Stochastic stability in monotone economies

This paper extends a family of well-known stability theorems for monotone economies to a significantly larger class of models. We provide a set of general conditions for existence, uniqueness and stability of stationary distributions when monotonicity holds. The conditions in our main result are both necessary and sufficient for global stability of monotone economies that satisfy a weak mixing condition introduced in the paper. Through our analysis we develop new insights into the nature and causes of stability and instability.

[1]  J. Stachurski,et al.  Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem , 2011 .

[2]  Gerald B. Folland,et al.  Real Analysis: Modern Techniques and Their Applications , 1984 .

[3]  Antonia Díaz,et al.  Precautionary savings and wealth distribution under habit formation preferences , 2003 .

[4]  Kazuo Nishimura,et al.  Stability of stochastic optimal growth models: a new approach , 2005, J. Econ. Theory.

[5]  P. Ranjan Dynamic evolution of income distribution and credit-constrained human capital investment in open economies , 2001 .

[6]  Optimal unemployment insurance: transitional dynamics vs. steady state , 2003 .

[7]  R. Bhattacharya,et al.  ASYMPTOTICS OF A CLASS OF MARKOV PROCESSES WHICH ARE NOT IN GENERAL IRREDUCIBLE , 1988 .

[8]  John Stachurski Stochastic Optimal Growth with Unbounded Shock , 2002, J. Econ. Theory.

[9]  E. Prescott,et al.  Stochastic Monotonicity and Stationary Distributions for Dynamic Economies , 1992 .

[10]  Rabah Amir,et al.  Complementarity and Diagonal Dominance in Discounted Stochastic Games , 2002, Ann. Oper. Res..

[11]  D. Bernhardt,et al.  Enterprise, Inequality and Economic Development , 2000 .

[12]  Roberto M. Samaniego Can technical change exacerbate the effects of labor market sclerosis , 2008 .

[13]  Paul A. de Hek,et al.  On Endogenous Growth Under Uncertainty , 1999 .

[14]  D. Pollard A User's Guide to Measure Theoretic Probability by David Pollard , 2001 .

[15]  A. Díaz,et al.  Habit formation: implications for the wealth distribution , 2001 .

[16]  W. Whitt Uniform conditional stochastic order , 1980 .

[17]  Jess Benhabib,et al.  The Distribution of Wealth and Fiscal Policy in Economies with Finitely Lived Agents , 2009 .

[18]  Dudley,et al.  Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets , 2002 .

[19]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[20]  Kim C. Border,et al.  Infinite Dimensional Analysis: A Hitchhiker’s Guide , 1994 .

[21]  Leonard J. Mirman,et al.  Optimal economic growth and uncertainty: The discounted case , 1972 .

[22]  ON A FIXED POINT THEOREM AND ITS STOCHASTIC EQUIVALENT , 1975 .

[23]  Takashi Kamihigashi,et al.  An order-theoretic mixing condition for monotone Markov chains , 2012 .

[24]  Teturo Kamae,et al.  Stochastic Partial Ordering , 1978 .

[25]  K. Reffett,et al.  Stationary Markovian Equilibrium in Overlapping Generation Models with Stochastic Nonclassical Production , 2005 .

[26]  Ana Hidalgo Cabrillana Endogenous capital market imperfections, human capital, and intergenerational mobility , 2009 .

[27]  Buly A. Cardak Ability, Education, and Income Inequality , 2004 .

[28]  Hugo Hopenhayn Entry, exit, and firm dynamics in long run equilibrium , 1992 .

[29]  John Stachurski,et al.  Economic Dynamics: Theory and Computation , 2009 .

[30]  Rabi Bhattacharya,et al.  Limit theorems for monotone Markov processes , 2010 .

[31]  A. Cabrales,et al.  Labor-market flexibility and aggregate employment volatility , 1997 .

[32]  Tapan Mitra,et al.  Optimal exploitation of renewable resources under uncertainty and the extinction of species , 2006 .

[33]  T. Piketty,et al.  The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing , 1997 .

[34]  Takashi Kamihigashi,et al.  Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks , 2007 .

[35]  Albert Marcet,et al.  Incomplete Markets, Labor Supply and Capital Accumulation , 2002 .

[36]  Ann L. Owen,et al.  Intergenerational Earnings Mobility, Inequality, and Growth , 1997 .

[37]  Leonard J. Mirman,et al.  A qualitative approach to Markovian equilibrium in infinite horizon economies with capital , 2008, J. Econ. Theory.

