WPS6230


Policy Research Working Paper                     6230




                           Green Growth
                     Lessons from Growth Theory

                                  Cees Withagen
                                  Sjak Smulders




The World Bank
Development Research Group
Environment and Energy Team
  &
Sustainable Development Network
Office of the Chief Economist
October 2012
Policy Research Working Paper 6230


  Abstract
  This paper reviews dynamic general equilibrium models                             technical change. Green growth becomes within reach if
  in order to collect insights on the interaction between                           there is good substitution, a clean backstop technology,
  economic growth and environmental issues. The authors                             a small share of natural resources in gross domestic
  discuss the Ramsey model and extend it for natural                                product, and/or green directed technical change.
  resource inputs and pollution, as well as for endogenous




  This paper is a product of the Environment and Energy Team, Development Research Group, and the Office of the Chief
  Economist, Sustainable Development Network, in the World Bank. It was produced for the Green Growth Knowledge
  Platform (www.greengrowthknowledge.org), a joint initiative of the Global Green Growth Institute, Organisation for
  Economic Co-operation and Development, United Nations Environment Programme, and the World Bank. It is part of
  a larger effort by the World Bank to provide open access to its research and make a contribution to development policy
  discussions around the world. Policy Research Working Papers are posted on the Web at http:// econ.worldbank.org.
  The authors, Sjak Smulders and Cees Withagen may be contacted at j.a.smulders@tilburguniversity.edu and cwithagen@
  feweb.vu.nl.




         The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
         issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
         names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
         of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
         its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.


                                                       Produced by the Research Support Team
                    GREEN GROWTH – LESSONS FROM GROWTH THEORY




                                            Sjak Smulders

                                    Tilburg University and CentER

                                  j.a.smulders@tilburguniversity.edu



                                           Cees Withagen

                          VU University Amsterdam and Tinbergen Institute

                                        cwithagen@feweb.vu.nl




Key words: growth, environment, natural resources, innovation, R&D spillovers.

JEL codes: O1, O3, O4, Q2, Q3, Q4

Sectors: Environment, Economic Policy



*We thank Michael Toman for encouragement and comments. Views and errors remain ours alone, and
should not be attributed to the World Bank Group or its member countries.
1. Introduction
For more than 80 years, economists have used more or less complex versions of a standard
mathematical model to study the origins of overall economic growth (Ramsey, 1928; Solow,
1956; Dasgupta and Heal, 1974; Romer, 1986). Early versions of the model focused on how
savings by households (from spending less on immediate consumption than total income),
invested into increasing the overall stock of physical capital, could increase income per capita
over time under different sets of circumstances for the productivity of capital and labor, the
willingness to save for future consumption versus consume today, and the rate of population
growth. Over the decades, substantially more sophisticated models have been developed –
although the earlier “workhorse� models still are commonly used for empirical analysis of
growth prospects.
       For our purposes, the most important extensions have been (a) the incorporation of
explicit roles for natural resources and the environment in production of goods and services, and
direct contributions to human well-being; and (b) ways in which knowledge and skills can
change over time to improve productivity and expand growth possibilities. The former types of
extensions have examined how growth prospects are influenced by increases in natural resource
scarcity because of depletion or degradation – from degraded soils to negative effects of climate
change. The incorporation of technological change has brought new realism into the framework
by recognizing that innovation responds to economic incentives like other expenditures, and that
these processes can interact with other influences on growth in complex ways.
       In this paper we review these types of models in order to shed light on different
mechanisms for economy-wide “green growth.� This term has many definitions. In the context
of longer-term growth, we define it as growth in conventionally measured income and
production without unsustainable deterioration of the environment (i.e., deterioration that is large
scale and essentially irreversible). For nearer-term growth, we can view it as growth in
conventional income with “modest� negative impacts on the environment.
       The focus on conventional income versus a broader concept of economic well-being or
welfare is motivated by the “realpolitik� of current debates in and about developing countries
regarding their prospects for maintaining environmental and ecological services without
                                                 2
“significant� negative impacts on income, especially in the nearer term. Thus, we can also view
green growth as concerned with how environmental sustainability can be realized without
“unacceptable� limitations on income expansion. More formally, green growth policy can be
formulated in our view as the maximization of a broader concept of welfare under the constraint
that environmental quality increases and that the growth rate of (conventionally measured)
income does not deviate too much from a pre-specified target (where the target may be related to
some “business as usual� growth rate).
       The literature that looks at resource scarcity and the dynamics of environmental policy
through the lens of economic growth theory directly sheds light on green growth. When
reviewing this literature, we consider two crucial aspects of the temporal dimension: the long-run
dynamics (how much can we sustainably grow?) and the transitional dynamics aspect (how will
the nature of the growth process change over time?). We also need to account for how less-than
efficient environmental and growth policies could change the story.


2. The Ramsey Framework


2.1 Introduction
“How much of its income should a nation save?� This is the question raised in a path breaking
article by philosopher and mathematician Frank Ramsey in 1928 (Ramsey, 1928). The Ramsey
framework offers an extremely useful tool for studying growth and welfare. In this section we
review the original model. It will serve as a basis for extensions in subsequent sections.


2.2 Optimal investment
We study an economy on a highly aggregated level. All production takes place in a single
production sector that uses two inputs, capital and labor. There is a representative producer and
also a representative consumer. The latter is infinitely lived. An alternative interpretation is that
the consumer represents a sequence of generations that form an infinitely lived dynasty. There is
no population growth. The consumer is only interested in consumption. In the sequel we will use
the following symbols. The stock of man-made capital is K , the labor force is denoted by L .


                                                 3
The combination of these inputs leads to output Y . The maximal output that can be obtained
with given factor inputs is described by the production function F :


(1)      Y = F ( K , L)


Production is increasing in the inputs, but for a given input of labor the additional increase of
production if more capital is used is decreasing. This property is called decreasing returns.
Moreover, it is assumed that the marginal products are very high for low input of capital and
close to zero for a large input of capital. The same properties hold for labor. Total production is
used for consumption C and for investments consisting of net investments, which constitute the
increase in the capital stock, and depreciation, which is usually assumed to be a constant fraction
of the existing capital stock. The utility or happiness derived from consumption is represented by
a utility function U that is increasing in consumption and exhibits decreasing marginal utility:
utility increases at a decreasing rate with an increase in consumption. It is assumed that the
instantaneous utility function is the same for all generations. Moreover, all consumption
generated in a period of time is equally divided over the then existing population. So, with the
entire population working each gets C / L . With a constant fraction of the population working
the qualitative results are not affected.
        The question we started with, “How much should a nation save?� can only be answered if
the nation has an objective. Several possibilities arise. Two of them deserve special attention
because they are commonly used in economics.
        The first is the utilitarian framework. Here welfare is represented by the (discounted) sum
of all future utilities:


               ∞
(2)     Wu = ∫ Le − Ï?tU (C (t ) / L)dt
               0




Hence, total welfare consists of the sum of all individual utilities, but consumption into a more
distant future gets a lower weight. The rate at which the weight falls with time is represented by

                                                 4
Ï? ≥ 0 , which denotes the pure rate of time preference: if, for example the rate of time preference
is 2 percent and two generations are 25 years apart, then the weight given to the future generation
compared to the present is 60 percent. Note that labor (or population) is not given as a function
of time because in this section it is assumed that population is constant over time.
       The second type of welfare concept is egalitarian. Welfare is determined by the
instantaneous utility of the generation that is worst off.


