[PPT] - On the Direction of Innovation Hugo A. Hopenhayn Francesco PowerPoint Presentation

SLIDE 1

On the Direction of Innovation

Hugo A. Hopenhayn Francesco Squintani EARIE, Milan August 2014

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 2

Introduction

Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 3

Introduction

Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 4

Introduction

Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 5

Introduction

Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 6

Introduction

Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 7

Introduction

Most research on patents asks: “Is IP sufficient or excessive?” This paper: “Does it go in the right direction?” Basic theory: heterogenous patent races: hotter and cooler Equilibrium allocates scarce researchers to different patent races. Equilibrium and optimal allocation will rarely coincide. Under plausible assumptions, too many researchers in hot areas

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 8

A simple model

Two research areas (patent races), one potential discovery each. Social and private value of discovery z1 < z2. Total M homogenous researchers. Discovery with probability p (mj). Compare competitive and optimal allocations

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 9

A simple model

Two research areas (patent races), one potential discovery each. Social and private value of discovery z1 < z2. Total M homogenous researchers. Discovery with probability p (mj). Compare competitive and optimal allocations

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 10

Competitive equilibrium and optima

Expected probability of discovery for a researcher in area j: p (mj) /mj Equilibrium m1 + m2 = M and z1 p (m1) m1 = z2 p (m2) m2 Social planner maximizes z1p ( ˜ m1) + z2p ( ˜ m2) so: z1p′ ( ˜ m1) = z2p′ ( ˜ m2) In both cases m2 > m1 Wedge p(m)/m

p′(m) > 1 for concave p (m)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 11

Competitive equilibrium and optima

Expected probability of discovery for a researcher in area j: p (mj) /mj Equilibrium m1 + m2 = M and z1 p (m1) m1 = z2 p (m2) m2 Social planner maximizes z1p ( ˜ m1) + z2p ( ˜ m2) so: z1p′ ( ˜ m1) = z2p′ ( ˜ m2) In both cases m2 > m1 Wedge p(m)/m

p′(m) > 1 for concave p (m)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 12

Competitive equilibrium and optima

Expected probability of discovery for a researcher in area j: p (mj) /mj Equilibrium m1 + m2 = M and z1 p (m1) m1 = z2 p (m2) m2 Social planner maximizes z1p ( ˜ m1) + z2p ( ˜ m2) so: z1p′ ( ˜ m1) = z2p′ ( ˜ m2) In both cases m2 > m1 Wedge p(m)/m

p′(m) > 1 for concave p (m)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 13

Competitive equilibrium and optima

Expected probability of discovery for a researcher in area j: p (mj) /mj Equilibrium m1 + m2 = M and z1 p (m1) m1 = z2 p (m2) m2 Social planner maximizes z1p ( ˜ m1) + z2p ( ˜ m2) so: z1p′ ( ˜ m1) = z2p′ ( ˜ m2) In both cases m2 > m1 Wedge p(m)/m

p′(m) > 1 for concave p (m)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 14

Competitive equilibrium and optima

Expected probability of discovery for a researcher in area j: p (mj) /mj Equilibrium m1 + m2 = M and z1 p (m1) m1 = z2 p (m2) m2 Social planner maximizes z1p ( ˜ m1) + z2p ( ˜ m2) so: z1p′ ( ˜ m1) = z2p′ ( ˜ m2) In both cases m2 > m1 Wedge p(m)/m

p′(m) > 1 for concave p (m)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 15

Comparison

From equilibrium conditions: p (m1) /m1 p′ ( ˜ m1) = p (m2) /m2 p′ ( ˜ m2) Proposition Assume concave p (m) . Then m2 > ˜ m2 if (p(m)/m)

p′(m)

increases with m. Proof. By contradiction. If m2 ≤ ˜ m2 then p (m2) /m2 p′ ( ˜ m2) ≥ p (m2) /m2 p′ (m2) > p (m1) /m1 p′ (m1) ≥ p (m1) /m1 p′ ( ˜ m1) contradicting the equality above.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 16

Comparison

From equilibrium conditions: p (m1) /m1 p′ ( ˜ m1) = p (m2) /m2 p′ ( ˜ m2) Proposition Assume concave p (m) . Then m2 > ˜ m2 if (p(m)/m)

p′(m)

increases with m. Proof. By contradiction. If m2 ≤ ˜ m2 then p (m2) /m2 p′ ( ˜ m2) ≥ p (m2) /m2 p′ (m2) > p (m1) /m1 p′ (m1) ≥ p (m1) /m1 p′ ( ˜ m1) contradicting the equality above.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 17

