barr invshock v2_slides

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. . . . . . 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 [email protected] University of Rochester May 15, 2012

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Page 1: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

.

......

Permanent and Transitory Shocks in CapitalStructure and Their Relation to Investment,

Leverage, and Speed of Adjustment

Stephen J. [email protected]

University of Rochester

May 15, 2012

Page 2: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Introduction - Welcome to my presentation

Motivation: Better understand the profitability shock processand its industry-level variation, and its effect on capitalstructure

Economic Findings: Permanent shocks, although relativelysmall in magnitude, have a large impact on leverage andinvestment decisions

Page 3: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

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 byvolatility and autocorrelation of profitability, or is there moreto it?

Literature:Uncertainty in profitability usually modeled as strictlytransient process

Page 4: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

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 byvolatility and autocorrelation of profitability, or is there moreto it?

Literature:Uncertainty in profitability usually modeled as strictlytransient process

Page 5: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

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 byvolatility and autocorrelation of profitability, or is there moreto it?

Literature:Uncertainty in profitability usually modeled as strictlytransient process

Page 6: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

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 byvolatility and autocorrelation of profitability, or is there moreto it?

Literature:

Uncertainty in profitability usually modeled as strictlytransient process

Page 7: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

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 byvolatility and autocorrelation of profitability, or is there moreto it?

Literature:Uncertainty in profitability usually modeled as strictlytransient process

Page 8: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Motivation

Intuition - There are many different types of shocks toprofitability - legislation, technology, labor disputes, etc.Expectations differ.

Examples (Transitory):E. coli. scares in spinach,peanut butter (Gorbenkoand Strebulaev 2010).Mad cow in beef.Recall of a competitorsproductLabor issues (union strikesevery few years)

Page 9: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Motivation

Intuition - There are many different types of shocks toprofitability - legislation, technology, labor disputes, etc.Expectations differ.

Examples (Transitory):E. coli. scares in spinach,peanut butter (Gorbenkoand Strebulaev 2010).Mad cow in beef.Recall of a competitorsproductLabor issues (union strikesevery few years)

Page 10: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Motivation - Transient Shock - Mad Cow

..

Page 11: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Motivation

Intuition - There are many different types of shocks toprofitability - legislation, technology, labor disputes, etc.Expectations differ.

Examples (Permanent):Changes in legislationTechnological innovationsPatents expiringTrade agreements

Examples (Transitory):E. coli. scares in spinach,peanut butter (Gorbenkoand Strebulaev 2010).Mad cow in beef.Recall of a competitorsproductLabor issues (union strikesevery few years)

Page 12: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Motivation

Intuition - There are many different types of shocks toprofitability - legislation, technology, labor disputes, etc.Expectations differ.

Examples (Permanent):Changes in legislationTechnological innovationsPatents expiringTrade agreements

Examples (Transitory):E. coli. scares in spinach,peanut butter (Gorbenkoand Strebulaev 2010).Mad cow in beef.Recall of a competitorsproductLabor issues (union strikesevery few years)

Page 13: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

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

1TaxFoundation.org

Page 14: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Motivation - Summary

Why do we care about permanent shocks?

...1 In reality, not all shocks are permanent.

...2 In reality, not all shocks are temporary.

Page 15: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

...1 Introduction

...2 Related Literature

...3 Model

...4 Comparative Statics and IdentificationLeverageInvestmentIdentification

...5 Data - Full Sample

...6 Estimation ResultsWhere I can improve

...7 Conclusion

...8 Data - Industry Subsets

...9 Estimation Per Industry

...10 AppendicesDetrending The ModelProof: Model is a Contraction Mapping

Page 16: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Related Literature

Dynamic Trade-off Models - DeAngelo, DeAngelo, andWhited (2011), Hennesey and Whited (2005, 2007)

Permanent and Transitory Shocks in InvestmentGourio (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)

Page 17: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Economics of Productivity Shock

..

