ECON 4350: Growth and Investment
Lecture note 8
Department of Economics, University of Oslo
Made by: K˚are Bævre (kare.bavre@econ.uio.no)
Exploited by: Miroslav Hlouˇsek (hlousek@econ.muni.cz)
16 Endogeneous growth and the data
Secondary reading: Kremer (1993), Jones (1995)
16.1 Scale effects
• In the R&D models we have assumed that new ideas/technology is
produced according to
˙T = BLT T (1)
• In the long run the number of researchers, LT , must be proportional to
population (LT = aL), so we have
˙T/T = BaL
• We have also seen that we get a balanced growth path where Y grows
at the same rate as technology T
γ = ˙Y /Y = ˙T/T = BaL
• This implies that growth rates in the long run will increase in population,
or the scale of the economy. We call this a scale effect.
• We saw an example of such a scale effect also in the model with governmental
provision of a public good.
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• Over the long run it is likely that T flows quite freely across countries.
Thus, we should probably think primarily of scale effects as taking
place over time and at a global scale.
• But do we observe scale effects?
• Kremer (1993) adopts a long run perspective (1.000.000 BC-1990).
• His hypothesis is that population growth should depend positively on
the level of population.
• The argument is that since the level of population determines technological
growth it will also determine growth of per capita income, and
hence (by a simple Malthusian argument), it will determine population
growth.
• We would not see such an effect if technological growth was exogenous
and independent of population.
• His main findings are
1. Over most of the period population growth is proportional to the
population level.
2. Among regions that have historically been geographically separated
the initially larger (most populous) regions experienced
fastest growth.
• These findings are well in line with his hypothesis. A main problem is
that his analysis is not really convincing in explaining that growth has
leveled off recently.
16.2 Time series evidence
• As we saw, there has been no major increases in growth rates over the
last decennia.
• In fact, for an economy such as the U.S. there appears to be no trends
in growth rates over time over the last hundred years.
• As argued by Jones (1995) this is bad news for the endogenous growth
models also for another reason: Both the simple AK-models and the
R&D models predict that changes in several variables lead to permanent
changes in growth rates.
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• In particular, changes in investment rates should have permanent effects
on growth.
• He draws attention to the following observations:
1. There are only weak time-trends in growth rates.
2. There are strong upward time-trends in investment rates.
3. There are strong upward time-trends in resources devoted to R&D.
• He argues that these findings go strongly against endogenous growth
models with scale effects.
• He argues that the models are better in line with the data if we replace
the R&D production function (1) with
˙T = BLT Tφ
(2)
where φ < 1 (while (1) had φ = 1).
• As above we then have
γ(T) = ˙T/T = BaLT−(1−φ)
Now γ (T) < 0 for a given L, so the growth rate is ever declining
(towards 0) unless we have population growth. The level of population
growth n thus ties down γ∗
in the long run.
γ∗
= n/(1 − φ)
• The revised production function (2) can be integrated into the R&D
models without altering their basic microeconomic insights.
• However, we are than back in a situation where policy affects growth
only during the transition, and has level effects but not growth effects
in the long run.
• Based on present knowledge it is hard to judge a priori wether we should
trust (1) or (2).
• It is a major problem for theories of endogenous growth that two such
rather similar specifications yield so dramatically different results.
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17 Growth and infrastructure
Secondary reading: Hall and Jones (1999), Acemoglu, Johnson and Robinson
(2001)
17.1 Institutions
• Attempts at explaining cross-country differences in economic performance
based on variations in inputs (capital and human capital) show
large residuals of unexplained productivity differences.
• Further, we are left with the question: Why do capital accumulation
and education attainment levels differ so much?
• Differences across countries in institutions and government policies, in
short social infrastructure, seems a plausible fundamental determinant
both of productivity differences and differences in accumulation.
• By social infrastructure we understand the institutions and government
policies that provide the incentives for individuals and firms in
an economy.
• Incentives can encourage productive activities or instead encourage
predatory behavior such as rent-seeking, corruption and theft.
• Productive activities are vulnerable to predation. Thus prevalence of
predation can have two types of negative effects on productivity.
1. People use resources on protecting their production from diversion
rather than on productive activities.
2. People have too weak private incentives to engage in productive
activities.
• The first type of reason can explain productivity differences, the second
differences in factor accumulation.
