Quantile Regression

Nội dung

• Quantiles and the Quantile Function

  • Definition of quantiles and the quantile function.

  • Understanding conditional quantiles and their significance in econometric analysis.

• What Is Quantile Regression?

  • Definition and concept of quantile regression.

  • Why use quantile regression instead of ordinary least squares (OLS)? Capturing the distributional impact of covariates across different quantiles of the outcome variable.

  • Key differences between quantile regression and OLS.

• Applications and Motivation

  • Quantile regression in economic research.

  • Examples of applications: Wage inequality, housing prices, financial risk management.

  • Importance of quantile regression in understanding the entire distribution of the dependent variable.

Sách

• Koenker, R. (2005). Quantile regression. Cambridge Univ Press.

• Angrist, J. D., & Pischke, J. S. (2009). Mostly harmless econometrics: An empiricist's companion. Princeton university press.

• Cameron, A. C. (2005). Microeconometrics: methods and applications. Cambridge University.

• Cameron, A. C. (2010). Microeconometrics using stata. Revised Edition.

Bài báo

•  Koenker, R., & Hallock, K. F. (2001). Quantile regression. Journal of economic perspectives, 15(4), 143-156.

• Koenker, R. (2017). Quantile regression: 40 years on. Annual review of economics, 9, 155-176.

• Clarke, D., Llorca Jaña, M., & Pailañir, D. (2023). The use of quantile methods in economic history. Historical Methods: A Journal of Quantitative and Interdisciplinary History, 56(2), 115-132. (link)

Nội dung

Section 1: Introduction to Quantile Regression for Cross-sectional Data

• • Motivation for using quantile regression in cross-sectional settings.

  • Quantile regression in wage analysis, real estate pricing, and healthcare expenditure.

Section 2: The Quantile Regression Model for Cross-sectional Data

• Specification of the Quantile Regression Model

  • Conditional quantile function for cross-sectional data.

  • Mathematical formulation

    • 1. • Advantages of Quantile Regression for Cross-sectional Data

           • Ability to model the entire conditional distribution of the dependent variable.

           • Robustness to outliers and heteroskedasticity.

           • Flexibility in capturing different effects of covariates at different points in the distribution.

         • Limitations and Challenges

           • Interpretation complexities when quantile coefficients vary greatly across quantiles.

           • Computational challenges with large datasets.

           • Potential multi-collinearity issues in cross-sectional data.

Section 3: Estimation Techniques for Quantile Regression in Cross-sectional Data

• The Objective Function

  • Minimizing the asymmetric absolute loss function for different quantiles.

  • Formulation of the objective function for quantile regression in cross-sectional data.

• Linear Programming Approach

  • Using linear programming to estimate quantile regression coefficients.

  • Step-by-step example of how to solve the linear programming problem.

• Numerical Algorithms for Estimation

  • Simplex method and interior-point methods for solving quantile regression models.

  • Computational challenges and practical implementation for large cross-sectional datasets.

Section 4: Interpretation of Quantile Regression Results

• Interpreting Quantile Coefficients

  • Understanding the meaning of coefficients at different quantiles.

  • Comparing results across quantiles and with OLS estimates.

• Graphical Representation of Results

  • Visualizing the impact of covariates on different quantiles: Coefficient plots and quantile process plots.

  • Example: Graphical representation of wage determinants across quantiles in cross-sectional data.

Section 5: Hypothesis Testing and Inference in Quantile Regression

• Hypothesis Testing in Quantile Regression

  • Testing the significance of quantile regression coefficients.

  • Wald test and likelihood ratio tests for hypothesis testing across quantiles.

• Confidence Intervals and Standard Errors

  • Methods for calculating standard errors and confidence intervals: Bootstrapping and asymptotic standard errors.

  • Example: Constructing confidence intervals for wage determinants at different quantiles.

• Joint Tests Across Quantiles

  • Testing whether coefficients differ across quantiles.

  • Example: Testing the variation of education’s impact on income across quantiles.

Section 6: Applications of Quantile Regression 

• Wage Determination and Income Distribution

  • Application of quantile regression to study wage determinants and income inequality in cross-sectional data.

  • Example: Quantile regression analysis of gender wage gaps across different quantiles.

• Real Estate Pricing and Housing Markets

  • Application to real estate data: Modeling housing prices across different market segments.

  • Example: Quantile regression analysis of housing prices for different property characteristics.

• Healthcare Expenditure Analysis

  • Application of quantile regression in analyzing healthcare expenditures across income groups.

  • Example: Quantile regression model for understanding the distributional impact of health insurance on healthcare costs.

• Education and Labor Market Outcomes

  • Quantile regression applied to cross-sectional data on education and employment.

  • Example: Estimating the returns to education across different quantiles of the income distribution.

Section 10: Software Implementation for Quantile Regression 

• Quantile Regression in Stata

  • Commands and tools in Stata for estimating quantile regression models with cross-sectional data (qreg, bsqreg).

  • Example: Step-by-step guide for estimating wage determinants using quantile regression in Stata.

• Quantile Regression in R

  • Using the quantreg package in R to estimate quantile regression models.

  • Example: Running a quantile regression for housing price data in R.

• Quantile Regression in Python

  • Quantile regression implementation in Python using statsmodels.

  • Example: Quantile regression analysis for income distribution data in Python.

Section 11: Conclusion and Future Directions in Quantile Regression for Cross-sectional Data

• Recap of Key Concepts

  • Summary of quantile regression for cross-sectional data: Interpretation, estimation, and hypothesis testing.

• Challenges and Future Research

  • Addressing computational challenges and improving methods for large datasets.

  • Future applications of quantile regression in big data, machine learning, and policy evaluation.

Sách

•  Koenker, R. (2005). Quantile regression. Cambridge Univ Press.

• Angrist, J. D., & Pischke, J. S. (2009). Mostly harmless econometrics: An empiricist's companion. Princeton university press.

• Cameron, A. C. (2005). Microeconometrics: methods and applications. Cambridge University.

• Cameron, A. C. (2010). Microeconometrics using stata. Revised Edition.

Bài báo

• Eissa, M. A., Al Refai, H., & Chortareas, G. (2024). Heterogeneous impacts of geopolitical risk factors on stock markets in the Middle East: A quantile regression analysis across four emerging economies. The Journal of Economic Asymmetries, 30, e00374.

• Barra, C., D’Aniello, C., & Ruggiero, N. (2024). The effects of types of banks on financial access and income inequality in a heterogeneous sample: A quantile regression analysis. Journal of Economics and Business, 106197.

• Moridian, A., Radulescu, M., Kumar, P., Radu, M. T., & Mohammad, J. (2024). New insights on immigration, fiscal policy and unemployment rate in EU countries–A quantile regression approach. Heliyon, 10(13).

• Alvarado, R., Tillaguango, B., Toledo, E., Murshed, M., & Işık, C. (2024). Links between technological innovation, financial efficiency and environmental quality using quantile regressions: The role of foreign direct investment, institutional quality and natural resources. Journal of Open Innovation: Technology, Market, and Complexity, 10(3), 100360.

• Halkos, G., Leonti, A., & Sardianou, E. (2022). Determinants of willingness to pay for entrance to urban parks: A quantile regression analysis. Economic Analysis and Policy, 74, 421-431.

Bài giảng tham khảo

• Quantile Regression của Econometrics Academy (link)

Sách

Bài báo

•  Koenker, R., & Hallock, K. F. (2001). Quantile regression. Journal of economic perspectives, 15(4), 143-156.

• Koenker, R. (2017). Quantile regression: 40 years on. Annual review of economics, 9, 155-176.

Nội dung

Section 1: Introduction to Weighted Quantile Regression

• • Definition and motivation for weighted quantile regression.

  • Key differences between traditional quantile regression and weighted quantile regression.

  • When to use weighted quantile regression: Heterogeneity in data, varying reliability of observations, and survey data.

• Why Use Weighted Quantile Regression?

  • The role of observation weights: Accounting for varying importance or precision across observations.

  • Examples of applications: Survey data with sampling weights, financial data with volatility-based weights, and health economics data.

Section 2: Theoretical Foundations of Weighted Quantile Regression

• The Quantile Function and Weighting

  • Revisiting the quantile regression objective function

  • Incorporating observation weights into the quantile regression framework.

  • Mathematical formulation: Minimizing the weighted sum of absolute deviations for a given quantile 

• Types of Weights

  • Explanation of different types of weights: Survey weights, frequency weights, and importance weights.

  • The role of exogenous vs. endogenous weighting in quantile regression.

• Properties of Weighted Quantile Regression Estimators

  • Consistency, efficiency, and robustness of weighted quantile regression estimators.

  • Asymptotic properties of weighted quantile regression.

  • Comparison with unweighted quantile regression: When weighting improves model accuracy.

    1. 1. • Advantages of Weighted Quantile Regression

            • Handling heteroscedasticity and data with varying levels of reliability.

            • Improving robustness in cases where some observations are more important or reliable than others.

