PaperlayerView exact revision on arXiv

Source-linked AI summary

Machine Learning Methods Economists Should Know About

Susan Athey, Guido Imbens

arXiv:1903.10075v1econ.EMstat.ML

TL;DR

The paper argues that economists’ toolkit needs to adapt to the broader statistics and machine-learning communities while preserving traditional methods. It reviews machine-learning methods useful for economists and highlights their practical predictive value and relevance for sophisticated empirical work.

  • Problem

    Economists’ toolkit needs to adapt to developments in the broader statistics community while preserving traditional approaches.

  • Method

    The paper reviews machine-learning methods viewed as useful for economists and important for the core graduate economics curriculum.

  • Results

    Demonstrated ability to outperform alternative methods on specific data sets in out-of-sample predictive power is valuable in practice.

  • Takeaways & Limitations

    The reviewed methods can support sophisticated empirical work and help economists communicate more effectively with researchers in other fields.

  • Takeaways & Limitations

    No formal results show that deep learning or neural-network methods are uniformly superior to regression trees or other supervised-learning methods.

Abstract

from arXiv · show

We discuss the relevance of the recent Machine Learning (ML) literature for economics and econometrics. First we discuss the differences in goals, methods and settings between the ML literature and the traditional econometrics and statistics literatures. Then we discuss some specific methods from the machine learning literature that we view as important for empirical researchers in economics. These include supervised learning methods for regression and classification, unsupervised learning methods, as well as matrix completion methods. Finally, we highlight newly developed methods at the intersection of ML and econometrics, methods that typically perform better than either off-the-shelf ML or more traditional econometric methods when applied to particular classes of problems, problems that include causal inference for average treatment effects, optimal policy estimation, and estimation of the counterfactual effect of price changes in consumer choice models.

1 Introduction

The paper argues that economists should broaden their toolkit beyond exclusive reliance on traditional data models by incorporating machine-learning methods while preserving econometric strengths. It reviews where ML methods differ, where they help, and how adapting them to economic structure can improve empirical analysis.

  • Motivation: ML methods are especially relevant for “big data” settings involving many units, many features per unit, or both, including settings beyond simple cross-sections.The paper argues that economists’ toolkits should adapt while preserving traditional applied-econometrics strengths.
  • Motivation: ML adoption has been slower in economics partly because economics emphasizes formal estimator and test properties, whereas ML often emphasizes algorithmic performance in specific settings.Economics commonly values consistency, Normality, and efficiency; ML often emphasizes error-rate guarantees and working performance.
  • Limitations: There are no formal results showing that deep learning or neural networks are uniformly superior to regression trees or random forests for supervised learning problems.The paper considers general comparison results unlikely to become available soon, if ever.
  • Goals of analysis: Out-of-sample predictive power can be valuable in practice, particularly when substantive problems are naturally prediction problems or predictions feed into later analyses.In some settings, test-set goodness of fit may suffice; in others, valid confidence intervals for parameters such as average treatment effects remain important.
  • Adaptation to economics: Off-the-shelf ML can be effective in some cases, but economic applications often require tuning and adaptation to causal, endogenous, panel, discrete-choice, or theory-based structures.Adaptations include changing optimization criteria, sample splitting, and orthogonalization to address causal goals and desirable properties such as asymptotic normality.
  • Scope and contribution: The review covers supervised learning for regression and classification, unsupervised learning, and other tools viewed as important for the empirical economics toolkit.The authors aim to provide an introduction conveying the main ideas and insights, with references to more comprehensive treatments.

2 Econometrics and Machine Learning: Goals, Methods, and Settings

Traditional econometrics typically begins with a target estimand and evaluates parameter estimators, while machine learning emphasizes prediction or classification performance. These differing goals lead to different criteria for choosing and assessing methods.

  • Overview: The paper frames its discussion around how differing goals and concerns in econometrics and machine learning affect method choice.The comparison concerns both the objectives of the two literatures and the settings in which their methods are used.
  • Econometric goals: Econometrics typically specifies an estimand and evaluates parameter estimators using properties such as efficiency and confidence intervals.Researchers commonly report point estimates and standard errors.
  • Machine-learning goals: Machine learning typically develops algorithms for predicting variables or classifying units from limited information.Examples include predicting outcomes from features and classifying handwritten digits from pixel values.
  • Prediction criteria: Prediction settings evaluate estimators by their expected loss for new units, so least squares need not be optimal for prediction.When feature dimension exceeds two, other estimators can dominate least squares in expected squared error.
  • Prediction criteria: Decision-theoretic comparisons show that least squares is inadmissible for prediction when the feature dimension exceeds two.Other estimators can achieve lower expected squared error than least squares in that setting.

