A comparison of approaches for estimating the effect of women's education on the probability of using modern contraceptive methods in Malawi

The aim of this study is to estimate the effect of education on the probability of married Malawian women using modern contraceptive methods by accounting for both observed and unobserved confounders. We conduct a sensitivity analysis and compare the results of naive models with instrumental variable models to account for the potential endogeneity of education. Our findings demonstrate conflicting results between the two modelling approaches. The naive models report smaller education effects on the probability of using modern contraceptive methods compared to instrumental variable models. We also find that by relaxing the functional form assumption on the effect of continuous covariates, using a flexible instrumental variable model, the education's effect follows a positive, nonlinear pattern. This finding is not observed with a classic instrumental variable model.     

Regression spline bivariate probit models: A practical approach to testing for exogeneity

Bivariate probit models can deal with a problem usually known as endogeneity. This issue is likely to arise in observational studies when confounders are unobserved. We are concerned with testing the hypothesis of exogeneity (or absence of endogeneity) when using regression spline recursive and sample selection bivariate probit models. Likelihood ratio and gradient tests are discussed in this context and their empirical properties investigated and compared with those of the Lagrange multiplier and Wald tests through a Monte Carlo study. The tests are illustrated using two datasets in which the hypothesis of exogeneity needs to be tested.     

Analytic Hessian matrices and the computation of FIGARCH estimates

Long memory in conditional variance is one of the empirical features exhibited by many financial time series. One class of models that was suggested to capture this behavior is the so-called Fractionally Integrated GARCH (Baillie, Bollerslev and Mikkelsen 1996) in which the ideas of fractional integration originally introduced by Granger (1980) and Hosking (1981) for processes for the mean are applied to a GARCH framework. In this paper we derive analytic expressions for the second-order derivatives of the log-likelihood function of FIGARCH processes with a view to the advantages that can be gained in computational speed and estimation accuracy. The comparison is computationally intensive given the typical sample size of the time series involved and the way the likelihood function is built. An illustration is provided on exchange rate and stock index data. A preliminary version of this paper was presented at the conference S.Co. 2001 in Bressanone. We would like to thank Silvano Bordignon for being an insightful and constructive discussant and Luisa Bisaglia and Giorgio Calzolari for providing useful comments. We also thank Tim Bollerslev for providing the data on the DEM/USD exchange rate used in Baillie, Bollerslev and Mikkelsen (1996).     

Semi-parametric bivariate polychotomous ordinal regression

A pair of polychotomous random variables \((Y_1,Y_2)^\top =:{\varvec{Y}}\), where each \(Y_j\) has a totally ordered support, is studied within a penalized generalized linear model framework. We deal with a triangular generating process for \({\varvec{Y}}\), a structure that has been employed in the literature to control for the presence of residual confounding. Differently from previous works, however, the proposed model allows for a semi-parametric estimation of the covariate-response relationships. In this way, the risk of model mis-specification stemming from the imposition of fixed-order polynomial functional forms is also reduced. The proposed estimation methods and related inferential results are finally applied to study the effect of education on alcohol consumption among young adults in the UK.     

Copula regression spline models for binary outcomes

We introduce a framework for estimating the effect that a binary treatment has on a binary outcome in the presence of unobserved confounding. The methodology is applied to a case study which uses data from the Medical Expenditure Panel Survey and whose aim is to estimate the effect of private health insurance on health care utilization. Unobserved confounding arises when variables which are associated with both treatment and outcome are not available (in economics this issue is known as endogeneity). Also, treatment and outcome may exhibit a dependence which cannot be modeled using a linear measure of association, and observed confounders may have a non-linear impact on the treatment and outcome variables. The problem of unobserved confounding is addressed using a two-equation structural latent variable framework, where one equation essentially describes a binary outcome as a function of a binary treatment whereas the other equation determines whether the treatment is received. Non-linear dependence between treatment and outcome is dealt using copula functions, whereas covariate-response relationships are flexibly modeled using a spline approach. Related model fitting and inferential procedures are developed, and asymptotic arguments presented.     

Modelling the impact of women’s education on fertility in Malawi

Many studies have suggested that there is an inverse relationship between education and number of children among women from sub-Saharan Africa countries, including Malawi. However, a crucial limitation of these analyses is that they do not control for the potential endogeneity of education. The aim of our study is to estimate the role of women’s education on their number of children in Malawi, accounting for the possible presence of endogeneity and for nonlinear effects of continuous observed confounders. Our analysis is based on micro data from the 2010 Malawi Demographic Health Survey, and uses a flexible instrumental variable regression approach. The results suggest that the relationship of interest is affected by endogeneity and exhibits an inverted U-shape among women living in rural areas of Malawi, whereas it exhibits an inverse (nonlinear) relationship for women living in urban areas.     

Generalised joint regression for count data: a penalty extension for competitive settings

Statistics and Computing - We propose a versatile joint regression framework for count responses. The method is implemented in the R add-on package GJRM and allows for modelling linear and...     

Estimating the Effect of Perceived Risk of Crime on Social Trust in the Presence of Endogeneity Bias

This study aims to estimate the effect of perceived risk of crime on the social trust probability for Italian men and women, accounting for both observed and unobserved confounding. We use microdata collected by the Italian National Statistical Office for the year 2010 during a multi-scope survey of Italian households. The relationship under investigation is estimated after controlling for observed confounding by using a propensity score weighting approach. To control for both observed and unobserved confounding (better known as endogeneity), a semiparametric recursive bivariate probit approach is ultimately employed instead. Our findings show that the perceived risk of crime has a significant negative effect on the social trust probability regardless of gender and that endogeneity seems to be present for both genders. The paper represents the first such application in which the effect of interest is estimated accounting for the presence of endogeneity.     

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

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