Standard Quantile Regression Research Articles

Analyzing the impacts of renewable energy, patents, and trade on carbon emissions-evidence from the novel method of MMQR.

Achieving sustainable development necessitates proactive measures to mitigate the economy's negative impact on environmental standards. A new empirical association between renewable energy patent innovation and net international trade on carbon emissions in ASEAN countries from 1990 to 2021 is presented, along with its significance. Using present panel data techniques, this study investigates the connections between these factors. Second-generation cointegration and unit root tests, as well as a novel method of Moments Quantile Regression, are used in the econometric procedure. Compared to standard quantile regression, this method is more resistant to outliers and provides an asymmetric relationship between the variables. The findings show that trade increases carbon emissions in countries with medium to high emissions, that patent innovation contributes to increasing emissions, and that renewable energy mitigates carbon emissions in countries with low to medium emerging economies. Our results are consistent with other specifications, including quantile regression canay (Canay 2011), fully modified, dynamic, and fixed effect regressions, proving the EKC hypothesis. These countries need to prioritize greener products and adopt advanced manufacturing technologies to reduce carbon emissions from consumption. However, as prosperity increases, it also leads to higher consumption-based carbon emissions, worsening ecological damage in the region. Implementing policies like trade synchronization and increasing investment in patent innovations are proposed in this study to lower the current level of carbon emissions.

Quantile regression based on the skewed exponential power distribution

Bayesian quantile regression generally relies on the asymmetric Laplace distribution (ALD) as the error distribution. We consider methods for Lp -quantile regression based on the skewed exponential power distribution (SEPD). Both Bayesian and frequentist estimation procedures are outlined and compared with previous work based on the SEPD. We find that our proposed methods greatly outperform a previous method in terms of quantile estimation. Further, compared with standard quantile regression, we find that our proposed methods generally perform better in terms of root mean square error (RMSE). Empirical evidence of the statistical properties of the proposed models is provided through a simulation study. Further, a real data application illustrates their performance.

Inference for joint quantile and expected shortfall regression

AbstractQuantiles and expected shortfalls are commonly used risk measures in financial risk management. The two measurements are correlated while having distinguished features. In this project, our primary goal is to develop a stable and practical inference method for the conditional expected shortfall. We consider the joint modelling of conditional quantile and expected shortfall to facilitate the statistical inference procedure. While the regression coefficients can be estimated jointly by minimizing a class of strictly consistent joint loss functions, the computation is challenging, especially when the dimension of parameters is large since the loss functions are neither differentiable nor convex. We propose a two‐step estimation procedure to reduce the computational effort by first estimating the quantile regression parameters with standard quantile regression. We show that the two‐step estimator has the same asymptotic properties as the joint estimator, but the former is numerically more efficient. We develop a score‐type inference method for hypothesis testing and confidence interval construction. Compared to the Wald‐type method, the score method is robust against heterogeneity and is superior in finite samples, especially for cases with many confounding factors. The advantages of our proposed method over existing approaches are demonstrated by simulations and empirical studies based on income and college education data.

MINIMUM WAGES AND WAGE DISTRIBUTION IN THAILAND

Minimum wage policies were designed to raise the wages of low-skilled workers. In this study, we use data from the Thai Labor Force Survey (2011-2020) to examine the impact of the minimum wage policy on the wage distribution using a quantile regression model corrected for sample selection with a copula. We find that the minimum wage has the strongest effect on the lowest quantile and the effect decreases toward the higher quantiles. This confirms the effectiveness of the minimum wage policy in raising the wages of low-income individuals. In addition, there is also a spill-over effect on individuals in higher wage quantiles. The effect of the minimum wage estimated by our model is smaller compared to the standard quantile regression. This suggests that without correcting for sampling bias, the estimated effect of the minimum wage leads to an upward bias.

Two-step estimation of censored quantile regression for duration models with time-varying regressors

Common duration models are characterized by strong homogeneity and thus are highly restrictive in allowing for how regressors affect the conditional duration distribution. In particular, the implied sign and relative marginal quantile effects remain the same over the entire range of the conditional duration distribution, which rules out general heterogeneous effects in duration data. Quantile regression, which offers a flexible and unified framework that allows for general heterogeneous effects, is particularly well suited to duration analysis. Based on the insights behind the accelerated failure time model (AFT) with time-varying regressors (Cox and Oakes, 1984) and the standard quantile regression model (Koenker and Bassett, 1978), Chen (2019) recently developed a quantile regression framework with time-varying regressors. However, Chen’s (2019) estimator is very difficult to compute because the estimation procedure involves a non-convex and nonlinear high dimensional optimization problem due to censoring and the nonlinearity of the quantile function. In this paper I propose an easy-to-implement two-step quantile regression estimator, which significantly reduces the computational burden. The estimator is shown to be consistent and asymptotically normal. Monte Carlo experiments indicate that our estimator perform well in finite samples.

Can Tourism Development Reduce Gender Inequality?

This study evaluates the nonlinear relationship between gender inequality and tourism receipts using a standard quantile regression approach and advances the results with an asymmetric application. Gender inequality is a pervasive and complex phenomenon rooted in the socio-economic culture of many countries. The reasons for inequality have country-specific situations, and to gain a broader understanding, countries were grouped by their income levels to explore the relationships for different groups. The study concludes that not all countries stimulate overall gender inequality through tourism. The study results show that in all but the 10th quantile, tourism had a negative and significant relationship with gender inequality providing support for the notion that tourism helps narrow the gender gap. The exceptions were found only at the 10th quantile indicates that low-income countries with low levels of tourism development could not derive the benefits of tourism’s potential in reducing gender inequality.

Conditional quantile change test for time series based on support vector regression

The task of detecting a structural change in conditional quantiles of time series with time-varying volatilities is vital in the field of financial time series, especially risk management. Therefore, in this study, we aim to construct a change point test to detect a quantile change by hybridizing the cumulative sum of squares test with the support vector quantile regression. Compared to the test employing the standard quantile regression, this approach not only provides more robust property against a high degree of nonlinearity of time series but also exhibits better performance for the datasets contaminated with high-frequency noises, as demonstrated in our simulation study. It also has merits to provide more diverse interpretations and a deeper understanding of financial time series than the volatility change point test, as illustrated in a real data analysis of three financial indices, namely, S&P500, Nasdaq composite index, and the stock price of Apple Inc.

A bias-adjusted estimator in quantile regression for clustered data

Quantile regression models with random effects are useful for studying associations between covariates and quantiles of the response distribution for clustered data. Parameter estimation is examined for a class of mixed-effects quantile regression models, with focus on settings with many but small clusters. The main contributions are the following: (i) documenting that existing methods may lead to severely biased estimators for fixed effects parameters; (ii) proposing a new two-step estimation methodology where predictions of the random effects are first computed by a pseudo likelihood approach (the LQMM method) and then used as offsets in standard quantile regression; (iii) proposing a novel bootstrap sampling procedure in order to reduce bias of the two-step estimator and compute confidence intervals. The proposed estimation and associated inference is assessed numerically through rigorous simulation studies and applied to an AIDS Clinical Trial Group (ACTG) study.

Parametric modeling of quantile regression coefficient functions with count data

Applying quantile regression to count data presents logical and practical complications which are usually solved by artificially smoothing the discrete response variable through jittering. In this paper, we present an alternative approach in which the quantile regression coefficients are modeled by means of (flexible) parametric functions. The proposed method avoids jittering and presents numerous advantages over standard quantile regression in terms of computation, smoothness, efficiency, and ease of interpretation. Estimation is carried out by minimizing a “simultaneous” version of the loss function of ordinary quantile regression. Simulation results show that the described estimators are similar to those obtained with jittering, but are often preferable in terms of bias and efficiency. To exemplify our approach and provide guidelines for model building, we analyze data from the US National Medical Expenditure Survey. All the necessary software is implemented in the existing R package qrcm.

Social and demographic characteristics of frequent or high-charge emergency department users: A quantile regression application.

Heavy users of the emergency department (ED) are a heterogeneous population. Few studies have captured the social and demographic complexity of patients with the largest burden of ED use. Our objective was to model associations between social and demographic patient characteristics and quantiles of the distributions of ED use, defined as frequent and high-charge. We conducted a cross-sectional analysis of electronic health and billing records of 99 637 adults residing in an urban North Carolina county who visited an ED within Atrium Health, a large integrated health care system, in 2017. Mid-quantile and standard quantile regression models were used for count and continuous responses, respectively. Frequent and high-charge use outcomes were defined as the median (0.50) and upper quantiles (0.75, 0.95, 0.99) of the outcome distributions for total billed ED visits and associated charges during the study period. Patient characteristic predictors were: insurance coverage (Medicaid, Medicare, private, uninsured), total visits to ambulatory care during the study period (0, 1, >1), and patient demographics: age, gender, race, ethnicity, and living in an underprivileged community called a public health priority area (PHPA). Results showed heterogeneous relationships that were stronger at higher quantiles. Having Medicaid or Medicare insurance was positively associated with ED visits and ED charges at most quantiles. Racial and geographic disparities were observed. Black patients had more ED visits and lower ED charges than their White counterparts at most quantiles of the outcome distributions. Patients living in PHPAs, had lower charges than their counterparts at the median but higher charges at the 0.95 and 0.99 quantiles. The relationships between patient characteristics and frequent and high-charge use of the ED vary based on the level of use. These findings can be used to inform targeted interventions, tailored policy, and population health management initiatives.

Dynamic nonlinear impacts of oil price returns and financial uncertainties on credit risks of oil-exporting countries

Abstract This paper investigates the dynamic and nonlinear impact of oil price returns on the sovereign credit default swap (CDS) spreads for the oil-rich countries of the Gulf Cooperation Council (GCC) and other important oil-exporting countries, namely Venezuela, Mexico and Russia. We employ the standard quantile regression analysis, the rolling quantile regression, and finally, the Quantile-on-quantile (QQ) approach that allows one to investigate the dependence dynamics of the sovereign CDS spreads under different credit market conditions. The empirical results show that oil price returns significantly and favorably decrease the sovereign credit risk premium of the non-GCC oil-exporting countries under consideration. However, the results also suggest no or little impact on the sovereign credit risk premium of Saudi Arabia, UAE and Norway, which have the most significant sovereign wealth funds in the world. The negative (i.e. favorable) impact of oil price returns on the sovereign CDS spreads, where present, gradually increases with the quantile level and is the highest during the bullish credit market conditions. The results also show that those CDS spreads are more sensitive to the global bond market uncertainty factor than to the global equity market uncertainty factor.

Natural disasters and economic growth: a quantile on quantile approach

Natural disasters have caused over a million of deaths and $3 trillion in economic losses during the last 20 years. However, theoretical and empirical studies have not reached a conclusion as for their effect on economic growth, and the results can best be described as mixed. The present study proposes the use of a quantile on quantile (QQ) approach to shed more light on this complex relationship. This approach combines the standard quantile regression analysis with nonparametric estimations and allows us to examine how different quantiles of natural disasters affect different quantiles of GDP growth. Using data from over 100 countries over a 30-years period, we confirm that the results of the QQ approach differ from the ones obtained by standard approaches like fixed effects regressions. We document that the relationship between the intensity of natural disasters and economic growth is mostly negative. Nonetheless, there are some exceptions to this. Our findings reveal that the effect of natural disasters can be occasionally positive, depending on the quantiles that we examine. The magnitude of the effect also differs across different combinations of the quantile of economic growth and the quantile of natural disasters. Finally, we obtain somewhat different results when we estimate separate QQ regressions for groups of countries that differ in terms of climate, economic and democratic development, and across different year lags of the natural disaster index.

