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on Econometrics |
| By: | Grigory Franguridi; Lidia Kosenkova |
| Abstract: | It has long been established that, if a panel dataset suffers from attrition, auxiliary (refreshment) sampling restores full identification under additional assumptions that still allow for nontrivial attrition mechanisms. Such identification results rely on implausible assumptions about the attrition process or lead to theoretically and computationally challenging estimation procedures. We propose an alternative identifying assumption that, despite its nonparametric nature, suggests a simple estimation algorithm based on a transformation of the empirical cumulative distribution function of the data. This estimation procedure requires neither tuning parameters nor optimization in the first step, i.e. has a closed form. We prove that our estimator is consistent and asymptotically normal and demonstrate its good performance in simulations. We provide an empirical illustration with income data from the Understanding America Study. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.11263 |
| By: | Leonard Goff; D\'esir\'e K\'edagni; Huan Wu |
| Abstract: | In this paper, we propose a simple method for testing identifying assumptions in parametric separable models, namely treatment exogeneity, instrument validity, and/or homoskedasticity. We show that the testable implications can be written in the intersection bounds framework, which is easy to implement using the inference method proposed in Chernozhukov, Lee, and Rosen (2013), and the Stata package of Chernozhukov et al. (2015). Monte Carlo simulations confirm that our test is consistent and controls size. We use our proposed method to test the validity of some commonly used instrumental variables, such as the average price in other markets in Nevo and Rosen (2012), the Bartik instrument in Card (2009), and the test rejects both instrumental variable models. When the identifying assumptions are rejected, we discuss solutions that allow researchers to identify some causal parameters of interest after relaxing functional form assumptions. We show that the IV model is nontestable if no functional form assumption is made on the outcome equation, when there exists a one-to-one mapping between the continuous treatment variable, the instrument, and the first-stage unobserved heterogeneity. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.12098 |
| By: | Christopher D. Walker |
| Abstract: | Conditional moment equality models are regularly encountered in empirical economics, yet they are difficult to estimate. These models map a conditional distribution of data to a structural parameter via the restriction that a conditional mean equals zero. Using this observation, I introduce a Bayesian inference framework in which an unknown conditional distribution is replaced with a nonparametric posterior, and structural parameter inference is then performed using an implied posterior. The method has the same flexibility as frequentist semiparametric estimators and does not require converting conditional moments to unconditional moments. Importantly, I prove a semiparametric Bernstein-von Mises theorem, providing conditions under which, in large samples, the posterior for the structural parameter is approximately normal, centered at an efficient estimator, and has variance equal to the Chamberlain (1987) semiparametric efficiency bound. As byproducts, I show that Bayesian uncertainty quantification methods are asymptotically optimal frequentist confidence sets and derive low-level sufficient conditions for Gaussian process priors. The latter sheds light on a key prior stability condition and relates to the numerical aspects of the paper in which these priors are used to predict the welfare effects of price changes. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.16017 |
| By: | Jamil, Haziq; Moustaki, Irini; Skinner, Chris J. |
| Abstract: | This paper discusses estimation and limited-information goodness-of-fit test statistics in factor models for binary data using pairwise likelihood estimation and sampling weights. The paper extends the applicability of pairwise likelihood estimation for factor models with binary data to accommodate complex sampling designs. Additionally, it introduces two key limited-information test statistics: the Pearson chi-squared test and the Wald test. To enhance computational efficiency, the paper introduces modifications to both test statistics. The performance of the estimation and the proposed test statistics under simple random sampling and unequal probability sampling is evaluated using simulated data. |
| Keywords: | composite likelihood; pairwise likelihood; goodness-of-fit tests; complex sampling; factor analysis |
| JEL: | C1 |
| Date: | 2024–10–12 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:125419 |
| By: | Guo Yan |
| Abstract: | We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its computational efficiency. For instance, even when assuming a normal error distribution as in probit models, commonly used sieves for approximating an unknown function of covariates can lead to a large-dimensional optimization problem when the number of covariates is moderate. Our approach, motivated by kernel methods in machine learning, views certain reproducing kernel Hilbert spaces as special sieve spaces, coupled with spectral cut-off regularization for dimension reduction. We establish the consistency of the proposed estimator for both the systematic function of covariates and the distribution function of the error term, and asymptotic normality of the plug-in estimator for weighted average partial derivatives. Simulation studies show that, compared to parametric estimation methods, the proposed method effectively improves finite sample performance in cases of misspecification, and has a rather mild efficiency loss if the model is correctly specified. Using administrative data on the grant decisions of US asylum applications to immigration courts, along with nine case-day variables on weather and pollution, we re-examine the effect of outdoor temperature on court judges' "mood", and thus, their grant decisions. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.15734 |
