Sometimes, the pattern of coefficients on the year dummy variables is itself of interest. For example, a demographer may be interested in the following question: After controlling for education, has the pattern of fertility among women over age 35 changed between 1972 and 1984? The following table illustrates how this question is simply answered by using multiple regression analysis with year dummy variables. The table below presents the results from a study carried out on the total number of kids born to a woman. The factors that are controlled for are years of education, age, race, region of the country where living at age 16, and living environment at age 16. Dependent Variable: Kids Independent Variable Coefficients Standard Errors educ 0.128 0.018 age 0.532 0.138 age 0.006 0.002 black 1.076 0.174 east 0.217 0.133 northcen 0.363 0.121 west 0.198 0.167 farm 0.053 0.147 rural -0.163 0.175 town 0.084 0.124 smcity 0.212 0.160 y74 0.268 0.173 The Independent Institute of Education (Pty) Ltd 2022 Page 4 of 6 22 2022 y76 -0.097 0.179 y78 0.069 0.182 y80 -0.071 0.183 y82 -0.522 0.172 y84 -0.545 0.175 constant 7.742 3.052 n 1129 R2 0.1295 Adjusted R2 0.1162 Q.2.1 Interpret the results of the estimated model provided above. (10) Q.2.2 Why can we not use first differences when we have independent cross sections in two (5) years (as opposed to panel data)? Q.2.3 Suppose that we want to estimate the effect of several variables on annual saving and (5) that we have a panel data set on individuals collected on January 31, 1990, and January 31, 1992. If we include a year dummy for 1992 and use first differencing, can we also include age in the original model? Motivate you answer. Q.2.4 Explain the Chow Test for Structural Change across Time