计量经济学导论电子教案ch06章节幻灯片.pptVIP

Economics 20 - Prof. Anderson * Multiple Regression Analysis y = b0 + b1x1 + b2x2 + . . . bkxk + u 4. Further Issues Economics 20 - Prof. Anderson * Redefining Variables Changing the scale of the y variable will lead to a corresponding change in the scale of the coefficients and standard errors, so no change in the significance or interpretation Changing the scale of one x variable will lead to a change in the scale of that coefficient and standard error, so no change in the significance or interpretation Economics 20 - Prof. Anderson * Beta Coefficients Occasional you’ll see reference to a “standardized coefficient” or “beta coefficient” which has a specific meaning Idea is to replace y and each x variable with a standardized version – i.e. subtract mean and divide by standard deviation Coefficient reflects standard deviation of y for a one standard deviation change in x Economics 20 - Prof. Anderson * Functional Form OLS can be used for relationships that are not strictly linear in x and y by using nonlinear functions of x and y – will still be linear in the parameters Can take the natural log of x, y or both Can use quadratic forms of x Can use interactions of x variables Economics 20 - Prof. Anderson * Interpretation of Log Models If the model is ln(y) = b0 + b1ln(x) + u b1 is the elasticity of y with respect to x If the model is ln(y) = b0 + b1x + u b1 is approximately the percentage change in y given a 1 unit change in x If the model is y = b0 + b1ln(x) + u b1 is approximately the change in y for a 100 percent change in x Economics 20 - Prof. Anderson * Why use log models? Log models are invariant to the scale of the variables since measuring percent changes They give a direct estimate of elasticity For models with y 0, the conditional distribution is often heteroskedastic or skewed, while ln(y) is much less so The distribution of ln(y) is more narrow, limiting the effect of outliers Economics 20 - Prof. Anderson * Some Rules of Thu