![Page 1: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/1.jpg)
Asset Quality Dynamics
Dean Corbae and Erwan Quintin
Wisconsin School of Business
March 1, 2018
Corbae Quintin Asset Quality Dynamics
![Page 2: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/2.jpg)
Motivation
I Different corporate liabilities display different cyclicalities(Jerman and Quadrini, 2011, Covas and Den Haan, 2011)
I Debt use tends to be pro-cyclical, except for the largestfirms
I Safe corporate debt, in fact, is acyclical, at best (Erel, Kimand Weisbach, 2012)
I We propose a model that is quantitatively consistent withthis fact . . .
I . . . and use it to quantify the impact of safe corporate debtmarkets on the US business cycle
Corbae Quintin Asset Quality Dynamics
![Page 3: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/3.jpg)
Motivation
I Different corporate liabilities display different cyclicalities(Jerman and Quadrini, 2011, Covas and Den Haan, 2011)
I Debt use tends to be pro-cyclical,
except for the largestfirms
I Safe corporate debt, in fact, is acyclical, at best (Erel, Kimand Weisbach, 2012)
I We propose a model that is quantitatively consistent withthis fact . . .
I . . . and use it to quantify the impact of safe corporate debtmarkets on the US business cycle
Corbae Quintin Asset Quality Dynamics
![Page 4: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/4.jpg)
Motivation
I Different corporate liabilities display different cyclicalities(Jerman and Quadrini, 2011, Covas and Den Haan, 2011)
I Debt use tends to be pro-cyclical, except for the largestfirms
I Safe corporate debt, in fact, is acyclical, at best (Erel, Kimand Weisbach, 2012)
I We propose a model that is quantitatively consistent withthis fact . . .
I . . . and use it to quantify the impact of safe corporate debtmarkets on the US business cycle
Corbae Quintin Asset Quality Dynamics
![Page 5: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/5.jpg)
Motivation
I Different corporate liabilities display different cyclicalities(Jerman and Quadrini, 2011, Covas and Den Haan, 2011)
I Debt use tends to be pro-cyclical, except for the largestfirms
I Safe corporate debt, in fact, is acyclical, at best (Erel, Kimand Weisbach, 2012)
I We propose a model that is quantitatively consistent withthis fact . . .
I . . . and use it to quantify the impact of safe corporate debtmarkets on the US business cycle
Corbae Quintin Asset Quality Dynamics
![Page 6: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/6.jpg)
Motivation
I Different corporate liabilities display different cyclicalities(Jerman and Quadrini, 2011, Covas and Den Haan, 2011)
I Debt use tends to be pro-cyclical, except for the largestfirms
I Safe corporate debt, in fact, is acyclical, at best (Erel, Kimand Weisbach, 2012)
I We propose a model that is quantitatively consistent withthis fact . . .
I . . . and use it to quantify the impact of safe corporate debtmarkets on the US business cycle
Corbae Quintin Asset Quality Dynamics
![Page 7: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/7.jpg)
Motivation
I Different corporate liabilities display different cyclicalities(Jerman and Quadrini, 2011, Covas and Den Haan, 2011)
I Debt use tends to be pro-cyclical, except for the largestfirms
I Safe corporate debt, in fact, is acyclical, at best (Erel, Kimand Weisbach, 2012)
I We propose a model that is quantitatively consistent withthis fact . . .