Coordinating Marketing and Production with Asymmetric Costs: Theory and Estimation

This paper proposes a theoretical framework for decision making when the firm needs to make marketing and production/order decisions simultaneously before demand uncertainty is resolved. We discuss the theoretical properties of the framework for single and multi-product firms; in addition, we show that the framework can be extended to allow for competitive reaction in a duopoly setting. We propose an empirical method to operationalize the model and compare the results to those from extant methods. The empirical results for both single and multi-product firms show that the proposed method outperforms decision making using standard econometric methods. In particular, depending on customer lifetime value (CLV) and other error costs and price elasticities, the loss in potential profits by using the standard regression-based methodology or quantile regression can be considerable.

A penalized approach to covariate selection through quantile regression coefficient models

The coefficients of a quantile regression model are one-to-one functions of the order of the quantile. In standard quantile regression (QR), different quantiles are estimated one at a time. Another possibility is to model the coefficient functions parametrically, an approach that is referred to as quantile regression coefficients modeling (QRCM). Compared with standard QR, the QRCM approach facilitates estimation, inference and interpretation of the results, and generates more efficient estimators. We designed a penalized method that can address the selection of covariates in this particular modelling framework. Unlike standard penalized quantile regression estimators, in which model selection is quantile-specific, our approach permits using information on all quantiles simultaneously. We describe the estimator, provide simulation results and analyse the data that motivated the present article. The proposed approach is implemented in the qrcmNP package in R.

Do Energy and Banking CDS Sector Spreads Reflect Financial Risks and Economic Policy Uncertainty? A Time-Scale Decomposition Approach

The aim of this study is to investigate the dynamics of the co-movements of energy and banking sector credit default swaps (CDS) spreads with global financial and economic policy uncertainty and risk factors in the United States and Europe. We first employ the standard quantile regression approach to examine the co-movement dynamics under different credit market conditions. The empirical results show that the standard quantile regression fails to capture the co-movement between the U.S. and European CDS spreads and the economic policy uncertainty and risk factors for all quantiles. However, after decomposing the raw series at various scales of resolution, using the wavelet approach to capture the structure, we find that the financial and energy related CDS spreads co-move with the economic policy uncertainty and stock market risk in the intermediate and lower frequency domain. That is, there is a dependency in the intermediate and higher time scales or the intermediate and long investment horizons for both the United States and Europe. However, there are positive effects of the stock market risk index on the U.S. banking CDS spreads, which remain almost similar across quantiles, but the effects are asymmetric for the European banking spreads. The study also provides policy implications.

Inequality in the labor market: lower perceived returns among marginalized youths and girls

Purpose This paper examines perceived labor market earnings among adolescents and their parents by gender and caste. Previous research has established that lower subjective expectations of labor market returns among parents affect educational investment. Likewise, subjective expectations of adolescents about labor market returns are likely to affect their commitment to their education. In the labor market, gender and caste biases manifest itself in terms of lower wages for women and persons from marginalized communities. The authors ask if perceived earnings among adolescents and their parents vary by caste and gender over and above their intrinsic ability. Design/methodology/approach The authors use a unique dataset on adolescents that has been recently collected (2013-2015) by ASER Centre, the research and assessment wing of Pratham Education Foundation for the analysis. To answer the research question posed in the paper, they use standard OLS and quantile regression techniques. Findings Results confirm that girls have lower expected earnings than boys. Caste differences appear more rigid in Bihar. Research limitations/implications The authors recognize that the results presented do not take into consideration the issue of selection bias. Hence, they are applicable not to the average adolescents in the study districts, but only to those who reported expected earnings. That said, they do not think that this technical limitation dilutes the broad policy conclusions emerging from the study. Originality/value The paper uses cognition as a measure of an adolescent’s intrinsic ability. Therein lays the uniqueness of the paper. It brings into the discussion on expected earnings test scores as a measure of an adolescent’s cognitive ability. It is also unique in that it focuses on adolescents in the age group of 11-16 years who are likely to join the labor force in few years. Previous discussion of subjective expectations in India did not include any measure to capture cognitive ability and did not focus exclusively on adolescents.

