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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?
Knowledge Cycles and CorporateInvestment 1 / 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?
Knowledge Cycles and CorporateInvestment 1 / 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?
Knowledge Cycles and CorporateInvestment 1 / 13
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
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
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
Knowledge Cycles and CorporateInvestment 3 / 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
Knowledge Cycles and CorporateInvestment 3 / 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
Knowledge Cycles and CorporateInvestment 3 / 13
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)
Knowledge Cycles and CorporateInvestment 4 / 13
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 and CorporateInvestment 5 / 13
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 and CorporateInvestment 5 / 13
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
Mn
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
Knowledge Cycles and CorporateInvestment 6 / 13
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
Mn
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
Knowledge Cycles and CorporateInvestment 6 / 13
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
Mn
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
Knowledge Cycles and CorporateInvestment 6 / 13
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
Mn
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
Knowledge Cycles and CorporateInvestment 6 / 13
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
Mn
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
exploreMn+1∼N (0,τ−1
M )Mn⊥Mn+1
Knowledge Cycles and CorporateInvestment 6 / 13
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
Mn
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
exploreMn+1∼N (0,τ−1
M )Mn⊥Mn+1
exploreMn+2∼N (0,τ−1
M )Mn+1⊥Mn+2
Knowledge Cycles and CorporateInvestment 6 / 13
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
Mn
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
exploreMn+1∼N (0,τ−1
M )Mn⊥Mn+1
exploreMn+2∼N (0,τ−1
M )Mn+1⊥Mn+2
Exploration cycle
Knowledge Cycles and CorporateInvestment 6 / 13
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
Knowledge Cycles and CorporateInvestment 7 / 13
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
Knowledge Cycles and CorporateInvestment 7 / 13
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
Knowledge Cycles and CorporateInvestment 7 / 13
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
Knowledge Cycles and CorporateInvestment 8 / 13
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
Knowledge Cycles and CorporateInvestment 8 / 13
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
Knowledge Cycles and CorporateInvestment 8 / 13
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
Knowledge Cycles and CorporateInvestment 8 / 13
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
Knowledge Cycles and CorporateInvestment 8 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
a
b0b
a
time t
stockof
know
ledge
Z
Knowledge Cycles and CorporateInvestment 9 / 13
Firm Value• Firm is risk-neutral and discounts its cash flow at rate r ; its value is:
maxτn,it+s≥0
Et
∫ ∞0
e−rsΠt+sds−∑k≥0
γt+θk e−rθk
≡ Πt · v(Zt)
0 2 4 6 8 100
0.2
0.4
0.6
length τ of an exploration cycle
prob
ability
w/ experimentationw/o experimentation
Knowledge Cycles and CorporateInvestment 9 / 13
Firm ValueWe compute the intensive firm value piecewise:
v(Z ) =
a b 0 b aStock of Knowledge Z
ExplorationExperimentation
Knowledge Cycles and CorporateInvestment 10 / 13
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 ;
C 1,C
2)
h(Z ;C1 ,C
2 )
Stock of Knowledge Z
ExplorationExperimentation
Knowledge Cycles and CorporateInvestment 10 / 13
