Lecture 12 Joint Hypothesis Tests.ppt

Lecture 12: Joint Hypothesis Tests (Chapter 9.1–9.3, 9.5–9.6) Today’s Agenda Review Joint Hypotheses (Chapter 9.1) F-tests (Chapter 9.2–9.3) Applications of F-tests (Chapter 9.5–9.6) Review Perfect multicollinearity occurs when 2 or more of your explanators are jointly perfectly correlated. That is, you can write one of your explanators as a linear function of other explanators: Review (cont.) OLS breaks down with perfect multicollinearity (and standard errors blow up with near perfect multicollinearity). Multicollinearity most frequently occurs when you want to include: Time, age, and birth year effects A dummy variable for each category, plus a constant Review (cont.) Dummy variables (also called binary variables) take on only the values 0 or 1. Dummy variables let you estimate separate intercepts and slopes for different groups. To avoid multicollinearity while including a constant, you need to omit the dummy variable for one group (e.g. males or non-Hispanic whites). You want to pick one of the larger groups to omit. Review (cont.) Review (cont.) You can multiply 2 variables together to create interaction terms. Interaction terms let the slope of each variable depend on the value of the other variable. Review (cont.) Review (cont.) With many of the specifications covered last time, we encountered hypotheses that required us to test multiple conditions simultaneously. For example, to test: All categories have the same intercept (with 3 or more categories) All categories have the same slope (with 3 or more categories) One explanator has no effect on Y, when that explanator has been used in an interaction term Review (cont.) In economics, many processes are non-linear. Economic theory relies heavily on diminishing marginal returns, decreasing returns to scale, etc. We want a specification that lets the 50th unit of X have a different marginal effect than the 1st unit of X. Review (cont.) If we regress not but rather then the marginal benefit of a unit of