Growth Theory, green growth; Turnpike theory, multisector models, optimization
Abstract :
[en] We present an overview of selected contributions of the Journal
of Mathematical Economics' authors to growth theory in the last half
century. We start with the classical optimal growth theory within a
benchmark multisector model and outline the successive developments in the analysis of this model, including the turnpike theory. Different re finements of the benchmark are considered along the way. We then survey the abundant literature on endogenous
fluctuations in two sector models. We conclude with two strong trends in the recent growth literature: green growth and infi nite-dimensional growth models.
Disciplines :
Quantitative methods in economics & management
Author, co-author :
Augeraud-Veron, Emmanuelle
Bouicekkine, Raouf
Gozzi, Fausto
Venditti, Alain
ZOU, Benteng ; University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Department of Economics and Management (DEM)
External co-authors :
yes
Language :
English
Title :
Fifty years of mathematical growth theory: Classical topics and new trends
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Bibliography
Acemoglu, D., Recent Developments in Growth Theory. 2004, Edward Elgar Publishing.
Akao, K.-I., Kamihigashi, T., Nishimura, K., Monotonicity and continuity of the critical capital stock in the Dechert-Nishimura model. J. Math. Econom. 47 (2011), 677–682.
Alvarez, F., Stokey, N., Dynamic programming with homogenous functions. J. Econom. Theory 82 (1998), 167–189.
Amir, R., Multisector sensitivity analysis of multisector optimal economic dynamics. J. Math. Econom. 25 (1996), 123–141.
Arnold, L., Crauel, H., Wihstutz, V., Stabilization of linear systems by noise. SIAM J. Control Optim., 21(3), 1983, 10.1137/0321027.
Asheim, G., Buchholz, W., Tungodden, B., Justifying sustainability. J. Environ. Econ. Manag. 41 (2001), 252–268.
Augeraud-Veron, E., Bambi, M., Endogenous growth with addictive habits. J. Math. Econom. 56 (2015), 15–25.
Augeraud-Veron, E., Bambi, M., Gozzi, F., Solving internal habit formation models through dynamic programming in infinite dimension. J. Optim. Theory Appl. 173 (2017), 584–611.
Ballestra, L.V., The spatial AK model and the Pontryagin maximum principle. J. Math. Econom. 67 (2016), 87–94.
Banerjee, K., Suppes-sen maximality of cyclical consumption: The neoclassical growth model. J. Math. Econom. 70 (2017), 51–65.
Banerjee, K., Mitra, T., Equivalence of utilitarian maximal and weakly maximal programs. J. Math. Econom. 46 (2010), 279–292.
Barro, R., Are government bonds net wealth?. J. Polit. Econ. 82 (1974), 1095–1117.
Becker, R., On the long-run steady state in a simple dynamic model of equilibrium with heterogeneous households. Q. J. Econ. 95 (1980), 375–382.
Becker, R., Borissov, K., Dubey, R.S., Ramsey equilibrium with liberal borrowing. J. Math. Econom. 61 (2015), 296–304.
Becker, G.S., Mulligan, C., The endogenous determination of time preference. Q. J. Econ. 112:3 (1997), 729–758.
Benhabib, J., Nishimura, K., The Hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth. J. Econom. Theory 21 (1979), 421–444.
Benhabib, J., Nishimura, K., Competitive equilibrium cycles. J. Econom. Theory 35 (1985), 284–306.
Benhabib, J., Nishimura, K., Indeterminacy and sunspots with constant returns. J. Econom. Theory 81 (1998), 58–96.
Bensoussan, A., Da Prato, G., Delfour, M.C., Mitter, S.K., Representation and Control of Infinite Dimensional Systems, 2007, Birkhäuser, Boston, 1992–1993.
Bewley, T., An integration of equilibrium theory and turnpike theory. J. Math. Econom. 10 (1982), 233–267.
Boldrin, M., Montrucchio, L., On the indeterminacy of capital accumulation paths. J. Econom. Theory 40 (1986), 26–39.
Borissov, K., Dubey, R.S., A characterization of Ramsey equilibrium in a model with limited borrowing. J. Math. Econom. 56 (2015), 67–78.
Bosi, S., Magris, F., Venditti, A., Competitive equilibrium cycles with endogenous labor. J. Math. Econom. 41 (2005), 325–349.
Bosi, S., Nishimura, K., Venditti, A., Multiple equilibria in two-sector monetary economies: An interplay between preferences and the timing for money. J. Math. Econom. 46 (2010), 997–1014.
Bosi, S., Seegmuller, T., On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply. J. Math. Econom. 46 (2010), 475–492.
Boucekkine, R., Camacho, C., Fabbri, G., Spatial dynamics and convergence: The spatial AK model. J. Econom. Theory 148:6 (2013), 2719–2736.
