On the Nature of Capital Adjustment Costs

Russell W. COOPER, John C. HALTIWANGER

Presenter: Alessandro Peri

University of Carlos III, Madrid

Feb 3, 2014

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Introduction

The paper in a nutshell

1 What they do:

1 Investigation of the nature of Capital Adjustment Costs at the micro-level.

1 Estimate structural parameters of a rich capital adjustment cost specif.

2 How they do it: Simulated method of moments approach

3 Result:

Micro-level: convex non-convex adjustment costs fit the data best.

Aggregate-level: quadratic adjustment cost works fine.

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Introduction

Data

Panel Data:

Period: 1972-1988

Source: Longitudinal Research Database

It = EXPt −RETtKt+1 = (1− δt)Kt + It

it = It/Kt

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Facts

Facts: I/K

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Facts

Facts: I/K

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Facts

Facts: I/K

To recap:

1 Inaction

2 Large bursts of investments: Spikes

3 Negative Investment

4 Positive correlation It/Kt,profit shocks: ρ(it, At) > 0

5 Low positive serial correlation of: ρ(it, it−1) >≈ 0

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Model

Convex Adjustment Costs

V (A,K) = maxI

Π(A,K)− C(I, A,K)− p(I)I + βEA′|AV (A′,K ′)

Π(A,K) = maxL

R(A,K,L)− Lω(L) ≈ AKθ

0 No Adjustment Costs: C(I, A,K) ≡ 0, p(I) = p

1 Convex Adjustment Costs: C(I, A,K) = γ2 (I/K)2K, p(I) = p

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Model

Non Convexities

2 Non-Convex Adjustment Costs:

V (A,K) = max{V i(A,K), V a(A,K)}

V i(A,K) = Π(A,K) + βEA′|AV (A′,K(1− δ))V a(A,K) = max

IΠ(A,K)λ− FK − pI + βEA′|AV (A′,K ′) λ < 1

3 Transaction Costs:

V (A,K) = max{V i(A,K), V b(A,K), V s(A,K)}

V i(A,K) = Π(A,K) + βEA′|AV (A′,K(1− δ))

V b(A,K) = maxI

Π(A,K)− pbI + βEA′|AV (A′, (1− δ)K + I)

V s(A,K) = maxR

Π(A,K)− psR+ βEA′|AV (A′, (1− δ)K −R)

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Quantitative Analysis

Estimation

V (A,K) = max{V i(A,K), V b(A,K), V s(A,K)}

V i(A,K) = Π(A,K) + βEA′|AV (A′,K(1− δ))

V b(A,K) = maxI

Π(A,K)λ− FK − I − γ

2(I/K)2K + βEA′|AV (A′, (1− δ)K + I))

V s(A,K) = maxR

Π(A,K)λ−FK−psR−γ

2(R/K)2K+βEA′|AV (A′, (1−δ)K−R))

Specifications:

Fixed Cost Case: F > 0, λ = 1

Opportunity Cost Case: F = 0, λ ∈ (0, 1)

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Quantitative Analysis

Estimation

Simulated method of moments

L (Θ) = minΘ

[Ψd −Ψs(Θ)]′W [Ψd −Ψs(Θ)]

Estimates of θ and profitability shocks

Π(Ait,Kit) = AitKθit (1)

ln(Ait) = ait = bt + εi,t−1 (2)

εit = ρεεi,t−1 + ηit (3)

πit = ρεπi,t−1 + θkit − ρeθki,t−1 + bt − ρεbt−1 + ηit (4)

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Quantitative Analysis

Fixed Cost Case: F > 0, λ = 1

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Quantitative Analysis

Opportunity Cost Case: F = 0, λ < 1

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Quantitative Analysis

Aggregate..another story

Meaning: Aggregation from LRD (not aggregate from NIPA)

Data:

ρ(iaggrt , aaggrt ) = 0.46 (vs 0.058 at plant level)

ρ(iaggrt , iaggrt−1 ) = 0.5 (vs 0.143 at plant level)

Model:

ρ(iaggrt , aaggrt ) = 0.63 ≈ 0.46

ρ(iaggrt , iaggrt−1 ) = 0.54 ≈ 0.5

γ∗ = arg maxγ R2(XBfit

t , X(γ)t) = 0.195 with R2 = 0.859

Conclusion: convex adjustment costs explains a lot of aggregate!

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Conclusions

Conclusions

Estimate the structural parameter of a rich adjustment cost functions

Simulated Method of Moments

Document significant convex and non-convex adjustment costs

at plant levelat sector level ( Link )

Corroborate convex-adjustment costs at macro-level

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Appendix

Sectoral parameter estimates Back

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