Instrumental variable quantile regression: A robust inference approach

In this paper, we develop robust inference procedures for an instrumental variables model defined by Y=D^′α(U)$Y=D^{\prime }\alpha (U)$ where D^′α(U)$D^{\prime }\alpha (U)$ is strictly increasing in U and U is a uniform variable that may depend on D but is independent of a set of instrumental variables Z. The proposed inferential procedures are computationally convenient in typical applications and can be carried out using software available for ordinary quantile regression. Our inferential procedure arises naturally from an estimation algorithm and has the important feature of being robust to weak and partial identification and remains valid even in cases where identification fails completely. The use of the proposed procedures is illustrated through two empirical examples.     

Conditional empirical likelihood estimation and inference for quantile regression models

This paper considers two empirical likelihood-based estimation, inference, and specification testing methods for quantile regression models. First, we apply the method of conditional empirical likelihood (CEL) by Kitamura et al. [2004. Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72, 1667–1714] and Zhang and Gijbels [2003. Sieve empirical likelihood and extensions of the generalized least squares. Scandinavian Journal of Statistics 30, 1–24] to quantile regression models. Second, to avoid practical problems of the CEL method induced by the discontinuity in parameters of CEL, we propose a smoothed counterpart of CEL, called smoothed conditional empirical likelihood (SCEL). We derive asymptotic properties of the CEL and SCEL estimators, parameter hypothesis tests, and model specification tests. Important features are (i) the CEL and SCEL estimators are asymptotically efficient and do not require preliminary weight estimation; (ii) by inverting the CEL and SCEL ratio parameter hypothesis tests, asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators; and (iii) in contrast to CEL, the SCEL method can be implemented by some standard Newton-type optimization. Simulation results demonstrate that the SCEL method in particular compares favorably with existing alternatives.     

Two-stage rank estimation of quantile index models

This paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable. This class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction, thus allowing for very general forms of conditional heteroscedasticity. A two-stage approach is adopted to estimate the relevant parameters. In the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in Chaudhuri (Journal of Multivariate Analysis 39 (1991a) 246–269; Annals of Statistics 19 (1991b) 760–777) and Cavanagh (1996, Preprint). In the second stage, the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank-based objective function. The proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model.     

Instrumental quantile regression inference for structural and treatment effect models

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.     

Estimating and testing a quantile regression model with interactive effects

This paper proposes a quantile regression estimator for a model with interactive effects potentially correlated with covariates. We provide conditions under which the estimator is asymptotically Gaussian and we investigate the finite sample performance of the method. An approach to testing the specification against a competing fixed effects specification is introduced. The paper presents an application to study the effect of class size and composition on educational attainment. The evidence suggests that while smaller classes are beneficial for low performers, larger classes are beneficial for high performers. The fixed effects specification is rejected in favor of the interactive effects specification.     

SCAD‐penalized quantile regression for high‐dimensional data analysis and variable selection

The present penalized quantile variable selection methods are only applicable to finite number of predictors or do not have oracle property associated with estimator. This technique is considered as an alternative to ordinary least squares regression in case of the outliers and the heavy‐tailed errors existing in linear models. The variable selection through quantile regression with diverging number of parameters is investigated in this paper. The convergence rate of estimator with smoothly clipped absolute deviation penalty function is also studied. Moreover, the oracle property with proper selection of tuning parameter for quantile regression under certain regularity conditions is also established. In addition, the rank correlation screening method is used to accommodate ultra‐high dimensional data settings. Monte Carlo simulations demonstrate finite performance of the proposed estimator. The results of real data reveal that this approach provides substantially more information as compared with ordinary least squares, conventional quantile regression, and quantile lasso.     

Variable selection via composite quantile regression with dependent errors

We propose composite quantile regression for dependent data, in which the errors are from short‐range dependent and strictly stationary linear processes. Under some regularity conditions, we show that composite quantile estimator enjoys root‐n consistency and asymptotic normality. We investigate the asymptotic relative efficiency of composite quantile estimator to both single‐level quantile regression and least‐squares regression. When the errors have finite variance, the relative efficiency of composite quantile estimator with respect to the least‐squares estimator has a universal lower bound. Under some regularity conditions, the adaptive least absolute shrinkage and selection operator penalty leads to consistent variable selection, and the asymptotic distribution of the non‐zero coefficient is the same as that of the counterparts obtained when the true model is known. We conduct a simulation study and a real data analysis to evaluate the performance of the proposed approach.     

