Working Papers

Demand Estimation with Finitely Many Consumers
with Jonas Lieber. (Draft)

Abstract. Although market shares are frequently estimated via averages of finitely many consumer choices, commonly applied methods for demand estimation are not robust to estimation error in these shares. While non-negligible estimation error in market shares always introduces bias in the demand parameter estimators, the issue becomes most salient when estimated market shares are zero. In the presence of zero shares, widely applied estimators of the random coefficient logit model cannot be computed without ad-hoc data manipulations. This paper proposes a new estimator of demand parameters for settings with endogenous prices and estimated market shares that is robust to zero-valued market shares. The estimator generalizes the constrained optimization program of Dubé et al. (2012) with probabilistic bounds on the estimation error in market shares. We show consistency as the number of markets $T$ grows sufficiently slowly relative to the number of consumers $n$ such that $\log(T)/n\to 0$, and provide confidence intervals under the same regime. Simulations suggest improved finite sample properties of the proposed estimator to conventional alternatives.

Effects of Health Care Policy Uncertainty on Households’ Portfolio Choice
with Robin L Lumsdaine. (Draft)

Abstract. This paper develops a nonparametric identification approach for causal effects of an endogenous macroeconomic variable on microeconomic outcomes. The key assumption is the existence of an exogenous variable that shifts responsiveness to the variable of interest without shifting responsiveness to other macroeconomic time series. We apply the approach to study the effect of health care policy uncertainty (HCPU) on households’ portfolio choice using health shocks to capture cross-sectional heterogeneity. Under the additional assumption of risk averse agents, our approach provides an informative bound on the average causal effect of HCPU. The empirical results highlight HCPU as an important determinant of households’ financial behavior, and showcase substantial heterogeneity in HCPU effects across varying unexpected changes to health.

ddml: Double/debiased machine learning in Stata
with Achim Ahrens, Christian B Hansen, Mark E Schaffer. (arXiv)

Abstract. We introduce the package ddml for Double/Debiased Machine Learning (DDML) in Stata. Estimators of causal parameters for five different econometric models are supported, allowing for flexible estimation of causal effects of endogenous variables in settings with unknown functional forms and/or many exogenous variables. ddml is compatible with many existing supervised machine learning programs in Stata. We recommend using DDML in combination with stacking estimation which combines multiple machine learners into a final predictor. We provide Monte Carlo evidence to support our recommendation.

Work in Progress (Draft coming soon!)

Optimal Categorical Instrumental Variables

Abstract. This paper discusses estimation with a categorical instrumental variable in settings with potentially few observations per category. The proposed categorical instrumental variable estimator (CIV) leverages a regularization assumption that implies existence of a latent categorical variable with fixed finite support achieving the same first stage fit as the observed instrument. In asymptotic regimes that allow the number of observations per category to grow at arbitrary small polynomial rate with the sample size, I show that CIV is root-$n$ asymptotically normal and achieves the same asymptotic variance as the oracle IV estimator that presumes knowledge of the optimal instrument.

A Practitioner’s Guide to Double Machine Learning
with Achim Ahrens, Christian B Hansen, Mark E Schaffer.

Abstract. This paper discusses pairing double/debiased machine learning (DDML) with stacking, a weighted average of several candidate machine learners. The combination of the two methods leads to improved performance and addresses some of the recent concerns raised about the use of causal machine learning in economic applications. Additionally, we introduce DDML with short-stacking, which exploits the cross-fitting step of DDML to substantially reduce the computational burden of stacking. The central motivation for pairing DDML and stacking approaches is that, in practice, it is rarely obvious which machine learner performs best for a specific application, and we show that stacking can successfully reduce the risk of misspecification. Based on a diverse set of applications and calibrated simulation studies, we gauge the finite sample performance of DDML combined with stacking approaches on real data in various commonly encountered settings. We show that DDML with stacking is more robust than other approaches when the underlying data-generating process is unknown and develop practically-relevant recommendations for researchers.