Jianqing FanPrinceton University, Weining WangUniversity of Groningen, Yue ZhaoUniversity of York
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to their representation power. We ask the question whether individual covariates have additional contributions given the latent factors or more generally a set of variables. Our test statistics are based on the estimated partial derivative of the regression function of the candidate variable for screening and a observable proxy for the latent factors. Hence, our test reveals how much predictors contribute additionally to the non-parametric regression after accounting for the latent factors. Our derivative estimator is the convolution of a deep neural network regression estimator and a smoothing kernel. We demonstrate that when the neural network size diverges with the sample size, unlike estimating the regression function itself, it is necessary to smooth the partial derivative of the neural network estimator to recover the desired convergence rate for the derivative. Moreover, our screening test achieves asymptotic normality under the null after finely centering our test statistics that makes the biases negligible, as well as consistency for local alternatives under mild conditions. We demonstrate the performance of our test in a simulation study and two real world applications.
{"title":"Conditional nonparametric variable screening by neural factor regression","authors":"Jianqing FanPrinceton University, Weining WangUniversity of Groningen, Yue ZhaoUniversity of York","doi":"arxiv-2408.10825","DOIUrl":"https://doi.org/arxiv-2408.10825","url":null,"abstract":"High-dimensional covariates often admit linear factor structure. To\u0000effectively screen correlated covariates in high-dimension, we propose a\u0000conditional variable screening test based on non-parametric regression using\u0000neural networks due to their representation power. We ask the question whether\u0000individual covariates have additional contributions given the latent factors or\u0000more generally a set of variables. Our test statistics are based on the\u0000estimated partial derivative of the regression function of the candidate\u0000variable for screening and a observable proxy for the latent factors. Hence,\u0000our test reveals how much predictors contribute additionally to the\u0000non-parametric regression after accounting for the latent factors. Our\u0000derivative estimator is the convolution of a deep neural network regression\u0000estimator and a smoothing kernel. We demonstrate that when the neural network\u0000size diverges with the sample size, unlike estimating the regression function\u0000itself, it is necessary to smooth the partial derivative of the neural network\u0000estimator to recover the desired convergence rate for the derivative. Moreover,\u0000our screening test achieves asymptotic normality under the null after finely\u0000centering our test statistics that makes the biases negligible, as well as\u0000consistency for local alternatives under mild conditions. We demonstrate the\u0000performance of our test in a simulation study and two real world applications.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"1587 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the gradient wild bootstrap-based inference for instrumental variable quantile regressions in the framework of a small number of large clusters in which the number of clusters is viewed as fixed, and the number of observations for each cluster diverges to infinity. For the Wald inference, we show that our wild bootstrap Wald test, with or without studentization using the cluster-robust covariance estimator (CRVE), controls size asymptotically up to a small error as long as the parameter of endogenous variable is strongly identified in at least one of the clusters. We further show that the wild bootstrap Wald test with CRVE studentization is more powerful for distant local alternatives than that without. Last, we develop a wild bootstrap Anderson-Rubin (AR) test for the weak-identification-robust inference. We show it controls size asymptotically up to a small error, even under weak or partial identification for all clusters. We illustrate the good finite-sample performance of the new inference methods using simulations and provide an empirical application to a well-known dataset about US local labor markets.
{"title":"Gradient Wild Bootstrap for Instrumental Variable Quantile Regressions with Weak and Few Clusters","authors":"Wenjie Wang, Yichong Zhang","doi":"arxiv-2408.10686","DOIUrl":"https://doi.org/arxiv-2408.10686","url":null,"abstract":"We study the gradient wild bootstrap-based inference for instrumental\u0000variable quantile regressions in the framework of a small number of large\u0000clusters in which the number of clusters is viewed as fixed, and the number of\u0000observations for each cluster diverges to infinity. For the Wald inference, we\u0000show that our wild bootstrap Wald test, with or without studentization using\u0000the cluster-robust covariance estimator (CRVE), controls size asymptotically up\u0000to a small error as long as the parameter of endogenous variable is strongly\u0000identified in at least one of the clusters. We further show that the wild\u0000bootstrap Wald test with CRVE studentization is more powerful for distant local\u0000alternatives than that without. Last, we develop a wild bootstrap\u0000Anderson-Rubin (AR) test for the weak-identification-robust inference. We show\u0000it controls size asymptotically up to a small error, even under weak or partial\u0000identification for all clusters. We illustrate the good finite-sample\u0000performance of the new inference methods using simulations and provide an\u0000empirical application to a well-known dataset about US local labor markets.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The kendallknight package introduces an efficient implementation of Kendall's correlation coefficient computation, significantly improving the processing time for large datasets without sacrificing accuracy. The kendallknight package, following Knight (1966) and posterior literature, reduces the computational complexity resulting in drastic reductions in computation time, transforming operations that would take minutes or hours into milliseconds or minutes, while maintaining precision and correctly handling edge cases and errors. The package is particularly advantageous in econometric and statistical contexts where rapid and accurate calculation of Kendall's correlation coefficient is desirable. Benchmarks demonstrate substantial performance gains over the base R implementation, especially for large datasets.
