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Инновации, имитации
и рост
Александр Тонис, РЭШ, Москва
Эволюция распределения стран
по уровню развития
2
Чем объяснить отсутствие сходимости?
• Неоклассические модели роста не дают
объяснения: по накапливаемым
факторам есть тенденция к сближению, а
по TFP – нет (Easterly and Levine, 2000;
Feyrer, 2003)
• Современные модели роста: эндогенный
рост, шумпетерианская концепция
созидательного разрушения.
3
Шумпетерианская динамика
(Aghion and Howitt, 1988,1998)
• y(x) = Axα , x + n = L
(x – фактор пр-ва, n – исследования)
• Пуассоновский поток новых технологий (At+1 = γAt);
интенсивность их создания: λn
• Автор новой технологии становится монополистом (до
прихода следующей) – созид. разрушение
• Ожидаемый выигрыш монополиста:
Vt+1 = πt+1 dτ + (1 – λn t+1 dτ) e – r dτ Vt+1 =>
Vt+1 = πt+1 / (r + λn t+1)
• Монопольная прибыль:
πt = max xt (y' (xt) – wt+1) xt => xt = (α2At / wt)1/(1 – α) ;
πt = (1/ α – 1)wt xt
• Безразличие при выборе между работой на производстве
и в исследованиях: wt = y'(x) = λV t+1
4
Равновесие и общ. оптимум
• Стационарное равновесие (n = const):
1 = λ γ (1/ α – 1) (L – n) / (r + λn)
• Максимум обществ. благосостояния
W = A0 (L – n)α dτ + (1 – λn dτ) e –r dτ W + λn dτ e –r dτ γW
W = A0 (L – n)α / (r – λ n (γ – 1)) → maxn
1 = λ (γ – 1) (1/α) (L – n) / (r – λ n (γ – 1))
• + стимул к инновациям
– автор инновации присваивает лишь часть
общественного выигрыша (монополия + неучет
межвременных экстерналий – business stealing)
• Целесообразно ли распространение технологий?5
Инновации и имитации
• Долгосрочный рост основан на инновациях и
имитациях
• Концепция “преимущества отсталости” (Gerschenkron,
1962).
• Догоняющее развитие:
– заимствование технологий
– крупные инвестиции
– “неконкурентные” решения: крупные компании,
долгосрочные соглашения между компаниями и
банками (и интегрированные структуры),
вмешательство государства (пром. политика)
• Имитации дешевле инноваций => сходимость (Barro
and Sala-i-Martin, 1995).
6
Инновации и имитации на разных
стадиях развития
• Развитые страны совершают инновации;
развивающиеся – заимствуют:
– отбор менеджеров по способности к инновациям или
инвестициям (Acemoglu et al, 2006)
– вертикальная интеграция или малые инновационные
фирмы (Acemoglu et al, 2003)
– технологические и институциональные барьеры,
препятствующие инновациям (Howitt and MayerFoulkes, 2002)
• Темп роста зависит от положения среди остальных =>
сложная динамика (Полтерович, Хенкин, 1998, 1999)
7
Инновации, имитации и отбор
менеджеров (Acemoglu et al, 2006)
• Основная идея:
– развивающиеся страны растут за счет
заимствования технологий и инвестиций;
компании стремятся к долгосрочному найму
менеджеров, способных реинвестировать
накопленный капитал в крупные проекты;
– развитые страны растут за счет инноваций;
компании стремятся к найму талантливых
менеджеров, способных к инновациям, и
готовы для этого пожертвовать расширением
производства.
8
Модель: структура производства
• Конкурентное производство конечного
продукта из высокотехнологичных
“промежуточных товаров”
yt 
1
N
1
t
1
 A  
1
xt   d


0
• Монополистическое производство каждого из
промежуточных товаров из конечного продукта:
из единицы yt – единица xt(ν)
πt(ν) = (pt(ν) – 1) xt(ν) → max
s. t. pt(ν) ≤ χ
=> πt(ν) = δ(χ)At(ν) Nt, δ(χ) = (χ – 1) χ – 1(1 – α) ↑ χ 9
t
Модель: имитации и инновации
• Эволюция технологий в отрасли ν :
At(ν) = st(ν) (ηĀt – 1 + γt(ν) At – 1),
где At – 1 – средний уровень At – 1(ν);
Āt – 1 – максимальный среди всех стран
уровень At – 1 (мировая технологическая
граница);
Āt = (1 + g)Āt – 1
st(ν) = 1 или st(ν) = σ < 1 – масштаб
модернизации (размер проекта);
γt(ν) = 0 или γt(ν) = γ > 0 – инновационные
способности менеджера
10
Инновации, имитации и стратегия отбора
• Модель с перекрывающимися поколениями:
участники живут два периода
• Менеджер, выполнивший проект, получает долю μ
его прибыли.
