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on Econometrics |
| By: | Jad Beyhum; Lorenzo Tedesco; Ingrid Van Keilegom |
| Abstract: | This paper studies a semiparametric quantile regression model with endogenous variables and random right censoring. The endogeneity issue is solved using instrumental variables. It is assumed that the structural quantile of the logarithm of the outcome variable is linear in the covariates and censoring is independent. The regressors and instruments can be either continuous or discrete. The specification generates a continuum of equations of which the quantile regression coefficients are a solution. Identification is obtained when this system of equations has a unique solution. Our estimation procedure solves an empirical analogue of the system of equations. We derive conditions under which the estimator is asymptotically normal and prove the validity of a bootstrap procedure for inference. The finite sample performance of the approach is evaluated through numerical simulations. The method is illustrated by an application to the national Job Training Partnership Act study. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.01429&r= |
| By: | Max-Sebastian Dov\`i; Anders Bredahl Kock; Sophocles Mavroeidis |
| Abstract: | We consider hypothesis testing in instrumental variable regression models with few included exogenous covariates but many instruments -- possibly more than the number of observations. We show that a ridge-regularised version of the jackknifed Anderson Rubin (1949, henceforth AR) test controls asymptotic size in the presence of heteroskedasticity, and when the instruments may be arbitrarily weak. Asymptotic size control is established under weaker assumptions than those imposed for recently proposed jackknifed AR tests in the literature. Furthermore, ridge-regularisation extends the scope of jackknifed AR tests to situations in which there are more instruments than observations. Monte-Carlo simulations indicate that our method has favourable finite-sample size and power properties compared to recently proposed alternative approaches in the literature. An empirical application on the elasticity of substitution between immigrants and natives in the US illustrates the usefulness of the proposed method for practitioners. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.03259&r= |
| By: | Jieun Lee |
| Abstract: | I propose Robust Rao's Score (RS) test statistic to determine endogeneity of spatial weights matrices in a spatial dynamic panel data (SDPD) model (Qu, Lee, and Yu, 2017). I firstly introduce the bias-corrected score function since the score function is not centered around zero due to the two-way fixed effects. I further adjust score functions to rectify the over-rejection of the null hypothesis under a presence of local misspecification in contemporaneous dependence over space, dependence over time, or spatial time dependence. I then derive the explicit forms of our test statistic. A Monte Carlo simulation supports the analytics and shows nice finite sample properties. Finally, an empirical illustration is provided using data from Penn World Table version 6.1. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.05563&r= |
| By: | Maria Elvira Mancino; Tommaso Mariotti; Giacomo Toscano |
| Abstract: | The main contribution of the paper is proving that the Fourier spot volatility estimator introduced in [Malliavin and Mancino, 2002] is consistent and asymptotically efficient if the price process is contaminated by microstructure noise. Specifically, in the presence of additive microstructure noise we prove a Central Limit Theorem with the optimal rate of convergence $n^{1/8}$. The result is obtained without the need for any manipulation of the original data or bias correction. Moreover, we complete the asymptotic theory for the Fourier spot volatility estimator in the absence of noise, originally presented in [Mancino and Recchioni, 2015], by deriving a Central Limit Theorem with the optimal convergence rate $n^{1/4}$. Finally, we propose a novel feasible adaptive method for the optimal selection of the parameters involved in the implementation of the Fourier spot volatility estimator with noisy high-frequency data and provide support to its accuracy both numerically and empirically. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.08967&r= |
| By: | Daniel J. Lewis; Davide Melcangi; Laura Pilossoph; Aidan Toner-Rodgers |
| Abstract: | We propose a new, computationally-efficient way to approximate the “grouped fixed-effects” (GFE) estimator of Bonhomme and Manresa (2015), which estimates grouped patterns of unobserved heterogeneity. To do so, we generalize the fuzzy C-means objective to regression settings. As the regularization parameter m approaches 1, the fuzzy clustering objective converges to the GFE objective; moreover, we recast this objective as a standard Generalized Method of Moments problem. We replicate the empirical results of Bonhomme and Manresa (2015) and show that our estimator delivers almost identical estimates. In simulations, we show that our approach delivers improvements in terms of bias, classification accuracy, and computational speed. |