kendallknight 软件包引入了肯德尔相关系数计算的高效实现方法，在不牺牲准确性的前提下，显著改善了大型数据集的处理时间。kendallknight 软件包遵循 Knight (1966) 和后继文献，降低了计算复杂度，从而大幅减少了计算时间，将需要几分钟或几小时的操作转化为几毫秒或几分钟，同时保持了精度，并正确处理了边缘情况和错误。该软件包在计量经济学和统计领域尤其具有优势，因为这些领域需要快速、准确地计算肯德尔相关系数。基准测试表明，与基本 R 实现相比，该软件包的性能大幅提升，尤其是在大型数据集上。
{"title":"kendallknight: Efficient Implementation of Kendall's Correlation Coefficient Computation","authors":"Mauricio Vargas Sepúlveda","doi":"arxiv-2408.09618","DOIUrl":"https://doi.org/arxiv-2408.09618","url":null,"abstract":"The kendallknight package introduces an efficient implementation of Kendall's\u0000correlation coefficient computation, significantly improving the processing\u0000time for large datasets without sacrificing accuracy. The kendallknight\u0000package, following Knight (1966) and posterior literature, reduces the\u0000computational complexity resulting in drastic reductions in computation time,\u0000transforming operations that would take minutes or hours into milliseconds or\u0000minutes, while maintaining precision and correctly handling edge cases and\u0000errors. The package is particularly advantageous in econometric and statistical\u0000contexts where rapid and accurate calculation of Kendall's correlation\u0000coefficient is desirable. Benchmarks demonstrate substantial performance gains\u0000over the base R implementation, especially for large datasets.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"157 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abhinandan Dalal, Patrick Blöbaum, Shiva Kasiviswanathan, Aaditya Ramdas
Double (debiased) machine learning (DML) has seen widespread use in recent years for learning causal/structural parameters, in part due to its flexibility and adaptability to high-dimensional nuisance functions as well as its ability to avoid bias from regularization or overfitting. However, the classic double-debiased framework is only valid asymptotically for a predetermined sample size, thus lacking the flexibility of collecting more data if sharper inference is needed, or stopping data collection early if useful inferences can be made earlier than expected. This can be of particular concern in large scale experimental studies with huge financial costs or human lives at stake, as well as in observational studies where the length of confidence of intervals do not shrink to zero even with increasing sample size due to partial identifiability of a structural parameter. In this paper, we present time-uniform counterparts to the asymptotic DML results, enabling valid inference and confidence intervals for structural parameters to be constructed at any arbitrary (possibly data-dependent) stopping time. We provide conditions which are only slightly stronger than the standard DML conditions, but offer the stronger guarantee for anytime-valid inference. This facilitates the transformation of any existing DML method to provide anytime-valid guarantees with minimal modifications, making it highly adaptable and easy to use. We illustrate our procedure using two instances: a) local average treatment effect in online experiments with non-compliance, and b) partial identification of average treatment effect in observational studies with potential unmeasured confounding.
