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Now what do I do with this function? Enrique Pinzn StataCorp LP - PowerPoint PPT Presentation

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Now what do I do with this function? Enrique Pinzn StataCorp LP October 19, 2017 Madrid (StataCorp LP) October 19, 2017 Madrid 1 / 42 Initial thoughts Nonparametric regression and about effects/questions npregress Mean relation between

  1. Now what do I do with this function? Enrique Pinzón StataCorp LP October 19, 2017 Madrid (StataCorp LP) October 19, 2017 Madrid 1 / 42

  2. Initial thoughts Nonparametric regression and about effects/questions npregress Mean relation between an outcome and covariates ◮ Model birtweight : age, education level, smoked, number of prenatal visits, ... ◮ Model wages: age, education level, profession, tenure, ... ◮ E ( y | X ) , conditional mean Parametric models have a known functional form Linear regression: E ( y | X ) = X β E ( y | X ) = F ( X β ) Binary: Poisson: E ( y | X ) = exp ( X β ) Nonparametric E ( y | X ) . The result of using predict (StataCorp LP) October 19, 2017 Madrid 2 / 42

  3. Initial thoughts Nonparametric regression and about effects/questions npregress Mean relation between an outcome and covariates ◮ Model birtweight : age, education level, smoked, number of prenatal visits, ... ◮ Model wages: age, education level, profession, tenure, ... ◮ E ( y | X ) , conditional mean Parametric models have a known functional form Linear regression: E ( y | X ) = X β E ( y | X ) = F ( X β ) Binary: Poisson: E ( y | X ) = exp ( X β ) Nonparametric E ( y | X ) . The result of using predict (StataCorp LP) October 19, 2017 Madrid 2 / 42

  4. Initial thoughts Nonparametric regression and about effects/questions npregress Mean relation between an outcome and covariates ◮ Model birtweight : age, education level, smoked, number of prenatal visits, ... ◮ Model wages: age, education level, profession, tenure, ... ◮ E ( y | X ) , conditional mean Parametric models have a known functional form Linear regression: E ( y | X ) = X β E ( y | X ) = F ( X β ) Binary: Poisson: E ( y | X ) = exp ( X β ) Nonparametric E ( y | X ) . The result of using predict (StataCorp LP) October 19, 2017 Madrid 2 / 42

  5. Initial thoughts Nonparametric regression and about effects/questions npregress Mean relation between an outcome and covariates ◮ Model birtweight : age, education level, smoked, number of prenatal visits, ... ◮ Model wages: age, education level, profession, tenure, ... ◮ E ( y | X ) , conditional mean Parametric models have a known functional form Linear regression: E ( y | X ) = X β E ( y | X ) = F ( X β ) Binary: Poisson: E ( y | X ) = exp ( X β ) Nonparametric E ( y | X ) . The result of using predict (StataCorp LP) October 19, 2017 Madrid 2 / 42

  6. Initial thoughts Nonparametric regression and about effects/questions npregress Mean relation between an outcome and covariates ◮ Model birtweight : age, education level, smoked, number of prenatal visits, ... ◮ Model wages: age, education level, profession, tenure, ... ◮ E ( y | X ) , conditional mean Parametric models have a known functional form Linear regression: E ( y | X ) = X β E ( y | X ) = F ( X β ) Binary: Poisson: E ( y | X ) = exp ( X β ) Nonparametric E ( y | X ) . The result of using predict (StataCorp LP) October 19, 2017 Madrid 2 / 42

  7. Initial thoughts Nonparametric regression and about effects/questions npregress Mean relation between an outcome and covariates ◮ Model birtweight : age, education level, smoked, number of prenatal visits, ... ◮ Model wages: age, education level, profession, tenure, ... ◮ E ( y | X ) , conditional mean Parametric models have a known functional form Linear regression: E ( y | X ) = X β E ( y | X ) = F ( X β ) Binary: Poisson: E ( y | X ) = exp ( X β ) Nonparametric E ( y | X ) . The result of using predict (StataCorp LP) October 19, 2017 Madrid 2 / 42

  8. (StataCorp LP) October 19, 2017 Madrid 3 / 42

  9. But ... We had nonparametric regression tools lpoly lowess (StataCorp LP) October 19, 2017 Madrid 4 / 42

  10. But ... We had nonparametric regression tools lpoly lowess (StataCorp LP) October 19, 2017 Madrid 4 / 42

  11. What happened in the past lpoly bweight mage if (msmoke==0 & medu>12 & fedu>12), /// mcolor(%30) lineopts(lwidth(thick)) (StataCorp LP) October 19, 2017 Madrid 5 / 42

  12. Effects: A thought experiment I give you the true function . list y x a gx in 1/10, noobs y x a gx 13.46181 .7630615 2 12.73349 1.41086 .9241793 1 1.547555 22.88834 1.816095 2 21.43813 10.97789 .8206556 2 13.01466 11.37173 .0440157 2 10.13213 -.1938587 1.083093 1 .439635 55.87413 3.32037 2 56.56772 2.94979 .8900821 1 1.804343 -1.178733 -2.342678 0 -2.856946 48.79958 3.418333 0 49.94323 (StataCorp LP) October 19, 2017 Madrid 6 / 42

