The document discusses modeling the impact of permanent and transitory shocks to firm profitability on capital structure and investment decisions. It motivates the need to distinguish between permanent and transitory shocks, which prior literature has not done. The model aims to maximize the present value of equity for a firm that controls capital and debt levels, facing both types of profitability shocks.

1. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
.
Permanent and Transitory Shocks in Capital
Structure and Their Relation to Investment,
Leverage, and Speed of Adjustment
.
Stephen J. Barr
stephen.barr@simon.rochester.edu
University of Rochester
May 15, 2012
. . . . . .

2. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Introduction - Welcome to my presentation
Motivation: Better understand the profitability shock process
and its industry-level variation, and its effect on capital
structure
Economic Findings: Permanent shocks, although relatively
small in magnitude, have a large impact on leverage and
investment decisions
. . . . . .

3. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation
Firms:
. . . . . .

4. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation
Firms:
Q: What types of uncertainty to profitability do firms face,
and how does it affect their capital structure?
. . . . . .

5. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation
Firms:
Q: What types of uncertainty to profitability do firms face,
and how does it affect their capital structure?
Q: Is all uncertainty faced by a firm simply be summarized by
volatility and autocorrelation of profitability, or is there more
to it?
. . . . . .

6. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Motivation
Firms:
Q: What types of uncertainty to profitability do firms face,
and how does it affect their capital structure?
Q: Is all uncertainty faced by a firm simply be summarized by
volatility and autocorrelation of profitability, or is there more
to it?
Literature:
. . . . . .

7. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Motivation
Firms:
Q: What types of uncertainty to profitability do firms face,
and how does it affect their capital structure?
Q: Is all uncertainty faced by a firm simply be summarized by
volatility and autocorrelation of profitability, or is there more
to it?
Literature:
Uncertainty in profitability usually modeled as strictly
transient process
. . . . . .

8. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation
Intuition - There are many different types of shocks to
profitability - legislation, technology, labor disputes, etc.
Expectations differ.
. . . . . .

9. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation
Intuition - There are many different types of shocks to
profitability - legislation, technology, labor disputes, etc.
Expectations differ.
Examples (Transitory):
E. coli. scares in spinach,
peanut butter (Gorbenko
and Strebulaev 2010).
Mad cow in beef.
Recall of a competitors
product
Labor issues (union strikes
every few years)
. . . . . .

10. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation - Transient Shock - Mad Cow
. . . . . .

11. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation
Intuition - There are many different types of shocks to
profitability - legislation, technology, labor disputes, etc.
Expectations differ.
Examples (Transitory):
E. coli. scares in spinach,
peanut butter (Gorbenko
and Strebulaev 2010).
Mad cow in beef.
Recall of a competitors
product
Labor issues (union strikes
every few years)
. . . . . .

12. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Motivation
Intuition - There are many different types of shocks to
profitability - legislation, technology, labor disputes, etc.
Expectations differ.
Examples (Transitory):
E. coli. scares in spinach,
Examples (Permanent): peanut butter (Gorbenko
Changes in legislation and Strebulaev 2010).
Technological innovations Mad cow in beef.
Patents expiring Recall of a competitors
Trade agreements product
Labor issues (union strikes
every few years)
. . . . . .

13. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation - Permanent Shock - Legislation (Tobacco Tax)
“CHIPRA (Children’s Health Insurance Program Reauthorization Act)
substantially raised rates on cigarettes, roll-your-own tobacco, and small cigars,
but did not raise taxes on pipe tobacco to equivalent rates.”1
.
. . . . . .

14. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Motivation - Summary
Why do we care about permanent shocks?
. In reality, not all shocks are permanent.
1
. In reality, not all shocks are temporary.
2
. . . . . .

15. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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1. Introduction
2. Related Literature
.
3 Model
4. Comparative Statics and Identification
Leverage
Investment
Identification
5. Data - Full Sample
6. Estimation Results
Where I can improve
7. Conclusion
8. Data - Industry Subsets
.
9 Estimation Per Industry
.
10 Appendices
Detrending The Model
Proof: Model is a Contraction Mapping
. . . . . .

16. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Related Literature
Dynamic Trade-off Models - DeAngelo, DeAngelo, and
Whited (2011), Hennesey and Whited (2005, 2007)
Permanent and Transitory Shocks in Investment
Gourio (2008)
Permanent and Transitory Shocks in Capital Structure -
Gorbenko and Strebulaev 2010
Permanent and Transitory - Macro - Hall and Mishkin
(1982), Flavin 1984, Blundell and Preston (1998)
. . . . . .

17. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Economics of Productivity Shock
. . . . . .

18. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Results Preview
. . . . . .

19. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Results Preview
. Transient only (zT ∗ )
1 with ρ∗ 0.7
or
. . . . . .

20. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Results Preview
. Transient only (zT ∗ )
1 with ρ∗ 0.7
or
. Transient plus permanent (zT + zP )
2
. . . . . .

21. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Results Preview
. Transient only (zT ∗ )
1 with ρ∗ 0.7
or
. Transient plus permanent (zT + zP )
2
. ρ
1 0.3 to 0.5 and σ P 0.03 is also plausible
. . . . . .

22. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Intuition
Firms will react, in general, more quickly to a permanent
shock
WHY?: There is no concept of “waiting out” a permanent
shock - the marginal cost of adjusting is quickly swamped by
the marginal benefit to adjusting, as the change is expected to
be permanent
IMPLICATION: Change induced by a transient shock can be
induced by a much smaller permanent shock. This
framework can match many interesting moments with a much
lower autocorrelation than in the transient-only case
. . . . . .

23. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Model
Modeling Objective:
Create a dynamic capital structure model
Incorporate permanent and transitory shocks
Firm controls debt and capital
Firm’s Purpose:
Maximize Present Value of Firm
. . . . . .

24. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
. . . . . .

25. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
. . . . . .

26. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
. . . . . .

27. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
. . . . . .

28. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
( )
1
where β = 1+r , dΓ(zt , zt+1 ) where zt is the sum of a
permanent shock and a transitory shock.
. . . . . .

29. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT , zP )
t t
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , zt )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
( )
where β = 1
1+r , dΓ(zt , zt+1 ) where zt ≡ zT + zP
t t
. . . . . .

30. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
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Payout / Equity Issuance
FN: e(Kt , Kt+1 , Bt , Bt+1 , zT ,
t
P)
t
Economics:
e(·) < 0 ⇒ Firm needs financing ⇒ Firm issues equity
e(·) > 0 ⇒ Firm has excess cash ⇒ Firm makes
distribution to shareholders
e(·) = (1 − τc )πt (zt , Kt ) Production / Profits
− δKt τc Depreciation Tax Shield
+ It (Kt , Kt+1 ) Investment
− A(Kt , Kt+1 ) Capital Adjustment Costs
+ Dt Net Debt
. . . . . .

31. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Profits
Profits occur according to a Cobb-Douglas production
function
π = z ∗ Kθ
z profitability shock, K capital stock, θ production curvature
e(·) = (1 − τc )πt (zt , Kt ) Production / Profits
− δKt τc Depreciation Tax Shield
+ It (Kt , Kt+1 ) Investment
− A(Kt , Kt+1 ) Capital Adjustment Costs
+ Dt Net Debt
. . . . . .

32. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Profitability Shock Process
Transitory Shock
log zT = ρ ∗ log zT +
t+1 t
T
t , T
t ∼ N(0, σT ) , ρ ∈ (0, 1)
. . . . . .

33. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Profitability Shock Process
Transitory Shock
log zT = ρ ∗ log zT +
t+1 t
T
t , T
t ∼ N(0, σT ) , ρ ∈ (0, 1)
Permanent Shock
log zP = log zP +
t+1 t
P
t , P
t ∼ N(0, σP )
. . . . . .

34. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Profitability Shock Process
Transitory Shock
log zT = ρ ∗ log zT +
t+1 t
T
t , T
t ∼ N(0, σT ) , ρ ∈ (0, 1)
Permanent Shock
log zP = log zP +
t+1 t
P
t , P
t ∼ N(0, σP )
Total Shock Process
log zt = log zP + log zT
t t
. . . . . .

35. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Taxes
τc corporate tax rate, 35%
Profits taxed at this rate
Capital Depreciation is not taxed (depreciation tax shield)
Corporate debt also serves as a tax shield
e(·) = (1 − τc )πt (zt , Kt ) Production / Profits
− δKt τc Depreciation Tax Shield
+ It (Kt , Kt+1 ) Investment
− A(Kt , Kt+1 ) Capital Adjustment Costs
+ Dt Net Debt
. . . . . .

36. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Investment
Investment - Law of Motion
It+1 (Kt , Kt+1 ) ≡ Kt+1 − (1 − δ) ∗ Kt .
e(·) = (1 − τc )πt (zt , Kt ) Production / Profits
− δKt τc Depreciation Tax Shield
+ It (Kt , Kt+1 ) Investment
− A(Kt , Kt+1 ) Capital Adjustment Costs
+ Dt Net Debt
. . . . . .

37. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Capital Adjustment Costs
Convex Adjustment Cost Function
( )2
a Kt+1 − (1 − δ)Kt
A(Kt , Kt+1 ) = γKt Φi + Kt
2 Kt
where γ, a are constants. Φi indicates investment.
Cooper and Haltiwanger 2006, DDW 2011, HW 2005, 2007
e(·) = (1 − τc )πt (zt , Kt ) Production / Profits
− δKt τc Depreciation Tax Shield
+ It (Kt , Kt+1 ) Investment
− A(Kt , Kt+1 ) Capital Adjustment Costs
+ Dt Net Debt
. . . . . .

38. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Debt
Modeling debt as 1-period debt
Negative Debt ≡ Cash
¯
Bt ∈ [B, B] ⊂ R
Dt+1 ≡ Bt+1 − (1 + r(1 − τc ))Bt
e(·) = (1 − τc )πt (zt , Kt ) Production / Profits
− δKt τc Depreciation Tax Shield
+ It (Kt , Kt+1 ) Investment
− A(Kt , Kt+1 ) Capital Adjustment Costs
+ Dt Net Debt
. . . . . .

39. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
) (
1
where β = 1+r , dΓ(zt , zt+1 ) where zt is the sum of a permanent
shock and a transitory shock.
. . . . . .

40. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
) (
1
where β = 1+r , dΓ(zt , zt+1 ) where zt is the sum of a permanent
shock and a transitory shock.
. . . . . .

41. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Equity Issuance II, Issuance Costs
Firms pay a cost to issue equity
U-shaped cost curve
Altınkılıç and Hansen (2000)
More capital beyond some amount entails rising costs of
underwriter certification, monitoring, and marketing, which
increase the spread.
( )
1
φ(e(Kt , Bt , Kt+1 , Bt+1 , z∗ )) = Φe ∗ λ1 e(·) − λ2 e(·)2
t
2
where λi ≥ 0, i = 1, 2, and Φe indicates equity issuance (e(· < 0))
. . . . . .

42. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
) (
1
where β = 1+r , dΓ(zt , zt+1 ) where zt is the sum of a permanent
shock and a transitory shock.
. . . . . .

43. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
) (
1
where β = 1+r , dΓ(zt , zt+1 ) where zt is the sum of a permanent
shock and a transitory shock.
. . . . . .

44. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
) (
1
where β = 1+r , dΓ(zt , zt+1 ) where zt is the sum of a permanent
shock and a transitory shock.
. . . . . .

45. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Maximizing the Present Value of Equity
V(kt ,bt , zt ) =
[
max e(kt , kt+1 , bt , bt+1 , zT ,
t
P
t)
kt+1 ,bt+1 ∈K×B
Payout/Equity
]
( )
T P
+ φ e(kt , kt+1 , bt , bt+1 , zt , t )
Equity Issuance Costs
∫
+β ∗ V(kt+1 , bt+1 , zt+1 ) dΓ(zt , zt+1 )
Continuation Value (Dynamic Model)
) (
1
where β = 1+r , dΓ(zt , zt+1 ) where zt is the sum of a permanent
shock and a transitory shock. Use Value Iteration to solve.
. . . . . .

46. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Note: Detrending
As written, the model is non-stationary and thus cannot be
solved using standard techniques
To solve, detrend the model. .. See Details
Detrending refers to the idea that, with permanent shocks,
firm size can grow without bound
Main Idea:
f (..., zT ,
t zP
t )
Non-stationary
Detail: Proof of sufficient conditions to solve .. See Proof
. . . . . .

47. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Note: Detrending
As written, the model is non-stationary and thus cannot be
solved using standard techniques
To solve, detrend the model. .. See Details
Detrending refers to the idea that, with permanent shocks,
firm size can grow without bound
Main Idea:
f (..., zT ,
t zP
t ) ⇒ ˆ (..., zT ,
f t
P
t )
Non-stationary Stationary
Detail: Proof of sufficient conditions to solve .. See Proof
. . . . . .

48. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Comparative Statics
. . . . . .

49. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock and Mean Leverage
P
σt ↑⇒ Mean Leverage ↓
Slope is as expected.
Economics: More
volatility ⇒ less leverage
. . . . . .

50. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock and Mean Leverage
Economics: Small
magnitude shocks have
large effects
P
σt ↑⇒ Mean Leverage ↓
Slope is as expected.
Economics: More
volatility ⇒ less leverage
. . . . . .

51. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock and Mean Leverage - Quantiles
Many go to zero
For a few at the highest
levels, they increase their
leverage when σ P ↑
. . . . . .

52. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
For Comparison: Transient Shock and Mean Leverage
In the transient only case,
mean leverage acts as
expected, but σ T has to
increase substantially to
show this drop in mean
leverage
When permanent shocks
are added, the affect of
changes in σ T is muted
. . . . . .

53. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock and Mean Investment
Why does investment
increase?
. . . . . .

54. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock and Mean Investment
P
σt ↑⇒ Mean Investment
↑, ceteris paribus
. . . . . .

55. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock and Mean Investment
Economics: What is
driving this behavior?
P
σt ↑⇒ Mean Investment
↑, ceteris paribus
. . . . . .

56. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock and Mean Investment - Quantiles
The 75% percentile is
downward sloping
“Mean Investment” is
being pulled up by the
90% percentile
Economics: Intuition is
right for MOST firms
(σ P ↑⇒ higher volatility
⇒ less investment).
For a small number of
firms, it is better to
increase investment even
in the face of additional
uncertainty
. . . . . .

57. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
For Comparison: Transient Shock and Mean Investment
T
σt ↑⇒ Mean Investment
↓, but only slightly
This is consistent with
Gourio 2008 - “investment
reacts more the a
permanent shock”
. . . . . .

58. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
For Comparison: Transient Shock and Mean Investment
Economics: Firm invests
more when it expects
productivity to be higher
in the future
T
σt ↑⇒ Mean Investment
↓, but only slightly
This is consistent with
Gourio 2008 - “investment
reacts more the a
permanent shock”
. . . . . .

59. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Comparative Static Analysis Summary
. Permanent shocks, for their magnitude, have a large impact
1
on moments of interest (investment and leverage) relative to
transient shocks of similar magnitude
. When dealing with simulated firms that can experience
2
permanent shocks, the behavior of the extremes can affect the
sign if the partial derivative of that moment
. . . . . .

60. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock Identification Strategy
Using established moments PLUS two additional moments
. . . . . .

61. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock Identification Strategy
Using established moments PLUS two additional moments
. Speed of Adjustment to Target Leverage - Regression-based
1
SOA
Justification: Firms react much more quickly to permanent
shocks
. . . . . .

62. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Permanent Shock Identification Strategy
Using established moments PLUS two additional moments
. Speed of Adjustment to Target Leverage - Regression-based
1
SOA
Justification: Firms react much more quickly to permanent
shocks
. Covariance of Long-Run Growth of Firm size and Lagged
2
Profitability
Justification: In the long run, what differentiates a permanent
shock from a temporary shock is the size of the firm
( )
Kit πi,t−3
Cov log ,
Ki,t−3 Ki,t−3
. . . . . .

63. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Speed of Adjustment to Target Leverage -
Regression-based SOA
Interpretation:
Increasing
permanent shock
variance (σ P )
does, to a point,
increase SOA
However, this
affect eventually
gets swamped by
other factors
. . . . . .

64. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Covariance of Investment and Profitability
Moment:
( )
Kit πi,t−3
Cov log ,
Ki,t−3 Ki,t−3
Interpretation:
As σ P increases,
the shock becomes
more permanent.
Permanent shocks
lead to
long-lasting
changes in firm
size.
. . . . . .

65. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Identification - Moments 1 and 2
Note that for any given σ P , there is a unique pair:
( ( ))
⇒ σ P is identified
π
SOAβ, Cov log KKit , Ki,t−3
i,t−3 i,t−3
. . . . . . .

66. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Full Sample - Summary Statistics
Table: Summary Statistics for Full Sample
Panel A: Moment Means and Variances
Statistic Mean Var 3rd Central
Leverage 0.2608 0.0349
Investment 0.1161 0.0053 0.0130
Equity Issuance 0.0173 0.0019
Tobin’s Q 2.5702
Operating Income 0.1628 0.0068
Ser. Cor. of OpInc 0.7877
Var ( Innov to OpInc
of ) 0.0028
Kit π
Cov log , i,t−3
Ki,t−3 Ki,t−3
0.0063
SOA βLEVt−1 0.8814
Num. firm-year Obs 4769
. . . . . .

67. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Full Sample - Summary Statistics
Table: Summary Statistics for Full Sample
Panel A: Moment Means and Variances
Statistic Mean Var 3rd Central
Leverage 0.2608 0.0349
Investment 0.1161 0.0053 0.0130
Equity Issuance 0.0173 0.0019
Tobin’s Q 2.5702
Operating Income 0.1628 0.0068
Ser. Cor. of OpInc 0.7877
Var ( Innov to OpInc
of ) 0.0028
Kit π
Cov log , i,t−3
Ki,t−3 Ki,t−3
0.0063
SOA βLEVt−1 0.8814
Num. firm-year Obs 4769
. . . . . .

68. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Table: Compustat Variables and Moments
Moment Compustat Variables
(
Investment CAPX (Capital Expenditures) −
)
SPPE (Sale of Property) /
PPEGT (Property, Plant, and Equipment - Total (Gross)
(
Leverage DLTT (Long-Term Debt - Total) + )
DLC (Debt in Current Liabilities - Total) /
AT (Assets - Total)
Operating Income OIBDP (Operating Income Before Depreciation) /
AT (Assets - Total)
Equity Issuance SSTK (Sale of Common and Preferred Stock) /
AT (Assets - Total)
Cash Flow CHE (Cash and Short-Term Investments) /
AT (Assets - Total)
(
Market Value CSHO (Common Shares of Stock Outstanding) ∗
)
PRCCF Price Close - Annual (Fiscal Year)
(
Market-to-Book DLTT (Long-Term Debt - Total) +
DLC (Debt in Current Liabilities - Total) +
PRSTKC (Purchase of Command and Preferred Stock) +
)
Market Value /
AT (Assets - Total)
Book Equity SEQ (Stockholders’ Equity - Total) +
TXDITC (Deferred Taxes and Investment Tax Credit)
− PSTK (Preferred stock)
Book Debt AT (Assets - Total)
−
( Book Equity
Tobin’s Q Market Value +
Book Debt + )
ACT (Current Assets - Total) /
PPEGT (Property, Plant, and Equipment - Total (Gross)
Definitions taken from the documentation for the Compustat Annual Data - Industrial documentation.
. . . . . .

69. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Full Sample - Estimation
Table: Full Sample Estimations for Barr and DDW Models
DDW S.E BARR S.E.
Parameter Estimate Estimate
Autocorrelation ρ 0.585518 0.297351
Std Dev σT 0.298915 0.206295
Agency s 0.078320 0.181950
Fixed γ 0.002986 0.002928
Convex a 0.153295 0.859097
Equity - Fixed λ1 0.099852 0.102322
Equity - Convex λ2 0.003255 0.003502
Curvature θ 0.837924 0.790740
Permanent Shock σP 0.026600
. . . . . .

70. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Full Sample Estimation - Discussion
The estimation seems to indicate that a combination of
permanent and transitory shock can also match the data
The introduction of even a relatively small permanent shock
(σ P = 0.0266) takes away a large portion of the
autocorrelation of the transient shock
ρT = 0.5855 ↓ ρT+P = 0.2974
. . . . . .

71. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Another Estimation
Table: Full Sample Estimations With and Without Permanent Shocks
Trans. Only Both Shocks
Parameter Estimate Estimate
Autocorrelation ρ 0.585518 0.517682
Std Dev σT 0.298915 0.0794019
Agency s 0.078320 1.204867
Fixed γ 0.002986 0.012505
Convex a 0.153295 0.226857
Equity - Fixed λ1 0.099852 0.024780
Equity - Convex λ2 0.003255 0.006924
Curvature θ 0.837924 0.815899
Permanent Shock σP 0.030197
. . . . . .

72. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Moment Match
Moment Diff ≡ Simulated − Data
Mean Investment -0.1357 0.2378 0.101983
Investment Variance -0.1867 0.192035 0.00525221
3rd Central Moment of Inv. -0.0740 0.0744569 0.000374579
Mean Leverage 0.1792 0.100575 0.279821
Leverage Variance 0.0246 0.0175781 0.0421828
Mean Opr. Income -0.0805 0.231223 0.150638
Ser. Cor. of Op. Inc. 0.0275 0.760189 0.78767
Var. Opr. Inc. Innov 0.0020 0.000780283 0.00276893
Mean Tobin’s Q -3.7123 5.82386 2.11158
Mean Equity Issuance -0.3352 0.349156 0.0139093
Var Equity Issuance -0.1111 0.112791 0.00180158
Mean Cash Balances 0.0718 4.06533e-17 0.0718038
Cov(Asset Growth, Profit) 4.39693e-05 0.00622209 0.00626606
Table: An SMM estimation - Moments Fit
. . . . . .

73. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
One possible reason the estimations are struggling is that I am
calculating my moments without trimming the extremes. Recalling
the plot where mean investment was increasing in σ P , and this was
being driven by a very small amount of firms. However, from the
perspective of the optimizer,
∂[Mean Investment]
>0
∂σ P
This is going to lead to perverse matches.
It is possible that there may be a similar but reversed affect
for some other parameter that affects investment. This, the
matching is being pulled in opposite directions.
. . . . . .

74. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Conclusion
Permanent shocks matter, disproportionate to their size
It is possible to match many interesting moments with a
different shock process
This shock process seems economically plausible - in reality,
both and permanent and transitory shocks exist
More work needed to properly estimate
. . . . . .

75. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Data - Industry Subsets - Summary Statistics
Moment Full Manuf. Mining Retail Svcs. Transport
Mean Inv. 0.1020 0.0948 0.1195 0.1071 0.1138 0.1037
Var Inv. 0.0053 0.0044 0.0078 0.0054 0.0061 0.0063
Inv. 3rd 0.0004 0.0003 0.0007 0.0002 0.0005 0.0004
Mean Lev. 0.2798 0.2529 0.2941 0.2845 0.3370 0.3413
Var Lev. 0.0422 0.0334 0.0372 0.0522 0.0649 0.0516
Mean OpInc. 0.1506 0.1528 0.1403 0.1498 0.1677 0.1521
Ser Cor OpInc. 0.7877 0.8269 0.4935 0.8757 0.8809 0.8283
Var OpInc Innov 0.0028 0.0026 0.0079 0.0015 0.0017 0.0015
Mean Tobin’s Q 2.1116 2.4069 0.9768 1.5688 3.6498 1.5691
Mean Eq. Iss. 0.0139 0.0115 0.0311 0.0090 0.0217 0.0135
Var Eq. Iss. 0.0018 0.0012 0.0044 0.0008 0.0038 0.0024
Mean Cash Bal. 0.0718 0.0763 0.0519 0.0656 0.0952 0.0689
SOA Beta Lev.t−1 0.8815 0.8733 0.7314 0.9226 0.8708 0.9158
Cov(Size,Profit) 0.0063 0.0072 0.0139 0.0078 0.0044 0.0010
N Firm-Year 4769 2362 462 793 385 552
. . . . . .

76. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Table: SMM Estimation By Industry
MODEL Industry ρ σT σP
BARR ALL 0.297351 0.20629564 0.026608675
DDW ALL 0.585518 0.29891501
BARR Manuf 0.594036 0.088540518 1.7910021e-3
DDW Manuf 0.445501 0.094870450
BARR Mining 0.607389 0.039622347 1.2838319e-3
DDW Mining 0.394985 0.090336292
BARR Transport 0.613267 0.093294045 3.3792821e-3
DDW Transport
BARR Retail 0.319490 0.15415480 1.1743024e-3
DDW Retail 0.410377 0.091564558
BARR Services 0.975731 0.027947906 1.1740852e-3
DDW Services 0.926724 0.039731578
. . . . . .

77. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Detrending the Model
The permanent shock introduces a challenge:
non-stationarity.
Economic issues: Add content here
Solving issues: the state space of permanent shocks is infinite
. . . . . .

78. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Detrending - Intuition
The permanent shock process can be detrended.
. . . . . .

79. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Detrending - Intuition
Normal Model:
( )
f levels: zP , Kt , Bt , ...
t
Detrended Model:
( )
ˆ
f innovations: P, kt , bt , ...
t
Notation:
UPPERCASE implies normal model (Kt , Bt ...)
lowercase implies detrended model (kt , bt ...)
. . . . . .

80. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Detrending - Primitives
Permanent shock
log zP = log zP +
t t−1
P
t + zP + µ ,
0
P
t ∼ N(0, σP )
zP t P
= exp( t + zP + µ)
0
zP t−1
Capital Stock
(1/(1−α))
Kt = kt ∗ zP
t−1
Debt
dt = bt+1 ∗ exp( P ) − (1 + r (1 − τc ))bt .
t
. . . . . .

81. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Detrended Equity Issuance
e(kt , kt+1 , bt ,bt+1 , zT t , P
t)=
zT exp(µ
t + P + zP )kα
t 0 t + δ ∗ k t τc
Profit Depreciation Tax Shield
 
kt+1
− ( ) − (1 − δ)kt 
exp 1 P + zP )
α−1 (µ + t 0
Investment
( ( )2 )
a kt+1
− γkΦi + − (1 − δ) exp( p )1/(1−α)
2 kt
Adjustment Costs
P
+ bt+1 ∗ exp( t) − (1 + r(1 − τc ))bt
Debt . . . . . .

82. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Detrended Equity Issuance
e(kt , kt+1 , bt ,bt+1 , zT t , P
t) =
P (
(
zT
t exp(µ ((( P
(((+ t + z0 ) kα
t + δ ∗ k t τc
Profit Depreciation Tax Shield
 
kt+1
− ( ( ( − (1 − δ)kt 
()
P(
exp (((((( + zP )
1
(( α−1 (µ + t 0
Investment
( ( ) )
a kt+1 2
− γkΦi + − (1 − δ)
exp( p )1/(1−α)
2 kt
Adjustment Costs
+ bt+1 ∗ ) − (1 + r(1 − τc ))bt
exp( P
t
Debt . . . . . .

83. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Detrended Equity Issuance
e(kt , kt+1 , bt ,bt+1 , zT t , P
t) =
zT
t exp(µ + P
t + zP ) kα
0 t + δ ∗ k t τc
Profit Depreciation Tax Shield
 
kt+1
− ( ) − (1 − δ)kt 
exp 1 P + zP )
α−1 (µ + t 0
Investment
( ( )) )
a kt+1 2
− γkΦi + − (1 − δ)exp( p )1/(1−α)
2 kt
Adjustment Costs
P
+ bt+1 ∗ exp( t )−(1 + r(1 − τc ))bt
Debt
. . . . . .

84. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Proof: Model is a Contraction Mapping
To prove that the model is a contraction mapping, it is sufficient
to satisfy Blackwell’s sufficient conditions.
.
1 Monotonicity
. Discounting
2
. . . . . .

85. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Condition 1: Monotonicity
Write model as
T(V) = max e(a) + φ(e(a)) + βE[V(a)]
a∈A
Then, take V1 V2 under the sup norm.
T(V1 ) = max [e(a) + φ(e(a)) + βE[V1 (a)]]
a∈A
≤ max [e(a) + φ(e(a)) + βE[V1 (a)]]
a∈A
. . . . . .

86. Introduction Related Literature Model Comparative Statics and Identification Data - Full Sample Estimation Results Conclusion
............ .
Condition 2: Discounting
Let β β 1.
[ ]
T(V + m) = max e(a) + φ(e(a)) + βE[V(a) + m]
a∈A
[ ]
= max e(a) + φ(e(a)) + βE[V(a)] + βm
a∈A
[ ]
≤ max e(a) + φ(e(a))βE[V(a)] + β m
a∈A
.. Back to Main
. . . . . .