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on Econometrics |
| By: | Masahiro Kato |
| Abstract: | This study introduces a doubly robust (DR) estimator for regression discontinuity (RD) designs. In RD designs, treatment effects are estimated in a quasi-experimental setting where treatment assignment depends on whether a running variable surpasses a predefined cutoff. A common approach in RD estimation is to apply nonparametric regression methods, such as local linear regression. In such an approach, the validity relies heavily on the consistency of nonparametric estimators and is limited by the nonparametric convergence rate, thereby preventing $\sqrt{n}$-consistency. To address these issues, we propose the DR-RD estimator, which combines two distinct estimators for the conditional expected outcomes. If either of these estimators is consistent, the treatment effect estimator remains consistent. Furthermore, due to the debiasing effect, our proposed estimator achieves $\sqrt{n}$-consistency if both regression estimators satisfy certain mild conditions, which also simplifies statistical inference. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.07978 |
| By: | Daniele Ballinari; Alexander Wehrli |
| Abstract: | We introduce a double/debiased machine learning (DML) estimator for the impulse response function (IRF) in settings where a time series of interest is subjected to multiple discrete treatments, assigned over time, which can have a causal effect on future outcomes. The proposed estimator can rely on fully nonparametric relations between treatment and outcome variables, opening up the possibility to use flexible machine learning approaches to estimate IRFs. To this end, we extend the theory of DML from an i.i.d. to a time series setting and show that the proposed DML estimator for the IRF is consistent and asymptotically normally distributed at the parametric rate, allowing for semiparametric inference for dynamic effects in a time series setting. The properties of the estimator are validated numerically in finite samples by applying it to learn the IRF in the presence of serial dependence in both the confounder and observation innovation processes. We also illustrate the methodology empirically by applying it to the estimation of the effects of macroeconomic shocks. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.10009 |
| By: | Michal Koles\'ar; Mikkel Plagborg-M{\o}ller |
| Abstract: | Applied macroeconomists frequently use impulse response estimators motivated by linear models. We study whether the estimands of such procedures have a causal interpretation when the true data generating process is in fact nonlinear. We show that vector autoregressions and linear local projections onto observed shocks or proxies identify weighted averages of causal effects regardless of the extent of nonlinearities. By contrast, identification approaches that exploit heteroskedasticity or non-Gaussianity of latent shocks are highly sensitive to departures from linearity. Our analysis is based on new results on the identification of marginal treatment effects through weighted regressions, which may also be of interest to researchers outside macroeconomics. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.10415 |
| By: | Irene Botosaru; Isaac Loh; Chris Muris |
| Abstract: | We introduce a novel framework to characterize identified sets of structural and counterfactual parameters in econometric models. Our framework centers on a discrepancy function, which we construct using insights from convex analysis. The zeros of the discrepancy function determine the identified set, which may be a singleton. The discrepancy function has an adversarial game interpretation: a critic maximizes the discrepancy between data and model features, while a defender minimizes it by adjusting the probability measure of the unobserved heterogeneity. Our approach enables fast computation via linear programming. We use the sample analog of the discrepancy function as a test statistic, and show that it provides asymptotically valid inference for the identified set. Applied to nonlinear panel models with fixed effects, it offers a unified approach for identifying both structural and counterfactual parameters across exogeneity conditions, including strict and sequential, without imposing parametric restrictions on the distribution of error terms or functional form assumptions. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.04239 |
| By: | Fan Wu; Yi Xin |
| Abstract: | We propose a new method for estimating nonseparable selection models. We show that, given the selection rule and the observed selected outcome distribution, the potential outcome distribution can be characterized as the fixed point of an operator, and we prove that this operator is a functional contraction. We propose a two-step semiparametric maximum likelihood estimator to estimate the selection model and the potential outcome distribution. The consistency and asymptotic normality of the estimator are established. Our approach performs well in Monte Carlo simulations and is applicable in a variety of empirical settings where only a selected sample of outcomes is observed. Examples include consumer demand models with only transaction prices, auctions with incomplete bid data, and Roy models with data on accepted wages. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.01799 |