I . . . and use it to quantify the impact of safe corporate debtmarkets on the US business cycle
Corbae Quintin Asset Quality Dynamics
![Page 8: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/8.jpg)
Methodological approach
I We lay out a macroeconomic model that is standard on thereal side but where the security space respondsendogenously to changes in fundamentals
I We do so by embedding Allen and Gale’s 1988 “OptimalSecurity Design” model into a dynamic environment
I Fixed point problem:1. Taking the contingent path of financial structures as given,
agents choose an optimal consumption policy2. This consumption path, in turn, determines agents’
willingness to pay for different securities3. Taking this willingness to pay as given, producers issue
menus of securities that maximize their profits4. The resulting financial structure must coincide with the
guess agents made in the first place
Corbae Quintin Asset Quality Dynamics
![Page 9: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/9.jpg)
Methodological approach
I We lay out a macroeconomic model that is standard on thereal side but where the security space respondsendogenously to changes in fundamentals
I We do so by embedding Allen and Gale’s 1988 “OptimalSecurity Design” model into a dynamic environment
I Fixed point problem:1. Taking the contingent path of financial structures as given,
agents choose an optimal consumption policy2. This consumption path, in turn, determines agents’
willingness to pay for different securities3. Taking this willingness to pay as given, producers issue
menus of securities that maximize their profits4. The resulting financial structure must coincide with the
guess agents made in the first place
Corbae Quintin Asset Quality Dynamics
![Page 10: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/10.jpg)
Data
I Firms in Compustat, 1985-2016 (394,682 firm-year)I Exclude foreign, utility and financial firms (197,629)I Exclude missing or bad data (96,994)
Corbae Quintin Asset Quality Dynamics
![Page 11: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/11.jpg)
Firm count details
AAA AA A BBB <BBB No rating
1986 13 64 159 108 258 2,040
1987 13 59 137 117 316 2,023
1988 13 60 136 100 291 1,996
1989 14 51 140 102 230 1,980
1990 14 54 129 107 255 2,098
1991 13 55 130 114 222 2,292
1992 13 55 131 117 225 2,526
1993 13 54 134 132 270 2,697
1994 13 49 136 141 283 2,863
1995 12 48 135 155 289 3,251
1996 12 45 146 176 331 3,282
1997 12 43 149 186 336 3,175
1998 10 35 158 208 387 3,244
1999 9 32 144 218 383 3,065
2000 9 27 136 223 406 2,739
2001 8 22 124 223 425 2,522
2002 7 20 115 219 465 2,516
2003 6 15 113 220 482 2,531
2004 6 13 115 210 504 2,466
2005 6 12 113 205 509 2,466
2006 6 11 113 201 495 2,399
2007 6 11 101 203 478 2,287
2008 6 12 93 200 454 2,226
2009 6 13 86 194 461 2,190
2010 5 14 83 197 448 2,166
2011 4 13 89 209 441 2,131
2012 4 13 87 205 453 2,198
2013 4 13 88 212 472 2,232
2014 4 15 90 211 488 2,095
2015 3 19 87 208 467 2,046
2016 3 20 76 209 456 1,9422
Corbae Quintin Asset Quality Dynamics
![Page 12: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/12.jpg)
Frequency of default by rating, 1920-2010
0
2
4
6
8
10
12
14
16
AAA AA A BAA BA B CAA-C
Corbae Quintin Asset Quality Dynamics
![Page 13: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/13.jpg)
Rating by size
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
>AA >A >BBB
Large firms (>99%) Small firms
Corbae Quintin Asset Quality Dynamics
![Page 14: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/14.jpg)
Cyclicality of safe corporate debt
Firm rating ≥ AA ≥ A ≥ BBB <BBB Allρ(D,Y ) 0.06 0.28∗ 0.29∗ 0.70∗∗∗ 0.55∗∗∗
ρ (E ,Y ) 0.07 −0.07 0.06 0.33∗∗ 0.27∗
HP filter
Corbae Quintin Asset Quality Dynamics
![Page 15: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/15.jpg)
Cyclicality of safe corporate yields
1985-2006 1985-2016 1947-2016ρ(AAA yield,Y ) -0.0439 -0.2114 -0.3060
ρ(BAA-AAA spread,Y ) -0.2991 -0.3774 -0.6028
Corbae Quintin Asset Quality Dynamics
![Page 16: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/16.jpg)
Related work
1. Allen and Gale (1988, 1991)2. Quadrini and Jerman (2011), Covas and Den Haan (2011),
Karabarbounis, Macnamara and McCord (2014), Eler et. al(2012), Khale and Stulz (2011)
3. Bernanke et. al. (2011)4. Brunnermeier and Sannikov (2012)
Corbae Quintin Asset Quality Dynamics
![Page 17: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/17.jpg)
The model
I Time is discrete and infinite, one goodI Mass 1 of households who value consumption only,
time-separable CRRA preferencesI Large mass of producers characterized by
talent/productivity z ∼ µ
Corbae Quintin Asset Quality Dynamics
![Page 18: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/18.jpg)
Producers
