Econ 388 R. Butler 2014 revisions lecture13 I. BENCHMARKING TRAINING PROGRAMS: Training Affects over Salesman Lifetimes: Your merge company has a sales force drawn from individuals who have experience one of three sales training progams: the Covey (C ) program, the Dilbert (D) program, and the Frodo (F) program. You have been asked to evaluate the effectiveness of each training program on the basis of a random sample of sales people. For all three programs, it is believed that age increases the effectiveness as a salesperson. Hence, the “model” is that there is a relationship between sales and age (sales increase generally increase with age as sales gain experience). You want to know how alternative training programs affect that sales-age relationship. That is, how do the training programs affect the slope and intercept of the sales-age regression line. The data is as follows: [[[show them lec14trn.ppt….discuss that it looks like three separate regression lines]]]] annual sales 56 55 63 52 58 65 64 61 69 73 62 70 41 40 46 48 45 58 55 57 62 47 64 60 28 25 71 62 50 Age 21 28 33 33 38 43 48 53 53 58 63 67 23 30 33 42 43 43 45 48 58 29 66 67 19 23 67 56 45 training C C C C C C C C C C C C D D D D D D D D D D D D F F F F F Covey=1 others=0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Dilbert=1 others=0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 age*Covy age*Dilb 21 28 33 33 38 43 48 53 53 58 63 67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 30 33 42 43 43 45 48 58 29 66 67 0 0 0 0 0 1 46 34 59 36 71 62 71 37 27 47 29 59 51 63 F F F F F F F 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 training.do (training.sas) ***STATA *****; # delimit ; * training.sha the impact of the 3 training programs; infile ann_sale age covey dilbert age_cov age_dil using "e:\classrm_data\training.txt", clear; regress ann_sale age in 1/12; regress ann_sale age in 13/24; regress ann_sale age in 25/36; regress ann_sale age; regress ann_sale age covey dilbert age_cov age_dil; test (covey = 0) (dilbert =0) (age_cov = 0) (age_dil = 0); ***SAS *****; data one; * training.sas the impact of the 3 training programs; infile 'e:\classrm_data\training.txt'; /* use the following infile options if the data set is tab delimited: infile 'e:\classrm_data\training.txt' delimiter='09'x dsd truncover;*/ input ann_sale age covey dilbert age_cov age_dil; run; data two; set one; if (1<=_N_<=12); run; proc reg; model ann_sale= age ; run; data three; set one; if (1<=_N_<=12); run; proc reg data=three; model ann_sale= age;run; data four; set one; if (1<=_N_<=12); run; proc reg data=four; model ann_sale= age;run; proc reg data=one; model ann_sale= age covey dilbert age_cov age_dil; test covey, dilbert, age_cov, age_dil; run; a) Running each of the three samples as separate regressions ... b) are the intercepts different for each of these 3 training programs? How do we know that they are statistically different or not? b) are the slopes different? c) how do you interpret these differences? d) what is the best training program? II. Difference in Difference Estimates Revisited (recall the presentation in lecture 1) Empirical example(s) III Chow Tests: All Purpose F-Statistics 2 When we want to test the simultaneous significance of more than 1 variable (in the salesman training example above, are slopes and intercepts statistically distinguishable, after accounting for natural sampling variability?), then we can use "F-tests." These are also called Chow tests, after the first econometrican to call peoples attention to the usefulness of these tests. The usefulness of this is fairly well discussed in the text; it can be used to test any kind of linear restriction on the coefficients. These tests are simply F-statistic type of tests generated by examining the residual sum of squares from a restricted and unrestricted model. If the restrictions aren't important, then residual sums of squares from both the restricted and unrestricted models ought to be about the same and their difference should be close to zero. The Chow test exploits this fact with a vengeance, as we have seen with previous lecture on this useful F-statistic. Now we will do some examples from the papers you are working on this semester. Who will be first? A. Class participants examples from your papers IN SUMMARY, CHOW OR F-TESTS ARE LINEAR RESTRICTIONS ACROSS PARAMETERS EITHER TO 1. TEST IF A SUBSET OF PARAMETERS ARE SIGNIFICANTLY DIFFERENT (SAY FROM ZERO), OR 2. TEST IF THERE IS A SHIFT IN PARAMETERS ACROSS REGIMES (MALE EARNINGS EQUATIONS ARE DIFFERENT THAN FEMALE EARNINGS EQUATIONS). B. TESTING FOR DIFFERENCES IN INTERCEPTS, OR SLOPES # delimit ; infile ann_sale age covey dilbert age_cov age_dil using "e:\classrm_data\training.txt", clear; regress ann_sale age covey dilbert age_cov age_dil; test (covey = 0) (dilbert =0); test (age_cov = 0) (age_dil = 0); C. TESTING FOR DIFFERENCES BETWEEN GROUPS ( like the salesman receiving different types of training)-- revisit the results for the salesman/age and training example from the beginning of the lecture. Testing whether all slopes and all intercepts are equal. An approach also useful for looking at male/female differences, white/non-white differences, corporate/field office differences, exempt/non-exempt differences, and before the program was implemented vs. after the program was implemented (whatever the program was). # delimit ; infile ann_sale age covey dilbert age_cov age_dil using "e:\classrm_data\training.txt", clear; regress ann_sale age in 1/12; regress ann_sale age in 13/24; regress ann_sale age in 25/36; regress ann_sale age; regress ann_sale age covey dilbert age_cov age_dil; test (covey = 0) (dilbert =0) (age_cov = 0) (age_dil = 0); Two ways to do F-tests from these equations (either use the first four, or the fifth one with the test statement. 3