Page 18: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Results Preview

...1 Transient only (zT∗) with ρ∗ u 0.7

or

...2 Transient plus permanent (zT + zP)...1 ρ u 0.3 to 0.5 and σP u 0.03 is also plausible

Page 19: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Results Preview

...1 Transient only (zT∗) with ρ∗ u 0.7

or

...2 Transient plus permanent (zT + zP)...1 ρ u 0.3 to 0.5 and σP u 0.03 is also plausible

Page 20: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Results Preview

...1 Transient only (zT∗) with ρ∗ u 0.7

or

...2 Transient plus permanent (zT + zP)

...1 ρ u 0.3 to 0.5 and σP u 0.03 is also plausible

Page 21: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Results Preview

...1 Transient only (zT∗) with ρ∗ u 0.7

or

...2 Transient plus permanent (zT + zP)...1 ρ u 0.3 to 0.5 and σP u 0.03 is also plausible

Page 22: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Intuition

Firms will react, in general, more quickly to a permanentshock

WHY?: There is no concept of “waiting out” a permanentshock - the marginal cost of adjusting is quickly swamped bythe marginal benefit to adjusting, as the change is expected tobe permanent

IMPLICATION: Change induced by a transient shock can beinduced by a much smaller permanent shock. Thisframework can match many interesting moments with a muchlower autocorrelation than in the transient-only case

Page 23: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

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

Page 24: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/Equity

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a

permanent shock and a transitory shock.

Page 25: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/Equity

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a

permanent shock and a transitory shock.

Page 26: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/Equity

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a

permanent shock and a transitory shock.

Page 27: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/Equity

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a

permanent shock and a transitory shock.

Page 28: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/Equity

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a

permanent shock and a transitory shock.

Page 29: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , zPt )︸ ︷︷ ︸

Payout/Equity

+ φ(

e(kt, kt+1, bt, bt+1, zTt , zP

t ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt ≡ zT

t + zPt

Page 30: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Payout / Equity Issuance

FN: e(Kt,Kt+1,Bt,Bt+1, zTt , ε

Pt )

Economics:e(·) < 0 ⇒ Firm needs financing ⇒ Firm issues equity

e(·) > 0 ⇒ Firm has excess cash ⇒ Firm makesdistribution to shareholders

e(·) = (1− τc)πt(zt,Kt) Production / Profits− δKtτc Depreciation Tax Shield+ It(Kt,Kt+1) Investment− A(Kt,Kt+1) Capital Adjustment Costs+ Dt Net Debt

Page 31: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Profits

Profits occur according to a Cobb-Douglas productionfunction

π = z ∗ Kθ

z profitability shock, K capital stock, θ production curvature

e(·) = (1− τc)πt(zt,Kt) Production / Profits− δKtτc Depreciation Tax Shield+ It(Kt,Kt+1) Investment− A(Kt,Kt+1) Capital Adjustment Costs+ Dt Net Debt

Page 32: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Profitability Shock Process

Transitory Shock

log zTt+1 = ρ ∗ log zT

t + εTt , εT

t ∼ N(0, σT) , ρ ∈ (0, 1)

Permanent Shock

log zPt+1 = log zP

t + εPt , εP

t ∼ N(0, σP)

Total Shock Process

log zt = log zPt + log zT

t

Page 33: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Profitability Shock Process

Transitory Shock

log zTt+1 = ρ ∗ log zT

t + εTt , εT

t ∼ N(0, σT) , ρ ∈ (0, 1)

Permanent Shock

log zPt+1 = log zP

t + εPt , εP

t ∼ N(0, σP)

Total Shock Process

log zt = log zPt + log zT

t

Page 34: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Profitability Shock Process

Transitory Shock

log zTt+1 = ρ ∗ log zT

t + εTt , εT

t ∼ N(0, σT) , ρ ∈ (0, 1)

Permanent Shock

log zPt+1 = log zP

t + εPt , εP

t ∼ N(0, σP)

Total Shock Process

log zt = log zPt + log zT

t

Page 35: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Taxes

τc corporate tax rate, 35%Profits taxed at this rateCapital Depreciation is not taxed (depreciation tax shield)Corporate debt also serves as a tax shield

e(·) = (1− τc)πt(zt,Kt) Production / Profits− δKtτc Depreciation Tax Shield+ It(Kt,Kt+1) Investment− A(Kt,Kt+1) Capital Adjustment Costs+ Dt Net Debt

Page 36: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Investment

Investment - Law of Motion

It+1(Kt,Kt+1) ≡ Kt+1 − (1− δ) ∗ Kt.

e(·) = (1− τc)πt(zt,Kt) Production / Profits− δKtτc Depreciation Tax Shield+ It(Kt,Kt+1) Investment− A(Kt,Kt+1) Capital Adjustment Costs+ Dt Net Debt