• Control of diversion by social action generally can benefit from economies
of scale in protecting against predation. Successful social action can
also serve to abolish the need for protection by moving the economy
from a bad to a good equilibrium.
• Note however, that if the government can make and enforce rules it
can itself turn into a highly effective agent of diversion (rent-seeking,
corruption).
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17.2 Some evidence
• To assess the empirical role of social infrastructure we want to estimate
the equation
log Y/L = α + βS + (3)
where S is an index of social infrastructure.
• There is a major problem with estimating (3), namely that there is
every reason to expect that social infrastructure is itself dependent
upon production (Y/L). That is, S is endogenous.
• It is thus likely that (3) holds jointly with
S = γ + δ log Y/L + Xθ + η (4)
where X is a collection of other variables influencing social infrastruc-
ture.
• To be able to estimate (3) we must therefore use an instrument variable
approach.
• A legitimate instrument is a variable that is correlated with S but
uncorrelated with (that is, it does not have a causal impact on Y/L).
• The instrumental variable approach is based on first regressing S on
Y/L and the instrument(s) and then entering the predicted values from
this regression in the regression (3).
• Note that we do not have to include as instruments everything that
explains S, we only need at least one of the factors that explains it.
(That is, we do not need to a have very good model for explaining S).
• There are therefore two challenges here: 1) finding suitable indicators
of social infrastructure, 2) finding good instrument variables. Where
the last is perhaps the most difficult one.
• Two of the most important contributions to this literature are Hall and
Jones (1999) (HJ) and Acemoglu et al. (2001) (AJR)
• The two studies differ primarily in their choice of instruments.
• HJ uses up to four instruments
1. Distance from the equator
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2. The fractions of the population speaking English
3. The fractions of the population speaking another European lan-
guage
4. Frankel-Romer predicted trade share based on a gravity model of
international trade
• The three first instruments are supposed to reflect the early European
influence on countries during the era of colonization. These appear to
be appropriate instruments:
1. in as far as European influence lead to development of better social
infrastructure, and to the degree that these effects where perma-
nent.
2. If these factors have no independent impact on production today.
• Using these instruments HJ find evidence of a strong effect of social
infrastructure on production. And argue that according to their results
differences in social infrastructure can explain between 25.2- and 35.1fold
differences in output. (While the richest country in their sample
has 35.1 times the output of the poorest).
• They also show by decomposing production according to a neo-classical
production function that social infrastructure contributes both by way
of productivity and by way of higher levels of the inputs.
• Further, they find that this result is rather robust. They also report
results suggesting that social infrastructure is indeed the fundamental
determinant of economic performance
• Their choice of instruments can, however, be criticized.
1. Their notion of European influence is crude and theoretically the
link is weak.
2. Ethnolinguistic fragmentation is probably endogenous (depends
on Y/L?).
3. The geographical instruments might be correlated with .
• In light of this critique Acemoglu et al. (2001) (AJR) provide a more
elaborate perspective on the colonial impact story.
• As their instruments AJR instead use the mortality facing settlers during
colonization.
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• Their story is as follows: High settler mortality lead to ‘extractive state’
colonies (e.g. the Belgian Congo) while low mortality lead to permanent
settlements of Europeans (e.g. Australia) with subsequent development
of the appropriate institutions for running these new ’European’ soci-
eties.
• Their evidence is similar to that reported by HJ. But their instrument
does appear to have a better foundation.
• To sum up: It seems evident that social infrastructure is fundamental to
the question why are some countries so rich and some so poor. However,
we still lack knowledge about which institutions are the most important
and what are effective policies for implementing or improving these
institutions.
References
[1] Acemoglu, D., S. Johnson and J.A. Robinson The Colonial Origins
of Comparative Development: an Empirical Investigation, American
Economic Review, 2001, 91 (5). pp. 1369-1401.
[2] Hall, R.E. and C.I. Jones Why Do Some Countries Produce So
Much More Output Per Worker Than Others? Quarterly Journal of
Economics, February 1999, 114 (1): 83-116.
[3] Jones, C.I. Time Series Tests of Endogenous Growth Models, Quarterly
Journal of Economics, May 1995, Vol. 110, pp. 495-525.
[4] Kremer, M. Population Growth and Technological Change: One Million
B.C. to 1990, Quarterly Journal of Economics 1993, 108 (3). Pp.
681-716.
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