2.2 Terminology

Machine-learning terminology often renames familiar statistical concepts and distinguishes supervised prediction from unsupervised structure discovery. Its validation and regularization practices prioritize out-of-sample predictive performance and control model complexity.

  • Terminology: Machine-learning terminology calls the estimation sample a training sample, covariates features, parameters weights, and estimation training.These labels describe familiar regression objects using machine-learning vocabulary.
  • Learning settings: Supervised learning observes features and outcomes, whereas unsupervised learning observes features alone and seeks clusters or their joint distribution.Discrete response problems are generally called classification problems.
  • Validation: Unlike traditional model specification, machine-learning procedures use out-of-sample comparisons to guide predictive decisions.Cross-validation can help decide whether to include features, and out-of-sample comparisons provide unbiased fit comparisons.
  • Regularization: Machine learning emphasizes over-fitting and controls model complexity by adding penalties to objectives such as residual sums of squares or likelihoods.Complexity may be measured through parameters or the Vapnik–Chervonenkis dimension.
  • Regularization: Regularization strength is commonly selected through cross-validation to optimize out-of-sample predictive performance rather than fixed subjectively.The paper contrasts this data-driven choice with Bayesian prior-based regularization.

2.5 Sparsity

High-dimensional prediction often involves many features with limited individual relevance, making feature selection important. Sparsity-based methods can help when only a few features matter, but sparsity and related selection assumptions constrain performance and inference.

  • Sparsity: The sparsity problem arises when many features are minor or irrelevant and researchers do not know which can be dropped without harming predictive power.This motivates data-dependent feature selection.
  • Sparsity: The sparsity principle assumes the underlying signal is sparse and uses an ℓ1 penalty to recover it.Under the assumption, the cited discussion says recovery can be good; if the assumption fails, performance is limited.
  • Limitations: If the chosen basis is unsuitable, the ℓ1 penalty may perform poorly, and no method can do well relative to the Bayes error in that instance.The limitation concerns the representation and the attainable prediction error.
  • Sparsity: Approximate sparsity can suffice when most explanatory variables have limited power and only a few features are substantially important.Exact zero coefficients are not always required.
  • Variable selection: Allowing data to guide variable selection is presented as an improvement over limiting explanatory variables by hand.The paper notes that approximate sparsity remains a strong assumption and that inference after data-dependent selection can be challenging.

2.6 Computational Issues and Scalability

The section emphasizes computational scalability as a central concern in machine learning methods, especially for large feature sets and datasets. It discusses regularization, subset selection, stochastic gradient descent, and related computational trade-offs.

  • Computational motivation: Machine learning methods often prioritize computational tractability and implementation at large scale over methods with attractive statistical efficiency that do not scale well.The discussion contrasts computationally feasible methods with approaches whose theoretical properties may be attractive but whose implementation is difficult for large datasets.
  • Regularization and subset selection: LASSO adds an absolute-value penalty and can be estimated effectively when the number of regressors is in the millions.Best subset selection is computationally harder, although recent work suggests feasibility with numbers of regressors in the 1000s.
  • Regularization and subset selection: The relative merits of LASSO and best subset selection remain unresolved, with LASSO showing indications of better performance in low-signal-to-noise settings.The comparison depends partly on whether both methods are computationally feasible in the application.
  • Stochastic gradient descent: Stochastic gradient descent updates parameters using noisy minibatch gradient estimates rather than repeatedly evaluating the full derivative.Its appeal is computational: many small, noisy steps can be preferable to spending equivalent cost calculating one highly accurate direction.
  • Stochastic gradient descent: With an appropriately decreasing learning rate, stochastic gradient descent converges almost surely to a global minimum for convex or pseudoconvex objectives and to a local minimum otherwise.The method can use randomly selected subsets of observations to form unbiased but noisy gradient estimates.
  • Stochastic gradient descent: Stochastic gradient methods can also approximate expectations inside gradients using only a small number of Monte Carlo draws, including a single draw.This further reduces computational burden in models where gradient evaluation itself involves integration.

2.7 Ensemble Methods and Model Averaging

Ensemble methods combine predictions from different models, often assigning weights according to out-of-sample performance. Because models have distinct strengths, averaging can outperform individual predictors.

