Parameter Definition Values for simulation
ρ discount rate 0.03
n rate of population growth 0.015
α1 share of public resources used to build up new public capital
0.1
α2 share of public resources used for the transfers and public consumption
0.7
α3 share of public resources used for the functioning of the administration
0.1
η exponent in the utility function 0.1
Mf pre-industrial level of GHG concentration 1
ε exponent in the utility function 1.1
ν1 fraction of public capital to support market activity 0.6 (∈[0,1]) ν2 fraction of public capital to mitigate climate change
damages
0.3 (∈[0,1])
ν3 fraction of public capital to reduce GHG emissions 0.1 (∈[0,1])
ω exponent in the utility function 0.05
σ exponent in the utility function 1.1
A prductivity of output production 1
An efficiency index of private capital in production 1 Ar efficiency index of non-renewable resources in
produc-tion
30 (∈[10,100])
α exponent of private capital and resource in the pro-duction function
0.5
β exponent of public capital in the production function 0.5
δk depreciation of private capital 0.075
δg depreciation of public capital 0.05
ψ parameter in extraction cost function 1
τ parameter in extraction cost function 2
ifp foreign aid per period earmarked for investment in public capital
0.05
ibp net borrowing per period earmarked for investment in public capital
0
γ fraction of GHG emissions not absorbed by the ocean 0.9 µ inverse of the atmospheric lifetime of GHG emissions 0.01 κ parameter deterimining the level where GHG
cocen-tration can be stabilized
2 θ efficiency of public sector’s efforts to reduce GHGs 0.01
References
Amrit, R., Rawlings, J. B. and Angeli, D. (2011). Economic optimization using model predictive control with a terminal cost,Annual Rev. Control35: 178–186.
Angeli, D., Amrit, R. and Rawlings, J. B. (2009). Receding horizon cost optimization for overly constrained nonlinear plants,Proceedings of the 48th IEEE Conference on Decision and Control – CDC 2009, Shanghai, China, pp. 7972–7977.
Angeli, D. and Rawlings, J. B. (2010). Receding horizon cost optimization and control for nonlinear plants,Proceedings of the 8th IFAC Symposium on Nonlinear Control Systems – NOLCOS 2010, Bologna, Italy, pp. 1217–1223.
Aruoba, S. B., Fernandez-Villaverde, J. and Rubio-Ramirez, J. F. (2006). Comparing solution methods for dynamic equilibrium economies,J. Econ. Dyn. Control 30: 2477–
2508.
Azariadis, C. and Drazen, A. (1990). Thresholds externalities in economic development, Quarterly Journal of Economics105(2): 501–526.
Bertsekas, D. P. (2005). Dynamic Programming and Optimal Control, Vol. 1, 3 edn, Athena Scientific.
Bréchet, C., Camacho, C. and Veliov, V. M. (2012). Adaptive model-predictive climate policies in a multi-country setting, Documents de Travail du Centre d’Economie de la Sorbonne 2012.29.
Brock, W. A. and Mirman, L. (1972). Optimal economic growth and uncertainty: the discounted case,J. Econ. Theory 4: 479–513.
Brock, W. A. and Scheinkman, J. A. (1976). Global asymptotic stability of optimal con-trol systems with applications to the theory of economic growth, J. Econom. Theory 12(1): 164–190. Hamiltonian dynamics in economics.
Brock, W. and Starrett, D. (1999). Nonconvexities in ecological management problems, SSRI Working Paper 2026, Department of Economics, University of Wisconsin–Madison.
Camilli, F. and Falcone, M. (1995). An approximation scheme for the optimal control of diffusion processes,RAIRO, Modélisation Math. Anal. Numér.29: 97–122.
Cannon, M., Kouvaritakis, B. and Wu, X. (2009). Probabilistic constrained MPC for multi-plicative and additive stochastic uncertainty,IEEE Trans. Automat. Control54(7): 1626–
1632.
Capuzzo Dolcetta, I. (1983). On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming,Appl. Math. Optim. 10: 367–377.
Collard, F. and Juillard, M. (2001). Accuracy of stochastic perturbation methods: The case of asset pricing models,J. Econ. Dyn. Control 25: 979–999.
Couchman, P. D., Cannon, M. and Kouvaritakis, B. (2006). Stochastic MPC with inequality stability constraints,Automatica 42(12): 2169–2174.
Damm, T., Grüne, L., Stieler, M. and Worthmann, K. (2014). An exponential turnpike theorem for dissipative discrete time optimal control problems,SIAM Journal on Control and Optimization52(3): 1935–1957.
Diehl, M., Amrit, R. and Rawlings, J. B. (2011). A Lyapunov function for economic optimizing model predictive control,IEEE Trans. Autom. Control 56: 703–707.
