arXiv subjects

Iván Fernández-Val

Publications and source records attributed to Iván Fernández-Val.

31 records · Page 2Linked to original sources

arXiv2020

Fast Algorithms for the Quantile Regression Process

The widespread use of quantile regression methods depends crucially on the existence of fast algorithms. Despite numerous algorithmic improvements, the computation time is still non-negligible because researchers often estimate many quantile regressions and use the bootstrap for inference. We suggest two new fast algorithms for the estimation of a sequence of quantile regressions at many quantile indexes. The first algorithm applies the preprocessing idea of Portnoy and Koenker (1997) but exploits a previously estimated quantile regression to guess the sign of the residuals. This step allows for a reduction of the effective sample size. The second algorithm starts from a previously estimated quantile regression at a similar quantile index and updates it using a single Newton-Raphson iteration. The first algorithm is exact, while the second is only asymptotically equivalent to the traditional quantile regression estimator. We also apply the preprocessing idea to the bootstrap by using the sample estimates to guess the sign of the residuals in the bootstrap sample. Simulations show that our new algorithms provide very large improvements in computation time without significant (if any) cost in the quality of the estimates. For instance, we divide by 100 the time required to estimate 99 quantile regressions with 20 regressors and 50,000 observations.

econ.EM↗

arXiv2019

SortedEffects: Sorted Causal Effects in R

Chernozhukov et al. (2018) proposed the sorted effect method for nonlinear regression models. This method consists of reporting percentiles of the partial effects in addition to the average commonly used to summarize the heterogeneity in the partial effects. They also proposed to use the sorted effects to carry out classification analysis where the observational units are classified as most and least affected if their causal effects are above or below some tail sorted effects. The R package SortedEffects implements the estimation and inference methods therein and provides tools to visualize the results. This vignette serves as an introduction to the package and displays basic functionality of the functions within.

econ.EM↗

arXiv2019

Nonlinear Factor Models for Network and Panel Data

Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer of incidental parameter bias. We show how models with factor structures can also be applied to capture important features of network data such as reciprocity, degree heterogeneity, homophily in latent variables and clustering. We illustrate this applicability with an empirical example to the estimation of a gravity equation of international trade between countries using a Poisson model with multiple factors.

stat.ME↗

arXiv2019

Semiparametric Estimation of Structural Functions in Nonseparable Triangular Models

Triangular systems with nonadditively separable unobserved heterogeneity provide a theoretically appealing framework for the modelling of complex structural relationships. However, they are not commonly used in practice due to the need for exogenous variables with large support for identification, the curse of dimensionality in estimation, and the lack of inferential tools. This paper introduces two classes of semiparametric nonseparable triangular models that address these limitations. They are based on distribution and quantile regression modelling of the reduced form conditional distributions of the endogenous variables. We show that average, distribution and quantile structural functions are identified in these systems through a control function approach that does not require a large support condition. We propose a computationally attractive three-stage procedure to estimate the structural functions where the first two stages consist of quantile or distribution regressions. We provide asymptotic theory and uniform inference methods for each stage. In particular, we derive functional central limit theorems and bootstrap functional central limit theorems for the distribution regression estimators of the structural functions. These results establish the validity of the bootstrap for three-stage estimators of structural functions, and lead to simple inference algorithms. We illustrate the implementation and applicability of all our methods with numerical simulations and an empirical application to demand analysis.

econ.EM↗

arXiv2019

Censored Quantile Instrumental Variable Estimation with Stata

Many applications involve a censored dependent variable and an endogenous independent variable. Chernozhukov et al. (2015) introduced a censored quantile instrumental variable estimator (CQIV) for use in those applications, which has been applied by Kowalski (2016), among others. In this article, we introduce a Stata command, cqiv, that simplifes application of the CQIV estimator in Stata. We summarize the CQIV estimator and algorithm, we describe the use of the cqiv command, and we provide empirical examples.

econ.EM↗

arXiv2019

Mastering Panel 'Metrics: Causal Impact of Democracy on Growth

The relationship between democracy and economic growth is of long-standing interest. We revisit the panel data analysis of this relationship by Acemoglu, Naidu, Restrepo and Robinson (forthcoming) using state of the art econometric methods. We argue that this and lots of other panel data settings in economics are in fact high-dimensional, resulting in principal estimators -- the fixed effects (FE) and Arellano-Bond (AB) estimators -- to be biased to the degree that invalidates statistical inference. We can however remove these biases by using simple analytical and sample-splitting methods, and thereby restore valid statistical inference. We find that the debiased FE and AB estimators produce substantially higher estimates of the long-run effect of democracy on growth, providing even stronger support for the key hypothesis in Acemoglu, Naidu, Restrepo and Robinson (forthcoming). Given the ubiquitous nature of panel data, we conclude that the use of debiased panel data estimators should substantially improve the quality of empirical inference in economics.

