Proceedings 2009

Identifying the Returns to Lying When the Truth is Unobserved, Arthur Lewbel, Boston College Consider an outcome Y, an observed binary regressor D, and an unobserved binary D*. This paper considers nonparametric identification and estimation of the effect of D on Y, conditioning on D*. Suppose Y is wages, unobserved D* indicates college experience, and D indicates claiming to have been to college. This paper identifies the ’returns to lying’ difference in wages, about 6% to 20%, between those who falsely claim college versus those who tell the truth about not having college. Identification is obtained either by observing a variable V roughly analogous to an instrument, or by imposing restrictions on model error moments. Testing Conditional Factor Models, Dennis Kristensen, Columbia University We develop a new methodology for estimating time-varying factor loadings and conditional alphas based on nonparametric techniques. We test whether long-run alphas, or averages of conditional alphas over the sample, are equal to zero and derive test statistics for the constancy of factor loadings. The tests can be performed for a single asset or jointly across portfolios. The traditional Gibbons, Ross and Shanken (1989) test arises as a special case when there is no time variation in the factor loadings. As applications of the methodology, we estimate conditional CAPM and Fama and French (1993) models. We reject the null that long-run alphas on book-to-market and momentum decile portfolios are equal to zero even though there is substantial variation in the conditional factor loadings of these portfolios. Semiparametric modeling and estimation of the dispersion function in regression, Ingrid Van Keilegom, Universite catholique de Louvain Modeling heteroscedasticity in semiparametric regression can improve the efficiency of the estimator of the parametric component in the regression function, and is important for inference problems such as plug-in bandwidth selection and the construction of confidence intervals. However, the literature on exploring heteroscedasticity in a semiparametric setting is rather limited. Existing work is mostly restricted to the partially linear mean regression model with a fully nonparametric variance structure. The nonparametric modeling of heteroscedasticity is hampered by the curse of dimensionality in practice. Moreover, the approaches used in existing work need to assume smooth objective functions, therefore exclude the emerging important class of semiparametric quantile regression models. To overcome these drawbacks, we propose a general semiparametric location-dispersion regression framework, which enriches the currently available semiparametric regression models. With our general framework, we do not need to impose a special semiparametric form for the location or dispersion function. Rather, we provide easy to check sufficient conditions such that the asymptotic normality theory we establish is valid for many commonly used semiparametric structures, for instance, the partially linear structure and single-index structure. Our theory permits non-smooth location or dispersion functions, thus allows for semiparametric quantile heteroscedastic regression. We demonstrate the proposed method via simulations and the analysis of a real data set. (This is joint work with Lan Wang). 40 Five-day Workshop Reports Asymptotic Theory for Nonparametric and Semiparametric Estimation with Spatial Data, Peter Robinson, London School of Economics We develop conditions for asymptotic statistical theory for estimates of nonparametric and semiparametric models when the data are spatial, or spatio-temporal. We attempt to cover data that are regularly or irregularlyspaced, as well as ones where only pairwise distances are available, and cross-sectional data in which even this information is lacking but dependence is feared. The stress is on allowing for a broad range of spatial dependence, including long-range dependence, and heterogeneity, including conditional and unconditional heteroscedasticitya On the Regularization Power of the Prior Distribution in Linear ill-Posed Inverse Problems, Anna Simoni, Toulouse School of Economics We consider a functional equation of type ˆY = Kx + U in an Hilbert space. We wish to recover the functional parameter of interest x after observing ˆY . This problem is ill-posed because the operator K is assumed to be compact. We consider a class of models where the prior distribution on x is able to correct the ill-posedness even for an infinite dimensional problem. The prior distribution must be of the g-prior type and depends on the regularization parameter and on the degree of penalization. We prove that, under some conditions, the posterior distribution is consistent in the sampling sense. In particular, the prior-to-posterior transformation can be interpreted as a Tikhonov regularization in the Hilbert scale induced by the prior covariance operator. Finally, the regularization parameter may be treated as an hyperparameter and may be estimated using its posterior distribution or integrated out. Efficient Estimation in ICA and ICA-Like Models, P.J. Bickel, UC Berkeley The ICA (Independent Component Analysis) generalization of the multivariable Gaussian model corresponds to observing n iid observations of the form: