knowledgecyclesandcorporateinvestment...the economics of exploration and experimentation...

Knowledge Cycles and Corporate Investment

Cecilia Bustamante Julien Cujean Laurent Frésard

May 2019

Knowledge Cycles and CorporateInvestment 0 / 13

Motivation - The increasing importance of knowledge

• Knowledge accounts for an increasing share of firms’ assets• e.g., employees’ knowhow, internal data, proprietary technologies,

organization design, customer relationships, etc.

• The recent shift towards knowledge-assets appears related to physicalinvestment patterns

• Low investment despite high valuations – Q (Gutierrez and Philippon(2017) and Crouzet and Eberly (2018))

• Weak relation between investment and Q (Peters and Taylor (2017))• Investment-Q relation varies over product life-cycle (Hoberg and

Maksimovic (2019))

• Open (relevant) questions:• How does knowledge interact with physical investment and valuation?• Does knowledge affect the investment-Q relation? How?

Maksimovic (2019))

Our starting point - the process of knowledge creation

• New (neo-classical) model of investment to shed light on thesequestions

• Our focus: The process of knowledge creation within firms

• Starting point: Knowledge is not a typical capital input in production• Hard to buy directly (unlike physical capital)• Difficult to accumulate and retain (the human part)• Can depreciate very fast (obsolescence)• Effect on profits is highly uncertain

• Existing models (simply) add intangible capital as an extra factor ofproduction (with different adjustment costs)

• Our view: Knowledge results from exploration and experimentationKnowledge Cycles and Corporate

Investment 2 / 13

The Economics of exploration and experimentation• Firms use a given “technology” (products or processes)

• e.g., screens for mobile phones, oil extraction process, organizationalstructure, data curation process, etc.

• Unsure about the true quality of the technology (good or bad)

• Knowledge = Information about current technology’s quality• Passive learning-by-doing (i.e., passage of time)• Active Experimentation – learning-by-investing• e.g., learn more by operating more machines or larger R&D labs

• Key: Knowledge is a by-product of economic activities (Arrow(1962))

• Explore new tech when firms are confident that current tech is• Poor quality (unprofitable)• High quality (more entry eroding profits) – innovation needs

Illustration: Samsung recent knowledge cycle• Explore and adopt “color” screen• Investment/experimentation (knowledge ⇑)• Confidence that quality is high ⇑• Competitive pressure ⇒ innovation needed

• Explore and adopt “touch” screen• Investment/experimentation (knowledge ⇑)• Confidence that quality is high ⇑• Competitive pressure ⇒ innovation needed

• Explore and adopt “foldable” touch screen• Investment/experimentation (knowledge ⇑)• Confidence that quality is low ⇑• Explore something else (or fix)

• Such knowledge cycles are present in most firms (in various forms)

New insight: The key role of knowledge cycles

• The model generates endogenous knowledge cycles

• Investment and firm value (Q) are function of knowledge cycles

• Knowledge creates a distortion between investment and Q• Over- or Under-investment in some states• Investment-Q relation concentrates in low or intermediate knowledge

(i.e., early cycle)• Varies with competitive pressure and uncertainty about tech quality

(noise)

• Rationalize some recent empirical puzzles

• Interesting (new) economic forces in investment models

New insight: The key role of knowledge cycles

• The model generates endogenous knowledge cycles

• Investment and firm value (Q) are function of knowledge cycles

• Knowledge creates a distortion between investment and Q• Over- or Under-investment in some states• Investment-Q relation concentrates in low or intermediate knowledge

(i.e., early cycle)• Varies with competitive pressure and uncertainty about tech quality

(noise)

• Rationalize some recent empirical puzzles

• Interesting (new) economic forces in investment models

Knowledge Cycles• Firm combines physical capital K with technology n to produce:

Yt = An,tKαt

• Productivity of technology n evolves as:

dAn,tAn,t

= τ1/2A

Ω1/2t

dt +dBt

• Quality of each technology, Mn, is unobservable; Ω is the conditionalvariance of firm’s estimate of quality

• At all dates, the firm chooses either to continue operating the cur-rent technology, or abandon it and explore a new, unknown technology:

