Diffusion of Innovation

Question 1

What are stylised fact on the diffusion of innovation?

Answer 1

• Diffusion is slow (“slower than expected”)
• Diffusion path is “sigmoid” (S-shaped, diffusion starts high, and the slows down)
• Diffusion speed varies across:
  
  • Innovations
  • Markets (industries, regions)

Question 2

What types of models are there that can explain the stylized facts on diffusion of innovation?

Answer 2

• Information-based models
  1. “Critical Mass” information
  2. Network models
• Incentive-based models
  1. “threshold models”: basic microeconomics of adoption of innovation
  2. Decreasing returns form adoption and strategic interaction

Question 3

Talk about Critical Mass Information-based models

Answer 3

Earliest models: date back to US agricultural studies in the 1930s.

Key assumption: innovation is immediately superior to old tech for all potential adopters.
Questions: why not adopted immediately?
Answer: because not all potential adopters know about its existence/performance.

What diffuses in reality is not the technology itself, but the information on the new technology.

They propose classification of information sources:
• Internal to the adopters (acquired through experience and transmitted by word of mouth to community)
• External (from universities, not recognised by farmers community

Basic idea of the models:
Shape of curve reveals the dominant information sources of the diffusion model.
Possible combination of sources = Complementary diffusion curves

Position of the inflexion point (distance from origin) reflects the balance between internal and external information. The closed to the origin, the more external sources dominate.

Question 4

Talk about Internal-information sourced information based models

Answer 4

EPIDEMIC MODELS:

• Word of mouth info dissemination process
• Probability of catching the disease increases with the n. of infected people
• Probability of new infection case increases with n. of not yet infected people.

[Equation] 
Nt = number of infected people 
N* = size of population
Beta = parameter that determines the diffusion speed
Alpha = start parameter 

Name of this curve: logistic curve (S-shaped) Symmetric path

Question 5

Talk about External-source information based models

Answer 5

Continuous info provision by external agent: suppliers, public institutions etc.
- Probability of new infection case still increases with number of not yet infected people
BUT probability of catching the disease independent from n° of already infected people

[Equation]
Name of curve: modified exponential: positively skewed path, No inflection point.

Question 6

Talk about Network Information based models

Answer 6

Society where ties are dense, distance between nodes is smaller, hence beta will be higher.

Social network and the adoption order:

• Individual adoption speed as a function of distance from central actors.
• Diffusion speed as function of network density

Individual adoption speed = position of individual in roger’s theory
Total diffusion speed = value of beta

Roger’s Theory (Innovators, Early adopters, Early majority, Late majority, laggards)

Question 7

How did Coleman study the Network Theory of Influence?

Answer 7

It wanted to measure diffusion of innovation as a function to the innovation’s technological strength

• Diffusion of a new antibiotic (tetracycline)
• Doctors were asked to name other doctors to investigate the connection of the social network.

1. Questionnaire contents:
   a. Innovation Awareness
   b. Sociometric Choice (Advisors, Discussion Partners, Friends)
   c. Data on contacts with the medical profession (what medical school went to? What year did you graduate?)
   d. Data on respondents’ medical practice (Length of residence in the community, Science/Profession vs Patient Orientations, etc)
2. Adoption data: date of when the doctors prescribe the medicine for the first time, not from the questionnaire, but from the pharmacies prescription records.

Adoption delay = t_when medicine available – t_first prescription by doctor

Intuitive evidence from graphs:
Professional doctors want to test the novelty, they are ahead in the diffusion process. But the shape of the curve is the same, so diffusion happens at the same speed.

We observe that initially the diffusion levels are very similar, but the doctors with most friends (/nominations) reach 90% adoption very fast with respect of the others.

Statistical evidence: with simultaneity index:
(r - o)/r
r = avg delay interval for random pair of doctors
o = avg delay interval for tied pairs of doctors

If Simultaneity index is high, people are sensitive to connection choices, when close to zero means that people are indifferent to connection’s choice.

Findings:
At the beginning of the diffusion process, when information on the new technology is scarce, advisor-ship and discussion network is very important, and it tends to decline over time.

Question 8

What are the economic’s critique to information-based models?

Answer 8

1. Excessive simplification of the diffusion process.
   a. Only two actors in the play: innovation and adopters.
   b. Both actors don’t change over the different periods.
2. Lack of economics microeconomic foundations

Question 9

Talk about Early Threshold model of Adoption (Incentive-based models)

Answer 9

• Less (no) emphasis on information:

1. Diffusion takes time not because of information problems, but because innovation may be technologically superior, but not economically superior.
2. No information dissemination, but a process during which the new technology and the adoption environment change and make adoption profitable.

At any time t, all firms for which adoption is profitable have adopted.
Non-adopters are not ill informed, they are waiting for the tech to become profitable.

Question 10

What is the first Early Threshold Incentive-based model of adoption?

Answer 10

1966 Paul David
“The mechanization of reaping in Ante Bellum Midwest”

Key Assumptions:

1. Input-saving device. ∆a = savings on labor input per acre of land
2. Indivisibility: the reaper costs p per year –> long term loan at rate r.
3. Size heterogeneity, farm’s land extension S_i changes across firms.
4. Price of corn p is not affected by reaper’s diffusion.
5. Wages w are not affected by reaper’s diffusion.

Adoption benefits from firm i, per year = w ∆a Si
Adoption costs are same for any firm, per year = rp

Adoption condition:
w ∆a Si > rp
Si > Scr –> Critical size
Scr = rp/w∆a

Results:

1. The reaper’s diffusion was driven by the steady increases in wages in XIX century US –> exogenous drive to diffusion
2. Diffusion takes time because firms are heterogeneous –> at any time t only some firms find adoptions profitable
3. Diffusion path is sigmoid as long as heterogeneity source distribution is bell shaped and diffusion speed constant.

Question 11

How does Learning by Doing affect Paul David’s threshold Incentive based model?

Answer 11

• The equation for critical size contains two variables affected by events on the supply side of technology market: p and ∆a
• Learning by doing on the supply side may turn them into the ENDOGENOUS DRIVE to diffusion

The more diffusion –> the more cumulated experience –> the lower marginal cost –> decline of price –> drives down critical size threshold for diffusion –> more diffusion –> repeat cycle

More diffusion –> suppliers cumulate experience –> incremental innovation and improve in performance ∆a –> decrease in critical size threshold –> more diffusion

Diffusion speed now depends on:

• Supplier’s learning speed
• supply side market structure –> speed at which suppliers transfer their LbD onto prices/performance of the innovation (monopoly = slow)

Two theoretical problems that slow down diffusion:

- Expectations. "wait and see"
- Decreasing returns from adoption.    So far we have assumed that the price good produced doesn’t change. But in reality, early adopters make it less convenient for the later adopters to adopt