{"title":"Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameters","authors":"Abhinandan Dalal, Patrick Blöbaum, Shiva Kasiviswanathan, Aaditya Ramdas","doi":"arxiv-2408.09598","DOIUrl":"https://doi.org/arxiv-2408.09598","url":null,"abstract":"Double (debiased) machine learning (DML) has seen widespread use in recent\u0000years for learning causal/structural parameters, in part due to its flexibility\u0000and adaptability to high-dimensional nuisance functions as well as its ability\u0000to avoid bias from regularization or overfitting. However, the classic\u0000double-debiased framework is only valid asymptotically for a predetermined\u0000sample size, thus lacking the flexibility of collecting more data if sharper\u0000inference is needed, or stopping data collection early if useful inferences can\u0000be made earlier than expected. This can be of particular concern in large scale\u0000experimental studies with huge financial costs or human lives at stake, as well\u0000as in observational studies where the length of confidence of intervals do not\u0000shrink to zero even with increasing sample size due to partial identifiability\u0000of a structural parameter. In this paper, we present time-uniform counterparts\u0000to the asymptotic DML results, enabling valid inference and confidence\u0000intervals for structural parameters to be constructed at any arbitrary\u0000(possibly data-dependent) stopping time. We provide conditions which are only\u0000slightly stronger than the standard DML conditions, but offer the stronger\u0000guarantee for anytime-valid inference. This facilitates the transformation of\u0000any existing DML method to provide anytime-valid guarantees with minimal\u0000modifications, making it highly adaptable and easy to use. We illustrate our\u0000procedure using two instances: a) local average treatment effect in online\u0000experiments with non-compliance, and b) partial identification of average\u0000treatment effect in observational studies with potential unmeasured\u0000confounding.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The study of experimental design offers tremendous benefits for answering causal questions across a wide range of applications, including agricultural experiments, clinical trials, industrial experiments, social experiments, and digital experiments. Although valuable in such applications, the costs of experiments often drive experimenters to seek more efficient designs. Recently, experimenters have started to examine such efficiency questions from an optimization perspective, as experimental design problems are fundamentally decision-making problems. This perspective offers a lot of flexibility in leveraging various existing optimization tools to study experimental design problems. This manuscript thus aims to examine the foundations of experimental design problems in the context of causal inference as viewed through an optimization lens.
{"title":"Experimental Design For Causal Inference Through An Optimization Lens","authors":"Jinglong Zhao","doi":"arxiv-2408.09607","DOIUrl":"https://doi.org/arxiv-2408.09607","url":null,"abstract":"The study of experimental design offers tremendous benefits for answering\u0000causal questions across a wide range of applications, including agricultural\u0000experiments, clinical trials, industrial experiments, social experiments, and\u0000digital experiments. Although valuable in such applications, the costs of\u0000experiments often drive experimenters to seek more efficient designs. Recently,\u0000experimenters have started to examine such efficiency questions from an\u0000optimization perspective, as experimental design problems are fundamentally\u0000decision-making problems. This perspective offers a lot of flexibility in\u0000leveraging various existing optimization tools to study experimental design\u0000problems. This manuscript thus aims to examine the foundations of experimental\u0000design problems in the context of causal inference as viewed through an\u0000optimization lens.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the finite sample performance of the flexible estimation approach of Farrell, Liang, and Misra (2021a), who propose to use deep learning for the estimation of heterogeneous parameters in economic models, in the context of discrete choice models. The approach combines the structure imposed by economic models with the flexibility of deep learning, which assures the interpretebility of results on the one hand, and allows estimating flexible functional forms of observed heterogeneity on the other hand. For inference after the estimation with deep learning, Farrell et al. (2021a) derive an influence function that can be applied to many quantities of interest. We conduct a series of Monte Carlo experiments that investigate the impact of regularization on the proposed estimation and inference procedure in the context of discrete choice models. The results show that the deep learning approach generally leads to precise estimates of the true average parameters and that regular robust standard errors lead to invalid inference results, showing the need for the influence function approach for inference. Without regularization, the influence function approach can lead to substantial bias and large estimated standard errors caused by extreme outliers. Regularization reduces this property and stabilizes the estimation procedure, but at the expense of inducing an additional bias. The bias in combination with decreasing variance associated with increasing regularization leads to the construction of invalid inferential statements in our experiments. Repeated sample splitting, unlike regularization, stabilizes the estimation approach without introducing an additional bias, thereby allowing for the construction of valid inferential statements.
