Using the NAG Fortran Library to model the economic impact of climate change.

Using the NAG Fortran Library to model the economic impact of climate change.

Stuart Fitz-Gerald
(Written May 13th 2007)

Since its publication the Stern Review (Stern 2007) has fuelled concerns about the apparent lack of success by governments in implementing systematic measures to avert the World's headlong rush into irreversible climate change.

The picture painted by Stern is bleak indeed. If a “business as usual” position is maintained and concerted joint action is not taken by governments on a global scale, there is a significant likelihood that the build-up of greenhouse gases (GHGs) will result in economic and environmental disaster.

The case presented by Stern is exceedingly persuasive, supported as it is by properly researched science and powerful economic analysis. His conclusions really are difficult to argue with. Of course, much of the argument depends upon reliable prediction, and the Review recognises that caution must be applied to the precision of the predictions. None the less the underlying message is clear - do something now or expect serious consequences in the future.

It is attractive to examine the Stern position from the perspective of an economic modeller. Initially by exploring various scenarios, under the guise of a world economy, using this to test the position proposed under various Stern regimes. The structure can then be adjusted to that of a small number of collaborating and non-collaborating large economies and examining the possible effects of these adjustments on outcomes.

A fruitful, but recently underused, approach to modelling these types of situations is recursive linear programming. The technique was first proposed by Day (1963), extended and enhanced by Day & Groves (1975) and presented formally with numerous applications in Day & Cigno (1978). The conclusions of these early studies suggest that recursive linear programming is a highly appropriate addition to the current research agenda, see for example Cigno (1978). The preoccupation of environmentalists and economists with the impact of climate change calls for just such a mechanism for tracking trajectories of economic variables under a variety of guises. So where does NAG come in?

A central component of any recursive linear programming model is the ability to solve a sequence of linear programmes, whose parameters are inter alia updated by the solution of earlier linear programmes in the sequence. Solution values are passed to updating routines which supply new values for the next problem to be solved. Conclusion of the simulation can either be forced i.e. simulate for n years or to finish naturally as a result of the system reaching some end-point. In the case of a climate simulation model this could be when the world dies or from an economic standpoint when the economy is no longer viable. As indicated earlier, the simulation requires the calling of a linear programming solution algorithm in each period, using the updated parameters supplied by the routines in the program.

NAG is particularly well positioned to help in developing and properly testing such simulations. The NAG Fortran Library (Numerical Algorithms Group 2006) offers a suite of solution routines for linear programmes which can be easily called from within a programme. The Fortran language itself is an ideal candidate for producing the programmes which drive the simulation, allowing repeated updating computations and calls to fast routines to solve possibly hundreds of linear programming problems. The extended capabilities of the revised Fortran standard (see Metcalf, Reid & Cohen (2004)) itself presents a rich array of computational possibilities. There are also many routines available in the NAG Library which can be used for subsequent testing of the performance of each simulation.

NAG have kindly offered to help in the development of these simulation experiments, partly under the CHEST agreement and through an extended trial use of their Fortran 95 compiler. The simulations will be run on a MAC powerbook running MacOS 10.3.9. The research is part of a wider project based at Kingston Business School, Kingston University and is led by Stuart Fitz-Gerald (email id: fitzgerald@kingston.ac.uk).

References
Cigno, A. (1978), Population and Natural Resources, in R. H. Day & A. Cigno, eds, ‘Modelling Economic Change: The Recursive Programming Approach’, North-Holland, chapter 7, pp. 287-308.
Day, R. H. (1963), Recursive Programming and Production Response, North-Holland.
Day, R. H. & Cigno, A., eds (1978), Modelling Economic Change: The Recursive Programming Approach, North-Holland.
Day, R. H. & Groves, T., eds (1975), Adaptive Economic Models, Academic Press.
Metcalf, M., Reid, J. & Cohen, M. (2004), fortran 95/2003 explained, Oxford University Press.
Numerical Algorithms Group (2006), NAG Library Manual, Mark 21, Oxford.
Stern, N. (2007), The Economics of Climate Change: The Stern Review, Cambridge University Press.

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