buy, keep, or sell · introduction walter hunt (1796-1859) akcigit, celik, greenwood buy, keep, or...
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Buy, Keep, or SellTheory and Evidence from Patent Resales 1
Ufuk Akcigit, Murat Alp Celik, Jeremy Greenwood
University of Pennsylvania
May 4, 2013
1Please contact [email protected] to obtain a copy of the paper.Akcigit, Celik, Greenwood Buy, Keep, or Sell May 4, 2013
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Introduction
Safety Pin
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Introduction
Walter Hunt (1796-1859)
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Introduction
Patent 6281
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Introduction
Patent 6281
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Introduction
Introduction
Ideas are the engines of economic progress.
Ideas may be initially mismatched.
Patent resales:I 15.6% of all patents registered in the US between 1976-2006 are sold
to other firms.I Average duration of sale: 6.56 years.
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Introduction
0
5
10
15
20
25
1975 1980 1985 1990 1995 2000grant year
domestic only all
in % terms
Fraction of Patents Sold
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Introduction
0
.02
.04
.06
.08
.1
freq
uenc
y
0 5 10 15 20year
in number of years, since the application date
Patent Sale Durations
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Introduction
Motivation
Questions:I Is there a misallocation of ideas?I Can we quantify its degree?I Does the patent resale market mitigate misallocation?I How does the misallocation affect growth?
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Introduction
This study
Empirics of Firm Dynamics and PatentsI An empirical measure of technological distance is constructed.I A number of empirical facts are obtained from firm & patent data.
Theoretical ModelI Ingriedients:
F the misallocation of ideasF the nature of the search frictionsF the implications for economic growth
I BGP is completely characterizedI Stationary firm-size distribution
Quantitative AnalysisI The model is calibrated to moments derived from patent technology
class, citations, resale, and firm dynamics.I Thought experiments to quantify the extent of misallocation due to
frictions.
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Introduction
Outline
1 Model
2 Data Description
3 Empirical Results
4 Calibration
5 Quantitative Exercises
6 Conclusion
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Model
Model
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Model
Constructing a Patent-to-Patent Distance Metric
d(X , Y ) ≡ 1− #(X ∩ Y )
#(X ∪ Y )∈ [0, 1]
#(X ∩ Y ): Number of patents that cite both X and Y.
#(X ∪ Y ): Number of patents that cite either X or Y or both.
The more X and Y are cited together, the closer they are.
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Model
Empirical Facts We Document
1 Real sales and market value are negatively correlated with thedistance between a firm and its patents.
2 Patents which are more distant are more likely to be sold.
3 After a patent resale, the distance between a patent and its ownerdecreases.
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Model
Environment
Time is discrete.
3 types of agents: Households, firms, and patent agents.
Preferences:∞
∑t=0
βt c1−εt
1− ε
1 unit of labor is supplied inelastically.
Household owns all the firms and the capital stock.
Capital depreciates at rate δ.
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Model
Firms
Firms produce final output:
o = zζkκ l1−ζ−κ
Perfect competition.
Firms are characterized by their productivity z , and technologicallocation.
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Model
Technology Circle
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Model
Evolution of Productivity
A firm can increase its productivity by using an idea:
z ′ = L(z , x ; •) = z + γ x z
I z : initial productivityI z ′: new productivityI x : proximity of the idea to the firm
x ≡ 1− d
I z =∫
zdZ (z): average productivityI γ: scale parameter
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Model
Technology Circle
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Model
Innovation
Innovation is costly:
C (i ; •) = i1+ρ χ1+ρz
ζ/(ζ+λ)
I i : probability of inventing a new ideaI χ: R&D cost scale parameterI ρ: R&D elasticity parameterI zζ/(ζ+λ): endogenous scale factor
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Model
Timing of Events for a Firm
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Model
Patent Agency & Agents...
Agency:
I buys patents from firms at the competitive price q instantenously (w/oS&M frictions).
Each agent:
I goes to the market with a single patent to sell,I tries to meet a buyer and sell their patent.I Matching is subject to search frictions.I The buying price P is determined by Nash Bargaining.I Bargaining power of patent agents: ωI Patents expire at exogeneous rate σ ≈ 1/17.