econ.EM↗

arXiv2018

Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes

Quantile and quantile effect functions are important tools for descriptive and causal analyses due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This paper offers a simple, practical construction of simultaneous confidence bands for quantile and quantile effect functions of possibly discrete random variables. It is based on a natural transformation of simultaneous confidence bands for distribution functions, which are readily available for many problems. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling methods for observed and counterfactual distributions, and does not depend on the sampling scheme. We apply our method to characterize the distributional impact of insurance coverage on health care utilization and obtain the distributional decomposition of the racial test score gap. We find that universal insurance coverage increases the number of doctor visits across the entire distribution, and that the racial test score gap is small at early ages but grows with age due to socio economic factors affecting child development especially at the top of the distribution. These are new, interesting empirical findings that complement previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering existing inference methods invalid for obtaining uniform confidence bands for observed and counterfactual quantile functions and for their difference -- the quantile effects functions.

stat.ME↗

arXiv2018

Conditional Quantile Processes based on Series or Many Regressors

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR-series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a linear combination of series terms with quantile-specific coefficients and estimate the function-valued coefficients from the data. We develop large sample theory for the QR-series coefficient process, namely we obtain uniform strong approximations to the QR-series coefficient process by conditionally pivotal and Gaussian processes. Based on these strong approximations, or couplings, we develop four resampling methods (pivotal, gradient bootstrap, Gaussian, and weighted bootstrap) that can be used for inference on the entire QR-series coefficient function. We apply these results to obtain estimation and inference methods for linear functionals of the conditional quantile function, such as the conditional quantile function itself, its partial derivatives, average partial derivatives, and conditional average partial derivatives. Specifically, we obtain uniform rates of convergence and show how to use the four resampling methods mentioned above for inference on the functionals. All of the above results are for function-valued parameters, holding uniformly in both the quantile index and the covariate value, and covering the pointwise case as a by-product. We demonstrate the practical utility of these results with an example, where we estimate the price elasticity function and test the Slutsky condition of the individual demand for gasoline, as indexed by the individual unobserved propensity for gasoline consumption.

stat.ME↗

arXiv2018

Nonseparable Multinomial Choice Models in Cross-Section and Panel Data

Multinomial choice models are fundamental for empirical modeling of economic choices among discrete alternatives. We analyze identification of binary and multinomial choice models when the choice utilities are nonseparable in observed attributes and multidimensional unobserved heterogeneity with cross-section and panel data. We show that derivatives of choice probabilities with respect to continuous attributes are weighted averages of utility derivatives in cross-section models with exogenous heterogeneity. In the special case of random coefficient models with an independent additive effect, we further characterize that the probability derivative at zero is proportional to the population mean of the coefficients. We extend the identification results to models with endogenous heterogeneity using either a control function or panel data. In time stationary panel models with two periods, we find that differences over time of derivatives of choice probabilities identify utility derivatives "on the diagonal," i.e. when the observed attributes take the same values in the two periods. We also show that time stationarity does not identify structural derivatives "off the diagonal" both in continuous and multinomial choice panel models.

stat.ME↗

arXiv2018

Fixed Effect Estimation of Large T Panel Data Models

This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano and Hahn 2007; a section in Arellano and Bonhomme 2011) we discuss models with both individual and time effects, split-panel Jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects is our main focus, and the unifying theme is that the order of this bias is given by the simple formula p/n for all models discussed, with p the number of estimated parameters and n the total sample size.

econ.EM↗

arXiv2017

Extremal Quantile Regression: An Overview

Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants of low infant birth weights, and auction models. This chapter provides an overview of recent developments in the theory and empirics of extremal quantile regression. The advances in the theory have relied on the use of extreme value approximations to the law of the Koenker and Bassett (1978) quantile regression estimator. Extreme value laws not only have been shown to provide more accurate approximations than Gaussian laws at the tails, but also have served as the basis to develop bias corrected estimators and inference methods using simulation and suitable variations of bootstrap and subsampling. The applicability of these methods is illustrated with two empirical examples on conditional value-at-risk and financial contagion.

stat.ME↗

arXiv2016

quantreg.nonpar: An R Package for Performing Nonparametric Series Quantile Regression

The R package quantreg.nonpar implements nonparametric quantile regression methods to estimate and make inference on partially linear quantile models. quantreg.nonpar obtains point estimates of the conditional quantile function and its derivatives based on series approximations to the nonparametric part of the model. It also provides pointwise and uniform confidence intervals over a region of covariate values and/or quantile indices for the same functions using analytical and resampling methods. This paper serves as an introduction to the package and displays basic functionality of the functions contained within.

stat.CO↗

arXiv2016

Counterfactual: An R Package for Counterfactual Analysis

The Counterfactual package implements the estimation and inference methods of Chernozhukov, Fernández-Val and Melly (2013) for counterfactual analysis. The counterfactual distributions considered are the result of changing either the marginal distribution of covariates related to the outcome variable of interest, or the conditional distribution of the outcome given the covariates. They can be applied to estimate quantile treatment effects and wage decompositions. This paper serves as an introduction to the package and displays basic functionality of the commands contained within.

stat.CO↗