An Exploration of Technology Diffusion

Diego Comin &Brat Hobijn (2010)

Technology Diffusion

Settings:

• Technology（技术）• Vintages（生产方式） =production methods

• A technology= a group of vintages producing a particular intermediate good (homogeneous)

• Vintage specific capital

Settings:

• Capital goods suppliers: monopolistic make the adoption decision

• Workers: choose which vintages to use

Settings:

• Indexes

Worker’ Technology Choice

• Production function of an intermediate good with vintage .

• Worker’s decision: PMP

Worker’ Technology Choice

• What we can get from PMP?

• Quantity of K, given vintage。• Which vintage to choose?

Worker’ Technology Choice

• Some transformations

• Choose vintage v that satisfies

YPY

Worker’ Technology Choice

• Shocks should satisfy:

• Suppose that shocks are identically distributed:

Worker’ Technology Choice

• The probability:

• The probability that worker will choose vintage v as

Worker’ Technology Choice

• Aggregation• Number of workers using vintage v

• Corresponding output level

Worker’ Technology Choice

• Output produced with a particular technology type

• Three sources

Worker’ Technology Choice

• Review now• What are all these about?

• Worker’s decision: PMP?• Transformation?

• 为什么没有加其他的均衡条件就多得出来一个结果？？？

Capital good supplier

• Settings about technology:• The productivity embodied in vintage v is

• Adoption lag

• Vintages available for production

Capital good supplier

• Produce a particular vintage of capital good at the unit production cost Q.

• Q is the same across vintages among the same technology and Z distinguishes them.

Capital good supplier

• Producers’ choice of price and quantity

s.t.

• Why (11)?__Equilibrium in workers’ choice?

Capital good supplier

• Price:

• Market value:

Capital good supplier

• Critical assumption:• The cost of adoption

• (Without this the adoption will be infinitely large. Then, once the vintage is invented, it will be adopted by any supplier. This is also the source of monopolistic power)

Capital good supplier

• Equilibrium：

• Anything lost?

Free entry condition

• Zero profit condition?(Why is this necessary?)• Simplification of (11)

• Competitive wage equalizes the average profit per worker

Free entry condition

• The price level

• Aggregation

Free entry condition

• Aggregation

where,

Review of the Model

• Workers: PMP-quantity and quality

• Capital supplier: Adoption

Equlibrium

• Adoption lag

• Technology choice in aggregation level? Why?

Embodiment & Variety

• The endogenous adoption decisions determine the growth rate of productivity embodied in the technology through two channels.(2008)

• Embodiment effect: suppliers

• Variety effect: workers

Embodiment & Variety

• Measures of technology diffusion

• Embodiment & Variety

Several Questions

• Why introduce workers choice of vintages into the model?

• It seems that it has nothing to do with the adoption question except in the deciding of R. (18)

• Does it change anything if we remove this part?

Several Questions

• Why this the adoption lag is endogenous? Which assumption made it?

• And what are the situation in those previous papers?

Empirical Study

• Linearizing_ Taylor Expansion （ Talyor Series）