(3)     We = min tU (C (t ) / L)


       We first consider the implications of the egalitarian welfare concept. In an optimum the
minimum rate of consumption over time should be maximized, because what counts for welfare
is the minimum level of consumption. The golden rule capital stock K * is defined as the
constant capital stock that maximizes output net of depreciation. This capital stock is determined
by the condition that the marginal product of capital equals the rate of depreciation. Indeed, if
capital would be lower, then a marginally larger capital stock would yield more output than is
needed to compensate for the higher depreciation. For a higher capital stock the reasoning is
similar. The golden rule capital stock that yields the highest possible constant consumption rate,
denoted by C * . If the actual initial capital stock K 0 is smaller than K * it is optimal to keep this
capital stock intact. An increase in the capital stock goes at the expense of present consumption
and therefore leads to lower social welfare, although it might considerably increase the utility
experienced by future generations. In this welfare approach consumption is instantaneously
fixed, even if maybe some initial investment in capital would lead to a much higher consumption
level forever thereafter. One of the problems with this approach is precisely that giving up some
consumption in the present in order to gain more consumption in the future is not considered
optimal. In spite of this objection, the egalitarian approach emphasizes the equal treatment of
generations, which is pertinent in many definitions of sustainability. If K 0 > K * then it isn’t
optimal to keep capital constant at its initial level. If it would, then disposing of some capital so
that the golden rule capital stock remains, yields higher constant consumption forever. However,


                                                   5
note that doing so is not efficient: one can increase consumption for an initial interval of time
without endangering future consumption possibilities.
       Turning to the utilitarian optimum, we have to make a distinction between discounting
and no discounting. With discounting, optimum long-run consumption and capital levels are
below their golden rule levels, with the consequence that investing more in the present would
increase consumption for future generations. However, with discounting, the investment cost
incurred today gets a bigger weight than the returns to investment that accrue only in future.
Hence, any point in time, it is optimal to not invest too much (less than under the Golden Rule).
The lower the discount rate, the higher consumption levels for future generations.
       This raises the question what is the appropriate discount rate in view of our preferences to
future generations. Instead of a constant rate of time preference, maybe all future generations
should get the same weight, which is still below the weight of current generations (Schelling,
1995. See also Chichilnisky (2007), for a comparable notion of dealing with future generations).
This would produce more investment but also time-inconsistency: the optimum for current
generations would arise if they themselves invest relatively little (reflecting the low weight on
the future) and if future generations invest a lot for future generations (reflecting the non-
declining weight on future generations). However, if these investment plans are not binding for
future generations, these generations will deviate from the plans and again plan for low
investment during their life span. Hence in the absence of commitment, the result would be low
investment again.
       A more radical alternative is no discounting at all, giving all generations the same weight
in the objective function. The optimal savings path then brings society to the golden rule levels
of consumption and capital. In the Ramsey model sketched above the welfare integral (2)
diverges if there is zero discounting, so that it seems that an optimum doesn’t exist. However,
Ramsey found an elegant way out of this problem. The argument runs as follows. An optimal
program has to be efficient, meaning that it should be impossible to find an alternative feasible
program that never has smaller consumption but does have larger consumption during some
interval of time. A useful benchmark is the golden rule level of consumption. It can be shown
that, even in the case of no discounting, the total difference between optimal utility and the utility
associated with the golden rule converges.
                                                  6
2.3 The Ramsey rule and growth
In the utilitarian optimum, the marginal cost of postponing consumption to the future should
equal the marginal benefits, such that society is indifferent between investing now and investing
later. The net benefit of investing equals, in terms of goods, the net marginal product of capital.
To express the net benefits in terms of utility, one has to take into account that future
consumption counts less than current consumption because of discounting and declining
marginal utility of consumption. Hence, in utility terms, the net benefit of postponing
consumption equals the net marginal product of capital minus the rate of decline of discounted
marginal utility. The optimality condition, the so-called (Keynes-)Ramsey rule, says that this net
benefit is zero.
        There are various ways to express the Ramsey rule. The interest rate (to which firms
equate the net marginal product of capital) should equal the sum of the rate of time preference (Ï?)
and the rate of decline of marginal utility. Since (marginal) utility depends on the level of
consumption, the latter term is related to the growth rate of consumption and the Ramsey rule
can be also written as a relationship between interest rate, discount rate and the optimal
consumption growth rate. In particular, consumption optimally grows faster if the interest rate
exceeds the rate of time preference more: although fast consumption growth quickly diminishes
the marginal utility of consumption, such a cost is offset by the high benefits that accrue from the
high interest rate.
        An important role in the Ramsey rule is played by the so called elasticity of intertemporal
substitution. This is defined as the percentage increase in consumption that generates a 1 percent
decrease in marginal utility. Its role can be illustrated by considering an example in which this
elasticity is constant and independent of the level of consumption. If the elasticity is small, then
the optimal level of consumption changes only at a very small rate, even if the economy starts far
away from its steady state. The reason is that even a small increase in consumption reduces the
marginal utility a lot, which makes it less attractive to deviate from an egalitarian outcome.
        Denoting the elasticity of intertemporal substitution by σ and the return to investment by
r, the Ramsey rule can be written as:


                                                 7
(4)     /
        C =C σ (r − Ï? ) ,


In words, the growth rate of consumption is proportional to the difference between rate of return
on investment and the rate of time preference, where the factor of proportionality is the elasticity
of intertemporal substitution. With a positive rate of time preference Ï? we define the modified
golden rule by the stock of capital, K**, that yields a marginal product equal to the sum of the
rate of time preference and the depreciation rate (so that the interest rate equals the rate of time
preference and consumption growth is zero). The optimal economy now converges to the
modified golden rule state. Note that with a low rate of time preference, the steady state values
are higher than with a high rate of time preference. Hence, with a low rate of time preference the
future generations are better off.
        If the economy starts with a low capital stock ( K 0 < K ** ), both the capital stock and
consumption rate monotonically increase and approach the steady state. The reason is that the
return to investment, r, equals the marginal product of capital net of depreciation; its value is
high when the capital stock is still small (because of diminishing returns to capital), thus
stimulating consumption growth according to the Ramsey rule (4). In contrast, consumption
decreases over time if the economy is rich initially ( K 0 > K ** ).
        Ramsey formulated his savings rule for answering the question how much a nation
should save. However, the Ramsey rule (4) should also hold for any agent that maximizes utility
from consumption C and can borrow and lend against the same rate r . The Ramsey rule
therefore typically shows up as part of any model with optimizing households, no matter how
much more complex than the economy described above. For example, in the case of multiple
investment options, each with their own rate of return, and a single consumption good (or
basket), the Ramsey rule should hold for all these assets and their rates of return should be
equalized. In this setting it makes sense to interpret the Ramsey rule as the characterization of the
total supply of savings as a function of the economy-wide interest rate, while the division of
savings over different investment opportunities is governed by the equality of rates of return.
However, for the optimum for individual households to coincide with the social optimum, it is
necessary that the rates of time preference and the utility functions are identical in the two
                                                    8
settings. Moreover, although in a world with externalities, such as environmental deterioration,
the Ramsey rule may characterize growth of consumption, externalities may depress the private
rate of return r below the social rate of return to investment. This reduces the growth rate of
consumption below the socially desirable growth rate. If the externalities imply binding credit
constraints on investors, however, the link between investment rates and investment returns
becomes weaker and the Ramsey rule cannot be used directly. In the sequel we will address the
crucial issue of the discrepancy between the market and the social optimum in more detail,
because it plays an important role understanding what it means to get the prices right.
       One final remark is in order. With labor growing exponentially at an exogenous rate and
with constant returns to scale in production all variables can be written in per capita terms and
the analysis is essentially unaffected.


3. Including Nature


3.1. Introduction
Numerous extensions of the Ramsey model present themselves. One could include other stocks
than man-made capital, such as human capital, natural capital and social capital. One could also
distinguish between many sectors. Or introduce technical change. The latter option will be
pursued in section 4. In the present section we focus on introducing nature into the picture. An
instructive way of doing so in general recognizes that nature has several functions. Nature as a
stock provides direct benefits to consumers. A high quality forest has amenity value, the
existence of a stock of whales has a value per se, the accumulated stock of CO2 poses a negative
value or a negative externality, etc. So, there is good reason to incorporate nature, denoted by
N , into the utility function. One could do the same for the production function: Pollution, the
presence of lead, for example, may hurt the productivity of workers, whereas clean water is
beneficial for the production process. In addition, nature provides services as a flow. Examples
are the extraction of oil to be used for production, fish caught for consumption, timber for
furniture. So, a rudimentary stylized model would have Y = F ( K , N , R ) where R denotes the
extraction rate from nature. The utility function would read U (C , N ) , where consumption C
could now include consumption of flows from nature, such as fish. Nature has many dimensions,
                                                 9
so that one should think of the symbol N as multidimensional, representing the various relevant
stocks. This also holds for R that represents the various flows from nature. Finally, we should
add an equation describing how nature, or quality of nature, develops over time


(5) = E(N ) − R
     N


       denotes the change in nature’s stock and the function E describes how nature
where N
regenerates. If the stock is nonrenewable, then regeneration doesn’t take place and E ( N ) ≡ 0 . The
stock N and its depletion rate R may both enter the utility and the production function. When it
comes to fisheries the fish consumed is an argument of the utility function and oil extracted from
an oil well is a factor of production. But the fish stock by itself will probably not enter the
production function, nor will the oil stock be an element of the utility function (although some
types of mining may cause a negative externality that appears in the utility function) . If N is an
environmental or health characteristic, then it could appear in F (degradation of nature hurts
output) and U through direct impacts. An example can be temperature or other indicators for
climate change. In case of nonrenewables such as oil no regeneration is possible at all.
       The model presented here is interesting from a conceptual point of view. But nature
appears in many specific forms. Hence we now move on to particular interpretations of nature.
We start by introducing nonrenewables in section 3.2 and link them to climate change in section
3.3. In section 3.4 we go more deeply into the ecosystem services. Section 3.5 deals with the
phenomenon that natural resources may constitute an obstacle to economic growth, sometimes
labeled as the resource curse.



