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Eco 205: Econometrics

Eco 205: Econometrics. Any questions? GH solutions & Lab do-files in class space, but not okay to consult during review. Formula sheet rules … Just symbols & equations, no words or explanations it is okay to put “starting point” equation on there Notes in lab book okay, within reason .

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Eco 205: Econometrics

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  1. Eco 205: Econometrics • Any questions? • GH solutions & Lab do-files in class space, but not okay to consult during review. • Formula sheet rules … • Just symbols & equations, no words or explanations • it is okay to put “starting point” equation on there • Notes in lab book okay, within reason

  2. Multiple Regression (SW Ch.6) • Omitted variable bias • Causality and regression analysis • Multiple regression and OLS • Measures of fit • Sampling distribution of the OLS estimator • Multicollinearity

  3. Back to our Policy Question

  4. Omitted Variable Bias

  5. Omitted Variable Bias Formula

  6. Omitted Variable Bias Formula

  7. Omitted variable bias formula: two X’s case • is slope coefficient from regression of excluded X2 on included X1 • Bias term

  8. Omitted variable bias formula: two X’s case … application . reg prate mrate age, r Linear regression Number of obs = 1534 F( 2, 1531) = 98.18 Prob > F = 0.0000 R-squared = 0.0922 Root MSE = 15.937 ------------------------------------------------------------------------------ | Robust prate | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mrate | 5.521289 .4498478 12.27 0.000 4.638906 6.403672 age | .2431466 .0393743 6.18 0.000 .1659133 .3203798 _cons | 80.11905 .846797 94.61 0.000 78.45804 81.78005 ------------------------------------------------------------------------------ • prate = participation rate in company’s 401(k) plan • mrate = match rate (amount firm contributes for each $1 worker contributes) • age = age of the 401(k) plan

  9. Omitted variable bias formula: two X’s case … application . reg prate mrate, r Linear regression Number of obs = 1534 F( 1, 1532) = 157.77 Prob > F = 0.0000 R-squared = 0.0747 Root MSE = 16.085 ------------------------------------------------------------------------------ | Robust prate | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mrate | 5.861079 .4666276 12.56 0.000 4.945783 6.776376 _cons | 83.07546 .6112819 135.90 0.000 81.87642 84.27449 ------------------------------------------------------------------------------

  10. Omitted variable bias formula: two X’s case … application . reg age mrate, r Linear regression Number of obs = 1534 F( 1, 1532) = 18.75 Prob > F = 0.0000 R-squared = 0.0141 Root MSE = 9.1092 ------------------------------------------------------------------------------ | Robust age | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mrate | 1.39747 .322743 4.33 0.000 .7644054 2.030535 _cons | 12.15896 .3132499 38.82 0.000 11.54451 12.7734 ------------------------------------------------------------------------------ • Conclusion?

  11. Digression on Causality and Regression analysis

  12. Ideal Randomized Controlled Experiment • Ideal • subjects all follow the treatment protocol – perfect compliance, no errors in reporting, etc. • Randomized • subjects from the population of interest are randomly assigned to a treatment or control group (so there are no confounding factors) • Controlled • having a control group permits measuring the differential effect of the treatment • Experiment • treatment is assigned as part of the experiment • subjects have no choice, so there is no “reverse causality” in which subjects choose the treatment they think will work best.

  13. RCT for Student-Teacher Ratio

  14. RCT for Breast Cancer Treatment Source: http://www.nytimes.com/2010/06/08/health/08canc.html?ref=andrew_pollack

  15. RCT for Breast Cancer Treatment Source: http://www.nytimes.com/2010/06/08/health/08canc.html?ref=andrew_pollack

  16. RCT for Breast Cancer Treatment Source: http://abstract.asco.org/AbstView_74_47842.html

  17. RCT for Breast Cancer Treatment Source: http://abstract.asco.org/AbstView_74_47842.html

  18. 3 “solutions” to Omitted Variable Bias Run a randomized controlled experiment in which treatment (lowSTR, axillary dissection) is randomly assigned. Use the “cross tabulation” approach, but … Include the variable as an additional covariate in the multiple regression.

  19. Interpretation of coefficients in multiple regression

  20. The OLS Estimator in Multiple Regression

  21. Multiple regression in STATA

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