• Ценность “молодых” менеджеров – только в том,
что среди них есть талантливые
• Ценность “опытных” менеджеров – еще и в том,
что они могут реинвестировать свой капитал в
крупный проект (несовершенство рынка капитала:
взятие кредита извне невозможно)
• Trade-off: уволить неспособного к инновациям
опытного менеджера или оставить?
11
Имитации и инновации:
стратегия фирмы
• Эволюция технологий:
At(ν) = st(ν) (ηĀt – 1 + γt(ν) At – 1)
• На ранних стадиях развития выгодно оставить
опытного менеджера; ближе к “переднему
краю” выгодно нанять нового
b
c

• Пороговое значение a = A / Ā : ar   ,   
1    1   
a < ar(μ,δ) => оставить; a > ar(μ, δ) => уволить;
ar(μ, δ) ↑ δ (чем сильнее конкуренция, тем
скорее переход к инновационной стратегии)
ar(μ, δ) ↑ μ при слабой конкуренции (большом δ);
ar(μ, δ) ↓ μ при сильной конкуренции (малом δ) 12
Равновесие, макс. рост и
ловушка экстенсивного развития
13
Недостатки модели
Acemoglu et al. (2006)
• Заимствуется самая передовая технология –
не реалистично: в слаборазвитых странах
заимствование имеет мало шансов на успех
• Мотивация выбора между имитациями и
инновациями довольно специфическая
(объяснение “пожизненного найма” в Японии)
• Не отражено должным образом накопление
капитала
14
15
16
17
18
19
20
21
Evolution of distance to frontier and capital
• Assume that TFP of the most developed
country increases with a constant growth
rate.gEvolution of a and k:
1
a1  a,

1 g
 
1 
 f ( x)  (1   )k
k1 
(1  g ) 1   
22
23
24
25
Abs.Capacity – Introduction
• The concept of absorptive capacity has been
originally introduced as a characteristic of a firm,
namely its "ability to recognize the value of new,
external information, assimilate it, and apply it to
commercial ends" (Cohen, Levinthal, 1990). Later on,
this concept was applied to a country as a whole.
• L. Suarez-Villa in 1990: a concept of innovative
capability: the ability of a country – as both a
political and economic entity – to produce and
commercialize a flow of innovative technology over
the long term». Furman, Porter, Stern (2002, p.1).
26
Abs.Capacity – Introduction
• Possibilities to arrange good policies depend on our
knowledge of absorptive and innovative capacities
as well as on factors which influence both quantities.
However, the task to separate and measure two
abilities is not trivial. Instead, a number of
researches try to suggest indicators that
characterize technological capabilities of countries.
• In Archibugi , Coco (2005), authors describe and
compare five indicators developed by different
organizations.
• All of them are based on a set of country
characteristics and on “arbitrary weighting schemes
with limited theoretical or empirical bases” (World
Bank, 2008).
27
Abs.Capacity – Introduction
• In UNIDO (2005), weights were chosen by factor
analysis that was carried out on 29 indicators, and five
principal factors were labeled as knowledge, inward
openness, financial system, governance, and the
political system.
• A similar methodology has been used in World Bank
(2008). As much as 34 variables were used over the
1990–2006 period. To calculate overall index of
technological absorptive capacity four types of
characteristics were taken into account:
Macroeconomic environment; Financial structure and
intermediation; Human capital, Governance.
• Dutta, S. and I. Mia in their Global Information
Technology Report (2009) suggested two indexes based
on surveys: CI (Capacity for innovation) and FA (Firmlevel technology absorption).
28
Importance
• “Both policy analysts and academic researchers
need new and improved measures of technological
capabilities on the performance of nations to
understand economic and social transformations.
With regard to policy analysis, this has relevance for
public and business practitioners. Governments
constantly require information about the
performance of their own country, and this is often
better understood in comparison to the performance
of their partners and competitors” (Archibugi and
Coco , 2005, pp.175-176).
• Up to now there is neither general strict definition of
absorptive capacity nor convincing methodology to
measure it. This paper tries to fill in this gap.
29
In this paper
• We try to build indicators that could not only serve for
comparisons of different countries technology levels but also
could help to choose most efficient direction to invest.
• New definitions of absorptive capacity and innovative
capability
• An approach to measure them
1)based on Schumpeterian-type model
(Acemoglu, Aghion and Zilibotti, (200) ;
2) combines calibration and econometric approach;
3) included analyses of both indicators on
characteristics of countries.
• Poltrovich, Tonis (2003, 2005), Piklina (MT, 2009)
30
New Definitions
• The absorptive capacity is defined as the
cost of 1% TFP increase of a country's
capital unit through technology imitation of
other economies.
• Analogously, the innovative capability is
defined as the cost of 1% TFP increase of a
country's capital unit through technology
innovations.
