Bayesian Quantile Regression Approach Research Articles

Variable selection in macroeconomic stress test: a Bayesian quantile regression approach

AbstractThe key assumption in stress test scenarios is that selected risk factors are useful in predicting banks’ tail risks under severe economic conditions. We argue that high-dimensional Bayesian quantile regression models with shrinkage priors are ideal for identifying those factors. We illustrate our methods by identifying key drivers for banks with different asset sizes from a high-dimensional database. We found that leverage indicators, asset prices, and labor market measures are the best predictors of banks’ performance. The usefulness of our methods is further demonstrated by a forecast comparison between the selected variables and those used in the regulatory stress tests.

How does digitalization affect the urban-rural disparity at different disparity levels: A Bayesian Quantile Regression approach

The digital revolution is bringing profound changes to the production, lifestyle, and governance in urban and rural areas. However, the varying impacts of different digitalization dimensions on urban-rural disparity have been understudied, particularly in developing countries. Based on 1931 county-level administrative units, this study used cluster analysis and a novel Bayesian Quantile Regression approach to explore the digitalization characteristics, and how digitalization influences urban-rural disparity at different disparity levels and in different regions. We found three types of digitalization development, including Balanced Digital Progression (29.26 %), Digital Consumption Powerhouse (17.50 %), and Digital Development Potential (53.24 %). Digitalization played an essential role in alleviating urban-rural disparity, with a more pronounced effect in areas with higher levels of disparity. The access to information infrastructure related to the first-level digital divide may exacerbate the urban-rural disparity, while the digitalization dimensions related to the second-level digital divide could mitigate the urban-rural disparity. Regarding the regional effects, information infrastructure adoption has different impacts on urban-rural disparity across various regions, while digitalization usage is consistently mitigating urban-rural disparities. By comprehensively examining the role of digitalization, we provided a scientific basis for formulating more precise and effective policies for a more balanced and integrated urban-rural development.

Variable Selection in Macroeconomic Stress Test: A Bayesian Quantile Regression Approach

Variable Selection in Macroeconomic Stress Test: A Bayesian Quantile Regression Approach

A Study of Bayesian Quantile Regression for Forecasting RMB Exchange Rates

Accurate forecasting of the RMB exchange rate is crucial for global financial market participants. This study proposes a Bayesian quantile regression approach to enhance the forecasting method. This paper uses RMB and US dollar exchange rate data from the State Administration of Foreign Exchange from 2018 to 2022 to build a Bayesian quantile regression model and empirically analyze the RMB exchange rate forecast. The results show that the proposed Bayesian quantile regression model yields accurate forecasts, with a root mean squared error (RMSE) of 1.8329 and a mean absolute error (MAE) of 1.2988. Furthermore, robustness and sensitivity analyses confirm the model's reliability. The findings of this study have practical implications for financial market participants and policymakers in managing and responding to foreign exchange risk.

How spatial patterns affect urban green space equity at different equity levels: A Bayesian quantile regression approach

In many cities, urban green space (UGS) is not evenly distributed, and marginalized communities often lack UGS due to legacies of disinvestment. Existing research mainly focused on the effect of socioeconomic factors to understand the disparity in access to UGS. However, little is known on how spatial patterns affect UGS equality at the regional and subregional levels. Moreover, the potential quantile effects in the UGS pattern and equality relationship remain unclear. Here, we explored how UGS equality varied among UGS spatial patterns and socioeconomic gradients in seven counties (1,227 census tracts) in Southeast Michigan. First, we quantified UGS equality of each tract with a spatially explicit Gini coefficient and UGS spatial patterns via landscape metrics. Then, we applied a Bayesian quantile regression model to investigate the nonlinear relationship between spatial pattern and UGS equality in the whole study area and its three subregions of different population density. Our results showed that spatial patterns had quantile effects on UGS equality. At the regional scale, patch density and the largest patch index had significant positive effects on UGS equality at all equality levels. The mean patch shape index positively correlated with UGS equality in areas with higher equality level (Gini coefficient: 0.52–0.92). At the subregional level, patch density most efficiently predicted UGS equality in densely populated areas, while the largest patch index also affected UGS equality in areas with low population density. We suggest policymakers should focus on areas with extremely unequal access to UGS to increase the number rather than the cumulative area of UGS. Besides, more linear and irregular UGS patches with longer perimeters have potential to serve more communities.

