|
on Econometrics |
| By: | Xingyu Chen; Lin Liu; Rajarshi Mukherjee |
| Abstract: | In this paper, we consider the estimation of regression coefficients and signal-to-noise (SNR) ratio in high-dimensional Generalized Linear Models (GLMs), and explore their implications in inferring popular estimands such as average treatment effects in high-dimensional observational studies. Under the ``proportional asymptotic'' regime and Gaussian covariates with known (population) covariance $\Sigma$, we derive Consistent and Asymptotically Normal (CAN) estimators of our targets of inference through a Method-of-Moments type of estimators that bypasses estimation of high dimensional nuisance functions and hyperparameter tuning altogether. Additionally, under non-Gaussian covariates, we demonstrate universality of our results under certain additional assumptions on the regression coefficients and $\Sigma$. We also demonstrate that knowing $\Sigma$ is not essential to our proposed methodology when the sample covariance matrix estimator is invertible. Finally, we complement our theoretical results with numerical experiments and comparisons with existing literature. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.06103 |
| By: | Nelly K. Djuazon; Emmanuel Selorm Tsyawo |
| Abstract: | Quantile and Distribution Treatment effects on the Treated (QTT/DTT) for non-continuous outcomes are either not identified or inference thereon is infeasible using existing methods. By introducing functional index parallel trends and no anticipation assumptions, this paper identifies and provides uniform inference procedures for QTT/DTT. The inference procedure applies under both the canonical two-group and staggered treatment designs with balanced panels, unbalanced panels, or repeated cross-sections. Monte Carlo experiments demonstrate the proposed method's robust and competitive performance, while an empirical application illustrates its practical utility. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.07842 |
| By: | Santiago Acerenza; Ot\'avio Bartalotti; Federico Veneri |
| Abstract: | This paper develops sharp testable implications for Tobit and IV-Tobit models' identifying assumptions: linear index specification, (joint) normality of latent errors, and treatment (instrument) exogeneity and relevance. The new sharp testable equalities can detect all possible observable violations of the identifying conditions. We propose a testing procedure for the model's validity using existing inference methods for intersection bounds. Simulation results suggests proper size for large samples and that the test is powerful to detect large violation of the exogeneity assumption and violations in the error structure. Finally, we review and propose new alternative paths to partially identify the parameters of interest under less restrictive assumptions. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.02573 |
| By: | Zhan Gao; Hyungsik Roger Moon |
| Abstract: | This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the Huber estimator and the least absolute deviation (LAD) estimator, exhibit significant bias when outliers are endogenous. Motivated by this finding, we investigate $L_0$-regularized estimation methods. We propose systematic heuristic algorithms, notably an iterative hard-thresholding algorithm and a local combinatorial search refinement, to solve the combinatorial optimization problem of the \(L_0\)-regularized estimation efficiently. Our Monte Carlo simulations yield two key results: (i) The local combinatorial search algorithm substantially improves solution quality compared to the initial projection-based hard-thresholding algorithm while offering greater computational efficiency than directly solving the mixed integer optimization problem. (ii) The $L_0$-regularized estimator demonstrates superior performance in terms of bias reduction, estimation accuracy, and out-of-sample prediction errors compared to $L_1$-regularized alternatives. We illustrate the practical value of our method through an empirical application to stock return forecasting. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.03930 |
| By: | Maximilian Osterhaus |
| Abstract: | A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of dimensionality, restricts the application of such estimators to models with moderately few random coefficients. This paper proposes a scalable nonparametric estimator for high-dimensional random coefficient models. The estimator uses a truncated tensor product of one-dimensional hierarchical basis functions to approximate the underlying random coefficients' distribution. Due to the truncation, the number of parameters increases at a much slower rate than in the regular tensor product basis, rendering the nonparametric estimation of high-dimensional random coefficient models feasible. The derived estimator allows estimating the underlying distribution with constrained least squares, making the approach computationally simple and fast. Monte Carlo experiments and an application to data on the regulation of air pollution illustrate the good performance of the estimator. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.07185 |
| By: | Dor Leventer; Daniel Nevo |