Boucekkine, R., Fabbri, G., Federico, S., Gozzi, F., Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution. J. Math. Econom., 98, 2021, 102577.
Boucekkine, R., Fabbri, G., Gozzi, F., Egalitarianism under population change: Age structure does matter. J. Math. Econom. 55 (2014), 86–100.
Boucekkine, R., Germain, M., Licandro, O., Replacement echoes in the vintage capital growth model. J. Econom. Theory 74:2 (1997), 333–348.
Boucekkine, R., Hritonenko, N., Yatsenko, Y., Scarcity, regulation and endogenous technical progress. J. Math. Econ. 47 (2011), 186–199.
Boucekkine, R., Martinez, B., Ruiz-Tamarit, R., Growth vs level effect of population change on economic development: An inspection into human-capital-related mechanisms. J. Math. Econom. 49 (2013), 312–334.
Boucekkine, R., Ruiz-Tamarit, R., Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model. J. Math. Econom. 44 (2008), 33–54.
Brito, P.B., The dynamics of growth and distribution in a spatially heterogeneous world. Portuguese Econ. J. 21 (2022), 311–350.
Brito, P., Venditti, A., Local and global indeterminacy in two-sector models of endogenous growth. J. Math. Econom. 46 (2010), 893–911.
Brock, W., On existence of weakly maximal programmes in a multi-sector economy. Rev. Econom. Stud. 37 (1970), 275–280.
Brock, W., Xepapadeas, A., Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control. J. Econom. Dynam. Control 32 (2008), 2745–2787.
Chichilnisky, G., Existence of optimal savings policies with imperfect information and non-convexities. J. Math. Econom. 8 (1981), 1–14.
de la Croix, D., Licandro, O., Life expectancy and endogenous growth. Econom. Lett. 65 (1999), 255–263.
d'Albis, H., Augeraud-Véron, E., Endogenous retirement and monetary cycles. Math. Popul. Stud. 15 (2008), 214–229.
d'Albis, H., Augeraud-Véron, E., Hupkes, H.J., Multiple solutions in systems of functional differential equations. J. Math. Econom. 52 (2014), 50–56.
d'Albis, H., Augeraud-Véron, E., Venditti, A., Business cycle fluctuations and learning-by-doing externalities in a one-sector model. J. Math. Econom. 48 (2012), 295–308.
d'Albis, H., Le Van, C., Existence of a competitive equilibrium in the Lucas (1988) model without physical capital. J. Math. Econ. 42 (2006), 46–55.
Dana, R., Le Van, C., Optimal growth and Pareto optimality. J. Math. Econom. 20 (1991), 155–180.
Dechert, R., Nishimura, N., A complete characterization of optimal growth paths in an aggregated model with a non-concave production function. J. Econom. Theory 31 (1983), 332–354.
Delfour, M.C., Mitter, S.K., Controllability and observability for infinite-dimensional systems. SIAM J. Control 10 (1972), 329–333.
Deng, L., Khan, A., Mitra, T., Exact parametric restrictions for 3-cycles in the RSS model: A complete and comprehensive characterization. J. Math. Econom. 90 (2020), 48–56.
Diekmann, O., Van Gils, S.A., Lunel, S.M., Walther, H.O., Delay Equations: Functional-, Complex-, and Nonlinear Analysis, 2012, Springer Science & Business Media.
Drugeon, J.P., On intersectoral asymmetries in factors substitutability, equilibrium production possibility frontiers and the emergence of indeterminacies. J. Math. Econ. 44 (2008), 277–315.
Dubey, R.S., Mitra, T., On the nature of suppes-sen maximal paths in an aggregative growth model. Soc. Choice Welf. 40 (2013), 173–205.
Dufourt, F., Vivès, R., Venditti, A., On sunspot fluctuations in variable capacity utilization models. J. Math. Econom. 76 (2018), 80–94.
Epstein, L., Implicitly additive utility and the nature of optimal economic growth. J. Math. Econom. 15 (1986), 111–128.
Erol, S., Le Van, C., Saglam, C., Existence, optimality and dynamics of equilibria with endogenous time preference. Journal of Mathematical Economics 47 (2011), 170–179.
Etro, F., Technologies for endogenous growth. J. Math. Econom., 105, 2023, 102808.
Fabbri, G., Gozzi, F., Solving optimal growth models with vintage capital: The dynamic programming approach. J. Econ. Theory 143 (2008), 331–373.
Flandoli, F., Gubinelli, M., Priola, E., Well-posedness of the transport equation by stochastic perturbation. Invent. Math. 180 (2010), 1–53.
Ghiglino, C., Trade, redistribution and indeterminacy. J. Math. Econ. 43 (2007), 365–389.