| By: | Myunghyun Song |
| Abstract: | This paper develops a formal econometric framework and tools for the identification and inference of a structural parameter in general bunching designs. We present both point and partial identification results, which generalize previous approaches in the literature. The key assumption for point identification is the analyticity of the counterfactual density, which defines a broader class of distributions than many well-known parametric families. In the partial identification approach, the analyticity condition is relaxed and various shape restrictions can be incorporated, including those found in the literature. Both of our identification results account for observable heterogeneity in the model, which has previously been permitted only in limited ways. We provide a suite of counterfactual estimation and inference methods, termed the generalized polynomial strategy. Our method restores the merits of the original polynomial strategy proposed by Chetty et al. (2011) while addressing several weaknesses in the widespread practice. The efficacy of the proposed method is demonstrated compared to a version of the polynomial estimator in a series of Monte Carlo studies within the augmented isoelastic model. We revisit the data used in Saez (2010) and find substantially different results relative to those from the polynomial strategy. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.03625 |
| By: | Richard K. Crump; Nikolay Gospodinov; Ignacio Lopez Gaffney |
| Abstract: | We introduce a new jackknife variance estimator for panel-data regressions. Our variance estimator can be motivated as the conventional leave-one-out jackknife variance estimator on a transformed space of the regressors and residuals using orthonormal trigonometric basis functions. We prove the asymptotic validity of our variance estimator and demonstrate desirable finite-sample properties in a series of simulation experiments. We also illustrate how our method can be used for jackknife bias-correction in a variety of time-series settings. |
| Keywords: | leave-one-out jackknife; Panel data model; strong time-series and cross-sectional dependence; cluster-robust variance estimation; trigonometric basis functions |
| JEL: | C12 C13 C22 C23 |
| Date: | 2024–10–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:99064 |
| By: | Heshani Madigasekara; D. S. Poskitt; Lina Zhang; Xueyan Zhao |
| Abstract: | This paper aims to partially identify the distributional treatment effects (DTEs) that depend on the unknown joint distribution of treated and untreated potential outcomes. We construct the DTE bounds using panel data and allow individuals to switch between the treated and untreated states more than once over time. Individuals are grouped based on their past treatment history, and DTEs are allowed to be heterogeneous across different groups. We provide two alternative group-wise copula equality assumptions to bound the unknown joint and the DTEs, both of which leverage information from the past observations. Testability of these two assumptions are also discussed, and test results are presented. We apply this method to study the treatment effect heterogeneity of exercising on the adults' body weight. These results demonstrate that our method improves the identification power of the DTE bounds compared to the existing methods. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.04450 |
| By: | Sihui Zhao; Xinbo Wang; Lin Liu; Xin Zhang |
| Abstract: | Higher-Order Influence Functions (HOIF), developed in a series of papers over the past twenty years, is a fundamental theoretical device for constructing rate-optimal causal-effect estimators from observational studies. However, the value of HOIF for analyzing well-conducted randomized controlled trials (RCT) has not been explicitly explored. In the recent US Food \& Drug Administration (FDA) and European Medical Agency (EMA) guidelines on the practice of covariate adjustment in analyzing RCT, in addition to the simple, unadjusted difference-in-mean estimator, it was also recommended to report the estimator adjusting for baseline covariates via a simple parametric working model, such as a linear model. In this paper, we show that an HOIF-motivated estimator for the treatment-specific mean has significantly improved statistical properties compared to popular adjusted estimators in practice when the number of baseline covariates $p$ is relatively large compared to the sample size $n$. We also characterize the conditions under which the HOIF-motivated estimator improves upon the unadjusted estimator. Furthermore, we demonstrate that a novel debiased adjusted estimator proposed recently by Lu et al. is, in fact, another HOIF-motivated estimator under disguise. Finally, simulation studies are conducted to corroborate our theoretical findings. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.08491 |
| By: | Haowen Bao; Yongmiao Hong; Yuying Sun; Shouyang Wang |