I Can activate a project by investing 1 unit of capital at thestart of the period
I Gross output isAtz1−αnαt + (1− δ)
I At is aggregate TFP and nt is labor inputI TFP follows a first-order markov process with transition GA
I Net operating income is:
Π(At ,wt ; z) ≡ maxn>0
Atz1−αnα − nwt
I Labor demand is:
n∗(At ,wt ; z) ≡ arg maxn>0
Atz1−αnα − nwt
Corbae Quintin Asset Quality Dynamics
![Page 19: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/19.jpg)
Producers
I Can activate a project by investing 1 unit of capital at thestart of the period
I Gross output isAtz1−αnαt + (1− δ)
I At is aggregate TFP and nt is labor inputI TFP follows a first-order markov process with transition GA
I Net operating income is:
Π(At ,wt ; z) ≡ maxn>0
Atz1−αnα − nwt
I Labor demand is:
n∗(At ,wt ; z) ≡ arg maxn>0
Atz1−αnα − nwt
Corbae Quintin Asset Quality Dynamics
![Page 20: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/20.jpg)
Security markets
I Producers sell claims to households and to world marketsI Take as given the households’ willingness to pay qH
t (A)
I Claims sold to world markets must be risk-freeI Participation in that market costs κ > 0 per periodI World markets pay qW
t per unit of risk-free claims at date tI qW is measurable with respect to the history of aggregate
shocks
Corbae Quintin Asset Quality Dynamics
![Page 21: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/21.jpg)
Security markets
I Producers sell claims to households and to world marketsI Take as given the households’ willingness to pay qH
t (A)
I Claims sold to world markets must be risk-freeI Participation in that market costs κ > 0 per periodI World markets pay qW
t per unit of risk-free claims at date t
I qW is measurable with respect to the history of aggregateshocks
Corbae Quintin Asset Quality Dynamics
![Page 22: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/22.jpg)
Security markets
I Producers sell claims to households and to world marketsI Take as given the households’ willingness to pay qH
t (A)
I Claims sold to world markets must be risk-freeI Participation in that market costs κ > 0 per periodI World markets pay qW
t per unit of risk-free claims at date tI qW is measurable with respect to the history of aggregate
shocks
Corbae Quintin Asset Quality Dynamics
![Page 23: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/23.jpg)
Producer problem
MVt (z) ≡ maxbs≥0
bsqWt +
∫A
qHt (A)
[(Π(A,wt ; z) + 1− δ)− bs
]dA
−(1 + 1{bs>0}κ
),
subject to:
bs ≤ Π(At ,w ; z)
Debt vs. EBITDA
Producers issue risk-free debt if:(qW
t −∫
AqH
t (A)dA)
Π(At ,wt ; z) ≥ κ.
Corbae Quintin Asset Quality Dynamics
![Page 24: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/24.jpg)
Producer problem
MVt (z) ≡ maxbs≥0
bsqWt +
∫A
qHt (A)
[(Π(A,wt ; z) + 1− δ)− bs
]dA
−(1 + 1{bs>0}κ
),
subject to:
bs ≤ Π(At ,w ; z)
Debt vs. EBITDA
Producers issue risk-free debt if:(qW
t −∫
AqH
t (A)dA)
Π(At ,wt ; z) ≥ κ.
Corbae Quintin Asset Quality Dynamics
![Page 25: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/25.jpg)
Risky security prices and returns
I Securities sold by producers of type z pay
Π(A,wt ; z) + 1− δ − bst (z)
and sell for:∫A
qHt (A)
[(Π(A,wt ; z) + 1− δ)− bs
t (z)
]dA
I Stochastic return on the same security is
rt (A; z) =Π(A,wt ; z) + 1− δ − bs
t (z)∫A qH
t (A)
[(Π(A,wt ; z) + 1− δ)− bs
t (z)
]dA
.
Corbae Quintin Asset Quality Dynamics
![Page 26: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/26.jpg)
Risky security prices and returns
I Securities sold by producers of type z pay
Π(A,wt ; z) + 1− δ − bst (z)
and sell for:∫A
qHt (A)
[(Π(A,wt ; z) + 1− δ)− bs
t (z)
]dA
I Stochastic return on the same security is
rt (A; z) =Π(A,wt ; z) + 1− δ − bs
t (z)∫A qH
t (A)
[(Π(A,wt ; z) + 1− δ)− bs
t (z)
]dA
.
Corbae Quintin Asset Quality Dynamics
![Page 27: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/27.jpg)
Household problem
I Ht : possible histories of aggregate TFP shocks up to date tI Households assume a mapping
St : Ht 7→ S
I . . . where St (ht ) = {qWt , rt (•, z) : z ≥ 0}
Corbae Quintin Asset Quality Dynamics
![Page 28: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/28.jpg)
Household problem
maxbd≥0,ed≥0
E+∞∑t=0
βtU(ct )
subject to:
qWt bd
t +
∫ed
t (z)dµ(z) + ct = at (ht ) +
∫max {MVt (z),0}dµ(z),
at+1(ht ,A) =
∫ed
t (z)rt (A, z)dµ(z)
+ bdt + wt (ht ,A), for all A ∈ A
where:{qW
t , rt (•, z) : z ≥ 0} = St (ht ),
Corbae Quintin Asset Quality Dynamics
![Page 29: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/29.jpg)
Equilibrium
Prices, security menus and and decisions such that:1. Decision plans are optimal given prices;2.∫{z:MVt (z)≥0} n∗(A,wt ; z) = 1 for all A ∈ A;
3.∫{z:MVt (z)≥0} bs
t (z)dµ ≥ bdt ;
4. edt (z)rt (A, z) = Π(A,wt ; z) + 1− δ − bs(z) for all A ∈ A;
5. MVt (z) = bst (z)qW
t +∫A qH
t (A)
[(Π(A,wt ; z) + 1− δ)−
bst (z)
]dA−
(1 + 1{bs
t >0}κ).
