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on Econometrics |
| By: | Likai Chen; Georg Keilbar; Liangjun Su; Weining Wang |
| Abstract: | Numerous studies use regression discontinuity design (RDD) for panel data by assuming that the treatment effects are homogeneous across all individuals/groups and pooling the data together. It is unclear how to test for the significance of treatment effects when the treatments vary across individuals/groups and the error terms may exhibit complicated dependence structures. This paper examines the estimation and inference of multiple treatment effects when the errors are not independent and identically distributed, and the treatment effects vary across individuals/groups. We derive a simple analytical expression for approximating the variance-covariance structure of the treatment effect estimators under general dependence conditions and propose two test statistics, one is to test for the overall significance of the treatment effect and the other for the homogeneity of the treatment effects. We find that in the Gaussian approximations to the test statistics, the dependence structures in the data can be safely ignored due to the localized nature of the statistics. This has the important implication that the simulated critical values can be easily obtained. Simulations demonstrate our tests have superb size control and reasonable power performance in finite samples regardless of the presence of strong cross-section dependence or/and weak serial dependence in the data. We apply our tests to two datasets and find significant overall treatment effects in each case. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.01162&r=ecm |
| By: | Luther Yap |
| Abstract: | This paper proposes three novel test procedures that yield valid inference in an environment with many weak instrumental variables (MWIV). It is observed that the t statistic of the jackknife instrumental variable estimator (JIVE) has an asymptotic distribution that is identical to the two-stage-least squares (TSLS) t statistic in the just-identified environment. Consequently, test procedures that were valid for TSLS t are also valid for the JIVE t. Two such procedures, i.e., VtF and conditional Wald, are adapted directly. By exploiting a feature of MWIV environments, a third, more powerful, one-sided VtF-based test procedure can be obtained. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.15932&r=ecm |
| By: | Guido W. Imbens; Davide Viviano |
| Abstract: | This paper studies inference on treatment effects in panel data settings with unobserved confounding. We model outcome variables through a factor model with random factors and loadings. Such factors and loadings may act as unobserved confounders: when the treatment is implemented depends on time-varying factors, and who receives the treatment depends on unit-level confounders. We study the identification of treatment effects and illustrate the presence of a trade-off between time and unit-level confounding. We provide asymptotic results for inference for several Synthetic Control estimators and show that different sources of randomness should be considered for inference, depending on the nature of confounding. We conclude with a comparison of Synthetic Control estimators with alternatives for factor models. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00955&r=ecm |
| By: | Joseph Fry |
| Abstract: | A common approach to constructing a Synthetic Control unit is to fit on the outcome variable and covariates in pre-treatment time periods, but it has been shown by Ferman and Pinto (2021) that this approach does not provide asymptotic unbiasedness when the fit is imperfect and the number of controls is fixed. Many related panel methods have a similar limitation when the number of units is fixed. I introduce and evaluate a new method in which the Synthetic Control is constructed using a General Method of Moments approach where if the Synthetic Control satisfies the moment conditions it must have the same loadings on latent factors as the treated unit. I show that a Synthetic Control Estimator of this form will be asymptotically unbiased as the number of pre-treatment time periods goes to infinity, even when pre-treatment fit is imperfect and the set of controls is fixed. Furthermore, if both the number of pre-treatment and post-treatment time periods go to infinity, then averages of treatment effects can be consistently estimated and asymptotically valid inference can be conducted using a subsampling method. I conduct simulations and an empirical application to compare the performance of this method with existing approaches in the literature. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.01209&r=ecm |
| By: | S. Yaser Samadi; Tharindu P. De Alwis |