  • Model averaging: Modern ensemble methods can average substantially different models, with weights chosen by optimizing out-of-sample predictive performance.This differs from averaging models that share a specification and vary only in parameter values.
  • Why ensembles help: Averaging predictions from different models may produce strictly better out-of-sample predictions than any single model.The paper presents model combinations as useful when no single algorithm performs well across all relevant structures.
  • Model averaging: A test sample can determine nonnegative weights for random-forest, neural-network, and LASSO predictions by minimizing the sum of squared residuals.The weights may be constrained to sum to one, although unconstrained regression-based alternatives are also discussed.
  • Why ensembles help: Random forests, neural nets, and LASSO have distinct strengths in handling irrelevant features, nonlinearities, and interactions.These differences motivate combining their predictions rather than relying on one model.
  • Applications: In panel-data applications, combinations of synthetic-control and matrix-completion methods outperform the individual methods.This provides an economic application of ensemble methods beyond the random-forest, neural-network, and LASSO example.

2.8 Inference

Machine learning has emphasized out-of-sample prediction, whereas econometrics and statistics have traditionally emphasized valid inference. The section highlights a trade-off: inferential requirements can reduce predictive performance, while valid confidence intervals remain unavailable for many methods.

  • Different priorities: The machine-learning literature focuses heavily on out-of-sample performance, while traditional statistics and econometrics emphasize valid confidence intervals, at least asymptotically.The section frames these as differing priorities rather than mutually exclusive objectives.
  • Inference: Prediction has advanced faster than its inferential justification, leaving confidence-interval construction impossible for many methods even asymptotically.Recent progress exists for low-dimensional functionals in specific settings, but broad inferential guarantees remain limited.
  • Different priorities: For many decision problems, prediction may be primary while inference is secondary.The paper presents this as an open question about the relative importance of confidence intervals in applied work.
  • Prediction–inference trade-off: Requirements that permit inference can come at the expense of predictive performance.Traditional kernel regression illustrates the trade-off through bandwidth choices balancing bias and variance.
  • Prediction–inference trade-off: Reducing bandwidth can eliminate asymptotic bias and restore valid confidence intervals, but increases variance.The adjustment explicitly trades predictive variance for inferential validity.

3 Supervised Learning for Regression Problems

Supervised-learning methods address regression by predicting conditional means without requiring simple monotonic or additive relationships. The section covers regularization, trees and forests, neural networks, boosting, and adaptations that improve inference or exploit economic structure.

  • Regression setting: Regression problems in machine learning focus on out-of-sample prediction, often allowing many covariates, complex interactions, and non-monotone conditional expectations.This differs from settings where covariate-specific derivatives or structural parameters are the primary objects of interest.
  • Kernel regression: Kernel methods perform poorly with high-dimensional covariates in practice, so econometric applications of kernels are generally limited to low-dimensional settings.The cited discussion notes a slow basic rate and the need for stronger smoothness assumptions to improve it.
  • Trees and forests: Random forests can exploit sparsity by ignoring many irrelevant covariates, whereas traditional kernel implementations spend degrees of freedom accounting for them.Their advantage is especially pronounced in sparse settings with many irrelevant features.
  • Trees and forests: Modern methods detect severe nonlinearities and high-order interactions, while linearized models may perform well when economic relationships are plausibly monotone.Locally linear random forests can improve on standard forests when a simple polynomial approximation is plausible.
  • Inference and adaptation: Generalized random forests can produce asymptotically normal estimates centered on the true conditional mean and provide variance estimates for inference.Locally linear corrections can address forest bias while retaining the ability to uncover complex interactions across multiple dimensions.
  • Neural networks: Neural networks with one hidden layer can approximate a rich class of smooth functions, while increasing depth substantially improves practical flexibility.The discussion distinguishes approximation capacity from the additional flexibility obtained through multiple hidden layers.
  • Boosting: Boosting constructs predictors from sums of functions of subsets of features, allowing additive effects when L = 1 and general second-order effects when L = 2.The representation becomes more flexible as the number of features included in each component increases.

4 Supervised Learning for Classification Problems

Classification assigns observations to discrete labels rather than necessarily estimating label probabilities. The section presents trees, forests, SVMs, and kernels, emphasizing different objectives and robust nonlinear classification.