            • Flexibility in modeling complex datasets (e.g., survey data with sampling weights).

          • Limitations and Challenges of Weighted Quantile Regression

            • Interpretation challenges: Understanding how weights affect the estimation results.

            • Sensitivity to choice of weights: How different weighting schemes can lead to different results.

            • Computational complexity: Increased computation time for large datasets with weights.

Section 3: Estimation Techniques for Weighted Quantile Regression

• Objective Function for Weighted Quantile Regression

  • Formulation of the weighted quantile regression problem: Minimizing the weighted absolute residuals.

  • Mathematical setup and notation for solving the weighted quantile regression optimization problem.

• Linear Programming Approach for Weighted Quantile Regression

  • Adapting the traditional linear programming approach to handle observation weights.

  • Step-by-step breakdown of how to solve the weighted quantile regression problem using linear programming.

• Numerical Methods and Optimization Algorithms

  • Using interior-point methods and gradient-based algorithms for estimating weighted quantile regression.

  • Practical considerations for large datasets: Efficiency and computational complexity.

Section 4: Interpretation of Weighted Quantile Regression Results

• Interpreting Weighted Quantile Coefficients

  • How to interpret the coefficients in weighted quantile regression models.

  • Comparing weighted and unweighted results: Understanding the impact of weights on coefficient estimates.

• Differences Across Quantiles

  • Exploring how weights affect different quantiles of the conditional distribution.

  • Example: Interpreting the impact of household income on healthcare expenditure at different quantiles with survey weights.

• Graphical Representation of Weighted Quantile Regression

  • Visualization techniques: Coefficient plots, quantile process plots, and residual plots for weighted quantile regression.

  • Example: Plotting weighted quantile regression results for wage determinants.

Section 5: Hypothesis Testing and Inference in Weighted Quantile Regression

• Hypothesis Testing for Weighted Quantile Regression Coefficients

  • Testing the significance of weighted quantile regression coefficients.

  • Comparison of weighted coefficients across quantiles: Wald test, likelihood ratio test, and score test.

• Standard Errors and Confidence Intervals

  • Bootstrapping methods for inference in weighted quantile regression models.

  • Calculating asymptotic standard errors and confidence intervals.

• Testing the Impact of Weights

  • Hypothesis testing for the inclusion of weights: Testing if weighted estimates differ significantly from unweighted estimates.

Section 6: Applications of Weighted Quantile Regression

• Survey Data Analysis with Sampling Weights

  • Application of weighted quantile regression to survey data where different observations have different sampling probabilities.

  • Example: Using weighted quantile regression to analyze income distribution in nationally representative household survey data.

• Financial Risk Modeling with Volatility-based Weights

  • Application of weighted quantile regression in finance: Modeling asset returns with volatility-based weights.

  • Example: Estimating Value-at-Risk (VaR) with weighted quantile regression using market volatility as weights.

• Healthcare Expenditure Analysis with Frequency Weights

  • Application of weighted quantile regression to healthcare expenditure data with frequency weights (e.g., repeated measurements).

  • Example: Modeling healthcare costs using weighted quantile regression to account for frequency differences across patients.

Section 7: Weighted Quantile Regression vs. Other Estimation Methods

• Weighted Quantile Regression vs. Ordinary Quantile Regression

  • Key differences in estimation and interpretation between weighted and unweighted quantile regression.

  • When to prefer weighted models over unweighted models.

• Weighted Quantile Regression vs. Weighted Least Squares (WLS)

  • Comparison of weighted quantile regression with WLS: Focus on conditional quantiles vs. conditional means.

  • Application scenarios where weighted quantile regression outperforms WLS.

Section 8: Extensions of Weighted Quantile Regression

• Penalized Weighted Quantile Regression

  • Introduction to Lasso and Ridge regularization in weighted quantile regression for high-dimensional data.

  • Example: Using penalized weighted quantile regression to handle large datasets in financial risk modeling.

• Nonparametric and Semiparametric Weighted Quantile Regression

  • Nonparametric approaches to weighted quantile regression for capturing complex nonlinear relationships.

  • Semiparametric models combining flexible nonparametric methods with parametric components.

Section 10: Software Implementation of Weighted Quantile Regression

• Implementing Weighted Quantile Regression in Stata

  • Commands and tools available in Stata for estimating weighted quantile regression (qreg, bsqreg, and weights option).

  • Step-by-step guide to applying weighted quantile regression in survey data.

• Weighted Quantile Regression in R

  • Using the quantreg package in R for weighted quantile regression.

  • Example: Running a weighted quantile regression for income distribution analysis in R.

• Weighted Quantile Regression in Python

  • Quantile regression implementation in Python using statsmodels and weighted options.

  • Example: Implementing weighted quantile regression for healthcare expenditure data in Python.

Section 11: Conclusion and Future Directions in Weighted Quantile Regression

• Summary of Key Concepts

  • Recap of weighted quantile regression: When and why to use it.

  • Interpretation of weighted quantile regression results in applied contexts.

• Challenges and Future Research

  • Addressing computational challenges in weighted quantile regression for large datasets.

  • Future research directions: Extensions to machine learning applications and dynamic weighted quantile regression models.

Sách

Bài báo

• Huang, M. L., Xu, X., & Tashnev, D. (2015). A weighted linear quantile regression. Journal of Statistical Computation and Simulation, 85(13), 2596-2618.

• Liu, F., Gao, F., Yang, L., Han, C., Hao, W., & Tang, J. (2022). Exploring the spatially heterogeneous effect of the built environment on ride-hailing travel demand: A geographically weighted quantile regression model. Travel Behaviour and Society, 29, 22-33.

• Taylor, J. W. (2007). Forecasting daily supermarket sales using exponentially weighted quantile regression. European Journal of Operational Research, 178(1), 154-167.

Nội dung

Section 1: Introduction to Wavelet Quantile Regression

• • Definition of wavelet quantile regression.

  • Combining wavelet analysis with quantile regression to model time-varying and scale-dependent relationships.

  • When to use wavelet quantile regression: Data with complex structures, such as non-stationary time series or spatial data.

  • Applications in volatility forecasting, stock market analysis, and macroeconomic time series.

  • Example: Modeling financial returns with time-varying volatility using wavelet quantile regression.

Section 2: Theoretical Foundations of Wavelet Quantile Regression

• Overview of Wavelet Analysis

  • Introduction to wavelet theory: Wavelet transforms and decomposition.

  • The continuous and discrete wavelet transforms: Differences and applications in econometrics.

• Quantile Regression: Revisiting the Basics

  • Brief review of the quantile regression model: Estimating conditional quantiles and robustness to outliers.

  • Incorporating wavelets into the quantile regression framework.

• Combining Wavelets with Quantile Regression

  • Mathematical formulation of wavelet quantile regression.

  • Decomposing the data into different frequency components using wavelets, then applying quantile regression to each component.

    1. 1. • Advantages of Wavelet Quantile Regression

            • Capturing both short-term and long-term dynamics in data.

            • Ability to model scale-dependent relationships and time-varying patterns.

            • Robustness to outliers and non-linearities in the data.

          • Limitations and Challenges

            • Interpretation challenges: Understanding the meaning of coefficients across both time and frequency domains.

            • Computational complexity: Estimating wavelet quantile regression for large datasets.

            • Choice of wavelet basis: How different wavelet types may yield different results.

Section 3: Estimation of Wavelet Quantile Regression Models

• Wavelet Decomposition of the Data

  • Steps for wavelet decomposition: Breaking the data into high-frequency and low-frequency components.

  • Example: Wavelet decomposition of a financial time series (e.g., stock prices or exchange rates).

• Quantile Regression at Different Scales

  • Applying quantile regression to each wavelet component.

  • Example: Estimating different quantiles for high-frequency and low-frequency components of GDP growth data.

• Estimation Techniques

  • Wavelet transforms (e.g., Haar, Daubechies, Symlets) and their implementation in quantile regression models.

  • Optimization methods for estimating wavelet quantile regression.

Section 4: Interpretation of Wavelet Quantile Regression Results

• Interpreting Wavelet Coefficients in Quantile Regression

  • How to interpret wavelet quantile coefficients for different frequency bands.

  • Understanding short-term vs. long-term effects in the data using wavelet quantile regression.

• Comparing Results Across Different Quantiles and Scales

  • Analyzing the differences in the impact of covariates across different quantiles and frequency scales.

  • Example: Interpreting the impact of macroeconomic shocks on output at different quantiles and timescales.

• Visualization of Wavelet Quantile Regression Results

  • Graphical representation: Visualizing the relationship between variables across both time and frequency domains.

  • Example: Plotting the wavelet quantile regression results for inflation data across different scales.

Section 5: Hypothesis Testing and Inference in Wavelet Quantile Regression

• Hypothesis Testing for Wavelet Quantile Regression

  • Testing the significance of wavelet quantile regression coefficients.

  • Comparing coefficients across different quantiles and time scales.

• Confidence Intervals and Standard Errors

  • Bootstrap and other resampling techniques for inference in wavelet quantile regression.