6. qHt (At ) =
βGA(At |At−1)U′(ct+1(ht ,At ))U′(ct )
;
Corbae Quintin Asset Quality Dynamics
![Page 30: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/30.jpg)
Equilibrium
Prices, security menus and and decisions such that:1. Decision plans are optimal given prices;2.∫{z:MVt (z)≥0} n∗(A,wt ; z) = 1 for all A ∈ A;
3.∫{z:MVt (z)≥0} bs
t (z)dµ ≥ bdt ;
4. edt (z)rt (A, z) = Π(A,wt ; z) + 1− δ − bs(z) for all A ∈ A;
5. MVt (z) = bst (z)qW
t +∫A qH
t (A)
[(Π(A,wt ; z) + 1− δ)−
bst (z)
]dA−
(1 + 1{bs
t >0}κ).
6. qHt (At ) =
βGA(At |At−1)U′(ct+1(ht ,At ))U′(ct )
;
Corbae Quintin Asset Quality Dynamics
![Page 31: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/31.jpg)
Aggregation
Given capital K , labor N and exogenous TFP A, aggregateoutput is:
F (A,K ,N) = AE [z|z ≥ z(K )]1−α K 1−αNα.
GDP accounting:
ct+1+Kt+1−(1−δ)Kt +
∫bs
t >0κdµ+bW
t −qWt+1bW
t+1 = F (At ,Kt ,Nt ).
Corbae Quintin Asset Quality Dynamics
![Page 32: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/32.jpg)
Aggregation
Given capital K , labor N and exogenous TFP A, aggregateoutput is:
F (A,K ,N) = AE [z|z ≥ z(K )]1−α K 1−αNα.
GDP accounting:
ct+1+Kt+1−(1−δ)Kt +
∫bs
t >0κdµ+bW
t −qWt+1bW
t+1 = F (At ,Kt ,Nt ).
Corbae Quintin Asset Quality Dynamics
![Page 33: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/33.jpg)
Security markets
PropositionThe solution to the producer security design problem at a givendate t is fully described by two thresholds 0 ≤ z t ≤ zt such that:
1. Producers issue securities if and only if z ≥ z t ;2. bs
t (z) = 0 if z < zt ;3. bs
t (z) = Π(At ,wt ; z) if z > zt .
Proof: Producers issue risk-free debt if:(qW
t −∫
AqH
t (A)dA)
Π(At ,wt ; z) ≥ κ.
Corbae Quintin Asset Quality Dynamics
![Page 34: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/34.jpg)
Security markets
PropositionThe solution to the producer security design problem at a givendate t is fully described by two thresholds 0 ≤ z t ≤ zt such that:
1. Producers issue securities if and only if z ≥ z t ;2. bs
t (z) = 0 if z < zt ;3. bs
t (z) = Π(At ,wt ; z) if z > zt .
Proof: Producers issue risk-free debt if:(qW
t −∫
AqH
t (A)dA)
Π(At ,wt ; z) ≥ κ.
Corbae Quintin Asset Quality Dynamics
![Page 35: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/35.jpg)
Household portfolio
Effectively, households invest in one security/portfolio whosestochastic payoff is
F (At ,Kt ,1) + (1− δ)Kt − bWt ,
and whose price at the start of the period is∫A
qHt (A)
[F (At ,Kt ,1) + (1− δ)Kt − bW
t
]dA,
hence whose return, for all possible values of At is
rH(At ) =F (At ,Kt ,1) + (1− δ)Kt − bW
t∫A qH
t (A)
[F (At ,Kt ,1) + (1− δ)Kt − bW
t
]dA
.
Corbae Quintin Asset Quality Dynamics
![Page 36: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/36.jpg)
Recursive equilibrium
I Aggregate state is: θ = (a,A−1) ∈ IR+ ×A,I An equilibrium consists of the following objects:
1. g : Θ×A 7→ Θ2. K : Θ 7→ IR+
3. z × z : Θ 7→ IR2+
4. qH : Θ×A 7→ IR+
5. rH : Θ×A 7→ IR+
6. eH : Θ× IR+ 7→ IR+
7. c : Θ× IR+ 7→ IR+
8. w : Θ×A 7→ IR+
9. bW : Θ 7→ IR+
10. MV : Θ× IR+ 7→ IR+
11. V H : Θ× IR+ 7→ IR
Corbae Quintin Asset Quality Dynamics
![Page 37: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/37.jpg)
Household value function
V H(θ,a) = maxeH>0,b>0
U(
a +
∫z≥z
MV (z)dz − eH − qW b)
+ β
∫A
V H (g(θ,A),a′(A))dG(A|A−1)
where, for all A ∈ A
a′(A) = b + eH rH(θ,A) + w(θ,A).
