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on Econometrics |
| By: | Zhaonan Qu; Yongchan Kwon |
| Abstract: | Instrumental variables (IV) estimation is a fundamental method in econometrics and statistics for estimating causal effects in the presence of unobserved confounding. However, challenges such as untestable model assumptions and poor finite sample properties have undermined its reliability in practice. Viewing common issues in IV estimation as distributional uncertainties, we propose DRIVE, a distributionally robust framework of the classical IV estimation method. When the ambiguity set is based on a Wasserstein distance, DRIVE minimizes a square root ridge regularized variant of the two stage least squares (TSLS) objective. We develop a novel asymptotic theory for this regularized regression estimator based on the square root ridge, showing that it achieves consistency without requiring the regularization parameter to vanish. This result follows from a fundamental property of the square root ridge, which we call ``delayed shrinkage''. This novel property, which also holds for a class of generalized method of moments (GMM) estimators, ensures that the estimator is robust to distributional uncertainties that persist in large samples. We further derive the asymptotic distribution of Wasserstein DRIVE and propose data-driven procedures to select the regularization parameter based on theoretical results. Simulation studies confirm the superior finite sample performance of Wasserstein DRIVE. Thanks to its regularization and robustness properties, Wasserstein DRIVE could be preferable in practice, particularly when the practitioner is uncertain about model assumptions or distributional shifts in data. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.15634 |
| By: | Thomas von Brasch; Arvid Raknerud; Trond C. Vigtel (Statistics Norway) |
| Abstract: | This paper introduces a panel GMM framework for identifying and estimating demand elasticities via heteroscedasticity. While existing panel estimators address the simultaneity problem, the state-ofthe-art Feenstra/Soderbery (F/S) estimator suffers from inconsistency, inefficiency, and lacks a valid framework for inference. We develop a constrained GMM (C-GMM) estimator that is consistent and derive a uniform formula of its asymptotic standard error that is valid even at the boundary of the parameter space. A Monte Carlo study demonstrates the consistency of the C-GMM estimator and shows that it substantially reduces bias and root mean squared error compared to the F/S estimator. Unlike the F/S estimator, the C-GMM estimator maintains high coverage of confidence intervals across a wide range of sample sizes and parameter values, enabling more reliable inference. |
| Keywords: | Demand Elasticity; Panel Data; Heteroscedasticity; GMM; Constrained Estimation; Bagging |
| JEL: | C13 C33 C36 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:ssb:dispap:1015 |
| By: | Robert F. Phillips; Benjamin D. Williams |
| Abstract: | We study the interactive effects (IE) model as an extension of the conventional additive effects (AE) model. For the AE model, the fixed effects estimator can be obtained by applying least squares to a regression that adds a linear projection of the fixed effect on the explanatory variables (Mundlak, 1978; Chamberlain, 1984). In this paper, we develop a novel estimator -- the projection-based IE (PIE) estimator -- for the IE model that is based on a similar approach. We show that, for the IE model, fixed effects estimators that have appeared in the literature are not equivalent to our PIE estimator, though both can be expressed as a generalized within estimator. Unlike the fixed effects estimators for the IE model, the PIE estimator is consistent for a fixed number of time periods with no restrictions on serial correlation or conditional heteroskedasticity in the errors. We also derive a statistic for testing the consistency of the two-way fixed effects estimator in the possible presence of iterative effects. Moreover, although the PIE estimator is the solution to a high-dimensional nonlinear least squares problem, we show that it can be computed by iterating between two steps, both of which have simple analytical solutions. The computational simplicity is an important advantage relative to other strategies that have been proposed for estimating the IE model for short panels. Finally, we compare the finite sample performance of IE estimators through simulations. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.12709 |
| By: | Chad Brown |
| Abstract: | This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNNs estimators are given. The first establishes rates for convergence in probability under nonstationary data. The second provides non-asymptotic probability bounds on $\mathcal{L}^{2}$-errors under stationary $\beta$-mixing data. I apply these results to DNN estimators in both regression and classification contexts imposing only a standard H\"older smoothness assumption. These results are then used to demonstrate how asymptotic inference can be conducted on the finite dimensional parameter of a partially linear regression model after first-stage DNN estimation of infinite dimensional parameters. The DNN architectures considered are common in applications, featuring fully connected feedforward networks with any continuous piecewise linear activation function, unbounded weights, and a width and depth that grows with sample size. The framework provided also offers potential for research into other DNN architectures and time-series applications. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.11113 |