Page 37: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Capital Adjustment Costs

Convex Adjustment Cost Function

A(Kt,Kt+1) = γKtΦi +a2

(Kt+1 − (1− δ)Kt

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− δKtτc Depreciation Tax Shield+ It(Kt,Kt+1) Investment− A(Kt,Kt+1) Capital Adjustment Costs+ Dt Net Debt

Page 38: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Debt

Modeling debt as 1-period debtNegative Debt ≡ CashBt ∈ [B, B̄] ⊂ R

Dt+1 ≡ Bt+1 − (1 + r(1− τc))Bt

e(·) = (1− τc)πt(zt,Kt) Production / Profits− δKtτc Depreciation Tax Shield+ It(Kt,Kt+1) Investment− A(Kt,Kt+1) Capital Adjustment Costs+ Dt Net Debt

Page 39: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/Equity

X

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a permanent

shock and a transitory shock.

Page 40: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/EquityX

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a permanent

shock and a transitory shock.

Page 41: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Equity Issuance II, Issuance Costs

Firms pay a cost to issue equityU-shaped cost curveAltınkılıç and Hansen (2000)More capital beyond some amount entails rising costs ofunderwriter certification, monitoring, and marketing, whichincrease the spread.

φ(e(Kt,Bt,Kt+1,Bt+1, z∗t )) = Φe ∗(λ1e(·)−

1

2λ2e(·)2

)where λi ≥ 0, i = 1, 2, and Φe indicates equity issuance (e(· < 0))

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/EquityX

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a permanent

shock and a transitory shock.

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. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/EquityX

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]

X

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

X

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a permanent

shock and a transitory shock.

Use Value Iteration to solve.

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/EquityX

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]X

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

X

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a permanent

shock and a transitory shock.

Use Value Iteration to solve.

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Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Maximizing the Present Value of Equity

V(kt,bt, zt) =

maxkt+1,bt+1∈K×B

[e(kt, kt+1, bt, bt+1, zT

t , εPt )︸ ︷︷ ︸

Payout/EquityX

+ φ(

e(kt, kt+1, bt, bt+1, zTt , ε

Pt ))

︸ ︷︷ ︸Equity Issuance Costs

]X

+ β ∗∫

V(kt+1, bt+1, zt+1) dΓ(zt, zt+1)︸ ︷︷ ︸Continuation Value (Dynamic Model)

X

where β =(

11+r

), dΓ(zt, zt+1) where zt is the sum of a permanent

shock and a transitory shock. Use Value Iteration to solve.

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Note: Detrending

As written, the model is non-stationary and thus cannot besolved using standard techniquesTo solve, detrend the model. .. See Details

Detrending refers to the idea that, with permanent shocks,firm size can grow without boundMain Idea:

f (..., zTt , zP

t︸︷︷︸Non-stationary

)

⇒ f̂ (..., zTt , εP

t︸︷︷︸Stationary

)

Detail: Proof of sufficient conditions to solve .. See Proof

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Note: Detrending

As written, the model is non-stationary and thus cannot besolved using standard techniquesTo solve, detrend the model. .. See Details

Detrending refers to the idea that, with permanent shocks,firm size can grow without boundMain Idea:

f (..., zTt , zP

t︸︷︷︸Non-stationary

) ⇒ f̂ (..., zTt , εP

t︸︷︷︸Stationary

)

Detail: Proof of sufficient conditions to solve .. See Proof

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Comparative Statics

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Permanent Shock and Mean Leverage

..

Economics: Smallmagnitude shocks havelarge effects

σPt ↑⇒ Mean Leverage ↓

Slope is as expected.Economics: Morevolatility ⇒ less leverage

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

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Permanent Shock and Mean Leverage

..

Economics: Smallmagnitude shocks havelarge effectsσP

t ↑⇒ Mean Leverage ↓Slope is as expected.Economics: Morevolatility ⇒ less leverage

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

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Permanent Shock and Mean Leverage - Quantiles

..

Many go to zeroFor a few at the highestlevels, they increase theirleverage when σP ↑

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

For Comparison: Transient Shock and Mean Leverage

..

In the transient only case,mean leverage acts asexpected, but σT has toincrease substantially toshow this drop in meanleverageWhen permanent shocksare added, the affect ofchanges in σT is muted

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Permanent Shock and Mean Investment

..

Why does investmentincrease?