  • Classification goals: Classification maps feature vectors to discrete labels, closely relating to discrete-choice analysis but differing in its frequent focus on label assignment.Classification methods need not first estimate probabilities for each label, whereas econometric discrete-choice models typically specify conditional probabilities.
  • Applications: Machine learning methods have been highly successful in digit recognition, with SVMs outperforming earlier methods and deep convolutional networks reducing error rates further.The example classifies images represented by black-and-white pixels into ten digit labels.
  • Trees and forests: Random forests extend the tree framework to classification, while regularization penalizes the number of leaves.The classification-specific objective replaces the regression squared-residual criterion with an impurity measure.
  • Trees and forests: Classification trees choose covariate thresholds by optimizing an impurity function based on label shares in each leaf.For multiple labels, the Gini impurity is minimized by pure leaves and maximized when label shares are equal.
  • Support vector machines: Support vector machines select a separating hyperplane by maximizing the margin, with support vectors lying closest to that boundary.When perfect separation is unavailable, constraining the dual coefficients produces a workable classifier.
  • Support vector machines: SVMs differ from logistic regression through their loss function, giving distant observations less influence and producing more robust estimates.Their nonlinear power comes from transforming features implicitly through kernels, whose smoothing parameters are typically selected by cross-validation.

5 Unsupervised Learning

Unsupervised learning analyzes feature observations without outcome labels to find clusters, distributions, or useful representations. The section discusses k-means, mixture models, and GANs, while noting that unsupervised solutions often lack natural benchmarks.

  • Overview: Unsupervised learning uses covariates without outcomes to partition observations into clusters or estimate their joint distribution.The resulting clusters can organize units, create features, or support models estimated separately within subspaces.
  • Uses and limitations: Clustering can organize units into types that may receive different treatment exposures, but unsupervised solutions have no natural benchmark for judging quality.This absence makes it difficult to determine whether one partition is preferable to another.
  • Mixture models: Mixture models provide a related econometric and statistical approach by modeling the data-generating distribution as a mixture of different distributions.Their mixture components are similar in nature to clusters.
  • K-means: K-means alternates between assigning each observation to its nearest centroid and updating each centroid to the cluster average.The algorithm partitions the feature space into K clusters using distance minimization.
  • K-means: Choosing the number of k-means clusters is difficult because there is no direct cross-validation criterion for comparing candidate values of K.The number of clusters is often selected using substantive considerations instead.
  • Generative adversarial networks: GANs generate data resembling an observed sample and assess success by training a classifier to distinguish generated observations from original ones.If the classifier cannot distinguish the sources, the generator is treated as successful; such algorithms may help design realistic simulations.

6 Machine Learning and Causal Inference

Econometric applications often target causal or structural parameters rather than prediction alone, so machine learning must be adapted to preserve inferential performance. The section develops this point through treatment-effect estimation and related econometric methods.

  • Motivation: Economists often prioritize estimating average treatment effects and other causal or structural parameters over maximizing predictive accuracy.Covariates with limited predictive value can still matter substantially for structural-parameter estimation.
  • Average treatment effects: Under unconfoundedness, the average treatment effect is identified and can be represented using outcome expectations, propensity scores, or an influence function.These representations motivate different estimators and combinations of nuisance-function estimates.
  • Average treatment effects: Selecting covariates solely for outcome prediction can bias treatment-effect estimates because treatment-predictive confounders may be omitted.Belloni et al. propose selecting variables predictive of both outcomes and treatment, improving the properties of the estimator for τ.
  • Robust estimation: Doubly robust and covariate-balancing methods combine flexible nuisance estimation or directly optimize weights to improve treatment-effect estimation.Balancing weights can remain effective when the propensity score is too complex to estimate well and can be more effective with many weak confounders.
  • Orthogonalization and cross-fitting: Orthogonalized influence-function estimators can remain efficient when nuisance components converge at rates close to N^-1/4.Orthogonalization makes nuisance-estimation errors orthogonal to errors in the target score, while cross-fitting addresses overfitting concerns from flexible models.
  • Broader developments: The ML–econometrics intersection also includes optimal-policy algorithms, performance bounds, non-unconfounded settings, and confidence intervals with asymptotic guarantees.These developments use econometric efficiency theory and adapted regularization to support inference and policy estimation.

7 Experimental Design, Reinforcement Learning, and Multi-Armed Bandits

Adaptive experimental-design methods use incoming outcomes to balance exploration against exploitation, reducing assignments to treatments that appear inferior. Multi-armed bandits and contextual extensions provide flexible assignment rules but require care with uncertainty, model specification, and bias.