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Model
Matching Technology
Total matches:
M(#a, #b) = η(#a)µ(#b)1−µ
#a: measure of patent agents.
#b: measure of potential buyers.
η: matching scale parameter.
µ: Cobb-Douglas weight of patent agents.
Matches are completely random with respect to technology class.
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Model
Value Function of a Patent Resale Agent
A(•) = ma(#a
#b)︸ ︷︷ ︸
Meet a buyer
∫ ∫Ia(z , x ; •)P(z , x ; •)dG (z)dD(x)︸ ︷︷ ︸
Expected sale revenue
+
[ma(
#a
#b)∫ ∫
[1− Ia(z , x ; •)]dG (z)dD(x)︸ ︷︷ ︸Meet but no trade
+[1−ma(#a
#b)]︸ ︷︷ ︸
Fail to meet
]rσA(•′)︸ ︷︷ ︸
Continuation value
Ia(z , x ; •) = 1 if sale, 0 otherwise
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Model
Value Function of a Buyer Firm
B(z ; •) = mb(#a
#b)︸ ︷︷ ︸
Meet an agent
∫ [[1− Ia(z , x ; •)][Π(z ; •) + rV (z ; •′)]︸ ︷︷ ︸
Don’t buy
+Ia(z , x ; •)[Π(
z ′︷ ︸︸ ︷L(z , x ; •); •)− P(z , x ; •) + rV (
z ′︷ ︸︸ ︷L(z , x ; •); •)︸ ︷︷ ︸
Buy
]
]dD(x) + [1−mb(
#a
#b)]︸ ︷︷ ︸
Don’t meet
[Π(z ; •) + rV (z ; •′)]︸ ︷︷ ︸Produce with old productivity
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Model
Value Function of a Keeper Firm
K (L(z , x ; •); •) = Π(
z ′︷ ︸︸ ︷L(z , x ; •); •)︸ ︷︷ ︸Period profit
+ rV (
z ′︷ ︸︸ ︷L(z , x ; •); •′)︸ ︷︷ ︸
Continuation value
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Model
Value Function of a Seller Firm
S(z ; •) = Π(z ; •)︸ ︷︷ ︸Period profit
+ σq︸︷︷︸Proceeds from sale
+ rV (z ; •′)︸ ︷︷ ︸Continuation value
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Model
Value Function Before Innovation
V (z ; •) = maxi∈[0,1]
{i︸︷︷︸
Innovate
∫ [Ik(z , x ; •)K (
z ′︷ ︸︸ ︷L(z , x ; •); •′)︸ ︷︷ ︸
Keep
+[1− Ik(z , x ; •)]S(z ; •′)︸ ︷︷ ︸Sell
]dX (x)︸ ︷︷ ︸
Proximity distribution
+ (1− i)︸ ︷︷ ︸Fail to innovate
B(z ; •)︸ ︷︷ ︸Buyer
− C (i ; •)︸ ︷︷ ︸Cost of R&D
}
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Model
Symmetric BGP Equilibrium
A set of prices and allocations such that:
Mean productivity grows at the constant rate g
Market tightness is constant.
Policy functions for keeping and selling patents are optimal.
Innovation decision maximizes a firm’s value function.
Firms hire capital and labor optimally.
Households save and consume optimally.
Markets clear.
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Model
Symmetric BGP Equilibrium
All value functions and policy rules have tractable closed-formsolutions.
I Linear value functions.I Cut-off policy rules.
Solving a nonlinear system of 17 equations and 17 unknowns.
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Model
Invariant Firm-Size Distribution
Firm size is equal to relative productivity: l = zz = z
Recall the law of motion:
z ′ = z + γxz
z ′ =1
gz +
γ
gx
Proposition
Existence of a Unique Stationary Firm-Size Distribution: Thestochastic process for the relative productivity converges weakly to aunique invariant distribution.
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Data Description
Data Description
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Data Description
Data Sources
NBER-USPTO Utility Patents Grant Data (PDP):I Contains information on all 3,210,261 utility patents granted between
1976-2006 in the US.I Citation links between patents are available.I Each patent is assigned a technology class according to International
Patent Classification (IPC).I The innovating firms are uniquely identifiable.