| Abstract: | By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance estimation, which covers point-based estimators are special cases. We establish the consistency and oracle properties of the proposed penalized estimator, regardless of whether the number of predictors is diverging with the sample size. Monte Carlo simulations demonstrate the favorable finite sample properties of the proposed estimation. Empirical applications to interval-valued crude oil price forecasting and sparse index-tracking portfolio construction illustrate the robustness and effectiveness of our method against competing approaches, including random forest and multilayer perceptron for interval-valued data. Our findings highlight the potential of machine learning techniques in interval-valued time series analysis, offering new insights for financial forecasting and portfolio management. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09452 |
| By: | Philipp Gersing |
| Abstract: | We provide estimation and inference for the Generalised Dynamic Factor Model (GDFM) under the assumption that the dynamic common component can be expressed in terms of a finite number of lags of contemporaneously pervasive factors. The proposed estimator is simply an OLS regression of the observed variables on factors extracted via static principal components and therefore avoids frequency domain techniques entirely. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.20885 |
| By: | Amilcar Velez |
| Abstract: | This paper studies the properties of debiased machine learning (DML) estimators under a novel asymptotic framework, offering insights for improving the performance of these estimators in applications. DML is an estimation method suited to economic models where the parameter of interest depends on unknown nuisance functions that must be estimated. It requires weaker conditions than previous methods while still ensuring standard asymptotic properties. Existing theoretical results do not distinguish between two alternative versions of DML estimators, DML1 and DML2. Under a new asymptotic framework, this paper demonstrates that DML2 asymptotically dominates DML1 in terms of bias and mean squared error, formalizing a previous conjecture based on simulation results regarding their relative performance. Additionally, this paper provides guidance for improving the performance of DML2 in applications. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.01864 |
| By: | Ying-Ying Lee; Chu-An Liu |
| Abstract: | Sample selection problems arise when treatment affects both the outcome and the researcher's ability to observe it. This paper generalizes Lee (2009) bounds for the average treatment effect of a binary treatment to a continuous/multivalued treatment. We evaluate the Job Crops program to study the causal effect of training hours on wages. To identify the average treatment effect of always-takers who are selected regardless of the treatment values, we assume that if a subject is selected at some sufficient treatment values, then it remains selected at all treatment values. For example, if program participants are employed with one month of training, then they remain employed with any training hours. This sufficient treatment values assumption includes the monotone assumption on the treatment effect on selection as a special case. We further allow the conditional independence assumption and subjects with different pretreatment covariates to have different sufficient treatment values. The estimation and inference theory utilize the orthogonal moment function and cross-fitting for double debiased machine learning. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.04312 |
| By: | Apoorva Lal |
| Abstract: | We examine the challenges in ranking multiple treatments based on their estimated effects when using linear regression or its popular double-machine-learning variant, the Partially Linear Model (PLM), in the presence of treatment effect heterogeneity. We demonstrate by example that overlap-weighting performed by linear models like PLM can produce Weighted Average Treatment Effects (WATE) that have rankings that are inconsistent with the rankings of the underlying Average Treatment Effects (ATE). We define this as ranking reversals and derive a necessary and sufficient condition for ranking reversals under the PLM. We conclude with several simulation studies conditions under which ranking reversals occur. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.02675 |
| By: | Filip Obradovi\'c |
| Abstract: | Recent literature proposes combining short-term experimental and long-term observational data to provide credible alternatives to conventional observational studies for identification of long-term average treatment effects (LTEs). I show that experimental data have an auxiliary role in this context. They bring no identifying power without additional modeling assumptions. When modeling assumptions are imposed, experimental data serve to amplify their identifying power. If the assumptions fail, adding experimental data may only yield results that are farther from the truth. Motivated by this, I introduce two assumptions on treatment response that may be defensible based on economic theory or intuition. To utilize them, I develop a novel two-step identification approach that centers on bounding temporal link functions -- the relationship between short-term and mean long-term potential outcomes. The approach provides sharp bounds on LTEs for a general class of assumptions, and allows for imperfect experimental compliance -- extending existing results. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.04380 |