Corbae Quintin Asset Quality Dynamics
![Page 38: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/38.jpg)
Allen-Gale condition
PropositionThe household value function V H is concave and differentiablein assets. Furthermore, for all possible values θ ∈ Θ of theaggregate state,
∂V (θ,a)
∂a= U
′(c(θ,a)) .
Corbae Quintin Asset Quality Dynamics
![Page 39: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/39.jpg)
RCE conditions
1. K (θ) =∫
z≥z dµ
2. eH(θ,a) =∫A qH(θ,A)
[F (A,K (θ),1) + (1− δ)K (θ)− bW (θ)
]dA
3.∫
z≥z MV (θ, z)dz = qW (θ)bW (θ) +∫A qH
t (A)
[(Π(A,w(θ); z) + 1− δ)− bs(θ, z)
]dA
4. c(θ,a) = a +∫
z≥z MV (θ, z)dz − eH(θ,a)
5. a′(θ,A) = eH(θ,A)rH(θ,A) + w(θ,A)
6. qH(θ,A) =βG(A|A−1)U
′(c i (g(θ,A),a′(θ,A))
U′ (c(θ,a)for A ∈ A
7. Financial structure solves producer problems
Corbae Quintin Asset Quality Dynamics
![Page 40: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/40.jpg)
Mapping from model to data
1.∫
max {MVt (z),0}dµ(z)
⇒ Income of top managers andproprietors
2. Y ≡ F (A,K ,N)⇒ Value added by the private sector minusthe compensation of top managers and proprietors
Corbae Quintin Asset Quality Dynamics
![Page 41: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/41.jpg)
Mapping from model to data
1.∫
max {MVt (z),0}dµ(z)⇒ Income of top managers andproprietors
2. Y ≡ F (A,K ,N)⇒ Value added by the private sector minusthe compensation of top managers and proprietors
Corbae Quintin Asset Quality Dynamics
![Page 42: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/42.jpg)
Mapping from model to data
1.∫
max {MVt (z),0}dµ(z)⇒ Income of top managers andproprietors
2. Y ≡ F (A,K ,N)
⇒ Value added by the private sector minusthe compensation of top managers and proprietors
Corbae Quintin Asset Quality Dynamics
![Page 43: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/43.jpg)
Mapping from model to data
1.∫
max {MVt (z),0}dµ(z)⇒ Income of top managers andproprietors
2. Y ≡ F (A,K ,N)⇒ Value added by the private sector minusthe compensation of top managers and proprietors
Corbae Quintin Asset Quality Dynamics
![Page 44: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/44.jpg)
Parameters set to standard values
Parameter Description Valueβ Discount rate 0.95σ Utility curvature 2.00δ Depreciation rate 0.10α Labor share 0.60
Corbae Quintin Asset Quality Dynamics
![Page 45: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/45.jpg)
Calibration
Parameter Value Target Data ModelTFP (A) {0.97,1.00,1.03} σ(log(Y )) 2.75% 2.51%
σ(log(z)) 0.40 RentsY 11.00% 10.80%
κ 0.0043 Ds
Y 3.11% 3.47%
Transition matrix for TFP:
GA =
0.47 0.53 0.000.28 0.44 0.280.00 0.53 0.47
Risk-free process:
qW = {0.972,0.968,0.976}
Corbae Quintin Asset Quality Dynamics
![Page 46: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/46.jpg)
Calibration
Parameter Value Target Data ModelTFP (A) {0.97,1.00,1.03} σ(log(Y )) 2.75% 2.51%
σ(log(z)) 0.40 RentsY 11.00% 10.80%
κ 0.0043 Ds
Y 3.11% 3.47%
Transition matrix for TFP:
GA =
0.47 0.53 0.000.28 0.44 0.280.00 0.53 0.47
Risk-free process:
qW = {0.972,0.968,0.976}
Corbae Quintin Asset Quality Dynamics
![Page 47: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/47.jpg)
Calibration
Parameter Value Target Data ModelTFP (A) {0.97,1.00,1.03} σ(log(Y )) 2.75% 2.51%
σ(log(z)) 0.40 RentsY 11.00% 10.80%
κ 0.0043 Ds
Y 3.11% 3.47%
Transition matrix for TFP:
GA =
0.47 0.53 0.000.28 0.44 0.280.00 0.53 0.47
Risk-free process:
qW = {0.972,0.968,0.976}
