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Modeling heterogeneity: a praise for varying-coefficient models in causal analysis

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Abstract

This article considers the question of how to cope with heterogeneity when studying causal effects. The standard approach in empirical economics is still to use a linear model and interpret the coefficients as the average returns or effects. Nowadays, instrumental variables (IV) are quite popular to account for (unobserved) heterogeneity when estimating these parameters. First the inadequacy of these standard methods is illustrated. Then it is shown why varying-coefficient models have a strong natural potential to model heterogeneity in many interesting regression problems. Moreover, it is straight forward to develop alternative IV specifications in the varying-coefficient models framework. The corresponding modeling and implementation facilities that are nowadays available in R are studied.

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Notes

  1. A covariate \(X\) is said to be endogenous if the error terms is not mean independent of it. This typically leads to identification problems, biased estimators and invalids causal inference. Else it is called exogenous.

  2. We put bias in quotation marks as the OLS estimate is actually not biased in the statistical sense, it does simply estimate something different than the average slope. Alternatively you may say that not the estimator is wrong but the interpretation that people often attach to it.

  3. The preposition real indicates that the numbers \(E^R\) assigned to the different households—in this example from all-over Canada—refer to the same purchase power.

  4. Simplified, this means that if a household switches from a product to a substitute because of a special discount, he will switch back if this discount is no longer conceded.

  5. The published consumer price index refers to a representative mean basket of goods and services. This basket clearly varies a lot over the different income groups, resulting in different effectively realized inflation rates for each group.

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Authors and Affiliations

  1. Geneva School for Economics and Management, Université de Genève, Bd du Pont d’Arve 40, 1211, Geneva, Switzerland

    Stefan Sperlich & Raoul Theler

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  1. Stefan Sperlich
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  2. Raoul Theler
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Correspondence to Stefan Sperlich.

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Sperlich, S., Theler, R. Modeling heterogeneity: a praise for varying-coefficient models in causal analysis. Comput Stat 30, 693–718 (2015). https://doi.org/10.1007/s00180-015-0581-y

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