| Keywords: | clustering; unobserved heterogeneity; panel data |
| JEL: | C23 C63 |
| Date: | 2022–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fednsr:94840&r= |
| By: | Gabriel Okasa; Kenneth A. Younge |
| Abstract: | Researchers frequently test and improve model fit by holding a sample constant and varying the model. We propose methods to test and improve sample fit by holding a model constant and varying the sample. Much as the bootstrap is a well-known method to re-sample data and estimate the uncertainty of the fit of parameters in a model, we develop Sample Fit Reliability (SFR) as a set of computational methods to re-sample data and estimate the reliability of the fit of observations in a sample. SFR uses Scoring to assess the reliability of each observation in a sample, Annealing to check the sensitivity of results to removing unreliable data, and Fitting to re-weight observations for more robust analysis. We provide simulation evidence to demonstrate the advantages of using SFR, and we replicate three empirical studies with treatment effects to illustrate how SFR reveals new insights about each study. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.06631&r= |
| By: | Christian, Paul; Barrett, Christopher B. |
| Abstract: | The long-recognized spurious regressions problem can lead to mistaken inference in panel instrumental variables (IV) estimation. Spurious correlations arising from correlated cycles in finite time horizons can make irrelevant instruments appear strong with signable consequences for estimated IV coefficients, or interfere with valid of inference of causal effects from IV coefficients estimated using relevant instruments. The inclusion of time fixed effects in interacted specifications does not always resolve these problems. We demonstrate these concerns by revisiting recent studies of the causal origins of conflict. We offer diagnostic and corrective recommendations for avoiding the pitfalls arising from time series exhibiting persistence. |
| Keywords: | Instrumental Variables,Conflict,Economic Shocks,Panel Data |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:i4rdps:1&r= |
| By: | Robert Adamek; Stephan Smeekes; Ines Wilms |
| Abstract: | In this paper, we estimate impulse responses by local projections in high-dimensional settings. We use the desparsified (de-biased) lasso to estimate the high-dimensional local projections, while leaving the impulse response parameter of interest unpenalized. We establish the uniform asymptotic normality of the proposed estimator under general conditions. Finally, we demonstrate small sample performance through a simulation study and consider two canonical applications in macroeconomic research on monetary policy and government spending. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.03218&r= |
| By: | Sourabh Balgi; Jose M. Pe\~na; Adel Daoud |
| Abstract: | We propose a new sensitivity analysis model that combines copulas and normalizing flows for causal inference under unobserved confounding. We refer to the new model as $\rho$-GNF ($\rho$-Graphical Normalizing Flow), where $\rho{\in}[-1,+1]$ is a bounded sensitivity parameter representing the backdoor non-causal association due to unobserved confounding modeled using the most well studied and widely popular Gaussian copula. Specifically, $\rho$-GNF enables us to estimate and analyse the frontdoor causal effect or average causal effect (ACE) as a function of $\rho$. We call this the $\rho_{curve}$. The $\rho_{curve}$ enables us to specify the confounding strength required to nullify the ACE. We call this the $\rho_{value}$. Further, the $\rho_{curve}$ also enables us to provide bounds for the ACE given an interval of $\rho$ values. We illustrate the benefits of $\rho$-GNF with experiments on simulated and real-world data in terms of our empirical ACE bounds being narrower than other popular ACE bounds. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.07111&r= |
| By: | Luca Aiello; Matteo Fontana; Alessandra Guglielmi |
| Abstract: | We propose a statistical emulator for a climate-economy deterministic integrated assessment model ensemble, based on a functional regression framework. Inference on the unknown parameters is carried out through a mixed effects hierarchical model using a fully Bayesian framework with a prior distribution on the vector of all parameters. We also suggest an autoregressive parameterization of the covariance matrix of the error, with matching marginal prior. In this way, we allow for a functional framework for the discretized output of the simulators that allows their time continuous evaluation. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.05767&r= |
| By: | Michael Lechner; Jana Mareckova |