Comparison

From equilibrium conditions: p (m1) /m1 p′ ( ˜ m1) = p (m2) /m2 p′ ( ˜ m2) Proposition Assume concave p (m) . Then m2 > ˜ m2 if (p(m)/m)

p′(m)

increases with m. Proof. By contradiction. If m2 ≤ ˜ m2 then p (m2) /m2 p′ ( ˜ m2) ≥ p (m2) /m2 p′ (m2) > p (m1) /m1 p′ (m1) ≥ p (m1) /m1 p′ ( ˜ m1) contradicting the equality above.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 18

Generalization

Set of innovations/goods indexed by z with distribution F Welfare/utility: ´ 1

0 zp (m (z)) dF (z)

Resource constraint: ´ 1

0 m (z) dF (z) = M

Equilibrium and optimal conditions same as before. p (m (z)) /m (z) p′ ( ˜ m (z)) = k(constant)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 19

Generalization

Set of innovations/goods indexed by z with distribution F Welfare/utility: ´ 1

0 zp (m (z)) dF (z)

Resource constraint: ´ 1

0 m (z) dF (z) = M

Equilibrium and optimal conditions same as before. p (m (z)) /m (z) p′ ( ˜ m (z)) = k(constant)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 20

Bias

Definition The competitive equilibrium is biased to hot areas iff there exists a z∗ and m (z) < ˜ m (z) for z < z∗ and m (z) > ˜ m (z) for z > z∗. If the opposite inequalities hold, we say it is biased to cold areas.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 21

Biased to hot areas

z m

m(z) m(z) ~ * Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 22

Comparison

p (m (z)) /m (z) p′ ( ˜ m (z)) = k(constant) Proposition The competitive equilibrium is biased to hot (cold) areas if the wedge p(m)/m

p′(m)

is increasing (decreasing) in m. Proof. Both in the equilibrium and optimum m(resp ˜ m) are strictly

increasing. Take z where m (z) = ˜

m (z) . For any z′ > z it follows that p (m (z′)) /m (z′) p′ (m (z′)) > p (m (z)) /m (z) p′ (m (z)) = k. So ˜ m (z′) < m (z) .

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 23

Comparison

p (m (z)) /m (z) p′ ( ˜ m (z)) = k(constant) Proposition The competitive equilibrium is biased to hot (cold) areas if the wedge p(m)/m

p′(m)

is increasing (decreasing) in m. Proof. Both in the equilibrium and optimum m(resp ˜ m) are strictly

increasing. Take z where m (z) = ˜

m (z) . For any z′ > z it follows that p (m (z′)) /m (z′) p′ (m (z′)) > p (m (z)) /m (z) p′ (m (z)) = k. So ˜ m (z′) < m (z) .

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 24

Comparison

p (m (z)) /m (z) p′ ( ˜ m (z)) = k(constant) Proposition The competitive equilibrium is biased to hot (cold) areas if the wedge p(m)/m

p′(m)

is increasing (decreasing) in m. Proof. Both in the equilibrium and optimum m(resp ˜ m) are strictly

increasing. Take z where m (z) = ˜

m (z) . For any z′ > z it follows that p (m (z′)) /m (z′) p′ (m (z′)) > p (m (z)) /m (z) p′ (m (z)) = k. So ˜ m (z′) < m (z) .

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 25

Example: exponential arrivals

Time interval is [0, 1]. Final consumption. No discounting. No redeployment Arrival rate λ per innovator. Independent. p (m) = 1 − exp (−λm) . p (m) /m p′ (m) = (1 − exp (−λm)) mλ exp (−λm) Taking derivative with respect to m and simplifying, same sign as: λ − 1 − exp (−λm) m > 0 Remark λm enter jointly above, so result generalizes to λ (z) increasing in z even if payoffs are independent of z.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 26