{"title":"Deep Learning for the Estimation of Heterogeneous Parameters in Discrete Choice Models","authors":"Stephan Hetzenecker, Maximilian Osterhaus","doi":"arxiv-2408.09560","DOIUrl":"https://doi.org/arxiv-2408.09560","url":null,"abstract":"This paper studies the finite sample performance of the flexible estimation\u0000approach of Farrell, Liang, and Misra (2021a), who propose to use deep learning\u0000for the estimation of heterogeneous parameters in economic models, in the\u0000context of discrete choice models. The approach combines the structure imposed\u0000by economic models with the flexibility of deep learning, which assures the\u0000interpretebility of results on the one hand, and allows estimating flexible\u0000functional forms of observed heterogeneity on the other hand. For inference\u0000after the estimation with deep learning, Farrell et al. (2021a) derive an\u0000influence function that can be applied to many quantities of interest. We\u0000conduct a series of Monte Carlo experiments that investigate the impact of\u0000regularization on the proposed estimation and inference procedure in the\u0000context of discrete choice models. The results show that the deep learning\u0000approach generally leads to precise estimates of the true average parameters\u0000and that regular robust standard errors lead to invalid inference results,\u0000showing the need for the influence function approach for inference. Without\u0000regularization, the influence function approach can lead to substantial bias\u0000and large estimated standard errors caused by extreme outliers. Regularization\u0000reduces this property and stabilizes the estimation procedure, but at the\u0000expense of inducing an additional bias. The bias in combination with decreasing\u0000variance associated with increasing regularization leads to the construction of\u0000invalid inferential statements in our experiments. Repeated sample splitting,\u0000unlike regularization, stabilizes the estimation approach without introducing\u0000an additional bias, thereby allowing for the construction of valid inferential\u0000statements.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
José Luis Montiel Olea, Brenda Prallon, Chen Qiu, Jörg Stoye, Yiwei Sun
We present a decision-theoretic justification for viewing the question of how to best choose where to experiment in order to optimize external validity as a k-median (clustering) problem, a popular problem in computer science and operations research. We present conditions under which minimizing the worst-case, welfare-based regret among all nonrandom schemes that select k sites to experiment is approximately equal - and sometimes exactly equal - to finding the k most central vectors of baseline site-level covariates. The k-median problem can be formulated as a linear integer program. Two empirical applications illustrate the theoretical and computational benefits of the suggested procedure.
我们提出了一种决策理论依据，将如何最佳选择实验地点以优化外部有效性的问题视为一个中值（聚类）问题，这是计算机科学和运营研究中的一个流行问题。我们提出了一些条件，在这些条件下，在所有选择 ks 个地点进行实验的非随机方案中，最小化最坏情况下基于福利的遗憾，近似等于（有时甚至完全等于）找到基线地点级协变量的 k 个最中心向量。k-中值问题可以表述为一个线性整数程序。两个经验应用说明了所建议程序的理论和计算优势。
{"title":"Externally Valid Selection of Experimental Sites via the k-Median Problem","authors":"José Luis Montiel Olea, Brenda Prallon, Chen Qiu, Jörg Stoye, Yiwei Sun","doi":"arxiv-2408.09187","DOIUrl":"https://doi.org/arxiv-2408.09187","url":null,"abstract":"We present a decision-theoretic justification for viewing the question of how\u0000to best choose where to experiment in order to optimize external validity as a\u0000k-median (clustering) problem, a popular problem in computer science and\u0000operations research. We present conditions under which minimizing the\u0000worst-case, welfare-based regret among all nonrandom schemes that select k\u0000sites to experiment is approximately equal - and sometimes exactly equal - to\u0000finding the k most central vectors of baseline site-level covariates. The\u0000k-median problem can be formulated as a linear integer program. Two empirical\u0000applications illustrate the theoretical and computational benefits of the\u0000suggested procedure.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for moments of any order. Consequently, we propose our moment estimators. We then establish a central limit theorem for our estimators and derive the explicit formulas for the asymptotic covariance matrix. Finally, we provide numerical results to validate our method.
