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Comparative Statics, Informativeness, and the Interval Dominance Order

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Abstract

We identify a natural way of ordering functions, which we call the interval dominance order and develop a theory of monotone comparative statics based on this order. This way of ordering functions is weaker then the standard one based on the single crossing property (Milgrom and Shannon, 1994) and so our results apply in some settings where the single crossing property does not hold. For example, they are useful when examining the comparative statics of optimal stopping time problems. We also show that certain basic results in statistical decision theory which are important in economics – specifically, the complete class theorem of Karlin and Rubin (1956) and the results connected with Lehmann’s (1988) concept of informativeness – generalize to payoff functions obeying the interval dominance order.

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  • John K.-H. Quah & Bruno Strulovici, 2007. "Comparative Statics, Informativeness, and the Interval Dominance Order," Economics Papers 2007-W04, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:0704
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    File URL: http://www.nuffield.ox.ac.uk/economics/papers/2007/w4/hlp27.pdf
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    1. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 187-223.
    2. Susan Athey & Jonathan Levin, 1998. "The Value of Information In Monotone Decision Problems," Working papers 98-24, Massachusetts Institute of Technology (MIT), Department of Economics.
    3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    4. Ormiston Michael B. & Schlee Edward E., 1993. "Comparative Statics under Uncertainty for a Class of Economic Agents," Journal of Economic Theory, Elsevier, vol. 61(2), pages 412-422, December.
    5. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    Keywords

    single crossing property; interval dominance order; supermodularity; comparative statics; optimal stopping time; complete class theorem; statistical decision theory; informativeness;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • F11 - International Economics - - Trade - - - Neoclassical Models of Trade
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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