Asymmetric dependence structures for regional stock markets: An unconditional quantile regression approach

Owing to the asymmetry of stock markets, this study investigates the dependence structures for six regional stock markets according to different market conditions by applying the unconditional quantile regression (UQR) approach. This approach can address the traditional conditional quantile regression (CQR) approach’s limitation that its distributions are defined conditional on specific covariates. Specifically, we not only examine the detailed linkages among these six regional stock markets, but also explore the effect of global economic factors on them, given the strengthening of both international investment and the globalization of financial markets. The results show these dependence structures are often an asymmetric U-shaped or inverted U-shaped structure, which indicates that the impacts of both other geographically and economically close stock markets and economic factors are more pronounced during bear and bull markets than during normal markets, especially so in bear markets. Moreover, the UQR approach provides stronger extreme-value relationships and more significant asymmetric effects than the traditional CQR approach.     

Small‐sample testing inference in symmetric and log‐symmetric linear regression models

This paper deals with the issue of testing hypotheses in symmetric and log‐symmetric linear regression models in small and moderate‐sized samples. We focus on four tests, namely, the Wald, likelihood ratio, score, and gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement between the exact distribution of the test statistic and the corresponding chi‐squared asymptotic distribution. Bartlett and Bartlett‐type corrections typically attenuate the size distortion of the tests. These corrections are available in the literature for the likelihood ratio and score tests in symmetric linear regression models. Here, we derive a Bartlett‐type correction for the gradient test. We show that the corrections are also valid for the log‐symmetric linear regression models. We numerically compare the various tests and bootstrapped tests, through simulations. Our results suggest that the corrected and bootstrapped tests exhibit type I probability error closer to the chosen nominal level with virtually no power loss. The analytically corrected tests as well as the bootstrapped tests, including the Bartlett‐corrected gradient test derived in this paper, perform with the advantage of not requiring computationally intensive calculations. We present a real data application to illustrate the usefulness of the modified tests.     

Conditional empirical likelihood for quantile regression models

In this paper, we propose a new Bayesian quantile regression estimator using conditional empirical likelihood as the working likelihood function. We show that the proposed estimator is asymptotically efficient and the confidence interval constructed is asymptotically valid. Our estimator has low computation cost since the posterior distribution function has explicit form. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies.     

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

We study quantile regression estimation for dynamic models with partially varying coefficients so that the values of some coefficients may be functions of informative covariates. Estimation of both parametric and nonparametric functional coefficients are proposed. In particular, we propose a three stage semiparametric procedure. Both consistency and asymptotic normality of the proposed estimators are derived. We demonstrate that the parametric estimators are root-n$n$ consistent and the estimation of the functional coefficients is oracle. In addition, efficiency of parameter estimation is discussed and a simple efficient estimator is proposed. A simple and easily implemented test for the hypothesis of a varying-coefficient is proposed. A Monte Carlo experiment is conducted to evaluate the performance of the proposed estimators.     

Robust penalized quantile regression estimation for panel data

This paper investigates a class of penalized quantile regression estimators for panel data. The penalty serves to shrink a vector of individual specific effects toward a common value. The degree of this shrinkage is controlled by a tuning parameter λ$\lambda$. It is shown that the class of estimators is asymptotically unbiased and Gaussian, when the individual effects are drawn from a class of zero-median distribution functions. The tuning parameter, λ$\lambda$, can thus be selected to minimize estimated asymptotic variance. Monte Carlo evidence reveals that the estimator can significantly reduce the variability of the fixed-effect version of the estimator without introducing bias.     

Recent contributions to censored regression models

A brief survey of estimation of parameters in a censored regression model (known as the Tobit model) and some details of the properties of LAD (least absolute deviation) estimates and tests of significance of linear hypotheses are given.     