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 ;
C 1,C
2)
h(Z ;C1 ,C
2 )
v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)
Stock of Knowledge Z
ExplorationExperimentation
Knowledge Cycles and CorporateInvestment 10 / 13
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 ;
C 1,C
2)
h(Z ;C1 ,C
2 )
v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)
Stock of Knowledge Z
ExplorationExperimentation
Knowledge Cycles and CorporateInvestment 10 / 13
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 ;
C 1,C
2)
h(Z ;C1 ,C
2 )
v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)
Stock of Knowledge Z
ExplorationExperimentation
Knowledge Cycles and CorporateInvestment 10 / 13
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 ;
C 1,C
2)
h(Z ;C1 ,C
2 )
v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)
Stock of Knowledge Z
ExplorationExperimentation
Knowledge Cycles and CorporateInvestment 10 / 13
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 ;
C 1,C
2)
h(Z ;C1 ,C
2 )
v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)
Stock of Knowledge Z
ExplorationExperimentation
Knowledge Cycles and CorporateInvestment 10 / 13
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 ;
C 1,C
2)
h(Z ;C1 ,C
2 )
v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)
Stock of Knowledge Z
ExplorationExperimentation
Knowledge Cycles and CorporateInvestment 10 / 13
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 ;
C 1,C
2)
h(Z ;C1 ,C
2 )
V(Z
)
v(0)(1−ω)α(1−η) v(0)(1−ω)α(1−η)
Stock of Knowledge Z
ExplorationExperimentation
v(Z )
Knowledge Cycles and CorporateInvestment 10 / 13
Corporate Investment and the Knowledge ChannelFOC for the optimal knowledge-contingent investment plan is:
i(Z ) = 1γ
(q(Z ) +
∫R
V (·,K + I,x)Π(·,K )
ddi ϕ(x , i ,Z )dx︸ ︷︷ ︸
knowledge channel
),i(Z ) = 1
γ
(q(Z ) +
∫R
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))
a 0 a
1
1.5
2
2.5
Stock of Knowledge Z
investment
i(Z
)
benchmark (τS = 0 and κ= 0)
b 0 b
2.4
2.6
2.8
3
Stock of Knowledge Z
competitive pressures
Knowledge Cycles and CorporateInvestment 11 / 13
Corporate Investment and the Knowledge ChannelFOC for the optimal knowledge-contingent investment plan is:
i(Z ) = 1γ
(q(Z ) +
∫R
V (·,K + I,x)Π(·,K )
ddi ϕ(x , i ,Z )dx︸ ︷︷ ︸
knowledge channel ∝τS
),
where q(Z )≡∫
RVK (·,K+I,x)
Π(·,K) ϕ(x , i ,Z )dx (Abel & Blanchard (1986))
a 0 a
1
1.5
2
2.5
Stock of Knowledge Z
investment
i(Z
)
benchmark (τS = 0 and κ= 0)
b 0 b
2.4
2.6
2.8
3
Stock of Knowledge Z
competitive pressures
Knowledge Cycles and CorporateInvestment 11 / 13
Corporate Investment and the Knowledge ChannelFOC for the optimal knowledge-contingent investment plan is:
i(Z ) = 1γ
(q(Z ) +
∫R
V (·,K + I,x)Π(·,K )
ddi ϕ(x , i ,Z )dx︸ ︷︷ ︸
knowledge channel ∝τS
),
i(Z ) = 1γq(Z ),
where q(Z )≡∫
RVK (·,K+I,x)
Π(·,K) ϕ(x , i ,Z )dx (Abel & Blanchard (1986))
a 0 a
1
1.5
2
2.5
Stock of Knowledge Z
investment
i(Z
)
benchmark (τS = 0 and κ= 0)
b 0 b
2.4
2.6
2.8
3
Stock of Knowledge Z
competitive pressures
Knowledge Cycles and CorporateInvestment 11 / 13
Corporate Investment and the Knowledge ChannelFOC for the optimal knowledge-contingent investment plan is:
i(Z ) = 1γ
(q(Z ) +
∫R
V (·,K + I,x)Π(·,K )
ddi ϕ(x , i ,Z )dx︸ ︷︷ ︸
knowledge channel ∝τS
),
where q(Z )≡∫
RVK (·,K+I,x)
Π(·,K) ϕ(x , i ,Z )dx (Abel & Blanchard (1986))
a 0 a
1
1.5
2
2.5
Stock of Knowledge Z
investment
i(Z
)
benchmark (τS = 0 and κ= 0)
b 0 b
2.4
2.6
2.8
3
Stock of Knowledge ZKnowledge Cycles and Corporate
Investment 11 / 13
Corporate Investment and the Knowledge ChannelUse Stein’s lemma to decompose knowledge channel:∫
R
V (·,K + I,x)Π(·,K )
ddi ϕ(x , i ,Z )dx︸ ︷︷ ︸
knowledge channel ∝τS
= τS2 (1+ i)α(1−η)
( Z√1+ τS i
∫R
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)
Π(·,K) ϕ(x , i ,Z )dx (Abel & Blanchard (1986))
a 0 a
1
1.5
2
2.5
Stock of Knowledge Z
investment
i(Z
)
benchmark (τS = 0 and κ= 0)
b 0 b
2.4
2.6
2.8
3
Stock of Knowledge ZKnowledge Cycles and Corporate
