Stochastic growth with short-run prediction of shocks
Tóm tắt
We study a variation of the one-sector stochastic optimal growth model with independent and identically distributed shocks where agents acquire information that enables them to accurately predict the next period’s productivity shock (but not shocks in later periods). Optimal policy depends on the forthcoming shock. A “better” predicted realization of the shock that increases both marginal and total product always increases next period’s optimal output. We derive conditions on the degree of relative risk aversion and the elasticity of marginal product under which optimal investment increases or decreases with a better shock. Under fairly regular restrictions, optimal outputs converge in distribution to a unique invariant distribution whose support is bounded away from zero. We derive explicit solutions to the optimal policy for three well-known families of production and utility functions and use these to show that volatility of output, sensitivity of output to shocks, and expected total investment may be higher or lower than in the standard model where no new information is acquired over time; the limiting steady state may also differ significantly from that in the standard model.
Tài liệu tham khảo
Arkin V.I., Evstigneev I.: Stochastic Models of Control and Economic Dynamics. Academic Press, London (1987)
Beaudry P., Portier F.: An exploration into Pigou’s theory of cycles. J Monet Econ 51, 1183–1216 (2004)
Beaudry P., Portier F.: When can changes in expectations cause business cycle fluctuations. J Econ Theor 135, 458–477 (2007)
Bhattacharya R.N., Majumdar M.: On a theorem of Dubins and Freedman. J Theor Prob 12, 1067–1087 (1999)
Bhattacharya R.N., Majumdar M.: Random dynamical systems: a review. Econ Theor 23, 13–38 (2003)
Blackwell D.: Equivalent comparison of experiments. Ann Math Statist 24, 265–272 (1953)
Brock W., Mirman L.: Optimal economic growth and uncertainty: the discounted case. J Econ Theor 4, 479–513 (1972)
Cass D.: Optimum growth in an aggregative model of capital accumulation. Rev Econ Stud 32, 233–240 (1965)
Costello C., Polasky S., Solow A.: Renewable resource management with environmental prediction. Can J Econ 34, 196–211 (2001)
Danthine J.P., Donaldson J., Johnsen T.: Productivity growth, consumer confidence and business cycle. Eur Econ Rev 42, 1113–1140 (1998)
De Hek P.: On endogenous growth under uncertainty. Int Econ Rev 40, 727–744 (1999)
De Hek P., Roy S.: On sustained growth under uncertainty. Int Econ Rev 42, 801–814 (2001)
Demers M.: Investment under uncertainty, irreversibility and the arrival of information over time. Rev Econ Stud 58, 333–350 (1991)
Donaldson J., Mehra R.: Stochastic growth with correlated production shocks. J Econ Theor 29, 282–312 (1983)
Dubins L.E., Freedman D.A.: Invariant probabilities for certain Markov processes. Ann Math Statist 37, 837–847 (1966)
Eckwert B., Zilcha I.: Economic implications of better information in a dynamic framework. Econ Theor 24, 561–581 (2004)
Edlin A., Shannon C.: Strict monotonicity in comparative statics. J Econ Theor 81, 201–219 (1998)
Freixas X.: Optimal growth with experimentation. J Econ Theor 24, 296–309 (1981)
Hansen G.D., Prescott E.C.: Did technology shocks cause the 1990–1991 recession?. Am Econ Rev 83, 280–286 (1993)
Jaimovich N., Rebelo S.: An news about the future drive the business cycle?. Am Econ Rev 99, 1097–1118 (2009)
Koopmans T.C.: On the concept of optimal economic growth. Pont Acad Sci Scripta Varia 28, 225–300 (1965)
Koulovatianos C., Mirman L., Santugini M.: Optimal growth and uncertainty: learning. J Econ Theor 144, 280–295 (2009)
Landsberger M., Meilijson I.: Co-monotone allocations, Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion. Ann Oper Res 52, 97–106 (1994)
Levhari D., Srinivasan T.N.: Optimal savings under uncertainty. Rev Econ Stud 36, 153–163 (1969)
Majumdar M.: A note on learning and optimal decisions with a partially observable state space. In: Mirman, L.J., Spulber, D. (eds) Essays in the Economics of Renewable Resources, North Holland, Amsterdam (1982)
Majumdar M., Mitra T., Nyarko Y.: Dynamic optimization under uncertainty: non-convex feasible sets. In: Feiwel, GR (eds) Joan Robinson and Modern Economic Theory, pp. 545–590. Macmillan, New York (1989)
Mirman L., Samuelson L., Urbano A.: Monopoly experimentation. Int Econ Rev 34, 549–563 (1993)
Mirman L., Zilcha I.: On optimal growth under uncertainty. J Econ Theor 11, 329–339 (1975)
Mitra K.: On optimal capital accumulation paths in a neoclassical stochastic growth model. Econ Theor 11, 457–464 (1998)
Mitra T., Montrucchio L., Privileggi F.: The nature of the steady state in models of optimal growth under uncertainty. Econ Theor 23, 39–71 (2003)
Mitra T., Roy S.: Optimal exploitation of renewable resources under uncertainty and the extinction of species. Econ Theor 28, 1–23 (2006)
Mitra, T., Roy, S.: Sustained positive consumption in a model of stochastic growth: the role of risk aversion. CAE working paper # 10-03, Cornell University. J Econ Theor (2010) (forthcoming)
Nyarko Y., Olson L.J.: Optimal growth with unobservable resources and learning. J Econ Behav Organ 29, 465–491 (1996)
Olson L.J., Roy S.: Theory of stochastic optimal economic growth. In: Dana, R.A., Le Van, C., Mitra, T., Nishimura, K. (eds) Handbook on Optimal Growth, vol. 1, Springer, Berlin (2006)
Pigou A.: Industrial Fluctuations. MacMillan, London (1927)
Ramsey F.: A mathematical theory of savings. Econ J 38, 543–559 (1928)
Rothschild M., Stiglitz J.: Increasing risk I: a definition. J Econ Theor 2, 225–243 (1970)
Schäl M.: Conditions for optimality in dynamic programming and for the limit of n-stage optimal policies to be optimal. Z Wahrscheinlichkeitstheorie verw Gebiete 32, 179–196 (1975)
Schmitt-Grohe, S., Uribe, M.: What’s news in business cycles. NBER working paper 14215, National Bureau of Economic Research (2008)
Stokey N., Lucas R. Jr: Recursive Methods in Economic Dynamics. Harvard University Press, Cambridge (1989)