Corbae Quintin Asset Quality Dynamics
![Page 48: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/48.jpg)
Calibration
Parameter Value Target Data ModelTFP (A) {0.97,1.00,1.03} σ(log(Y )) 2.75% 2.51%
σ(log(z)) 0.40 RentsY 11.00% 10.80%
κ 0.0043 Ds
Y 3.11% 3.47%
Transition matrix for TFP:
GA =
0.47 0.53 0.000.28 0.44 0.280.00 0.53 0.47
Risk-free process:
qW = {0.972,0.968,0.976}
Corbae Quintin Asset Quality Dynamics
![Page 49: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/49.jpg)
Calibration
Parameter Value Target Data ModelTFP (A) {0.97,1.00,1.03} σ(log(Y )) 2.75% 2.51%
σ(log(z)) 0.40 RentsY 11.00% 10.80%
κ 0.0043 Ds
Y 3.11% 3.47%
Transition matrix for TFP:
GA =
0.47 0.53 0.000.28 0.44 0.280.00 0.53 0.47
Risk-free process:
qW = {0.972,0.968,0.976}
Corbae Quintin Asset Quality Dynamics
![Page 50: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/50.jpg)
Calibration
Parameter Value Target Data ModelTFP (A) {0.97,1.00,1.03} σ(log(Y )) 2.75% 2.51%
σ(log(z)) 0.40 RentsY 11.00% 10.80%
κ 0.0043 Ds
Y 3.11% 3.47%
Transition matrix for TFP:
GA =
0.47 0.53 0.000.28 0.44 0.280.00 0.53 0.47
Risk-free process:
qW = {0.972,0.968,0.976}
Corbae Quintin Asset Quality Dynamics
![Page 51: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/51.jpg)
Calibration
Parameter Value Target Data ModelTFP (A) {0.97,1.00,1.03} σ(log(Y )) 2.75% 2.50%
σ(log(z)) 0.40 RentsY 11.00% 10.81%
κ 0.0043 Ds
Y 3.11% 2.61%
Transition matrix for TFP:
GA =
0.47 0.53 0.000.28 0.44 0.280.00 0.53 0.47
Risk-free process:
qW = {0.972,0.968,0.976} ⇒ ρ
(1
qW − 1,Y)
= −0.31
Corbae Quintin Asset Quality Dynamics
![Page 52: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/52.jpg)
Basic horse race
Recall that producers issue risk-free debt if(qW
t −∑
A
qHt (A)
)Π(At ,wt ; z) ≥ κ.
Two sources of procyclicality for safe debt use:1. At is procyclical (Jerman-Quadrini effect)2. qW is procyclical
Two sources of countercyclicality:1. qH is procyclical2. wt is procyclical
Corbae Quintin Asset Quality Dynamics
![Page 53: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/53.jpg)
Basic horse race
Recall that producers issue risk-free debt if(qW
t −∑
A
qHt (A)
)Π(At ,wt ; z) ≥ κ.
Two sources of procyclicality for safe debt use:1. At is procyclical (Jerman-Quadrini effect)2. qW is procyclical
Two sources of countercyclicality:1. qH is procyclical2. wt is procyclical
Corbae Quintin Asset Quality Dynamics
![Page 54: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/54.jpg)
Basic horse race
Recall that producers issue risk-free debt if(qW
t −∑
A
qHt (A)
)Π(At ,wt ; z) ≥ κ.
Two sources of procyclicality for safe debt use:1. At is procyclical (Jerman-Quadrini effect)2. qW is procyclical
Two sources of countercyclicality:1. qH is procyclical2. wt is procyclical
Corbae Quintin Asset Quality Dynamics
![Page 55: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/55.jpg)
RCE (1)
3 3.5 4 4.5 5 5.5 6 6.5 7
Assets
0.2
0.25
0.3
0.35
0.4
0.45Household state prices
qAlow
qAmed
qAhigh
3 3.5 4 4.5 5 5.5 6 6.5 7
Assets
2
2.5
3
3.5
4
4.5
5
5.5Capital stock
Medium
Bad
Good
3 3.5 4 4.5 5 5.5 6 6.5 7
Assets
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9Consumption
3 3.5 4 4.5 5 5.5 6 6.5 7
Assets
1.5
1.6
1.7
1.8
1.9
2
2.1Aggegrate output (F)
Low TFP
Med TFP
High TFP
Corbae Quintin Asset Quality Dynamics
![Page 56: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/56.jpg)
RCE (2)
3 3.5 4 4.5 5 5.5 6 6.5 7
Assets
