Abstract:
We analyse models in which additional “controls” or proxies are included in a regression. This might
occur intentionally if there is significant measurement error in a key regressor or if a key variable is not
measured at all. We develop a test of the hypothesis that a subset of the regressors are all proxying for
the same latent variable and we show how an estimate of the structural coefficient might be obtained
more efficiently than is available in the current literature.
We apply the procedure to the determinants of sleep among young South Africans. We show that the
income variable in the time use survey is badly measured. Nevertheless the measured impact of income
on sleep is significant and amounts to 35 minutes per day between children with the median income and
those in the topmost income bracket. Including a variety of asset proxies increases the estimated size
of the coefficient enormously. The specification tests indicate that some of the asset proxies, however,
have independent effects. Access to electricity, in particular, is not simply proxying for income. Instead
it seems to be capturing access to various forms of entertainment, such as television. Even when this
independent effect is properly accounted for, the size of the income coefficient is still 40% to 100% larger than in the specifications without the proxies.