| Abstract: | A common approach to Regression Discontinuity (RD) designs relies on a continuity assumption of the mean potential outcomes at the cutoff defining the RD design. In practice, this assumption is often implausible when changes other than the intervention of interest occur at the cutoff (e.g., other policies are implemented at the same cutoff). When the continuity assumption is implausible, researchers often retreat to ad-hoc analyses that are not supported by any theory and yield results with unclear causal interpretation. These analyses seek to exploit additional data where either all units are treated or all units are untreated (regardless of their running variable value). For example, when data from multiple time periods are available. We first derive the bias of RD designs when the continuity assumption does not hold. We then present a theoretical foundation for analyses using multiple time periods by the means of a general identification framework incorporating data from additional time periods to overcome the bias. We discuss this framework under various RD designs, and also extend our work to carry-over effects and time-varying running variables. We develop local linear regression estimators, bias correction procedures, and standard errors that are robust to bias-correction for the multiple period setup. The approach is illustrated using an application that studied the effect of new fiscal laws on debt of Italian municipalities. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.05847 |
| By: | Artem Prokhorov; Peter Radchenko; Alexander Semenov; Anton Skrobotov |
| Abstract: | We use cutting-edge mixed integer optimization (MIO) methods to develop a framework for detection and estimation of structural breaks in time series regression models. The framework is constructed based on the least squares problem subject to a penalty on the number of breakpoints. We restate the $l_0$-penalized regression problem as a quadratic programming problem with integer- and real-valued arguments and show that MIO is capable of finding provably optimal solutions using a well-known optimization solver. Compared to the popular $l_1$-penalized regression (LASSO) and other classical methods, the MIO framework permits simultaneous estimation of the number and location of structural breaks as well as regression coefficients, while accommodating the option of specifying a given or minimal number of breaks. We derive the asymptotic properties of the estimator and demonstrate its effectiveness through extensive numerical experiments, confirming a more accurate estimation of multiple breaks as compared to popular non-MIO alternatives. Two empirical examples demonstrate usefulness of the framework in applications from business and economic statistics. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.05665 |
| By: | Ranieri Dugo (DEF, University of Rome "Tor Vergata"); Giacomo Giorgio (Dept of Mathematics, University of Rome "Tor Vergata"); Paolo Pigato (DEF, University of Rome "Tor Vergata") |
| Abstract: | Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a multivariate version of the fractional Ornstein-Uhlenbeck process. This multivariate Gaussian process is stationary, ergodic and allows for different Hurst exponents on each component. We characterize its correlation matrix and its short and long time asymptotics. Besides the marginal parameters, the cross correlation between one-dimensional marginal components is ruled by two parameters. We consider the problem of their inference, proposing two types of estimator, constructed from discrete observations of the process. We establish their asymptotic theory, in one case in the long time asymptotic setting, in the other case in the infill and long time asymptotic setting. The limit behavior can be asymptotically Gaussian or non-Gaussian, depending on the values of the Hurst exponents of the marginal compo-nents. The technical core of the paper relies on the analysis of asymptotic properties of functionals of Gaussian processes, that we establish using Malliavin calculus and Stein's method. We provide numerical experiments that support our theoretical analysis and also suggest a conjecture on the application of one of these estimators to the multivariate fractional Brownian Motion. |
| Keywords: | Fractional process, multivariate process, ergodic process, long-range dependence, cross-correlation, parameters inference, rough volatility. |
| Date: | 2024–08–28 |
| URL: | https://d.repec.org/n?u=RePEc:rtv:ceisrp:581 |
| By: | Gilles Koumou; Emmanuel Selorm Tsyawo |
| Abstract: | Pooled panel analyses tend to mask heterogeneity in unit-specific treatment effects. For example, existing studies on the impact of democracy on economic growth do not reach a consensus as empirical findings are substantially heterogeneous in the country composition of the panel. In contrast to pooled panel analyses, this paper proposes a Difference-in-Differences (DiD) estimator that exploits the temporal dimension in the data and estimates unit-specific average treatment effects on the treated (ATT) with as few as two cross-sectional units. Under weak identification and temporal dependence conditions, the DiD estimator is asymptotically normal. The estimator is further complemented with a test of identification granted at least two candidate control units. Empirical results using the DiD estimator suggest Benin's economy would have been 6.3% smaller on average over the 1993-2018 period had she not democratised. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.13047 |
| By: | Arthur Lewbel (Boston College); Xi Qu (Antai College of Economics and Management, Shanghai Jiao Tong University); Xun Tang (Department of Economics, Rice University) |