  • Constructing confidence intervals for wavelet quantile estimates.

Section 6: Applications of Wavelet Quantile Regression

• Financial Markets and Volatility Analysis

  • Application of wavelet quantile regression in modeling financial time series with time-varying volatility.

  • Example: Estimating the quantile effects of market shocks on stock returns across different frequencies.

• Macroeconomic Time Series

  • Wavelet quantile regression applied to macroeconomic data with long-term and short-term components.

  • Example: Modeling inflation rates across different quantiles and timescales.

• Energy Economics

  • Application of wavelet quantile regression to model energy prices and volatility.

  • Example: Analyzing the impact of global oil price shocks on energy demand and prices at different quantiles and timescales.

Section 8: Comparison with Other Models

• Comparison with Traditional Quantile Regression

  • Differences in capturing time-varying effects and multi-scale relationships.

  • When to use wavelet quantile regression over traditional quantile regression.

• Comparison with Wavelet Least Squares

  • Key differences between wavelet quantile regression and wavelet least squares.

  • Applications where wavelet quantile regression outperforms wavelet least squares.

Section 9: Software Implementation for Wavelet Quantile Regression

• Implementing Wavelet Quantile Regression in R

  • Using R packages like WaveletComp and quantreg to estimate wavelet quantile regression models.

  • Example: Step-by-step guide for implementing wavelet quantile regression on financial time series data in R.

• Implementing Wavelet Quantile Regression in Python

  • Tools available in Python: Using pywt for wavelet transforms and statsmodels for quantile regression.

  • Example: Python implementation for modeling stock market volatility with wavelet quantile regression.

• Implementing Wavelet Quantile Regression in MATLAB

  • MATLAB functions for wavelet transforms and quantile regression: wavedec, quantreg.

  • Example: Estimating wavelet quantile regression for macroeconomic data in MATLAB.

Section 10: Conclusion and Future Directions in Wavelet Quantile Regression

• Summary of Key Concepts

  • Recap of wavelet quantile regression: Combining time and frequency analysis with quantile regression.

  • Summary of advantages and limitations.

• Future Research and Applications

  • Potential applications in big data and machine learning.

  • Future challenges: Handling high-dimensional data, further development of inference techniques, and expanding applications to new fields (e.g., environmental data, social sciences).

Sách

Bài báo

• Liu, L., Adebayo, T. S., Hu, J., Irfan, M., & Abbas, S. (2024). Exploring resource blessing hypothesis within the coffin of technological innovation and economic risk: Evidence from wavelet quantile regression. Energy Economics, 137, 107802.

• Huo, C., Hameed, J., Sharif, A., Albasher, G., Alamri, O., & Alsultan, N. (2022). Recent scenario and nexus of globalization to CO2 emissions: evidence from wavelet and Quantile on Quantile Regression approach. Environmental Research, 212, 113067.

Nội dung

Section 1: Introduction to Quantile Regression with Panel Data

• Overview of Quantile Regression in Panel Data Context

  • Motivation for using quantile regression with panel data: Modeling heterogeneity across individuals and over time.

  • Capturing conditional quantiles: Going beyond the mean to understand different parts of the outcome distribution.

• Applications of Quantile Regression with Panel Data

  • Common applications in economics, finance, and health.

  • Example: Wage dynamics, investment patterns, or firm performance across different quantiles.

Section 2: Quantile Regression with Panel Data

• Quantile Regression Model for Panel Data

  • Conditional quantile function for panel data: Qyit(τ∣Xit)Q_{y_{it}}(\tau | X_{it})Qyit​​(τ∣Xit​), where τ\tauτ is the quantile of interest, iii indexes individuals, and ttt indexes time.

  • Key assumptions and setup: Fixed effects, random effects, and individual heterogeneity.

• Dealing with Fixed and Random Effects

  • Fixed effects in quantile regression: Controlling for individual-specific heterogeneity.

  • Random effects in quantile regression: When individual-specific effects are assumed to be random.

• Endogeneity and Selection Bias in Quantile Regression with Panel Data

  • Addressing endogenous variables in quantile regression.

  • Dealing with selection bias: When certain observations are not randomly selected into the dataset.

    1. 1. • Advantages of Quantile Regression for Panel Data

            • Modeling heterogeneity across quantiles and over time.

            • Robustness to outliers and non-normality in the distribution of the dependent variable.

          • 8.2 Limitations and Challenges

            • Computational complexity of estimating quantile regression with panel data, particularly for large datasets.

            • Interpretation challenges: Understanding the impact of time and individual effects across quantiles.

            • Potential issues with endogeneity and measurement error.

Section 3: Estimation Techniques for Quantile Regression with Panel Data

• Estimation with Fixed Effects

  • Estimating quantile regression models while controlling for fixed individual effects.

  • Approaches: Difference methods and within-transformation to eliminate fixed effects.

• Estimation with Random Effects

  • Using random effects quantile regression to account for random individual heterogeneity.

  • Example: Random effects quantile regression for firm productivity across different quantiles.

• Penalized Quantile Regression for Panel Data

  • Introduction to penalized methods (e.g., Lasso, Ridge) to handle high-dimensional panel data.

  • Example: Penalized quantile regression for large panel datasets with many covariates.

• Generalized Method of Moments (GMM) for Quantile Regression with Panel Data

  • GMM estimation to account for endogeneity and dynamic structures in panel quantile regression.

  • Example: GMM-based quantile regression for dynamic investment models in panel data.

Section 4: Dynamic Quantile Regression Models for Panel Data

• Incorporating Dynamics in Quantile Regression Models

  • Modeling lagged dependent variables in panel quantile regression models.

  • Capturing short-term and long-term effects across quantiles.

• Arellano-Bond Estimation for Dynamic Panel Quantile Regression

  • Adapting the Arellano-Bond approach for dynamic panel data in a quantile regression context.

  • Example: Dynamic quantile regression for wage growth across different income levels.

• System GMM for Dynamic Quantile Regression with Panel Data

  • Using system GMM to estimate dynamic panel quantile regression models with both lagged variables and endogenous regressors.

  • Example: System GMM applied to investment and output in firms across different quantiles.

Section 5: Interpretation of Quantile Regression Results in Panel Data

• Interpreting Coefficients in Quantile Regression with Panel Data

  • How to interpret quantile regression coefficients for different quantiles in the presence of fixed or random effects.

  • Comparing coefficients across quantiles and over time.

• Understanding Heterogeneity in Quantile Regression Results

  • Identifying and understanding individual-level and time-level heterogeneity in panel data.

  • Example: Interpreting how education affects wages differently across quantiles over time.

• Visualization of Quantile Regression Results

  • Graphical representation of results: Quantile process plots and coefficient paths.

  • Example: Visualizing the relationship between firm size and productivity across quantiles and over time.

Section 6: Hypothesis Testing and Inference in Quantile Regression with Panel Data

• Hypothesis Testing for Quantile Regression Coefficients

  • Wald test, Likelihood Ratio test, and Score test for quantile regression models.

  • Testing the significance of coefficients across quantiles.

• Confidence Intervals and Standard Errors

  • Bootstrap methods for panel quantile regression models.

  • Calculating robust standard errors for quantile estimates in panel data.

• Joint Tests Across Quantiles

  • Testing if coefficients differ across quantiles: Understanding differences in the impact of covariates across the outcome distribution.

Section 7: Applications of Quantile Regression with Panel Data

• Wage Dynamics and Income Inequality

  • Application of quantile regression to model wage dynamics across quantiles, accounting for individual fixed effects.

  • Example: Analyzing income inequality and wage growth using panel quantile regression.

• Firm Performance and Productivity Analysis

  • Application of quantile regression to study firm performance and productivity across different quantiles.

  • Example: Investigating how different factors (capital, labor, R&D) affect firm productivity at various quantiles.

• Healthcare Expenditure and Policy Evaluation

  • Quantile regression applied to healthcare data to understand expenditure distribution across different population segments.

  • Example: Studying the effects of healthcare policy changes on low-income vs. high-income households over time.

• Education and Labor Market Outcomes

  • Application of quantile regression to study returns to education and labor market outcomes across different quantiles.

  • Example: Quantile regression for panel data on educational attainment and wage growth over time.

Section 8: Comparison with Other Methods

• Quantile Regression vs. Mean-based Panel Data Models

  • Differences between quantile regression and traditional mean-based models like fixed and random effects.

  • When to prefer quantile regression over OLS or fixed/random effects models.

• Quantile Regression vs. Other Robust Methods for Panel Data

  • Comparison with robust methods like M-estimators and other median-based estimators.

  • Applications where quantile regression provides additional insights.

Section 9: Software Implementation for Quantile Regression with Panel Data

• Implementing Quantile Regression for Panel Data in Stata

  • Commands and tools in Stata for panel quantile regression (xtqreg, bsqreg).

  • Step-by-step guide to estimating panel quantile regression for wage dynamics in Stata.