| By: | Ter Steege, Lucas |
| Abstract: | We study the application of approximate mean field variational inference algorithms to Bayesian panel VAR models in which an exchangeable prior is placed on the dynamic parameters and the residuals follow either a Gaussian or a Student-t distribution. This reduces the estimation time of possibly several hours using conventional MCMC methods to less than a minute using variational inference algorithms. Next to considerable speed improvements, our results show that the approximations accurately capture the dynamic effects of macroeconomic shocks as well as overall parameter uncertainty. The application with Student-t residuals shows that it is computationally easy to include the COVID-19 observations in Bayesian panel VARs, thus offering a fast way to estimate such models. JEL Classification: C18, C32, C33 |
| Keywords: | panel-VAR, student-t distribution, variational Bayes |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20242991 |
| By: | Chengwang Liao; Ziwei Mei; Zhentao Shi |
| Abstract: | In panel predictive regressions with persistent covariates, coexistence of the Nickell bias and the Stambaugh bias imposes challenges for hypothesis testing. This paper introduces a new estimator, the IVX-X-Jackknife (IVXJ), which effectively removes this composite bias and reinstates standard inferential procedures. The IVXJ estimator is inspired by the IVX technique in time series. In panel data where the cross section is of the same order as the time dimension, the bias of the baseline panel IVX estimator can be corrected via an analytical formula by leveraging an innovative X-Jackknife scheme that divides the time dimension into the odd and even indices. IVXJ is the first procedure that achieves unified inference across a wide range of modes of persistence in panel predictive regressions, whereas such unified inference is unattainable for the popular within-group estimator. Extended to accommodate long-horizon predictions with multiple regressions, IVXJ is used to examine the impact of debt levels on financial crises by panel local projection. Our empirics provide comparable results across different categories of debt. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.09825 |
| By: | Yannick Hoga |
| Abstract: | Forecasting risk (as measured by quantiles) and systemic risk (as measured by Adrian and Brunnermeiers's (2016) CoVaR) is important in economics and finance. However, past research has shown that predictive relationships may be unstable over time. Therefore, this paper develops structural break tests in predictive quantile and CoVaR regressions. These tests can detect changes in the forecasting power of covariates, and are based on the principle of self-normalization. We show that our tests are valid irrespective of whether the predictors are stationary or near-stationary, rendering the tests suitable for a range of practical applications. Simulations illustrate the good finite-sample properties of our tests. Two empirical applications concerning equity premium and systemic risk forecasting models show the usefulness of the tests. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.05861 |
| By: | Gawain Heckley (Health Economics, Faculty of Medicine, Lund University); Dennis Petrie (Centre for Health Economics, Monash Business School, Monash University) |
| Abstract: | This paper presents a flexible method, Parameter Estimation by Raw Moments (PERM), to evaluate a policy’s impact on parameters of the distribution of outcomes. Such parameters include the variance (E[Y2]−E[Y]2), skewness and covariance. While many studies estimate the mean (first moment), PERM extends this to estimate higher order moments, enabling calculation of distribution parameter treatment effects. Two implementations are discussed: regression with controls and DiD with staggered rollout. Applying PERM DiD to a Swedish school reform shows it reduced education inequality but increased earnings variance resulting in a lower covariance between education and earnings. |
| Keywords: | Causal Inference, Policy Evaluation, Distribution Impacts, Income Inequality, Education Inequality |
| JEL: | I24 I26 I28 C10 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:mhe:chemon:2024-18 |
| By: | Kalinke, Florian; Szabo, Zoltan |
| Abstract: | Kernel techniques are among the most popular and powerful approaches of data science. Among the key features that make kernels ubiquitous are (i) the number of domains they have been designed for, (ii) the Hilbert structure of the function class associated to kernels facilitating their statistical analysis, and (iii) their ability to represent probability distributions without loss of information. These properties give rise to the immense success of Hilbert-Schmidt independence criterion (HSIC) which is able to capture joint independence of random variables under mild conditions, and permits closed-form estimators with quadratic computational complexity (w.r.t. the sample size). In order to alleviate the quadratic computational bottleneck in large-scale applications, multiple HSIC approximations have been proposed, however these estimators are restricted to M=2 random variables, do not extend naturally to the M≥2 case, and lack theoretical guarantees. In this work, we propose an alternative Nyström-based HSIC estimator which handles the M≥2 case, prove its consistency, and demonstrate its applicability in multiple contexts, including synthetic examples, dependency testing of media annotations, and causal discovery. |