3.2 Nonrenewables
The first substantial extension of the Ramsey model that we consider is a world with a
commodity extracted from a nonrenewable resource as a production factor, say oil. In this world
there is no alternative for the nonrenewable resource (no wind, no solar) as a source of energy
inputs and in this first extension neither the use of oil nor the stock of oil brings about an
externality. This approach proved very valuable in the seventies of the previous century, when
                                                 10
the oil crises triggered the debate on �limits to growth�, in the presence of scarce fossil fuel
energy resources. Nowadays, it attracts much attention again because of the relationship between
use of fossil fuels and CO2 emissions, causing climate change. Let us sketch the main results of
the so called Dasgupta-Heal-Solow-Stiglitz model (Dasgupta and Heal, 1974; Solow, 1974; and
Stiglitz, 1974). Several questions can be addressed.
       The first one is related to sustainability: Is it possible to maintain a positive level of
consumption and hence welfare? To answer this question we have a look at the new equation
describing production


(6)     Y = F ( K , L, R )


To keep the analysis simple we maintain the assumption that labor input is constant and suppose
that extraction from the nonrenewable resource is costless. Total production is used for
consumption and investments. The sustainability issue has to do with the technology, which is
determined by the production function and the depreciation of capital. If oil is not necessary for
production, F ( K , L,0) > 0 for K , L > 0 , then we are basically back in the Ramsey model. So we
consider the opposite case where without oil there is no production. Since the stock of oil is
finite, the use of oil will eventually approach zero. So, if the aim is to have a maintained positive
level of consumption the loss of oil input should be compensated for by an unbounded increase
in the use of capital. And then the question is how easily substitution between oil and capital can
take place. Some technologies have the property of limited substitution possibilities. This would
mean that total production over time is bounded regardless of the amount of capital and labor
available, in view of the limited availability of oil. In that case it is impossible to maintain a
positive level of output indefinitely, and consequently no constant positive level of consumption
is feasible: The economy is unsustainable. But there are also production functions in which oil is
indispensable for production, but that still allow for unbounded production over time, by
substituting oil for capital. An example of such a production function is the Cobb-Douglas
production function, where a 1 percent increase in an input, given the inputs of other production



                                                 11
factors, leads to a fixed and constant percentage increase in output. This percentage is called the
production elasticity of capital or oil or labor. We denote them by α , β and γ respectively.
        The Cobb-Douglas production function is extensively studied in the literature. Several
results are quite intuitive. A necessary condition for having the technological possibility to
maintain a positive constant level of consumption is that the production elasticity of capital is
larger than that of oil ( α > β ). Indeed, since less and less oil is available over time in view of the
limited stock of oil, an increasing capital stock must make up for the loss in output. The
economy can only produce enough capital to replace oil if capital is sufficiently productive, i.e.,
has a relatively large production elasticity. But this is not a sufficient condition. If a fixed
fraction of the capital stock depreciates per time period, the growing capital stock implies a
growing burden of depreciation that cannot be financed out of a constant production level
without hurting consumption. Hence a necessary and sufficient condition for sustainability is
α > β and no depreciation of capital.
        We could include population growth as well as labor growth in an exponential way, both
growing at a constant rate. Growth of labor allows for larger output, but this is not enough to be
able to maintain a positive per capita consumption rate, because labor as an input has decreasing
returns. Under these circumstances, in particular without technological progress, population
growth is bad for sustainability. However, if population growth is not exponential but quasi-
arithmetic, allowing still for population going to infinity, but at a rate that approaches zero as the
population gets large, the prospects are better. In particular, if the production elasticity of capital
is large enough relative to the production elasticity of energy, then a positive maintained per
capita consumption is feasible (see Asheim et al. (2007)). Technological progress might also
help. Suppose that there is no capital depreciation and that exogenous technological progress
causes labor productivity to grow at a constant rate. Then with a Cobb-Douglas production
function and exponential labor growth, sustainability is enhanced by lower population growth,
higher technological progress, a higher production elasticity of capital, and a higher production
elasticity of labor.
        In a utilitarian world many development paths can be optimal. We limit ourselves here to
the case without population growth, technological change and capital depreciation. Then, with a

                                                  12
positive rate of time preference, consumption will necessarily decline to zero in the long run.
However, in the short and medium run various time patterns can emerge. In the Cobb-Douglas
case, for a low rate of time preference the rate of consumption will rise initially and will then fall
monotonically (see Benchekroun and Withagen (2011)). For high rates of time preference,
consumption will be high initially and it will monotonically decrease over the entire future. With
a rate of time preference equal to zero, it might be optimal to have ever increasing consumption
over time. This occurs, as expected, when the rate of intertemporal substitution is small.
       The next question that needs to be addressed is whether and how the optimum can be
implemented in a market economy. Within the model, the answer to this question is obvious: If
there are no externalities the market will realize the social optimum. However, in a more realistic
situation, market failures should be taken into account. First, when it comes to the supply of
nonrenewable resources, and in particular oil, the market is far from perfectly competitive. It
goes beyond the scope of this paper to survey this literature. The reader is referred to Groot et al.
(2003). A second obstacle to efficiency is the absence of perfect forward markets. It has been
shown by Dasgupta and Heal (1979) that is this may lead to over- or under-exploitation of the
natural resource.
       An important extension of the Dasgupta-Heal-Solow-Stiglitz model discussed above can
be attributed to Krautkraemer (1985). He maintains the assumption of costless extraction of oil.
But the extraction of oil irreversibly damages the environment, which is modeled by including
the existing remaining resource stock directly in the instantaneous welfare function.
Krautkraemer interprets this as local damage, but an alternative is to argue that a small remaining
resource stock implies that a lot of oil has been extracted, which has led to considerable
accumulation of CO2, assuming there is no decay of CO2. The main question that is addressed is
whether or not in these circumstances it is optimal to fully exhaust the resource. The answer is
that with a low rate of time preference the optimal economy tends to preserve some of the oil
reserves. The reason is that future generations should then benefit from the amenity value of the
resource. In the next section we return to climate change as a consequence of burning fossil fuel.




                                                 13
3.3 Nonrenewable resources, renewable resources, and climate change
A particularly interesting example of nonrenewables is fossil fuels. These play a crucial role in
the production process and the question addressed in the previous section was therefore whether,
given the limited availability of fossil fuels, the economy is capable of maintaining welfare. But
fossil fuels are important for another reason as well. Their use is causing the accumulation of
CO2, which may lead to climate change. Although there is huge uncertainty regarding the exact
processes that play a role, most economists take it that there is a relationship between the
emissions of CO2 and climate change. Hence, nonrenewables are special in that they play a
crucial part in aggregate production, but also cause a negative externality. This is what we
address in the present section. One question that could be raised is how the existence of the
negative externality will impact the optimal use of oil. The answer is that in a utilitarian
framework the time profile use of oil should be flatter than without the externality: Since harmful
emissions arise from extraction, it is optimal to postpone the extraction of polluting resources,
and hence accept slower growth in output, such that the loss in output is traded off against the
increase in damages from emissions. Another question that could be posed is how the ordering of
the use of oil and coal should be? Coal is cheaper to extract but leads to more emission. So, there
is another trade off there. We will focus on another question that involves renewables, such as
wind energy or solar energy, which do not contribute to climate change. Then the question
becomes at what instant of time a transition to these renewables should take place in a welfare
framework. And, obviously, what policy instrument is most suited to provide an incentive to the
market economy to achieve the socially desirable outcome?
       In the sequel we study an economy that extends the original Ramsey framework in a
number of ways, and that encompasses nonrenewables, renewables and climate change (see Van
der Ploeg and Withagen (2011) and Golosov et al. (2010)). It is a simple vehicle to study green
growth. As before, we work on the highest possible level of aggregation, the world economy.
There are three stocks: oil, accumulated CO2 and man-made capital. The oil stock diminishes as
extraction goes on. Total extraction over time cannot exceed the initial oil stock. We neglect
exploration activities that might increase the available oil stock. Oil extraction is costly. The
existing oil stock plays a role in the sense that a high oil stock makes it relatively easy to extract
oil and the other way around. Growth in the stock of accumulated CO2 is proportional to
                                                 14
   emissions from burning oil. Without loss of generality the factor of proportionality is set equal to
   unity. To keep the analysis simple we abstract from natural degradation of CO2 in the
   atmosphere, so the stock of CO2 simply equals the initial stock plus the accumulated sum of past
   CO2 emissions, consisting of the initial CO2 stock plus the total extracted amount of oil. Oil
   serves as an input in the production process which can be represented as