Giuseppe, F., Gozzi, F., Pignotti, C., Optimal strategies in linear multisector models: Value function and optimality conditions. J. Math. Econom. 44 (2008), 55–86.
Goenka, A., Jafarey, S., Pouliot, W., Pollution, mortality and time consistent abatement taxes. J. Math. Econ. 88 (2020), 1–15.
Goenka, A., Nguyen, M.-H., General existence of competitive equilibrium in the growth model with an endogenous labor-leisure choice. J. Math. Econom. 91 (2020), 90–98.
Gong, L., Zhao, X., Yang, Y., Hengfu, Z., Stochastic growth with social-status concern: The existenceof a unique stable distribution. J. Math. Econom. 46 (2010), 505–518.
Gozzi, F., Leocata, M., Stochastic time-space AK models. SIAM J. Control Optim. 28 (2022), 851–902.
Guerrero-Luchtenberg, C.L., A uniform neighborhood turnpike theorem and applications. J. Math. Econom. 34 (2000), 329–357.
Ha-Huy, T., Thien Tran, N., A simple characterisation for sustained growth. J. Math. Econom. 91 (2020), 141–147.
Hale, J.K., Lunel, S.M.V., Introduction To Functional Differential Equations, 2013, Springer Science & Business Media.
Hartl, R., Kort, P., History dependence without unstable steady state: A non-differentiable framework. J. Math. Econom. 39 (2003), 891–900.
Haurie, A., Optimal control on an infinite time horizon: The turnpike approach. J. Math. Econom. 3 (1976), 81–102.
Hori, H., A turnpike theorem for rolling plans. J. Math. Econom. 16 (1987), 223–235.
Hritonenko, N., Yatsenko, Y., Modeling and Optimization of the Lifetime of Technologies. 1996, Kluwer Academic Publishers.
Isard, W., Liossatos, P., Spatial Dynamics and Optimal Space-Time Development. 1979, North-Holland.
Iwasa, K., Zhao, L., Inequality and catching-up under decreasing marginal impatience. J. Math. Econom. 91 (2020), 99–110.
Iwaza, K., Sorger, G., Periodic solutions of the one-sector growth model: The role of income effects. J. Math. Econom. 78 (2018), 59–63.
Jensen, M., On unbounded growth with heterogenous consumers. J. Math. Econom. 42 (2006), 807–826.
Johansen, L., Substitution versus fixed production coefficients in the theory of economic growth: A synthesis. Econometrica 27 (1959), 157–176.
Jovanovic, B., Yatsenko, Y., Investment in vintage capital. J. Econom. Theory 147 (2012), 551–569.
Kamihigashi, T., Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks. J. Math. Econom. 43 (2007), 477–500.
Khan, A., Mitra, T., Growth in the robinson-solow-srinivasan model: Undiscounted optimal policy with a strictly concave welfare function. J. Math. Econom. 44 (2008), 707–732.
Khan, A., Zaslavski, A., On existence of optimal programs: The RSS model without concavity assumptions on felicities. J. Math. Econom. 45 (2009), 624–633.
La Torre, D., Liuzzi, D., Marsiglio, S., Transboundary pollution externalities: Think globally, act locally?. J. Math. Econ., 96, 2021, 102511.
Le Van, C., Morhaim, L., Optimal growth models with bounded or unbounded returns: A unifying approach. J. Econom. Theory 105 (2002), 158–187.
Le Van, C., Nguyen, M., Vailakis, Y., Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor. J. Math. Econom. 43 (2007), 287–317.
Llavador, H., Roemer, J., Silvestre, J., Intergenerational justice when future worlds are uncertain. J. Math. Econ. 46 (2010), 728–761.
Lucas, R.E., On the mechanics of economic development. J. Monetary Econ. 22 (1988), 3–42.
Lucas, R.E., Stokey, N., Optimal growth with many consumers. J. Econom. Theory 32 (1984), 139–171.
Ma, Q., Stachurski, J., Toda, A., Unbounded dynamic programming via the Q-transform. J. Math. Econom., 100, 2022, 102652.
Mallet-Paret, J., Verduyn-Lunel, S.M., Exponential dichotomies and Wiener–Hopf factorizations for mixed-type functional differential equations. J. Differential Equations, 2001 (in press).
Malliaris, A.G., Brock, W., Stochastic Methods in Economics and Finance Advanced Textbooks in Economics, vol. 17, 1982, North Holland.
Mavi, Askan, Can harmful events be another source of environmental traps?. J. Math. Econom. 89 (2020), 29–46.
McKenzie, L., Optimal economic growth, turnpike theorems and comparative dynamics. Arrow, K., Intriligator, M., (eds.) Handbook of Mathematical Economics, vol. III, 1986, North Holland, 1281–1355.
Miao, J., Wang, P., Sectoral bubbles, misallocation, and endogenous growth. J. Math. Econ. 53 (2014), 153–163.
