The Experts below are selected from a list of 15990 Experts worldwide ranked by ideXlab platform
Andrea Weber - One of the best experts on this subject based on the ideXlab platform.
-
Regression Kink Design: Theory and Practice
Advances in Econometrics, 2017Co-Authors: David Card, David S. Lee, Zhuan Pei, Andrea WeberAbstract:A regression kink design (RKD or RK design) can be used to identify casual effects in settings where the regressor of interest is a kinked function of an Assignment Variable. In this paper, we apply an RKD approach to study the effect of unemployment benefits on the duration of joblessness in Austria, and discuss implementation issues that may arise in similar settings, including the use of bandwidth selection algorithms and bias-correction procedures. Although recent developments in nonparametric estimation (e.g. Imbens et al. (2012) and Calonico et al. (2014)) are sometimes interpreted by practitioners as pointing to a default estimation procedure, we show that in any given application different procedures may perform better or worse. In particular, Monte Carlo simulations based on data generating processes that closely resemble the data from our application show that some asymptotically dominant procedures may actually perform worse than “sub-optimal” alternatives in a given empirical application.
-
Regression kink design: Theory and practice
2017Co-Authors: David Card, David S. Lee, Zhuan Pei, Andrea WeberAbstract:Abstract A regression kink design (RKD or RK design) can be used to identify casual effects in settings where the regressor of interest is a kinked function of an Assignment Variable. In this chapter, we apply an RKD approach to study the effect of unemployment benefits on the duration of joblessness in Austria, and discuss implementation issues that may arise in similar settings, including the use of bandwidth selection algorithms and bias-correction procedures. Although recent developments in nonparametric estimation (Calonico, Cattaneo, & Farrell, 2014; Imbens & Kalyanaraman, 2012) are sometimes interpreted by practitioners as pointing to a default estimation procedure, we show that in any given application different procedures may perform better or worse. In particular, Monte Carlo simulations based on data-generating processes that closely resemble the data from our application show that some asymptotically dominant procedures may actually perform worse than “sub-optimal” alternatives in a given empirical application.
-
Inference on Causal Effects in a Generalized Regression Kink Design
Econometrica, 2015Co-Authors: David Card, David S. Lee, Zhuan Pei, Andrea WeberAbstract:We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed Assignment Variable. This design arises in many institutional settings where a policy Variable (such as weekly unemployment benefits) is determined by an observed but potentially endogenous Assignment Variable (like previous earnings). We provide new results on identification and estimation for these settings, and apply our results to obtain estimates of the elasticity of joblessness with respect to UI benefit rates. We characterize a broad class of models in which a sharp "Regression Kink Design" (RKD, or RK Design) identifies a readily interpretable treatment-on-the-treated parameter (Florens et al. (2008)). We also introduce a "fuzzy regression kink design" generalization that allows for omitted Variables in the Assignment rule, noncompliance, and certain types of measurement errors in the observed values of the Assignment Variable and the policy Variable. Our identifying assumptions give rise to testable restrictions on the distributions of the Assignment Variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. We then use a fuzzy RKD approach to study the effect of unemployment insurance benefits on the duration of joblessness in Austria, where the benefit schedule has kinks at the minimum and maximum benefit level. Our preferred estimates suggest that changes in UI benefit generosity exert a relatively large effect on the duration of joblessness of both low-wage and high-wage UI recipients in Austria.
-
nonlinear policy rules and the identification and estimation of causal effects in a generalized regression kink design
National Bureau of Economic Research, 2012Co-Authors: David Card, Andrea WeberAbstract:We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed Assignment Variable. This design arises in many institutional settings where a policy Variable (such as weekly unemployment benefits) is determined by an observed but potentially endogenous Assignment Variable (like previous earnings). We provide new results on identification and estimation for these settings, and apply our results to obtain estimates of the elasticity of joblessness with respect to UI benefit rates. We characterize a broad class of models in which a "Regression Kink Design" (RKD, or RK Design) provides valid inferences for the treatment-on-the-treated parameter (Florens et al. (2008)) that would be identified in an ideal randomized experiment. We show that the smooth density condition that is sufficient for identification rules out extreme sorting around the kink, but is compatible with less severe forms of endogeneity. It also places testable restrictions on the distribution of predetermined covariates around the kink point. We introduce a generalization of the RKD - the "fuzzy regression kink design" - that allows for omitted Variables in the Assignment rule, as well as certain types of measurement errors in the observed values of the Assignment Variable and the policy Variable. We also show how standard local polynomial regression techniques can be adapted to obtain nonparametric estimates for the sharp and fuzzy RKD. We then use a fuzzy RKD approach to study the effect of unemployment insurance benefits on the duration of joblessness in Austria, where the benefit schedule has kinks at the minimum and maximum benefit level. Our estimates suggest that the elasticity of joblessness with respect to the benefit rate is on the order of 1.5.
