Bayesian quantile regression methods

This paper is a study of the application of Bayesian exponentially tilted empirical likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys' method. For regression quantiles we derive the asymptotic form of the posterior density. We also examine Markov chain Monte Carlo simulations with a proposal density formed from an overdispersed version of the limiting normal density. We show that the algorithm works well even in models with an endogenous regressor when the instruments are not too weak. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian analysis of a Tobit quantile regression model

This paper develops a Bayesian framework for Tobit quantile regression. Our approach is organized around a likelihood function that is based on the asymmetric Laplace distribution, a choice that turns out to be natural in this context. We discuss families of prior distributions on the quantile regression vector that lead to proper posterior distributions with finite moments. We show how the posterior distribution can be sampled and summarized by Markov chain Monte Carlo methods. A method for comparing alternative quantile regression models is also developed and illustrated. The techniques are illustrated with both simulated and real data. In particular, in an empirical comparison, our approach out-performed two other common classical estimators.     

The dynamics of changes in the female wage distribution in the USA: a quantile regression approach

This paper examines the female wage structure focusing on changes at different points in the wage distribution. Newly developed quantile regression methods are used in analysing data from the March Current Population Survey. The results show that while the most significant changes for the less skilled women took place at the bottom of the wage distribution, for the more skilled groups changes occurred at both ends of the distribution. Consequently, wage inequality decreased for the high-school graduates and increased for the younger college graduates. Furthermore, the more highly skilled women experienced the steepest gain in wages regardless of their position in the distribution. © 1998 John Wiley & Sons, Ltd.     

Corporate social responsibility and corporate performance: a quantile regression approach

This paper investigates the impact of corporate social responsibility activities on corporate performance. In view of the inconsistent empirical findings in the literature, and the limitations of least squares regressions, we adopt a quantile regression method to fill this gap in the literature. An important finding is that the sensitivity of a company’s performance to its engagement in corporate social responsibility activities does not vary with the quantile location of the firm’s performance level, and the engagement in corporate social responsibility activities has a significant positive relation with corporate performance across all quantiles. This study argues that undertaking corporate social responsibility leads to greater financial returns than the related costs. Therefore, this study concludes that engaging in corporate social responsibility is beneficial for firms, and thus worth implementing.     

Determinants of house prices in Istanbul: a quantile regression approach

This paper uses quantile regression methods where a hedonic equation is estimated for each quantile of the conditional distribution of housing prices. The survey data are used to investigate the relationship between house prices and housing characteristics in Istanbul. This data set includes some housing characteristics of the dwellings like numbers of room, bathroom, heating system, location of house etc. In the results of this paper show some similarities and differences from earlier studies on housing prices. We find that age, cable tv, security, heating system, garage, kitchen area, increasing numbers of room and bathroom increase the house prices. Our findings also show that side variable which is a special factor for Istanbul real estate market has negative effect on the prices. It is clear that the factors of housing prices can change because of the properties of country, region or city. The results of this study may give some important interpretations for developing real estate market.     

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.     

Endogeneity in quantile regression models: A control function approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature.     

Decomposition of differences in distribution using quantile regression

This paper proposes a semiparametric estimator of distribution functions in the presence of covariates. The method is based on the estimation of the conditional distribution by quantile regression. The conditional distribution is then integrated over the range of covariates. Counterfactual distributions can be estimated, allowing the decomposition of changes in distribution into three factors: coefficients, covariates and residuals. Sources of changes in wage inequality in the USA between 1973 and 1989 are examined. Unlike most of the literature, we find that residuals account for only 20% of the explosion of inequality in the 80s.     

Stress-testing US bank holding companies: A dynamic panel quantile regression approach

We propose an econometric framework for estimating capital shortfalls of bank holding companies (BHCs) under pre-specified macroeconomic scenarios. To capture the nonlinear dynamics of bank losses and revenues during periods of financial stress, we use a fixed effects quantile autoregressive (FE-QAR) model with exogenous macroeconomic covariates, an approach that delivers a superior out-of-sample forecasting performance relative to the standard linear framework. According to the out-of-sample forecasts, the realized net charge-offs during the 2007–09 crisis fall within the multi-step-ahead density forecasts implied by the FE-QAR model, but are frequently outside the density forecasts generated using the corresponding linear model. This difference reflects the fact that the linear specification substantially underestimates loan losses, especially for real estate loan portfolios. Employing the macroeconomic stress scenario used in CCAR 2012, we use the density forecasts generated by the FE-QAR model to simulate capital shortfalls for a panel of large BHCs. For almost all institutions in the sample, the FE-QAR model generates capital shortfalls that are considerably higher than those implied by its linear counterpart, which suggests that our approach has the potential to detect emerging vulnerabilities in the financial system.     