Example: exponential arrivals

Time interval is [0, 1]. Final consumption. No discounting. No redeployment Arrival rate λ per innovator. Independent. p (m) = 1 − exp (−λm) . p (m) /m p′ (m) = (1 − exp (−λm)) mλ exp (−λm) Taking derivative with respect to m and simplifying, same sign as: λ − 1 − exp (−λm) m > 0 Remark λm enter jointly above, so result generalizes to λ (z) increasing in z even if payoffs are independent of z.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 27

Example: exponential arrivals

Time interval is [0, 1]. Final consumption. No discounting. No redeployment Arrival rate λ per innovator. Independent. p (m) = 1 − exp (−λm) . p (m) /m p′ (m) = (1 − exp (−λm)) mλ exp (−λm) Taking derivative with respect to m and simplifying, same sign as: λ − 1 − exp (−λm) m > 0 Remark λm enter jointly above, so result generalizes to λ (z) increasing in z even if payoffs are independent of z.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 28

Example: exponential arrivals

Time interval is [0, 1]. Final consumption. No discounting. No redeployment Arrival rate λ per innovator. Independent. p (m) = 1 − exp (−λm) . p (m) /m p′ (m) = (1 − exp (−λm)) mλ exp (−λm) Taking derivative with respect to m and simplifying, same sign as: λ − 1 − exp (−λm) m > 0 Remark λm enter jointly above, so result generalizes to λ (z) increasing in z even if payoffs are independent of z.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 29

Time and discounting - no redeployment

m (z) chosen at time zero line ends with discovery no redeployment after discovery p (t, m) density Welfare U = ˆ U (z, m (z)) dF (z) U (z, m) = ˆ z exp (−rt) p (t, m) dt Can redefine problem letting P (m) = ´ exp (−rt) p (t, m) dt and same propositions apply.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 30

Time and discounting - no redeployment

m (z) chosen at time zero line ends with discovery no redeployment after discovery p (t, m) density Welfare U = ˆ U (z, m (z)) dF (z) U (z, m) = ˆ z exp (−rt) p (t, m) dt Can redefine problem letting P (m) = ´ exp (−rt) p (t, m) dt and same propositions apply.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 31

Time and discounting - no redeployment

m (z) chosen at time zero line ends with discovery no redeployment after discovery p (t, m) density Welfare U = ˆ U (z, m (z)) dF (z) U (z, m) = ˆ z exp (−rt) p (t, m) dt Can redefine problem letting P (m) = ´ exp (−rt) p (t, m) dt and same propositions apply.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 32

Example: Poisson case

P (m) = mλ ˆ exp (− (r + mλ) t) dt = mλ r + mλ Key ratio for proposition: P (m) /m P′ (m) = λ r + mλ/ λr (r + mλ)2 = r + mλ r Again, increasing in m.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 33

Example: Poisson case

P (m) = mλ ˆ exp (− (r + mλ) t) dt = mλ r + mλ Key ratio for proposition: P (m) /m P′ (m) = λ r + mλ/ λr (r + mλ)2 = r + mλ r Again, increasing in m.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 34

Size of distortion: example

Poisson model F (z) = 1 − z−η with η > 1. Pareto z ≥ 1 Closed form, very simple formulas: zo/z = η − 1 2η − 1 1/η Uo/U = η η − 1 2η − 1 η − 1 −1/η Maximal wedge U0/U approximately 1.2 (η = 1.34) and zo/z = 0.3

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 35

Size of distortion: example

Poisson model F (z) = 1 − z−η with η > 1. Pareto z ≥ 1 Closed form, very simple formulas: zo/z = η − 1 2η − 1 1/η Uo/U = η η − 1 2η − 1 η − 1 −1/η Maximal wedge U0/U approximately 1.2 (η = 1.34) and zo/z = 0.3

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 36

Size of distortion: example

Poisson model F (z) = 1 − z−η with η > 1. Pareto z ≥ 1 Closed form, very simple formulas: zo/z = η − 1 2η − 1 1/η Uo/U = η η − 1 2η − 1 η − 1 −1/η Maximal wedge U0/U approximately 1.2 (η = 1.34) and zo/z = 0.3

