Multidimensional Stochastic Dominance

Gaston
Yalonetzky

  • Unidimensional versus multidimensional stochastic dominance.
  • Introduction to the four conditions for bivariate dominance.
  • Extending the bivariate case to the multidimensional case.
  • Illustration of the link between ALEP property and dominance conditions.
  • The application of dominance in well-being to poverty measurement.
  • Statistical inference techniques

Key readings

Related lectures

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Key readings covered in this lecture

Atkinson, A. and Bourguignong, F. (1982). The comparison of multi-dimensional distributions of economic status. Review of Economic Studies XLIX, 183-201

Barret, G. and Donald, S. (2003). Consistent tests for stochastic dominance. Econometrica. 71(1): 71-104

Yalonettzky, G. (2011). Stochastic dominance for ordinal variables: conditions and tests. Forthcoming in Econometric review.

Related lectures

Unidimensional Poverty Measurement: Axioms, Measures and Dominance

Video

Guide to the video

00:00 Introduction and outline of lecture

05:45 Defining dominance (see also Unidimensional Poverty Measurement: Axioms, Measures and Dominance)

Part 1: Unidimensional Dominance

15:21 Unidimensional dominance

Part 2: Bivariate Dominance Conditions

24:09 The bivariate case of dominance, first order conditions, survival functions, ALEP complements and substitutes

32:07 Dominance condition 1 – A condition for monotonically increasing functions with ALEP substitute arguments

40:50 Dominance condition 2 – A condition for monotonically increasing functions with ALEP complement arguments

45:32 Dominance condition 3 – A condition for monotonically increasing functions with ALEP neutral arguments

52:22 Dominance condition 4 (strongest condition) -A condition for ALL individual welfare functions that are monotonically increasing

Part 3: Multidimensional Dominance Conditions

58:52 Extending the bivariete dominance to the multivariate case (see Yalonetzky (2011))

66:40 The relationship between ALEP properties and dominance conditions

Part 4: From Well-Being to Poverty Measurement

78:26 the application of well-being dominance to poverty measurement

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