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on Econometrics |
| By: | Fotso, Chris Toumping; Sibbertsen, Philipp |
| Abstract: | This paper proposes an estimator that accounts for time variation in a regression relationship with stochastic regressors exhibiting long-range dependence, covering weak fractional cointegration as a special case. An interesting application of this estimator is its ability to handle situations where the regression coefficient changes abruptly. The parametric formulation of this estimator is introduced using the Block-Whittle-based estimation. We analyze the asymptotic properties of this estimator, including consistency and asymptotic normality. Furthermore, we examine the finite sample behavior of the estimator through Monte Carlo simulations. Additionally, we consider a real-life application to demonstrate its advantages over the constant case. |
| Keywords: | Stochastic regressors, weak fractional cointegration, Block-Whittle-based estimation, consistency, asymptotic normality |
| JEL: | C13 C22 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-730 |
| By: | Philip Marx; Elie Tamer; Xun Tang |
| Abstract: | We study the identification and estimation of heterogeneous, intertemporal treatment effects (TE) when potential outcomes depend on past treatments. First, applying a dynamic panel data model to observed outcomes, we show that instrument-based GMM estimators, such as Arellano and Bond (1991), converge to a non-convex (negatively weighted) aggregate of TE plus non-vanishing trends. We then provide restrictions on sequential exchangeability (SE) of treatment and TE heterogeneity that reduce the GMM estimand to a convex (positively weighted) aggregate of TE. Second, we introduce an adjusted inverse-propensity-weighted (IPW) estimator for a new notion of average treatment effect (ATE) over past observed treatments. Third, we show that when potential outcomes are generated by dynamic panel data models with homogeneous TE, such GMM estimators converge to causal parameters (even when SE is generically violated without conditioning on individual fixed effects). Finally, we motivate SE and compare it with parallel trends (PT) in various settings with observational data (when treatments are dynamic, rational choices under learning) or experimental data (when treatments are sequentially randomized). |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.19060 |
| By: | Michel F. C. Haddad; Martin Huber; Lucas Z. Zhang |
| Abstract: | We propose a difference-in-differences (DiD) method for a time-varying continuous treatment and multiple time periods. Our framework assesses the average treatment effect on the treated (ATET) when comparing two non-zero treatment doses. The identification is based on a conditional parallel trend assumption imposed on the mean potential outcome under the lower dose, given observed covariates and past treatment histories. We employ kernel-based ATET estimators for repeated cross-sections and panel data adopting the double/debiased machine learning framework to control for covariates and past treatment histories in a data-adaptive manner. We also demonstrate the asymptotic normality of our estimation approach under specific regularity conditions. In a simulation study, we find a compelling finite sample performance of undersmoothed versions of our estimators in setups with several thousand observations. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.21105 |
| By: | Liudas Giraitis (School of Economics and Finance, Queen Mary University of London); George Kapetanios (Kings College London); Yufei Li (Kings College London) |
| Abstract: | This paper introduces and analyses a setting with general heterogeneity in regression modelling. It shows that regression models with fixed or time-varying parameters can be estimated by OLS or time-varying OLS methods, respectively, for a very wide class of regressors and noises, not covered by existing modelling theory. The new setting allows the development of asymptotic theory and the estimation of standard errors. The proposed robust confidence interval estimators permit a high degree of heterogeneity in regressors and noise. The estimates of robust standard errors coincide with the wellknown estimator of heteroskedasticity-consistent standard errors by White (1980), but are applicable to more general circumstances than just the presence of heteroscedastic noise. They are easy to compute and perform well in Monte Carlo simulations. Their robustness, generality and ease of use make them ideal for applied work. The paper includes a brief empirical illustration. |
| Keywords: | robust estimation, structural change, time-varying parameters, non-parametric estimation |
| JEL: | C12 C51 |
| Date: | 2024–08–22 |
| URL: | https://d.repec.org/n?u=RePEc:qmw:qmwecw:983 |
| By: | Shakeeb Khan; Elie Tamer; Qingsong Yao |