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 37

Dynamic allocation with redeployment

Poisson model (r, λ) with 2 research lines z1 < z2 Researchers can redeploy immediately after first arrival. Atomistic researchers. Allocation (m1, m2) and mi = M immediately after arrival in

ther area

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 38

Competitive equilibrium

innovator’s expected value from second arrival ˆ vi =

Mλ

r + Mλ

zi/M =

λzi r + Mλ Value functions for initial research lines: v1 (m1) = m1λ r + Mλ (z1/m1 + ˆ v2) + m2λ r + Mλ (ˆ v1) v2 (m2) = m1λ r + Mλ (ˆ v2) + m2λ r + Mλ (z2/m2 + ˆ v1) At interior solution v1 (m1) = v2 (m2). Subtracting both equations: 0 = λ (z1 − z2) < 0

Contradiction. Solution m1 = 0, m2 = M.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 39

Competitive equilibrium

innovator’s expected value from second arrival ˆ vi =

Mλ

r + Mλ

zi/M =

λzi r + Mλ Value functions for initial research lines: v1 (m1) = m1λ r + Mλ (z1/m1 + ˆ v2) + m2λ r + Mλ (ˆ v1) v2 (m2) = m1λ r + Mλ (ˆ v2) + m2λ r + Mλ (z2/m2 + ˆ v1) At interior solution v1 (m1) = v2 (m2). Subtracting both equations: 0 = λ (z1 − z2) < 0

Contradiction. Solution m1 = 0, m2 = M.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 40

Competitive equilibrium

innovator’s expected value from second arrival ˆ vi =

Mλ

r + Mλ

zi/M =

λzi r + Mλ Value functions for initial research lines: v1 (m1) = m1λ r + Mλ (z1/m1 + ˆ v2) + m2λ r + Mλ (ˆ v1) v2 (m2) = m1λ r + Mλ (ˆ v2) + m2λ r + Mλ (z2/m2 + ˆ v1) At interior solution v1 (m1) = v2 (m2). Subtracting both equations: 0 = λ (z1 − z2) < 0

Contradiction. Solution m1 = 0, m2 = M.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 41

Competitive equilibrium

innovator’s expected value from second arrival ˆ vi =

Mλ

r + Mλ

zi/M =

λzi r + Mλ Value functions for initial research lines: v1 (m1) = m1λ r + Mλ (z1/m1 + ˆ v2) + m2λ r + Mλ (ˆ v1) v2 (m2) = m1λ r + Mλ (ˆ v2) + m2λ r + Mλ (z2/m2 + ˆ v1) At interior solution v1 (m1) = v2 (m2). Subtracting both equations: 0 = λ (z1 − z2) < 0

Contradiction. Solution m1 = 0, m2 = M.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 42

Social planner

Value after first arrival ˆ wi =

Mλ

r + Mλ

zi

Initial value W ( ˜ m1, ˜ m2) = ˜ m1λ (z1 + ˆ w2) + ˜ m2λ (z2 + ˆ w1) r + Mλ This problem is linear in ( ˜ m1, ˜ m2) so solution is extreme. Obviously invest first in more productive. Same as equilibrium! Two variations:

1

Redeployment with congestion

2

Costly redeployment

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 43

Social planner

Value after first arrival ˆ wi =

Mλ

r + Mλ

zi

Initial value W ( ˜ m1, ˜ m2) = ˜ m1λ (z1 + ˆ w2) + ˜ m2λ (z2 + ˆ w1) r + Mλ This problem is linear in ( ˜ m1, ˜ m2) so solution is extreme. Obviously invest first in more productive. Same as equilibrium! Two variations:

1

Redeployment with congestion

2

Costly redeployment

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 44

Social planner

Value after first arrival ˆ wi =

Mλ

r + Mλ

zi

Initial value W ( ˜ m1, ˜ m2) = ˜ m1λ (z1 + ˆ w2) + ˜ m2λ (z2 + ˆ w1) r + Mλ This problem is linear in ( ˜ m1, ˜ m2) so solution is extreme. Obviously invest first in more productive. Same as equilibrium! Two variations:

1

Redeployment with congestion

2

Costly redeployment

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 45

Social planner

Value after first arrival ˆ wi =

Mλ

r + Mλ

zi

Initial value W ( ˜ m1, ˜ m2) = ˜ m1λ (z1 + ˆ w2) + ˜ m2λ (z2 + ˆ w1) r + Mλ This problem is linear in ( ˜ m1, ˜ m2) so solution is extreme. Obviously invest first in more productive. Same as equilibrium! Two variations:

