Jonathan Wand

In moving from analytical models to empirical tests, the sharpest implications of formal theories are often not tested. Formal models almost always imply re- strictions on derivatives of functions of key variables, but these are left untested. Standard methods test partial correlations that are not in general even estimates of the average quantity of interest. As an alternative, I propose semiparametric methods which directly test shape constraints on otherwise unspecified curves. This study considers in a unified manner both complex shapes as well as the more common theoretical implication of monotonicity that are usually tested by linear regression. A key aspect of this study is the use of isotonic regression, which employs minimal assumptions to obtain exact shape constraints (about which we have theories) at the cost of giving up smoothness about which we neither have have theories nor adequate data to test.