An Exploration of Technology Diffusion

TLDR: In this article, the authors developed and estimated a model where technology diffusion depends on the level of productivity embodied in capital and where this is, in turn, determined by two key mechanisms: the rate at which the quality embodied in new technology vintages increases (embodiment) and the gains from varieties induced by the introduction of new Vintages (variety).

Abstract: We develop and estimate a model where technology diffusion depends on the level of productivity embodied in capital and where this is, in turn, determined by two key mechanisms: the rate at which the quality embodied in new technology vintages increases (embodiment) and the gains from varieties induced by the introduction of new vintages (variety). In our model, these two effects are related to technology adoption decisions taken at two different levels. The capital goods suppliers%u2019 decisions of when to adopt a given vintage determines the embodiment margin. The workers%u2019 decisions of which of the adopted vintages to use in production determines the variety margin.Estimation of our model for a sample of 19 technologies, 21 countries, and the period 1870-1998 reveals that embodied productivity growth is large for many of the technologies in our sample. On average, increases in the variety of vintages available is a more important source of growth than the increases in the embodiment margin. There is, however, substantial heterogeneity across technologies. Where adoption lags matter, they are largely determined by lack of educational attainment and lack of trade openness.

Figures

Table 7: Descriptive statistics of estimated level of Z due to embodiment and variety mechanisms

Table 2: Explanatory variables

Figure 4: Actual and fitted adoption paths for electricity

Table 3: Sample size and estimated coefficients (Transportation)

Table 6: Growth rate of the productivity embodied in each technology type and its decomposition

Figure 3: Actual and fitted adoption paths for personal computers

Full text

NBER WORKING PAPER SERIES
AN EXPLORATION OF TECHNOLOGY DIFFUSION
Diego Comin
Bart Hobijn
Working Paper 12314
http://www.nber.org/papers/w12314
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
June 2006
A previous version of this paper was circulated under the name “Neoclassical Growth and the Adoption of
Technologies”. We would like to thank Kristy Mayer, Bess Rabin and Rebecca Sela for their great research
assistance. We have benefitted a lot from comments and suggestions by Richard Rogerson and two
anonymous referees, Jess Benhabib, John Fernald, Simon Gilchrist, Peter Howitt, Boyan Jovanovic, Sam
Kortum, John Leahy, and Peter Rousseau, as well as seminar participants at ECB/IMOP, Harvard, the NBER,
NYU, the SED, and UC Santa Cruz. We also would like to thank the NSF (Grant # SES-0517910) and the
C.V. Starr Center for Applied Economics for their financial assistance. Corresponding author: Bart Hobijn,
Federal Reserve Bank of New York, Research and Statistics Group, 33 Liberty Street 3rd floor, New York
City, NY 10045, U.S.A.. E-mail: bart.hobijn@ny.frb.org. The views expressed in this paper solely reflect
those of the authors and not necessarily those of the National Bureau of Economic Research, the Federal
Reserve Bank of New York, nor those of the Federal Reserve System as a whole. The views expressed
herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic
Research.
©2006 by Diego Comin and Bart Hobijn. All rights reserved. Short sections of text, not to exceed two
paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given
to the source.

An Exploration of Technology Diffusion
Diego Comin and Bart Hobiijn
NBER Working Paper No. 12314
June 2006
JEL No. E13, O14, O33, O41
ABSTRACT
We develop and estimate a model where technology diffusion depends on the level of
productivity embodied in capital and where this is, in turn, determined by two key mechanisms: the
rate at which the quality embodied in new technology vintages increases (embodiment) and the gains
from varieties induced by the introduction of new vintages (variety). In our model, these two effects
are related to technology adoption decisions taken at two different levels. The capital goods
suppliers’ decisions of when to adopt a given vintage determines the embodiment margin. The
workers’ decisions of which of the adopted vintages to use in production determines the variety
margin.
Estimation of our model for a sample of 19 technologies, 21 countries, and the period
1870-1998 reveals that embodied productivity growth is large for many of the technologies in our
sample. On average, increases in the variety of vintages available is a more important source of
growth than the increases in the embodiment margin. There is, however, substantial heterogeneity
across technologies. Where adoption lags matter, they are largely determined by lack of educational
attainment and lack of trade openness.
Diego A. Comin
Department of Economics
New York University
269 Mercer Street, 725
New York, NY 10003
and NBER
diego.comin@nyu.edu
Bart Hobijn
Federal Reserve Bank of New York
Research and Statistics Group
33 Liberty Street, 3
rd
Floor
New York, NY 10045
bart.hobikn@ny.frb.org