1

Redeployment with congestion

2

Costly redeployment

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 46

Redeployment with congestion

Same as before, but λ (m) decreasing and λ (m) m concave Equilibrium condition: λ (m1) z1 = λ (m2) z2 Social planner maximizes W ( ˜ m1, ˜ m2) = ˜ m1λ ( ˜ m1) (z1 + ˆ w2) + ˜ m2λ ( ˜ m2) (z2 + ˆ w1) r + Mλ First order condition:

λ ( ˜

m1) + ˜ m1λ′ ( ˜ m1)

(z1 + ˆ

w2) =

λ ( ˜

m2) + ˜ m2λ′ ( ˜ m2)

(z2 + ˆ

w1)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 47

Redeployment with congestion

Same as before, but λ (m) decreasing and λ (m) m concave Equilibrium condition: λ (m1) z1 = λ (m2) z2 Social planner maximizes W ( ˜ m1, ˜ m2) = ˜ m1λ ( ˜ m1) (z1 + ˆ w2) + ˜ m2λ ( ˜ m2) (z2 + ˆ w1) r + Mλ First order condition:

λ ( ˜

m1) + ˜ m1λ′ ( ˜ m1)

(z1 + ˆ

w2) =

λ ( ˜

m2) + ˜ m2λ′ ( ˜ m2)

(z2 + ˆ

w1)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 48

Redeployment with congestion

Same as before, but λ (m) decreasing and λ (m) m concave Equilibrium condition: λ (m1) z1 = λ (m2) z2 Social planner maximizes W ( ˜ m1, ˜ m2) = ˜ m1λ ( ˜ m1) (z1 + ˆ w2) + ˜ m2λ ( ˜ m2) (z2 + ˆ w1) r + Mλ First order condition:

λ ( ˜

m1) + ˜ m1λ′ ( ˜ m1)

(z1 + ˆ

w2) =

λ ( ˜

m2) + ˜ m2λ′ ( ˜ m2)

(z2 + ˆ

w1)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 49

Comparison

λ (m1) z1 = λ (m2) z2

λ ( ˜

m1) + ˜ m1λ′ ( ˜ m1)

(z1 + ˆ

w2) =

λ ( ˜

m2) + ˜ m2λ′ ( ˜ m2)

(z2 + ˆ

w1) Two differences:

1 total continuation (option) value effect:

ˆ w2 > ˆ w1 ⇒ z2 + ˆ w1 z1 + ˆ w2 < z2 z1 = ⇒Excessive entry to area 2

2 Congestion wedge:

λ (m) λ (m) + mλ′ (m) = 1 1 − e (λ, m) = ⇒Excessive entry to area 2 when elasticity increasing in m. Constant elasticity: still excessive entry because of first effect.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 50

Comparison

λ (m1) z1 = λ (m2) z2

λ ( ˜

m1) + ˜ m1λ′ ( ˜ m1)

(z1 + ˆ

w2) =

λ ( ˜

m2) + ˜ m2λ′ ( ˜ m2)

(z2 + ˆ

w1) Two differences:

1 total continuation (option) value effect:

ˆ w2 > ˆ w1 ⇒ z2 + ˆ w1 z1 + ˆ w2 < z2 z1 = ⇒Excessive entry to area 2

2 Congestion wedge:

λ (m) λ (m) + mλ′ (m) = 1 1 − e (λ, m) = ⇒Excessive entry to area 2 when elasticity increasing in m. Constant elasticity: still excessive entry because of first effect.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 51

Comparison

λ (m1) z1 = λ (m2) z2

λ ( ˜

m1) + ˜ m1λ′ ( ˜ m1)

(z1 + ˆ

w2) =

λ ( ˜

m2) + ˜ m2λ′ ( ˜ m2)

(z2 + ˆ

w1) Two differences:

1 total continuation (option) value effect:

ˆ w2 > ˆ w1 ⇒ z2 + ˆ w1 z1 + ˆ w2 < z2 z1 = ⇒Excessive entry to area 2

2 Congestion wedge:

λ (m) λ (m) + mλ′ (m) = 1 1 − e (λ, m) = ⇒Excessive entry to area 2 when elasticity increasing in m. Constant elasticity: still excessive entry because of first effect.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 52

Comparison

λ (m1) z1 = λ (m2) z2

λ ( ˜

m1) + ˜ m1λ′ ( ˜ m1)

(z1 + ˆ

w2) =

λ ( ˜

m2) + ˜ m2λ′ ( ˜ m2)

(z2 + ˆ

w1) Two differences:

1 total continuation (option) value effect:

ˆ w2 > ˆ w1 ⇒ z2 + ˆ w1 z1 + ˆ w2 < z2 z1 = ⇒Excessive entry to area 2

2 Congestion wedge:

λ (m) λ (m) + mλ′ (m) = 1 1 − e (λ, m) = ⇒Excessive entry to area 2 when elasticity increasing in m. Constant elasticity: still excessive entry because of first effect.