(7) Y F ( K , L, R + X )
=


   Next to oil we have another energy input, which is denoted by X . This energy is generated from
   renewable sources such as solar and wind. Its production has a cost. When it comes to renewable
   energy there are high fixed costs in reality. We neglect these cost and assume in addition that the
   cost of producing one unit of energy from renewable is constant. A heroic assumption implicit in
   (7) is that these energy sources produce exactly the same type of energy. It is well known that oil
   is best suited for transportation purposes and wind not, but this is not taken into account in the
   chosen specification of the technology.
          Total production is used for consumption and investments, as before, but in addition we
   need some of the output to extract oil and to produce the energy from renewable resources.
          Social welfare W now has two components: Utility from consumption and damage from
   the accumulation of CO2. We know that climate change has detrimental effects. There are
   several ways to take that into account in a green growth model. One option is to let production be
   hampered by climate change. This could apply to agriculture in certain regions and certain
   fisheries. Alternatively, and this is the approach taken here, one introduces a damage function
   supposedly taking these effects into account. We will describe total welfare as the difference
   between utility from consumption and the damage from pollution. Another way would be to have
   a multiplicative welfare function, recognizing that marginal utility of consumption might be
   negatively impacted by CO2 accumulation and climate change. So, we write

                   ∞
=
(8) W          ∫       e − Ï?t [U (C (t )) − D( Z (t )) ] dt ,
                0



   where D is the damage function, depending on the accumulated CO2 stock, Z.

                                                                15
       This framework integrates the Ramsey growth model and climate change. We are back in
the Ramsey model if there is no oil, if there are no climate change damages and if there are no
renewables. So, we extend the Ramsey model in three ways and the DHSS model in two ways:
renewables and climate change. However, technically, the mere introduction of renewables
doesn’t pose any additional problem. If only the renewable are used from some instant of time
on, then they will be used up to the point where their marginal product equals their marginal
cost. From this equality we can solve the use of renewables as a function of the capital stock. By
substituting we are then back in the Ramsey model, with the same characteristics, including the
absence of negative externalities. What makes the analysis essentially different from
Krautkraemer’s is the timing of the transition from fossil fuel to the so-called backstop
technology, like solar of wind, that is not limited by a nonrenewable resource, and by the
introduction of stock dependent extraction costs of oil. We assume that in the absence of the
backstop technology the economy cannot maintain a constant positive level of consumption. As
outlined in the previous section, this is warranted if the production function is Cobb-Douglas
with a production elasticity of the resource being larger than the production elasticity of capital,
or if in the Cobb-Douglas case the depreciation rate is positive, or if for any positive capital
stock, the marginal product of oil goes to infinity as oil input approaches zero.
       The problem posed is rather complicated. Nevertheless some simple economic reasoning
provides valuable insights. The state in which the economy finds itself is given by the existing
man-made capital stock, the oil stock, and the stock of accumulated CO2. For each of these
stocks a shadow price can be calculated. The shadow price of capital can be interpreted as the
increase in welfare were an additional unit of capital available. The same interpretation can be
given to the shadow price of oil. Since CO2 accumulation reduces welfare, the shadow price of
the accumulated CO2 stock is negative. The negative (or absolute value) of this shadow price is
the social (marginal) cost of carbon: it measures the welfare cost of the marginal unit of
accumulated CO2, or the value of a removing the marginal unit of CO2 from the atmosphere.
       Renewable resources are used up to the point where the marginal product of energy they
provide is equal to their marginal cost. If the marginal cost is higher than the marginal product,
then the backstop is not used. The marginal product of oil should equal its marginal costs, if oil is
in place. The marginal costs consist of three terms. First, there are direct marginal extraction
                                                 16
costs that depend on the existing oil stock. Second, there are future extraction costs that are
higher due to more extraction today, because easily extractible resources are extracted first.
Third, there is additional extraction of oil bringing along additional climate change damages
caused by the accumulation of CO2.
       Most of the results depend on the scarcity of oil relative to capital. To that end we can
compare two economies, with the same technology and preferences, but that differ in terms of
initial situation. For example, if at some instant of time both have the same oil stock and have
accumulated the same amount of CO2, but one economy has more physical capital, then in the
latter economy the shadow price of oil relative to the shadow price of capital is bigger, because
capital is relatively abundant and therefore its shadow price is low relative to that of oil.
       At each instant of time three regimes are possible: a regime with only oil use, a regime
with only backstop use and a regime with simultaneous use of oil and the backstop. We have
restricted ourselves to economies that cannot sustain a positive level of consumption in case
there were no renewable resources. Hence, a regime with only oil use cannot last forever. An
economy that only uses renewable forever is called the carbon free economy. As has been argued
before this economy bears close resemblance to the Ramsey economy discussed earlier, and it
has a stable steady state, where the marginal product of capital equals the sum of the rate of
depreciation and the rate of pure time preference. We will call an economy developing if its
capital stock is below its carbon-free steady state. In such an economy consumption is low,
meaning that the marginal utility of consumption is high, relative to the marginal damage of
climate change. Hence, there will be a tendency to use only oil initially, because its climate costs
a still low. For a given initial capital stock below the carbon-free steady state there exist several
critical levels of the oil stock. If the oil stock is very low, only renewables are used forever. The
economy converges to the carbon free steady state. For oil above some threshold, but not too
high, the optimal sequence is to have an initial phase with only oil use, due to the fact that the oil
extraction costs are now lower than in the first regime. But after a while oil use comes to an end
and a transition to a phase with only renewable takes place. This phase lasts forever thereafter
and the economy converges to the carbon free steady state. Some oil is left unexploited. For a
high initial oil stock, it is optimal to start with oil again, but this goes on even in such a way that
there occurs growth beyond the carbon-free steady state. But this regime cannot last forever, and
                                                  17
there will be a final phase with simultaneous use of oil and the renewables along which the
economy converges to the carbon-free steady state, from above. In the latter scenario the
renewable are only used alongside oil. But, in the long run oil use vanishes. In a developed
economy, an economy endowed with a capital stock larger than the carbon-free steady state
stock, matters are different. Here consumption will be high, with a small marginal utility,
compared to marginal damage. Hence, it is well possible to use the backstop only in an initial
phase. The idea is not that this gives the economy the opportunity to recover from a state with
high climate damages, since it has been assumed that damages are irreversible, due to the
absence of decay of the CO2 stock. But, the point is that it is just too costly in environmental
terms to use oil. If the oil stock is low, there will, as before, only be use of the renewables. For
higher oil stock it is optimal to start with only renewables and then to make a switch to
simultaneous use forever. Finally, with a very high oil stock, and hence low extraction costs, it is
optimal to start with only oil and make the transition to simultaneous use later. So, although the
model seems rather complicated at the outset, the results are quite intuitive.
       Since climate change is a negative externality, it is interesting to consider the
implementation of the optimum in a market economy. Without environmental policy, the market
doesn’t take account of climate change and only trades off marginal extraction costs and costs of
the renewables. Hence, there will be too much oil use, and less, if any, will be left unextracted.
Since the only externality is the climate externality, brought about by the use of oil, a carbon tax
corresponding with marginal damage will do the job. The carbon tax is increasing in a
developing economy, but it might decrease in a developed economy. Introducing a carbon tax is
an example of “getting the prices right�, generally considered a necessary condition for obtaining
green growth. However, even if a carbon tax is politically feasible, getting the carbon tax right is
not an easy task. This is not much of a problem if in the social optimum the same preference
parameters (rate of time preference, utility function, damage function) are used as in the market
economy. But, it is also clear from the analysis that the optimal carbon tax does depend on the
rate of time preference used as well as on the elasticity of intertemporal substitution. For
example, a lower rate of intertemporal substitution implies a more equal distribution of welfare
over time, giving more welfare to the present poor generations, and therefore requires a lower