Measuring sovereign contagion in Europe

This paper analyzes sovereign risk shift-contagion, i.e. positive and significant changes in the propagation mechanisms, using bond yield spreads for the major eurozone countries. By emphasizing the use of two econometric approaches based on quantile regressions (standard quantile regression and Bayesian quantile regression with heteroskedasticity) we find that the propagation of shocks in euro's bond yield spreads shows almost no presence of shift-contagion in the sample periods considered (2003–2006, Nov. 2008–Nov. 2011, Dec. 2011–Apr. 2013). Shock transmission is no different on days with big spread changes and small changes. This is the case even though a significant number of the countries in our sample have been extremely affected by their sovereign debt and fiscal situations. The risk spillover among these countries is not affected by the size or sign of the shock, implying that so far contagion has remained subdued. However, the US crisis does generate a change in the intensity of the propagation of shocks in the eurozone between the 2003–2006 pre-crisis period and the Nov. 2008–Nov. 2011 post-Lehman one, but the coefficients actually go down, not up! All the increases in correlation we have witnessed over the last years come from larger shocks and the heteroskedasticity in the data, not from similar shocks propagated with higher intensity across Europe. These surprising, but robust, results emerge because this is the first paper, to our knowledge, in which a Bayesian quantile regression approach allowing for heteroskedasticity is used to measure contagion. This methodology is particularly well-suited to deal with nonlinear and unstable transmission mechanisms especially when asymmetric responses to sign and size are suspected.

Directional quantile regression in R

Recently, the eminently popular standard quantile regression has been generalized to the multiple-output regression setup by means of directional regression quantiles in two rather interrelated ways. Unfortunately, they lead to complicated optimization problems involving parametric programming, and this may be the main obstacle standing in the way of their wide dissemination. The presented R package modQR is intended to address this issue. It originates as a quite faithful translation of the authors' moQuantile toolbox for Octave and MATLAB, and provides all the necessary computational support for both the directional multiple-output quantile regression methods to the wide statistical public. The article offers a concise summary of the statistical theory behind modQR, overviews the package in brief, points out its departures from moQuantile, comments on its use and performance, and demonstrates its application.

Interquantile shrinkage in additive models

ABSTRACTIn this paper, we investigate the commonality of nonparametric component functions among different quantile levels in additive regression models. We propose two fused adaptive group Least Absolute Shrinkage and Selection Operator penalties to shrink the difference of functions between neighbouring quantile levels. The proposed methodology is able to simultaneously estimate the nonparametric functions and identify the quantile regions where functions are unvarying, and thus is expected to perform better than standard additive quantile regression when there exists a region of quantile levels on which the functions are unvarying. Under some regularity conditions, the proposed penalised estimators can theoretically achieve the optimal rate of convergence and identify the true varying/unvarying regions consistently. Simulation studies and a real data application show that the proposed methods yield good numerical results.

Variable selection for additive partial linear quantile regression with missing covariates

The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. These assumptions are relaxed by considering a partial linear model with missing covariates. A weighted objective function using inverse probability weighting is proposed to remove the potential bias caused by missing data. Estimators using parametric and nonparametric estimates of the probability an observation has fully observed covariates are examined. A penalized and weighted objective function using the nonconvex penalties MCP or SCAD is used for variable selection of the linear terms in the presence of missing data. Assuming the missing data problems remains a low dimensional problem the penalized estimator has the oracle property including cases where p≫n. Theoretical challenges include handling missing data and partial linear models while working with a nonsmooth loss function and a nonconvex penalty function. The performance of the method is evaluated using Monte Carlo simulations and the methods are applied to model amount of time sober for patients leaving a rehabilitation center.