Lose weight for a raise only if overweight: Marginal integration for semi-linear panel models

Some studies have shown that body mass index (BMI), weight (kg)/height (m)2, has a negative (or no) effect on wage. But BMI representing obesity is a tightly specified function of weight and height, and there is a room for weight given height (i.e. obesity given height) to better explain wage when the tight specification gets relaxed. In this paper, we address the question of weight effect on wage given height, employing twowave panel data for white females and adopting a semi-linear model consisting of a nonparametric function of weight and height and a linear function of the other regressors. We find that there is no weight effect on wage up to the average weight, beyond which a large negative effect kicks in. Linear BMI models give the incorrect impression of the presence of a 'wage gain' by becoming slimmer than the average and of a 'wage loss' that is less than what it actually is when going above the average.