| Abstract: | A class of simultaneous equation models arise in the many domains where observed binary outcomes are themselves a consequence of the existing choices of of one of the agents in the model. These models are gaining increasing interest in the computer science and machine learning literatures where they refer the potentially endogenous sample selection as the {\em selective labels} problem. Empirical settings for such models arise in fields as diverse as criminal justice, health care, and insurance. For important recent work in this area, see for example Lakkaruju et al. (2017), Kleinberg et al. (2018), and Coston et al.(2021) where the authors focus on judicial bail decisions, and where one observes the outcome of whether a defendant filed to return for their court appearance only if the judge in the case decides to release the defendant on bail. Identifying and estimating such models can be computationally challenging for two reasons. One is the nonconcavity of the bivariate likelihood function, and the other is the large number of covariates in each equation. Despite these challenges, in this paper we propose a novel distribution free estimation procedure that is computationally friendly in many covariates settings. The new method combines the semiparametric batched gradient descent algorithm introduced in Khan et al.(2023) with a novel sorting algorithms incorporated to control for selection bias. Asymptotic properties of the new procedure are established under increasing dimension conditions in both equations, and its finite sample properties are explored through a simulation study and an application using judicial bail data. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.18381 |
| By: | Attia, Iman M. |
| Abstract: | Parametric quantile regression is illustrated for the one parameter new unit Rayleigh distribution called Median Based Unit Rayleigh distribution (MBUR) distribution. The estimation process using re-parameterized maximum likelihood function is highlighted with real dataset example. The inference and goodness of fit is also explored. |
| Date: | 2024–10–17 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:x9qnt |
| By: | Andreas Petrou-Zeniou; Azeem M. Shaikh |
| Abstract: | While policymakers and researchers are often concerned with conducting inference based on a data-dependent selection, a strictly larger class of inference problems arises when considering multiple data-dependent selections, such as when selecting on statistical significance or quantiles. Given this, we study the problem of conducting inference on multiple selections, which we dub the inference on multiple winners problem. In this setting, we encounter both selective and multiple testing problems, making existing approaches either not applicable or too conservative. Instead, we propose a novel, two-step approach to the inference on multiple winners problem, with the first step modeling the selection of winners, and the second step using this model to conduct inference only on the set of likely winners. Our two-step approach reduces over-coverage error by up to 96%. We apply our two-step approach to revisit the winner's curse in the creating moves to opportunity (CMTO) program, and to study external validity issues in the microcredit literature. In the CMTO application, we find that, after correcting for the inference on multiple winners problem, we fail to reject the possibility of null effects in the majority of census tracts selected by the CMTO program. In our microcredit application, we find that heterogeneity in treatment effect estimates remains largely unaffected even after our proposed inference corrections. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.19212 |
| By: | Enzo D'Innocenzo (University of Bologna); Andre Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute); Bernd Schwaab (European Central Bank); Xin Zhang (Sveriges Riksbank) |
| Abstract: | We propose a robust semi-parametric framework for persistent time-varying extreme tail behavior, including extreme Value-at-Risk (VaR) and Expected Shortfall (ES). The framework builds on Extreme Value Theory and uses a conditional version of the Generalized Pareto Distribution (GPD) for peaks-over-threshold (POT) dynamics. Unlike earlier approaches, our model (i) has unit root-like, i.e., integrated autoregressive dynamics for the GPD tail shape, and (ii) re-scales POTs by their thresholds to obtain a more parsimonious model with only one time-varying parameter to describe the entire tail. We establish parameter regions for stationarity, ergodicity, and invertibility for the integrated time-varying parameter model and its filter, and formulate conditions for consistency and asymptotic normality of the maximum likelihood estimator. Using four exchange rate series, we illustrate how the new model captures the dynamics of extreme VaR and ES. |
| Keywords: | dynamic tail risk, integrated score-driven models, extreme value theory |
| JEL: | C22 G11 |
| Date: | 2024–11–08 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240069 |
| By: | Federico Crippa; Danil Fedchenko |
| Abstract: | This paper considers the problem of ranking objects based on their latent merits using data from pairwise interactions. Existing approaches rely on the restrictive assumption that all the interactions are either observed or missed randomly. We investigate what can be inferred about rankings when this assumption is relaxed. First, we demonstrate that in parametric models, such as the popular Bradley-Terry-Luce model, rankings are point-identified if and only if the tournament graph is connected. Second, we show that in nonparametric models based on strong stochastic transitivity, rankings in a connected tournament are only partially identified. Finally, we propose two statistical tests to determine whether a ranking belongs to the identified set. One test is valid in finite samples but computationally intensive, while the other is easy to implement and valid asymptotically. We illustrate our procedure using Brazilian employer-employee data to test whether male and female workers rank firms differently when making job transitions. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.18272 |