Bjorn Ottersten - One of the best experts on this subject based on the ideXlab platform.
-
A RAN Resource Slicing Mechanism for Multiplexing of eMBB and URLLC Services in OFDMA Based 5G Wireless Networks
IEEE Access, 2020Co-Authors: Praveen Kumar Korrai, Eva Lagunas, Symeon Chatzinotas, S K Sharma, Ashok Bandi, Bjorn OtterstenAbstract:Enhanced mobile broadband (eMBB) and ultra-reliable and low-latency communications (URLLC) are the two main expected services in the next generation of wireless networks. Accommodation of these two services on the same wireless infrastructure leads to a challenging resource allocation problem due to their heterogeneous specifications. To address this problem, slicing has emerged as an architecture that enables a logical network with specific radio access functionality to each of the supported services on the same network infrastructure. The allocation of radio resources to each slice according to their requirements is a fundamental part of the network slicing that is usually executed at the radio access network (RAN). In this work, we formulate the RAN resource allocation problem as a sum-rate maximization problem subject to the orthogonality constraint (i.e., service isolation), latency-related constraint and minimum rate constraint while maintaining the reliability constraint with the incorporation of adaptive modulation and coding (AMC). However, the formulated problem is not mathematically tractable due to the presence of a step-wise function associated with the AMC and a binary Assignment Variable. Therefore, to solve the proposed optimization problem, first, we relax the mathematical intractability of AMC by using an approximation of the non-linear AMC achievable throughput, and next, the binary constraint is relaxed to a box constraint by using the penalized reformulation of the problem. The result of the above two-step procedure provides a close-to-optimal solution to the original optimization problem. Furthermore, to ease the complexity of the optimization-based scheduling algorithm, a low-complexity heuristic scheduling scheme is proposed for the efficient multiplexing of URLLC and eMBB services. Finally, the effectiveness of the proposed optimization and heuristic schemes is illustrated through extensive numerical simulations.
-
slicing based resource allocation for multiplexing of embb and urllc services in 5g wireless networks
Computer Aided Modeling and Design of Communication Links and Networks, 2019Co-Authors: Praveen Kumar Korrai, Eva Lagunas, Symeon Chatzinotas, S K Sharma, Bjorn OtterstenAbstract:The next generation of wireless networks is intended to accommodate two major services: enhanced mobile broadband (eMBB), and ultra-reliable and low-latency communications (URLLC). The eMBB applications require higher data rates while URLLC applications require a stringent latency and high transmission success probability (i.e., reliability). The multiplexing of eMBB and URLLC services on the same network infrastructure leads to a challenging resource optimization problem. In this paper, we formulate the network slicing problem in the context of time-frequency resource blocks (RBs) allocation to the wireless system consisting of eMBB and URLLC users. In particular, we address the sum-rate maximization problem subject to latency and slice isolation constraints while assuring certain reliability requirements with the use of adaptive modulation coding (AMC). We relax the mathematical intractability of AMC and binary Assignment Variable and show the effectiveness of the proposed approach through numerical simulations.