1Introduction
Most cross-country differences in levels of output per capita are due to differences in the level of total
factor productivity (TFP), rather than differences in the levels of factor inputs.
1
These cross-country TFP
disparities can be divided in to two parts: productivity differences from countries using different ranges of
technologies and different levels of efficiency with which technologies are operated.
In this paper, w e assess the relative importance of the economic mechanisms that influence the range
of technologies a coun t ry uses. In particular, we answer the following two questions: ‘What are the key
economic aspects that differ across technologies that influence the speed of diffusion?’ and ‘What are the
key cross-count ry differences in endowments, institutions, and policies that impinge on technology diffusion?’
We answer these questions by developing and estimating a model of one of the key determinants of
technology diffusion, the lev el of productivity embodied in the capital goods associated with a technology.
In our model, agents adopt tec hnologies at two different levels. First, a capital good producer decides whether
to incur the fixed cost of adopting a capital good that embodies a new vintage of the particular technology
(e.g. t he Pentium as a new vintage of microprocessor). As in Parente and Prescott (1994), the size of the
adoption costs determine the adoption lag at the country level.
In addition, each worker that uses a given technology (e.g. microprocessors) decides which of the vintages,
associated with this technology and available in the country, to use in production (i.e. Pentium vs. Intel
IV). Heterogeneity across workers in the productivity of each vintage introduces a smooth adoption of new
vintages at the micro level.
These adoption decisions endogenously determine the level and evolution of productivity embodied in
the technology. The introduction of vintages with higher embodied productivity raises the overall level of
productivit y. It also increases the range of vintages available for production. As this range increases, workers
obtain a gain from variety, which also raises the average level of productivity embodied in capital.
When the number of available vintages is very small, an increase in the number of varieties has a relatively
large effect on embodied productivity. As this n um ber increases, the productivity gains from such an increase
decline. This leads to curvature in the embodied productivity level.
This curvature in embodied productivity translates into similar non-linearities in the evolution of available
measures of technology, such as the number of units of capital that embody a given technology or the output
produced with these units. For each of these technologies, this allows us to estimate the growth rate of
productivity embodied in new vintages, as well as the determinants of the costs of adopting new vin tages
that generate adoption lags.
We estimate the model taking advantage of the historical data set on technology measures from Comin
and Hobijn (2004). This data set cov ers 19 types of technologies, for 21 industrialized countries, ov er the
1
Klenow and Rodr´ıquez-Clare (1997), Hall and Jones (1999), and Jerzmanowski (2004).
2

period 1870 - 1998.
To explore the determinants of adoption lags, we assume that the costs of adopting new vintages are
functions of the following variables: human capital, in line with Nelson and Phelps (1966) and Chari and
Hopenhayn (1991), the degree of trade openness, as emphasized by Coe and Helpman (1995) and Holmes
and Schmitz (2001), the degree of democracy, as proposed by Hall and Jones (1999) and Acemoglu, Johnson,
and Robinson (2005), as well as income per capita as a proxy for relative factor endowments, consisten t with
Basu and Weil’s (1998) appropriate technology hypothesis.
We find that for several of our technologies, such as computers, robots, planes, electricity and steel, new
vintages embody significantly more productivity than old vintages. In terms of the determinants of the
adoption lags, we find that technologies such as PC’s, robots and electricity are complementary to hu man
capital in the sense that human capital reduces the adoption lags for these technologies. Trade openness
tends to reduce the adoption lags of transportation technologies, such as passenger and cargo aviation as
well as sail and motor shipping. Other factors, such as the degree of democracy, do not seem to be very
importan t for explaining the variation in the range of vintages used, but might still affect the intensity with
whic h technologies are used.
Our model of endogenous embodied productivity generates a diffusionpaththatfits the data quite closely
for most of the technologies in our sample. The R
2
sarehigh,evenafterfiltering out the exogenous trends,
coun t ry fixed effects and interest rate effects that the technology adoption mechanism in our model does not
accoun t for.
We find that the average growth rate of embodied productivity over the periods studied is large for
most of the technologies in our sample. The relative importance of the two adoption margins, however,
varies substantially across technologies. This heterogeneit y in the results emphasizes the importance of the
multi-technology character of our analysis. On average, the increase in the number of available varieties is
a more important source of growth in embodied productivity than the actual productivity embodied in the
best adopted vintages.
This paper is related to various strands of the literature. It is closely related to the empirical diffusion
literature (Griliches 1957, Mansfield, 1961, Gort and Klepper 1982, among others) which has estimated
logistic diffusion curves for a relatively small number of technologies and countries. Our model is consistent
with this micro evidence because the work e rs adoption decisions generate a (quasi) logistic diffusion pattern
at the micro level.
The logistic diffusion curve in our model differs from that in the empirical literature because it results
from the optimizing behavior of agents. There are two other important factors that differentiate our paper
from this literature. First, our approach only requires the use of widely available aggregate data to estimate
the diffusion processes. Therefore, our analysis covers more technologies and countries than if we had to
3