| Abstract: | Uncovering the heterogeneity of causal effects of policies and business decisions at various levels of granularity provides substantial value to decision makers. This paper develops estimation and inference procedures for multiple treatment models in a selection-on-observed-variables framework by modifying the Causal Forest approach (Wager and Athey, 2018) in several dimensions. The new estimators have desirable theoretical, computational, and practical properties for various aggregation levels of the causal effects. While an Empirical Monte Carlo study suggests that they outperform previously suggested estimators, an application to the evaluation of an active labour market pro-gramme shows their value for applied research. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.03744&r= |
| By: | Fabre, Anaïs |
| Abstract: | I use a generalized decomposition of the Two-Way Fixed Effects (TWFE) estimator to show that it is a weighted sum of five different types of two-by-two comparisons, with positive weights. I impose the same assumptions as de Chaisemartin and d’Haultfoeuille (2020a) for their heterogeneity-robust estimator to be unbiased. I find that these restrictions are sufficient for each comparison to estimate without bias the Average Treatment Effect (ATE) of the group switching treatment status. Thus, the TWFE estimator weighs each ATE positively, even with heterogeneous treatment effects. I exploit all available comparisons to build unbiased estimators of the ATT and ATE. |
| Date: | 2022–09–21 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:127362&r= |
| By: | Rutger-Jan Lange (Erasmus University Rotterdam); Bram van Os (Erasmus University Rotterdam); Dick van Dijk (Erasmus University Rotterdam) |
| Abstract: | We propose a novel observation-driven modeling framework that allows for time variation in the model’s parameters using a proximal-parameter (ProPar) update. The ProPar update is the solution to an optimization problem that maximizes the logarithmic observation density with respect to the parameter, while penalizing the squared distance of the parameter from its one-step-ahead prediction. The associated first-order condition has the form of an implicit stochastic-gradient update; replacing this implicit update with its explicit counterpart yields the popular class of score-driven models. Key advantages of the ProPar setup are stronger invertibility properties (especially under model misspecification) as well as extended (global rather than local) optimality properties. For the class of postulated observation densities whose logarithm is concave, ProPar’s robustness is evident from its (i) muted response to large shocks in endogenous and exogenous variables, (ii) stability under poorly specified learning rates, and (iii) global contractivity towards a pseudo-truth—in all cases, even under model misspecification. We illustrate the general applicability and the practical usefulness of the ProPar framework for time-varying regressions, volatility, and quantiles. |
| JEL: | C10 C32 C51 |
| Date: | 2022–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20220066&r= |
| By: | Gregory Cox |
| Abstract: | The argmax theorem is a useful result for deriving the limiting distribution of estimators in many applications. The conclusion of the argmax theorem states that the argmax of a sequence of stochastic processes converges in distribution to the argmax of a limiting stochastic process. This paper generalizes the argmax theorem to allow the maximization to take place over a sequence of subsets of the domain. If the sequence of subsets converges to a limiting subset, then the conclusion of the argmax theorem continues to hold. We demonstrate the usefulness of this generalization in three applications: estimating a structural break, estimating a parameter on the boundary of the parameter space, and estimating a weakly identified parameter. The generalized argmax theorem simplifies the proofs for existing results and can be used to prove new results in these literatures. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.08793&r= |
| By: | D Barrera (UNIANDES); S Cr\'epey (LPSM, UPCit\'e); E Gobet (CMAP, X); Hoang-Dung Nguyen (LPSM, UPCit\'e); B Saadeddine (UPS) |
| Abstract: | We propose a non-asymptotic convergence analysis of a two-step approach to learn a conditional value-at-risk (VaR) and expected shortfall (ES) in a nonparametric setting using Rademacher and Vapnik-Chervonenkis bounds. Our approach for the VaR is extended to the problem of learning at once multiple VaRs corresponding to different quantile levels. This results in efficient learning schemes based on neural network quantile and least-squares regressions. An a posteriori Monte Carlo (non-nested) procedure is introduced to estimate distances to the ground-truth VaR and ES without access to the latter. This is illustrated using numerical experiments in a Gaussian toy-model and a financial case-study where the objective is to learn a dynamic initial margin. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.06476&r= |
| By: | Bram De Rock; Domenico Moramarco |
