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Addressing Endogeneity in Marketing Models

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Advanced Methods for Modeling Markets

Part of the book series: International Series in Quantitative Marketing ((ISQM))

Abstract

The marketing literature uses regression models based on observational data for causal inferences. Endogeneity issues are a threat to inferring causal effects. Endogeneity—the correlation between the regressors and the model error term—will lead to inconsistent estimates of the regression effects and potentially erroneous conclusions. We discuss this in more detail in Sect. 18.2. The standard approach to deal with endogeneity is to use an instrumental variables (IV) approach. In Sect. 18.3, we briefly introduce this technique before we highlight key aspects of IV selection.

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Notes

  1. 1.

    See also Vol. I, Sects. 6.5–6.7.

  2. 2.

    For sake of exposition we assume here that the observations are independent across time and we do not consider autocorrelations in the errors (e.g., Verbeek 2012, Chap.4).

  3. 3.

    See also Kremer et al. (2008).

  4. 4.

    We use the cross sectional case (Eq. 18.2) as the leading example. The same logic applies to a time series case (Eq. 18.1), which would in addition require a discussion of dealing with potential autocorrelation, which is beyond the scope of this chapter.

  5. 5.

    For the linear model, we do not need the bootstrap method. We can calculate \( {\widehat{\varepsilon}}_i={y}_i-\left({\widehat{\beta}}_0+{\widehat{\beta}}_p{p}_i\right) \) (hence we exclude the control function in the calculation of the residuals). Next, the standard error of the estimate is calculated as \( {\hat{\sigma}}^2={\sum}_{i=1}^n{\widehat{\varepsilon}}_i^2/\left(N-K\right) \), where N is the number of observations and K is the number of independent variables. The covariance matrix of \( {\widehat{\beta}}_p \) is calculated as \( \widehat{\Sigma}={\hat{\sigma}}^2{\left({X}^{\prime }X\right)}^{-1} \) where X is a matrix with the observations in rows and in the columns, in our example, a vector of ones and the values p i and \( {\widehat{\theta}}_i \). The standard error is the square root of the diagonal of \( \widehat{\Sigma} \).

  6. 6.

    Strictly speaking, “efficiency” refers to asymptotic standard errors. An efficient estimator has the lowest standard errors within a class of estimators when the sample size goes to infinity. In this chapter we use the term “efficiency” somewhat loosely as a synonym for “low standard errors” or “tight confidence intervals.”

  7. 7.

    See Vol. I, p. 210.

  8. 8.

    See also Sect. 6.7, Vol. I.

  9. 9.

    See Sect. 4.5, Vol. I.

  10. 10.

    This part relies heavily on Wooldridge (2010, p. 300). We recommend this as further reading for those interested in more details. Another very useful econometric resource is Verbeek (2012; Chap.10).

  11. 11.

    It is important to realize that the panel structure of data does not necessarily refer to repeated observations over time alone. It can also encompass other cases of a nested or multi-level data structure, e.g., brands are observed across multiple stores, schools contain multiple classes, which contain multiple students. The estimation approach applies to these cases as well (e.g., Ebbes et al. 2004; Kim and Frees 2006, 2007).

  12. 12.

    For scenarios 1–3, we assume Cov(p it  ε it ) = 0.

  13. 13.

    We also note that in this example the instrument only varies across time and not across hotels, similar to the omitted variable. Hence, in separating out the exogenous and endogenous variation which are both constant across hotels we only have the time dimension of the data.

  14. 14.

    In addition to the two approaches we discuss here, framed as a potential solution to measurement error, Lewbel (1997) introduced a method that obtains identification from higher moments when the endogenous regressor is skewed. Ebbes et al. (2009) provide a detailed analysis.

  15. 15.

    We thank Sungho Park for sharing his Gauss code with us.

  16. 16.

    The standard deviation of the OLS estimates in Table 18.11 appears large. The reason is that the distribution of the estimates is not normal, which is due to outliers that arise because of the non-normal distribution of the endogenous regressor.

  17. 17.

    See Vol. I, Sect. 8.2.2.1.

  18. 18.

    See, for example, Franses and Paap (2001, p. 138).

  19. 19.

    Compare Sects. 8.2 and 8.5, Vol. I.

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Authors and Affiliations

  1. School of Business and Economics, University of Tübingen, Nauklerstr. 47, Tübingen, 72074, Germany

    Dominik Papies

  2. Department of Marketing, HEC Paris, 1, Rue de la Libération, Jouy-en-Josas, 78351, France

    Peter Ebbes

  3. School of Communication, Journalism and Marketing, Massey University, Private Bag 102904, Auckland, 0745, New Zealand

    Harald J. Van Heerde

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  1. Dominik Papies
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Correspondence to Dominik Papies .

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Editors and Affiliations

  1. Department of Marketing, University of Groningen, Groningen, The Netherlands

    Peter S. H. Leeflang

  2. Department of Marketing, University of Groningen, Groningen, The Netherlands

    Jaap E. Wieringa

  3. Department of Marketing, University of Groningen, Groningen, The Netherlands

    Tammo H.A Bijmolt

  4. Department of Marketing, D’Amore-McKim School of Business, Northeastern University, Boston, USA

    Koen H. Pauwels

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Papies, D., Ebbes, P., Van Heerde, H.J. (2017). Addressing Endogeneity in Marketing Models. In: Leeflang, P., Wieringa, J., Bijmolt, T., Pauwels, K. (eds) Advanced Methods for Modeling Markets. International Series in Quantitative Marketing. Springer, Cham. https://doi.org/10.1007/978-3-319-53469-5_18

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