| Abstract: | Dimensionality reduction has always been one of the most significant and challenging problems in the analysis of high-dimensional data. In the context of time series analysis, our focus is on the estimation and inference of conditional mean and variance functions. By using central mean and variance dimension reduction subspaces that preserve sufficient information about the response, one can effectively estimate the unknown mean and variance functions of the time series. While the literature presents several approaches to estimate the time series central mean and variance subspaces (TS-CMS and TS-CVS), these methods tend to be computationally intensive and infeasible for practical applications. By employing the Fourier transform, we derive explicit estimators for TS-CMS and TS-CVS. These proposed estimators are demonstrated to be consistent, asymptotically normal, and efficient. Simulation studies have been conducted to evaluate the performance of the proposed method. The results show that our method is significantly more accurate and computationally efficient than existing methods. Furthermore, the method has been applied to the Canadian Lynx dataset. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.02110&r=ecm |
| By: | Morten {\O}rregaard Nielsen; Won-Ki Seo; Dakyung Seong |
| Abstract: | This paper studies statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends that are embedded in the time series, i.e., the dimension of the nonstationary subspace. We also consider hypotheses on the nonstationary subspace itself. The Hilbert space can be of an arbitrarily large dimension, and our methods remain asymptotically valid even when the time series of interest takes values in a subspace of possibly unknown dimension. This has wide applicability in practice; for example, in the case of cointegrated vector time series of finite dimension, in a high-dimensional factor model that includes a finite number of nonstationary factors, in the case of cointegrated curve-valued (or function-valued) time series, and nonstationary dynamic functional factor models. We include two empirical illustrations to the term structure of interest rates and labor market indices, respectively. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00590&r=ecm |
| By: | Maria Elena Bontempi; Jan Ditzen |
| Abstract: | The generalized method of moments (GMM) estimator applied to equations in levels, GMM-lev, has the advantage of being able to estimate the effect of measurable time-invariant covariates using all available information. This is not possible with GMM-dif, applied to equations in each period transformed into first differences, while GMM-sys uses little information, as it adds the equation in levels for only one period. The GMM-lev, by implying a two-component error term containing the individual heterogeneity and the shock, exposes the explanatory variables to possible double endogeneity. For example, the estimation of true persistence could suffer from bias if instruments were correlated with the unit-specific error component. We propose to exploit the \citet{Mundlak1978}'s approach together with GMM-lev estimation to capture initial conditions and improve inference. Monte Carlo simulations for different panel types and under different double endogeneity assumptions show the advantage of our approach. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.00399&r=ecm |
| By: | Mr. Sakai Ando; Mingmei Xiao |
| Abstract: | This paper proposes a novel shrinkage estimator for high-dimensional covariance matrices by extending the Oracle Approximating Shrinkage (OAS) of Chen et al. (2009) to target the diagonal elements of the sample covariance matrix. We derive the closed-form solution of the shrinkage parameter and show by simulation that, when the diagonal elements of the true covariance matrix exhibit substantial variation, our method reduces the Mean Squared Error, compared with the OAS that targets an average variance. The improvement is larger when the true covariance matrix is sparser. Our method also reduces the Mean Squared Error for the inverse of the covariance matrix. |
| Keywords: | High-Dimension; Covariance Matrix; Shrinkage; Diagonal Target |
| Date: | 2023–12–08 |
| URL: | http://d.repec.org/n?u=RePEc:imf:imfwpa:2023/257&r=ecm |
| By: | Xiaojun Song; Zhenting Sun |
| Abstract: | This paper proposes a general framework for inference on three types of almost dominances: Almost Lorenz dominance, almost inverse stochastic dominance, and almost stochastic dominance. We first generalize almost Lorenz dominance to almost upward and downward Lorenz dominances. We then provide a bootstrap inference procedure for the Lorenz dominance coefficients, which measure the degrees of almost Lorenz dominances. Furthermore, we propose almost upward and downward inverse stochastic dominances and provide inference on the inverse stochastic dominance coefficients. We also show that our results can easily be extended to almost stochastic dominance. Simulation studies demonstrate the finite sample properties of the proposed estimators and the bootstrap confidence intervals. We apply our methods to the inequality growth in the United Kingdom and find evidence for almost upward inverse stochastic dominance. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.02288&r=ecm |
| By: | Florian Huber |
| Abstract: | This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined by a logistic function that depends on a single threshold variable and two hyperparameters. Each of these individual models only accounts for a minor portion of the variation in the endogenous variables. But many of them are capable of capturing arbitrary nonlinear conditional mean relations. Conjugate priors enable fast and efficient inference. In simulations, we show that our approach produces accurate point and density forecasts. In a real-data exercise, we forecast US macroeconomic aggregates and consider the nonlinear effects of financial shocks in a large-scale nonlinear VAR. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.01881&r=ecm |