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Data Description
Data Sources
Compustat North American Fundamentals - Annual:I Contains balance sheet information on firms publicly traded between
1976-2006 in the US.I Can be linked to NBER patent data using existing procedures (Bessen
(2009)).
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Data Description
Data Sources
Patent Reassignment Data (PRD):I Recently released under Google Patents Beta.I Contains information on all 767,815 patents sales between 1980-2012
in the US.I Can be linked to NBER patent data using patent numbers or a
company name matching algorithm.
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Data Description
Constructing a Patent-to-Patent Distance Metric
The first two digits of the IPC code of a patent characterizes itstechnological position.
A notion of distance between 2-digit IPC codes is required.
d(X , Y ) ≡ 1− #(X ∩ Y )
#(X ∪ Y )∈ [0, 1]
#(X ∩ Y ): Number of patents that cite both X and Y.
#(X ∪ Y ): Number of patents that cite either X or Y or both.
The more X and Y are cited together, the closer they are to eachother.
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Data Description
Constructing a Patent-to-Firm Distance Metric
A patent has a single technology class.
A firm may have multiple patents belonging to different technologyclasses.
d (p, f ) ≡ 1
‖Pf ‖ ∑p′∈Pf
d (Xp, Yp′) ∈ [0, 1]
p: patent, f : firm
Pf : patent portfolio of firm f .
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Data Description
Distribution of Patent-to-Firm Proximity (1 - Distance)
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Data Description
Value of the Patent Stock
Citation number is accepted as a good proxy for patent quality afteradjusting for truncation and industry effects. (Hall, Jaffe, Trajtenberg(2005))
patent stock (f) = ∑p∈Pfcitation weight of patent p
distance adjusted patent stock (f) =
∑p∈Pfcitation weight of patent p × distance of patent p
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Empirical Results
Empirical Results
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Empirical Results
Fact 1: Firm Moments
The patent portfolio of a firm is positively correlated with real salesand market value.
The distance between the firm and its patents affects thesecorrelations negatively.
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Empirical Results
Fact 1: Firm Moments
Table 2: Firm Moment Regressions
Variable log real sales log market valuelog patent stock 0.191∗∗∗ 0.037∗∗∗
(0.008) (0.008)log dist-adj pat stock −0.006∗∗∗ −0.018∗∗∗
(0.003) (0.003)log employment 0.936∗∗∗ 0.728∗∗∗
(0.008) (0.008)intercept yes yesyear yes yesfirm fixed effect yes yesObs 23,028 36,094R2 0.96 0.92
Standard errors are reported in parantheses.
*10%, **5%, ***1% significance.
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Empirical Results
Fact 2: Patent Sale Decision
Firms are more likely to sell patents that are technologically distant.
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Empirical Results
Fact 2: Patent Sale Decision
Table 3: Patent Sale Decision
Variable Indicator (=1 if sold)distance 0.0227∗∗∗
(0.001)patent quality 0.0004∗∗∗
(0.000)log (size of patent portfolio) −0.0160∗∗∗
(0.000)intercept, year, firm f.e. yesObs 2,564,305R2 0.4158mean dep var 15.61
Standard errors are reported in parantheses.
*10%, **5%, ***1% significance.
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Empirical Results
Fact 3: Distance Reduction Following Patent Resale
On average, the distance between a patent and its owner decreasesafter it is sold.
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Empirical Results
Fact 3: Distance Reduction Following Patent Resale
Table 4: Distance Reduction on Resale
Variable Change in distanced (p, fb)− d (p, fs)
intercept −0.176∗∗∗
(0.056)year fixed effect yesseller fixed effect yesObs 24,159mean dep var 0.556
Standard errors are reported in parantheses.*10%, **5%, ***1% significance.