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Permanent Shock and Mean Investment

..

Economics: What isdriving this behavior?

σPt ↑⇒ Mean Investment

↑, ceteris paribus

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Permanent Shock and Mean Investment

..

Economics: What isdriving this behavior?

σPt ↑⇒ Mean Investment

↑, ceteris paribus

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Permanent Shock and Mean Investment - Quantiles

..

The 75% percentile isdownward sloping“Mean Investment” isbeing pulled up by the90% percentileEconomics: Intuition isright for MOST firms(σP ↑⇒ higher volatility⇒ less investment).For a small number offirms, it is better toincrease investment evenin the face of additionaluncertainty

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

For Comparison: Transient Shock and Mean Investment

..

Economics: Firm investsmore when it expectsproductivity to be higherin the future

σTt ↑⇒ Mean Investment

↓, but only slightlyThis is consistent withGourio 2008 - “investmentreacts more the apermanent shock”

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

For Comparison: Transient Shock and Mean Investment

..

Economics: Firm investsmore when it expectsproductivity to be higherin the futureσT

t ↑⇒ Mean Investment↓, but only slightlyThis is consistent withGourio 2008 - “investmentreacts more the apermanent shock”

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

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Comparative Static Analysis Summary

...1 Permanent shocks, for their magnitude, have a large impacton moments of interest (investment and leverage) relative totransient shocks of similar magnitude

...2 When dealing with simulated firms that can experiencepermanent shocks, the behavior of the extremes can affect thesign if the partial derivative of that moment

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Permanent Shock Identification Strategy

Using established moments PLUS two additional moments

...1 Speed of Adjustment to Target Leverage - Regression-basedSOA

Justification: Firms react much more quickly to permanentshocks

...2 Covariance of Long-Run Growth of Firm size and LaggedProfitability

Justification: In the long run, what differentiates a permanentshock from a temporary shock is the size of the firm

Cov(

log KitKi,t−3

,πi,t−3

Ki,t−3

)

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.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Permanent Shock Identification Strategy

Using established moments PLUS two additional moments...1 Speed of Adjustment to Target Leverage - Regression-based

SOAJustification: Firms react much more quickly to permanentshocks

...2 Covariance of Long-Run Growth of Firm size and LaggedProfitability

Justification: In the long run, what differentiates a permanentshock from a temporary shock is the size of the firm

Cov(

log KitKi,t−3

,πi,t−3

Ki,t−3

)

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Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Permanent Shock Identification Strategy

Using established moments PLUS two additional moments...1 Speed of Adjustment to Target Leverage - Regression-based

SOAJustification: Firms react much more quickly to permanentshocks

...2 Covariance of Long-Run Growth of Firm size and LaggedProfitability

Justification: In the long run, what differentiates a permanentshock from a temporary shock is the size of the firm

Cov(

log KitKi,t−3

,πi,t−3

Ki,t−3

)

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Speed of Adjustment to Target Leverage -Regression-based SOA

..

Interpretation:Increasingpermanent shockvariance (σP)does, to a point,increase SOAHowever, thisaffect eventuallygets swamped byother factors

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Covariance of Investment and Profitability

..

Moment:

Cov(

log KitKi,t−3

,πi,t−3

Ki,t−3

)Interpretation:

As σP increases,the shock becomesmore permanent.Permanent shockslead tolong-lastingchanges in firmsize.

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Identification - Moments 1 and 2

.. ..

Note that for any given σP, there is a unique pair:(SOAβ, Cov

(log Kit

Ki,t−3,πi,t−3

Ki,t−3

))⇒ σP is identified

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Full Sample - Summary Statistics

Table: Summary Statistics for Full Sample

Panel A: Moment Means and Variances

Statistic Mean Var 3rd CentralLeverage 0.2608 0.0349Investment 0.1161 0.0053 0.0130Equity Issuance 0.0173 0.0019Tobin’s Q 2.5702Operating Income 0.1628 0.0068Ser. Cor. of OpInc 0.7877Var of Innov to OpInc 0.0028

Cov(

log KitKi,t−3

,πi,t−3

Ki,t−3

)0.0063

SOA βLEVt−10.8814

Num. firm-year Obs 4769

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Full Sample - Summary Statistics

Table: Summary Statistics for Full Sample

Panel A: Moment Means and Variances

Statistic Mean Var 3rd CentralLeverage 0.2608 0.0349Investment 0.1161 0.0053 0.0130Equity Issuance 0.0173 0.0019Tobin’s Q 2.5702Operating Income 0.1628 0.0068Ser. Cor. of OpInc 0.7877Var of Innov to OpInc 0.0028Cov

(log Kit

Ki,t−3,πi,t−3

Ki,t−3

)0.0063

SOA βLEVt−10.8814

Num. firm-year Obs 4769

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Table: Compustat Variables and MomentsMoment Compustat VariablesInvestment

(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 Compustatr Annual Data - Industrial documentation.