Asymptotics for panel quantile regression models with individual effects

This paper studies panel quantile regression models with individual fixed effects. We formally establish sufficient conditions for consistency and asymptotic normality of the quantile regression estimator when the number of individuals, n$n$, and the number of time periods, T$T$, jointly go to infinity. The estimator is shown to be consistent under similar conditions to those found in the nonlinear panel data literature. Nevertheless, due to the non-smoothness of the objective function, we had to impose a more restrictive condition on T$T$ to prove asymptotic normality than that usually found in the literature. The finite sample performance of the estimator is evaluated by Monte Carlo simulations.     

Asymmetric effects of corporate sustainability strategy on value creation among global automotive firms: A dynamic panel quantile regression approach

This study explores the asymmetric effects of corporate sustainability strategy on firm value at different conditioning quantiles by performing a dynamic panel quantile regression analysis on global automotive firms from 2011 to 2017. Further, this study measures the distinct effects of positive and negative corporate sustainability strategies on firm value, which has remained unconsidered as yet. The findings suggest that low-value and midvalue firms respond more strongly to positive and negative corporate sustainability strategies than high-value firms. This implies that for low-value and midvalue corporations that are in a growth phase, an investment in positive corporate sustainability strategies is essential to increase firm value by enhancing public perception of their efforts. Therefore, positive corporate sustainability strategy contributes substantially to future growth. Conversely, positive corporate sustainability strategy may not be a priority in increasing firm value for high-value corporations, because these strategies do not enhance the public's discernment of their efforts in ethics management and hence do not contribute to a future increase in value. Meanwhile, engagement in negative corporate sustainability strategy worsens firm value in all quantiles, although the effect is somewhat weaker for high-value firms. Nevertheless, however high valued and well established a firm is, it is not immune to crisis.     

Identification and inference in two-pass asset pricing models

We introduce a framework that robustifies two-pass Fama–MacBeth regressions, in the sense that confidence regions for the ex post price of risk can be derived reliably even with weak identification. This region can be unbounded, if risk price is hard to identify, empty, if the model lacks fit, and bounded otherwise. Our framework thus provides automatic weak-identification and lack-of-fit warnings, and informative model rejections. Empirically relevant simulations document attractive size and power properties. Empirical applications with well known models and data sets illustrate practical usefulness and the potential value of additional cross-sectional information.     

Time-frequency effect of crude oil and exchange rates on stock markets in BRICS countries: Evidence from wavelet quantile regression analysis

This study examines the effects of oil prices and exchange rates on stock market returns in BRICS countries (Brazil, Russia, China, India and South Africa) from a time–frequency perspective over the period 2009–2020. We use wavelet decomposition series to develop a threshold rolling window quantile regression to detect time–frequency effects at various scales. The empirical results are as follows. First, our findings confirm that the effects of both crude oil prices and exchange rates on BRICS stock returns are asymmetric. Positive shocks of crude oil have a greater impact on a bull market, whereas negative shocks have a greater impact on a bear market. Second, there is a short-term enhancement effect of crude oil and exchange rate on BRICS stock markets. In addition, volatility in the macro financial environment also exacerbates the impacts of oil prices and exchange rates on the stock market, and these fluctuations are heterogeneous. Overall, these findings provide useful insights for international investors and policy makers.     

Probabilistic energy forecasting using the nearest neighbors quantile filter and quantile regression

Parametric quantile regression is a useful tool for obtaining probabilistic energy forecasts. Nonetheless, traditional quantile regressions may be complicated to obtain using complex data mining techniques (e.g., artificial neural networks), since they are trained using a non-differentiable cost function. This article presents a method that uses a new nearest neighbors quantile filter to obtain quantile regressions independently of the data mining technique utilized and without the non-differentiable cost function. This method is subsequently validated using the dataset from the 2014 Global Energy Forecasting Competition. The results show that the method presented here is able to solve the competition’s task with a similar accuracy to the competition’s winner and in a similar timeframe, but requiring a much less powerful computer. This property may be relevant in an online forecasting service for which the fast computation of probabilistic forecasts using less powerful machines is required.