| By: | Klaus Nordhausen (JYU - University of Jyväskylä); Anne Ruiz-Gazen (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also encompass methods that handle dependent data such as time series or spatial data. |
| Keywords: | Blind source separation, Dimension reduction, Independent component analysis, Invariant component selection, Scatter matrices, Supervised dimension reduction |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04296111&r=ecm |
| By: | Oren Danieli; Daniel Nevo; Itai Walk; Bar Weinstein; Dan Zeltzer |
| Abstract: | Studies using instrumental variables (IV) often assess the validity of their identification assumptions using falsification tests. However, these tests are often carried out in an ad-hoc manner, without theoretical foundations. In this paper, we establish a theoretical framework for negative control tests, the predominant category of falsification tests for IV designs. These tests are conditional independence tests between negative control variables and either the IV or the outcome (e.g., examining the ``effect'' on the lagged outcome). We introduce a formal definition for threats to IV exogeneity (alternative path variables) and characterize the necessary conditions that proxy variables for such unobserved threats must meet to serve as negative controls. The theory highlights prevalent errors in the implementation of negative control tests and how they could be corrected. Our theory can also be used to design new falsification tests by identifying appropriate negative control variables, including currently underutilized types, and suggesting alternative statistical tests. The theory shows that all negative control tests assess IV exogeneity. However, some commonly used tests simultaneously evaluate the 2SLS functional form assumptions. Lastly, we show that while negative controls are useful for detecting biases in IV designs, their capacity to correct or quantify such biases requires additional non-trivial assumptions. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.15624&r=ecm |
| By: | Haoyu Wei; Runzhe Wan; Lei Shi; Rui Song |
| Abstract: | Many real applications of bandits have sparse non-zero rewards, leading to slow learning rates. A careful distribution modeling that utilizes problem-specific structures is known as critical to estimation efficiency in the statistics literature, yet is under-explored in bandits. To fill the gap, we initiate the study of zero-inflated bandits, where the reward is modeled as a classic semi-parametric distribution called zero-inflated distribution. We carefully design Upper Confidence Bound (UCB) and Thompson Sampling (TS) algorithms for this specific structure. Our algorithms are suitable for a very general class of reward distributions, operating under tail assumptions that are considerably less stringent than the typical sub-Gaussian requirements. Theoretically, we derive the regret bounds for both the UCB and TS algorithms for multi-armed bandit, showing that they can achieve rate-optimal regret when the reward distribution is sub-Gaussian. The superior empirical performance of the proposed methods is shown via extensive numerical studies. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.15595&r=ecm |
| By: | Martin Bruns (School of Economics, University of East Anglia); Sascha A. Keweloh (TU Dortmund University) |
| Abstract: | Proxy variables have gained widespread prominence as indispensable tools for identifying structural VAR models. Analogous to instrumental variables, proxies need to be exogenous, i.e. uncorrelated with all non-target shocks. Assessing the exogeneity of proxies has traditionally relied on economic arguments rather than statistical tests. We argue that the economic rational underlying the construction of commonly used proxy variables aligns with a stronger form of exogeneity. Specifically, proxies are typically constructed as variables not containing any information on the expected value of non-target shocks. We show conditions under which this enhanced concept of proxy exogeneity is testable without additional identifying assumptions. |
| Keywords: | Structural vector autoregression, proxy VAR, exogeneity test |
| JEL: | C32 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:uea:ueaeco:2023-07&r=ecm |
| By: | George Gui; Olivier Toubia |
| Abstract: | Large Language Models (LLMs) have demonstrated impressive potential to simulate human behavior. Using a causal inference framework, we empirically and theoretically analyze the challenges of conducting LLM-simulated experiments, and explore potential solutions. In the context of demand estimation, we show that variations in the treatment included in the prompt (e.g., price of focal product) can cause variations in unspecified confounding factors (e.g., price of competitors, historical prices, outside temperature), introducing endogeneity and yielding implausibly flat demand curves. We propose a theoretical framework suggesting this endogeneity issue generalizes to other contexts and won't be fully resolved by merely improving the training data. Unlike real experiments where researchers assign pre-existing units across conditions, LLMs simulate units based on the entire prompt, which includes the description of the treatment. Therefore, due to associations in the training data, the characteristics of individuals and environments simulated by the LLM can be affected by the treatment assignment. We explore two potential solutions. The first specifies all contextual variables that affect both treatment and outcome, which we demonstrate to be challenging for a general-purpose LLM. The second explicitly specifies the source of treatment variation in the prompt given to the LLM (e.g., by informing the LLM that the store is running an experiment). While this approach only allows the estimation of a conditional average treatment effect that depends on the specific experimental design, it provides valuable directional results for exploratory analysis. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.15524&r=ecm |