• Quantile Regression for Panel Data in R

  • Using the quantreg and plm packages for quantile regression in panel data.

  • Example: Running a quantile regression model for firm performance using R.

• Quantile Regression in Python for Panel Data

  • Implementing quantile regression in Python using statsmodels for panel data.

  • Example: Python implementation for modeling investment patterns across firms.

Section 10: Conclusion and Future Directions in Quantile Regression for Panel Data

• Summary of Key Concepts

  • Recap of quantile regression for panel data: Interpretation, estimation techniques, and applications.

  • Key takeaways for researchers and practitioners.

• Future Research and Applications

  • Addressing computational challenges with large-scale panel data.

  • Expanding applications in machine learning, dynamic models, and high-dimensional data.

Sách

Bài báo

• Baruník, J., & Čech, F. (2021). Measurement of common risks in tails: A panel quantile regression model for financial returns. Journal of Financial Markets, 52, 100562.

• Jawadi, F., Jawadi, N., Cheffou, A. I., Ameur, H. B., & Louhichi, W. (2017). Modelling the effect of the geographical environment on Islamic banking performance: A panel quantile regression analysis. Economic Modelling, 67, 300-306.

• Agan, B. (2024). Sustainable development through green transition in EU countries: New evidence from panel quantile regression. Journal of Environmental Management, 365, 121545.

Nội dung

Section 1: Introduction to Quantile Regression for Time Series Data

• Motivation for Quantile Regression in Time Series Analysis

  • Capturing heterogeneous effects across different parts of the distribution of the time series.

  • Handling non-linearity and non-stationarity in time series data.

  • Example: Forecasting stock market returns or exchange rates at different quantiles.

    1. 1. •  Advantages of Quantile Regression for Time Series Analysis

            • Capturing time-varying relationships at different parts of the distribution.

            • Robustness to outliers and extreme events (e.g., financial crises, sudden shocks).

          • Limitations and Challenges

            • Computational complexity: Estimating quantile regression for large time series datasets.

            • Interpretation challenges: Understanding how coefficients evolve over time and across quantiles.

            • Dealing with non-stationarity and autocorrelation in time series data.

Section 2: Quantile Regression for Time Series Data

• The Quantile Regression Model for Time Series

  • Conditional quantile function for time series

  • Estimation of quantiles for a time-dependent process.

• Time Series Characteristics and Quantile Regression

  • Accounting for time dependence, autocorrelation, and stationarity in quantile regression models.

  • Example: Estimating quantile regression for financial returns that exhibit volatility clustering.

• Differences Between Quantile Regression and Mean-based Time Series Models

  • Capturing different dynamics at various quantiles.

  • Robustness to outliers and skewed distributions in time series data.

Section 3: Estimation Techniques for Quantile Regression in Time Series

• Conditional Quantile Function and Lagged Variables

  • Incorporating lagged variables in quantile regression models to capture autocorrelation.

  • Example: Quantile regression for lagged interest rates in macroeconomic time series.

• Autoregressive Quantile Regression (QAR) Models

  • Introduction to quantile autoregression (QAR) models.

  • Estimation of QAR models for different quantiles in the time series.

  • Example: Using QAR for forecasting GDP growth at different quantiles.

• Generalized Method of Moments (GMM) for Time Series Quantile Regression

  • GMM-based estimation techniques for dealing with endogeneity and autocorrelation in quantile regression models for time series data.

  • Example: GMM estimation for quantile regression in dynamic interest rate models.

Section 4: Dynamic Quantile Regression Models for Time Series

• Dynamic Quantile Models

  • Incorporating lagged dependent variables in quantile regression models for time series.

  • Example: Dynamic quantile regression for inflation forecasting using lagged inflation rates.

• Quantile Autoregressive Distributed Lag (QARDL) Models

  • Introduction to QARDL models: Combining quantile regression with autoregressive distributed lag models.

  • Example: Estimating the impact of exchange rate changes on export prices across quantiles with a QARDL model.

• Time-Varying Quantile Models

  • Models that allow quantile regression coefficients to change over time.

  • Example: Time-varying quantile regression for modeling volatility in the stock market.

Section 5: Interpretation of Quantile Regression Results in Time Series Data

• Interpreting Quantile Regression Coefficients for Time Series

  • How to interpret quantile regression coefficients at different quantiles and across time.

  • Example: Understanding the asymmetric impact of oil price shocks on inflation rates at different quantiles.

• Visualization of Quantile Regression Results for Time Series

  • Graphical representation of quantile regression results: Quantile process plots, coefficient paths, and impulse response functions.

  • Example: Plotting the relationship between GDP growth and unemployment across different quantiles over time.

Section 6: Hypothesis Testing and Inference in Quantile Regression for Time Series

• Hypothesis Testing in Quantile Regression Models

  • Testing the significance of quantile regression coefficients in time series data.

  • Example: Wald test, likelihood ratio test, and score test for time series quantile regression models.

• Confidence Intervals and Standard Errors for Time Series Quantile Regression

  • Using bootstrapping techniques and asymptotic methods to compute standard errors and confidence intervals.

  • Example: Constructing confidence intervals for quantile regression models in stock price forecasting.

Section 7: Applications of Quantile Regression for Time Series

• Financial Time Series

  • Application of quantile regression to model financial returns and volatility at different quantiles.

  • Example: Estimating the effect of market shocks on stock returns across quantiles.

• Macroeconomic Time Series

  • Application of quantile regression for macroeconomic indicators (GDP, inflation, unemployment).

  • Example: Modeling the relationship between unemployment and inflation at different quantiles of the inflation distribution.

• Energy Markets

  • Using quantile regression to model energy prices and volatility in energy markets.

  • Example: Quantile regression for oil price volatility forecasting across different quantiles.

Section 8: Extensions of Quantile Regression for Time Series

• Quantile Vector Autoregression (QVAR) Models

  • Extending quantile regression to vector autoregression (VAR) models: Multivariate time series quantile regression.

  • Example: Estimating QVAR models for inflation, interest rates, and GDP growth across quantiles.

• Nonlinear Quantile Regression for Time Series

  • Using nonlinear quantile regression methods to model time series with complex dynamics.

  • Example: Nonlinear quantile regression for high-frequency financial data.

• Machine Learning and Quantile Regression for Time Series

  • Integrating machine learning techniques (e.g., random forests, neural networks) with quantile regression to handle large and complex time series datasets.

  • Example: Machine learning-based quantile regression for high-frequency stock price forecasting.

Section 9: Software Implementation for Quantile Regression with Time Series Data

• Quantile Regression for Time Series in Stata

• Quantile Regression for Time Series in R

• Quantile Regression for Time Series in Python

Section 10: Conclusion and Future Directions in Quantile Regression for Time Series

• 0Summary of Key Concepts

  • Recap of quantile regression for time series data: Interpretation, estimation techniques, and applications.

  • Key advantages over traditional time series models.

• Future Research and Challenges

  • Addressing computational challenges for large-scale time series data.

  • Expanding applications of quantile regression in machine learning, nonparametric methods, and real-time forecasting.

Sách

Bài báo

•  Iacopini, M., Poon, A., Rossini, L., & Zhu, D. (2023). Bayesian mixed-frequency quantile vector autoregression: Eliciting tail risks of monthly US GDP. Journal of Economic Dynamics and Control, 157, 104757.

• Khalfaoui, R., Hammoudeh, S., & Rehman, M. Z. (2023). Spillovers and connectedness among BRICS stock markets, cryptocurrencies, and uncertainty: Evidence from the quantile vector autoregression network. Emerging Markets Review, 54, 101002.

Nội dung

Section 1: Introduction to Nonparametric and Semiparametric Quantile Regression

• Motivation for Nonparametric and Semiparametric Methods

  • Why move beyond parametric quantile regression?

  • Flexibility of nonparametric and semiparametric methods: Capturing complex, nonlinear relationships between variables.

• Applications and Importance

  • Common applications: Wage distributions, environmental economics, financial markets, and health economics.

  • Example: Modeling the effect of education on wages when relationships are nonlinear across quantiles.

• Advantages of Nonparametric Methods

  • Flexibility: Capturing complex and nonlinear relationships without assuming a specific functional form.

  • Robustness to model misspecification.

• Advantages of Semiparametric Methods

  • Balancing flexibility with interpretability: Structuring part of the model while allowing for flexibility in others.

  • Improved efficiency compared to fully nonparametric models.

• Limitations of Nonparametric and Semiparametric Methods

  • Computational complexity: Nonparametric methods can be computationally intensive, especially with large datasets.

  • Interpretation challenges: Difficulty in interpreting nonparametric components compared to parametric models.

  • Bandwidth and smoothing parameter selection: Sensitivity of results to the choice of bandwidth or smoothing parameters.

Section 2: Nonparametric Quantile Regression

• Nonparametric Methods in Econometrics

  • Introduction to nonparametric estimation: No assumptions about the functional form of relationships.

  • Comparison with parametric methods: Flexibility vs. interpretability.

