Seminars 2003 — Abstracts
Friday 22nd August
Speaker: Dr
Phil Cross, Georgetown University.
Title: Partial Identification of
Conditional Means and Variances: Using Marginal Distributions to Sharpen
Inference on Mean Regressions
Abstract: A typical empirical study
in economics analyses a single, small-sample dataset to estimate the parameters
of interest. However a larger auxiliary dataset containing a coarser set
of covariates is often available. This paper discusses how marginal information
from the auxiliary dataset can be combined with the primary dataset to
sharpen inference. The estimation method exploits restrictions imposed
by the auxiliary dataset upon the parameters of interest. The most fundamental
of these restrictions are those implied by the Law of Total Probability.
Additional a priori restrictions from from economic theory may also be
utilised. When the auxiliary dataset samples the entire population of
interest (as in a census), these restrictions are nonstochastic, which
leads to a relatively straightforward estimation theory. When the auxiliary
dataset is merely a random sample from the population of interest, the
restrictions are stochastic. In this case, deriving estimators with good
power properties can be a little subtle. In either case, the marginal
information from the auxiliary dataset substantially sharpens inference
about many interesting counterfactual questions. An application to returns
to schooling is considered. Most studies of returns to schooling in the
U.S. use the National Longitudinal Survey of Youth (NLSY), since one of
very few datasets that contains proxies for ability. However, the Current
Population Survey (CPS), while not containing ability covariates, is a
much larger dataset and does contain marginal information about returns
to schooling. This marginal information implies restrictions on the distribution
of ability we can be exploited to substantially sharpen inference.