rely on scarce micro data.
2
Second, b y embedding the micro adoption decisions in a macro model, we can
explore their aggregate implications.
This paper is also related to the macro technology adoption literature (i.e. Parente and Prescott 1994,
and Basu and Weil, 1998). Contrary to our model, these studies are not based on models of adoption that
are sufficiently rich to be brought to the data. As a result, empirical analyses conducted with these models
are restricted to calibration exercises.
The rest of the paper is organized as follows. Next we present the model and derive analytical expressions
for the diffusion curves that we estimate. Section 3 contains the empirical analysis. Section 4 summarizes
our findings and presents directions for future research. For the sake of brevity, many of the mathematical
derivations are relegated to the Appendix.
2Model
The aim of our model is to explain the paths of aggregate measures of capital and output associated with
particular types of embodied technologies. For this purpose, we develop a model of endogenous technology
in whic h adoption occurs at two different levels. First, capital goods producers determine when to adopt
and start producing capital goods that embody a given level of productivit y. Second, workers decide which
of the adopted capital goods to use in production.
The model incorporates the following notion of technology. Each type of technology is used to produce a
particular good or service. For example, sail ships are used to provide sail shipping services. Of course, not
all sail ships are the same. Some sail ships, like clippers, belong to a more advanced technological vintage
than others, like schooners. Goods or services produced with similar technologies are aggregated into sectoral
output. For example, merchant shipping services are the result of the shipments provided with sail ships, as
well as steam and motor ships.
In terms of notation, w orkers are indexed by l, tec hnology vintages are inxed by v, technology types are
indexed by τ, sectors are indexed by s, and time is indexed by t. For example, Y
(v)
l,t
denotes the output
worker l produces using technology vintage v at time t, Y
(τ)
v,t
is the level of output of technology vintage v
of technology type τ , Y
(s)
τ ,t
is the output produced with tec hnology type τ in sector s,andY
s,t
is the output
of sector s, Y
t
is aggregate output (i.e. GDP).
We structure the presentation of the model as follows. First, we set up and solve the technology choice
problem of the worker. Then we analyze the adoption decision of the capital goods suppliers. Next we
2
Another strand of the literature has also used more aggregate measures of diffusion to explore the determinants of adoption
lags (Saxonhouse and Wright, 2000, and Caselli and Coleman, 2001) or the shape of technology diffusion (Manuelli and Seshadri,
2004) for one technology. Our paper differs from these three studies in that (i) it develops a different approach to modeling and
estimating the forces that shape technology diffusion and (ii) it covers a wider range of technologies and countries.
4

Frequently asked questions

Q1. What have the authors contributed in "Nber working paper series an exploration of technology diffusion" ?

Comin et al. this paper developed and estimated a model where technology diffusion depends on the level of productivity embodied in capital and where this is, in turn, determined by two key mechanisms: the rate at which the quality embodied in new technology vintages increases ( embodiment ) and the gains from varieties induced by the introduction of new Vintages ( variety ). 