| By: | Roberto Casarin; Antonio Peruzzi |
| Abstract: | The techniques suggested in Fr\"uhwirth-Schnatter et al. (2024) concern sparsity and factor selection and have enormous potential beyond standard factor analysis applications. We show how these techniques can be applied to Latent Space (LS) models for network data. These models suffer from well-known identification issues of the latent factors due to likelihood invariance to factor translation, reflection, and rotation (see Hoff et al., 2002). A set of observables can be instrumental in identifying the latent factors via auxiliary equations (see Liu et al., 2021). These, in turn, share many analogies with the equations used in factor modeling, and we argue that the factor loading restrictions may be beneficial for achieving identification. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.02531 |
| By: | Richard K. Crump; Nikolay Gospodinov; Ignacio Lopez Gaffney |
| Abstract: | We introduce a new regression diagnostic, tailored to time-series and panel-data regressions, which characterizes the sensitivity of the OLS estimate to distinct time-series variation at different frequencies. The diagnostic is built on the novel result that the eigenvectors of a random walk asymptotically orthogonalize a wide variety of time-series processes. Our diagnostic is based on leave-one-out OLS estimation on transformed variables using these eigenvectors. We illustrate how our diagnostic allows applied researchers to scrutinize regression results and probe for underlying fragility of the sample OLS estimate. We demonstrate the utility of our approach using a variety of empirical applications. |
| Keywords: | leave-one-out frequency approach; regression diagnostic; relative contributions of different frequencies; high time-series persistence and spurious regressions; trigonometric basis functions; orthogonalization |
| JEL: | C12 C13 C22 C23 |
| Date: | 2024–10–01 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fednsr:99063 |
| By: | Tanmoy Das; Dohyeon Lee; Arnab Sinha |
| Abstract: | In industry, online randomized controlled experiment (a.k.a A/B experiment) is a standard approach to measure the impact of a causal change. These experiments have small treatment effect to reduce the potential blast radius. As a result, these experiments often lack statistical significance due to low signal-to-noise ratio. To improve the precision (or reduce standard error), we introduce the idea of trigger observations where the output of the treatment and the control model are different. We show that the evaluation with full information about trigger observations (full knowledge) improves the precision in comparison to a baseline method. However, detecting all such trigger observations is a costly affair, hence we propose a sampling based evaluation method (partial knowledge) to reduce the cost. The randomness of sampling introduces bias in the estimated outcome. We theoretically analyze this bias and show that the bias is inversely proportional to the number of observations used for sampling. We also compare the proposed evaluation methods using simulation and empirical data. In simulation, evaluation with full knowledge reduces the standard error as much as 85%. In empirical setup, evaluation with partial knowledge reduces the standard error by 36.48%. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.03530 |
| By: | Yuehao Bai; Max Tabord-Meehan |
| Abstract: | This paper studies the sharp testable implications of an additive random utility model with a discrete multi-valued treatment and a discrete multi-valued instrument, in which each value of the instrument only weakly increases the utility of one choice. Borrowing the terminology used in randomized experiments, we call such a setting an encouragement design. We derive inequalities in terms of the conditional choice probabilities that characterize when the distribution of the observed data is consistent with such a model. Through a novel constructive argument, we further show these inequalities are sharp in the sense that any distribution of the observed data that satisfies these inequalities is generated by this additive random utility model. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09808 |
| By: | Augusto Cerqua; Marco Letta; Gabriele Pinto |
| Abstract: | Machine Learning (ML) is increasingly employed to inform and support policymaking interventions. This methodological article cautions practitioners about common but often overlooked pitfalls associated with the uncritical application of supervised ML algorithms to panel data. Ignoring the cross-sectional and longitudinal structure of this data can lead to hard-to-detect data leakage, inflated out-of-sample performance, and an inadvertent overestimation of the real-world usefulness and applicability of ML models. After clarifying these issues, we provide practical guidelines and best practices for applied researchers to ensure the correct implementation of supervised ML in panel data environments, emphasizing the need to define ex ante the primary goal of the analysis and align the ML pipeline accordingly. An empirical application based on over 3, 000 US counties from 2000 to 2019 illustrates the practical relevance of these points across nearly 500 models for both classification and regression tasks. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09218 |