{"title":"Method of Moments Estimation for Affine Stochastic Volatility Models","authors":"Yan-Feng Wu, Xiangyu Yang, Jian-Qiang Hu","doi":"arxiv-2408.09185","DOIUrl":"https://doi.org/arxiv-2408.09185","url":null,"abstract":"We develop moment estimators for the parameters of affine stochastic\u0000volatility models. We first address the challenge of calculating moments for\u0000the models by introducing a recursive equation for deriving closed-form\u0000expressions for moments of any order. Consequently, we propose our moment\u0000estimators. We then establish a central limit theorem for our estimators and\u0000derive the explicit formulas for the asymptotic covariance matrix. Finally, we\u0000provide numerical results to validate our method.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The fundamental problem of causal inference lies in the absence of counterfactuals. Traditional methodologies impute the missing counterfactuals implicitly or explicitly based on untestable or overly stringent assumptions. Synthetic control method (SCM) utilizes a weighted average of control units to impute the missing counterfactual for the treated unit. Although SCM relaxes some strict assumptions, it still requires the treated unit to be inside the convex hull formed by the controls, avoiding extrapolation. In recent advances, researchers have modeled the entire data generating process (DGP) to explicitly impute the missing counterfactual. This paper expands the interactive fixed effect (IFE) model by instrumenting covariates into factor loadings, adding additional robustness. This methodology offers multiple benefits: firstly, it incorporates the strengths of previous SCM approaches, such as the relaxation of the untestable parallel trends assumption (PTA). Secondly, it does not require the targeted outcomes to be inside the convex hull formed by the controls. Thirdly, it eliminates the need for correct model specification required by the IFE model. Finally, it inherits the ability of principal component analysis (PCA) to effectively handle high-dimensional data and enhances the value extracted from numerous covariates.
{"title":"Counterfactual and Synthetic Control Method: Causal Inference with Instrumented Principal Component Analysis","authors":"Cong Wang","doi":"arxiv-2408.09271","DOIUrl":"https://doi.org/arxiv-2408.09271","url":null,"abstract":"The fundamental problem of causal inference lies in the absence of\u0000counterfactuals. Traditional methodologies impute the missing counterfactuals\u0000implicitly or explicitly based on untestable or overly stringent assumptions.\u0000Synthetic control method (SCM) utilizes a weighted average of control units to\u0000impute the missing counterfactual for the treated unit. Although SCM relaxes\u0000some strict assumptions, it still requires the treated unit to be inside the\u0000convex hull formed by the controls, avoiding extrapolation. In recent advances,\u0000researchers have modeled the entire data generating process (DGP) to explicitly\u0000impute the missing counterfactual. This paper expands the interactive fixed\u0000effect (IFE) model by instrumenting covariates into factor loadings, adding\u0000additional robustness. This methodology offers multiple benefits: firstly, it\u0000incorporates the strengths of previous SCM approaches, such as the relaxation\u0000of the untestable parallel trends assumption (PTA). Secondly, it does not\u0000require the targeted outcomes to be inside the convex hull formed by the\u0000controls. Thirdly, it eliminates the need for correct model specification\u0000required by the IFE model. Finally, it inherits the ability of principal\u0000component analysis (PCA) to effectively handle high-dimensional data and\u0000enhances the value extracted from numerous covariates.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"141 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Helmut Farbmacher, Rebecca Groh, Michael Mühlegger, Gabriel Vollert
We use recent results from the theory of random matrices to improve instrumental variables estimation with many instruments. In settings where the first-stage parameters are dense, we show that Ridge lowers the implicit price of a bias adjustment. This comes along with improved (finite-sample) properties in the second stage regression. Our theoretical results nest existing results on bias approximation and bias adjustment. Moreover, it extends them to settings with more instruments than observations.
{"title":"Revisiting the Many Instruments Problem using Random Matrix Theory","authors":"Helmut Farbmacher, Rebecca Groh, Michael Mühlegger, Gabriel Vollert","doi":"arxiv-2408.08580","DOIUrl":"https://doi.org/arxiv-2408.08580","url":null,"abstract":"We use recent results from the theory of random matrices to improve\u0000instrumental variables estimation with many instruments. In settings where the\u0000first-stage parameters are dense, we show that Ridge lowers the implicit price\u0000of a bias adjustment. This comes along with improved (finite-sample) properties\u0000in the second stage regression. Our theoretical results nest existing results\u0000on bias approximation and bias adjustment. Moreover, it extends them to\u0000settings with more instruments than observations.","PeriodicalId":501293,"journal":{"name":"arXiv - ECON - Econometrics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142184219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：