Q2. What future works have the authors mentioned in the paper "Nber working paper series an exploration of technology diffusion" ?

The line of research developed in this paper leaves several doors open for future research. 19 Finally, it will be interesting to extend this analysis to other technologies and countries. 18One potential difficulty of pursuing this route at this point is the quality of sectoral TFP data. 

Q3. What are the main determinants that the authors allow for in the vector with explanatory variables?

The main determinants that the authors allow for in the vector with explanatory variables, xτ ,t, can be classified into four groups: (i) human capital, (ii) openness and trade, (iii) quality of institutions and (iv) relative level of overall advancement. 

Q4. What are the determinants of the adoption lags?

In terms of the determinants of the adoption lags, the authors find that technologies such as PC’s, robots and electricity are complementary to human capital in the sense that human capital reduces the adoption lags for these technologies. 

Q5. Why is the speed of diffusion fast for some technologies?

for others, such as electricity and robots, the speed of diffusion has been fast both because of the rapid productivity growth embodied in new vintages and because of the increase in the number of varieties. 

Q6. What is the common reason for the differences in levels of output per capita?

bart.hobikn@ny.frb.orgMost cross-country differences in levels of output per capita are due to differences in the level of total factor productivity (TFP), rather than differences in the levels of factor inputs. 

Q7. What is the effect of trade openness on the adoption of new technologies?

Trade openness tends to reduce the adoption lags of transportation technologies, such as passenger and cargo aviation as well as sail and motor shipping. 

Q8. What is the effect of secondary enrollment on the quality of the adopted vintage?

The marginal effect of secondary enrollment is that a 1 percent increase in secondary enrollment reduces adoption lags such that the quality of the best adopted vintage increases by 0.45%. 

Q9. How do the authors avoid the problem with D (s) ,t and ?

The authors avoid the problem withD (s) τ ,t and γ (s) τ by linearizing (36) around the immediate adoption path in which D (s) τ ,t = 0 for all t. 

Q10. What is the average detrended R2 for each technology type?

For those technologies with fewer observations, like textiles, steel and robots, the authors obtain a slightly higher detrended R2 and those technologies with a bad fit of the curvature, like radios and TV’s, have a detrended R2 lower than0.5. 

Q11. Why does the logistic diffusion curve differ from the empirical literature?

The logistic diffusion curve in their model differs from that in the empirical literature because it results from the optimizing behavior of agents. 

Q12. What is the number of workers that use vintage v?

The number ofworkers that use vintage v is then given byL (τ) v,t = S (τ) v,t L (s) τ ,t (9)The corresponding level of output produced with vintage v isY (τ) v,t = CL (s) τ ,t ³ Y (τ) v,t ´³ S (τ) v,t ´1−µ (10)where the constant C depends only on µ. 

Q13. What is the effect of new vintages on productivity?

The authors find that for several of their technologies, such as computers, robots, planes, electricity and steel, new vintages embody significantly more productivity than old vintages. 

Q14. what is the level of output that worker l would produce using vintage v?

Let the level of output that worker l would produce using vintage v at time t equalY (v) l,t = ³ Z(τ)v e ε (v) l,t ´1−α ³ K (v) l,t ´α , where 0 < α < 1 (1)where K (v) l,t is the number of units of the vintage specific capital good, Z (τ) v is the level of productivity embodied in capital of vintage v and ε (v) l,t is an idiosyncratic, time, worker, and vintage specific productivity shock. 

Q15. What factors might affect the intensity with which technologies are used?

Other factors, such as the degree of democracy, might still affect the intensity with which technologies are used, but do not seem to be very important in explaining which technology vintages are being used. 

Q16. what is the probability that vintage v satisfies?

The probability that vintage v satisfies (4) and that the associated productivity shock equals ε (v) l,t isπ ³ v, ε(v) l,t´ = 1µ exp" − ε (v) l,tµ − expà − ε (v) l,tµ !Z v0∈V (τ)t exp à − y (τ) v,t − y (τ) v0,t µ ! dv0 # (7)Because there is a continuum of vintages, this is not a proper probability but can better be interpreted as their continuous vintage approximation to the finite number of vintages case.