τn . . . τn+1 . . . τn+2

exploreMn∼N (0,τ−1

M )Mn−1⊥Mn

Yt = An,tKαt

dAn,tAn,t

= τ1/2A

Ω1/2t

dt +dBt

τn . . . τn+1 . . . τn+2

M )Mn−1⊥Mn

Yt = An,tKαt

dAn,tAn,t

= τ1/2A

Ω1/2t

dt +dBt

τn . . . τn+1 . . . τn+2

M )Mn−1⊥Mn

Yt = An,tKαt

dAn,tAn,t

= τ1/2A

Ω1/2t

dt +dBt

τn . . . τn+1 . . . τn+2

M )Mn−1⊥Mn

Yt = An,tKαt

dAn,tAn,t

= τ1/2A

Ω1/2t

dt +dBt

τn . . . τn+1 . . . τn+2

M )Mn−1⊥Mn

exploreMn+1∼N (0,τ−1

M )Mn⊥Mn+1

Yt = An,tKαt

dAn,tAn,t

= τ1/2A

Ω1/2t

dt +dBt

τn . . . τn+1 . . . τn+2

M )Mn−1⊥Mn

M )Mn⊥Mn+1

M )Mn+1⊥Mn+2

Yt = An,tKαt

dAn,tAn,t

= τ1/2A

Ω1/2t

dt +dBt

τn . . . τn+1 . . . τn+2

M )Mn−1⊥Mn

M )Mn⊥Mn+1

M )Mn+1⊥Mn+2

Exploration cycle

Investment as Knowledge Acquisition• The firm can actively learn by “experimenting through investment”.Investment (it ≡ It/Kt > 0) creates an informative signal flow:

dSt = 1it>0

τ1/2S i1/2t

Ω1/2t−

M + εt

, εt ∼N (0,1), i.i.d.

• Based on passive (At)t≥0 and active signals (St)t≥0 the firm obtainsan estimate Mt = Et [M] of quality, with error variance, Ωt = Vt [M]

• The t−stat ratio, Z ≡ M/Ω1/2, is a sufficient statistic for the firm’sstock of knowledge about its current technology:

dZt = τA/2Ztdt + τ1/2A dBt︸︷︷︸

passive learning

+Zt−(

(1+ τS it)1/2−1)

+ (τS it)1/2εt︸︷︷︸experimenting

− Zt−1t=τ︸︷︷︸knowledge reset

dSt = 1it>0

τ1/2S i1/2t

Ω1/2t−

M + εt

, εt ∼N (0,1), i.i.d.

passive learning

+Zt−(

(1+ τS it)1/2−1)

dSt = 1it>0

τ1/2S i1/2t

Ω1/2t−

M + εt

, εt ∼N (0,1), i.i.d.

passive learning

+Zt−(

(1+ τS it)1/2−1)

A Neoclassical Model of Investment• Firm operates in an industry with a continuum of identical firmsproducing the same good. Mass of firms at instant t is Nt .

• Assuming isoelastic demand with price elasticity η, firm’s revenues are:

Π(At ,Kt ,Nt) = Yt(NtYt)−η = A1−ηt Kα(1−η)

t N−ηt

• Adjustment costs γ(i) for purchasing and installing new capital are:

γ(i) = (κ+γ/2i2) ·Π(At ,Kt ,Nt), i ≥ 0

• Exploration is also costly; upon exploring a new technology, a fractionω of the firm’s capital K becomes obsolete:

dKt = itKt−1t=θ− δKtdt−ωKt−1t=τ

• To introduce competitive pressures we assume that new firms enterthe industry as knowledge about the current technology improves:

dNt/Nt = φZ 2t dt

t N−ηt

γ(i) = (κ+γ/2i2) ·Π(At ,Kt ,Nt), i ≥ 0

dNt/Nt = φZ 2t dt

t N−ηt

γ(i) = (κ+γ/2i2) ·Π(At ,Kt ,Nt), i ≥ 0

dNt/Nt = φZ 2t dt

t N−ηt

γ(i) = (κ+γ/2i2) ·Π(At ,Kt ,Nt), i ≥ 0

dNt/Nt = φZ 2t dt

t N−ηt

γ(i) = (κ+γ/2i2) ·Π(At ,Kt ,Nt), i ≥ 0

dNt/Nt = φZ 2t dt

Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:

maxτn,it+s≥0

∫ ∞0

e−rsΠt+sds−∑k≥0

γt+θk e−rθk

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

time t

stockof

maxτn,it+s≥0

∫ ∞0

γt+θk e−rθk

≡ Πt · v(Zt)