-
CAMAD - Slicing Based Resource Allocation for Multiplexing of eMBB and URLLC Services in 5G Wireless Networks
2019 IEEE 24th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD), 2019Co-Authors: Praveen Kumar Korrai, Eva Lagunas, Symeon Chatzinotas, Sanjay Sharma, Bjorn OtterstenAbstract:The next generation of wireless networks is intended to accommodate two major services: enhanced mobile broadband (eMBB), and ultra-reliable and low-latency communications (URLLC). The eMBB applications require higher data rates while URLLC applications require a stringent latency and high transmission success probability (i.e., reliability). The multiplexing of eMBB and URLLC services on the same network infrastructure leads to a challenging resource optimization problem. In this paper, we formulate the network slicing problem in the context of time-frequency resource blocks (RBs) allocation to the wireless system consisting of eMBB and URLLC users. In particular, we address the sum-rate maximization problem subject to latency and slice isolation constraints while assuring certain reliability requirements with the use of adaptive modulation coding (AMC). We relax the mathematical intractability of AMC and binary Assignment Variable and show the effectiveness of the proposed approach through numerical simulations.
David Card - One of the best experts on this subject based on the ideXlab platform.
-
Regression Kink Design: Theory and Practice
Advances in Econometrics, 2017Co-Authors: David Card, David S. Lee, Zhuan Pei, Andrea WeberAbstract:A regression kink design (RKD or RK design) can be used to identify casual effects in settings where the regressor of interest is a kinked function of an Assignment Variable. In this paper, we apply an RKD approach to study the effect of unemployment benefits on the duration of joblessness in Austria, and discuss implementation issues that may arise in similar settings, including the use of bandwidth selection algorithms and bias-correction procedures. Although recent developments in nonparametric estimation (e.g. Imbens et al. (2012) and Calonico et al. (2014)) are sometimes interpreted by practitioners as pointing to a default estimation procedure, we show that in any given application different procedures may perform better or worse. In particular, Monte Carlo simulations based on data generating processes that closely resemble the data from our application show that some asymptotically dominant procedures may actually perform worse than “sub-optimal” alternatives in a given empirical application.
-
Regression kink design: Theory and practice
2017Co-Authors: David Card, David S. Lee, Zhuan Pei, Andrea WeberAbstract:Abstract A regression kink design (RKD or RK design) can be used to identify casual effects in settings where the regressor of interest is a kinked function of an Assignment Variable. In this chapter, we apply an RKD approach to study the effect of unemployment benefits on the duration of joblessness in Austria, and discuss implementation issues that may arise in similar settings, including the use of bandwidth selection algorithms and bias-correction procedures. Although recent developments in nonparametric estimation (Calonico, Cattaneo, & Farrell, 2014; Imbens & Kalyanaraman, 2012) are sometimes interpreted by practitioners as pointing to a default estimation procedure, we show that in any given application different procedures may perform better or worse. In particular, Monte Carlo simulations based on data-generating processes that closely resemble the data from our application show that some asymptotically dominant procedures may actually perform worse than “sub-optimal” alternatives in a given empirical application.
-
Inference on Causal Effects in a Generalized Regression Kink Design
Econometrica, 2015Co-Authors: David Card, David S. Lee, Zhuan Pei, Andrea WeberAbstract:We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed Assignment Variable. This design arises in many institutional settings where a policy Variable (such as weekly unemployment benefits) is determined by an observed but potentially endogenous Assignment Variable (like previous earnings). We provide new results on identification and estimation for these settings, and apply our results to obtain estimates of the elasticity of joblessness with respect to UI benefit rates. We characterize a broad class of models in which a sharp "Regression Kink Design" (RKD, or RK Design) identifies a readily interpretable treatment-on-the-treated parameter (Florens et al. (2008)). We also introduce a "fuzzy regression kink design" generalization that allows for omitted Variables in the Assignment rule, noncompliance, and certain types of measurement errors in the observed values of the Assignment Variable and the policy Variable. Our identifying assumptions give rise to testable restrictions on the distributions of the Assignment Variable and predetermined covariates around the kink point, similar to the restrictions delivered by Lee (2008) for the regression discontinuity design. We then use a fuzzy RKD approach to study the effect of unemployment insurance benefits on the duration of joblessness in Austria, where the benefit schedule has kinks at the minimum and maximum benefit level. Our preferred estimates suggest that changes in UI benefit generosity exert a relatively large effect on the duration of joblessness of both low-wage and high-wage UI recipients in Austria.
