Quantile Regression Framework Research Articles

Wavelet-based LASSO in functional linear quantile regression

ABSTRACTIn this paper, we develop an efficient wavelet-based regularized linear quantile regression framework for coefficient estimations, where the responses are scalars and the predictors include both scalars and function. The framework consists of two important parts: wavelet transformation and regularized linear quantile regression. Wavelet transform can be used to approximate functional data through representing it by finite wavelet coefficients and effectively capturing its local features. Quantile regression is robust for response outliers and heavy-tailed errors. In addition, comparing with other methods it provides a more complete picture of how responses change conditional on covariates. Meanwhile, regularization can remove small wavelet coefficients to achieve sparsity and efficiency. A novel algorithm, Alternating Direction Method of Multipliers (ADMM) is derived to solve the optimization problems. We conduct numerical studies to investigate the finite sample performance of our method and applied it on real data from ADHD studies.

Financial development, government bond returns, and stability: International evidence

This paper investigates the effect of financial development on government bond returns in developed and emerging markets under different market conditions. Using a quantile regression framework for quarterly panel data from 28 countries over 1999–2015, our results reveal that the effect of financial development on government bond returns (changes in bond prices) differs according to conditions in the market and between developed and emerging markets. The effect is positive and significant only in good market conditions for developed markets. For emerging markets financial development has a positive and significant effect for good market conditions but the effect is negative and significant for bad market conditions.

Bayesian optimum accelerated life test plans based on quantile regression

Quantile regression has emerged as a significant extension of traditional linear models, and its appealing features, such as robustness, efficiency in the presence of censoring and flexibility of modeling stress-life relationship, have recently been recognized for analyzing accelerated life test data. Based on these merits, we present a method for planning accelerated life test in the quantile regression framework for better analysis of the ALT data. Bayesian D-optimality criterion based on accuracy of model parameters on a whole is used to find optimum test plans. We apply the criterion to accelerated life test planning for estimating a distribution quantile, and there is uncertainty as to which model best describes the lifetime distribution. Further, the proposed method is able to handle non-constant scale parameter models. General equivalence theorem is used to verify the global optimality of the numerically optimized ALT plan.

Analysing the systemic risk of Indian banks

This paper adopts the Tail-Event driven NETwork (TENET) risk model to assess the systemic risk of Indian banks. Building upon the Value at Risk (VaR), Conditional Value at Risk (CoVaR) and a Single Index Model (SIM) in a generalized quantile regression framework, the results suggest that the Indian banks exhibit high interconnectedness during the crisis period. The results also identify the systemically important banks and explain the banking networks.

Impact of Wind and Solar Production on Electricity Prices: Quantile Regression Approach

We study the impact of fuel prices, emission allowances, demand, past prices, wind and solar production on hourly day-ahead electricity prices in Germany over the period from January 2015 until June 2018. Working within a linear regression, ARX-EGARCH and quantile regression framework we compare how different pricing factors influence the mean and quantiles of the electricity prices. Contrary to the existing literature we find that short-term price fluctuations on the fuel markets and emission allowances have little effect on the electricity prices. We also find that day-of-the-week as well as monthly effects have significant impact on the electricity prices in Germany and should not be ignored in model specifications. Three main factors are found to drive extreme prices: price persistence, expected demand and expected wind production. Our findings contribute to understanding of extreme price movements, which can be used in pricing models and hedging strategies.

Quantile regression for duration models with time-varying regressors

Since the seminal work of Koenker and Bassett (1978), quantile regression has become a widely used tool in duration analysis. The existing literature, however, has focused on time-invariant regressors, even though time-varying regressors are common in practice. In this paper, we introduce a quantile regression framework with time-varying regressors and develop quantile regression estimators. Our estimators are motivated by Manski’s (1975, 1985) maximum score estimator and Chen’s (2010) integrated maximum score estimator. Our estimators are consistent and asymptotically normal under some regularity conditions, and perform well in finite samples. Our method is illustrated with an unemployment duration data set.

The spatial extent of agglomeration economies across the wage earnings distribution

AbstractWe investigate the spatial extent of agglomeration economies across the wage earnings distribution using economic mass (total employment) in four distance bands around each individual’s establishment in a quantile regression framework. We control for observable and unobservable individual and establishment characteristics. Remaining endogeneity in the model is assessed with a set of instrumental variables. Results indicate a positive effect of economic mass on wage earnings up to 25 km away from the establishment. The spatial extent of agglomeration economies is similar across the wage earnings distribution. However, increases in economic mass shift the wage earnings distribution in a nonsymmetric way.

Asset pricing factors and bank CDS spreads

This study compares the explanatory power of various asset pricing and macroeconomic risk factors in their ability to explain changes in the CDS spreads of global systemically important banks (G-SIBs). The factors include higher moment equity risks along with systematic sources of risk, such as investor uncertainty, interbank risk and foreign exchange volatility. For comparison, the five-factor asset pricing model by Fama and French (2017) is also implemented as a possible tool for explaining CDS spread changes. Estimation results from the quantile regression framework used herein show that heterogeneity in the explanatory power of the factors across low credit risk periods and high credit risk periods, such as during the 2008–09 financial crisis and 2011–13 European debt crisis, are a likely reason why extant time series regression models of CDS spreads yield instability in coefficient estimates and varying degrees of statistical significance across sample periods and time.

Decomposition methods for analyzing inequality changes in Latin America 2002–2014

This paper studies recent inequality patterns and the distributional effects of schooling and job informality on wage inequality in Argentina, Brazil, Colombia and Mexico during the 2002–2014 period. By means of a quantile regression framework, we decompose changes in the wage gap using several techniques including the Machado and Mata algorithm, the RIF regression unconditional quantile regression method and the random-coefficients quantile regression representation. Results show that the reduction in wage inequality is explained by the improvements in the lower part of the wage distribution in which the pricing rather than the composition effect explains most of the changes. We found that the composition effect of education was unequalizing, while their pricing effect was inequality reducing. Job formality favored relatively more workers in the lower part of the distribution and had an important pricing effect below the median for all countries, but only in the 2002–2008 period.

Formal and informal sectors: is there any wage differential?

ABSTRACTThe main objective of this paper is to investigate if a wage difference exists between formal and informal sectors in the case of the Turkish labour market using a sample of wageworkers. To this end, we use data for 2004 and 2009 and a novel definition of the informal sector. On the methodological front, we adopt three alternative decomposition techniques, namely, the Oaxaca-Ransom [(1994). On discrimination and the decomposition of wage differentials. Journal of Econometrics, 61, 5–21] decomposition in the context of mean regression, the Machado and Mata [(2005). Counterfactual decomposition of changes in wage distributions using quantile regression. Journal of Applied Econometrics, 20(4), 445–465] decomposition in the quantile regression framework and the non-parametric decomposition method proposed by Nopo [(2008). Matching as a tool to decompose wage gap. The Review of Economics and Statistics, 90(2), 290–299]. The results reveal the existence of a wage gap between the two sectors. We found education and experience to be key determinants of earnings. The findings of this paper have implications for policies, which might be directed towards developing approaches with a focus on education and experience.

Estimation of rainfall intensity\u2013duration\u2013frequency curves at ungauged locations using quantile regression methods

Intensity–duration–frequency (IDF) curves of extreme rainfall are used extensively in infrastructure design and water resources management. In this study, a novel regional framework based on quantile regression (QR) is used to estimate rainfall IDF curves at ungauged locations. Unlike standard regional approaches, such as index-storm and at-site ordinary least-squares regression, which are dependent on parametric distributional assumptions, the non-parametric QR approach directly estimates rainfall quantiles as a function of physiographic characteristics. Linear and nonlinear methods are evaluated for both the regional delineation and IDF curve estimation steps. Specifically, delineation by canonical correlation analysis (CCA) and nonlinear CCA (NLCCA) is combined, in turn, with linear QR and nonlinear QR estimation in a regional modelling framework. An exhaustive comparative study is conducted between standard regional methods and the proposed QR framework at sites across Canada. Overall, the fully nonlinear QR framework, which uses NLCCA for delineation and nonlinear QR for estimation of IDF curves at ungauged sites, leads to the best results.

Growth strategy with social capital, human capital and physical capital—Theory and evidence: The case of Vietnam

AbstractIn this paper, we develop a theoretical model to explain the impact of social capital (defined at the firm level) on individual firm performance and derive a critical optimal threshold for firms to invest in social capital. The theoretical model we propose reveals how social capital, human capital, and physical capital simultaneously affect firm performance under the main assumption of a decreasing function of social capital on unit cost of physical capital. Our theoretical model is then estimated using unique firm‐level longitudinal data from Vietnam for the period 2005–2015. Using a control function approach in a quantile regression framework, we attempt to establish the causal impact of social capital on firm performance. Our empirical results point to a range of revenue in which investment in social capital is efficient and to evidence suggesting that the role of social capital decreases when firms become richer.

Joint modeling for mixed-effects quantile regression of longitudinal data with detection limits and covariates measured with error, with application to AIDS studies

It is very common in AIDS studies that response variable (e.g., HIV viral load) may be subject to censoring due to detection limits while covariates (e.g., CD4 cell count) may be measured with error. Failure to take censoring in response variable and measurement errors in covariates into account may introduce substantial bias in estimation and thus lead to unreliable inference. Moreover, with non-normal and/or heteroskedastic data, traditional mean regression models are not robust to tail reactions. In this case, one may find it attractive to estimate extreme causal relationship of covariates to a dependent variable, which can be suitably studied in quantile regression framework. In this paper, we consider joint inference of mixed-effects quantile regression model with right-censored responses and errors in covariates. The inverse censoring probability weighted method and the orthogonal regression method are combined to reduce the biases of estimation caused by censored data and measurement errors. Under some regularity conditions, the consistence and asymptotic normality of estimators are derived. Finally, some simulation studies are implemented and a HIV/AIDS clinical data set is analyzed to to illustrate the proposed procedure.