Measuring systemic risk of the Chinese banking industry: A wavelet-based quantile regression approach

In systemic risk measure, a large amount of literature has emerged, but few of them take into account the multi-scale natures of financial data. Considering these natures, we develop a novel W-QR-CoVaR method to measure systemic risk. To be specific, the W-QR-CoVaR method combines the wavelet multiresolution analysis (MRA) with the conditional value-at-risk (CoVaR) method based on the quantile regression (QR) framework. We then apply it to measure the systemic risk in the Chinese banking industry covering the period from September 2007 to September 2018. Our experiment results show that the hybrid W-QR-CoVaR method performs better than the traditional CoVaR method in terms of predictive accuracy. Furthermore, we also explore the relation between the systemic risk contribution of each individual bank and the bank-specific characteristics. Size and leverage appear to be the most robustness determinants. The findings suggest that regulators should pay more attention to the banks with smaller size and higher leverage.     

Health and political regimes: Evidence from quantile regression

This study investigates how political regimes affect health conditions such as infant and child mortality rates and life expectancy using data from 180 countries observed between 1960 and 2013. Panel quantile regression is used to examine the effects at different intervals throughout the distribution of health outcomes. The estimation results indicate that democracy has significant positive effects on health outcomes and that its impacts are greater when health outcomes are worse. These results are robust to different democracy and health indices. The effects of different types of democracies and dictatorships are also considered, that is parliamentary, mixed (semi-presidential) and presidential democracies, and civilian, military and royal dictatorships. The parliamentary form of democracy has the largest positive impact on health outcomes at the worst quantile of health outcomes, although the difference in the impacts of the three types of democracies is not necessarily large. Furthermore, all types of dictatorships have a negative impact on health outcomes, with military dictatorship having the worst outcome when health outcomes are worse. Finally, the effects of democratization on health outcomes are significantly positive when the health outcomes are worse.     

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.     

Exact inference for Laplace distribution under progressive Type-II censoring based on BLUEs

In this paper, upon using the known expressions for the Best Linear Unbiased Estimators (BLUEs) of the location and scale parameters of the Laplace distribution based on a progressively Type-II right censored sample, we derive the exact moment generating function (MGF) of the linear combination of standard Laplace order statistics. By using this MGF, we obtain the exact density function of the linear combination. This density function is then utilized to develop exact marginal confidence intervals (CIs) for the location and scale parameters through some pivotal quantities. Next, we derive the exact density of the BLUEs-based quantile estimator and use it to develop exact CIs for the population quantile. A brief mention is made about the reliability and cumulative hazard functions and as to how exact CIs can be constructed for these functions based on BLUEs. A Monte Carlo simulation study is then carried out to evaluate the performance of the developed inferential results. Finally, an example is presented to illustrate the point and interval estimation methods developed here.     

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.     

A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model

Computationally efficient methods for Bayesian analysis of seemingly unrelated regression (SUR) models are described and applied that involve the use of a direct Monte Carlo (DMC) approach to calculate Bayesian estimation and prediction results using diffuse or informative priors. This DMC approach is employed to compute Bayesian marginal posterior densities, moments, intervals and other quantities, using data simulated from known models and also using data from an empirical example involving firms’ sales. The results obtained by the DMC approach are compared to those yielded by the use of a Markov Chain Monte Carlo (MCMC) approach. It is concluded from these comparisons that the DMC approach is worthwhile and applicable to many SUR and other problems.     

An integrated maximum score estimator for a generalized censored quantile regression model

Quantile regression techniques have been widely used in empirical economics. In this paper, we consider the estimation of a generalized quantile regression model when data are subject to fixed or random censoring. Through a discretization technique, we transform the censored regression model into a sequence of binary choice models and further propose an integrated smoothed maximum score estimator by combining individual binary choice models, following the insights of Horowitz (1992) and Manski (1985). Unlike the estimators of Horowitz (1992) and Manski (1985), our estimators converge at the usual parametric rate through an integration process. In the case of fixed censoring, our approach overcomes a major drawback of existing approaches associated with the curse-of-dimensionality problem. Our approach for the fixed censored case can be extended readily to the case with random censoring for which other existing approaches are no longer applicable. Both of our estimators are consistent and asymptotically normal. A simulation study demonstrates that our estimators perform well in finite samples.