-
nonlinear policy rules and the identification and estimation of causal effects in a generalized regression kink design
National Bureau of Economic Research, 2012Co-Authors: David Card, Andrea WeberAbstract:We consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known, deterministic, but kinked function of an observed Assignment Variable. This design arises in many institutional settings where a policy Variable (such as weekly unemployment benefits) is determined by an observed but potentially endogenous Assignment Variable (like previous earnings). We provide new results on identification and estimation for these settings, and apply our results to obtain estimates of the elasticity of joblessness with respect to UI benefit rates. We characterize a broad class of models in which a "Regression Kink Design" (RKD, or RK Design) provides valid inferences for the treatment-on-the-treated parameter (Florens et al. (2008)) that would be identified in an ideal randomized experiment. We show that the smooth density condition that is sufficient for identification rules out extreme sorting around the kink, but is compatible with less severe forms of endogeneity. It also places testable restrictions on the distribution of predetermined covariates around the kink point. We introduce a generalization of the RKD - the "fuzzy regression kink design" - that allows for omitted Variables in the Assignment rule, as well as certain types of measurement errors in the observed values of the Assignment Variable and the policy Variable. We also show how standard local polynomial regression techniques can be adapted to obtain nonparametric estimates for the sharp and fuzzy RKD. We then use a fuzzy RKD approach to study the effect of unemployment insurance benefits on the duration of joblessness in Austria, where the benefit schedule has kinks at the minimum and maximum benefit level. Our estimates suggest that the elasticity of joblessness with respect to the benefit rate is on the order of 1.5.
-
Quasi-Experimental Identification and Estimation in the Regression Kink Design
2009Co-Authors: David Card, David S. Lee, Zhuan PeiAbstract:We consider nonparametic identification of the average marginal effect of a continuous endogenous regressor in a generalized nonseparable model when the regressor of interest is a known, deterministic, but kiniked function of an observed continuous Assignment Variable. This design arises in many institutional settings where a policy Variable of interest (such as weekly unemployment benefits) is mechanically related to an observed but potentially endogenous Variable (like previous earnings). We characterize a broad class of models in which a "Regression Kink Design" (RKD) provides valid inferences for the underlying marginal effects. Importantly, this class includes cases where the Assignment Variable is endogenously chose. Under suitable conditions we show that the RKD estimand identifies the "treatment on the treated" parameter (Florens et al., 2009) or the "local average response" (altonji and Matzkin, 2005) that is identified in an ideal randomized experiment. As in a regression discontinuity design, the required indentification assumption implies strong and readilt testable predictions for the pattern of predetermined covariates around the kink point. Standard local linear regression techniques can be easily adapted to obtain "nonparametris" RKD estimates. We illustrate the RKD approach by examining the effect of unemployment insurance benefits on the duration of benefit claims, using rich microdata from the state of Washington.
Praveen Kumar Korrai - One of the best experts on this subject based on the ideXlab platform.
-
A RAN Resource Slicing Mechanism for Multiplexing of eMBB and URLLC Services in OFDMA Based 5G Wireless Networks
IEEE Access, 2020Co-Authors: Praveen Kumar Korrai, Eva Lagunas, Symeon Chatzinotas, S K Sharma, Ashok Bandi, Bjorn OtterstenAbstract:Enhanced mobile broadband (eMBB) and ultra-reliable and low-latency communications (URLLC) are the two main expected services in the next generation of wireless networks. Accommodation of these two services on the same wireless infrastructure leads to a challenging resource allocation problem due to their heterogeneous specifications. To address this problem, slicing has emerged as an architecture that enables a logical network with specific radio access functionality to each of the supported services on the same network infrastructure. The allocation of radio resources to each slice according to their requirements is a fundamental part of the network slicing that is usually executed at the radio access network (RAN). In this work, we formulate the RAN resource allocation problem as a sum-rate maximization problem subject to the orthogonality constraint (i.e., service isolation), latency-related constraint and minimum rate constraint while maintaining the reliability constraint with the incorporation of adaptive modulation and coding (AMC). However, the formulated problem is not mathematically tractable due to the presence of a step-wise function associated with the AMC and a binary Assignment Variable. Therefore, to solve the proposed optimization problem, first, we relax the mathematical intractability of AMC by using an approximation of the non-linear AMC achievable throughput, and next, the binary constraint is relaxed to a box constraint by using the penalized reformulation of the problem. The result of the above two-step procedure provides a close-to-optimal solution to the original optimization problem. Furthermore, to ease the complexity of the optimization-based scheduling algorithm, a low-complexity heuristic scheduling scheme is proposed for the efficient multiplexing of URLLC and eMBB services. Finally, the effectiveness of the proposed optimization and heuristic schemes is illustrated through extensive numerical simulations.