  • Multi-armed bandits: Multi-armed bandits improve on static experiments by adapting treatment assignments as outcome information accumulates.They balance exploring uncertain treatments with exploiting treatments currently assessed as high quality.
  • Thompson sampling: Thompson sampling assigns the next unit to each treatment with probability equal to that treatment’s probability of being optimal.As evidence accumulates, assignment probability approaches one for the optimal treatment and falls for treatments believed inferior.
  • Upper confidence bounds: UCB assigns the next unit to the treatment with the highest upper confidence bound on its average outcome.Large batch updates can be problematic when two arms have similar bounds, because a slight difference may trigger disproportionate assignment.
  • Contextual bandits: Contextual bandits use unit characteristics in assignment, but misspecified models can create unjustified certainty in regions with little treatment-arm data.The algorithm may then avoid experimenting in those regions and fail to learn the true optimal policy.
  • Contextual bandits: Treatment assignment based on observed characteristics can yield substantial gains when treatment effects are heterogeneous across units.This motivates simple assignment rules that target treatments to unit characteristics.
  • Contextual bandits: Propensity weighting and doubly robust outcome modeling address bias concerns arising because contextual assignment rules change with accumulated information.Real-world datasets show that propensity weighting improves contextual-bandit performance.

8 Matrix Completion and Recommender Systems

Matrix completion treats missing panel outcomes as values to impute, linking recommender-system methods to causal inference and consumer-choice applications. The approach can exploit stable patterns across units and time and accommodate complex missing-data structures.

  • The Netflix problem: The Netflix Prize asked researchers to predict unobserved movie ratings for movie–individual pairs using a training dataset.The competition accelerated development of methods for this setting, including model averaging, matrix factorization, and nearest-neighbor methods.
  • Causal and panel-data applications: Matrix completion recasts causal-effect estimation as imputing missing values in incomplete potential-outcome matrices.For binary treatments, observed data can be represented by separate treated- and control-outcome matrices.
  • Matrix-completion methods: The method models a complete outcome matrix through a low-rank representation, commonly regularized with the nuclear norm.The nuclear norm is the sum of singular values and supports effective algorithms when both N and T are large.
  • Connections to econometrics: Econometric panel-data and synthetic-control methods address related missing-data problems through factor models, regressions, or weighted averages.Panel-data work often estimates latent factors, while synthetic control traditionally focuses on missing values in a single matrix row.
  • Causal and panel-data applications: Matrix completion combines stable patterns over time with stable patterns between units when imputing missing values.Unlike horizontal or vertical regression approaches, it can also handle more complex missing-data patterns.
  • Consumer-choice applications: In consumer-choice models, matrix-completion techniques are part of hybrid methods for estimating preferences and counterfactual effects of price changes.The relevant applications include cross-price elasticities and analyses of mergers or price changes.

9 Text Analysis

Text analysis represents documents as data suitable for unsupervised or supervised learning. The section covers latent topic and semantic representations, prediction of document characteristics, and the information lost by simple word-indicator representations.

  • Text representations: Representing documents with word-presence indicators loses information about word order.Richer representations can include adjacent word pairs, such as bigrams.
  • Unsupervised learning: Text data can be analyzed with unsupervised learning to discover lower-rank representations and latent characteristics of documents.The representation uses latent document characteristics and weights, with performance evaluated on held-out matrix elements.
  • Topic models: Topic models estimate latent topics, word distributions for topics, and topic weights for each article.Latent Dirichlet Allocation is identified as a popular implementation of this generative approach.
  • Language representations: Word-embedding methods use vector representations to capture latent semantic structure in language.The section presents neural probabilistic language models as specifying word-sequence probabilities through vocabulary vectors.
  • Supervised learning: Supervised learning predicts a labeled characteristic of text, such as review favorability, political polarization, or sentiment.A simple model treats word-indicator columns as covariates and requires regularization when the number of words exceeds the number of documents.
  • Supervised learning: Supervised topic models incorporate observed characteristics into a generative model and predict those characteristics for unlabeled documents.Training labels inform estimation, while the fitted model is applied to a test dataset.

10 Conclusion

The review argues that machine learning offers useful methods for empirical researchers in economics and should be part of core econometrics training. Familiarity with these methods can support more sophisticated empirical work and communication across research communities.

  • Conclusion: The review identifies machine learning methods as useful for empirical researchers in economics.It presents the discussion as a high-level selection of methods considered important for economists.
  • Conclusion: The authors view familiarity with these methods as important to include in core graduate econometrics training.The stated rationale is that these methods can help researchers communicate more effectively with researchers in other fields.
  • Conclusion: Familiarity with machine learning methods can enable more sophisticated empirical work and more effective communication with researchers in other fields.This is presented as the practical consequence of learning the methods reviewed.
Loading 1903.10075v1…