A Bayesian approach for more reliable tail risk forecasts

This paper demonstrates that existing quantile regression models used for jointly forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. Given the importance of these measures in financial systems, this sensitivity is a critical issue. A new Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, new additive-type models are developed for the ES component that are more robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods.

How Urban Green Space Spatial Pattern Affects its Equity: a Bayesian Quantile Regression Approach

How Urban Green Space Spatial Pattern Affects its Equity: a Bayesian Quantile Regression Approach

Bayesian prediction of emergency department wait time

Increasingly, many hospitals are attempting to provide more accurate information about Emergency Department (ED) wait time to their patients. Estimation of ED wait time usually depends on what is known about the patient and also the status of the ED at the time of presentation. We provide a model for estimating ED wait time for prospective low acuity patients accessing information online prior to arrival. Little is known about the prospective patient and their condition. We develop a Bayesian quantile regression approach to provide an estimated wait time range for prospective patients. Our proposed approach incorporates a priori information in government statistics and elicited expert opinion. This methodology is compared to frequentist quantile regression and Bayesian quantile regression with non-informative priors. The test set includes 1, 024 low acuity presentations, of which 457 (44%) are Category 3, 425 (41%) are Category 4 and 160 (15%) are Category 5. On the Huber loss metric, the proposed method performs best on the test data for both median and 90th percentile prediction compared to non-informative Bayesian quantile regression and frequentist quantile regression. We obtain a benefit in the estimation of model coefficients due to the value contributed by a priori information in the form of elicited expert guesses guided by government wait time statistics. The use of such informative priors offers a beneficial approach to ED wait time prediction with demonstrable potential to improve wait time quantile estimates.

Changes in extreme rainfall and its implications for design rainfall using a Bayesian quantile regression approach

Abstract This study aims to explore possible distributional changes in annual daily maximum rainfalls (ADMRs) over South Korea using a Bayesian multiple non-crossing quantile regression model. The distributional changes in the ADMRs are grouped into nine categories, focusing on changes in the location and scale parameters of the probability distribution. We identified seven categories for a distributional change in the selected stations. Most of the stations (28 of 50) are classified as Category III, which is characterized by an upward trend with an increase in variance in the distribution. Moreover, stations with a downward trend with a decrease in the variance pattern (Category VII) are mainly distributed on the southern Korean coast. On the other hand, Category I stations are mostly located in eastern Korea and primarily show a statistically significant upward trend with a decrease in variance. Moreover, this study explored changes in design rainfall estimates for different categories in terms of distributional changes. For Categories I, II, III, and VI, a noticeable increase in design rainfall was observed, while Categories IV, V, and VII showed no evidence of association with risk of increased extreme rainfall.

Reducing the risk in tail risk forecasting models

This paper demonstrates that existing quantile regression models used for forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. A Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, a new additive-type model is developed for the ES component that is robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods.

A Bayesian Quantile Regression Approach for Nonstationary Frequency Analysis of Annual Maximum Sea Level in a Changing Climate

ABSTRACT Uranchimeg, S.; Kim, J-G.; Kim, J.-G.; Kwon, H.-H., and Lee, S.-O., 2018. A Bayesian Quantile Regression Approach for Nonstationary Frequency Analysis of Annual Maximum Sea Level in a Changing Climate. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 536–540. Coconut Creek (Florida), ISSN 0749-0208. Sea level rise is primarily caused by global warming and has been a key consideration in design practices in coastal engineering. The design of coastal structures is currently based on a frequency analysis of the local sea level under the stationary assumption, meaning that the maximum sea level will not vary significantly over time. However, the stationary assumption for sea levels might not be valid in a changing climate. In such a context, this study proposes a systematic approach to investigate nonstationarity in annual maximum sea levels (AMSLs) and of...

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.

