 ) is
¯
( K, Z ) = ϕZ
φ
K
1 − φ
+ θK, ϕ > 0 and 0 < φ < 1
#
θ = (1 − δ ) η , where η is a random shock affecting the resale value of undepreciated physical capital
Interest Rate Endogeneity & Robustness
Equilibrium Contract
Bond price/yield : q ( K
0
, B
0
, Z ) =
1
1 + r
"
1 −
Z
D ( K
0
,B
0
)
1 −
¯
( K
B
0
, Z
0
0
)
− χ
K
0
B 0
Q ( Z, dZ
0
)
Equilibrium class of contracts :
Contract bond yield depends on
¯
( K
0
, Z
0
)
Restrict attention to a class of contracts such that homogeneous of degree 1 in ( K, Z ) :
¯
( K 0 , Z 0 ) is
¯
( K, Z ) = ϕZ
φ
K
1 − φ
+ θK, ϕ > 0 and 0 < φ < 1
#
θ = (1 − δ ) η , where η is a random shock affecting the resale value of undepreciated physical capital
Interest Rate Endogeneity & Robustness
Equilibrium Contract
Bond price/yield : q ( K
0
, B
0
, Z ) =
1
1 + r
"
1 −
Z
D ( K
0
,B
0
)
1 −
¯
( K
B
0
, Z
0
0
)
− χ
K
0
B 0
Q ( Z, dZ
0
)
Equilibrium class of contracts :
Contract bond yield depends on
¯
( K
0
, Z
0
)
Restrict attention to a class of contracts such that homogeneous of degree 1 in ( K, Z ) :
¯
( K 0 , Z 0 ) is
¯
( K, Z ) = ϕZ
φ
K
1 − φ
+ θK, ϕ > 0 and 0 < φ < 1
#
θ = (1 − δ ) η , where η is a random shock affecting the resale value of undepreciated physical capital
Interest Rate Endogeneity & Robustness
Equilibrium Contract
Bond price/yield : q ( K
0
, B
0
, Z ) =
1
1 + r
"
1 −
Z
D ( K
0
,B
0
)
1 −
¯
( K
B
0
, Z
0
0
)
− χ
K
0
B 0
Q ( Z, dZ
0
)
Equilibrium class of contracts :
Contract bond yield depends on
¯
( K
0
, Z
0
)
Restrict attention to a class of contracts such that homogeneous of degree 1 in ( K, Z ) :
¯
( K 0 , Z 0 ) is
¯
( K, Z ) = ϕZ
φ
K
1 − φ
+ θK, ϕ > 0 and 0 < φ < 1
#
θ = (1 − δ ) η , where η is a random shock affecting the resale value of undepreciated physical capital
Interest Rate Endogeneity & Robustness
Equilibrium Contract
Bond price/yield : q ( K
0
, B
0
, Z ) =
1
1 + r
"
1 −
Z
D ( K
0
,B
0
)
1 −
¯
( K
B
0
, Z
0
0
)
− χ
K
0
B 0
Q ( Z, dZ
0
)
Equilibrium class of contracts :
Contract bond yield depends on
¯
( K
0
, Z
0
)
Restrict attention to a class of contracts such that homogeneous of degree 1 in ( K, Z ) :
¯
( K 0 , Z 0 ) is
¯
( K, Z ) = ϕZ
φ
K
1 − φ
+ θK, ϕ > 0 and 0 < φ < 1
#
θ = (1 − δ ) η , where η is a random shock affecting the resale value of undepreciated physical capital
Interest Rate Endogeneity & Robustness
Equilibrium Contract
Bond price/yield : q ( K
0
, B
0
, Z ) =
1
1 + r
"
1 −
Z
D ( K
0
,B
0
)
1 −
¯
( K
B
0
, Z
0
0
)
− χ
K
0
B 0
Q ( Z, dZ
0
)
Equilibrium class of contracts :
Contract bond yield depends on
¯
( K
0
, Z
0
)
Restrict attention to a class of contracts such that homogeneous of degree 1 in ( K, Z ) :
¯
( K 0 , Z 0 ) is
¯
( K, Z ) = ϕZ
φ
K
1 − φ
+ θK, ϕ > 0 and 0 < φ < 1
#
θ = (1 − δ ) η , where η is a random shock affecting the resale value of undepreciated physical capital
Interest Rate Endogeneity & Robustness
Value Function
20
15
10
5
0
−5
1.5
1 z(=Z/K)
0.5
3
2
1 b=(B/K)
0
6
5
1.5
8
7
12
11
10
9 eta
1
0.5
3
2
1 b=(B/K)
0
Bond Price
Interest Rate Endogeneity & Robustness
0.6
0.5
0.4
0.3
1.5
1
0.9
0.8
0.7
z=(Z/K) 1
0.5
1
3
2 bnew(=Bnew/Knew)
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
1.5
eta
1
0.5
3
1
2 bnew(=Bnew/Knew)
0
Interest Rate Endogeneity & Robustness
Debt Capacity
1.4
1.2
1
0.8
0.6
0.4
3
2
1.8
1.6
2 bnew
1
0 0.5
1 z=(Z/K)
1.5
1.4
1.2
1
0.8
0.6
0.4
3
2
1.8
1.6
2 bnew
1
0 0.5
1 eta
1.5
Interest Rate Endogeneity & Robustness
Investment and Credit Spreads
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−0.1
0 50 100 150 200
Spread(bps)
250 300 350