[38]  António R. Antunes,et al.  Start up costs, limited enforcement, and the hidden economy☆ , 2007 .

[39]  P. Bolton,et al.  A Theory of Trickle-Down Growth and Development , 1997 .

[40]  L. Gong,et al.  Stochastic growth with social-status concern: The existence of a unique stable distribution , 2010 .

[41]  P. Glynn,et al.  Markov Chains and Stochastic Stability: Heuristics , 2009 .

[42]  Adam Szeidl Stable Invariant Distribution in Buer-Stock Saving and Stochastic Growth Models , 2013 .

[43]  Dennis Kristensen Geometric Ergodicity of a Class of Markov Chains with Applications to Time Series Models , 2005 .

[44]  Moshe Levy,et al.  Investment Talent and the Pareto Wealth Distribution: Theoretical and Experimental Analysis , 2003, Review of Economics and Statistics.

[45]  Santanu Roy,et al.  Sustained positive consumption in a model of stochastic growth: The role of risk aversion , 2012, J. Econ. Theory.

[46]  Lars J. Olson Stochastic growth with irreversible investment , 1989 .

[47]  S. Carpenter,et al.  Interacting regime shifts in ecosystems: implication for early warnings , 2010 .

[48]  Yuzhe Zhang Stochastic Optimal Growth with a Non-Compact State Space , 2006 .

[49]  Kiminori Matsuyama,et al.  Financial Market Globalization, Symmetry-Breaking, and Endogenous Inequality of Nations , 2004 .

[50]  Roberto M. Samaniego Industrial subsidies and technology adoption in general equilibrium , 2006 .

[51]  W. Reed,et al.  Consumption/pollution tradeoffs in an environment vulnerable to pollution-related catastrophic collapse , 1994 .

[52]  K. Couch,et al.  Inequality, mobility, and the transmission of ability , 2004 .

[53]  J. Davies,et al.  The distribution of wealth , 2000 .

[54]  Partha Chatterjee,et al.  Note on positive lower bound of capital in the stochastic growth model , 2008 .

[55]  Rabi Bhattacharya,et al.  Random Dynamical Systems: Theory and Applications , 2007 .

[56]  Wolfgang Ziegler,et al.  Recursive Methods In Economic Dynamics , 2016 .

[57]  Mark Huggett,et al.  The risk-free rate in heterogeneous-agent incomplete-insurance economies , 1993 .

[58]  Lars J. Olson,et al.  Theory of Stochastic Optimal Economic Growth , 2004 .

[59]  Josep Pijoan-Mas,et al.  Precautionary Savings or Working Longer Hours? , 2005 .

[60]  D. Freedman,et al.  Invariant Probabilities for Certain Markov Processes , 1966 .

[61]  K. Reffett,et al.  Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment , 2010, BQGT.

[62]  P. Billingsley,et al.  Probability and Measure , 1980 .

[63]  Martin L. Weitzman,et al.  Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change , 2011, Review of Environmental Economics and Policy.

[64]  D. M. Topkis Supermodularity and Complementarity , 1998 .

[65]  Partha Chatterjee,et al.  A stochastic dynamic model of trade and growth: Convergence and diversification , 2012 .

[66]  J. Yahav,et al.  On Stochastic Models of Economic Growth , 1979 .

[67]  Thomas F. Cooley,et al.  Financial Markets and Firm Dynamics , 1999 .

[68]  Huw Lloyd-Ellis Public Education, Occupational Choice, and the Growth-Inequality Relationship , 2000 .

[69]  Satya P. Das Trade, skill acquisition and distribution , 2006 .

[70]  Rabi Bhattacharya,et al.  On a Class of Stable Random Dynamical Systems: Theory and Applications , 2001, J. Econ. Theory.

[71]  Allan Drazen,et al.  Threshold Externalities in Economic Development , 1990 .

[72]  O. Hernández-Lerma,et al.  Markov chains and invariant probabilities , 2003 .

[73]  I. Chueshov Monotone Random Systems Theory and Applications , 2002 .

[74]  R. Yin,et al.  The Effect of Catastrophic Risk on Forest Investment Decisions , 1996 .

[75]  Roberto M. Samaniego Does Employment Protection Inhibit Technical Diffusion , 2004 .

[76]  Hugo Hopenhayn,et al.  Job Turnover and Policy Evaluation: A General Equilibrium Analysis , 1993, Journal of Political Economy.

[77]  Asymptotics Of Stochastic Recursive Economies Under Monotonicity , 2009 .