0 2 4 6 8 100

length τ of an exploration cycle

ability

w/ experimentationw/o experimentation

Firm ValueWe compute the intensive firm value piecewise:

v(Z ) =

a b 0 b aStock of Knowledge Z

ExplorationExperimentation

Firm ValueWe compute the intensive firm value piecewise when idle:

v(Z ) = vP (Z ) + eg1Z+g2Z2 (C1Hn (Z ) + C2M (Z ))≡ h(Z ;C1,C2)

a b 0 b a

h(Z ;C1 ,C

Stock of Knowledge Z

Firm ValueWe compute the intensive firm value piecewise when exploring:

v(Z ) = v(0)(1−ω)α(1−η) ≡ g(0)

a b 0 b a

h(Z ;C1 ,C

v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)

Firm ValueFirm value solves a Bellman equation when experimenting:

V (Z ) = maxi−κ−γ/2i2+(1+ i)α(1−η)(∫ b

a h(x ; ·)dΦ(x ;Z ) +∫ a

b h(x ; ·)dΦ(x ;Z ) + g(0)∫

x /∈A dΦ(x ;Z ) +∫ b

b V (x)dΦ(x ;Z ))

a b 0 b a

h(Z ;C1 ,C

v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)

Firm ValueFirm value solves a Bellman equation when experimenting:V (Z ) = maxi−κ − γ/2i2 + (1 +i)α(1−η)

(∫ ba h(x ; ·)dΦ(x ;Z )+

∫ ab h(x ; ·)dΦ(x ;Z ) + g(0)

∫x /∈A dΦ(x ;Z ) +

∫ bb V (x)dΦ(x ;Z )

a b 0 b a

h(Z ;C1 ,C

v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)

Firm ValueFirm value solves a Bellman equation when experimenting:V (Z ) = maxi−κ − γ/2i2 + (1 + i)α(1−η)

(∫ ba h(x ; ·)dΦ(x ;Z ) +∫ a

b h(x ; ·)dΦ(x ;Z )+g(0)∫

x /∈A dΦ(x ;Z ) +∫ b

b V (x)dΦ(x ;Z ))

a b 0 b a

h(Z ;C1 ,C

v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)

Firm ValueFirm value solves a Bellman equation when experimenting:V (Z ) = maxi−κ−γ/2i2+(1+ i)α(1−η)

(∫ ba h(x ; ·)dΦ(x ;Z )+

∫ ab h(x ; ·)dΦ(x ;Z )+

g(0)∫

x /∈A dΦ(x ;Z )+∫ b

b V (x)dΦ(x ;Z ))

a b 0 b a

h(Z ;C1 ,C

v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)

(∫ ba h(x ; ·)dΦ(x ;Z )+

∫ ab h(x ; ·)dΦ(x ;Z )+

g(0)∫

x /∈A dΦ(x ;Z ) +∫ b

b V (x)dΦ(x ;Z ))

a b 0 b a

h(Z ;C1 ,C

v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)

(∫ ba h(x ; ·)dΦ(x ;Z )+

∫ ab h(x ; ·)dΦ(x ;Z )+

g(0)∫

x /∈A dΦ(x ;Z ) +∫ b

b V (x)dΦ(x ;Z ))

a b 0 b a

h(Z ;C1 ,C

v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)

Corporate Investment and the Knowledge ChannelFOC for the optimal knowledge-contingent investment plan is:

i(Z ) = 1γ

(q(Z ) +

V (·,K + I,x)Π(·,K )

ddi ϕ(x , i ,Z )dx︸︷︷︸

knowledge channel

),i(Z ) = 1

(q(Z ) +

V (·,K+I,x)Π(·,K)

ddiϕ(x , i ,Z )dx

where q(Z )≡∫

RVK (·,K+I,x)