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Full Sample - Estimation

Table: Full Sample Estimations for Barr and DDW Models

DDW S.E BARR S.E.Parameter Estimate EstimateAutocorrelation ρ 0.585518 0.297351Std Dev σT 0.298915 0.206295Agency s 0.078320 0.181950Fixed γ 0.002986 0.002928Convex a 0.153295 0.859097Equity - Fixed λ1 0.099852 0.102322Equity - Convex λ2 0.003255 0.003502Curvature θ 0.837924 0.790740Permanent Shock σP 0.026600

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Full Sample Estimation - Discussion

The estimation seems to indicate that a combination ofpermanent and transitory shock can also match the dataThe introduction of even a relatively small permanent shock(σP = 0.0266) takes away a large portion of theautocorrelation of the transient shock

ρT = 0.5855 ↓ ρT+P = 0.2974

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Another Estimation

Table: Full Sample Estimations With and Without Permanent Shocks

Trans. Only Both ShocksParameter Estimate EstimateAutocorrelation ρ 0.585518 0.517682Std Dev σT 0.298915 0.0794019Agency s 0.078320 1.204867Fixed γ 0.002986 0.012505Convex a 0.153295 0.226857Equity - Fixed λ1 0.099852 0.024780Equity - Convex λ2 0.003255 0.006924Curvature θ 0.837924 0.815899Permanent Shock σP 0.030197

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Moment Match

Moment Diff ≡ Simulated − DataMean Investment -0.1357 0.2378 0.101983Investment Variance -0.1867 0.192035 0.005252213rd Central Moment of Inv. -0.0740 0.0744569 0.000374579Mean Leverage 0.1792 0.100575 0.279821Leverage Variance 0.0246 0.0175781 0.0421828Mean Opr. Income -0.0805 0.231223 0.150638Ser. Cor. of Op. Inc. 0.0275 0.760189 0.78767Var. Opr. Inc. Innov 0.0020 0.000780283 0.00276893Mean Tobin’s Q -3.7123 5.82386 2.11158Mean Equity Issuance -0.3352 0.349156 0.0139093Var Equity Issuance -0.1111 0.112791 0.00180158Mean Cash Balances 0.0718 4.06533e-17 0.0718038Cov(Asset Growth, Profit) 4.39693e-05 0.00622209 0.00626606

Table: An SMM estimation - Moments Fit

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One possible reason the estimations are struggling is that I amcalculating my moments without trimming the extremes. Recallingthe plot where mean investment was increasing in σP, and this wasbeing driven by a very small amount of firms. However, from theperspective of the optimizer,

∂[Mean Investment]∂σP > 0

This is going to lead to perverse matches.It is possible that there may be a similar but reversed affectfor some other parameter that affects investment. This, thematching is being pulled in opposite directions.

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Conclusion

Permanent shocks matter, disproportionate to their sizeIt is possible to match many interesting moments with adifferent shock processThis shock process seems economically plausible - in reality,both and permanent and transitory shocks existMore work needed to properly estimate

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Data - Industry Subsets - Summary Statistics

Moment Full Manuf. Mining Retail Svcs. Transport

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

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Table: SMM Estimation By Industry

MODEL Industry ρ σT σP

BARR ALL 0.297351 0.20629564 0.026608675DDW ALL 0.585518 0.29891501BARR Manuf 0.594036 0.088540518 1.7910021e-3DDW Manuf 0.445501 0.094870450BARR Mining 0.607389 0.039622347 1.2838319e-3DDW Mining 0.394985 0.090336292BARR Transport 0.613267 0.093294045 3.3792821e-3DDW TransportBARR Retail 0.319490 0.15415480 1.1743024e-3DDW Retail 0.410377 0.091564558BARR Services 0.975731 0.027947906 1.1740852e-3DDW Services 0.926724 0.039731578

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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

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Detrending - Intuition

The permanent shock process can be detrended.