Spatial Distribution of Malnutrition among Children Under Five in Nigeria: A Bayesian Quantile Regression Approach

Issues of malnutrition among young children in developing countries are gaining more attention of policy-makers because of the adverse effects on the well-being of people and economic of these nations. Anthropometric variables used for determining malnutrition are measured through z-scores where those whose measures fall into the extreme ends of the scores are considered malnourished. Conditional mean regression has been adopted to examine the determinants but often times, covariates would have effect on the mean, but have no substantial influence on more extreme quantiles. We adopt Bayesian quantile regression approach to measure the spatial distributions of childhood undernutrition at state and local government levels in Nigeria. Markov random fields and Bayesian P-splines were used as priors for the spatial and nonlinear components respectively and estimation was through MCMC technique. Results show the existence of north-south divide in undernutrition in Nigeria and that observed socioeconomic variables could have little influence on the distribution of undernutrition across space in the country.

A sandwich likelihood correction for Bayesian quantile regression based on the misspecified asymmetric Laplace density

A sandwich likelihood correction is proposed to remedy an inferential limitation of the Bayesian quantile regression approach based on the misspecified asymmetric Laplace density, by leveraging the benefits of the approach. Supporting theoretical results and simulations are presented.

A Bayesian Quantile Regression Model for Insurance Company Costs Data

Summary We examine the average cost function for property and casualty insurers. The cost function describes the relationship between a firm's minimum production cost and outputs. A comparison of cost functions could shed light on the relative cost efficiency of individual firms, which is of interest to many market participants and has been given extensive attention in the insurance industry. To identify and to compare the cost function, current practice is to assume a common functional form between costs and outputs across insurers and then to rank insurers according to the centre of the cost distribution. However, the assumption of a common cost–output relationship could be misleading because insurers tend to adopt different technologies that are reflected by the cost function in their production process. The centre-based comparison could also lead to biased inference especially when the cost distribution is skewed with a heavy tail. To address these issues, we model the average production cost of insurers by using a Bayesian quantile regression approach. Quantile regression enables the modelling of different quantiles of the cost distribution as opposed to just the centre. The Bayesian approach helps to estimate the cost-to-output functional relationship at a firm level by borrowing information across firms. In the analysis of US property–casualty insurers, we show that better insights into efficiency are gained by comparing different quantiles of the cost distribution.

Measuring Sovereign Contagion in Europe

This paper analyzes the sovereign risk contagion using credit default swaps (CDS) and bond premiums for the major eurozone countries. By emphasizing several econometric approaches (nonlinear regression, quantile regression and Bayesian quantile regression with heteroskedasticity) we show that propagation of shocks in Europe's CDS has been remarkably constant for the period 2008-2011 even though a significant part of the sample periphery countries have been extremely affected by their sovereign debt and fiscal situations. Thus, the integration among the different eurozone countries is stable, and the risk spillover among these countries is not affected by the size of the shock, implying that so far contagion has remained subdue. Results for the CDS sample are conformed by examining bond spreads. However, the analysis of bond data shows that there is a change in the intensity of the propagation of shocks in the 2003-2006 pre-crisis period and the 2008-2011 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. This is the first paper, to our knowledge, where a Bayesian quantile regression approach is used to measure contagion. This methodology is particularly well-suited to deal with nonlinear and unstable transmission mechanisms.

Measuring Sovereign Contagion in Europe

This paper analyzes the sovereign risk contagion using credit default swaps (CDS) and bond premiums for the major eurozone countries. By emphasizing several econometric approaches (nonlinear regression, quantile regression and Bayesian quantile regression with heteroskedasticity) we show that propagation of shocks in Europe's CDS has been remarkably constant for the period 2008-2011 even though a significant part of the sample periphery countries have been extremely affected by their sovereign debt and fiscal situations. Thus, the integration among the different eurozone countries is stable, and the risk spillover among these countries is not affected by the size of the shock, implying that so far contagion has remained subdue. Results for the CDS sample are confirmed by examining bond spreads. However, the analysis of bond data shows that there is a change in the intensity of the propagation of shocks in the 2003-2006 pre-crisis period and the 2008-2011 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. This is the first paper, to our knowledge, where a Bayesian quantile regression approach is used to measure contagion. This methodology is particularly well-suited to deal with nonlinear and unstable transmission mechanisms.