                                                 18
carbon tax initially. Hence, “getting the prices right� cannot occur without precise knowledge of
the preferences, and technology.
       One may wonder what happens if the government is, for political or other reasons, unable
to impose the appropriate carbon tax and relies, as in many western countries, on subsidizing the
backstop technology. Then, for sure, this policy is suboptimal. But one may wonder how
detrimental it is. This question is related to the green paradox, a concept introduced by the
German economist Hans-Werner Sinn (see Sinn (2008a and 2008b)). In general the green
paradox can be defined as the phenomenon that well-intended climate change policies have
adverse effects. Subsidizing backstop might provide a good example. Oil suppliers, realizing that
in the long run, they can sell less oil at high prices (since the backstop becomes cheaper) start to
pump oil earlier and at higher rates, thereby enhancing rather than mitigating the climate
problem in the short run. The question then arises whether, given the absence of an optimal
carbon tax, the subsidy is bad, where not only green welfare but also, and maybe, in particular,
overall social welfare should be taken into account. Let us concentrate on the developing
economy, where it is optimal to start with only oil and to have a transition to the backstop before
the carbon-free steady state is reached. If the backstop is very expensive, then the market will
fully deplete the oil stock before the transition to the backstop is made. A (marginal) subsidy on
the backstop leads to oil being pumped up faster. Oil will be depleted fully and the transition to
the carbon free economy takes place earlier. Green welfare (the negative discounted total climate
damages) as well as social welfare falls. But, since the economy is still in the early phase of
development, the decrease in welfare need not be high, since marginal utility of consumption is
low. If the backstop is relatively cheap, the market will not fully exhaust all oil. Nor will
depletion occur in the optimum. The effect of a subsidy is that the market will leave more oil in
the ground than before. Hence, compared with the laissez-faire economy, green welfare is
enhanced. Still, aggregate social welfare is smaller than in the optimum because of the distorting
effect of the subsidy. But in this case the subsidy is beneficial and there is no green paradox.
Hence we see that the occurrence of the green paradox depends on oil being depleted or not, and,
which is new in this analysis, on the development stage in which the economy finds itself.
       Many extensions and modifications present themselves. Perfect substitutability of energy
types is too extreme an assumption that calls for refinement. Moreover, the real world is
                                                19
composed of many different countries with different characteristics regarding preferences,
technology, and endowments of natural and other types of capital. The question arises how to
tackle the problems in our decentralized world.
       Tsur and Zemel (2011) develop a theoretical framework to study transitions to alternative
energy in developing countries. These countries are distinguished from developed countries by
having a lower capital stock and a high marginal product of capital. Capital can be either
operated by a conventional energy source (say fossil) at a constant cost (constant fossil price), or
by a new energy source (say solar) that has a very low flow cost (the cost of operating the solar
panels) but requires upfront investment in capacity (this makes their analysis different from Van
der Ploeg and Withagen). A country has to decide whether to invest in capital only and fuel it
with conventional sources or invest in solar capacity. Developing countries with low capital
stocks have high opportunity costs of investing in solar capacity since the marginal product of
capital is large and choose to postpone the transition. Within the same framework, Smulders et al
(2012) study the impact of imperfect emission policies on short run emissions and growth. In
particular, they study the effects of an emission tax that the country is committed to impose at
some point in future, potentially to comply with an (international) agreement on combating
pollution and climate change. When a future emission tax is announced, households expect a
decrease in consumption possibilities in future as a result of the policy being implemented then.
The best way to cope with this future negative shock is to start saving more and build up the
economy’s production capacity faster. Hence, the commitment to future environmental policy
raises growth and future consumption, but at the cost of short-run consumption. As compared to
the situation without the policy announcement, short-run emissions grow faster before the policy
is implemented and stay higher even after the emission tax is in place. The reason is that, as long
as the economy uses fossil energy, growth and emissions are coupled.



3.4 Ecosystem services

Many parts of nature and ecosystems are essential for production and wellbeing in the economy,
either because they directly provide resource inputs in production and utility (as discussed
above), or because they are essential for the regeneration of these inputs. The regeneration term
                                                  20
E(N) in equation (5) can be seen as depending on other factors including environmental capital
stocks that do not enter production or utility directly. When nature is overused, regeneration is
impaired and this may hamper growth of the economy, be it in the short long run, then in the
long run. Examples are agricultural land, forests, fisheries, water. These assets provide important
and sometimes necessary services, but the assets themselves deteriorate and may even become
obsolete if too much of the services is used. Many of these assets are closely related to
biodiversity as a source of ecosystem services.
       Until recently ecosystems have not played a prominent role in (environmental)
economics (Dasgupta, 2010, Fisher et al., 2011). Hence, only few studies exist where the
interrelationships between sustainable growth and ecosystems are explicitly modeled and
discussed. This is surprising because conservation and equitable and efficient use of ecosystems
affects present and future welfare. Here we go briefly into one example of such a dynamic
model, analyzed by Lopez (2011), which considers a competitive economy with open access to a
renewable resource. The resource develops according to (5) with a natural growth function and
harvest, but there is an additional factor that causes depletion. This is the activity in another
sector of the economy, the industrial sector. This activity may have a negative impact on the
growth of the resource through, for example, oil spills as a consequence of nonrenewable
resource use. Man-made capital accumulates through savings from profits in the industrial sector
(workers don’t save). In the long run the equilibrium in this economy can be of two types. If the
negative impact of industrialization on the natural resource is not too large, then industrialization
will not threaten sustainable development, even if, as is assumed in the model, no property rights
are defined on the natural resource. However, in less favorable circumstances that are identified
in the analysis, expansion of the industrial sector will make economic development
unsustainable.
       In a development context many issues are still unresolved and need further study. In
particular the physical interaction between economy and ecology is complex. Moreover, the
issue of property rights and distributional elements should be addressed. Finally, many
ecosystems deliver services on a global level and therefore constitute global positive
externalities, whereas the direct services are local in nature. An example are forests that play a


                                                  21
crucial role in the carbon cycle and are important for biodiversity, but also provide wood locally,
and may be used for agriculture after burning.



3.5 The resource curse

In the framework of the optimal growth model outlined in sections 3.2 and 3.3 the availability of
natural resources is beneficial for the development of the economy. In practice, however, some
resource rich countries perform successfully, whereas other countries do not seem to benefit
from their resource wealth at all. The latter phenomenon is called the resource curse. The
question why these differences occur is relevant and interesting. We cannot give an exhaustive
account here. We will just touch upon some of the explanations (see Van der Ploeg (2011) for an
excellent survey of the existing literature). Several hypotheses have been put forward. One
possibility is that the export of resources leads to an appreciation of the real exchange rate,
implying less growth of the traditionally exporting sector of the economy and hence of the
economy as a whole, if this sector was the engine of growth. Alternative explanations emphasize
the role of institutions: Windfall profits may enhance corruption, but well-functioning financial
markets may mitigate the negative effect on growth. It is also put forward that the discovery of
resources may lead to armed conflicts. And, finally, some resource rich countries have high
income inequality and less freedom, which could lead to low growth rates. Numerous studies
have been carried out to test for these hypotheses. But still there is a long way to go. The
research so far is inconclusive and may suffer from methodological problems. “...more work is
needed on how to manage natural resource revenues in a way that promotes sustainable growth,
alleviates poverty, and avoids conflict� (Van der Ploeg, o.c. p.408).



