Hi friends,
Following the discussion on the distribution of 1/X I have a question in
the same area.
X and Y are IID. Using the Slutsky theorem it is possible to show that
E[X/Y] -> E[X]/E[Y]. However, the Slutsky theorem assumes IID, which in
a human context amounts to homogeneity in preferences. Now, assume that
we introduce heterogeneity defined in terms of two random terms h_X and
h_Y.
Now, I'm convinced that E[ (X+h_X) / (Y+h_Y) ] > E[X+h_X]/E[Y+h_Y] and
that the downward bias of E[X+h_X]/E[Y+h_Y] will depend on the degree of
heterogeneity. The higher var(h_Y) the more downward bias.
I need help on two things: Firstly, is my intuition correct! Secondly,
which theorem or strategy can be applied in the proof?
All the best
Jeppe Husted Rich
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Jeppe Husted Rich, MSc, PhD
Assistant Professor
Technical University of Denmark
Centre for Traffic and Transport
Building 115, 2800 Lyngby Denmark
Work: +45 45251536
Privat: +45 36308595
Fax: +45 45936412
E-mail: [log in to unmask]
Skype account: jeppe.husted.rich
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