..

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Detrending - Intuition

Normal Model:

f(

levels: zPt , Kt,Bt, ...

)

Detrended Model:

f̂(

innovations: εPt , kt, bt, ...

)

Notation:UPPERCASE implies normal model (Kt,Bt...)lowercase implies detrended model (kt, bt...)

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Detrending - Primitives

Permanent shock

log zPt = log zP

t−1 + εPt + zP

0 + µ , εPt ∼ N(0, σP)

zPtzPt−1

= exp(εPt + zP

0 + µ)

Capital StockKt = kt ∗ zP

t−1(1/(1−α))

Debtdt = bt+1 ∗ exp(εP

t )− (1 + r (1− τc))bt.

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Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Detrended Equity Issuance

e(kt, kt+1, bt,bt+1, zTt, ε

Pt ) =

zTt exp(µ+ εP

t + zP0 )kαt︸ ︷︷ ︸

Profit+ δ ∗ ktτc︸ ︷︷ ︸

Depreciation Tax Shield

kt+1

exp(

1α−1(µ+ εP

t + zP0 )) − (1− δ)kt

︸ ︷︷ ︸

Investment

(γkΦi +

a2

(kt+1

kt− (1− δ) exp(εp)

1/(1−α)

)2)

︸ ︷︷ ︸Adjustment Costs

+ bt+1 ∗ exp(εPt )− (1 + r(1− τc))bt︸ ︷︷ ︸

Debt

Page 82: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Detrended Equity Issuance

e(kt, kt+1, bt,bt+1, zTt, ε

Pt ) =

zTt (((((((((

exp(µ+ εPt + zP

0 ) kαt︸ ︷︷ ︸Profit

+ δ ∗ ktτc︸ ︷︷ ︸Depreciation Tax Shield

kt+1

((((((((((((exp

(1

α−1(µ+ εPt + zP

0 )) − (1− δ)kt

︸ ︷︷ ︸

Investment

(γkΦi +

a2

(kt+1

kt− (1− δ)�������exp(εp)

1/(1−α)

)2)

︸ ︷︷ ︸Adjustment Costs

+ bt+1 ∗����exp(εPt )− (1 + r(1− τc))bt︸ ︷︷ ︸

Debt

Page 83: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Detrended Equity Issuance

e(kt, kt+1, bt,bt+1, zTt, ε

Pt ) =

zTt exp(µ+ εP

t + zP0 ) kαt︸ ︷︷ ︸

Profit+ δ ∗ ktτc︸ ︷︷ ︸

Depreciation Tax Shield

kt+1

exp(

1α−1(µ+ εP

t + zP0 )) − (1− δ)kt

︸ ︷︷ ︸

Investment

−(γkΦi +

a2

(kt+1

kt− (1− δ)exp(εp)

1/(1−α)

))2)︸ ︷︷ ︸

Adjustment Costs+ bt+1∗ exp(εP

t )−(1 + r(1− τc))bt︸ ︷︷ ︸Debt

.. Back to Main

Page 84: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Proof: Model is a Contraction Mapping

To prove that the model is a contraction mapping, it is sufficientto satisfy Blackwell’s sufficient conditions.

...1 Monotonicity

...2 Discounting

Page 85: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Condition 1: Monotonicity

Write model as

T(V) = maxa∈A

e(a) + φ(e(a)) + βE[V(a)]

Then, take V1 < V2 under the sup norm.

T(V1) = maxa∈A

[e(a) + φ(e(a)) + βE[V1(a)]]

≤ maxa∈A

[e(a) + φ(e(a)) + βE[V1(a)]]

Page 86: Barr invshock v2_slides

. . . . . .

Introduction Related Literature Model. . . . . . . . . . . .Comparative Statics and Identification Data - Full Sample

.Estimation Results Conclusion Data - Industry Subsets Estimation Per Industry

. . . . . . . . . .Appendices

Condition 2: Discounting

Let β < β′ < 1.

T(V + m) = maxa∈A

[e(a) + φ(e(a)) + βE[V(a) + m]

]= max

a∈A

[e(a) + φ(e(a)) + βE[V(a)]

]+ βm

≤ maxa∈A

[e(a) + φ(e(a))βE[V(a)]

]+ β′m

.. Back to Main