| Abstract: | The paper proposes a framework of assess fairness in multidimensional distributions while respecting individuial preferences. We characterize a simple measure - Equivalent Advantage - that captures the distance from the current outcome to the potentially individual specific norm outcome. We introduce a non parametric approach to partially identify our measure via set identification of individual indifference curves. Our methodology is illustrated by analyzing multidimensional fairness in Belgium using the MEqIn database. Despite the set identification, we show that our analysis of the Equivalent Advantage distribution allows for interesting insights on multidimensional inequality, poverty and opportunity distribution. |
| Keywords: | fairness, multidimensional inequality, poverty, equal- ity of opportunity, Equivalent Advantage, individual preferences, nonparametric analysis |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/350076&r= |
| By: | Sheyu Li; Valentyn Litvin; Charles F. Manski |
| Abstract: | Medical journals have adhered to a reporting practice that seriously limits the usefulness of published trial findings. Medical decision makers commonly observe many patient covariates and seek to use this information to personalize treatment choices. Yet standard summaries of trial findings only partition subjects into broad subgroups, typically into binary categories. Given this reporting practice, we study the problem of inference on long mean treatment outcomes E[y(t)|x], where t is a treatment, y(t) is a treatment outcome, and the covariate vector x has length K, each component being a binary variable. The available data are estimates of {E[y(t)|xk = 0], E[y(t)|xk = 1], P(xk)}, k = 1, . . . , K reported in journal articles. We show that reported trial findings partially identify {E[y(t)|x], P(x)}. Illustrative computations demonstrate that the summaries of trial findings in journal articles may imply only wide bounds on long mean outcomes. One can realistically tighten inferences if one can combine reported trial findings with credible assumptions having identifying power, such as bounded-variation assumptions. |
| JEL: | C13 I10 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30461&r= |
| By: | Marc Hallin |
| Abstract: | For more than half a century, Manfred Deistler has been contributing to the construction of the rigorous theoretical foundations of the statistical analysis of time series and more general stochastic processes. Half a century of unremitting activity is not easily summarized in a few pages. In thisshort note, we chose to concentrate on a relatively little-known aspect of Manfred’s contribution which nevertheless had quite an impact on the development of one of the most powerful tools of contemporary time series and econometrics: dynamic factor models. |
| Keywords: | High-dimensional time series, General Dynamic Factor Models, spiked covariance model, reduced-rank process. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/350249&r= |
| By: | Benjamin Ferri (Boston College) |
| Abstract: | Shift-Share (Bartik) instruments are among the most important tools for causal identification in economics. In this paper, I crystallize main ideas underlying Shift-Share instruments - their core structure, distinctive claim to validity as instruments, history, uses, and wealth of varieties. I argue that the essence of the Shift-Share approach is to decompose the endogenous explanatory variable into an accounting identity with multiple component parts; preserve that which is most exogenous in the accounting identity, and neutralize that which is most endogenous. Following this framework, I show clearly how several variants in the literature are related. I then develop formulas for several new variants. Particularly, I show how to develop Shift-Share instruments for distribution summaries beyond the mean - the variance, skew, absolute deviation around a central point, and Gini coefficient. As an empirical application that highlights the themes of the paper, I measure the effect of earnings inequality on rates of single parenting in the U.S., comparing results using each of various alternative instruments for the Gini coefficient. |
| Keywords: | shift-share, bartik, instrumental variables, panel data, labor demand and supply, earnings inequality, single parenting |
| JEL: | C23 C26 D31 J20 R12 R23 |
| Date: | 2022–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:1053&r= |
| By: | Aur\'elien Alfonsi; Nerea Vadillo |
| Abstract: | This paper develops a new stochastic volatility model for the temperature that is a natural extension of the Ornstein-Uhlenbeck model proposed by Benth and Benth (2007). This model allows to be more conservative regarding extreme events while keeping tractability. We give a method based on Conditional Least Squares to estimate the parameters on daily data and estimate our model on eight major European cities. We then show how to calculate efficiently the average payoff of weather derivatives both by Monte-Carlo and Fourier transform techniques. This new model allows to better assess the risk related to temperature volatility. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.05918&r= |