| JEL: | C1 |
| Date: | 2023–08–31 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:118251 |
| By: | Qingliang Fan; Ruike Wu; Yanrong Yang |
| Abstract: | This paper proposes a robust, shocks-adaptive portfolio in a large-dimensional assets universe where the number of assets could be comparable to or even larger than the sample size. It is well documented that portfolios based on optimizations are sensitive to outliers in return data. We deal with outliers by proposing a robust factor model, contributing methodologically through the development of a robust principal component analysis (PCA) for factor model estimation and a shrinkage estimation for the random error covariance matrix. This approach extends the well-regarded Principal Orthogonal Complement Thresholding (POET) method (Fan et al., 2013), enabling it to effectively handle heavy tails and sudden shocks in data. The novelty of the proposed robust method is its adaptiveness to both global and idiosyncratic shocks, without the need to distinguish them, which is useful in forming portfolio weights when facing outliers. We develop the theoretical results of the robust factor model and the robust minimum variance portfolio. Numerical and empirical results show the superior performance of the new portfolio. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.01826 |
| By: | Osman Do\u{g}an; Raffaele Mattera; Philipp Otto; S\"uleyman Ta\c{s}p{\i}nar |
| Abstract: | We introduce a dynamic spatiotemporal volatility model that extends traditional approaches by incorporating spatial, temporal, and spatiotemporal spillover effects, along with volatility-specific observed and latent factors. The model offers a more general network interpretation, making it applicable for studying various types of network spillovers. The primary innovation lies in incorporating volatility-specific latent factors into the dynamic spatiotemporal volatility model. Using Bayesian estimation via the Markov Chain Monte Carlo (MCMC) method, the model offers a robust framework for analyzing the spatial, temporal, and spatiotemporal effects of a log-squared outcome variable on its volatility. We recommend using the deviance information criterion (DIC) and a regularized Bayesian MCMC method to select the number of relevant factors in the model. The model's flexibility is demonstrated through two applications: a spatiotemporal model applied to the U.S. housing market and another applied to financial stock market networks, both highlighting the model's ability to capture varying degrees of interconnectedness. In both applications, we find strong spatial/network interactions with relatively stronger spillover effects in the stock market. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.16526 |
| By: | Anubha Goel; Puneet Pasricha; Juho Kanniainen |
| Abstract: | This study is the first to explore the application of a time-series foundation model for VaR estimation. Foundation models, pre-trained on vast and varied datasets, can be used in a zero-shot setting with relatively minimal data or further improved through finetuning. We compare the performance of Google's model, called TimesFM, against conventional parametric and non-parametric models, including GARCH, Generalized Autoregressive Score (GAS), and empirical quantile estimates, using daily returns from the S\&P 100 index and its constituents over 19 years. Our backtesting results indicate that, in terms of the actual-over-expected ratio, the fine-tuned TimesFM model consistently outperforms traditional methods. Regarding the quantile score loss function, it achieves performance comparable to the best econometric approach, the GAS model. Overall, the foundation model is either the best or among the top performers in forecasting VaR across the 0.01, 0.025, 0.05, and 0.1 VaR levels. We also found that fine-tuning significantly improves the results, and the model should not be used in zero-shot settings. Overall, foundation models can provide completely alternative approaches to traditional econometric methods, yet there are challenges to be tackled. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.11773 |
| By: | Kirill Ponomarev; Vira Semenova |
| Abstract: | This article addresses the question of reporting a lower confidence band (LCB) for optimal welfare in policy learning problems. A straightforward procedure inverts a one-sided t-test based on an efficient estimator of the optimal welfare. We argue that in an empirically relevant class of data-generating processes, a LCB corresponding to suboptimal welfare may exceed the straightforward LCB, with the average difference of order N-{1/2}. We relate this result to a lack of uniformity in the so-called margin assumption, commonly imposed in policy learning and debiased inference. We advocate for using uniformly valid asymptotic approximations and show how existing methods for inference in moment inequality models can be used to construct valid and tight LCBs for the optimal welfare. We illustrate our findings in the context of the National JTPA study. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.07443 |
| By: | Andrew Alden; Carmine Ventre; Blanka Horvath |
