This study explores the instrumental variable estimation within the framework of the semi-parametric proportional odds model. The analysis accommodates both discrete instrumental and endogenous variables, alongside potentially continuous exogenous covariates. By employing a rank invariance hypothesis, it is possible to reformulate the proportional odds model into a semiparametric version of the instrumental variable quantile regression model of [3]. We based the estimation on the presmoothing methodology proposed in [10] which is composed of three steps. First, we estimate the model nonparametrically - and show that this nonparametric estimator has a closed-form solution in the leading case of interest of randomized experiments with one-sided noncompliance. Second, we use the nonparametric estimator to generate “proxy” observations for which exogeneity holds. Third, we apply the usual maximum likelihood estimator to the “proxy” data. The estimation procedure allows for random right-censoring. The approach is illustrated via simulation studies.

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Presmoothing Methodology for Instrumental Variable Estimation of the Proportional Odds Model Under Random Right Censoring

  • Lorenzo Tedesco

摘要

This study explores the instrumental variable estimation within the framework of the semi-parametric proportional odds model. The analysis accommodates both discrete instrumental and endogenous variables, alongside potentially continuous exogenous covariates. By employing a rank invariance hypothesis, it is possible to reformulate the proportional odds model into a semiparametric version of the instrumental variable quantile regression model of [3]. We based the estimation on the presmoothing methodology proposed in [10] which is composed of three steps. First, we estimate the model nonparametrically - and show that this nonparametric estimator has a closed-form solution in the leading case of interest of randomized experiments with one-sided noncompliance. Second, we use the nonparametric estimator to generate “proxy” observations for which exogeneity holds. Third, we apply the usual maximum likelihood estimator to the “proxy” data. The estimation procedure allows for random right-censoring. The approach is illustrated via simulation studies.