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Endogeneity or nonorthogonality in discrete choice models occurs when the systematic part of the utility is correlated with the error term. Under this misspecification, the model's estimators are inconsistent. When endogeneity occurs at the level of each observation, the principal technique used to treat for it is the control-function method, where a function that accounts for the endogenous part of the error term is constructed and is then included as an additional variable in the choice model. Alternatively, the latent-variable method can also address endogeneity. In this case, the omitted quality attribute is considered as a latent variable and modeled as a function of observed variables and/or measured through indicators. The link between the controlfunction and the latent-variable methods in the correction for endogeneity has not been established in previous work. This paper analyzes the similarities and differences between a set of variations of both methods, establishes the formal link between them in the correction for endogeneity, and illustrates their properties using a Monte Carlo experiment. The paper concludes with suggestions for future lines of research in this area.

We show that in sorting cross-sectional data, the endogeneity of a variable may be successfully detected by graphically examining the cumulative sum of the recursive residuals. Moreover, the sign of the bias implied by the endogeneity may be deducible through such graphs. In general, instrumental variables are needed to implement the graphical test. However, when a continuous or ordered (e.g. years of schooling) variable is suspected to be endogenous, a graphical test for misspecification due to endogeneity (e.g. self-selection) can be obtained without instrumental variables.

An important but often overlooked obstacle in multivariate discrete data models is the specification of endogenous covariates. Endogeneity can be modeled as latent or observed, representing competing hypotheses about the outcomes being considered. However, little attention has been applied to deciphering which specification is best supported by the data. This paper highlights the use of existing Bayesian model comparison techniques to investigate the proper specification for endogenous covariates and to understand the nature of endogeneity. Consideration of both observed and latent modeling approaches is emphasized in two empirical applications. The first application examines linkages for banking contagion and the second application evaluates the impact of education on socioeconomic outcomes.

Without controlling for selection bias and the potential endogeneity of the treatment by using proper methods, the estimation of treatment effect could lead to biased or incorrect conclusions. However, these issues are not addressed adequately and properly in higher education research. This study reviews the essence of self-selection bias, treatment assignment endogeneity, and treatment effect estimation. We introduce three treatment effect estimators – propensity score matching analysis, doubly robust estimation (augmented inverse probability weighted approach), and endogenous treatment estimator (control-function approach) – and examine literature that applies these methods to research in higher education. We then use the three methods in a case study that estimates the effects of transfer student pre-enrollment debt on persistence and first year grades. The final discussion provides guidelines and recommendations for causal inference research studies that use such quasi-experimental methods.

The authors propose inference methods for endogeneity parameters in linear simultaneous equation models allowing for weak identification and missing instruments. Endogeneity parameters measure the impact of unobserved variables which may be correlated with observed explanatory variables, and play a central role in determining the “bias” associated with endogeneity and measurement errors in structural equations. These results expand, in several ways, the finite-sample theory in Doko Tchatoka and Dufour (2014) for this problem. The latter theory relies on relatively restrictive assumptions, in particular the hypothesis that the reduced form is complete (e.g., contains all the relevant instruments), which is questionable in many practical situations. While the new proposed inference methods retain identification robustness, they also allow the reduced form to be incomplete, for example, due to missing instruments. The authors propose easily applicable inference methods for endogeneity parameters – in particular, two-stage procedures (similar to those in Dufour, 1990). An application to a model of returns to schooling is presented.

This chapter examines the asymptotic properties of the Stein-type shrinkage combined (averaging) estimation of panel data models. We introduce a combined estimation when the fixed effects (FE) estimator is inconsistent due to endogeneity arising from the correlated common effects in the regression error and regressors. In this case, the FE estimator and the CCEP estimator of Pesaran (2006) are combined. This can be viewed as the panel data model version of the shrinkage to combine the OLS and 2SLS estimators as the CCEP estimator is a 2SLS or control function estimator that controls for the endogeneity arising from the correlated common effects. The asymptotic theory, Monte Carlo simulation, and empirical applications are presented. According to our calculation of the asymptotic risk, the Stein-like shrinkage estimator is more efficient estimation than the CCEP estimator.

This study extends prior research on the relation between information technology (IT) and firm performance by using both univariate and multivariate econometric models to assess the hypothesized relationships. Additionally, sample selection bias and endogeneity are examined to determine their effect, if any, on the results. The univariate results indicate that, on average, IT leaders outperform non-IT leaders. After controlling for sample selection bias and endogeneity, using Wooldridge (2002) 2SLS-IV, the coefficient of the endogenous variable is higher than suggested by ordinary least squares estimation and the Hausman F-Test is significant, indicating that the relationship between IT and firm performance is endogenous. Thus, it is important to control for sample selection bias and endogeneity to properly estimate the relationship between IT and firm performance.

This chapter examines the effect of the division of labor from a Bayesian viewpoint. While organizational reforms are crucial for cost reduction in the Japanese water supply industry, the effect of labor division in intra-organizational units on total costs has, to the best of our knowledge, not been examined empirically. Fortunately, a one-time survey of 79 Japanese water suppliers conducted in 2010 enables us to examine the effect. To examine this problem, a cost stochastic frontier model with endogenous regressors is considered in a cross-sectional setting, because the cost and the division of labor are regarded as simultaneously determined factors. From the empirical analysis, we obtain the following results: (1) total costs rise when the level of labor division becomes high; (2) ignoring the endogeneity leads to the underestimation of the impact of labor division on total costs; and (3) the estimation bias on inefficiency can be mitigated for relatively efficient organizations by including the labor division variable in the model, while the bias for relatively inefficient organizations needs to be controlled by considering its endogeneity. In summary, our results indicate that integration of internal sections is better than specialization in terms of costs for Japanese water supply organizations.

It is often found that the value of travel time (VTT) is higher for car drivers than for public transport passengers. This paper examines the possible explanation that the difference could be due to a selection effect. The result is an inability to measure the effect of a mode difference, e.g., comfort, among transport modes. We specify a model that captures the mode difference through a mode dummy and use econometric techniques that allow treatment of the mode dummy as the result of an individual choice and hence endogenous. Using first a standard logit model we find a large and significant difference between the VTT for bus and car. When we control for endogeneity using instruments, the mode dummy becomes smaller and just significant. Our investigation is novel in that it allows for endogeneity in the estimation of VTT but like other applications using instruments the results indicate that we have difficulty in finding good instrumental variables.

This chapter presents a Bayesian analysis of the endogenous treatment model with misclassified treatment participation. Our estimation procedure utilizes a combination of data augmentation, Gibbs sampling, and Metropolis–Hastings to obtain estimates of the misclassification probabilities and the treatment effect. Simulations demonstrate that the proposed Bayesian estimator accurately estimates the treatment effect in light of misclassification and endogeneity.