| Abstract: | Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent works have demonstrated the ability of such solutions to leverage the information encoded in paths via signature-based features. However, current state of the art DR solutions are memory intensive and incur a high computation cost. This leads to a trade-off between path length and the number of paths considered. This computational bottleneck limits the application to small sample sizes which consequently introduces estimation uncertainty. In this paper, we present a methodology for addressing the above issues; resolving estimation uncertainties whilst also proposing a pipeline that enables us to use DR for a wide variety of learning tasks. Integral to our approach is our novel distance approximator. This allows us to seamlessly apply our methodology across different application domains, sampling rates, and stochastic process dimensions. We show that our model performs well in applications related to estimation theory, quantitative finance, and physical sciences. We demonstrate that our model generalises well, not only to unseen data within a given distribution, but also under unseen regimes (unseen classes of stochastic models). |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.09196 |
| By: | Luca Vincenzo Ballestra; Enzo D'Innocenzo; Christian Tezza |
| Abstract: | Christoffersen, Jacobs, Ornthanalai, and Wang (2008) (CJOW) proposed an improved Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model for valuing European options, where the return volatility is comprised of two distinct components. Empirical studies indicate that the model developed by CJOW outperforms widely-used single-component GARCH models and provides a superior fit to options data than models that combine conditional heteroskedasticity with Poisson-normal jumps. However, a significant limitation of this model is that it allows the variance process to become negative. Oh and Park [2023] partially addressed this issue by developing a related model, yet the positivity of the volatility components is not guaranteed, both theoretically and empirically. In this paper we introduce a new GARCH model that improves upon the models by CJOW and Oh and Park [2023], ensuring the positivity of the return volatility. In comparison to the two earlier GARCH approaches, our novel methodology shows comparable in-sample performance on returns data and superior performance on S&P500 options data. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.14513 |
| By: | Robert Fairlie; Daniel Oliver; Glenn Millhauser; Randa Roland; Robert W. Fairlie |
| Abstract: | An extensive literature in the social sciences analyzes peer effects among students, but estimation is complicated by several major problems some of which cannot be solved even with random assignment. We design a field experiment and propose a new estimation technique to address these estimation problems including the mechanical problems associated with repeated observations within peer groups noted by Angrist (2014). The field experiment randomly assigns students to one-to-one partnerships in an important gateway STEM course at a large public university. We find no evidence of peer effects from estimates of exogenous peer effect models. We push further and estimate outcome-on-outcome models which sometimes reveal peer effects when exogenous models do not provide good proxies for ability. We find some limited evidence of small, positive outcome-on-outcome peer effects (which would have been missed without our new estimation technique). Standard estimation methods fail to detect peer effects and even return negative estimates in our Monte Carlo simulations because of the downward bias due to mechanical problems. Simulations reveal additional advantages of our technique especially when peer group sizes are fixed. Estimates of non-linear effects, heterogeneous effects, and different measures of peer ability and outcomes reveal mostly null effects but we find some evidence that low-ability peers negatively affect low-ability and medium-ability students. The findings in this setting of long-term, intensive interactions with classroom random assignment and “throwing everything at it” provide evidence of, at most, small positive peer effects contrasting with the common finding of large peer effects in previous studies in education. |
| Keywords: | peer effects, higher education, STEM, field experiment |
| JEL: | I21 I23 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11404 |
| By: | Pulikandala Nithish Kumar; Nneka Umeorah; Alex Alochukwu |
| Abstract: | Volatility forecasting is essential for risk management and decision-making in financial markets. Traditional models like Generalized Autoregressive Conditional Heteroskedasticity (GARCH) effectively capture volatility clustering but often fail to model complex, non-linear interdependencies between multiple indices. This paper proposes a novel approach using Graph Neural Networks (GNNs) to represent global financial markets as dynamic graphs. The Temporal Graph Attention Network (Temporal GAT) combines Graph Convolutional Networks (GCNs) and Graph Attention Networks (GATs) to capture the temporal and structural dynamics of volatility spillovers. By utilizing correlation-based and volatility spillover indices, the Temporal GAT constructs directed graphs that enhance the accuracy of volatility predictions. Empirical results from a 15-year study of eight major global indices show that the Temporal GAT outperforms traditional GARCH models and other machine learning methods, particularly in short- to mid-term forecasts. The sensitivity and scenario-based analysis over a range of parameters and hyperparameters further demonstrate the significance of the proposed technique. Hence, this work highlights the potential of GNNs in modeling complex market behaviors, providing valuable insights for financial analysts and investors. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.16858 |