4. Long-run Growth and Technical Change


4.1. The role of technical change in sustaining growth
So far we have considered growth mainly as the result of the accumulation of man-made capital:
growth takes place if the returns to capital are large enough to warrant net investment in the

                                                 22
capital stock. With the expansion of the capital stock, however, the returns to capital fall, growth
slows down, and at some point (in the Ramsey model when the net return equals the discount
rate) growth stops. Output converges to a steady state without further growth if only physical
capital accumulation drives growth and there are diminishing returns.
       Real world growth rates have been fairly stable – or better trendless. This applies to the
US over the past century, and to the OECD countries as well as some fast growing developing
countries (India, China) over the past few decades. We can explain steady growth rates if some
force offsets the diminishing returns to capital. Various forces can be identified. First, if
investment rates increase over time, growth can be maintained at high levels (Jones, 2002), but
this necessarily comes at the cost of consumption, and cannot be maintained for a very long
period (as investment rates cannot grow forever). Second, technical change may improve the
productivity of inputs, including capital, thus increasing the returns to capital. As long as capital
grows fast relative to the rate of technical change, diminishing returns dominate and the growth
rate slows down over time. But before the growth of capital has slowed down to zero, the rate of
return becomes stable over time as soon as ongoing technical change (of the type that increases
the marginal product of capital) keeps exactly offsetting the diminishing returns from capital
investment. In the resulting balanced growth situation output grows thanks to technical change,
not only because it directly increases output, but also because it sustains capital accumulation.
The rate of technical change is therefore the most important source of long-run growth. Growth
accounting studies (see Caselli (2006) for a survey) confirm that technological change is the
main source of growth, dominating other important sources like (human) capital accumulation.
       The question now arises what growth rate can be maintained in the long run, and how
resource use affects this growth rate. In the subsections that follow we explore how technical
change can sustain growth if natural resources are an important input in production, what are the
different types of technological change that affect growth and resource use, and what forces
account for sustained innovation.


4.2. Non-renewable resources and long-run growth
If non-renewable resources, like oil and other energy resources, are necessary complementary
inputs in production and hard to substitute away from (i.e., if no backstop technology is available
                                                 23
at a large scale), resource use over time must reduce – ceteris paribus – the return to capital and
therefore the growth rate. This is because remaining reserves gradually get exhausted and
resource inputs in production ultimately have to fall over time. Since less energy is available to
run the capital stock, the return to capital falls. In this sense, non-renewable resources drag
growth down for two reasons: directly, since fewer resources are available in production over
time; and indirectly, since this scarcity reduces returns to investment and lowers the capital
stock.
         As a result, three forces shape the rate of return: capital accumulation, technical change,
and changes in resource inputs. Growth can only be sustained in the long run if the diminishing
returns from capital expansion and the drag from declining resource availability are offset by
technical change. Based on this logic, countries that are more dependent on non-renewables, or
in which capital and non-renewable resources are closer complements (countries that are more
“oil addicted�), grow correspondingly slower in the long-run for a given rate of technical change.
Also, an economy that extracts a bigger fraction of its reserves of non-renewables every period
(and therefore runs down this stock quicker over time) faces a lower long-run growth rate. All
these insights follow directly from the Dasgupta-Heal-Solow-Stiglitz model with given rates of
technological change.
         Groth and Schou (2002) study various (tax) policies in the DHSS model and show that
the above logic also leads to the conclusion that policies that affect resource use are more
important for long-run growth than policies that stimulate the accumulation of man-made capital.
The latter has a temporary effect only because of diminishing returns. However, any policy that
affects long-run resource use will affect the long-run growth rate: resource conservation will
reduce the resource drag and stimulate growth. Extending their conclusion to Green Growth
policies, one might state that moving from a development path along which resources ultimately
have to fall quickly over time (because of exhaustion of reserves) to a more conservationist
resource extraction path yields more sustained growth for future generations.




                                                 24
4.3 The effect of renewable resource conservation and environmental policy on growth
When the economy mainly depends on renewable (rather than non-renewable) resources, e.g.,
because of a large agricultural or fishery sector, a constant flow of resource inputs can be used in
production (at the level that is equal to regeneration capacity) in principle, so that the resource
drag on growth can be avoided. Nevertheless, when an economy starts from an unsustainably
high level of extraction (e.g., one above the maximum sustainable harvest, defined by the
maximum regeneration rate E(N)), resource use necessarily has to be reduced to a lower –
sustainable – level, either as a once-off shock or more gradually over time, in order to prevent
collapse of the resource. A resource drag then arises according to the same logic as above in the
case of non-renewables. There is an important difference, however. Investing in a larger
renewable resource stock is likely to generate production benefits. In the case of fishery, catching
cost fall and this enhances surplus in the sector. More generally, reduced pressure on renewable
resources can increase ecosystem services and improve the productivity of ecosystems and
ultimately also the productivity of the economic sectors that depend on the ecosystems. The
improved productivity (which typically takes time to materialize) may offset the reduced
production that follows (typically immediately) the reduced harvesting. Short-run costs generate
long-run benefits and the long-run rate of return may increase, thus stimulating investment and
growth.
       Similar effects are in place in the case of stock pollution. Reduced emission flows come
at a direct abatement cost, but lower concentrations of emissions in the atmosphere, water bodies
or soil generate productivity effects. These productivity gains could stem from health effects
(healthier workers are more productive) or eco-system services (a cleaner environment produces
more valuable services, such as more abundant fish stocks, lower costs of water treatment), or
tourism income if tourists are attracted by natural amenities. The DICE model that Nordhaus
(1994, 2008) developed to study the economics of climate change polices relies on a very similar
assumption, since in this Ramsey-type model the avoidance of climate change improves
productivity.
       Whenever resource use policies affect the rate of return, i.e., the marginal productivity of
man-made capital, there is an indirect effect on growth through capital investment. The cost of
environmental policy is magnified (the policy lowers output directly, and through reducing the
                                                25
marginal product of capital it also reduces investment indirectly), but the benefits are magnified
as well. How big these general equilibrium or interaction effects are depends on how important
man-made capital inputs are relative to resource inputs and how strong the diminishing returns
are (Smulders, 2000).
       Environmental improvements can spur growth through alternative mechanisms, which are
surveyed by Ricci (2007a). First, pollution taxes make consumption more expensive and
production labor less productive so that labor might shift from production to leisure and time
spent on education (e.g., Hettich (1998)). Second, the prospect of a cleaner environment might
induce households to save more and postpone consumption to the future if consumption and
amenities are complements (Michel and Rotillon, 1995; Mohtadi, 1996). Third, pollution taxes
might fall disproportionately on old goods if new generations of products become cleaner. Thus
a pollution tax speeds up obsolescence and stimulates innovation in new products (Hart, 2004;
Ricci, 2007b).


4.4. Green technology to sustain growth

Not all possible forms of technological change are equally conducive to sustained or sustainable
economic growth. Resource use is physically constrained: cumulative non-renewable resources
are fixed and finite and the flow of renewable resources is ultimately constrained by the natural
regeneration or natural growth rate of the resource stock. Hence, to reconcile growing output
with non-increasing resource use, the resource intensity of the economy, R/Y, has to fall over
time. This requires substitution (including substitution towards backstop use), or technical
change, or both. While substitution involves, as discussed before, the change in the mix of
inputs, technical change amounts to shifts of the production function for given amounts of inputs.
Technical change can stem from increased productivity of conventional inputs, better skills of
workers, higher thermodynamic efficiency to enhance the productivity of resource inputs, as well
as improvements in the organization, management, and marketing of the firm. A key
consideration in the context of Green Growth is the impact of technology on resource use and
incentives to accumulate man-made capital, which implies that we should carefully distinguish
between different types of technical change and sources of innovation.

                                               26
        A constant rate of growth can be sustained in the long run only if there is unbounded
factor-augmenting technological change for each non-growing (i.e., bounded) necessary factor of
production. The implication is that in an economy with limited natural resources, we need
resource-augmenting technical change, which is defined to occur if technological change has the
equivalent effect as an increase in resource inputs. Resource-augmenting technical change makes
it possible that effective inputs grow, while the inputs themselves (R) do not grow. Examples are
electricity-saving measures, fuel-efficiency improvements, improved drilling techniques that
increase effective economic reserves of resources, cost reductions in the production of alternative
energy.
        It is important to note that this notion of resource-augmenting technical change does not
necessarily play the same role as technical change in our previous section, where we focused on
technical change that increases the marginal product of capital. Nevertheless, as long as capital
and resources are complements, resource-augmenting technical change also enhances the return
to capital. 1 This situation arises for example if aggregate output can be represented by the often
used Cobb-Douglas production function. Technical change allows then for both reductions in
resource intensity and a constant rate of return to capital in the long run (i.e. along a balanced
growth path). Such a balanced growth path is technically feasible – whether it actually arises in a
market equilibrium or is preferred by society over other feasible paths is a different question.
        Another thing to notice from the definition and examples of resource-augmenting
technical change is that these are likely to involve specific effort. Sustained growth requires
sustained technical change, and there is no guarantee that it is technically feasible to sustain
technical change indefinitely or that there are sufficient incentives to generate unbounded
technical change in equilibrium. To say more about what drives innovation and technical change,
we first need to examine where various new technologies come from.