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 53

Costly redeployment

Suppose there is a cost c per researcher redeployed. Equilibrium redeploy fully iff c ≤ ˆ vi = λzi/ (r + Mλ) Planner’s threshold is lower Assume both hold z1 − z0 − c (m1 − m0) = (z1 − z0)

1 −

λM r + λM

− 2c ( ˜

m1 − ˜ m0) = Excessive entry to hot areas for two reasons:

1

Option value effect

2

Negative switching cost externality (mg cost of redeployment > average cost)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 54

Costly redeployment

Suppose there is a cost c per researcher redeployed. Equilibrium redeploy fully iff c ≤ ˆ vi = λzi/ (r + Mλ) Planner’s threshold is lower Assume both hold z1 − z0 − c (m1 − m0) = (z1 − z0)

1 −

λM r + λM

− 2c ( ˜

m1 − ˜ m0) = Excessive entry to hot areas for two reasons:

1

Option value effect

2

Negative switching cost externality (mg cost of redeployment > average cost)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 55

Costly redeployment

Suppose there is a cost c per researcher redeployed. Equilibrium redeploy fully iff c ≤ ˆ vi = λzi/ (r + Mλ) Planner’s threshold is lower Assume both hold z1 − z0 − c (m1 − m0) = (z1 − z0)

1 −

λM r + λM

− 2c ( ˜

m1 − ˜ m0) = Excessive entry to hot areas for two reasons:

1

Option value effect

2

Negative switching cost externality (mg cost of redeployment > average cost)

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 56

Extensions

Multiple products (non linear utility) Multiple possible innovations for each product class Smaller switching costs within product class than between

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 57

Persistence in the data

Definition Patent p′ succeeds patent p if it has later approval date and at least one common author. Consider all successors of patent p within a period What fraction of successors of p share a common class with p? After t years Persistence 1 75 % 2 74 % 3 72 % 4 70 % 5 68 %

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 58

Persistence in the data

Definition Patent p′ succeeds patent p if it has later approval date and at least one common author. Consider all successors of patent p within a period What fraction of successors of p share a common class with p? After t years Persistence 1 75 % 2 74 % 3 72 % 4 70 % 5 68 %

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 59

Persistence in the data

Definition Patent p′ succeeds patent p if it has later approval date and at least one common author. Consider all successors of patent p within a period What fraction of successors of p share a common class with p? After t years Persistence 1 75 % 2 74 % 3 72 % 4 70 % 5 68 %

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 60

Final remarks

Condition for excess entry into hot patent races Satisfied in Poisson case With redeployment analysis changes

no immediate externality but external effect on future values and switching costs/congestion

Option value effect: Planner’s valuation of research lines in general different than private (less disperse) Also internalizes costs of switching/congestion

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 61

Final remarks

Condition for excess entry into hot patent races Satisfied in Poisson case With redeployment analysis changes

no immediate externality but external effect on future values and switching costs/congestion

Option value effect: Planner’s valuation of research lines in general different than private (less disperse) Also internalizes costs of switching/congestion

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 62

Final remarks

Condition for excess entry into hot patent races Satisfied in Poisson case With redeployment analysis changes

no immediate externality but external effect on future values and switching costs/congestion

Option value effect: Planner’s valuation of research lines in general different than private (less disperse) Also internalizes costs of switching/congestion

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation

SLIDE 63

Final remarks

Condition for excess entry into hot patent races Satisfied in Poisson case With redeployment analysis changes

no immediate externality but external effect on future values and switching costs/congestion

Option value effect: Planner’s valuation of research lines in general different than private (less disperse) Also internalizes costs of switching/congestion

Hugo A. Hopenhayn, Francesco Squintani On the Direction of Innovation