Monte Carlo sampling processes and incentive compatible allocations in large economies
- PDF / 499,832 Bytes
- 27 Pages / 439.37 x 666.142 pts Page_size
- 100 Downloads / 202 Views
Monte Carlo sampling processes and incentive compatible allocations in large economies Peter J. Hammond1
· Lei Qiao2 · Yeneng Sun3
Received: 6 November 2019 / Accepted: 6 October 2020 © The Author(s) 2020
Abstract Monte Carlo simulation is used in Hammond and Sun (Econ Theory 36:303–325, 2008. https://doi.org/10.1007/s00199-007-0279-7) to characterize a standard stochastic framework involving a continuum of random variables that are conditionally independent given macro shocks. This paper presents some general properties of such Monte Carlo sampling processes, including their one-way Fubini extension and regular conditional independence. In addition to the almost sure convergence of Monte Carlo simulation considered in Hammond and Sun (2008), here we also consider norm convergence when the random variables are square integrable. This leads to a necessary and sufficient condition for the classical law of large numbers to hold in a general Hilbert space. Applying this analysis to large economies with asymmetric information shows that the conflict between incentive compatibility and Pareto efficiency is resolved asymptotically for almost all sampling economies, following some similar results in McLean and Postlewaite (Econometrica 70:2421–2453, 2002) and Sun and Yannelis (J Econ Theory 134:175–194, 2007. https://doi.org/10.1016/j.jet.2006.03. 001). Keywords Law of large numbers · Monte Carlo sampling process · One-way Fubini property · Hilbert space · Incentive compatibility · Asymmetric information · Pareto efficiency
B
Peter J. Hammond [email protected] Lei Qiao [email protected] Yeneng Sun [email protected]
1
Department of Economics, University of Warwick, Coventry CV4 7AL, UK
2
School of Economics, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai 200433, China
3
Departments of Economics and Mathematics, National University of Singapore, Singapore 119076, Singapore
123
P. J. Hammond et al.
JEL Classification C65 · D51 · D61 · D82
1 Introduction Following the early writings by Lucas and Prescott (1974) and Bewley (1986), macroeconomists have made widespread use of a model of an economy with many agents who face individual random shocks. These shocks are typically modelled as a continuum of random variables that are conditionally independent given common macro level shocks. Proposition 4 in Hammond and Sun (2008), however, shows that in this framework, the joint measurability condition that is usually imposed on a stochastic process can be satisfied only if there is essentially no idiosyncratic risk at all. The approach of Monte Carlo simulation, initiated in Hammond and Sun (2003) for the symmetric case and extended in Hammond and Sun (2008) for the general case, can be used to characterize when, even in the absence of the usual joint measurability assumption, the standard stochastic framework for many heterogeneous agents facing individual uncertainty may still be valid. This paper provides a systematic study of the underlying Monte Carlo sampling processes. W
Data Loading...
