A non-technical guide to instrumental variables and regressor-error dependencies (in Russian)

We provide a non-technical summary of most of the recent results that have appeared in the econometric literature on instrumental variables estimation for the linear regression model. Standard inferential methods, such as OLS, are biased and inconsistent when the regressors are correlated with the error term. Instrumental variables methods were developed to overcome this problem, but finding instruments of good quality is cumbersome in any given situation and empirical researchers are often confronted with weak instruments. We review most of the recent studies on weak instruments and point to several methods that have been proposed to deal with such instruments, including "frugal" IV alternatives that do not rely on observed instruments to identify the regression parameters in presence of regressor-error dependencies.

Solving and Testing for Regressor-Error (in)Dependence When no Instrumental Variables are Available: With New Evidence for the Effect of Education on Income

This paper has two main contributions. Firstly, we introduce a new approach, the latent instrumental variables (LIV) method, to estimate regression coefficients consistently in a simple linear regression model where regressor-error correlations (endogeneity) are likely to be present. The LIV method utilizes a discrete latent variable model that accounts for dependencies between regressors and the error term. As a result, additional ‘valid’ observed instrumental variables are not required. Furthermore, we propose a specification test based on Hausman (1978) to test for these regressor-error correlations. A simulation study demonstrates that the LIV method yields consistent estimates and the proposed test-statistic has reasonable power over a wide range of regressor-error correlations and several distributions of the instruments.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47579/1/11129_2005_Article_1177.pd

Regressor and random-effects dependencies in multilevel models

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72623/1/j.0039-0402.2003.00254.x.pd

Addressing Endogeneity in International Marketing Applications of Partial Least Squares Structural Equation Modeling

Partial least squares structural equation modeling (PLS-SEM) has become a key method in international marketing research. Users of PLS-SEM have, however, largely overlooked the issue of endogeneity, which has become an integral component of regression analysis applications. This lack of attention is surprising because the PLS-SEM method is grounded in regression analysis, for which numerous approaches for handling endogeneity have been proposed. To identify and treat endogeneity, and create awareness of how to deal with this issue, this study introduces a systematic procedure that translates control variables, instrumental variables, and Gaussian copulas into a PLS-SEM framework. We illustrate the procedure's efficacy by means of empirical data and offer recommendations to guide international marketing researchers on how to effectively address endogeneity concerns in their PLS-SEM analyses

Latent instrumental variables : a new approach to solve for endogeneity

This thesis aims at resolving problems surrounding classical independence assumptions in mixed linear models. Those assumptions involve independence of the regressors and the random coefficients and independence of the regressors and the (model) error term. To tackle the dependence between regressors and error terms we develop a general instrumental variable approach, the latent instrumental variable (LIV) method, where the instruments are unobserved and are estimated from the data. This leads to a finite mixture formulation. We prove identifiability and discuss estimation of the model parameters. Furthermore, we propose methodologies to investigate regressor and error dependencies. We present results of various simulation studies and illustrate the LIV method on previously published datasets. Our simulation results show that the LIV method yields consistent estimates for the model parameters without having observable instrumental variables at hand. We reanalyze data of three studies that examine the effect of education on income, where the variable ‘education’ is potentially endogenous due to omitted ‘ability’ or other causes. In all three applications we find an upward bias in the OLS estimates of approximately 7%.

Properties of Instrumental Variables Estimation in Logit-Based Demand Models: Finite Sample Results

Endogeneity problems in demand models occur when certain factors, unobserved by the researcher, affect both demand and the values of a marketing mix variable set by managers. For example, unobserved factors such as style, prestige, or reputation might result in higher prices for a product and higher demand for that product. If not addressed properly, endogeneity can bias the elasticities of the endogenous variable and subsequent optimization of the marketing mix. In practice, instrumental variables estimation techniques are often used to remedy an endogeneity problem. It is well known that, for linear regression models, the use of instrumental variables techniques with poor quality instruments can produce very poor parameter estimates, in some circumstances even worse than those that result from ignoring the endogeneity problem altogether. The literature has not addressed the consequences of using poor quality instruments to remedy endogeneity problems in nonlinear models, such as logit-based demand models. Using simulation methods, we investigate the effects of using poor quality instruments to remedy endogeneity in logit-based demand models applied to finite-sample datasets. The results show that, even when the conditions for lack of parameter identification due to poor quality instruments do not hold exactly, estimates of price elasticities can still be quite poor. That being the case, we investigate the relative performance of several nonlinear instrumental variables estimation procedures utilizing readily available instruments in finite samples. Our study highlights the attractiveness of the control function approach (Petrin and Train 2010) and readily-available instruments, which together reduce the mean squared elasticity errors substantially for experimental conditions in which the theory-backed instruments are poor in quality. We find important effects for sample size, in particular for the number of brands, for which it is shown that endogeneity problems are exacerbated with increases in the number of brands, especially when poor quality instruments are used. In addition, the number of stores is found to be important for likelihood ratio testing. The results of the simulation are shown to generalize to situations under Nash pricing in oligopolistic markets, to conditions in which cross-sectional preference heterogeneity exists, and to nested logit and probit-based demand specifications as well. Based on the results of the simulation, we suggest a procedure for managing a potential endogeneity problem in logit-based demand models

Using Social Network Activity Data to Identify and Target Job Seekers

An important challenge for many firms is to identify the life transitions of its customers, such as job searching, expecting a child, or purchasing a home. Inferring such transitions, which are generally unobserved to the firm, can offer the firms opportunities to be more relevant to their customers. In this paper, we demonstrate how a social network platform can leverage its longitudinal user data to identify which of its users are likely to be job seekers. Identifying job seekers is at the heart of the business model of professional social network platforms. Our proposed approach builds on the hidden Markov model (HMM) framework to recover the latent state of job search from noisy signals obtained from social network activity data. Specifically, we use the latent states of the HMM to fuse cross-sectional survey responses to a job-seeking status question with longitudinal user activity data, resulting in a partially HMM. Thus, in some time periods, and for some users, we observe a direct measure of the true job-seeking status. We demonstrate that the proposed model can predict not only which users are likely to be job seeking at any point in time but also what activities on the platform are associated with job search and how long the users have been job seeking. Furthermore, we find that targeting job seekers based on our proposed approach can lead to a 29% increase in profits of a targeting campaign relative to the approach that was used by the social network platform. This paper was accepted by Juanjuan Zhang, marketing. </jats:p