Bayesian quantile regression using the skew exponential power distribution

Traditional Bayesian quantile regression relies on the Asymmetric Laplace (AL) distribution due primarily to its satisfactory empirical and theoretical performances. However, the AL displays medium tails and it is not suitable for data characterized by strong deviations from the Gaussian hypothesis. An extension of the AL Bayesian quantile regression framework is proposed to account for fat tails using the Skew Exponential Power (SEP) distribution. Linear and Additive Models (AM) with penalized splines are considered to show the flexibility of the SEP in the Bayesian quantile regression context. Lasso priors are used in both cases to account for the problem of shrinking parameters when the parameters space becomes wide while Bayesian inference is implemented using a new adaptive Metropolis within Gibbs algorithm. Empirical evidence of the statistical properties of the proposed models is provided through several examples based on both simulated and real datasets.

A plug-in bandwidth selector for nonparametric quantile regression

In the framework of quantile regression, local linear smoothing techniques have been studied by several authors, particularly by Yu and Jones (J Am Stat Assoc 93:228–237, 1998). The problem of bandwidth selection was addressed in the literature by the usual approaches, such as cross-validation or plug-in methods. Most of the plug-in methods rely on restrictive assumptions on the quantile regression model in relation to the mean regression, or on parametric assumptions. Here we present a plug-in bandwidth selector for nonparametric quantile regression that is defined from a completely nonparametric approach. To this end, the curvature of the quantile regression function and the integrated squared sparsity (inverse of the conditional density) are both nonparametrically estimated. The new bandwidth selector is shown to work well in different simulated scenarios, particularly when the conditions commonly assumed in the literature are not satisfied. A real data application is also given.

The role of partisan conflict in forecasting the U.S. equity premium: A nonparametric approach

Information on partisan conflict is shown to matter in forecasting the U.S. equity premium, especially when accounting for omitted nonlinearities in their relationship, via a nonparametric predictive regression approach over the monthly period 1981:01–2016:06. Unlike as suggested by a linear predictive model, the nonparametric functional coefficient regression that includes the partisan conflict index enhances significantly the out-of-sample excess stock returns predictability. This result is found to be robust when we use a quantile predictive regression framework to capture nonlinearity, especially when the market is found to be in its bullish mode (i.e., upper quantiles of the conditional distribution of the equity premium).

The Returns to Personality Traits Across the Wage Distribution

This paper investigates variation in the wage effects of non-cognitive skills across the wage distribution. I expect (i) increasing explanatory power and (ii) increasing magnitudes of the effects of non-cognitive skills on wages across the wage distribution. I test these hypotheses using unconditional quantile regressions with data from Germany, the UK and Australia. To test the joint explanatory contribution of multiple variables within a quantile-regression framework, I propose a new statistic that quantifies the realtive rise in explanatory power generated by additional explanatory variables. The findings support both hypotheses and provide further evidence for the importance of non-cognitive skills in the labor market.

Predicting risk premium under changes in the conditional distribution of stock returns

The goal of this paper is to assess time-variation in asset returns while considering the whole conditional distribution. We use a quantile regression framework and quarterly data for the U.S., and show that the probabilistic distribution of expectations about future stock returns changes in response to variation in commonly used explanatory variables. Moreover, our results support the idea that lower quantiles are less stable than upper quantiles, thus, suggesting that asset pricing models are particularly accurate in capturing the expectations that less risk-averse agents have about future returns.

POLITICAL TIES AND FIRM PERFORMANCE IN CHINA: EVIDENCE FROM A QUANTILE REGRESSION

AbstractWhether political ties enhance or weaken firm performance has been widely investigated in a number of studies, including some on China. Based on a database of non-financial A-share listed firms from 2004 to 2012, we study the effects of political ties on firm performance within a quantile regression framework. We find that there is a positive relationship between political ties and economic performance, but that it is diminishing with respect to firm performance. Political ties appear particularly important for weaker firms.

International Announcements and WTI Crude Oil Futures: Evidence from the 2008 Crisis Period

We examine the impact of international monetary policy and professionals’ announcements on WTI crude oil futures. The methodology is an event and case study. The event study refers to an analysis of each category of events, while the case study refers to the selection of a particular time period, that is, a time period around the Lehman Brothers collapse. The direction, magnitude and significance of impacts are assessed in returns and volatility for price, volume and open interest series in both daily and weekly frequency. The research questions are assessed in a non-parametric quantile regression framework. Announcements are classified into four categories in total, three of which concern international monetary policy from the UK, the US, and the European Monetary Union, with the fourth category concerning financial professionals’ announcements.