Abstract
This chapter reviews cumulative distribution function (CDF) difference approach, the ratio approach, and the deterministic transformation approach specifying common restrictions to impose on the changes in the random variable and examines definitions, graphical examples and the comparative statics results of subsets of First-degree Stochastic Dominance (FSD) shifts. This chapter also presents some properties among these subclasses of FSD shifts used in obtaining general comparative statics results.
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Notes
- 1.
Only one crossing at a point \(m\mathrm {\in }\left[ x_{2},\, x_{3} \right] \) implies that \(f\!\!\left( x \right) \le g\!\left( x \right) \) for all \(x\mathrm {\in }\left[ x_{2},\, \left. m \right) \right. \)and \(f\!\!\left( x \right) \ge g\!\left( x \right) \) for all \(x\mathrm {\in }\left( m,\, \left. x_{3} \right] \right. \). At the point m, it is usual that \(f\!\!\left( m \right) =g\!\left( m \right) \) but if the PDF g or f is discontinuous at m, both the cases of \(f\!\!\left( m \right) <g\!\left( m \right) \) are possible, and thus Definition 9.3 includes the case where \(f\!\!\left( x \right) \le g\!\left( x \right) \) for all \(x\mathrm {\in }\left[ x_{2},\, m \right] \) and \(f\!\!\left( x \right) \ge g\!\left( x \right) \) for all \(x\mathrm {\in }\left( m,\, \left. x_{3} \right] \right. \). This discussion is applied for all the other definitions given in this section.
- 2.
See numerical example, Ryu and Kim (2003).
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Kim, I., Kim, S., Ryu, S. (2020). The Subclasses of First-Degree Stochastic Dominance (FSD) Shifts and Their Comparative Statics. In: Hosoe, M., Kim, I. (eds) Applied Economic Analysis of Information and Risk . Springer, Singapore. https://doi.org/10.1007/978-981-15-3300-6_9
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