• The Nonparametric Quantile Function

  • Defining the nonparametric quantile function

  • Estimating conditional quantiles using nonparametric methods.

• Properties of Nonparametric Quantile Regression Estimators

  • Consistency and asymptotic properties of nonparametric quantile estimators.

  • Trade-offs between flexibility and efficiency.

Section 3: Estimation Techniques for Nonparametric Quantile Regression

• Kernel Smoothing for Quantile Regression

  • Introduction to kernel density estimation: Kernel weights and bandwidth selection.

  • Applying kernel methods to quantile regression: Estimating the conditional quantile function.

  • Example: Estimating wage quantiles with nonparametric kernel quantile regression.

• Local Polynomial Quantile Regression

  • Introduction to local polynomial smoothing: Using local fits to estimate quantiles.

  • Benefits of local polynomial regression for quantile estimation: Handling boundary effects.

  • Example: Estimating income distributions using local polynomial quantile regression.

• Spline-Based Nonparametric Quantile Regression

  • Introduction to spline regression: Using piecewise polynomials for quantile regression.

  • Spline smoothing for conditional quantiles: Choosing knots and penalties.

  • Example: Spline-based nonparametric quantile regression for house price distributions.

Section 4: Semiparametric Quantile Regression

• Overview of Semiparametric Models

  • Definition and motivation for semiparametric quantile regression: Combining parametric and nonparametric components.

  • When to use semiparametric methods: Flexibility with more structure than fully nonparametric models.

• Partially Linear Quantile Regression

  • Partially linear models: Modeling some variables parametrically while others nonparametrically.

  • Example: Estimating the effect of education parametrically while allowing nonparametric effects for experience on wage quantiles.

• Additive Quantile Regression Models

  • Introduction to additive models: Allowing separate nonparametric effects for each covariate.

  • Example: Additive quantile regression for modeling environmental variables’ impact on crop yield at different quantiles.

Section 5: Estimation Techniques for Semiparametric Quantile Regression

• Generalized Additive Models for Quantile Regression

  • Estimating generalized additive models (GAMs) for quantile regression: Penalized splines for flexibility.

  • Example: Estimating income inequality using GAM-based semiparametric quantile regression.

• Penalized Methods for Semiparametric Quantile Regression

  • Introduction to penalization: Ridge and Lasso penalties for semiparametric quantile models.

  • Example: Penalized semiparametric quantile regression for high-dimensional wage data.

• Two-Step Estimation Procedures

  • Estimating parametric and nonparametric components in two steps.

  • Example: Two-step estimation for partially linear quantile regression in labor market analysis.

Section 6: Inference and Hypothesis Testing in Nonparametric and Semiparametric Quantile Regression

• Hypothesis Testing in Nonparametric Quantile Regression

  • Testing the significance of nonparametric components.

  • Example: Wald and Likelihood Ratio tests for kernel-based quantile regression models.

• Confidence Intervals and Standard Errors for Nonparametric and Semiparametric Estimators

  • Bootstrap methods for inference: Bootstrapping to obtain standard errors and confidence intervals.

  • Example: Bootstrapped confidence intervals for spline-based quantile regression.

• Testing for Nonlinearity in Semiparametric Quantile Regression

  • Testing whether nonparametric components add value beyond a linear model.

  • Example: Hypothesis testing in partially linear models for education and income.

Section 7: Applications of Nonparametric and Semiparametric Quantile Regression

• Wage Distribution and Labor Economics

  • Application of nonparametric quantile regression to estimate wage inequality across education and experience levels.

  • Example: Nonparametric quantile regression for analyzing wage distribution in different industries.

• Financial Markets and Volatility Analysis

  • Using semiparametric quantile regression to model volatility in stock markets.

  • Example: Estimating conditional volatility quantiles with semiparametric models in financial returns.

• Environmental Economics

  • Application of semiparametric quantile regression in studying environmental data, such as pollution and climate change impacts.

  • Example: Modeling the impact of temperature on crop yield across quantiles.

Section 8: Software Implementation of Nonparametric and Semiparametric Quantile Regression

• Nonparametric and Semiparametric Quantile Regression in R

  • Using the quantreg and np packages for nonparametric quantile regression in R.

  • Example: Step-by-step guide to implementing kernel-based quantile regression in R for wage data.

• Nonparametric and Semiparametric Quantile Regression in Python

  • Using Python libraries such as statsmodels and scikit-learn for semiparametric quantile regression.

  • Example: Python implementation of partially linear quantile regression for financial market analysis.

• Nonparametric and semiparametric Quantile Regression in Stata

  • Stata commands for nonparametric quantile regression and spline-based models.

  • Example: Estimating nonparametric quantile regression for income distribution analysis in Stata.

Section 9: Conclusion and Future Directions in Nonparametric and Semiparametric Quantile Regression

• Summary of Key Concepts

  • Recap of nonparametric and semiparametric quantile regression: Flexibility and robustness in modeling complex relationships.

• Challenges and Future Research

  • Addressing computational challenges for large-scale datasets.

  • Expanding the application of nonparametric and semiparametric quantile regression to big data, machine learning, and real-time decision-making contexts.

Sách

Bài báo

• Gijbels, I., Karim, R., & Verhasselt, A. (2021). Semiparametric quantile regression using family of quantile-based asymmetric densities. Computational Statistics & Data Analysis, 157, 107129.

• Fan, Y., & Liu, R. (2016). A direct approach to inference in nonparametric and semiparametric quantile models. Journal of Econometrics, 191(1), 196-216.

• Cai, Z., & Xiao, Z. (2012). Semiparametric quantile regression estimation in dynamic models with partially varying coefficients. Journal of Econometrics, 167(2), 413-425.

Nội dung

Section 1: Introduction to Quantile Treatment Effects

• Overview of Treatment Effects in Econometrics

  • Definition of treatment effects: Estimating the impact of a binary treatment (e.g., policy, intervention).

  • Differences between Average Treatment Effects (ATE) and Quantile Treatment Effects (QTE).

• What Are Quantile Treatment Effects (QTE)?

  • Definition and interpretation of Quantile Treatment Effects: Estimating treatment effects at different points of the outcome distribution.

  • Motivation for QTE: Understanding treatment heterogeneity across different subgroups and quantiles of the outcome.

• Examples of Applications in Economics and Social Sciences

  • Common QTE applications: Labor market programs, educational interventions, and healthcare policies.

  • Example: Estimating the impact of a job training program on wage distribution across different income quantiles.

• Advantages of QTE

  • Capturing treatment heterogeneity: QTE reveals differential effects across the outcome distribution.

  • Flexibility in applications: Applicable to a wide range of fields (education, labor, health, etc.).

• Limitations and Challenges of QTE

  • Computational complexity: Estimating QTE can be computationally intensive, especially for large datasets.

  • Sensitivity to outliers and model specification.

  • Interpretation challenges: Understanding QTE results across quantiles and translating them into policy insights.

Section 2: Theoretical Foundations of Quantile Treatment Effects

• Quantile Regression as a Foundation for QTE

  • Review of quantile regression: Modeling conditional quantiles of the outcome variable.

  • Extending quantile regression to estimate treatment effects at different quantiles.

• Definition and Interpretation of QTE

  • Definition of the Quantile Treatment Effect for a particular quantile

  • Understanding how QTE captures treatment effect heterogeneity across the outcome distribution.

• QTE vs. ATE

  • Differences between QTE and traditional ATE: Capturing heterogeneous treatment effects across the distribution of the outcome variable.

  • Why focusing solely on ATE can obscure important variation in treatment effects.

Section 3: Estimation Techniques for Quantile Treatment Effects

• Naive Estimation of QTE Using Quantile Regression

  • Basic quantile regression with treatment as a covariate.

  • Limitations of naive quantile regression for estimating QTE due to selection bias and confounding.

• Instrumental Variables (IV) for Quantile Treatment Effects

  • Addressing endogeneity and selection bias in QTE using instrumental variables (IVQR).

  • Example: Using random assignment or natural experiments as instruments to estimate QTE in an educational intervention.

• Inverse Probability Weighting (IPW) for QTE

  • Applying inverse probability weighting to address selection bias and estimate causal QTE.

  • Example: IPW in estimating the impact of a healthcare subsidy program across different income quantiles.

• Difference-in-Differences (DiD) for QTE

  • Estimating QTE using Difference-in-Differences for panel data.

  • Example: Estimating the differential effect of minimum wage policies on wage distribution using DiD-QTE.

• Matching Methods for QTE

  • Using propensity score matching and covariate matching to estimate QTE.

  • Example: Matching methods for estimating the impact of a job training program on the distribution of wages.

Section 4: Dynamic Quantile Treatment Effects

• Time-Varying QTE

  • Estimating QTE for panel data with time-varying treatment effects.

  • Example: Dynamic QTE for understanding the long-term effects of a poverty alleviation program across income quantiles.

• QTE in the Presence of Lagged Treatment Effects

  • Modeling lagged treatment effects in quantile regression frameworks.