Mitra, T., Privileggi, F., On Lipschitz continuity of the iterated function system in a stochastic optimal growth model. J. Math. Econom. 45 (2009), 185–198.
Mitra, T., Ray, D., Efficient and optimal programs when investment is irreversible: A duality theory. J. Math. Econom. 11:1 (1983), 81–113.
Mitra, T., Roy, S., On the possibility of extinction in a class of Markov processes in economics. J. Math. Econom. 43 (2007), 842–854.
Montrucchio, L., Sorger, G., Topological entropy of policy functions in concave dynamic optimization models. J. Math. Econom. 25 (1996), 181–194.
Morimoto, H., Stochastic Control and Mathematical Modeling: Applications in Economics. 2010, Cambridge Books.
Nikaido, H., Convex Structures and Economic Theory. 1968, Academic Press, New York.
Nishimura, K., Rudnicki, R., Stachurski, J., Stochastic optimal growth with nonconvexities. J. Math. Econom. 42 (2006), 74–96.
Nishimura, K., Seegmuller, T., Venditti, A., Fiscal policy, debt constraint and expectations-driven volatility. J. Math. Econ. 61 (2015), 305–316.
Nishimura, K., Venditti, A., Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor. J. Math. Econom. 43 (2007), 446–476.
Nourry, C., Venditti, A., Local indeterminacy under dynamic efficiency in a two-sector overlapping generations economy. J. Math. Econom. 47 (2011), 164–169.
Orlov, S., Rovenskaya, E., Optimal transition to greener production in a pro-environmental society. J. Math. Econom., 98, 2022, 102554.
Parfit, D., Reasons and Persons. 1984, Oxford University Press.
Peleg, B., Ryder, H., The modified golden rule of a multi-sector economy. J. Math. Econom. 1 (1974), 193–198.
Pelgrin, F., Venditti, A., On the long-run fluctuations of inheritance in two-sector OLG models. J. Math. Econom., 101, 2022, 102670.
Raines, B., Stockman, D., Chaotic sets and Euler equation branching. J. Math. Econom. 46 (2010), 1173–1193.
Robinson, J., Exercises in Economic Analysis. 1960, MacMillan, London.
Scheinkman, J., On optimal steady states of N-sector growth models when utility is discounted. J. Econom. Theory 12 (1976), 11–30.
Schumacher, I., Zou, B., Threshold preferences and the environment. J. Math. Econom. 60 (2015), 17–27.
Skiba, A.K., Optimal growth with a convex-concave production function. Econometrica 46 (1978), 527–539.
Solow, R.M., Substitution and fixed proportions in the theory of capital. Rev. Econom. Stud. 29 (1962), 207–218.
Sorger, G., On the sensitivity of optimal growth paths. J. Math. Econom. 24 (1995), 353–369.
Sorger, G., Some notes on discount factor restrictions for dynamic optimization problems. J. Math. Econom. 45 (2009), 435–448.
Srinivasan, T.N., Investment criteria and choice of techniques of production. Yale Econ. Essays 1 (1962), 58–115.
Stachurski, J., Economic dynamical systems with multiplicative noise. J. Math. Econom. 39 (2003), 135–152.
Stiglitz, J., 1974. Growth with exhaustible natural resources: Efficient and optimal growth paths. In: Review of Economic Studies (Symposium on the Economics of Exhaustible Resources). pp. 123–137.
Stokey, N., Lucas, R., Prescott, E., Recursive Methods in Economic Dynamics. 1979, Harvard University Press.
Takekuma, S., A sensitivity analysis on optimal economic growth. J. Math. Econom. 7 (1980), 193–208.
Uzawa, H., Optimum technical change in an aggregative model of economic growth. Internat. Econom. Rev. 6 (1965), 18–31.
van Geldrop, J., Jilin, S., Withagen, C., Existence of general equilibria in economies with natural exhaustible resources and an infinite horizon. J. Math. Econom. 20 (1991), 225–248.
Vinter, R.B., Kwong, R.H., The infinite time quadratic control problem for linear systems with state and control delays: An evolution equation approach. SIAM J. Control Optim. 19:1 (1981), 139–153.
Woodford, M., Stationary sunspot equilibria in a finance constrained economy. J. Econom. Theory 40 (1986), 128–137.
Xepapadeas, A., Yannacopoulos, A.N., Spatial growth with exogenous saving rates. J. Math. Econom. 67 (2016), 125–137.
Xepapadeas, A., Yannacopoulos, A.N., Spatial growth theory: Optimality and spatial heterogeneity. J. Econom. Dynam. Control, 146, 2023, 104584.
Zhang, Y., Stochastic optimal growth with a non-compact state space. J. Math. Econom. 43 (2007), 115–129.