  13. Effects: A thought experiment I give you the true function . list y x a gx in 1/10, noobs y x a gx 13.46181 .7630615 2 12.73349 1.41086 .9241793 1 1.547555 22.88834 1.816095 2 21.43813 10.97789 .8206556 2 13.01466 11.37173 .0440157 2 10.13213 -.1938587 1.083093 1 .439635 55.87413 3.32037 2 56.56772 2.94979 .8900821 1 1.804343 -1.178733 -2.342678 0 -2.856946 48.79958 3.418333 0 49.94323 (StataCorp LP) October 19, 2017 Madrid 6 / 42

  14. Effects: A thought experiment I give you the true function Do we know what are the marginal effects Do we know causal/treatment effects Do we know counterfactuals It seems cosmetic We cannot use margins (StataCorp LP) October 19, 2017 Madrid 7 / 42

  15. Effects: A thought experiment I give you the true function Do we know what are the marginal effects Do we know causal/treatment effects Do we know counterfactuals It seems cosmetic We cannot use margins (StataCorp LP) October 19, 2017 Madrid 7 / 42

  16. Effects: A thought experiment I give you the true function Do we know what are the marginal effects Do we know causal/treatment effects Do we know counterfactuals It seems cosmetic We cannot use margins (StataCorp LP) October 19, 2017 Madrid 7 / 42

  17. Effects: A thought experiment I give you the true function Do we know what are the marginal effects Do we know causal/treatment effects Do we know counterfactuals It seems cosmetic We cannot use margins (StataCorp LP) October 19, 2017 Madrid 7 / 42

  18. A detour margins (StataCorp LP) October 19, 2017 Madrid 8 / 42

  19. Effects: outcome of interest (StataCorp LP) October 19, 2017 Madrid 9 / 42

  20. Data crash 1 if crash traffic Measure of vehicular traffic tickets Number of traffic tickets male 1 if male (StataCorp LP) October 19, 2017 Madrid 10 / 42

  21. Probit model and average marginal effects probit crash tickets traffic i.male . margins Predictive margins Number of obs = 948 Model VCE : OIM Expression : Pr(crash), predict() Delta-method Margin Std. Err. z P>|z| [95% Conf. Interval] _cons .1626529 .0044459 36.58 0.000 .153939 .1713668 . margins, dydx(traffic tickets) Average marginal effects Number of obs = 948 Model VCE : OIM Expression : Pr(crash), predict() dy/dx w.r.t. : tickets traffic Delta-method dy/dx Std. Err. z P>|z| [95% Conf. Interval] tickets .0857818 .0031049 27.63 0.000 .0796963 .0918672 traffic .0055371 .0020469 2.71 0.007 .0015251 .009549 (StataCorp LP) October 19, 2017 Madrid 11 / 42

  22. Probit model and average marginal effects probit crash tickets traffic i.male . margins Predictive margins Number of obs = 948 Model VCE : OIM Expression : Pr(crash), predict() Delta-method Margin Std. Err. z P>|z| [95% Conf. Interval] _cons .1626529 .0044459 36.58 0.000 .153939 .1713668 . margins, dydx(traffic tickets) Average marginal effects Number of obs = 948 Model VCE : OIM Expression : Pr(crash), predict() dy/dx w.r.t. : tickets traffic Delta-method dy/dx Std. Err. z P>|z| [95% Conf. Interval] tickets .0857818 .0031049 27.63 0.000 .0796963 .0918672 traffic .0055371 .0020469 2.71 0.007 .0015251 .009549 (StataCorp LP) October 19, 2017 Madrid 11 / 42

  23. Probit model and average marginal effects probit crash tickets traffic i.male . margins Predictive margins Number of obs = 948 Model VCE : OIM Expression : Pr(crash), predict() Delta-method Margin Std. Err. z P>|z| [95% Conf. Interval] _cons .1626529 .0044459 36.58 0.000 .153939 .1713668 . margins, dydx(traffic tickets) Average marginal effects Number of obs = 948 Model VCE : OIM Expression : Pr(crash), predict() dy/dx w.r.t. : tickets traffic Delta-method dy/dx Std. Err. z P>|z| [95% Conf. Interval] tickets .0857818 .0031049 27.63 0.000 .0796963 .0918672 traffic .0055371 .0020469 2.71 0.007 .0015251 .009549 (StataCorp LP) October 19, 2017 Madrid 11 / 42

  24. Not calculus . margins, at(traffic=generate(traffic*1.10)) at(traffic=generate(traffic)) /// > contrast(atcontrast(r) nowald) Contrasts of predictive margins Model VCE : OIM Expression : Pr(crash), predict() 1._at : traffic = traffic*1.10 2._at : traffic = traffic Delta-method Contrast Std. Err. [95% Conf. Interval] _at (2 vs 1) -.0028589 .0010882 -.0049917 -.0007262 (StataCorp LP) October 19, 2017 Madrid 12 / 42

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