Investment 11 / 13
Corporate Investment and the Knowledge ChannelUse Stein’s lemma to decompose knowledge channel:∫
R
V (·,K + I,x)Π(·,K )
ddi ϕ(x , i ,Z )dx︸ ︷︷ ︸
knowledge channel ∝τS
= τS2 (1+ i)α(1−η)
( Z√1+ τS i
∫R
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)
Π(·,K) ϕ(x , i ,Z )dx (Abel & Blanchard (1986))
a 0 a
1
1.5
2
2.5
Stock of Knowledge Z
investment
i(Z
)
benchmark (τS = 0 and κ= 0)
b 0 b
2.4
2.6
2.8
3
Stock of Knowledge ZKnowledge Cycles and Corporate
Investment 11 / 13
Corporate Investment and the Knowledge ChannelUse Stein’s lemma to decompose knowledge channel:∫
R
V (·,K + I,x)Π(·,K )
ddi ϕ(x , i ,Z )dx︸ ︷︷ ︸
knowledge channel ∝τS
= τS2 (1+ i)α(1−η)
( Z√1+ τS i
∫R
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)
Π(·,K) ϕ(x , i ,Z )dx (Abel & Blanchard (1986))
a 0 a
1
1.5
2
2.5
Stock of Knowledge Z
investment
i(Z
)
benchmark (τS = 0 and κ= 0)
b 0 b
2.4
2.6
2.8
3
Stock of Knowledge Z
competitive pressures
Knowledge Cycles and CorporateInvestment 11 / 13
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
imin
imax
invest.rate
i
qmin
qmax
time t
benchm
ark
q
Knowledge Cycles and CorporateInvestment 12 / 13
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
imin
imax
invest.rate
i
Qmin
Qmax
time t
average
Q
Knowledge Cycles and CorporateInvestment 12 / 13
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
imin
imax
invest.rate
i
Qmin
Qmax
time t
average
Q
Knowledge Cycles and CorporateInvestment 12 / 13
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
5
high competition
1 2 3 4
0
2
k−th knowledge deciles
investment−
qsensitivityβ
k
5
baseline
1 2 3 4
0
2
k−th knowledge deciles
5
low noise
1 2 3 4
0
2
k−th knowledge decilesHoberg and Maksimovic (2019)Q on CAPX across product cycle
Knowledge Cycles and CorporateInvestment 12 / 13
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
5
high competition
1 2 3 4
0
2
k−th knowledge deciles
investment−
qsensitivityβ
k
5
baseline
1 2 3 4
0
2
k−th knowledge deciles
5
low noise
1 2 3 4
0
2
k−th knowledge decilesHoberg and Maksimovic (2019)Q on CAPX across product cycle
Knowledge Cycles and CorporateInvestment 12 / 13
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
5
high competition
1 2 3 4
0
2
k−th knowledge deciles
investment−
qsensitivityβ
k
5
baseline
1 2 3 4
0
2
k−th knowledge deciles
5
low noise
1 2 3 4
0
2
k−th knowledge decilesHoberg and Maksimovic (2019)Q on CAPX across product cycle
Knowledge Cycles and CorporateInvestment 12 / 13
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
5
high competition
1 2 3 4
0
2
k−th knowledge deciles
investment−
qsensitivityβ
k
5
baseline
1 2 3 4
0
2
k−th knowledge deciles
5
low noise
1 2 3 4
0
2
k−th knowledge decilesHoberg and Maksimovic (2019)Q on CAPX across product cycle
Knowledge Cycles and CorporateInvestment 12 / 13
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
5
high competition
1 2 3 4
0
2
k−th knowledge deciles
investment−
qsensitivityβ
k
5
baseline
1 2 3 4
0
2
k−th knowledge deciles
5
low noise
1 2 3 4
0
2
k−th knowledge decilesHoberg and Maksimovic (2019)Q on CAPX across product cycle
Knowledge Cycles and CorporateInvestment 12 / 13
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
5
high competition
1 2 3 4
0
2
k−th knowledge deciles
investment−
qsensitivityβ
k
5
baseline
1 2 3 4
0
2
k−th knowledge deciles1 2 3 4
0
2
4
6
life k
βk t−stat
Hoberg and Maksimovic (2019)Q on CAPX across product cycle
Knowledge Cycles and CorporateInvestment 12 / 13
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
5
high competition
1 2 3 4
0
2
k−th knowledge deciles
investment−
qsensitivityβ
k
5
baseline
1 2 3 4
0
2
k−th knowledge deciles1 2 3 4
-4-202468
1012
life k
βk t−stat
Hoberg and Maksimovic (2019)Q on R&D across product cycle
Knowledge Cycles and CorporateInvestment 12 / 13
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?)
Knowledge Cycles and CorporateInvestment 13 / 13
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.