| By: | Sung Jae Jun; Sokbae Lee |
| Abstract: | The persuasion rate is a key parameter for measuring the causal effect of a directional message on influencing the recipient's behavior. Its identification analysis has largely relied on the availability of credible instruments, but the requirement is not always satisfied in observational studies. Therefore, we develop a framework for identifying, estimating, and conducting inference for the average persuasion rates on the treated using a difference-in-differences approach. The average treatment effect on the treated is a standard parameter with difference-in-differences, but it underestimates the persuasion rate in our setting. Our estimation and inference methods include regression-based approaches and semiparametrically efficient estimators. Beginning with the canonical two-period case, we extend the framework to staggered treatment settings, where we show how to conduct rich analyses like the event-study design. We revisit previous studies of the British election and the Chinese curriculum reform to illustrate the usefulness of our methodology. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.14871 |
| By: | Sylvia Klosin |
| Abstract: | This paper identifies an important bias - termed dynamic bias - in fixed effects panel estimators that arises when dynamic feedback is ignored in the estimating equation. Dynamic feedback occurs if past outcomes impact current outcomes, a feature of many settings ranging from economic growth to agricultural and labor markets. When estimating equations omit past outcomes, dynamic bias can lead to significantly inaccurate treatment effect estimates, even with randomly assigned treatments. This dynamic bias in simulations is larger than Nickell bias. I show that dynamic bias stems from the estimation of fixed effects, as their estimation generates confounding in the data. To recover consistent treatment effects, I develop a flexible estimator that provides fixed-T bias correction. I apply this approach to study the impact of temperature shocks on GDP, a canonical example where economic theory points to an important feedback from past to future outcomes. Accounting for dynamic bias lowers the estimated effects of higher yearly temperatures on GDP growth by 10% and GDP levels by 120%. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.16112 |
| By: | Bian, Zeyu; Shi, Chengchun; Qi, Zhengling; Wang, Lan |
| Abstract: | Abstract–: This work aims to study off-policy evaluation (OPE) under scenarios where two key reinforcement learning (RL) assumptions—temporal stationarity and individual homogeneity are both violated. To handle the “double inhomogeneities”, we propose a class of latent factor models for the reward and transition functions, under which we develop a general OPE framework that consists of both model-based and model-free approaches. To our knowledge, this is the first article that develops statistically sound OPE methods in offline RL with double inhomogeneities. It contributes to a deeper understanding of OPE in environments, where standard RL assumptions are not met, and provides several practical approaches in these settings. We establish the theoretical properties of the proposed value estimators and empirically show that our approach outperforms state-of-the-art methods. Finally, we illustrate our method on a dataset from the Medical Information Mart for Intensive Care. An R implementation of the proposed procedure is available athttps://github.com/ZeyuBian/2FEOPE. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. |
| Keywords: | double inhomogeneities; off-policy evaluation; reinforcement learning; two-way fixed model |
| JEL: | C1 |
| Date: | 2024–10–11 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:124630 |
| By: | Eyo I. Herstad; Myungkou Shin |
| Abstract: | This paper develops an econometric model to analyse heterogeneity in peer effects in network data with endogenous spillover across units. We introduce a rank-dependent peer effect model that captures how the relative ranking of a peer outcome shapes the influence units have on one another, by modeling the peer effect to be linear in ordered peer outcomes. In contrast to the traditional linear-in-means model, our approach allows for greater flexibility in peer effect by accounting for the distribution of peer outcomes as well as the size of peer groups. Under a minimal condition, the rank-dependent peer effect model admits a unique equilibrium and is therefore tractable. Our simulations show that that estimation performs well in finite samples given sufficient covariate strength. We then apply our model to educational data from Norway, where we see that higher-performing students disproportionately drive GPA spillovers. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.14317 |
| By: | Apoorva Lal; Alexander Fischer; Matthew Wardrop |
| Abstract: | Large-scale randomized experiments are seldom analyzed using panel regression methods because of computational challenges arising from the presence of millions of nuisance parameters. We leverage Mundlak's insight that unit intercepts can be eliminated by using carefully chosen averages of the regressors to rewrite several common estimators in a form that is amenable to weighted-least squares estimation with frequency weights. This renders regressions involving arbitrary strata intercepts tractable with very large datasets, optionally with the key compression step computed out-of-memory in SQL. We demonstrate that these methods yield more precise estimates than other commonly used estimators, and also find that the compression strategy greatly increases computational efficiency. We provide in-memory (pyfixest) and out-of-memory (duckreg) python libraries to implement these estimators. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.09952 |
| By: | Andrew Fleck; Edward Furman; Yang Shen |