| By: | Florian Huber; Christian Matthes; Michael Pfarrhofer |
| Abstract: | We provide a framework for efficiently estimating impulse response functions with Local Projections (LPs). Our approach offers a Bayesian treatment for LPs with Instrumental Variables, accommodating multiple shocks and instruments per shock, accounts for autocorrelation in multi-step forecasts by jointly modeling all LPs as a seemingly unrelated system of equations, defines a flexible yet parsimonious joint prior for impulse responses based on a Gaussian Process, allows for joint inference about the entire vector of impulse responses, and uses all available data across horizons by imputing missing values. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17105 |
| By: | Facundo Arga\~naraz; Juan Carlos Escanciano |
| Abstract: | Models with Conditional Moment Restrictions (CMRs) are popular in economics. These models involve finite and infinite dimensional parameters. The infinite dimensional components include conditional expectations, conditional choice probabilities, or policy functions, which might be flexibly estimated using Machine Learning tools. This paper presents a characterization of locally debiased moments for regular models defined by general semiparametric CMRs with possibly different conditioning variables. These moments are appealing as they are known to be less affected by first-step bias. Additionally, we study their existence and relevance. Such results apply to a broad class of smooth functionals of finite and infinite dimensional parameters that do not necessarily appear in the CMRs. As a leading application of our theory, we characterize debiased machine learning for settings of treatment effects with endogeneity, giving necessary and sufficient conditions. We present a large class of relevant debiased moments in this context. We then propose the Compliance Machine Learning Estimator (CML), based on a practically convenient orthogonal relevant moment. We show that the resulting estimand can be written as a convex combination of conditional local average treatment effects (LATE). Altogether, CML enjoys three appealing properties in the LATE framework: (1) local robustness to first-stage estimation, (2) an estimand that can be identified under a minimal relevance condition, and (3) a meaningful causal interpretation. Our numerical experimentation shows satisfactory relative performance of such an estimator. Finally, we revisit the Oregon Health Insurance Experiment, analyzed by Finkelstein et al. (2012). We find that the use of machine learning and CML suggest larger positive effects on health care utilization than previously determined. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.23785 |
| By: | Kieran Marray |
| Abstract: | Empirical researchers often estimate spillover effects by fitting linear or non-linear regression models to sampled network data. Here, we show that common sampling schemes induce dependence between observed and unobserved spillovers. Due to this dependence, spillover estimates are biased, often upwards. We then show how researchers can construct unbiased estimates of spillover effects by rescaling using aggregate network statistics. Our results can be used to bound true effect sizes, determine robustness of estimates to missingness, and construct estimates when missingness depends on treatment. We apply our results to re-estimate the propagation of idiosyncratic shocks between US public firms, and peer effects amongst USAFA cadets. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17154 |
| By: | Dierkes, Maik; Fitter, Krischan; Sibbertsen, Philipp |
| Abstract: | We extend the monitoring of structural breaks in classic cointegration proposed by Wagner and Wied (2017) to explicitly allow for fractional cointegration and breaks in these fractional relations with possible deterministic trends. To estimate the parameters we use a fully modified OLS estimator and we estimate the integration order by the exact local whittle. In order to build the test statistic we establish a CUSUM test for a break in parameters or a break in the order of integration and derive the limiting distribution of the cumulative sum of the modified OLS residuals by using representations by Davidson and Hashimzade (2009) and Fox and Taqqu (1987). Using these limiting results we propose a detector and its limiting distribution as a function of fractional Brownian motions and prove the consistency of our procedure against fixed and local alternatives. The critical values for the monitoring are derived by bootstrap. In a Monte-Carlo study we show the finite sample behavior of our test and compare it to the one by Wagner and Wied (2017) in different scenarios of fractional cointegration. To conclude we show the applicability of the test by presenting the results of applying the test in the context of momentum investing. |
| Keywords: | long-memory time series, fractional cointegration, structural change, monitoring |
| JEL: | C32 C12 C52 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-728 |
| By: | Page, Garritt L.; San Martin, Ernesto; Torres Irribarra, David; Van Bellegem, Sébastien (Université catholique de Louvain, LIDAM/CORE, Belgium) |
