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Using Machine Learning Methods to Support Causal Inference in Econometrics

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Behavioral Predictive Modeling in Economics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 897))

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Abstract

We provide an introduction to the use of machine learning methods in econometrics and how these methods can be employed to assist in causal inference. We begin with an extended presentation of the lasso (least absolute shrinkage and selection operator) of Tibshirani [50]. We then discuss the ‘Post-Double-Selection’ (PDS) estimator of Belloni et al. [13, 19] and show how it uses the lasso to address the omitted confounders problem. The PDS methodology is particularly powerful for the case where the researcher has a high-dimensional set of potential control variables, and needs to strike a balance between using enough controls to eliminate the omitted variable bias but not so many as to induce overfitting. The last part of the paper discusses recent developments in the field that go beyond the PDS approach.

Invited paper for the International Conference of the Thailand Econometric Society, ‘Behavioral Predictive Modeling in Econometrics’, Chiang Mai University, Thailand, 8–10 January 2020. Our exposition of the ‘rigorous lasso’ here draws in part on our paper Ahrens et al. [1]. All errors are our own.

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Notes

  1. 1.

    Previous research on that topic had relied instead on anecdotal evidence, or restricted its attention to a subset of the literature that is not representative because it is not feasible to manually classify the full corpus of work (Hamermesh [36] and Backhouse and Cherrier [10]).

  2. 2.

    That said, traditional methods such as k-means cluster analysis and ridge regression are often now associated with ML.

  3. 3.

    Bickel et al. [21] use instead the weaker restricted eigenvalue condition (REC). The RSEC implies the REC and has the advantage of being sufficient for both the lasso and the post-lasso.

  4. 4.

    See, for example, Hastie et al. ( [35], Ch. 2).

  5. 5.

    In this special case, the requirement of the slack is loosened and \(c=1\).

  6. 6.

    These conditions relate to the use of the moderate deviation theory of self-normalized sums [39] that allows the extension of the theory to cover non-Gaussianity. See Belloni et al. [13].

  7. 7.

    The alternative is to simulate the distribution of the score vector. This is known as the ‘exact’ or X-dependent approach. See Belloni and Chernozhukov [14] for details and Ahrens et al. [1] for a summary discussion and an implementation in Stata.

  8. 8.

    The formula in (16) for the penalty loading is familiar from the standard Eicker-Huber-White heteroskedasticty-robust covariance estimator.

  9. 9.

    These authors are careful to note that the problem readily arises when researchers make decisions contingent on their data analysis; no conscious attempt to deceive is needed. Deliberate falsification, sometimes called ‘p-hacking’, is special case and likely much rarer.

  10. 10.

    Wooldridge [56], pp. 450-3, 474 and Wooldridge [57], pp. 153-4.

  11. 11.

    To treat it as a causal variable and obtain a valid standard error, we would have to estimate an additional lasso regression with y81 as the dependent variable etc.

  12. 12.

    Of course, this discussion raises a more fundamental question: given a specification like that above, how does one construct such a function? The answer is a little technical, unfortunately. Interested readers can find a detailed discussion in van der Vaart  [52].

  13. 13.

    \(\partial _{\eta }\) is shorthand for \(\partial /\partial \eta '\). This version of the condition is actually more stringent than required. A more general definition of it, based on Gateaux derivatives, can be found in Belloni et al. [16] and Chernozhukov et al. [22].

  14. 14.

    The estimators that possess this property need not be semiparametrically efficient, but because they can be, we restrict our focus to those that are.

  15. 15.

    Estimators based on the efficient influence function are also double-robust (Robins et al. [48]).

  16. 16.

    Sample splitting was originally introduced by Angrist and Krueger [3] and Altonji and Segal [2] in the context of bias reduction of IV and GMM estimators.

  17. 17.

    There are a number of conditions that are intimately related to the size of the function class, as measured by its bracketing and covering numbers, which if satisfied are sufficient for it to be Donsker. See Vaart and Wellner [51] for a full statement.

  18. 18.

    Note that this observation can be connected to the discussion in the paragraph above: if one of the models is estimated parametrically based on a relationship that is known to be true, the other model need only be consistent, since the product of the two rates would be \(o_{p}\left( n^{-1/2}\right) \).

  19. 19.

    Laan et al. [42] provide asymptotic justifications for weighted combinations of estimators, particularly those which use cross-validation to calculate the weights.

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Author information

Authors and Affiliations

  1. ETH Zürich, Zürich, Switzerland

    Achim Ahrens

  2. Heriot-Watt University, Edinburgh, UK

    Christopher Aitken

  3. Heriot-Watt University, Edinburgh, UK

    Mark E. Schaffer

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  1. Achim Ahrens
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  2. Christopher Aitken
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  3. Mark E. Schaffer
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Correspondence to Mark E. Schaffer .

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Editors and Affiliations

  1. Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand

    Songsak Sriboonchitta

  2. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

  3. Faculty of Economics, Center of Excellence in Econometrics, Chiang Mai University, Chiang Mai, Thailand

    Woraphon Yamaka

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Ahrens, A., Aitken, C., Schaffer, M.E. (2021). Using Machine Learning Methods to Support Causal Inference in Econometrics. In: Sriboonchitta, S., Kreinovich, V., Yamaka, W. (eds) Behavioral Predictive Modeling in Economics. Studies in Computational Intelligence, vol 897. Springer, Cham. https://doi.org/10.1007/978-3-030-49728-6_2

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