B1439
Title: Sufficient dimension reduction meets two-sample regression estimation
Authors: Masayuki Hirukawa - Ryukoku University (Japan) [presenting]
Abstract: When conducting regression analysis, econometricians often face situations where some regressors are unavailable in the dataset (e.g., an ability measure in wage regression). Suppose they can find an auxiliary dataset containing the missing regressors and several other variables common across two datasets. Previously, the problem of estimating regression parameters consistently by combining two datasets, proposing the matched-sample indirect inference (MSII) and plug-in least squares (PILS) estimators, respectively, was studied. However, these estimators can attain the parametric convergence rate only if the number of common variables is no greater than four. Then, under the assumption that the reduced form of each missing regressor can be expressed in a single-index form of the common variables, MSII and PILS are extended to overcome the curse of dimensionality. Restoring the parametric convergence rate for these estimators takes three steps, namely, (i) estimating index coefficients via some algorithms for sufficient dimension reduction, (ii) imputing proxies of the missing regressors, and (iii) estimating coefficients of the regression model. The convergence properties of these estimators are explored, and their finite-sample properties are examined via Monte Carlo simulations.