0.88
0.9
0.92
0.94
0.96
0.98
1Household willingness to pay for risk-free claims
3 3.5 4 4.5 5 5.5 6 6.5 7
Assets
0
5
10
15
20Securitization cutoffs
zhigh
zlow
3 3.5 4 4.5 5 5.5 6 6.5 7
Assets
0
0.2
0.4
0.6
0.8
1Fraction of establishments that issue risk-free debt
3 3.5 4 4.5 5 5.5 6 6.5 7
Assets
0
0.5
1
1.5
2
2.5
3
3.5Volume of risk-free debt
Corbae Quintin Asset Quality Dynamics
![Page 57: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/57.jpg)
Sample paths
Corbae Quintin Asset Quality Dynamics
![Page 58: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/58.jpg)
Cyclical properties of key model variables
Moment Data Modelρ(DS,Y ) 0.06 -0.06
ρ(ES,Y ) 0.07 -0.05
ρ(E ,Y ) 0.27 0.21
ρ (D + E ,Y ) 0.62 0.57
ρ(E(rH)− rF ,Y
)-0.25 -0.04
ρ(E(rH)− rF , I
)-0.37 -0.27
ρ(E(rH)− rF ,C
)-0.54
Corbae Quintin Asset Quality Dynamics
![Page 59: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/59.jpg)
Cyclical properties of key model variables
Moment Data Modelρ(DS,Y ) 0.06 -0.06
ρ(ES,Y ) 0.07 -0.05
ρ(E ,Y ) 0.27 0.21
ρ (D + E ,Y ) 0.62 0.57
ρ(E(rH)− rF ,Y
)-0.25 -0.04
ρ(E(rH)− rF , I
)-0.37 -0.27
ρ(E(rH)− rF ,C
)-0.54
Corbae Quintin Asset Quality Dynamics
![Page 60: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/60.jpg)
Cyclical properties of key model variables
Moment Data Modelρ(DS,Y ) 0.06 -0.06
ρ(ES,Y ) 0.07 -0.05
ρ(E ,Y ) 0.27 0.21
ρ (D + E ,Y ) 0.62 0.57
ρ(E(rH)− rF ,Y
)-0.25 -0.04
ρ(E(rH)− rF , I
)-0.37 -0.27
ρ(E(rH)− rF ,C
)-0.54
Corbae Quintin Asset Quality Dynamics
![Page 61: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/61.jpg)
Cyclical properties of key model variables
Moment Data Modelρ(DS,Y ) 0.06 -0.06
ρ(ES,Y ) 0.07 -0.05
ρ(E ,Y ) 0.27 0.21
ρ (D + E ,Y ) 0.62 0.57
ρ(E(rH)− rF ,Y
)-0.25 -0.04
ρ(E(rH)− rF , I
)-0.37 -0.27
ρ(E(rH)− rF ,C
)-0.54
Corbae Quintin Asset Quality Dynamics
![Page 62: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/62.jpg)
Cyclical properties of key model variables
Moment Data Modelρ(DS,Y ) 0.06 -0.06
ρ(ES,Y ) 0.07 -0.05
ρ(E ,Y ) 0.27 0.21
ρ (D + E ,Y ) 0.62 0.57
ρ(E(rH)− rF ,Y
)-0.25 -0.04
ρ(E(rH)− rF , I
)-0.37 -0.27
ρ(E(rH)− rF ,C
)-0.54
Corbae Quintin Asset Quality Dynamics
![Page 63: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/63.jpg)
Cyclical properties of key model variables
Moment Data Modelρ(DS,Y ) 0.06 -0.06
ρ(ES,Y ) 0.07 -0.05
ρ(E ,Y ) 0.27 0.21
ρ (D + E ,Y ) 0.62 0.57
ρ(E(rH)− rF ,Y
)-0.25 -0.04
ρ(E(rH)− rF , I
)-0.37 -0.27
ρ(E(rH)− rF ,C
)-0.54
Corbae Quintin Asset Quality Dynamics
![Page 64: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/64.jpg)
Cyclical properties of key model variables
Moment Data Modelρ(DS,Y ) 0.06 -0.06
ρ(ES,Y ) 0.07 -0.05
ρ(E ,Y ) 0.27 0.21
ρ (D + E ,Y ) 0.62 0.57
ρ(E(rH)− rF ,Y
)-0.25 -0.04
ρ(E(rH)− rF , I
)-0.37 -0.27
ρ(E(rH)− rF ,C
)-0.54
Corbae Quintin Asset Quality Dynamics
![Page 65: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/65.jpg)
Tranching cost and capital formation
3 3.5 4 4.5 5 5.5 6 6.5 71.5
2
2.5
3
3.5
4
4.5
5
5.5
BenchmarkHigh kappa
Corbae Quintin Asset Quality Dynamics
![Page 66: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/66.jpg)
Low safe yields and capital formation
3 3.5 4 4.5 5 5.5 6 6.5 72
2.5
3
3.5
4
4.5
5
5.5
BenchmarkLow safe yields
Corbae Quintin Asset Quality Dynamics
![Page 67: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/67.jpg)
Safe debt markets and the business cycle
Benchmark High κ Low safe yieldsMean Ds