| By: | Jean-Yves Pitarakis |
| Abstract: | We introduce a novel approach for comparing out-of-sample multi-step forecasts obtained from a pair of nested models that is based on the forecast encompassing principle. Our proposed approach relies on an alternative way of testing the population moment restriction implied by the forecast encompassing principle and that links the forecast errors from the two competing models in a particular way. Its key advantage is that it is able to bypass the variance degeneracy problem afflicting model based forecast comparisons across nested models. It results in a test statistic whose limiting distribution is standard normal and which is particularly simple to construct and can accommodate both single period and longer-horizon prediction comparisons. Inferences are also shown to be robust to different predictor types, including stationary, highly-persistent and purely deterministic processes. Finally, we illustrate the use of our proposed approach through an empirical application that explores the role of global inflation in enhancing individual country specific inflation forecasts. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.16099&r=ecm |
| By: | Sören Blomquist |
| Abstract: | Estimated labor supply functions are important tools when designing an optimal income tax or calculating the effect of tax reforms. It is therefore of large importance to use estimation methods that give reliable results and to know their properties. In this paper Monte Carlo simulations are used to evaluate two different methods to estimate labor supply functions; the discrete choice method and a nonparametric method suggested in Blomquist and Newey (2002). The focus is on the estimators’ ability to predict the hours of work for a given tax system and the change in hours of work when there is a tax reform. The simulations show that the DC method is quite sensitive to misspecifications of the likelihood function and to measurement errors in hours of work. A version of the Blomquist Newey method shows the overall best performance to predict the hours of work. |
| Keywords: | labor supply, tax reform, predictive power, estimation methods, Monte Carlo simulations |
| JEL: | C40 C52 C53 H20 H30 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10827&r=ecm |
| By: | Bas Sanders |
| Abstract: | Counterfactuals in equilibrium models are functions of the current state of the world, the exogenous change variables and the model parameters. Current practice treats the current state of the world, the observed data, as perfectly measured, but there is good reason to believe that they are measured with error. The main aim of this paper is to provide tools for quantifying uncertainty about counterfactuals, when the current state of the world is measured with error. I propose two methods, a Bayesian approach and an adversarial approach. Both methods are practical and theoretically justified. I apply the two methods to the application in Adao et al. (2017) and find non-trivial uncertainty about counterfactuals. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2311.14032&r=ecm |
| By: | Riveros-Gavilanes, J. M. |
| Abstract: | Traditional tests for parallel trends in the context of differences-in-differences are based on the observation of the mean values of the dependent variable in the treatment and control groups over time. However, given the new discussions brought by the development of the event study designs, it is clear that controlling for observable factors may intervene in the fulfilment of the parallel trend as-sumption. This article presents a simple test based on the statistical significance of pre-treatment periods which can be extended from the classic differences-in-differences up to event study designs in universal absorbing treatments. The test requires at least two pre-treatment periods and can done by constructing appro-priate dummy variables. |
| Keywords: | difference in difference; parallel trend test; treatment. |
| JEL: | C10 C12 C15 C50 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:119367&r=ecm |
| By: | Otsu, Taisuke; Sunada, Keita |
| Abstract: | In spatial price competition models, demand factors have correlation with prices through the markup so that their identification power decreases as the number of product grows. Asymptotic results indicate lack of consistency of the estimator due to weak instruments. |
| Keywords: | spatial price competition; weak instruments; Elsevier deal |
| JEL: | C13 |
| Date: | 2024–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:120588&r=ecm |