-
slicing based resource allocation for multiplexing of embb and urllc services in 5g wireless networks
Computer Aided Modeling and Design of Communication Links and Networks, 2019Co-Authors: Praveen Kumar Korrai, Eva Lagunas, Symeon Chatzinotas, S K Sharma, Bjorn OtterstenAbstract:The next generation of wireless networks is intended to accommodate two major services: enhanced mobile broadband (eMBB), and ultra-reliable and low-latency communications (URLLC). The eMBB applications require higher data rates while URLLC applications require a stringent latency and high transmission success probability (i.e., reliability). The multiplexing of eMBB and URLLC services on the same network infrastructure leads to a challenging resource optimization problem. In this paper, we formulate the network slicing problem in the context of time-frequency resource blocks (RBs) allocation to the wireless system consisting of eMBB and URLLC users. In particular, we address the sum-rate maximization problem subject to latency and slice isolation constraints while assuring certain reliability requirements with the use of adaptive modulation coding (AMC). We relax the mathematical intractability of AMC and binary Assignment Variable and show the effectiveness of the proposed approach through numerical simulations.
-
CAMAD - Slicing Based Resource Allocation for Multiplexing of eMBB and URLLC Services in 5G Wireless Networks
2019 IEEE 24th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD), 2019Co-Authors: Praveen Kumar Korrai, Eva Lagunas, Symeon Chatzinotas, Sanjay Sharma, Bjorn OtterstenAbstract:The next generation of wireless networks is intended to accommodate two major services: enhanced mobile broadband (eMBB), and ultra-reliable and low-latency communications (URLLC). The eMBB applications require higher data rates while URLLC applications require a stringent latency and high transmission success probability (i.e., reliability). The multiplexing of eMBB and URLLC services on the same network infrastructure leads to a challenging resource optimization problem. In this paper, we formulate the network slicing problem in the context of time-frequency resource blocks (RBs) allocation to the wireless system consisting of eMBB and URLLC users. In particular, we address the sum-rate maximization problem subject to latency and slice isolation constraints while assuring certain reliability requirements with the use of adaptive modulation coding (AMC). We relax the mathematical intractability of AMC and binary Assignment Variable and show the effectiveness of the proposed approach through numerical simulations.
Thomas D Cook - One of the best experts on this subject based on the ideXlab platform.
-
Statistical Power for the Comparative Regression Discontinuity Design With a Pretest No-Treatment Control Function: Theory and Evidence From the National Head Start Impact Study
Evaluation review, 2018Co-Authors: Yang Tang, Thomas D CookAbstract:The basic regression discontinuity design (RDD) has less statistical power than a randomized control trial (RCT) with the same sample size. Adding a no-treatment comparison function to the basic RDD creates a comparative RDD (CRD); and when this function comes from the pretest value of the study outcome, a CRD-Pre design results. We use a within-study comparison (WSC) to examine the power of CRD-Pre relative to both basic RDD and RCT. We first build the theoretical foundation for power in CRD-Pre, then derive the relevant variance formulae, and finally compare them to the theoretical RCT variance. We conclude from this theoretical part of this article that (1) CRD-Pre's power gain depends on the partial correlation between the pretest and posttest measures after conditioning on the Assignment Variable, (2) CRD-Pre is less responsive than basic RDD to how the Assignment Variable is distributed and where the cutoff is located, and (3) under a variety of conditions, the efficiency of CRD-Pre is very close to that of the RCT. Data from the National Head Start Impact Study are then used to construct RCT, RDD, and CRD-Pre designs and to compare their power. The empirical results indicate (1) a high level of correspondence between the predicted and obtained power results for RDD and CRD-Pre relative to the RCT, and (2) power levels in CRD-Pre and RCT that are very close. The study is unique among WSCs for its focus on the correspondence between RCT and observational study standard errors rather than means.