Y 3.47% 0.00% 17.55%
Mean Y 1.9540 -0.01% -0.03%std(log(Y ) 0.0250 -1.60% -0.40%
Mean Cons 1.5840 +0.23% -0.81%std(log(C)) 0.0148 +6.48% +0.00%
Mean Assets 5.1825 +1.40% -5.53%std(log(a)) 0.0275 -16.73% +17.09%
Mean K 3.6656 +0.05% -0.05%std(log(K )) 0.0271 -2.21% -7.75%
Corbae Quintin Asset Quality Dynamics
![Page 68: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/68.jpg)
Safe debt markets and the business cycle
Benchmark High κ Low safe yieldsMean Ds
Y 3.47% 0.00% 17.55%
Mean Y 1.9540 -0.01% -0.03%std(log(Y ) 0.0250 -1.60% -0.40%
Mean Cons 1.5840 +0.23% -0.81%std(log(C)) 0.0148 +6.48% +0.00%
Mean Assets 5.1825 +1.40% -5.53%std(log(a)) 0.0275 -16.73% +17.09%
Mean K 3.6656 +0.05% -0.05%std(log(K )) 0.0271 -2.21% -7.75%
Corbae Quintin Asset Quality Dynamics
![Page 69: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/69.jpg)
Safe debt markets and the business cycle
Benchmark High κ Low safe yieldsMean Ds
Y 3.47% 0.00% 17.55%
Mean Y 1.9540 -0.01% -0.03%std(log(Y ) 0.0250 -1.60% -0.40%
Mean Cons 1.5840 +0.23% -0.81%std(log(C)) 0.0148 +6.48% +0.00%
Mean Assets 5.1825 +1.40% -5.53%std(log(a)) 0.0275 -16.73% +17.09%
Mean K 3.6656 +0.05% -0.05%std(log(K )) 0.0271 -2.21% -7.75%
Corbae Quintin Asset Quality Dynamics
![Page 70: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/70.jpg)
Safe debt markets and the business cycle
Benchmark High κ Low safe yieldsMean Ds
Y 3.47% 0.00% 17.55%
Mean Y 1.9540 -0.01% -0.03%std(log(Y ) 0.0250 -1.60% -0.40%
Mean Cons 1.5840 +0.23% -0.81%std(log(C)) 0.0148 +6.48% +0.00%
Mean Assets 5.1825 +1.40% -5.53%std(log(a)) 0.0275 -16.73% +17.09%
Mean K 3.6656 +0.05% -0.05%std(log(K )) 0.0271 -2.21% -7.75%
Corbae Quintin Asset Quality Dynamics
![Page 71: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/71.jpg)
Safe debt markets and the business cycle
Benchmark High κ Low safe yieldsMean Ds
Y 3.47% 0.00% 17.55%
Mean Y 1.9540 -0.01% -0.03%std(log(Y ) 0.0250 -1.60% -0.40%
Mean Cons 1.5840 +0.23% -0.81%std(log(C)) 0.0148 +6.48% +0.00%
Mean Assets 5.1825 +1.40% -5.53%std(log(a)) 0.0275 -16.73% +17.09%
Mean K 3.6656 +0.05% -0.05%std(log(K )) 0.0271 -2.21% -7.75%
Corbae Quintin Asset Quality Dynamics
![Page 72: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/72.jpg)
Summary
1. A dynamic model of costly security creation can accountfor the acyclicality of safe corporate debt issues
2. Access to safe debt markets has little effect on the level ofoutput but helps reduce consumption volatility
3. Exogenous, permanent reductions in safe yields havelimited effects on the level of GDP because the reduction ininterest rates depresses household wealth accumulation
Corbae Quintin Asset Quality Dynamics
![Page 73: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/73.jpg)
Cyclicality of safe corporate debt (HP filter)
Firm rating ≥ AA ≥ A ≥ BBB <BBB Allρ(D,Y ) 0.22 0.23 0.28 0.67∗∗∗ 0.47∗∗∗
ρ (E ,Y ) 0.07 −0.16 0.09 0.31 0.31
Back
Corbae Quintin Asset Quality Dynamics
![Page 74: Asset Quality Dynamicserwan.marginalq.com/index_files/wp_files/slidesUGA.pdf1998 10 35 158 208 387 3,244 1999 9 32 144 218 383 3,065 2000 9 27 136 223 406 2,739 2001 8 22 124 223 425](https://reader033.vdocument.in/reader033/viewer/2022042204/5ea597aba5f9e175f563779a/html5/thumbnails/74.jpg)
Safe debt vs. EBITDA
0
100000
200000
300000
400000
500000
600000
1985 1990 1995 2000 2005 2010 2015
Debt (US$, million) EBITDA (US$, million)
BackCorbae Quintin Asset Quality Dynamics