  • Example: Estimating lagged QTE in the context of healthcare interventions with delayed outcomes.

Section 5: Interpretation of Quantile Treatment Effects

• Interpreting QTE Results Across Quantiles

  • How to interpret the estimated treatment effects across different quantiles of the outcome distribution.

  • Example: Interpreting QTE for an educational program’s impact on test scores for low-, middle-, and high-performing students.

• Visualization of QTE Results

  • Graphical representation of QTE: Coefficient plots, quantile process plots, and treatment effect curves.

  • Example: Plotting the QTE of a wage subsidy program across income quantiles.

• Comparing QTE to ATE Results

  • How QTE offers insights into treatment heterogeneity that ATE might miss.

  • Example: Showing differences in ATE and QTE for a financial aid program’s impact on student performance.

Section 6: Hypothesis Testing and Inference in QTE

• Hypothesis Testing for QTE Coefficients

  • Testing the significance of QTE at individual quantiles.

  • Example: Wald and Likelihood Ratio tests for QTE models.

• Joint Tests Across Quantiles

  • Testing for differences in treatment effects across quantiles.

  • Example: Joint hypothesis testing for QTE in a labor market intervention.

• Confidence Intervals and Standard Errors

  • Bootstrapping methods for estimating standard errors and confidence intervals in QTE.

  • Example: Constructing bootstrapped confidence intervals for QTE in a healthcare program evaluation.

Section 7: Applications of Quantile Treatment Effects

• Labor Market Programs

  • QTE for evaluating the impact of job training programs on wage distribution.

  • Example: QTE for estimating differential wage impacts of a government job training program on low-income vs. high-income workers.

• Educational Interventions

  • QTE in education policy: Measuring the effect of school reforms on students across different performance levels.

  • Example: Estimating QTE for the impact of tutoring programs on students at different quantiles of test scores.

• Healthcare and Public Health Policies

  • QTE in healthcare: Estimating how a health subsidy program affects medical expenses or health outcomes across income groups.

  • Example: QTE analysis of the impact of Medicaid expansion on healthcare spending for low-income households.

• Social Welfare and Poverty Alleviation Programs

  • Using QTE to evaluate the effect of social welfare programs on income distribution.

  • Example: Estimating the impact of a conditional cash transfer program across income quantiles.

Section 9: Extensions of Quantile Treatment Effects

• Quantile Instrumental Variable Methods (IVQR)

  • Using instrumental variables to estimate causal QTE in the presence of endogeneity.

  • Example: IVQR for estimating QTE in job training programs where selection bias is a concern.

• Quantile Difference-in-Differences (DiD-QTE)

  • Combining quantile regression with DiD for estimating QTE in panel data settings.

  • Example: Estimating the impact of minimum wage changes on wage distribution using DiD-QTE.

• Nonparametric and Semiparametric QTE

  • Nonparametric methods for estimating QTE: Capturing complex and nonlinear relationships.

  • Example: Nonparametric QTE for studying the effect of education on wage inequality.

Section 10: Software Implementation for Quantile Treatment Effects

• QTE Implementation in Stata

• 10.2 QTE in R

• QTE in Python

Section 11: Conclusion and Future Directions in Quantile Treatment Effects

• Summary of Key Concepts

  • Recap of the importance of QTE for understanding treatment heterogeneity.

  • Differences between QTE and ATE, and the value of studying the entire outcome distribution.

• Challenges and Future Research

  • Addressing computational challenges and improving estimation techniques for large datasets.

  • Expanding QTE applications in machine learning, big data, and real-time decision-making in policy evaluation.

Sách

Bài báo

• Liao, W. C., & Zhao, D. (2019). The selection and quantile treatment effects on the economic returns of green buildings. Regional Science and Urban Economics, 74, 38-48.

• Schiele, V., & Schmitz, H. (2016). Quantile treatment effects of job loss on health. Journal of Health Economics, 49, 59-69.

• Messinis, G. (2013). Returns to education and urban-migrant wage differentials in China: IV quantile treatment effects. China Economic Review, 26, 39-55.

Nội dung

Section 1: Quantile Regression for Censored and Truncated Data

• Challenges of Censored and Truncated Data in Quantile Regression

  • Censoring mechanisms and their effects on estimation bias.

  • Truncation and how it alters the observed distribution of the outcome variable.

• Quantile Regression in the Presence of Censoring

  • Adjusting quantile regression for censored data: Estimating conditional quantiles when outcomes are partially observed.

• Quantile Regression for Truncated Data

  • Understanding truncated models: Dealing with truncation at different points of the outcome distribution.

  • Example: Estimating a truncated wage distribution for individuals earning above a certain threshold.

Section 2: Estimation Techniques for Quantile Regression with Censored Data

• Tobit Quantile Regression Models

  • Introduction to Tobit models: Combining quantile regression with Tobit-style censoring.

  • Example: Estimating Tobit quantile regression for censored wage data with an upper threshold.

• Powell's Censored Quantile Regression (CQR)

  • Overview of Powell’s method for censored quantile regression.

  • Estimation techniques: Adapting standard quantile regression to account for censoring.

  • Example: Censored quantile regression applied to consumer expenditure data with upper censoring.

• Inverse Probability Weighting for Censored Quantile Regression

  • Using inverse probability weighting (IPW) to handle censoring in quantile regression models.

  • Example: Estimating IPW-adjusted quantile regression for censored health expenditure data.

• Penalized Quantile Regression for Censored Data

  • Introduction to penalized methods (Lasso, Ridge) for censored quantile regression models.

  • Example: Estimating penalized censored quantile regression for high-dimensional survey data with income caps.

Section 3: Estimation Techniques for Quantile Regression with Truncated Data

• Truncated Quantile Regression Models

  • Estimating quantile regression for truncated data: Adjusting for non-observed portions of the distribution.

  • Example: Truncated quantile regression for investment decisions of firms with a minimum size threshold.

• Maximum Likelihood Estimation for Truncated Quantile Regression

  • Overview of maximum likelihood estimation for truncated quantile models.

  • Example: Using MLE-based quantile regression for truncated housing price data where observations are truncated at a lower bound.

• Two-step Estimation Procedures for Truncated Quantile Regression

  • Combining a first-step truncation adjustment with a second-step quantile regression.

  • Example: Two-step estimation for modeling productivity distributions in firms above a certain size.

Section 4: Interpretation of Quantile Regression Results for Censored and Truncated Data

• Interpreting Coefficients in Censored Quantile Regression

  • How to interpret the results of censored quantile regression models at different quantiles.

  • Example: Analyzing the impact of education on censored wage data across quantiles.

• Interpreting Coefficients in Truncated Quantile Regression

  • How to interpret coefficients for truncated models, accounting for the absence of data beyond truncation points.

  • Example: Understanding the effects of market conditions on house prices when data is truncated at a certain lower bound.

• Visualization of Censored and Truncated Quantile Regression Results

  • Graphical representation of results: Coefficient plots and quantile process plots for censored and truncated data.

  • Example: Visualizing censored quantile regression results for healthcare costs across different income levels.

Section 5: Hypothesis Testing and Inference in Quantile Regression for Censored and Truncated Data

• 6.1 Hypothesis Testing for Censored Quantile Regression Models

  • Testing the significance of coefficients for censored quantile models.

  • Example: Wald and Likelihood Ratio tests for censored quantile regression.

• 6.2 Hypothesis Testing for Truncated Quantile Regression Models

  • Testing for truncation effects and parameter significance in truncated quantile models.

  • Example: Testing the impact of truncation on wage growth across quantiles.

• 6.3 Confidence Intervals and Standard Errors

  • Bootstrap and asymptotic methods for estimating standard errors and confidence intervals in censored and truncated quantile regression.

  • Example: Constructing confidence intervals for censored quantile regression in real estate data.

Section 6: Applications of Quantile Regression for Censored and Truncated Data

• Wage Distributions with Censored and Truncated Data

  • Application of censored and truncated quantile regression to analyze wage distribution in labor markets.

  • Example: Estimating wage quantiles when wages are censored at the upper end due to reporting caps.

• Healthcare and Expenditure Data

  • Application to censored healthcare expenditure data, where costs are censored or truncated due to subsidy caps.

  • Example: Censored quantile regression for modeling healthcare spending distribution across income groups.

• Financial and Investment Data

  • Application of truncated quantile regression to investment decisions in firms, where only data above a certain threshold is observed.

  • Example: Analyzing investment returns in high-value firms using truncated quantile regression.

Section 7: Advantages and Limitations of Quantile Regression for Censored and Truncated Data

• Advantages of Censored and Truncated Quantile Regression

  • Flexibility: Modeling heterogeneous effects at different quantiles while accounting for censoring or truncation.

  • Robustness: Handling non-normality, outliers, and heteroskedasticity in censored/truncated datasets.

• Limitations and Challenges

  • Computational complexity: Censored and truncated quantile models are computationally more demanding than standard models.

  • Interpretation challenges: Understanding and communicating the effects of censoring and truncation.

