Semiparametric Modeling and Estimation of Instrumental Variable Models

Radice

2011

Can J Statistics

The classic recursive bivariate probit model is of particular interest to researchers since it allows for the estimation of the treatment effect that a binary endogenous variable has on a binary outcome in the presence of unobservables. In this article, the authors consider the semiparametric version of this model and introduce a model fitting procedure which permits to estimate reliably the parameters of a system of two binary outcomes with a binary endogenous regressor and smooth functions of continuous covariates. They illustrate the empirical validity of the proposal through an extensive simulation study. The approach is applied to data from a survey, conducted in Botswana, on the impact of education on women's fertility. Some studies suggest that the estimated effect could have been biased by the possible endogeneity arising because unobservable confounders (e.g., ability and motivation) are associated with both fertility and education. The Canadian Journal of Statistics 39: 259–279; 2011 © 2011 Statistical Society of Canada

Section: Introductionmentioning

confidence: 99%

Estimation of a semiparametric recursive bivariate probit model in the presence of endogeneity

Radice

2011

Can J Statistics

“…For example, to model covariate-response relationships in a more flexible way Chib and Greenberg (2007) and Marra and Radice (2011) Figure 1: Examples of copulae implemented in SemiParBIVProbit that can be used to capture symmetric or asymmetric dependences among error terms of endogenous variables in a simultaneous likelihood model. A narrowing of the copula indicates stronger dependence; so, for example, the Clayton copula describes a strong dependence between negative shocks to the endogenous variables, while the Joe copula describes a strong dependence between positive shocks.…”

Section: Flexible Simultaneous Likelihood Methodsmentioning

confidence: 99%

Flexible Causal Inference for Political Science

Braumoeller¹,

Radice

et al. 2018

Polit. Anal.

Measuring the causal impact of state behavior on outcomes is one of the biggest methodological challenges in the field of political science, for two reasons: behavior is generally endogenous, and the threat of unobserved variables that confound the relationship between behavior and outcomes is pervasive. Matching methods, widely considered to be the state of the art in causal inference in political science, are generally ill-suited to inference in the presence of unobserved confounders.Heckman-style multiple-equation models offer a solution to this problem; however, they rely on functional form assumptions that can produce substantial bias in estimates of average treatment effects. We describe a category of models, flexible simultaneous likelihood models, that account for both features of the data while avoiding reliance on rigid functional form assumptions. We then assess these models' performance in a series of neutral simulations, in which they produce substantial (55% to >90%) reduction in bias relative to competing models. Finally, we demonstrate their utility in a reanalysis of Simmons' (2000) classic study of the impact of Article VIII commitment on compliance with the IMF's currency-restriction regime.

“…This extension is important because the neglect of the presence of nonlinearity may have severe consequences on the estimation of covariate effects [22]. The semiparametric version of the classic bivariate probit can be written as

\begin{matrix} y_{1 i}^{*} = {\tilde{x}}_{1 i}^{T} δ_{1} + \sum_{k_{normal1} = normal1}^{K_{normal1}} s_{1 k_{1}} ({\overset{˘}{x}}_{1 k_{1} i}) + ε_{1 i}, \\ y_{2 i}^{*} = γ y_{1 i} + {\tilde{x}}_{2 i}^{T} δ_{2} + \sum_{k_{normal2} = normal1}^{K_{normal2}} s_{2 k_{2}} ({\overset{˘}{x}}_{2 k_{2} i}) + ε_{2 i}, \\ i = 1, \dots, n, \end{matrix}

where

{\overset{boldx}{true}}_{normal1 i}^{sans-serifT} = (normal1, {\overset{x}{true}}_{normal12 i}, \dots, {\overset{x}{true}}_{normal1 Q_{normal1} i})

is the i th row vector of

…”

Section: Recursive Bivariate Probit Modelmentioning

confidence: 99%

A Semiparametric Bivariate Probit Model for Joint Modeling of Outcomes in STEMI Patients

Ieva

Computational and Mathematical Methods in Medicine

Paganoni

et al. 2014

In this work we analyse the relationship among in-hospital mortality and a treatment effectiveness outcome in patients affected by ST-Elevation myocardial infarction. The main idea is to carry out a joint modeling of the two outcomes applying a Semiparametric Bivariate Probit Model to data arising from a clinical registry called STEMI Archive. A realistic quantification of the relationship between outcomes can be problematic for several reasons. First, latent factors associated with hospitals organization can affect the treatment efficacy and/or interact with patient's condition at admission time. Moreover, they can also directly influence the mortality outcome. Such factors can be hardly measurable. Thus, the use of classical estimation methods will clearly result in inconsistent or biased parameter estimates. Secondly, covariate-outcomes relationships can exhibit nonlinear patterns. Provided that proper statistical methods for model fitting in such framework are available, it is possible to employ a simultaneous estimation approach to account for unobservable confounders. Such a framework can also provide flexible covariate structures and model the whole conditional distribution of the response.