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Stochastic optimal growth with risky labor supply. (English) Zbl 1284.91357

Summary: Production takes time, and labor supply and profit maximization decisions that relate to current production are typically made before all shocks affecting that production have been realized. In this paper we re-examine the problem of stochastic optimal growth with aggregate risk where the timing of the model conforms to this information structure. We provide a set of conditions under which the economy has a unique, nontrivial and stable stationary distribution. In addition, we verify key optimality properties in the presence of unbounded shocks and rewards, and provide the sample path laws necessary for consistent estimation and simulation.

MSC:

91B62 Economic growth models

References:

[1] Balbus, L.; Reffett, K.; Woźny, L., Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment, Journal of Mathematical Economics, 48, 115-132 (2012) · Zbl 1236.91097
[2] Bhattacharya, R.; Majumdar, M., Random Dynamical Systems: Theory and Applications (2007), Cambridge University Press · Zbl 1114.37027
[3] Bosi, S.; Le Van, C., On the existence of a Ramsey equilibrium with endogenous labor supply and borrowing constraints, (DEPOCEN Working Paper Series, No. 2011/24 (2011))
[4] Brock, W. A.; Majumdar, M., Global asymptotic stability results for multisector models of optimal growth under uncertainty when future utilities are discounted, Journal of Economic Theory, 18, 225-243 (1978) · Zbl 0414.90022
[5] Brock, W. A.; Mirman, L. J., Optimal economic growth and uncertainty: the discounted case, Journal of Economic Theory, 4, 479-513 (1972)
[6] Brock, W. A.; Mirman, L. J., Optimal economic growth and uncertainty: the no discounting case, International Economic Review, 14, 560-573 (1973) · Zbl 0277.90022
[8] Coleman, W. J., Equilibria in distorted infinite-horizon economies with capital and labor, Journal of Economic Theory, 72, 446-461 (1997) · Zbl 0883.90036
[9] Datta, M.; Mirman, L. J.; Reffett, K. L., Existence and uniqueness of equilibrium in distorted dynamic economies with capital and labor, Journal of Economic Theory, 103, 377-410 (2002) · Zbl 1050.91071
[10] Donaldson, J. B.; Mehra, R., Stochastic growth with correlated production shocks, Journal of Economic Theory, 29, 282-312 (1983) · Zbl 0512.90029
[11] Durlauf, S. N.; Quah, D., The new empirics of economic growth, (NBER Working Papers, No. 6422 (1999))
[12] Galí, J., Monetary Policy, Inflation, and the Business Cycle (2008), Princeton University Press: Princeton University Press Princeton, Oxford
[13] Goenka, A.; Le Van, C.; Nguyen, M., Existence of competitive equilibrium in an optimal growth model with heterogeneous agents and endogenous leisure, Macroeconomic Dynamics, 16, 33-51 (2012) · Zbl 1246.91084
[14] Greenwood, J.; Huffman, G. W., On the existence of nonoptimal equilibria in dynamic stochastic economies, Journal of Economic Theory, 65, 611-623 (1995) · Zbl 0834.90038
[15] Hansen, G. D., Indivisible labor and the business cycle, Journal of Monetary Economics, 16, 309-327 (1985)
[16] Hopenhayn, H. A.; Prescott, E. C., Stochastic monotonicity and stationary distributions for dynamic economies, Econometrica, 60, 1387-1406 (1992) · Zbl 0766.90017
[17] Kamihigashi, T., Stochastic optimal growth with bounded or unbounded utiltity and bounded or unbounded shocks, Journal of Mathematical Economics, 43, 477-500 (2007) · Zbl 1154.91032
[19] Kamihigashi, T.; Stachurski, J., Stochastic stability in monotone economies, Theoretical Economics (2013), (forthcoming)
[20] Kydland, F. E.; Prescott, E. C., Time to build and aggregate fluctuations, Econometrica, 50, 1345-1370 (1982) · Zbl 0493.90017
[21] Long, John B.; Plosser, Charles I., Real business cycles, Journal of Political Economy, 91, 1, 39-69 (1983)
[22] Meyn, S.; Tweedie, R. L., Markov Chains and Stochastic Stability (2009), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1165.60001
[23] Mirman, L. J., On the existence of steady state measure for one sector growth models with uncertain technology, International Economic Review, 13, 271-286 (1973) · Zbl 0257.90006
[24] Mirman, L. J.; Zilcha, I., On optimal growth under uncertainty, Journal of Economic Theory, 11, 329-339 (1975) · Zbl 0362.90024
[25] Nishimura, K.; Stachurski, J., Stability of stochastic optimal growth models: a new approach, Journal of Economic Theory, 122, 100-118 (2005) · Zbl 1118.91067
[26] Razin, A.; Yahav, J. A., On stochastic models of economic growth, International Economic Review, 20, 599-604 (1979) · Zbl 0427.90023
[27] Stachurski, J., Stochastic optimal growth with unbounded shock, Journal of Economic Theory, 106, 40-65 (2002) · Zbl 1026.91081
[28] Stachurski, J., Log-linearization of stochastic economic models, Journal of Difference Equations and Applications, 13, 217-222 (2007) · Zbl 1114.91089
[29] Stachurski, J., Economic Dynamics: Theory and Computation (2009), MIT Press: MIT Press Cambridge, MA · Zbl 1163.91300
[30] Stokey, N. L.; Lucas, R. E.; Prescott, E. C., Recursive Methods in Economic Dynamics (1989), Harvard University Press: Harvard University Press Cambridge, MA · Zbl 0774.90018
[31] Zhang, Y., Stochastic optimal growth with a non-compact state space, Journal of Mathematical Economics, 43, 115-129 (2007) · Zbl 1280.91120
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