• Technology is understood in a broad sense
as a method of production, trade,
governance, etc.
31
Hypotheses
• 1) Absorptive capacity is negatively correlated with
relative level of development; the higher is this level
the larger is innovative capacity. Barro and Sala-IMartin (1995) Acemoglu, Aghion and Zilibotti (2002).
• 2) International trade positively influences absorptive
capacity.
• 3) Human capital has positive impact on innovative
capability.
Acemoglu, Aghion, Zilibotti (2003, 2006),
Vandenbussche, Aghion, Meghir (2004), Rogers
(2004).
• 4) Institutional quality positively influences both
absorptive and innovative capacities.
• 5) Banking system is more important for imitation
whereas financial markets play decisive role for
innovative development. Chakraborty, Ra (2006),
32
Deidda, Fattouh (2008)).
Absorptive and innovative capacities
• ci , i =1,2 may be calculated as c1= q1b1 , c2=
q2b2 where projects b1 , b2 each gives 1%
increase of TFP productivity of a capital unit.
• This means
• b1ψ1( b1)=0.01,
• b2ψ2( b2)=0.01.
• Therefore,
ci  0.01i qi / ( i  0.01), i  1, 2
33
Modification 1: human capital provided
by the state
• Assume that output Y of the final good is taxed to finance education
sector:
• τ(a) - education tax rate depending on a.
• q1 (a, H, S), q2 (a, H, S), H –human capital. Evolution of capital :
 (1   (a )) f ( x )  (1   K )k
k1 
(1  g ) 1   
N 1 H 1  (1   H ) NH  m(a ) (a )Y
where δH is the human capital depreciation rate
(0 ≤ δH ≤ 1), m(a) is a multiplier measuring the
impact of education on human capital.
34
Modification 2: human capital provided
by firms
• Suggested by Pikulina (2009) in her Master
Thesis at NES.
• Human capital is financed by firms directly, as
a result of their optimal choice
• Firm’s cost of providing Hv units
of human capital (under average human
capital H):
35
Methodology of calibration-1
• Calibration involves estimating the following
parameters:
• α –parameter of the Cobb-Douglas production
function;
• μ1– maximal growth rate due to imitation;
• μ2 – maximal growth rate due to innovation;
• ρ – technology obsolescence rate;
• λ – adjustment ratio used for estimating the share of
innovation and imitation in TFP growth (see below);
• β – parameters of cost functions qi (see below).
36
Methodology of calibration-2
• y-relative per capita GDP - ratio of country’s per
capita GDP to ŷthat of the USA.
• Start from y1981, the relative per capita GDP in 1981
(corresponding to the earliest period 1980-1982 in
our data series) and, using the model, try to predict ,
the relative per capita GDP in 2005 (corresponding to
the latest period 2004-2006).
• Criterion: the sum of squares of logarithmic errors
E    ln( yˆ 2005 )  ln( y2005 )   min
2
yˆ  actual , y  predicted
37
Methodology of calibration-3
•
•
1.
2.
3.
4.
Combination of calibration and regressions
Four steps:
Estimate α, the parameter of the Cobb-Douglas
production function, from the standard growth
regression and calculate TFP.
Fix parameters μ1, μ2, ρ, λ, calculate q1 ,q2 from the
model, and estimate two linear regressions with
dependent variables q1 ,q2 as functions of a, S
(coefficients β).
Using this functions, find optimal values of μ1, μ2, ρ, λ.
Go to the Step 2, or finish if criterion improvement is
small enough.
38
Methodology of calibration-4
Decomposition of the calibration problem
•
simplifies the process of calibration
•
allows estimation of statistical significance of
factors contributing to the absorptive and
innovative capacities.
•
A seeming disadvantage: the result is not an exact
solution to the calibration problem.
•
In fact, we restrict our opportunities for adjustment
getting in return for an opportunity to interpret key
results at intermediate stages, and, in the case of
success, to get higher confidence that the success
is not occasional.
39
Methodology of calibration-5
•
•
Important hypothesis: ratio of rates of
growth induced by innovations and
imitations is proportional to royalty
receipts over royalty payments.
We have no microfoundations behind
this hypothesis. Implicitly, it describes a
mechanism by which domestic knowledge,
embodied into royalty receipts, and foreign
knowledge, embodied into royalty
payments, both influence domestic rate of
growth.
40
Data
•
World Development Indicators (WDI, 2008), International
Country Risk Guide (ICRG, 2004), physical capital stock dataset
(Nehru and Dhareshwar, 1993), Barro-Lee dataset on human
capital.