| Abstract: | We propose an adjusted 2SLS estimator for social network models when the network links reported in samples are subject to two-sided misclassification errors (due, e.g., to recall errors by survey respondents, or lapses in data input). Misclassified links make all covariates endogenous, and add a new source of correlation between the structural errors and peer outcomes (in addition to simultaneity), thus invalidating conventional estimators used in the literature. We resolve these issues by adjusting endogenous peer outcomes with estimates of the misclassification rates and constructing new instruments that exploit properties of the noisy network measures. Simulation results confirm our adjusted 2SLS estimator corrects the bias from a naive, unadjusted 2SLS estimator which ignores misclassification and uses conventional instruments. We apply our method to study peer effects in household decisions to participate in a microfinance program in Indian villages. |
| Keywords: | Social Network, Link Misclassification |
| JEL: | D11 D13 |
| Date: | 2024–08–31 |
| URL: | https://d.repec.org/n?u=RePEc:boc:bocoec:1079 |
| By: | F. Blasques (Vrije Universiteit Amsterdam); S.J. Koopman (Vrije Universiteit Amsterdam); G. Mingoli (Vrije Universiteit Amsterdam); S. Telg (Vrije Universiteit Amsterdam) |
| Abstract: | In economics and finance, speculative bubbles take the form of locally explosive dynamics that eventually collapse. We propose a test for the presence of speculative bubbles in the context of mixed causal-noncausal autoregressive processes. The test exploits the fact that bubbles are anticipative, that is, they are generated by an extreme shock in the forward- looking dynamics. In particular, the test uses both path level deviations and growth rates to assess the presence of a bubble of given duration and size, at any moment of time. We show that the distribution of the test statistic can be either analytically determined or numerically approximated, depending on the error distribution. Size and power properties of the test are analyzed in controlled Monte Carlo experiments. An empirical application is presented for a monthly oil price index. It demonstrates the ability of the test to detect bubbles and to provide valuable insights in terms of risk assessments in the spirit of Value-at-Risk. |
| Keywords: | noncausality, bubbles, testing, date-stamping, risk assessment |
| JEL: | C22 E31 E37 |
| Date: | 2024–05–30 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240036 |
| By: | Jean-Michel Benkert; Shuo Liu; Nick Netzer |
| Abstract: | Response times contain information about economically relevant but unobserved variables like willingness to pay, preference intensity, quality, or happiness. Here, we provide a general characterization of the properties of latent variables that can be detected using response time data. Our characterization generalizes various results in the literature, helps to solve identification problems of binary response models, and paves the way for many new applications. We apply the result to test the hypothesis that marginal happiness is decreasing in income, a principle that is commonly accepted but so far not established empirically. |
| Keywords: | Response times, chronometric effect, binary response model, non-parametric identification, decreasing marginal happiness |
| JEL: | C14 D60 D91 I31 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:449 |
| By: | Yi Cui; D\'esir\'e K\'edagni; Huan Wu |
| Abstract: | This paper considers a robust identification of causal parameters in a randomized experiment setting with noncompliance where the standard local average treatment effect assumptions could be violated. Following Li, K\'edagni, and Mourifi\'e (2024), we propose a misspecification robust bound for a real-valued vector of various causal parameters. We discuss identification under two sets of weaker assumptions: random assignment and exclusion restriction (without monotonicity), and random assignment and monotonicity (without exclusion restriction). We introduce two causal parameters: the local average treatment-controlled direct effect (LATCDE), and the local average instrument-controlled direct effect (LAICDE). Under the random assignment and monotonicity assumptions, we derive sharp bounds on the local average treatment-controlled direct effects for the always-takers and never-takers, respectively, and the total average controlled direct effect for the compliers. Additionally, we show that the intent-to-treat effect can be expressed as a convex weighted average of these three effects. Finally, we apply our method on the proximity to college instrument and find that growing up near a four-year college increases the wage of never-takers (who represent more than 70% of the population) by a range of 4.15% to 27.07%. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.03530 |
| By: | Ke Sun; Linglong Kong; Hongtu Zhu; Chengchun Shi |