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Calibration
Calibration
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Calibration
Table 5: Parameter Values
Parameter Description Identificationβ = 0.98 Discount factor Real interest rateε = 2.00 CRRA parameter Kaplow (2005)κ = 0.25 Capital’s share Corrado et. al. (2006)λ = 0.60 Labor’s share ”δ = 0.07 Depreciation rate NIPAσ = 0.94 Patent survival rate U.S. patent lawγ = 0.25 Law of motion, productivity Growth rate in GDPχ = 1.42 Cost of R&D R&D expenditure to GDPµ = 0.52 Matching function Fraction of patents soldη = 0.18 Matching function Duration until saleω = 0.50 Bargaining power Equal for sellers and buyersρ = 3.00 R&D cost elasticity CompustatX (x) Proximity distribution Empirical distribution
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Calibration
Table 6: Calibration Targets
Target U.S. Data ModelLong-run growth in output 2.00% 2.00%Ratio of R&D expenditure to GDP 2.91% 2.84%Fraction of patents that are sold 15.6% 16.9%Sale duration distribution See next figures
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Calibration
0
.05
.1
.15
freq
uenc
y
1 2 3 4 5 6 7 8 9 1011121314151617
in number of years, since the grant date
Patent Sale Durations
data model
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Calibration
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Thought Experiments: Quantifying Misallocation
Quantitative Analysis
(preliminary)
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Thought Experiments: Quantifying Misallocation
Quantifying the Misallocation
A series of thought experiments will be conducted, where the marketsare successively getting more efficient.
Effect on innovation rate i is ambiguous:I Markets are more efficient:
F q increases ⇒ i increases
I Markets are more efficient:F buying ideas is easier ⇒ i decreases
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Thought Experiments: Quantifying Misallocation
Changing the Contact Rate for Matches
η : Scale factor in the matching function
Higher η ⇒ Increased number of matches
η = 0⇒ Closing patent markets
What is the welfare contribution of the patent resale market?
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Thought Experiments: Quantifying Misallocation
Changing the Contact Rate for Matches
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Thought Experiments: Quantifying Misallocation
Perfectly Directed Search
Baseline model: Conditional upon meeting, proximity x ∼ U [0, 1]
What if search was perfectly directed?
Table 7: Perfectly Directed Search
Baseline Model Directed Search
Output growth rate, gζ/(ζ+λ) − 1 0.020 0.024Innovation rate, i 0.56 0.53Welfare gain, α− 1 0.00 0.10Fraction of patents sold 0.169 0.275Growth from patents sold 0.195 0.424Seller patent price, q 0.13 0.19Sellers/Buyers, #a/#b 2.19 2.88
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Thought Experiments: Quantifying Misallocation
Perfectly Directed Search with Maximum Contact Rate
What if perfectly directed search was accompanied by maximumcontact rate?
η is such that buyer meets a seller with probability 1.
Table 8: Perfectly Directed Search + Max. Contact Rate
Baseline Model Directed Search
Output growth rate, gζ/(ζ+λ) − 1 0.020 0.035Innovation rate, i 0.56 0.55Welfare gain, α− 1 0.00 0.36Fraction of patents sold 0.169 0.802Growth from patents sold 0.195 0.866Seller patent price, q 0.13 0.30Agents/Buyers, #a/#b 2.19 1.36
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Thought Experiments: Quantifying Misallocation
Removing Misallocation of Ideas
The main source of inefficiency: X (x)
What if there were no misallocation of ideas?
Table 8: No Misallocation
Baseline Model No Misallocation
Output growth rate, gζ/(ζ+λ) − 1 0.020 0.04Innovation rate, i 0.56 0.60Welfare gain, α− 1 0.00 0.50
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Thought Experiments: Quantifying Misallocation
Proximity Distribution of Utilized Patents
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Thought Experiments: Quantifying Misallocation
Proximity Distribution of Utilized Patents
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Thought Experiments: Quantifying Misallocation
Proximity Distribution of Utilized Patents
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Conclusion
Conclusion
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Conclusion
Conclusion
A model of misallocation of ideas is developed.
Misallocation can be mitigated by the patent resale market.
Efficiency of patent resale market has implications for economicgrowth.
Implications on firm size and firm productivity dynamics.
An empirical strategy is offered to measure technologicalmisallocation of ideas.
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