  • Sensitivity to assumptions: The results can be sensitive to assumptions about censoring/truncation mechanisms.

Section 8: Software Implementation for Censored and Truncated Quantile Regression

• Implementing Censored Quantile Regression in Stata

• Censored and Truncated Quantile Regression in R

• Python Implementation of Censored and Truncated Quantile Regression

• Other software for Censored and Truncated Quantile Regression

Section 9: Conclusion and Future Directions in Censored and Truncated Quantile Regression

• Summary of Key Concepts

  • Recap of censored and truncated quantile regression: Estimation techniques, interpretation, and applications.

• Challenges and Future Research

  • Expanding censored and truncated quantile regression models to handle more complex data structures (e.g., panel data).

  • Improving computational efficiency for large datasets with censoring/truncation.

  • Potential for applications in machine learning and big data contexts.

Sách

Bài báo

• Baker, M. (2013). MCMCCQREG: Stata module to perform simulation assisted estimation of censored quantile regression using adaptive Markov chain Monte Carlo.

• Frumento, P., & Bottai, M. (2017). An estimating equation for censored and truncated quantile regression. Computational Statistics & Data Analysis, 113, 53-63.

• Chen, S. (2023). Two-step estimation of censored quantile regression for duration models with time-varying regressors. Journal of Econometrics, 235(2), 1310-1336.

• Narisetty, N., & Koenker, R. (2022). Censored quantile regression survival models with a cure proportion. Journal of Econometrics, 226(1), 192-203.

• Ji, Y., Lin, N., & Zhang, B. (2012). Model selection in binary and tobit quantile regression using the Gibbs sampler. Computational Statistics & Data Analysis, 56(4), 827-839.

• Fitzenberger, B. (1997). 15 a guide to censored quantile regressions. Handbook of statistics, 15, 405-437.

• Yu, K., & Stander, J. (2007). Bayesian analysis of a Tobit quantile regression model. Journal of Econometrics, 137(1), 260-276.

• Frumento, P. (2023). A quantile regression estimator for interval-censored data. The International Journal of Biostatistics, 19(1), 81-96.

Nội dung

Section 1: Introduction to Extremal Quantile Regression

• What Is Extremal Quantile Regression (EQR)?

  • Definition and key concept of extremal quantile regression.

  • Motivation for EQR: Focus on extreme values at the tails of the distribution (both upper and lower tails).

  • Applications: Financial risk (Value-at-Risk), extreme weather events, insurance, healthcare costs.

Section 2: Theoretical Foundations of Extremal Quantile Regression

• Extremes and Heavy Tails in Distributions

  • Introduction to extreme value theory (EVT): Heavy tails and rare events.

  • How extremal quantile regression addresses the distribution tails where extreme events occur.

• Quantile Function in Extremal Quantile Regression

  • Revisiting the quantile function for extremal quantiles.

  • Estimating conditional quantiles close to the boundaries of the distribution (near 0 or 1).

• Tail Behavior and Asymptotic Properties

  • Asymptotic properties of the extremal quantiles.

  • Tail behavior and the role of extreme value distributions in EQR.

  • Connection between extreme value theory and EQR for tail estimation.

Section 3: Estimation Techniques for Extremal Quantile Regression

• Standard Quantile Regression for Extremes

  • Applying traditional quantile regression to estimate extreme quantiles.

  • Limitations of standard quantile regression for extreme values: Issues with sparsity and bias.

• Regularization Techniques for EQR

  • Lasso and Ridge regularization for EQR: Reducing bias in extreme quantile estimates.

  • Example: Estimating the 99th quantile of stock market returns using Lasso-regularized EQR.

• Extreme Value Theory-Based Estimation

  • Incorporating extreme value theory (EVT) into the EQR framework.

  • Peak-over-threshold (POT) models and Generalized Pareto Distribution (GPD) for EQR.

  • Example: EVT-based EQR for modeling extreme wind speeds in climate data.

• Kernel-Based Methods for EQR

  • Using kernel density estimation to improve the estimation of extremal quantiles.

  • Example: Kernel-based EQR for predicting extreme healthcare expenditures.

• Bayesian Approaches to Extremal Quantile Regression

  • Bayesian inference techniques for estimating extreme quantiles.

  • Example: Bayesian EQR for risk modeling in insurance portfolios.

Section 4: Tail Risk Measures Using Extremal Quantile Regression

• Value-at-Risk (VaR)

  • Introduction to Value-at-Risk: Measuring the potential loss at extreme quantiles.

  • Using EQR to estimate VaR for financial portfolios.

  • Example: Estimating the 99th percentile VaR for a stock portfolio using EQR.

• Expected Shortfall (ES)

  • Definition of Expected Shortfall: The average loss beyond a specific quantile (e.g., beyond the 99th percentile).

  • Estimating ES using EQR: Capturing the tail risk beyond the extremal quantile.

  • Example: Calculating Expected Shortfall for a bond portfolio using EQR.

Section 5: Interpretation of Extremal Quantile Regression Results

• Interpreting EQR Coefficients

  • How to interpret coefficients for extremal quantile regression models.

  • Differences in interpretation between central and extremal quantiles.

  • Example: Understanding the impact of macroeconomic variables on extreme quantiles of GDP growth.

• Visualization of Extremal Quantile Regression Results

  • Graphical representation of EQR results: Quantile process plots and tail behavior analysis.

  • Example: Visualizing the extremal quantile estimates for stock market returns in a financial risk model.

Section 6: Hypothesis Testing and Inference in Extremal Quantile Regression

• Hypothesis Testing for EQR Coefficients

  • Testing the significance of coefficients in extremal quantile models.

  • Example: Wald test and Likelihood Ratio test for EQR models in climate risk modeling.

• Confidence Intervals and Standard Errors

  • Bootstrapping and asymptotic methods for estimating standard errors and confidence intervals for extremal quantiles.

  • Example: Constructing confidence intervals for extremal quantile estimates in housing price analysis.

• Joint Tests for Multiple Extremal Quantiles

  • Testing differences in tail behavior across different quantiles (e.g., comparing 95th, 99th, and 99.5th quantiles).

  • Example: Testing for significant differences in extreme quantiles of asset returns before and after a financial crisis.

Section 7: Applications of Extremal Quantile Regression

• Financial Markets and Risk Management

  • Application of EQR in estimating financial tail risks (VaR and ES).

  • Example: EQR for assessing extreme downside risks in stock returns during periods of market volatility.

• Climate and Environmental Data

  • Application of EQR in modeling extreme weather events (e.g., extreme rainfall, temperatures).

  • Example: EQR for forecasting extreme temperature variations under climate change scenarios.

• Insurance and Actuarial Sciences

  • EQR for estimating tail risks in insurance claims (e.g., catastrophic losses, rare events).

  • Example: Modeling the distribution of large insurance claims using EQR.

• Healthcare Costs

  • Using EQR to model extreme healthcare expenditures (e.g., outliers in patient treatment costs).

  • Example: Estimating the extreme quantiles of hospitalization costs in a healthcare dataset.

Section 8: Advantages and Limitations of Extremal Quantile Regression

• Advantages of EQR

  • Capturing tail behavior and rare events.

  • Robustness to skewness and heavy-tailed distributions.

  • Applicability to risk management and forecasting extreme events.

• Limitations of EQR

  • Computational complexity: Estimating extremal quantiles in large datasets.

  • Data sparsity in the tails: Challenges in obtaining reliable estimates for very extreme quantiles.

  • Sensitivity to assumptions about the distribution of extremes (e.g., heavy tails).

Section 9: Extensions and Alternative Methods in Extremal Quantile Regression

• Quantile Regression with Extreme Value Theory (EVT)

  • Combining EVT with quantile regression for better tail estimation.

  • Example: EVT-based quantile regression for modeling financial tail risks in a global stock market dataset.

• Penalized Extremal Quantile Regression

  • Introducing penalization techniques (e.g., Lasso, Ridge) to reduce overfitting in EQR models.

  • Example: Using penalized EQR for high-dimensional financial data.

• Nonparametric and Semiparametric Approaches to EQR

  • Nonparametric methods for estimating extremal quantiles without strong distributional assumptions.

  • Example: Kernel-based nonparametric EQR for extreme environmental risk assessment.

Section 10: Software Implementation for Extremal Quantile Regression

• EQR Implementation in R

  • Using R packages such as quantreg and extRemes for extremal quantile regression.

  • Example: Step-by-step guide to implementing EQR for financial market data in R.

• Extremal Quantile Regression in Python

  • Implementing EQR using Python libraries such as statsmodels and SciPy.

  • Example: Python implementation of EQR for estimating extreme weather event risks.

• EQR in Stata

  • Stata commands and tools for implementing extremal quantile regression models.

  • Example: Using Stata for EQR in economic forecasting under extreme conditions.

Section 11: Conclusion and Future Directions in Extremal Quantile Regression

• Summary of Key Concepts

  • Recap of extremal quantile regression: Estimation techniques, applications, and interpretation.

