(c) Use 1m function to estimate the treatment effect parameter in the model. summary(1m(y-treat + post + treat*post)) ## ## Call: ## ln(formula y treat + post + treat post) ## ## Residuals: ## Min 10 Median 30 0.0320 0.7163 3.2142 ## -3.4845 -0.6348 ## ## Coefficients: ## ## (Intercept) 0.04146 8.86312 8.657 Estimate Std. Error t value Pr(>|t|) 0.511 ## treat 1.00124 #post ## treat: post 2.81261 3.99694 0.08909 11.238 8.89862 22.209 0.12868 31.088 <20-16 *** <20-16 ## --- signif. codes: 8 0.001 0.01 0.85 8.1 residual standard error: 1.016 on 996 degrees of freedom multiple r-squared: 8.8729, adjusted 0.8725 f-statistic: 2280 3 and df, p-value: <2.20-16 summary(1m(y-treat + post )) call: 1n(formula y treat post) residuals: min 10 median 30 # -4.2999 -1.8788 -0.8042 1.0650 4.2358 coefficients: estimate std. error t value pr(>|t|) ## (Intercept) -8.92137 8.87714 -11.94 <20-16 *** 1 ## treat #post ##--- 0.09813 32.39 <20-16 *** <20-16 *** 2.91951 3.99744 8.89828 44.32 ## Signif. codes: 0.001 0.01 0.85 8.11 ## ## Residual standard error: 1.425 on 997 degrees of freedom ## Multiple R-squared: 8.7496, Adjusted R-squared: 0.7491 ## F-statistic: 1492 on 2 and 997 DF, p-value: < 2.20-16 (d) Use the following code to estimate > using the definition of a difference-in-difference estimator. Explain the estimate. (mean (y[treat--1 & post--1]) - mean(y[treat--1 & post--8])) - + (mean(y[treat--8 & post--1]) ## [1] 3.99694 mean(y[treat--8 & post--8])) (e) Compare the estimate of & in part (c) to what you found in part (d)