| Abstract: | Nowadays insurers have to account for potentially complex dependence between risks. In the field of loss reserving, there are many parametric and non-parametric models attempting to capture dependence between business lines. One common approach has been to use additive background risk models (ABRMs) which provide rich and interpretable dependence structures via a common shock model. Unfortunately, ABRMs are often restrictive. Models that capture necessary features may have impractical to estimate parameters. For example models without a closed-form likelihood function for lack of a probability density function (e.g. some Tweedie, Stable Distributions, etc). We apply a modification of the continuous generalised method of moments (CGMM) of [Carrasco and Florens, 2000] which delivers comparable estimators to the MLE to loss reserving. We examine models such as the one proposed by [Avanzi et al., 2016] and a related but novel one derived from the stable family of distributions. Our CGMM method of estimation provides conventional non-Bayesian estimates in the case where MLEs are impractical. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.14985 |
| By: | Hongqi Chen; Ji Hyung Lee |
| Abstract: | This paper advances a variable screening approach to enhance conditional quantile forecasts using high-dimensional predictors. We have refined and augmented the quantile partial correlation (QPC)-based variable screening proposed by Ma et al. (2017) to accommodate $\beta$-mixing time-series data. Our approach is inclusive of i.i.d scenarios but introduces new convergence bounds for time-series contexts, suggesting the performance of QPC-based screening is influenced by the degree of time-series dependence. Through Monte Carlo simulations, we validate the effectiveness of QPC under weak dependence. Our empirical assessment of variable selection for growth-at-risk (GaR) forecasting underscores the method's advantages, revealing that specific labor market determinants play a pivotal role in forecasting GaR. While prior empirical research has predominantly considered a limited set of predictors, we employ the comprehensive Fred-QD dataset, retaining a richer breadth of information for GaR forecasts. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.15097 |
| By: | Sylvia Kaufmann (Study Center Gerzensee); Markus Pape (Ruhr-University Bochum) |
| Abstract: | We use the geometric representation of factor models to represent the factor loading structure by sets corresponding to unit-specific non-zero loadings. We formulate global and local identification conditions based on set conditions. We propose two algorithms to efficiently evaluate Sato (1992)’s counting rule. We demonstrate the efficiency and the performance of the algorithms with a simulation study. An application to exchange rate returns illustrates the approach. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:szg:worpap:2406 |
| By: | Yong Li (Renmin University of China); Zhou Wu (Zhejiang University); Jun Yu (University of Macau); Tao Zeng (Zhejiang University) |
| Abstract: | This note gives a rigorous justification to Akaike information criterion (AIC) and Takeuchi information criterion (TIC). The existing literature has shown that, when the candidate model is a good approximation of the true data generating process (DGP), AIC is an asymptotic unbiased estimator of the expected Kullback-Leibler divergence between the DGP and the plug-in predictive distribution. When the candidate model is misspecified, TIC can be regraded as a robust version of AIC with its justification following a similar line of argument. However, the justifications in current literature are predominantly confined to the iid scenario. In this note, we establish the asymptotic unbiasedness of AIC and TIC under certain regular conditions. These conditions are applicable in various scenarios, encompassing weakly dependent data. |
| JEL: | C11 C52 C25 C22 C32 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202420 |
| By: | Christopher Walters (UC Berkeley) |
| Abstract: | Labor economists increasingly work in empirical contexts with large numbers of unit-specific parameters. These settings include a growing number of value-added studies measuring causal effects of individual units like firms, managers, neighborhoods, teachers, schools, doctors, hospitals, police officers, and judges. Empirical Bayes (EB) methods provide a powerful toolkit for value-added analysis. The EB approach leverages distributional information from the full population of units to refine predictions of value-added for each individual, leading to improved estimators and decision rules. This chapter offers an overview of EB methods in labor economics, focusing on properties that make EB useful for value-added studies and practical guidance for EB implementation. Applications to school value-added in Boston and employer-level discrimination in the US labor market illustrate the EB toolkit in action. |
| Keywords: | empirical Bayes, labor economics, value-added, shrinkage, Bayesian methods, multiple testing |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:crm:wpaper:2422 |
| By: | Luca Vincenzo Ballestra; Enzo D'Innocenzo; Christian Tezza |
| Abstract: | We introduce a novel GARCH model that integrates two sources of uncertainty to better capture the rich, multi-component dynamics often observed in the volatility of financial assets. This model provides a quasi closed-form representation of the characteristic function for future log-returns, from which semi-analytical formulas for option pricing can be derived. A theoretical analysis is conducted to establish sufficient conditions for strict stationarity and geometric ergodicity, while also obtaining the continuous-time diffusion limit of the model. Empirical evaluations, conducted both in-sample and out-of-sample using S\&P500 time series data, show that our model outperforms widely used single-factor models in predicting returns and option prices. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.14585 |