-
the comparative regression discontinuity crd design an overview and demonstration of its performance relative to basic rd and the randomized experiment
Advances in Econometrics, 2017Co-Authors: Yang Tang, Yasemin Kisbusakarya, Thomas D Cook, Heinrich Hock, Hanley ChiangAbstract:Abstract Relative to the randomized controlled trial (RCT), the basic regression discontinuity (RD) design suffers from lower statistical power and lesser ability to generalize causal estimates away from the treatment eligibility cutoff. This chapter seeks to mitigate these limitations by adding an untreated outcome comparison function that is measured along all or most of the Assignment Variable. When added to the usual treated and untreated outcomes observed in the basic RD, a comparative RD (CRD) design results. One version of CRD adds a pretest measure of the study outcome (CRD-Pre); another adds posttest outcomes from a nonequivalent comparison group (CRD-CG). We describe how these designs can be used to identify unbiased causal effects away from the cutoff under the assumption that a common, stable functional form describes how untreated outcomes vary with the Assignment Variable, both in the basic RD and in the added outcomes data (pretests or a comparison group’s posttest). We then create the two CRD designs using data from the National Head Start Impact Study, a large-scale RCT. For both designs, we find that all untreated outcome functions are parallel, which lends support to CRD’s identifying assumptions. Our results also indicate that CRD-Pre and CRD-CG both yield impact estimates at the cutoff that have a similarly small bias as, but are more precise than, the basic RD’s impact estimates. In addition, both CRD designs produce estimates of impacts away from the cutoff that have relatively little bias compared to estimates of the same parameter from the RCT design. This common finding appears to be driven by two different mechanisms. In this instance of CRD-CG, potential untreated outcomes were likely independent of the Assignment Variable from the start. This was not the case with CRD-Pre. However, fitting a model using the observed pretests and untreated posttests to account for the initial dependence generated an accurate prediction of the missing counterfactual. The result was an unbiased causal estimate away from the cutoff, conditional on this successful prediction of the untreated outcomes of the treated.
-
statistical power for the comparative regression discontinuity design with a nonequivalent comparison group
Psychological Methods, 2017Co-Authors: Yang Tang, Thomas D Cook, Yasemin KisbusakaryaAbstract:: In the "sharp" regression discontinuity design (RD), all units scoring on one side of a designated score on an Assignment Variable receive treatment, whereas those scoring on the other side become controls. Thus the continuous Assignment Variable and binary treatment indicator are measured on the same scale. Because each must be in the impact model, the resulting multi-collinearity reduces the efficiency of the RD design. However, untreated comparison data can be added along the Assignment Variable, and a comparative regression discontinuity design (CRD) is then created. When the untreated data come from a non-equivalent comparison group, we call this CRD-CG. Assuming linear functional forms, we show that power in CRD-CG is (a) greater than in basic RD; (b) less sensitive to the location of the cutoff and the distribution of the Assignment Variable; and that (c) fewer treated units are needed in the basic RD component within the CRD-CG so that savings can result from having fewer treated cases. The theory we develop is used to make numerical predictions about the efficiency of basic RD and CRD-CG relative to each other and to a randomized control trial. Data from the National Head Start Impact study are used to test these predictions. The obtained estimates are closer to the predicted parameters for CRD-CG than for basic RD and are generally quite close to the parameter predictions, supporting the emerging argument that CRD should be the design of choice in many applications for which basic RD is now used. (PsycINFO Database Record
-
Analyzing Regression-Discontinuity Designs With Multiple Assignment Variables A Comparative Study of Four Estimation Methods
Journal of Educational and Behavioral Statistics, 2013Co-Authors: Vivian C. Wong, Peter M. Steiner, Thomas D CookAbstract:In a traditional regression-discontinuity design (RDD), units are assigned to treatment on the basis of a cutoff score and a continuous Assignment Variable. The treatment effect is measured at a single cutoff location along the Assignment Variable. This article introduces the multivariate regression-discontinuity design (MRDD), where multiple Assignment Variables and cutoffs may be used for treatment Assignment. For an MRDD with two Assignment Variables, we show that the frontier average treatment effect can be decomposed into a weighted average of two univariate RDD effects. The article discusses four methods for estimating MRDD treatment effects and compares their relative performance in a Monte Carlo simulation study under different scenarios.