•
Y– GDP, years 1980-2006; N– population; I – gross fixed capital
formation; K – capital stock;
R– ICRG composite risk index, is higher for lower risks;
LB– royalty payments, total value of licenses boughtI;
LS– royalty receipts, total value of licenses sold;
T– manufactures trade (export+import) ;
B – domestic credit provided by banking sector;
F – foreign direct investment;
P – the number of scientific publications per 1000 people;
H– total years of schooling (age 15+), measure of human capital
stock,
ED – public spendings on education.
Data is averaged by 9 three-year periods
•
•
•
•
•
•
•
•
•
•
41
Accessorial variables
42
Regressions for H , R, B
• H = 7.940***a + 3.479***
• R = 40.08***a + 53.52***
• B = 1.213***a + 0.0235***I + 2.140***
43
Model with exogenous
human capital: parameters calibrated
44
Model with exogenous human capital:
estimated imitation cost function.
45
Model with exogenous human capital:
estimated innovation cost function.
46
Model with exogenous human
capital:results-1
• The results confirm, at least partially, our main
hypotheses about the absorptive capacity and
innovative capability.
• More developed countries have higher innovation
capacity and lower absorptive capacity. For poor
countries, both indicators are less sensitive to
changes of the distance to the frontier than for rich
ones.
•
Human capital enhances the innovative capability
and does not affect significantly the absorptive
capacity. This does not contradict our hypothesis
that imitation is less sensitive to educational level.
However, it may happen that another indicator –
literacy rate – could be more appropriate for this
case. Unfortunately, we have data on literacy rates
for short period of time only.
47
Model with exogenous human
capital:results-2
• Institutional quality improves both absorptive
capacity and innovative capability.
• Absorptive capacity is positively affected by the
international trade. Its correlation with innovative
capability is negative, the fact for which we have not
any clear explanation.
• FDI contribution into both abilities is insignificant.
This does not contradict to the observation that FDI
influence on rate of growth is mixed.
• Number of scientific publications is positively
related to the innovative capability.
48
Regression
49
Regression
50
Distribution of ln(y), 1981
51
Distribution of ln(y), 2005
52
Regressions for m and τ
53
m(a) = efficiency of education
spendings
54
τ(a) = education spendings
GDP
55
increment of human capital
m(a)τ(a) =
GDP
56
Model with endogenous
human capital: parameters calibrated
57
Model with endogenous
human capital: regression for q1
Model with endogenous
human capital: regression for q2
Results
• Comparing these results to the results of
calibrating the basic model shows that the
way of computing human capital does not
matter: all the qualitative implications are the
same.
• The accuracy of the calibration has become
slightly better (standard error 0.0857 versus
0.0881). So, the human capital data implied
from the data on the education spending is
slightly better predictor than the data based
on the schooling years only.
60
Absorptive capacities and
innovative capabilities
61
Absorptive capacities and
innovative capabilities
62
Relation to other measures of technological
capabilities-1
• Dutta, S. and I. Mia (eds) (2009). The Global
Information Technology Report 2008–2009.
• Two indexes based on surveys:
- CI: Capacity for innovation (1 = companies obtain
technologies exclusively from licensing or
imitating foreign companies, 7 = by conducting
formal research and pioneering their own new
products and processes).
- FA: Firm-level technology absorption (1 =
companies are not able to absorb new
technology, 7= companies are aggressive in
63
absorbing new technology);
CI and our measures of absorptive
and innovative capacities
64
FA and our measures of absorptive
and innovative capacities
65
Relation to other measures of
technological capabilities
• Archibugi, D. and A. Coco (2005). Measuring
technological capabilities at the country
level: A survey and a menu for choice.
• Five technology indexes (WEF, UNDP, ArCo,
UNIDO, RAND), each including innovation,
infrastructure, technology diffusion, human
capital, competitiveness. For each of them,
countries are ranked.
• TR: mean rank of WEF, UNDP, ArCo, and
RAND.
66
Relation to other measures of technological capabilities
– conclusion
• These indexes capture innovation capability
rather than absorption capacity. In particular,
FA refers to firms’ ability to absorb any new
technologies rather than imitated ones.
• Probably, these indexes do not take into
account high imitation costs in
technologically advanced countries.
• Our indexes of absorptive capacities and
innovative capabilities take into account
these factors.
67
Conclusions
• We develop an approach to the estimation of
country absorptive capacities and innovative
capabilities.
• New more precise definitions.
• The method of calculation uses a simple
dynamic model and combines calibration
and econometric approaches. This gives a
possibility to analyze how calculated
indicators depend on different factors.
68
Conclusions
• The model predicts main feature of the real evolution
of countries distribution by GDP per capita.
• The estimations are conducted not for each country
separately but for a group of economies jointly. This
gives us additional information which is not
contained in data on a country alone.
There are a lot of possibilities to improve our
approach.
• OLG model instead of one period model.
• Include labor markets with workers of different
qualifications
• Include sectors of education and research.
• To try different hypotheses to reach the separation
of imitation and innovation costs and results.
69