Interest in evaluating the effects of continuous treatments has been on the rise recently. To facilitate the estimation of causal effects in this setting, the present paper introduces entropy balancing for continuous treatments (EBCT) – an intuitive and user-friendly automated covariate balancing scheme – by extending the original entropy balancing methodology of Hainmueller, J. 2012. “Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies.” Political Analysis 20 (1): 25–46. In order to estimate balancing weights, the proposed approach solves a globally convex constrained optimization problem, allowing for computationally efficient software implementation. EBCT weights reliably eradicate Pearson correlations between covariates (and their transformations) and the continuous treatment variable. As uncorrelatedness may not be sufficient to guarantee consistent estimates of dose–response functions, EBCT also allows to render higher moments of the treatment variable uncorrelated with covariates to mitigate this issue. Empirical Monte-Carlo simulations suggest that treatment effect estimates using EBCT display favorable properties in terms of bias and root mean squared error, especially when balance on higher moments of the treatment variable is sought. These properties make EBCT an attractive method for the evaluation of continuous treatments. Software implementation is available for Stata and R.
The current German start-up subsidy for unemployed individuals underwent a major reform in 2011 that altered key parameters of the program, leading to ambiguous ex ante predictions on the post-reform effectiveness of the program, making a new evaluation necessary. In our descriptive analysis, we find that participants after the reform differ significantly from pre-reform participants in terms of important characteristics and subsequent labor market performance. Our causal analysis reveals positive and sizable treatment effects on the treated regarding employment and income that are larger effects than what was estimated for the pre-reform program. Potential reasons for this are discussed.
This paper introduces entropy balancing for continuous treatments (EBCT) by extending the original entropy balancing methodology of Hainmüller (2012). In order to estimate balancing weights, the proposed approach solves a globally convex constrained optimization problem. EBCT weights reliably eradicate Pearson correlations between covariates and the continuous treatment variable. This is the case even when other methods based on the generalized propensity score tend to yield insufficient balance due to strong selection into different treatment intensities. Moreover, the optimization procedure is more successful in avoiding extreme weights attached to a single unit. Extensive Monte-Carlo simulations show that treatment effect estimates using EBCT display similar or lower bias and uniformly lower root mean squared error. These properties make EBCT an attractive method for the evaluation of continuous treatments.
While a growing body of literature finds positive impacts of Start-Up Subsidies (SUS) on labor market outcomes of participants, little is known about how the design of these programs shapes their effectiveness and hence how to improve policy. As experimental variation in program design is unavailable, we exploit the 2011 reform of the current German SUS program for the unemployed which strengthened case-workers' discretionary power, increased entry requirements and reduced monetary support. We estimate the impact of the reform on the program's effectiveness using samples of participants and non-participants from before and after the reform. To control for timeconstant unobserved heterogeneity as well as differential selection patterns based on observable characteristics over time, we combine Difference-in-Differences with inverse probability weighting using covariate balancing propensity scores. Holding participants' observed characteristics as well as macroeconomic conditions constant, the results suggest that the reform was successful in raising employment effects on average. As these findings may be contaminated by changes in selection patterns based on unobserved characteristics, we assess our results using simulation-based sensitivity analyses and find that our estimates are highly robust to changes in unobserved characteristics. Hence, the reform most likely had a positive impact on the effectiveness of the program, suggesting that increasing entry requirements and reducing support increased the program's impacts while reducing the cost per participant.
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