| Abstract: | We aim to estimate school value-added dynamically in time. Our principal motivation for doing so is to establish school effectiveness persistence while taking into account the temporal dependence that typically exists in school performance from one year to the next. We propose two methods of incorporating temporal dependence in value-added models. In the first we model the random school effects that are commonly present in value-added models with an auto-regressive process. In the second approach, we incorporate dependence in value-added estimators by modeling the performance of one cohort based on the previous cohort’s perfor- mance. An identification analysis allows us to make explicit the meaning of the corresponding value-added indicators: based on these meanings, we show that each model is useful for monitoring specific aspects of school persistence. Furthermore, we carefully detail how value-added can be estimated over time. We show through simulations that ignoring temporal dependence when it exists results in diminished efficiency in value-added estimation while incorporating it results in improved estimation (even when temporal dependence is weak). Finally, we illustrate the methodology by considering two cohorts from Chile’s national standardized test in mathematics. |
| Keywords: | School value persistence ; value-added models ; temporal dependence |
| Date: | 2024–04–30 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2024009 |
| By: | A. H Nzokem |
| Abstract: | The paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes the maximum likelihood estimation (MLE) inadequate for providing parameter estimations. Based on the function characteristic and the fractional Fourier transform (FRFT), We provide a comprehensive approach to circumvent the problem and yield a good parameter estimation of the GTS probability. The methodology was applied to fit two heavily tailed data (Bitcoin and Ethereum returns) and two peaked data (S&P 500 and SPY ETF returns). For each index, the estimation results show that the six parameter estimations are statistically significant except for the local parameter ($\mu$). The goodness of fit was assessed through Kolmogorov-Smirnov, Anderson-Darling, and Pearson's chi-squared statistics. While the two-parameter geometric Brownian motion (GBM) hypothesis is always rejected, the Generalized Tempered Sable (GTS) distribution fits significantly with a very high P_value; and outperforms the Kobol, CGMY, and Bilateral Gamma distributions. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.19751 |
| By: | Tomas Espana; Victor Le Coz; Matteo Smerlak |
| Abstract: | Markowitz's optimal portfolio relies on the accurate estimation of correlations between asset returns, a difficult problem when the number of observations is not much larger than the number of assets. Using powerful results from random matrix theory, several schemes have been developed to "clean" the eigenvalues of empirical correlation matrices. By contrast, the (in practice equally important) problem of correctly estimating the eigenvectors of the correlation matrix has received comparatively little attention. Here we discuss a class of correlation estimators generalizing Kendall's rank correlation coefficient which improve the estimation of both eigenvalues and eigenvectors in data-poor regimes. Using both synthetic and real financial data, we show that these generalized correlation coefficients yield Markowitz portfolios with lower out-of-sample risk than those obtained with rotationally invariant estimators. Central to these results is a property shared by all Kendall-like estimators but not with classical correlation coefficients: zero eigenvalues only appear when the number of assets becomes proportional to the square of the number of data points. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.17366 |
| By: | Sverdrup, Erik (Monash U); Wu, Han (Two Sigma); Athey, Susan (Stanford U); Wager, Stefan (Stanford U) |
| Abstract: | Qini curves have emerged as an attractive and popular approach for evaluating the benefit of data-driven targeting rules for treatment allocation. We propose a generalization of the Qini curve to multiple costly treatment arms that quantifies the value of optimally selecting among both units and treatment arms at different budget levels. We develop an efficient algorithm for computing these curves and propose bootstrap-based confidence intervals that are exact in large samples for any point on the curve. These confidence intervals can be used to conduct hypothesis tests comparing the value of treatment targeting using an optimal combination of arms with using just a subset of arms, or with a non-targeting assignment rule ignoring covariates, at different budget levels. We demonstrate the statistical performance in a simulation experiment and an application to treatment targeting for election turnout. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:ecl:stabus:4216 |
| By: | Hayri Alper Arslan; Brantly Callaway; Tong Li |
| Abstract: | Motivated by studying the effects of marriage prospects on students' college major choices, this paper develops a new econometric test for analyzing the effects of an unobservable factor in a setting where this factor potentially influences both agents' decisions and a binary outcome variable. Our test is built upon a flexible copula-based estimation procedure and leverages the ordered nature of latent utilities of the polychotomous choice model. Using the proposed method, we demonstrate that marriage prospects significantly influence the college major choices of college graduates participating in the National Longitudinal Study of Youth (97) Survey. Furthermore, we validate the robustness of our findings with alternative tests that use stated marriage expectation measures from our data, thereby demonstrating the applicability and validity of our testing procedure in real-life scenarios. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.19947 |
