dgpols - * * 4 reg y x * one unit increase in x leads to...

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use dgpols, clear u * 1 summ s * 2 * Cov(X,U)=0 because X and U are independent * Cov(X,U)=E[(X-E[X])(U-E[U])] * to calculate the sample covariance, we use the sample analogue of the above formula egen xbar=mean(x) egen ubar=mean(u) gen temp=(x-xbar)*(u-ubar) summ temp * sample covariance = -.0277908 * the value is close to zero * a formal test: reg temp * and observe that the 95% confidence interval includes 0 * * 3 * E[Y]=E[beta0+beta1*X+U]=2.8+4.2*1+0=7.0 gen y=2.8+4.2*x+u summ y * the sample mean is a realized value of E[Y] * therefore E[Y] is different from the sample mean
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Unformatted text preview: * * 4 reg y x * one unit increase in x leads to 4.12 unit increase in y * no: std error is small, t-stat large, p-value small, and confidence interval does not include 0 test x=4 * yes: p-value large, and confidence interval includes 4 * * 5 * beta1_hat is just a realization of beta1 * no * ideally, we want to reject any H0 which is different from beta1=4 * however, this is not possible because of sampling errors and finite sample sizes...
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