1
  Consider a production function that increases in the inputs capital, labor, resources, and technology (A). If
technology is resource augmenting, the function can be =            =
                                                       written as Y F                            ) , where R
                                                                                      ( K , L, R
                                                                      ( K , L, R, A) F                       ≡ AR
                                          (.) are functions that increase in all their arguments. Complementarity
is effective resource input and F(.) and F
between capital and resources means FKR > 0 . The return to capital is r = FK . An increase in technology increases
the rate of return since ∂r / ∂A         R= F R / A > 0 .
                                = FKA= FKR     KR




                                                        27
       Technical change can be most easily thought of as an increase over time in the
availability of (technical) knowledge that allows producing more per unit of inputs. Thus,
knowledge should be seen as a stock of ideas that changes only gradually over time. The total
stock of patents partially measures this stock (with the caveat that not all inventions are
patented), but also skills and experience that workers and firms accumulate are part of the
knowledge stock. New ideas arise from innovation activities, through public and commercial
R&D (Romer, 1990), learning-by-doing and learning-by-investing (Arrow, 1962; Romer, 1986)
and imitation with adaption to local circumstances (Grossman and Helpman, 1991). How much
of these activities take place is an economic decision with an associated cost-benefit calculation:
R&D requires effort to be devoted to innovation at the cost of other (notably production)
activities, learning-by-doing can be enhanced by producing (temporarily) more which requires
higher input costs. Changes in the returns and opportunity costs of innovation activities will
affect the equilibrium (or desired) level of innovation.
       Changes in resource use, e.g., as part of green policies, might affect both costs and
benefits of innovation activities and might change the rate and direction of technical change.
This endogeneity of technical change adds another channel that shapes the relationship between
growth and natural resources. The effect of resource use on technical change is in a way similar
to its effect on man-made capital accumulation that we discussed above. We argued that a
reduction in resource inputs or polluting inputs lowers the return to man-made or physical capital
and thus crowds out capital investment. Knowledge is one particular form of man-made capital
(since the stock of ideas can be expanded by innovation activities), which implies that reduced
resource use will not only crowd out physical capital but also knowledge capital so that
innovation might fall. For example, reduced energy use will reduce output and with it learning-
by-doing. Moreover, the returns to inventing new products will be lower since less energy is
available to manufacture these products, which makes them more costly and lowers the market
size for them. This same mechanism would make environmental policy more costly. Various
authors have analysed the effect of environmental policy in analytical growth models with
endogenous technology and find this crowding out effect (e.g., Stokey, 1998; Aghion and
Howitt, 1998). However, the mechanism also implies an increase in technical change (and hence
more growth) if the productivity effect of a cleaner environment or improved eco-service
                                                 28
systems dominates the effect from reduce resource inputs (Bovenberg and Smulders, 1995 and
1996). Thus, the more an economy has to endogenously generate its own technical change, the
more sensitive its growth is to changes in resource and environmental variables, in both
directions (Smulders, 2005). Growth in economies that mainly rely on imported (rather than
home-grown) technologies and diffusion of technologies from abroad may therefore be less
affected by resource and pollution policies, so that a Green Growth strategy (i.e. improving the
environment without hurting growth) is more realistic.
           The crowding out effect only arises for specific types of innovation (Smulders and Di
Maria, 2012). In particular, reduced energy inputs and polluting inputs crowd out innovation that
is complementary with polluting/resource inputs. These innovations can be characterized as
pollution-intensive (“brown�): they rely on polluting inputs and any decrease in these inputs
reduces the return to investing in physical capital or productivity-enhancing knowledge. These
innovations have to be distinguished from new “green technologies� which are substitutes for
polluting/resource inputs, i.e., the introduction of these technologies ceteris paribus reduces the
demand for polluting inputs or resource inputs. 2 Examples are improvements in abatement
technologies (like scrubbers or carbon capture and storage), cost reductions in alternative
(cleaner) energy production, and (under some circumstances 3) energy efficiency improvements.
Reduction in resource use and emission cuts can be expected to stimulate the demand for these
technologies, which implies crowding in of innovation.
           Several models incorporate opportunities for innovations of both types, green and brown
(e.g., Smulders and De Nooij (2003), Gerlagh (2008), Hart (2008), Grimaud and Rouge (2008),
Di Maria and Valente (2008), Gans (2011)), and thus allow for “Directed Technical Change�.
The issue here is which forces affect the innovators’ choices regarding the type of technical
change at which they direct their research efforts, and how this affects the overall rate of

2
    Formally, for the general production function Y = F ( K , L, R, A) , technology is defined to be brown if FAR > 0 .
Similarly, capital is defined to be brown if FKR > 0 . As before, K, A, and R are physical capital, knowledge capital,
and resource inputs respectively. Technology and capital are green if FAR < 0 and FKR < 0 .

3
 The exception is when the “rebound effect� occurs: higher energy efficiency might lower prices so much that
demand for energy increases.

                                                             29
technical change and growth. This literature returns to the question whether it is possible and
profitable to continue investing in new technologies at the rate that is needed to sustain growth.
         We identify four important lessons from the literature on DTC.
         First, investment in green technologies is needed to sustain growth in the long run if it is
hard to substitute man-made inputs for resource inputs. If there are opportunities for brown
innovations only or if the cost of green innovation becomes relatively high, the incentives to
innovate in the long run peter out. To see why this is so, recall that investment in brown
technologies is similar to investment in man-made capital in the models described above. If man-
made capital grows while the resource inputs, that are complements to this man-made capital, are
constant or even declining (maybe needed for environmental or resource scarcity reasons), the
return to investment in man-made capital stocks –including the return to brown innovation – falls
until growth stops. However, the benefits from green technologies would increase with the
reduction of pollution and resource use. This increases the incentives to invest in green
technologies, and this in itself stimulates productivity and growth at the aggregate level. Indeed,
in these types of models, a balanced growth path arises along which both innovations take place,
but the rate of green innovation is faster than the rate of brown innovation so that the drag of
reduced resource use is exactly offset by relatively green innovation (Smulders and De Nooij,
2003).
         The second insight from the DTC literature is that there are well defined circumstances
under which technology policy needs to focus more on green technologies than on conventional
technologies. This is not an obvious conclusion when one takes externalities as the rationale for
technology policies. As is well accepted, in general, the market for technology and innovation is
imperfect. Innovation builds on existing knowledge so that knowledge spillovers occur between
firms; innovators invent around previous patents and marginal improvements may drive existing
businesses out of the market, when entrants sell the new products and make the products of
incumbents obsolete (creative destruction). This implies that the reward that the innovator gets
by marketing her invention does not reflect the social benefits of her invention: she does not get
compensated for the knowledge spillovers that are created and she does not bear the cost of
business stealing. Most empirical studies find that the positive knowledge-spillover externality
dominates the negative externality from business stealing so that a subsidy to research is needed
                                                  30
to correct underinvestment in innovation. There are no reasons to expect that these imperfections
are different for brown and green innovations, so that one expects that both innovations should
be subsidized. This makes Newell et al. (2005) point out that environmental policy (and hence
green growth) is a problem of two interacting externalities: knowledge versus environmental
externalities.
        The general knowledge-externality-based argument in favor of technology policy has
been extended to answer the question whether green technologies warrant a higher subsidy than
brown ones. R&D subsidies should be bigger if the ideas that they generate benefit more
producers. This is an expression of the well-known Samuelson (1954) condition for public
goods: the social value of the innovation, which is a public good as far as it benefits many firms,
equals the sum of the benefits that all the firms derive from it in the form of knowledge
spillovers. With environmental policy, there will be a substitution to green methods of
production and more firms (or firms with larger markets) will benefit from spillovers from green
R&D. Hence, the total value of spillovers increases with environmental policy. For R&D related
to polluting sectors, the opposite happens. Hence, the optimal R&D subsidy for green
technologies is larger (Hart, 2008).
        The third insight from DTC literature is that environmental policy is less costly if there is
both green and brown innovation as compared to brown technology only, in so far as
environmental policy redirects innovation to green technologies. This confirms the insights from
the literature on innovation and environmental policy in a partial equilibrium context (cf.,
Goulder, 2004). It leads to the policy implication that environmental policy should harness
innovation forces. Unfortunately, in a second-best world there is no guarantee that the direction
of innovation responds to environmental policy in the socially desired way. For example, if
intellectual property rights are not well defined and protected across countries, innovators face
imitation and limited market potential for their innovations. It might imply that green technology
development in countries that implement stringent environmental policies is more than offset by
technical development in the opposite direction in other countries (see Di Maria and Van der
Werf (2008) and Di Maria and Smulders (2004) for DTC in the context of transboundary
pollution problems).


