Xun Lu

Causal Diagrams for Treatment Effect Estimation with Application to Efficient Covariate Selection

Careful examination of the structure determining treatment choice and outcomes, as advocated by Heckman (2008), is central to the design of treatment effect estimators and, in particular, proper choice of covariates. Here, we demonstrate how causal diagrams developed in the machine learning literature by Judea Pearl and his colleagues, but not so well known to economists, can play a key role in this examination by using these methods to give a detailed analysis of the choice of efficient covariates identified by Hahn (2004).

A Covariate Selection Criterion for Estimation of Treatment Effects

We study how to select or combine estimators of the average treatment effect (ATE) and the average treatment effect on the treated (ATT) in the presence of multiple sets of covariates. We consider two cases: (1) all sets of covariates satisfy the unconfoundedness assumption and (2) some sets of covariates violate the unconfoundedness assumption locally. For both cases, we propose a data-driven covariate selection criterion (CSC) to minimize the asymptotic mean squared errors (AMSEs). Based on our CSC, we propose new average estimators of ATE and ATT, which include the selected estimators based on a single set of covariates as a special case. We derive the asymptotic distributions of our new estimators and propose how to construct valid confidence intervals. Our Monte Carlo simulations show that in finite samples, our new average estimators achieve substantial efficiency gains over the estimators based on a single set of covariates. We apply our new estimators to study the impact of inherited control on firm performance.

Statin effects on aggression: results from the UCSD Statin Study, a randomized control trial

Background Low/ered cholesterol is linked to aggression in some study designs. Cases/series have reported reproducible aggression increases on statins, but statins also bear mechanisms that could reduce aggression. Usual statin effects on aggression have not been characterized. Methods 1016 adults (692 men, 324 postmenopausal women) underwent double-blind sex-stratified randomization to placebo, simvastatin 20mg, or pravastatin 40mg (6 months). The Overt-Aggression-Scale-Modified–Aggression-Subscale (OASMa) assessed behavioral aggression. A significant sex-statin interaction was deemed to dictate sex-stratified analysis. Exploratory analyses assessed the influence of baseline-aggression, testosterone-change (men), sleep and age. Results The sex-statin interaction was significant (P=0.008). In men, statins tended to decrease aggression, significantly so on pravastatin: difference=-1.0(SE=0.49)P=0.038. Three marked outliers (OASMa-change ≥40 points) offset otherwise strong significance-vs-placebo: statins:-1.3(SE=0.38)P=0.0007; simvastatin:-1.4(SE=0.43)P=0.0011; pravastatin:-1.2(SE=0.45)P=0.0083. Age≤40 predicted greater aggression-decline on statins: difference=-1.4(SE=0.64)P=0.026. Aggression-protection was emphasized in those with low baseline aggression: age<40-and-low-baseline-aggression (N=40) statin-difference-vs-placebo=-2.4(SE=0.71)P=0.0016. Statins (especially simvastatin) lowered testosterone, and increased sleep problems. Testosterone-drop on statins predicted aggression-decline: β=0.64(SE=0.30)P=0.034, particularly on simvastatin: β=1.29(SE=0.49)P=0.009. Sleep-worsening on statins significantly predicted aggression-increase: β=2.2(SE=0.55)P<0.001, particularly on simvastatin (potentially explaining two of the outliers): β=3.3(SE=0.83)P<0.001. Among (postmenopausal) women, a borderline aggression-increase on statins became significant with exclusion of one younger, surgically-menopausal woman (N=310) β=0.70(SE=0.34)P=0.039. The increase was significant, without exclusions, for women of more typical postmenopausal age (≥45): (N=304) β=0.68(SE=0.34)P=0.048 – retaining significance with modified age-cutoffs (≥50 or ≥55). Significance was observed separately for simvastatin. The aggression-increase in women on statins was stronger in those with low baseline aggression (N=175) β=0.84(SE=0.30)P=0.006. No statin effect on whole blood serotonin was observed; and serotonin-change did not predict aggression-change. Conclusion Statin effects on aggression differed by sex and age: Statins generally decreased aggression in men; and generally increased aggression in women. Both findings were selectively prominent in participants with low baseline aggression – bearing lower change-variance, rendering an effect more readily evident. Trial Registration Clinicaltrials.gov NCT00330980

Determining the number of groups in latent panel structures with an application to income and democracy

We consider a latent group panel structure as recently studied by Su, Shi, and Phillips (2016), where the number of groups is unknown and has to be determined empirically. We propose a testing procedure to determine the number of groups. Our test is a residual‐based Lagrange multiplier‐type test. We show that after being appropriately standardized, our test is asymptotically normally distributed under the null hypothesis of a given number of groups and has the power to detect deviations from the null. Monte Carlo simulations show that our test performs remarkably well in finite samples. We apply our method to study the effect of income on democracy and find strong evidence of heterogeneity in the slope coefficients. Our testing procedure determines three latent groups among 74 countries.

Granger Causality and Structural Causality in Cross-Section and Panel Data

Granger non-causality in distribution is fundamentally a probabilistic conditional independence notion that can be applied not only to time series data but also to cross-section and panel data. In this paper, we provide a natural de nition of structural causality in cross-section and panel data and forge a direct link between Granger (G-) causality and structural causality under a key conditional exogeneity assumption. To put it simply, when structural e¤ects are well de ned and identi able, G-non-causality follows from structural non-causality, and with suitable conditions (e.g., separability or monotonicity), structural causality also implies G-causality. This justi es using tests of G-non- causality to test for structural non-causality under the key conditional exogeneity assumption for both cross-section and panel data. We pay special attention to heterogeneous populations, allowing both structural heterogeneity and distributional heterogeneity. Most of our results are obtained for the general case, without assuming linearity, monotonicity in observables or unobservables, or separability between observed and unobserved variables in the structural relations.

Testing For Treatment Dependence Of Effects Of A Continuous Treatment

This paper provides nonparametric tests for hypotheses about the effects of a continuous treatment variable in a nonseparable structural equation. Specifically, we consider local average responses and average partial effects and test whether these effects are identical across different levels of treatment, including testing whether they are zero for all treatment levels as a special case. Our tests are based on consistent procedures of Bierens (1982, Journal of Econometrics 20, 105–134; 1990, Econometrica 58, 1443–1458) and Stinchcombe and White (1998, Econometric Theory 14, 295–324). The tests are easy to implement and achieve n-1/2 local power. Monte Carlo simulations show that the tests perform well in finite samples. We apply our tests to study the interest rate elasticities of loan demand in microfinance. We also extend our testing procedures to covariate-conditioned average effects and marginal effects.