| Abstract: | Time series experiments, in which experimental units receive a sequence of treatments over time, are frequently employed in many technological companies to evaluate the performance of a newly developed policy, product, or treatment relative to a baseline control. Many existing A/B testing solutions assume a fully observable experimental environment that satisfies the Markov condition, which often does not hold in practice. This paper studies the optimal design for A/B testing in partially observable environments. We introduce a controlled (vector) autoregressive moving average model to capture partial observability. We introduce a small signal asymptotic framework to simplify the analysis of asymptotic mean squared errors of average treatment effect estimators under various designs. We develop two algorithms to estimate the optimal design: one utilizing constrained optimization and the other employing reinforcement learning. We demonstrate the superior performance of our designs using a dispatch simulator and two real datasets from a ride-sharing company. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.05342 |
| By: | Helmut Farbmacher; Rebecca Groh; Michael M\"uhlegger; Gabriel Vollert |
| Abstract: | 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. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.08580 |
| By: | John Eric Humphries; Aurelie Ouss; Kamelia Stavreva; Megan T. Stevenson; Winnie van Dijk |
| Abstract: | Noncarceral conviction is a common outcome of criminal court cases: for every individual incarcerated, there are approximately three who are recently convicted but not sentenced to prison or jail. We develop an empirical framework for studying the consequences of noncarceral conviction by extending the binary-treatment judge IV framework to settings with multiple treatments. We outline assumptions under which widely-used 2SLS regressions recover margin-specific treatment effects, relate these assumptions to models of judge decision-making, and derive an expression that provides intuition about the direction and magnitude of asymptotic bias when they are not met. Under the identifying assumptions, we find that noncarceral conviction (relative to dismissal) leads to a large and long-lasting increase in recidivism for felony defendants in Virginia. In contrast, incarceration relative to noncarceral conviction leads to a short-run reduction in recidivism, consistent with incapacitation. While the identifying assumptions include a strong restriction on judge decision-making, we argue that any bias resulting from its failure is unlikely to change our qualitative conclusions. Lastly, we introduce an alternative empirical strategy, and find that it yields similar estimates. Collectively, these results suggest that noncarceral felony conviction is an important and potentially overlooked driver of recidivism. |
| JEL: | J0 K4 |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:32894 |
| By: | Lucas P. Harlaar (Vrije Universiteit Amsterdam); Jacques J.F. Commandeur (Vrije Universiteit Amsterdam); Jan A. van den Brakel (Maastricht University); Siem Jan Koopman (Vrije Universiteit Amsterdam); Niels Bos (SWOV Institute for Road Safety Research); Frits D. Bijleveld (Vrije Universiteit Amsterdam) |
| Abstract: | This paper investigates the feasibility of using earlier provisional data to improve the now- and forecasting accuracy of final and official statistics. We propose the use of a multivariate structural time series model which includes common trends and seasonal components to combine official statistics series with related auxiliary series. In this way, more precise and more timely nowcasts and forecasts of the official statistics can be obtained by exploiting the higher frequency and/or the more timely availability of the auxiliary series. The proposed method can be applied to different data sources consisting of any number of missing observations both at the beginning and at the end of the series simultaneously. Two empirical applications are presented. The first one focuses on fatal traffic accidents and the second one on labour force participation at the municipal level. The results demonstrate the effectiveness of our proposed approach in improving forecasting performance for the target series and providing early warnings to policy-makers. |
| Keywords: | nowcasting, multivariate structural time series model, seemingly unrelated time series equations, Kalman filter, road fatalities, labour market statistics |
| JEL: | C32 |
| Date: | 2024–05–30 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240037 |
| By: | Siyu Bie; Francis X. Diebold; Jingyu He; Junye Li |
| Abstract: | We explore tree-based macroeconomic regime-switching in the context of the dynamic Nelson-Siegel (DNS) yield-curve model. In particular, we customize the tree-growing algorithm to partition macroeconomic variables based on the DNS model's marginal likelihood, thereby identifying regime-shifting patterns in the yield curve. Compared to traditional Markov-switching models, our model offers clear economic interpretation via macroeconomic linkages and ensures computational simplicity. In an empirical application to U.S. Treasury bond yields, we find (1) important yield curve regime switching, and (2) evidence that macroeconomic variables have predictive power for the yield curve when the short rate is high, but not in other regimes, thereby refining the notion of yield curve ``macro-spanning". |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.12863 |
| By: | Kim Christensen; Alexei Kolokolov |