| By: | Ziming Lin; Fang Han |
| Abstract: | In a landmark paper, Abadie and Imbens (2008) showed that the naive bootstrap is inconsistent when applied to nearest neighbor matching estimators of the average treatment effect with a fixed number of matches. Since then, this finding has inspired numerous efforts to address the inconsistency issue, typically by employing alternative bootstrap methods. In contrast, this paper shows that the naive bootstrap is provably consistent for the original matching estimator, provided that the number of matches, $M$, diverges. The bootstrap inconsistency identified by Abadie and Imbens (2008) thus arises solely from the use of a fixed $M$. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.23525 |
| By: | Onil Boussim |
| Abstract: | This paper generalizes the changes-in-changes (CIC) model to handle discrete treatments with more than two categories, extending the binary case of Athey and Imbens (2006). While the original CIC model is well-suited for binary treatments, it cannot accommodate multi-category discrete treatments often found in economic and policy settings. Although recent work has extended CIC to continuous treatments, there remains a gap for multi-category discrete treatments. I introduce a generalized CIC model that adapts the rank invariance assumption to multiple treatment levels, allowing for robust modeling while capturing the distinct effects of varying treatment intensities. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.01617 |
| By: | Caio Waisman |
| Abstract: | This paper outlines a Bayesian approach to estimate finite mixtures of Tobit models. The method consists of an MCMC approach that combines Gibbs sampling with data augmentation and is simple to implement. I show through simulations that the flexibility provided by this method is especially helpful when censoring is not negligible. In addition, I demonstrate the broad utility of this methodology with applications to a job training program, labor supply, and demand for medical care. I find that this approach allows for non-trivial additional flexibility that can alter results considerably and beyond improving model fit. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.09771 |
| By: | Luo, Nanyu; Ji, Feng; Han, Yuting; He, Jinbo; Zhang, Xiaoya |
| Abstract: | PyTorch and TensorFlow are two widely adopted, modern deep learning frameworks that offer comprehensive computation libraries for deep learning models. We illustrate how to utilize these deep learning computational platforms and infrastructure to estimate a class of popular psychometric models, dichotomous and polytomous Item Response Theory (IRT) models, along with their multidimensional extensions. Through simulation studies, the estimation performance on the simulated datasets demonstrates low mean square error and bias for model parameters. We discuss the potential of integrating modern deep learning tools and views into psychometric research. |
| Date: | 2024–10–28 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:tjxab |
| By: | Yechan Park; Yuya Sasaki |
| Abstract: | Since LaLonde's (1986) seminal paper, there has been ongoing interest in estimating treatment effects using pre- and post-intervention data. Scholars have traditionally used experimental benchmarks to evaluate the accuracy of alternative econometric methods, including Matching, Difference-in-Differences (DID), and their hybrid forms (e.g., Heckman et al., 1998b; Dehejia and Wahba, 2002; Smith and Todd, 2005). We revisit these methodologies in the evaluation of job training and educational programs using four datasets (LaLonde, 1986; Heckman et al., 1998a; Smith and Todd, 2005; Chetty et al., 2014a; Athey et al., 2020), and show that the inequality relationship, Matching $\leq$ Hybrid $\leq$ DID, appears as a consistent norm, rather than a mere coincidence. We provide a formal theoretical justification for this puzzling phenomenon under plausible conditions such as negative selection, by generalizing the classical bracketing (Angrist and Pischke, 2009, Section 5). Consequently, when treatments are expected to be non-negative, DID tends to provide optimistic estimates, while Matching offers more conservative ones. Keywords: bias, difference in differences, educational program, job training program, matching. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.07952 |
| By: | Philipp Gersing |
| Abstract: | We consider the generalised dynamic factor model (GDFM) and assume that the dynamic common component is purely non-deterministic. We show that then the common shocks (and therefore the dynamic common component) can always be represented in terms of current and past observed variables. Hence, we further generalise existing results on the so called One-Sidedness problem of the GDFM. We may conclude that the existence of a one-sided representation that is causally subordinated to the observed variables is in the very nature of the GDFM and the lack of one-sidedness is an artefact of the chosen representation. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.18159 |