Monotone Comparative Statics under Uncertainty

By Susan Athey. 2002

444 citations recorded by the source corpus.

This paper analyzes monotone comparative statics predictions in several classes of stochastic optimization problems. The main results characterize necessary and sufficient conditions for comparative statics predictions to hold based on properties of primitive functions, that is, utility functions and probability distributions. The results apply when the primitives satisfy one of the following two properties: (i) a single-crossing property, which arises in applications such as portfolio investment problems and auctions, or (ii) log-supermodularity, which arises in the analysis of demand functions, affiliated random variables, stochastic orders, and orders over risk aversion.

Subfields: Economics and Econometrics, Management Science and Operations Research, Marketing

View Paper: https://www.semanticscholar.org/paper/d6d8f7ebda544a63c91fc3ac6eb5e31ca78bdac9

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Citations in the corpus

Agricultural production amid conflict: Separating the effects of conflict into shocks and uncertainty (2017, background): “The MLR dominance also generates first-order stochastic dominance (Athey 2002).”
Engel's Law in the Global Economy: Demand‐Induced Patterns of Structural Change, Innovation, and Trade (2019, unknown): “3See Athey (2002) and Vives (1999; Ch.2.7) for log-supermodularity and monotone comparative statics.”
Covariance Matrix Estimation under Total Positivity for Portfolio Selection* (2019, background): “Log-supermodularity has a long history in ecomomics, in particular in the context of complementarity and comparative statics [Top78, MR90, MS94, Top98, Ath02, Cos09].”
Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion (2011, background): “• Monotone Probability Ratio order (MPR) (Eeckhoudt and Gollier (1995), Athey (2002)): When the two random variables have the same support, we say that e x2 is dominated by e x1 in the sense of MPR if the cumulative probability ratio F2(x)/F1(x) is nonincreasing.”
Certifiable Pre‐Play Communication: Full Disclosure (2014, methodology): “This is a well known problem (see, for example, Athey, 2002), and we use the results of Quah and Strulovici (2012) who provide conditions under which the single crossing property is stable under aggregation.”
INTERNATIONAL TRADE PUZZLES: A SOLUTION LINKING PRODUCTION AND PREFERENCES (2014, background): “The proof follows from Athey (2002) since both Sik and k n are log-supermodular. at U niversity of C alifornia, B erkeley on Septem ber 12, 2014 http://qje.oxfordjournals.org/ D ow nloaded from effects dominate demand effects.11 For instance, a car producer may find it difficult to export cars to…”
Simplicity Creates Inequity: Implications for Fairness, Stereotypes, and Interpretability (2018, unknown): “ j= j> i= i. In the language of random variables, the disadvantage condition thus asserts that the random variable Y A exhibits likelihood-ratio dominance with respect to the random variable Y D [3, 20, 30, 37]. It is a standard fact from this literature that if one random variable likelihood-rat”
TESTING REGRESSION MONOTONICITY IN ECONOMETRIC MODELS (2012, background): “For example, monotone comparative statics has been a popular research topic in economic theory for many years; see, in particular, the seminal work on this topic by Milgrom and Shannon (1994) and Athey (2002).”
Identification and Estimation of Triangular Simultaneous Equations Models without Additivity (2002, background): “Applying monotone comparative statics results from Milgrom and Shannon (1994) and Athey (2002), Das (2001) discusses a number of examples where monotonicity of the decision rule h(Z, η) in the signal η is implied by conditions on the economic primitives.”
The Price Impact and Survival of Irrational Traders (2006, unknown): “3η?, (2) moderately optimistic, η = 0.”
An Elementary Theory of Comparative Advantage (2009, methodology): “…emphasize the role of logsupermodularity in a trade context, this property has been used previously in many areas of economics, including auction theory, Milgrom and Weber (1982); monotone comparative statics under uncertainty, Jewitt (1987) and Athey (2002); and matching, Shimer and Smith (2000).”
Contest architecture (2006, unknown): “c 1 s dF(p,n−1)(s)] (3) (15)We use the convention dF(0,n−1)(s) ≡ 0.”