Dasgupta-Heal-Solow-Stigliz Model (1974)
The following model adds limited natural resources to a model similar to the one developed by Sollow.
The stock of the non-renewable resource is depleted at the following rate and overall lower than the initial stock:
Another alternative of the model is resource augmenting technology, where that leads to an increase in effective natural resource avaialability bigger than the decline of the resource stock.
The third option to explain long term economic growth is by permanently increasing the other factors, capital and labor. That would be easier the higher the productivity of those factors is.
Green Solow Model with abatement
The green Solow model keeps the main construct of the Solow model, but adds an abatement sector, where a part of production is dedicated to abatement /reduction of emissions. The effectveness of that abatement depends on the exogeneously rate of abatement technology development.
It is showed that emissions reductions is compatible with growth, as long as the abatament effectiveness growth is greater the the technology and labor supply growth.
A less stringent condition is for the labor supply and technological growth to be zero, so it sufficies to have some abatement effectiveness growth to reduce emissions in the steady state.
The model gives concrete values for the rate of abatement effectiveness for an increase in environmental quality with and without economic growth, but it does not explain how this abatement effectiveness growth happens. There is no investment require for abatement to be more effective and compensate for the scale and compositions effects of effective labor growth.
AK Model with Abatement
The AK model with abatement considers abatament the source of technological change but not part of the resulting production explicitly, only explicitely as it conditions the state of technology. Here we explore two different abatament functions, one where abatement requirements are proportional to economic output, and another where the composition of the production inputs affect the required abatement rate to ensure certain levels of emissions.
Constant composition of abatement
In that specification, there exists a balanced growth path where all variables, including abatement, growth at the same rate and emissions stay constant. That is as long as the pollution resulting from production requires a proportional increase of abatement.
Elastic composition of inputs and emissions
If the abatement requirements change depending on the level of the input factors K or A, the composition of the emissions function will break that balanced growth path if K or A contributes differently. It is normally assumes that epsilon is greater than 1, so capital increases pollution more than the reduction in emissions for the same level in abatement.
The capacity for abatement to create sufficient technological change depends on mu. Bounded contributions of abatement to technology, where mu <1, leadsto the fact that output growth leads to emissions growth. On the contrary, when epsilon is lower than 1, economic growth is compatible with a decrease in emissions.
Zero growth conditions
The first suprising result we get is that pollution is not lower with zero than we positive growth under some conditions. The reason behind this is that the amount of technological change T grows with the amount of abatement, which leads to lower emissions per unit of ouput.
Nevertheless when the capacity of abatement to generate technological pogress is limited and mu<1, that shows that economic growth leads to increasing production. This is the most likely relationship, and there is marginal limited capacity of abatement to improve the technological state.
For the expected values of mu <1 and epsilon >1, the steady state of emissions is achieve only when output growth is zero. That means that capital accumulation should stop and hence output growth.
Directed Technical change with clean and dirty sectors
This model contains a dirty and clean sector. For simplicity the latter generates no emissions. Growth is explain by the amount of technological change, and emissions will depend on where the technological progress happens.
The developments of environmental quality depends on the size of the dirty sector and its pollution intensity:
The direction of the technological change depends on the expected profits from the investment of such inventions, and the state of the technology in that sector. The assumption here is that the clean sector (based on renewable energy, organic inputs...) has a lower return in the investment of technology (lower economies of scale, lower energy density, lower ER....) and therefore without state intervetions, investments will happen only in the dirty sector (fossil fuel intensive). It is therefore required that sufficient taxes are applied to the dirty sector or subsidies on the clean sector to change that situation and incentivize investments in the clean one.
The length of the regulation depends on the strength of substitution between the clean and dirty goods. If the goods are strong subtitutes, once the state of technology of the clean sector is sufficiently strong, there is no need to further regulate and the market will automatically invest in the clean sector.
When the goods are complentary, a permanent tax or subsidy is required, as the growth of one sector require the growh of the other (public transport and materials) .
Economic growth without increases emissions only happens with high susbtitution, with complementary output growth leads to pollution growth.
Zero growth conditions
Zero growth in emissions with growth in economic output depends heavily on high levels of substitution between the factors.
As the level of emissions both as a stock and flow is beyond safe levels, a reduction of the emissions is required, and hence a shrinkage of the overall output activity. That could mean even a reduction of the clean sector, if the assumption of zero emissions is removed.
Any transition to a stagnation or reduction of emissions should include some sort of regulation to achieve permanent investment in clean sector technological development. The extent of the tax or subsisdy depends on the substitutability of both sectors.
Labor reductions will be also required as the clean sector becomes more productive. That can start in the dirty sector and progressively in the clean sector dependent of the desire level of emissions. The extent of the reduction in the dirty sector depends on the productivity, and hence the bigger the gap between sectors in productiviy the smaller the reduction in worker hours needs to be, given the efficacy to reduce output.
Concluding remarks
The models presented here help us to understand conditions at which emissions or the state of the environment could be improved in the steady state of output.
The DHSS (1974) models proposes substitution of natural resources, resource augmenting technology and a reduction is resource use to reconcile economic growth and non-renewable resource availability. The degree at which one could substitute resources or improve its productivity is limited, and hence the conditions for permanent economic growth are very stringent. Even in zero growth economies, the non-renowable source decay affects long terms perspective of economic stability, and only finding renewable substitutors of energy or materials the economy could sustain a given size in time.
The Green Solow model adds abatement as part of the production efforts, and specify clearly the rate of technological progress of abatement to ensure emissions goes done as output rises. Increase in the effective supply of labor requires faster advances in the abatement technology. It is easier to achieve a better state of the environment without effective labor and output growth.
The Directed Technological change with a clean and dirty sectors indicate that the clean sector, given its lower footprint and profitability, requires goverment support in order to be the focus of private innovation investment. If the sectors are highly interchangeable, a temporal subsidy suffices to reduce emissions and transition to the clean sector, while permanent regulations are required for complements. The overall output and emissions levels will stay constant in the long term if effective labor also stagnate, as the growth of the productivity of the clean sector will lead to moderate but consistent emissions increases.
As we found in the ecological economics literature, it is simply easily to achieve lower emissions, better environmental state or resource availability in economies in the steady state than growing economies. The lack of tipping points or level effects on that models should not invalidate that insight.
In section 2.4 we provide a synthesis of the results from section 2 and list the main limitations of the theory, partiarly overcome by keynessian theories.
Comments
Post a Comment