                                                 31
       As a fourth insight from the DTC literature, we mention that an economy might get
locked into a pollution-intensive model of production. Acemoglu et al. (2011) illustrate this.
They distinguish between green and brown firms or sectors, which both produce a similar good,
but only the former produces without emissions. In both sectors innovation can take place that
enhances productivity. Hence, innovation taking place in the brown, pollution-intensive, sector
increases the demand for polluting inputs and is bad for the environment. Innovation in the green
sector reduces prices of clean goods relative to brown goods and reduces pollution if consumers
substitute away from brown goods to green goods. Without environmental taxes, brown goods
are initially cheaper because they have a longer history of cost-reducing R&D. Firms in the
brown sector learn from other firms in the sector, and green firms learn from other green firms,
both to the same degree; both types of firms also have the same cost of R&D. Without
environmental policy, only brown firms undertake R&D since they have a larger market. Thus,
brown firms become even more productive over time and capture an even larger market share:
the economy becomes locked into a more polluting industry structure and the productivity gap
between brown and green goods becomes wider.



4.5. General purpose technologies

For the long-run it seems reasonable to expect that both green and brown innovation
opportunities are available. However, in the medium-run, past inventions and coincidental
technological developments might favor one of the two types of innovation. For example, the
invention of the transistor and micro-chip started a wave of innovations in information and
communication technologies in the 1990; the invention of the dynamo paved the way for the
introduction of electricity and development of a whole range of electricity-based appliances
(David, 1990); and the steam engine in the 18th century is another classic case. The transistor,
micro-chip, electricity, and steam engine can be called General Purpose Technologies (GTP,
Bresnahan and Trajtenberg, 1995), with two essential characteristics: they have the potential to
be applied in many sectors in the economy, and they open up room for subsequent marginal
improvements. Green growth might require a green GPT, that is, a GPT that makes emission-free
(or emission-poor) production more feasible and profitable. Examples are new ways to store
                                               32
electricity, thereby enhancing wind power, or cheap carbon capturing and sequestration (CCS)
technologies. In contrast, green growth might be difficult to attain as long as an economy is still
adapting to a brown GPT, i.e. a technology that, once introduced and gradually being improved,
increases the demand for resources and polluting inputs.
       Most models take the introduction of a new GPT as a random event (e.g., Helpman and
Trajtenberg, 1998; an exception is Eriksson and Lindh, 2000). Following this tradition, Smulders
et al. (2011) model the advent of a green GPT and the market response to it. The GPT is called
green since it allows for producing output with environmentally less harmful inputs (e.g.
switching from coal to gas or renewable in electricity plants or from gasoline to electricity in
transport). The GPT is thus partly a product innovation, which creates new (energy) inputs,
partly a process innovation, allowing producers to remodel their production process. The
adoption of the GPT is costly for each firm. Hence firms have to invest in GPT adoption to be
able to reduce pollution. The other type of innovation firms can opt for is improving the quality
of their product. Before the GPT arrives, pollution can only be regulated by direct emission
reduction policies or by reducing growth and output. Once the GPT arrives, a stringent emission
reduction policy provides strong incentives for the different sectors in the economy to adopt the
GPT and the economy gradually greens. At first this comes at the cost of regular investment in
product quality, but after most sectors have made the transition to the new GPT, regular
investment resumes and the economy grows at its old (pre-GPT) rate. The model provides a
technology-based explanation of the empirical finding of the environmental Kuznets curve
(EKC), but it also sheds light on the maybe more relevant issue of energy transitions.
       The optimal regulatory response to the advent of a green GPT is likely to affect
technology subsidies. Heggedal’s (2008) analysis gives useful insights. He discusses the
implications of diminishing returns on developing new knowledge in a specific field, here to be
interpreted as green technologies. When a new technology field is opened by the advent of a new
GPT, progress may initially be relatively easy, but will run into diminishing returns later on. In
particular, the initial progress may be easy to absorb by other firms so that spillovers are
relatively large in the early stages. Popp (2002) finds evidence of this pattern for green
technologies. Large yet falling spillovers imply that R&D subsidies should be high initially but
lower or phased out later on. In Heggedal’s setting an exogenous event creates new technological
                                                33
opportunities, for example, a breakthrough in nanotechnology or carbon capture and storage. If
this breakthrough is on a green technology, the green technology deserves a high subsidy.
However, the breakthrough could easily be a non-environmentally-friendly breakthrough (a
“brown GPT�), maybe nanotechnology with great increases in productivity but harmful effects
on living organisms. In this case, additional technology support is justified on efficiency grounds
for brown, rather than green, technology. Of course, emission taxes are still justified as well. In
normal cases, the positive technology shock raises the efficient emission tax through an income
effect: the innovation drives growth and richer economies have a higher willingness to pay for
environmental quality improvements. As a result, efficient green policy has to shift from
technology instruments to environmental instruments. However, it is also conceivable that the
pollution-using breakthrough lowers the efficient pollution tax. Intuitively, a high pollution tax
would kill too many of the opportunities opened up by the brown breakthrough (Smulders and Di
Maria, 2012).



5. Conclusions
We have reviewed several mechanisms through which green policies are linked to economic
growth in the literature on aggregate growth and resource use. Technical change and (human)
capital accumulation drive growth in per capita income. Demand for resources and polluting
inputs are likely to grow in tandem, unless their (relative) prices increase over time. For non-
polluting non-renewable resources with well-developed (futures) markets, prices will reflect
scarcities, but this is only one case. In other cases, policies are needed to correct externalities and
fill the gap of missing markets. More practically, explicit policies must be implemented if the
aim is to prevent pollution from rising and resources from being depleted too quickly. From our
review of the mechanisms we can conclude that such policies do not necessarily reduce growth.
       First, reducing pollution and enhancing eco-system services improves productivity and
hence growth in the long run. Second, the policies may induce technical change to shift in the
greener direction, thus making it easier to grow without increasing pollution or depleting natural
resources in the future.



                                                  34
       In the short run, however, investment in the environment seems to entail a necessary cost
in terms of reducing energy and resource inputs. Before possible productivity effects have their
full weight, this entails a drag on growth. The drag is augmented when capital accumulation and
technical change are reduced in response to the green policies: pollution-intensive sectors suffer
and cut back on investment and innovation. In contrast, green sectors may benefit. In a first-best
world, the latter reallocation would not entail a first-order welfare change and only the aggregate
crowding out of investment would matter. However, in a second-best world with initially
distorted allocation between sectors, this reallocation could produce a growth bonus, in particular
if pollution-extensive sectors are too small.
       Even if reduced resource use drags down growth in the medium run, the cost may be still
quite small. The share of resources in total GDP is typically low (with the exception of resource-
dependent developing countries). In contrast the share of capital is much larger. This implies that
modest reductions in resource use cannot dramatically affect income and capital formation.
       Similarly, the effect of green policies on investment in technologies may be small on an
aggregate level but large when confined to green technologies. In the most optimistic scenario,
green technologies, i.e., technologies that make production without (or with less) pollution or
resources possible, can be developed at the same cost as traditional pollution-using technologies.
After a transition period during which firms and sectors introduce the new technology, the world
would then grow as before but is greener.
       It seems likely that long-run growth is not affected too much by green policies. The
challenge is how to not affect growth in the medium run. On top of this come distributional
issues and political economy obstacles to policy reform. Therefore, now that growth is still
robust in many developing countries, this seems the best time to start green policies.


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