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Register a new userTesting for Unobserved Heterogeneous Treatment Effects with Observational Data
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Unobserved heterogeneous treatment effects have been emphasized in the recent policy evaluation literature (see e.g., Heckman and Vytlacil, 2005). This paper proposes a nonparametric test for unobserved heterogeneous treatment effects in a treatment effect model with a binary treatment assignment, allowing for individuals self-selection to the treatment. Under the standard local average treatment effects assumptions, i.e., the no defiers condition, we derive testable model restrictions for the hypothesis of unobserved heterogeneous treatment effects. Also, we show that if the treatment outcomes satisfy a monotonicity assumption, these model restrictions are also sufficient. Then, we propose a modified Kolmogorov-Smirnov-type test which is consistent and simple to implement. Monte Carlo simulations show that our test performs well in finite samples. For illustration, we apply our test to study heterogeneous treatment effects of the Job Training Partnership Act on earnings and the impacts of fertility on family income, where the null hypothesis of homogeneous treatment effects gets rejected in the second case but fails to be rejected in the first application.
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Clustering methods such as k-means have found widespread use in a variety of applications. This paper proposes a formal testing procedure to determine whether a null hypothesis of a single cluster, indicating homogeneity of the data, can be rejected in favor of multiple clusters. The test is simple to implement, valid under relatively mild conditions (including non-normality, and heterogeneity of the data in aspects beyond those in the clustering analysis), and applicable in a range of contexts (including clustering when the time series dimension is small, or clustering on parameters other than the mean). We verify that the test has good size control in finite samples, and we illustrate the test in applications to clustering vehicle manufacturers and U.S. mutual funds.
Bartik regressions use locations differential exposure to nationwide sector-level shocks as an instrument to estimate the effect of a location-level treatment on an outcome. In the canonical Bartik design, locations differential exposure to industry-level employment shocks are used as an instrument to measure the effect of their employment evolution on their wage evolution. Some recent papers studying Bartik designs have assumed that the sector-level shocks are exogenous and all have the same expectation. This second assumption may sometimes be implausible. For instance, there could be industries whose employment is more likely to grow than that of other industries. We replace that second assumption by parallel trends assumptions. Under our assumptions, Bartik regressions identify weighted sums of location-specific effects, with weights that may be negative. Accordingly, such regressions may be misleading in the presence of heterogeneous effects, an issue that was not present under the assumptions maintained in previous papers. Estimating the weights attached to Bartik regressions is a way to assess their robustness to heterogeneous effects. We also propose an alternative estimator that is robust to location-specific effects. Finally, we revisit two applications. In both cases, Bartik regressions have fairly large negative weights attached to them. Our alternative estimator is substantially different from the Bartik regression coefficient in one application.
Given the unconfoundedness assumption, we propose new nonparametric estimators for the reduced dimensional conditional average treatment effect (CATE) function. In the first stage, the nuisance functions necessary for identifying CATE are estimated by machine learning methods, allowing the number of covariates to be comparable to or larger than the sample size. The second stage consists of a low-dimensional local linear regression, reducing CATE to a function of the covariate(s) of interest. We consider two variants of the estimator depending on whether the nuisance functions are estimated over the full sample or over a hold-out sample. Building on Belloni at al. (2017) and Chernozhukov et al. (2018), we derive functional limit theory for the estimators and provide an easy-to-implement procedure for uniform inference based on the multiplier bootstrap. The empirical application revisits the effect of maternal smoking on a babys birth weight as a function of the mothers age.
In order to explore the generic properties of a backreaction model for explaining the accelerated expansion of the Universe, we exploit two metrics to describe the late time Universe. Since the standard FLRW metric cannot precisely describe the late time Universe on small scales, the template metric with an evolving curvature parameter $kappa_{mathcal{D}}(t)$ is employed. However, we doubt the validity of the prescription for $kappa_{mathcal{D}}$, which motivates us apply observational Hubble parameter data (OHD) to constrain parameters in dust cosmology. First, for FLRW metric, by getting best-fit constraints of $Omega^{{mathcal{D}}_0}_m = 0.25^{+0.03}_{-0.03}$, $n = 0.02^{+0.69}_{-0.66}$, and $H_{mathcal{D}_0} = 70.54^{+4.24}_{-3.97} {rm km s^{-1} Mpc^{-1}}$, the evolutions of parameters are explored. Second, in template metric context, by marginalizing over $H_{mathcal{D}_0}$ as a prior of uniform distribution, we obtain the best-fit values of $n=-1.22^{+0.68}_{-0.41}$ and ${{Omega}_{m}^{mathcal{D}_{0}}}=0.12^{+0.04}_{-0.02}$. Moreover, we utilize three different Gaussian priors of $H_{mathcal{D}_0}$, which result in different best-fits of $n$, but almost the same best-fit value of ${{Omega}_{m}^{mathcal{D}_{0}}}sim0.12$. Also, the absolute constraints without marginalization of parameter are obtained: $n=-1.1^{+0.58}_{-0.50}$ and ${{Omega}_{m}^{mathcal{D}_{0}}}=0.13pm0.03$. With these constraints, the evolutions of the effective deceleration parameter $q^{mathcal{D}}$ indicate that the backreaction can account for the accelerated expansion of the Universe without involving extra dark energy component in the scaling solution context. Nevertheless, the results also verify that the prescription of $kappa_{mathcal{D}}$ is insufficient and should be improved.
We study the causal interpretation of regressions on multiple dependent treatments and flexible controls. Such regressions are often used to analyze randomized control trials with multiple intervention arms, and to estimate institutional quality (e.g. teacher value-added) with observational data. We show that, unlike with a single binary treatment, these regressions do not generally estimate convex averages of causal effects-even when the treatments are conditionally randomly assigned and the controls fully address omitted variables bias. We discuss different solutions to this issue, and propose as a solution anew class of efficient estimators of weighted average treatment effects.
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