Π(·,K) ϕ(x , i ,Z )dx (Abel & Blanchard (1986))

investment

benchmark (τS = 0 and κ= 0)

competitive pressures

i(Z ) = 1γ

(q(Z ) +

V (·,K + I,x)Π(·,K )

knowledge channel ∝τS

where q(Z )≡∫

RVK (·,K+I,x)

investment

i(Z ) = 1γ

(q(Z ) +

V (·,K + I,x)Π(·,K )

i(Z ) = 1γq(Z ),

where q(Z )≡∫

RVK (·,K+I,x)

investment

i(Z ) = 1γ

(q(Z ) +

V (·,K + I,x)Π(·,K )

where q(Z )≡∫

RVK (·,K+I,x)

investment

Stock of Knowledge ZKnowledge Cycles and Corporate

Investment 11 / 13

Corporate Investment and the Knowledge ChannelUse Stein’s lemma to decompose knowledge channel:∫

V (·,K + I,x)Π(·,K )

= τS2 (1+ i)α(1−η)

( Z√1+ τS i

v ′(x)ϕ(x , i ,Z )dx︸︷︷︸marginal product of knowledge

Rv ′′(x)ϕ(x , i ,Z )dx︸︷︷︸attitude towards risk

where q(Z )≡∫

RVK (·,K+I,x)

investment

Investment 11 / 13

V (·,K + I,x)Π(·,K )

= τS2 (1+ i)α(1−η)

( Z√1+ τS i

where q(Z )≡∫

RVK (·,K+I,x)

investment

Investment 11 / 13

V (·,K + I,x)Π(·,K )

= τS2 (1+ i)α(1−η)

( Z√1+ τS i

where q(Z )≡∫

RVK (·,K+I,x)

investment

Q-Investment Relation and Knowledge Cycles

Typical investment-average Q(Z )≡ V (K ,Z , ·)/Π(K , ·) regression:

i(Zt) = αk +βkQ(Zt) + εt , |Zt | ∈ decilek , k = 1, ...,10

invest.rate

time t

benchm

invest.rate

time t

average

invest.rate

time t

average

high competition

1 2 3 4

k−th knowledge deciles

investment−

qsensitivityβ

baseline

1 2 3 4

low noise

1 2 3 4

k−th knowledge decilesHoberg and Maksimovic (2019)Q on CAPX across product cycle

high competition

1 2 3 4

investment−

qsensitivityβ

baseline

1 2 3 4

low noise

1 2 3 4

high competition

1 2 3 4

investment−

qsensitivityβ

baseline

1 2 3 4

low noise

1 2 3 4

high competition

1 2 3 4

investment−

qsensitivityβ

baseline

1 2 3 4

low noise

1 2 3 4

high competition

1 2 3 4

investment−

qsensitivityβ

baseline

1 2 3 4

low noise

1 2 3 4

high competition

1 2 3 4

investment−

qsensitivityβ

baseline

1 2 3 4

k−th knowledge deciles1 2 3 4

life k

βk t−stat

Hoberg and Maksimovic (2019)Q on CAPX across product cycle

high competition

1 2 3 4

investment−

qsensitivityβ

baseline

1 2 3 4

k−th knowledge deciles1 2 3 4

-4-202468

life k

βk t−stat

Hoberg and Maksimovic (2019)Q on R&D across product cycle

Ideas for testing the model

• Measuring knowledge cycles from patents’ text• Appearance and disappearance of technological words• Similar to Bowen et al. (2019)• Exploit variation in investment (and Q) across industries

• Measuring knowledge cycles from product descriptions• Similar to Hoberg and Maksimovic (2019)• Exploit variation in investment (and Q) across firms

• Empirical relevance and economic quantification (structural?)

References I

Arrow, K. (1962). The economic implications of learning by doing. Review of EconomicStudies 29(3), 155–173.

Bowen, D., L. Fresard, and G. Hoberg (2019). Technological disruptiveness and the evolution ofipos and acquisitions.

Crouzet, N. and J. Eberly (2018, May). Intangibles, investment, and efficiency. AEA Papers andProceedings 108, 426–31.

Gutierrez, G. and T. Philippon (2017). Investmentless growth: An empirical investigation.Brookings Papers on Economic Activity , 89–169.

Hoberg, G. and V. Maksimovic (2019). Product Life Cycles in Corporate Finance. WorkingPaper .

Peters, R. H. and L. A. Taylor (2017). Intangible capital and the investment-q relation. Journalof Financial Economics 100, 251–272.

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