Dorfman, R., Samuelson, P. A. and Solow, R. M. (1987).Linear Programming and Economic Analysis, Dover Publications, New York. Reprint of the 1958 original.
Falcone, M. (1987). A numerical approach to the infinite horizon problem of deterministic control theory,Appl. Math. Optim. 15: 1–13. Corrigenda, ibid., 23 (1991), 213–214.
Farmer, R., Waggoner, D. and Zha, T. (2009). Understanding Markov-switching rational expectations models, Journal of Economic Theory144: 1849–1867.
Feichtinger, G., Kort, P., Hartl, R. F. and Wirl, F. (2001). The dynamics of a simple relative adjustment–cost framework, German Economic Review 2(3): 255–268.
Greiner, A., Grüne, L. and Semmler, W. (2014). Economic growth and the transition from non-renewable to renewable energy,Environment and Development Economics. To appear.
Greiner, A. and Semmler, W. (2008). The Global Environment, Natural Resources, and Economic Growth, Oxford University Press, Oxford, UK.
Greiner, A., Semmler, W., Diallo, B., Rezai, A. and Rajaram, A. (2007). Fiscal policy, public expenditure composition, and growth. Theory and Empirics, World Bank Policy Research Paper no. 4405.
Grüne, L. (1997). An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equa-tion,Numer. Math.75(3): 319–337.
Grüne, L. (2013). Economic receding horizon control without terminal constraints, Auto-matica 49: 725–734.
Grüne, L. and Pannek, J. (2011). Nonlinear Model Predictive Control. Theory and Algo-rithms, Springer-Verlag, London.
Grüne, L. and Semmler, W. (2004). Using dynamic programming with adaptive grid scheme for optimal control problems in economics, J. Econ. Dyn. Control28: 2427–2456.
Grüne, L. and Stieler, M. (2014). Asymptotic stability and transient optimality of economic MPC without terminal conditions,Journal of Process Control 24(8): 1187–1196.
Haunschmied, J. L., Kort, P. M., Hartl, R. F. and Feichtinger, G. (2003). A DNS-curve in a two-state capital accumulation model: a numerical analysis, J. Econ. Dyn. Control 27(4): 701–716.
Judd, K. and Guu, S.-M. (1997). Asymptotic methods for aggregate growth models, J.
Econ. Dyn. Control 21: 1025–1042.
Judd, K. L. (1998). Numerical methods in economics, MIT Press, Cambridge, MA.
Juillard, M. and Villemot, S. (2011). Multi-country real business cycle models: Accuracy tests and test bench,Journal of Economic Dynamics and Control35(2): 178 – 185.
Kaganovich, M. (1985). Efficiency of sliding plans in a linear model with time-dependent technology,The Review of Economic Stuidies52(4): 691–702.
Kerrigan, E. C. (2000). Robust constraint satisfaction: Invariant sets and predictive control, PhD Thesis, University of Cambridge.
McKenzie, L. W. (1986). Optimal economic growth, turnpike theorems and comparative dynamics, Handbook of Mathematical Economics, Vol. III, North-Holland, Amsterdam, pp. 1281–1355.
Parra-Alvarez, J. C. (2012). A comparison of numerical methods for the solution of continuous- time DSGE models, Manuscript, University of Aarhus.
Rawlings, J. B. and Mayne, D. Q. (2009). Model Predictive Control: Theory and Design, Nob Hill Publishing, Madison.
Santos, M. S. and Vigo-Aguiar, J. (1995). Accuracy estimates for a numerical approach to stochastic growth models, Discussion Paper 107, Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis.
Santos, M. S. and Vigo-Aguiar, J. (1998). Analysis of a numerical dynamic programming algorithm applied to economic models,Econometrica 66: 409–426.
Scheinkman, J. (1976). On optimal steady states ofn-sector growth models when utility is discounted,Journal of Economic Theory 12: 11–30.
Sims, C. A. (2005). Rational inattention: a research agenda, Discussion Paper Series 1:
Economic Studies, 34, Deutsche Bundesbank Research Centre.
Sims, C. A. (2006). Rational inattention: Beyond the linear-quadratic case, American Economic Review, American Economic Association96: 158–163.
Skiba, A. (1978). Optimal growth with a convex-concave a production function, Economet-rica46(3): 527–539.
von Neumann, J. (1945). A model of general economic equilibrium,The Review of Economic Studies13(1): 1–9.
Zaslavski, A. (2006).Turnpike Properties in the Calculus of Variations and Optimal Control, Springer, New York.
Zaslavski, A. (2014).Turnpike Phenomenon and Infinite Horizon Optimal Control, Springer International Publishing.