| Abstract: | We develop a model for point processes on the real line, where the intensity can be locally unbounded without inducing an explosion. In contrast to an orderly point process, for which the probability of observing more than one event over a short time interval is negligible, the bursting intensity causes an extreme clustering of events around the singularity. We propose a nonparametric approach to detect such bursts in the intensity. It relies on a heavy traffic condition, which admits inference for point processes over a finite time interval. With Monte Carlo evidence, we show that our testing procedure exhibits size control under the null, whereas it has high rejection rates under the alternative. We implement our approach on high-frequency data for the EUR/USD spot exchange rate, where the test statistic captures abnormal surges in trading activity. We detect a nontrivial amount of intensity bursts in these data and describe their basic properties. Trading activity during an intensity burst is positively related to volatility, illiquidity, and the probability of observing a drift burst. The latter effect is reinforced if the order flow is imbalanced or the price elasticity of the limit order book is large. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.06519 |
| By: | Junshu Jiang; Jordan Richards; Rapha\"el Huser; David Bolin |
| Abstract: | In econometrics, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for multivariate extremes focus on positive dependence, making them unsuitable for studying extremal dependence in financial markets where data often exhibit both positive and negative extremal dependence. To this end, we construct regular variation models on the entirety of $\mathbb{R}^d$ and develop a bivariate measure for asymmetry in the strength of extremal dependence between adjacent orthants. Our directional tail dependence (DTD) measure allows us to define the Efficient Tail Hypothesis (ETH) -- an analogue of the Efficient Market Hypothesis -- for the extremal behaviour of the market. Asymptotic results for estimators of DTD are described, and we discuss testing of the ETH via permutation-based methods and present novel tools for visualization. Empirical study of China's futures market leads to a rejection of the ETH and we identify potential profitable investment opportunities. To promote the research of microstructure in China's derivatives market, we open-source our high-frequency data, which are being collected continuously from multiple derivative exchanges. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.06661 |
| By: | Peter P. Caradonna; Christopher Turansick |
| Abstract: | We characterize those ex-ante restrictions on the random utility model which lead to identification. We first identify a simple class of perturbations which transfer mass from a suitable pair of preferences to the pair formed by swapping certain compatible lower contour sets. We show that two distributions over preferences are behaviorally equivalent if and only if they can be obtained from each other by a finite sequence of such transformations. Using this, we obtain specialized characterizations of which restrictions on the support of a random utility model yield identification, as well as of the extreme points of the set of distributions rationalizing a given data set. Finally, when a model depends smoothly on some set of parameters, we show that under mild topological assumptions, identification is characterized by a straightforward, local test. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.06547 |
| By: | Tianqi Wang; Shubham Singh |
| Abstract: | Inspired by recent advances in Kolmogorov-Arnold Networks (KANs), we introduce a novel approach to latent factor conditional asset pricing models. While previous machine learning applications in asset pricing have predominantly used Multilayer Perceptrons with ReLU activation functions to model latent factor exposures, our method introduces a KAN-based autoencoder which surpasses MLP models in both accuracy and interpretability. Our model offers enhanced flexibility in approximating exposures as nonlinear functions of asset characteristics, while simultaneously providing users with an intuitive framework for interpreting latent factors. Empirical backtesting demonstrates our model's superior ability to explain cross-sectional risk exposures. Moreover, long-short portfolios constructed using our model's predictions achieve higher Sharpe ratios, highlighting its practical value in investment management. |
| Date: | 2024–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2408.02694 |
| By: | Ankel-Peters, Jörg; Brodeur, Abel; Dreber, Anna; Johannesson, Magnus; Neubauer, Florian; Rose, Julian |
| Abstract: | Robustness reproductions and replicability discussions are on the rise in response to concerns about a potential credibility crisis in economics. This paper proposes a protocol to structure reproducibility and replicability assessments, with a focus on robustness. Starting with a computational reproduction upon data availability, the protocol encourages replicators to prespecify robustness tests, prior to implementing them. The protocol contains three different reporting tools to streamline the presentation of results. Beyond reproductions, our protocol assesses adherence to the pre-analysis plans in the replicated papers as well as external and construct validity. Our ambition is to put often controversial debates between replicators and replicated authors on a solid basis and contribute to an improved replication culture in economics. |
| Keywords: | replication, reproducibility, robustness, research transparency, meta-science |
| JEL: | A11 C18 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:i4rdps:143 |