• Future Research and Challenges

  • Addressing computational challenges for very large datasets.

  • Expanding EQR applications in machine learning and big data contexts.

  • Future directions: Integrating EQR into policy decision-making for rare event forecasting and risk management.

Sách

Bài báo

• Chernozhukov, V., Fernández-Val, I., & Kaji, T. (2017). Extremal quantile regression. Handbook of Quantile Regression, 333-362. 

• D’Haultfœuille, X., Maurel, A., & Zhang, Y. (2018). Extremal quantile regressions for selection models and the black–white wage gap. Journal of Econometrics, 203(1), 129-142.

• Schaumburg, J. (2012). Predicting extreme value at risk: Nonparametric quantile regression with refinements from extreme value theory. Computational Statistics & Data Analysis, 56(12), 4081-4096.

• Jurečková, J. (2000). Test of tails based on extreme regression quantiles. Statistics & probability letters, 49(1), 53-61.

• Bassett Jr, G. W. (1988). A property of the observations fit by the extreme regression quantiles. Computational Statistics & Data Analysis, 6(4), 353-359.

Nội dung

Section 1: Introduction to Quantile Regression and Machine Learning

• Motivation for Incorporating Machine Learning in Quantile Regression

  • Limitations of traditional parametric quantile regression (e.g., overfitting, underfitting in complex data).

  • The need for flexible and scalable models in big data contexts.

  • Advantages of machine learning approaches: Nonlinear relationships, high-dimensional data, feature selection, improved prediction accuracy.

• Applications of Machine Learning in Quantile Regression

  • Examples: Financial risk forecasting, pricing models, demand prediction, healthcare cost analysis.

Section 2: Machine Learning in Quantile Regression

• Machine Learning vs. Traditional Econometric Models

  • Key differences in objectives: Prediction vs. interpretation.

  • Role of machine learning in handling large, high-dimensional datasets.

• Quantile Loss Function in a Machine Learning Framework

  • Review of the quantile loss function (pinball loss).

  • Minimizing the asymmetric loss for different quantiles.

• Regularization and Overfitting in Machine Learning Quantile Regression

  • Introduction to overfitting in machine learning and the importance of regularization.

  • Regularization techniques: Lasso, Ridge, Elastic Net for quantile regression.

Section 3: Machine Learning Algorithms for Quantile Regression

• Decision Trees for Quantile Regression

  • Introduction to decision trees: Handling non-linear relationships and interactions.

  • Adapting decision trees for quantile regression: Splitting nodes based on the quantile loss function.

  • Example: Quantile regression decision trees for predicting income quantiles.

• Random Forests for Quantile Regression

  • Overview of random forests: Aggregating multiple decision trees for improved prediction.

  • Quantile regression forests (QRF): Estimating conditional quantiles using forest structure.

  • Example: QRF for predicting house price quantiles across different regions.

• Gradient Boosting Machines (GBM) for Quantile Regression

  • Introduction to gradient boosting: Sequentially building decision trees to minimize the quantile loss function.

  • Quantile regression boosting (QR-GBM): Estimating conditional quantiles using boosted trees.

  • Example: QR-GBM for financial risk modeling and Value-at-Risk estimation.

• Neural Networks for Quantile Regression

  • Overview of neural networks: Handling complex and high-dimensional data.

  • Adapting neural networks to minimize the quantile loss function.

  • Example: Deep learning models for estimating quantile effects in healthcare expenditure prediction.

• Support Vector Machines (SVM) for Quantile Regression

  • Adapting SVM to quantile regression: Using quantile-specific loss functions.

  • Example: SVM quantile regression for forecasting electricity demand quantiles.

Section 4: Advanced Machine Learning Approaches in Quantile Regression

• Regularization Techniques in Machine Learning Quantile Regression

  • Regularization in machine learning quantile models: Lasso, Ridge, and Elastic Net.

  • Example: Penalized quantile regression for large financial datasets.

• Nonparametric and Kernel-based Methods for Quantile Regression

  • Introduction to kernel methods in quantile regression.

  • Kernel quantile regression for capturing complex non-linear relationships.

  • Example: Nonparametric quantile regression for modeling customer demand with price changes.

• Ensemble Methods in Quantile Regression

  • Introduction to ensemble learning: Combining multiple models to improve quantile predictions.

  • Stacking and bagging for quantile regression.

  • Example: Using ensemble methods for predicting sales quantiles in retail.

Section 5: Interpretation of Machine Learning Quantile Regression Models

• Interpreting Machine Learning Models for Quantile Regression

  • Challenges of interpretation: Black-box nature of many machine learning models.

  • Feature importance in decision trees and random forests for quantile regression.

  • Example: Interpreting feature importance for income quantiles in a random forest model.

• Partial Dependence Plots and SHAP Values

  • Using partial dependence plots to interpret the relationship between variables and quantiles.

  • SHAP (SHapley Additive exPlanations) values for understanding feature contributions in quantile models.

  • Example: Using SHAP values to interpret the impact of macroeconomic factors on the lower quantiles of income distribution.

Section 6: Hyperparameter Tuning and Model Validation

• Hyperparameter Tuning in Machine Learning Quantile Regression

  • Key hyperparameters to tune in machine learning quantile regression models (e.g., max depth in decision trees, learning rate in boosting).

  • Cross-validation strategies: K-fold cross-validation, leave-one-out cross-validation for selecting the best quantile model.

  • Example: Tuning hyperparameters in quantile regression forests for house price prediction.

• Model Evaluation Metrics for Quantile Regression

  • Evaluating the performance of machine learning quantile regression models: Pinball loss, quantile residuals, and prediction intervals.

  • Example: Comparing the performance of quantile regression random forests and gradient boosting machines for stock price forecasting.

• Cross-validation for Quantile Regression

  • Cross-validation techniques for quantile regression models.

  • Example: K-fold cross-validation for model selection in quantile boosting.

Section 7: Applications of Machine Learning Quantile Regression

• Financial Risk Management

  • Using machine learning quantile regression to estimate Value-at-Risk (VaR) and Expected Shortfall (ES).

  • Example: Quantile regression forests for VaR estimation in portfolio management.

• Real Estate and Housing Market Analysis

  • Predicting house prices across quantiles using machine learning models.

  • Example: Gradient boosting for estimating the lower quantiles of house prices in different cities.

• Healthcare Cost Prediction

  • Estimating healthcare expenditures across quantiles using machine learning quantile regression.

  • Example: Neural networks for quantile regression in healthcare cost analysis.

• Energy Demand Forecasting

  • Using machine learning quantile regression for electricity and energy demand forecasting.

  • Example: Quantile boosting models for predicting electricity demand spikes.

• Climate and Environmental Data

  • Application of machine learning quantile regression to environmental data: Predicting climate impact quantiles.

  • Example: Random forests for quantile regression in rainfall and temperature forecasting.

Section 8: Advantages and Limitations of Machine Learning Quantile Regression

• Advantages of Machine Learning Quantile Regression

  • Flexibility in capturing complex, nonlinear relationships.

  • Scalability for large datasets and high-dimensional problems.

  • Robustness to outliers and heteroskedasticity.

• Limitations of Machine Learning Quantile Regression

  • Computational complexity: Higher resource requirements for large datasets.

  • Interpretability challenges: Black-box nature of machine learning models.

  • Sensitivity to hyperparameters and data preprocessing choices.

Section 9: Software Implementation of Machine Learning Quantile Regression

• Implementing Machine Learning Quantile Regression in Python

• Machine Learning Quantile Regression in R

• Other Software Tools for Machine Learning Quantile Regression

Section 10: Conclusion and Future Directions in Machine Learning Quantile Regression

• Summary of Key Concepts

  • Recap of the integration of machine learning and quantile regression: Flexibility, scalability, and improved prediction accuracy.

• Future Research and Challenges

  • Addressing interpretability issues in machine learning quantile models.

  • Potential for applications in big data, real-time forecasting, and policy evaluation.

  • Expanding the role of machine learning quantile regression in causal inference and treatment effects.

Sách

Bài báo

• Delcroix, B., Sansregret, S., Martin, G. L., & Daoud, A. (2021, November). Quantile regression using gradient boosted decision trees for daily residential energy load disaggregation. In Journal of Physics: Conference Series (Vol. 2069, No. 1, p. 012107). IOP Publishing.

• Dang, S., Peng, L., Zhao, J., Li, J., & Kong, Z. (2022). A quantile regression random forest-based short-term load probabilistic forecasting method. Energies, 15(2), 663.

• Xu, Q., Deng, K., Jiang, C., Sun, F., & Huang, X. (2017). Composite quantile regression neural network with applications. Expert Systems with Applications, 76, 129-139.

• Jantre, S. R., Bhattacharya, S., & Maiti, T. (2021). Quantile regression neural networks: a bayesian approach. Journal of Statistical Theory and Practice, 15(3), 68.

• Cannon, A. J. (2011). Quantile regression neural networks: Implementation in R and application to precipitation downscaling. Computers & geosciences, 37(9), 1277-1284.