| By: | Mansi Sharma; Steven Stern |
| Abstract: | We develop a new polynomial series generalization of the Weibull estimator using polynomials in log t in a Cox proportional hazards baseline hazard. We also show that we can allow the baseline hazard to depend on an observed explanatory variable. We provide two examples of how it can work: US life tables and first marriage and first birth in India. The India example shows the relationship between observed heterogeneity and duration dependence bias. |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:nys:sunysb:24-05 |
| By: | Jack Fitzgerald (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | Recent studies showing that some outcome variables do not statistically significantly differ between real-stakes and hypothetical-stakes conditions have raised methodological challenges to experimental economics' disciplinary norm that experimental choices should be incentivized with real stakes. I show that the hypothetical bias measures estimated in these studies do not econometrically identify the hypothetical biases that matter in most modern experiments. Specifically, traditional hypothetical bias measures are fully informative in 'elicitation experiments' where the researcher is uninterested in treatment effects (TEs). However, in 'intervention experiments' where TEs are of interest, traditional hypothetical bias measures are uninformative; real stakes matter if and only if TEs differ between stakes conditions. I demonstrate that traditional hypothetical bias measures are often misleading estimates of hypothetical bias for intervention experiments, both econometrically and through re-analyses of three recent hypothetical bias experiments. The fact that a given experimental outcome does not statistically significantly differ on average between stakes conditions does not imply that all TEs on that outcome are unaffected by hypothetical stakes. Therefore, the recent hypothetical bias literature does not justify abandoning real stakes in most modern experiments. Maintaining norms that favor completely or probabilistically providing real stakes for experimental choices is useful for ensuring externally valid TEs in experimental economics. |
| Keywords: | Interaction effects, meta-analysis, generalizability, bootstrap |
| JEL: | C18 C90 D91 |
| Date: | 2024–11–08 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20240070 |
| By: | Pietro Bogani; Matteo Fontana; Luca Neri; Simone Vantini |
| Abstract: | Accurate computation of robust estimates for extremal quantiles of empirical distributions is an essential task for a wide range of applicative fields, including economic policymaking and the financial industry. Such estimates are particularly critical in calculating risk measures, such as Growth-at-Risk (GaR). % and Value-at-Risk (VaR). This work proposes a conformal framework to estimate calibrated quantiles, and presents an extensive simulation study and a real-world analysis of GaR to examine its benefits with respect to the state of the art. Our findings show that CP methods consistently improve the calibration and robustness of quantile estimates at all levels. The calibration gains are appreciated especially at extremal quantiles, which are critical for risk assessment and where traditional methods tend to fall short. In addition, we introduce a novel property that guarantees coverage under the exchangeability assumption, providing a valuable tool for managing risks by quantifying and controlling the likelihood of future extreme observations. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2411.00520 |
| By: | Mustafa R. K{\i}l{\i}n\c{c}; Michael Massmann; Maximilian Ambros |
| Abstract: | This note proposes semi-parametric tests for investigating whether a stochastic process is fractionally integrated of order $\delta$, where $|\delta| |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.10749 |
| By: | Giuseppe Arbia; Vincenzo Nardelli |
| Abstract: | In the analysis of large spatial datasets, identifying and treating spatial outliers is essential for accurately interpreting geographical phenomena. While spatial correlation measures, particularly Local Indicators of Spatial Association (LISA), are widely used to detect spatial patterns, the presence of abnormal observations frequently distorts the landscape and conceals critical spatial relationships. These outliers can significantly impact analysis due to the inherent spatial dependencies present in the data. Traditional influence function (IF) methodologies, commonly used in statistical analysis to measure the impact of individual observations, are not directly applicable in the spatial context because the influence of an observation is determined not only by its own value but also by its spatial location, its connections with neighboring regions, and the values of those neighboring observations. In this paper, we introduce a local version of the influence function (LIF) that accounts for these spatial dependencies. Through the analysis of both simulated and real-world datasets, we demonstrate how the LIF provides a more nuanced and accurate detection of spatial outliers compared to traditional LISA measures and local impact assessments, improving our understanding of spatial patterns. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.18261 |