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Quantile Regression

Quantile Regression. The intuition. Hypothetical Distributions. The intuition. OLS Regression Results . The intuition. Quantile Regression Results . An alternative approach. Logistic Regression Models. Examples.

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Quantile Regression

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  1. Quantile Regression

  2. The intuition Hypothetical Distributions

  3. The intuition OLS Regression Results

  4. The intuition Quantile Regression Results

  5. An alternative approach Logistic Regression Models

  6. Examples Five ideas from your (or your friends’) research where this approach might be useful.

  7. Some examples Image from Koenker (http://www.econ.uiuc.edu/~roger/research/intro/jep.pdf)

  8. Some examples Image from Koenker (http://www.econ.uiuc.edu/~roger/research/intro/jep.pdf)

  9. Some examples Image from Koenker (http://www.econ.uiuc.edu/~roger/research/intro/jep.pdf)

  10. Some examples Image from Koenker (http://www.econ.uiuc.edu/~roger/research/intro/jep.pdf)

  11. Some examples Image from Bitler et al. 2006 AER paper.

  12. Some examples Image from Bitler et al. 2006 AER paper.

  13. Some examples

  14. Some more examples

  15. Some examples Pronghorn densities (y) by shrub canopy cover (X) on n = 28 winter ranges (data from Cook and Irwin 1985) and 0.90, 0.75, 0.50, 0.25, and 0.10 regression quantile estimates (solid lines) and least squares regression estimate (dashed line) for the model y = b0 + b1X +e . (From Cade and Noon, 2003).

  16. Some examples Quantile regression was used to estimate changes in Lahontan cutthroat trout density (y) as a function of the ratio of stream width to depth (X) for 7 years and 13 streams in the eastern Lahontan basin of the western US. A scatterplot of n = 71 observations of stream width:depth and trout densities with 0.95, 0.75, 0.50, 0.25, and 0.05 quantile (solid lines) and least squares regression (dashed line) estimates for the model ln y = b0 + b1X +e. From Cade and Noon, 2003.

  17. Technical intuitions Image from Pindyck and Rubinfield (Econometric models and economic forecasts)

  18. Formulae (OLS)

  19. Formulae (LAD)

  20. Formulae (LAD vs OLS)

  21. Formulae (LAD at t≠.5)

  22. Formulae (LAD at t≠.5) Negative residuals Positiveresiduals

  23. Technical (semi) intuitions Image from Koenker (http://www.econ.uiuc.edu/~roger/research/intro/jep.pdf)

  24. Why we might care

  25. Why we might care Skewed Distributions

  26. Issues • Small samples • Guidelines: The 30 observations rule? (Chernozhukov) • Suitable dependent variables • Does your metric make sense? • Accessibility • (Relatively) new outside of economics • Solution: Find a friend in economics? • More difficult with thornier data (categorical DV’s, panel data, etc)

  27. Issues • Cluster robust standard errors • Solutions: • Bootstrapping se’s • Sandwich estimators (see stata code online) • Thinking about effects • Effects on the distribution • Rank preservation assumptions • Distribution of Y not of X

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