Fatter attraction: anthropometric and socioeconomic matching ... - Ivie
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of) overweight women.<br />
All in all, these tables are consistent with the basic story presented above. Assortative<br />
<strong>matching</strong> takes place along the two dimensions of physical <strong>and</strong> <strong>socioeconomic</strong> attractiveness;<br />
moreover, a trade-o¤ seems to exist, whereby a lower level of physical attractiveness can be<br />
compensated by better <strong>socioeconomic</strong> characteristics <strong>and</strong> conversely. However, while these<br />
…ndings are globally supportive of our theory, they do not constitute clean tests of it. Developing<br />
such tests is the topic of the next section.<br />
6 Formal test <strong>and</strong> estimation<br />
6.1 A linear speci…cation<br />
In order to formally implement the model, we …rst need to further specify its form. We start<br />
with the benchmark case in which the functions I <strong>and</strong> J in (1) are linear, similarly to Hitsch<br />
et al. (2010):<br />
I X 1 i ; :::; X K i<br />
J Yj 1 ; :::; Yj<br />
L<br />
X<br />
= f k Xi<br />
k<br />
k<br />
<br />
=<br />
X<br />
We have concluded above that the distribution of any female characteristic conditional on the<br />
l<br />
g l Y l<br />
j<br />
husb<strong>and</strong>’s pro…le<br />
X 1 i ; :::; X K i<br />
<br />
only depends on I X<br />
1<br />
i ; :::; X K i<br />
<br />
: It follows from (3) that, for<br />
any female characteristic s:<br />
@E Yj<br />
s<br />
@E Yj<br />
s<br />
j X 1 ; :::; X K =@X n<br />
j X 1 ; :::; X K =@X = f n<br />
m f m<br />
<strong>and</strong> by the same token:<br />
@E X s i j Y 1 ; :::; Y L =@Y n<br />
@E [X s i j Y 1 ; :::; Y L ] =@Y m = g n<br />
g m<br />
17