| By: | Jordan Roulleau-Pasdeloup |
| Abstract: | I show that a class of Linear DSGE models with one endogenous state variable can be represented as a three-state Markov chain. I develop a new analytical solution method based on this representation, which amounts to solving for a vector of Markov states and one transition probability. These two objects constitute sufficient statistics to compute in closed form objects that have routinely been computed numerically: impulse response function, cumulative sum, present discount value multiplier. I apply the method to a standard New Keynesian model with habit formation. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.05081&r= |
| By: | Hugo Inzirillo; Ludovic De Villelongue |
| Abstract: | Deep learning is playing an increasingly important role in time series analysis. We focused on time series forecasting using attention free mechanism, a more efficient framework, and proposed a new architecture for time series prediction for which linear models seem to be unable to capture the time dependence. We proposed an architecture built using attention free LSTM layers that overcome linear models for conditional variance prediction. Our findings confirm the validity of our model, which also allowed to improve the prediction capacity of a LSTM, while improving the efficiency of the learning task. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.09548&r= |
| By: | Masahiro Kato; Masaaki Imaizumi; Takuya Ishihara; Toru Kitagawa |
| Abstract: | We study best-arm identification with a fixed budget and contextual (covariate) information in stochastic multi-armed bandit problems. In each round, after observing contextual information, we choose a treatment arm using past observations and current context. Our goal is to identify the best treatment arm, a treatment arm with the maximal expected reward marginalized over the contextual distribution, with a minimal probability of misidentification. First, we derive semiparametric lower bounds for this problem, where we regard the gaps between the expected rewards of the best and suboptimal treatment arms as parameters of interest, and all other parameters, such as the expected rewards conditioned on contexts, as the nuisance parameters. We then develop the "Contextual RS-AIPW strategy," which consists of the random sampling (RS) rule tracking a target allocation ratio and the recommendation rule using the augmented inverse probability weighting (AIPW) estimator. Our proposed Contextual RS-AIPW strategy is optimal because the upper bound for the probability of misidentification matches the semiparametric lower bound when the budget goes to infinity, and the gaps converge to zero. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.07330&r= |
| By: | Ziwei Mei; Peter C. B. Phillips; Zhentao Shi |
| Abstract: | The global financial crisis and Covid recession have renewed discussion concerning trend-cycle discovery in macroeconomic data, and boosting has recently upgraded the popular HP filter to a modern machine learning device suited to data-rich and rapid computational environments. This paper sheds light on its versatility in trend-cycle determination, explaining in a simple manner both HP filter smoothing and the consistency delivered by boosting for general trend detection. Applied to a universe of time series in FRED databases, boosting outperforms other methods in timely capturing downturns at crises and recoveries that follow. With its wide applicability the boosted HP filter is a useful automated machine learning addition to the macroeconometric toolkit. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.09810&r= |
| By: | Giulio Bottazzi; Taewon Kang; Federico Tamagni |
| Abstract: | We propose a new methodology to assess the degree of persistence in firm growth, based on Conditional Quantile Transition Probability Matrices (CQTPMs) and well-known indexes of intra-distributional mobility. Improving upon previous studies, the method allows for exact statistical inference about TPMs properties, at the same time controlling for spurious sources of persistence due to confounding factors such as firm size, and sector-, country- and time-effects. We apply our methodology to study manufacturing firms in the UK and four major European economies over the period 2010-2017. The findings reveal that, despite we reject the null of fully independent firm growth process, growth patterns display considerable turbulence and large bouncing effects. We also document that productivity, openness to trade, and business dynamism are the primary sources of firm growth persistence across sectors. Our approach is flexible and suitable to wide applicability in firm empirics, beyond firm growth studies, as a tool to examine persistence in other dimensions of firm performance. |
| Keywords: | Firm growth persistence; Transition probability matrices; Mobility indexes; Non-parametric statistics. |
| Date: | 2022–09–23 |
| URL: | http://d.repec.org/n?u=RePEc:ssa:lemwps:2022/27&r= |