Problem with DID interpretation

[Tim Chan]

Dear all,

I am trying to analyse the effect of higher tuition fees on grade outcomes. My data is university-level and the dependent variable is percentage of good honours.

I am using a DID estimation strategy with Scottish universities as a control group and the 2012 tuition fee reform as the treatment. I have panel data but I am very confused about whether I should be using reg or xtreg, fe - I'm not sure what the difference is.

My regression equation is: Y_jct = alpha + gamma*E_c + lambda*Post_t + delta(E_c * Post_t) + beta'X_jct + theta*t + epsilon_jct
(In the fixed effects regression, I have added time dummies alongside the linear time trend, t)

I have attached a .pdf of my results of the OLS regression and fixed effects regression side by side. Can you please explain to me:

(1) Why the coefficients are different and what that implies
(2) Which regression is better and should I just remove one of them?

* Example generated by -dataex-. To install: ssc install dataex
clear
input double goodhon float(higherfees english) int year float entry20 double(satis research) float pros10 double ssratio float(acaexp100 facexp100 comp10 noneu10)
65.6 0 1 2011  15.1 3.94 2.41 6.83 13.3  7.39 3.93 8.85  .8589342
  79 0 1 2011  23.4 3.98 2.72 7.78 15.9 11.41 7.76 9.78  .7641922
70.9 0 1 2011  18.3 3.93 2.67 6.27 14.9  9.55  4.1 9.32 1.4122394
68.2 0 1 2011    17 3.74 2.48 7.94 18.8  9.17  3.3 8.27 1.6675324
50.2 0 1 2011  13.5 4.07 1.96 5.99 15.9   6.7 4.19  8.7  .1251422
52.7 0 1 2011 13.35 3.62 2.23 5.32 16.4  7.11 2.54 7.94  .9929942
72.8 0 1 2011 20.55 3.96 2.72 7.23 14.3 10.66 3.69 9.21 1.0691475
  63 0 1 2011  13.7  3.7 2.05  6.3   19  7.26 2.35 8.52  .6398275
64.9 0 1 2011  13.7 3.77 1.85 6.42 18.7  8.11 2.95 7.64  .8425232
79.9 0 1 2011  23.2 3.92  2.8 7.79 13.3 15.55 4.02 9.53 1.6583195
70.3 0 1 2011  20.8 3.68 2.82 7.11 14.9 12.27 4.21 9.24  1.394457
  72 0 1 2011 19.95 3.94 2.63 7.24 15.1 11.43 4.13 9.29  1.128326
61.8 0 1 2011 13.95 3.82 2.18 5.77 15.6  8.21 2.99 8.39 .39222875
50.8 0 1 2011 12.05 3.83 1.62 6.74 19.6  8.33  3.4 7.97 .20336226
53.5 0 1 2011  12.9 3.95 1.99    6 20.1  7.16 2.26 7.12  .4969595
  80 0 1 2011 18.55 3.95 2.61 7.26 15.4  9.61 3.72 9.08  .7919688
87.3 0 1 2011 27.35  4.1 2.98 8.23 11.7 18.59 6.93 9.86  .9878049
65.9 0 1 2011 14.15 3.95 1.89 5.51 26.5  4.25 1.58 9.04 .12291484
50.6 0 1 2011  13.7 3.76 1.23 6.72 15.4  9.36 2.21 8.26 .04221954
49.7 0 1 2011 13.15 3.91 1.96  6.1 17.1  9.39 4.83 7.39  .6374574
  66 0 0 2011  16.4 3.85 2.01 6.26 23.9  9.31 1.66 7.97  .4706734
49.2 0 1 2011 12.35 3.87 1.79 6.47   21  6.15 1.81 8.05  .2932761
51.5 0 1 2011 12.35 3.88 2.32 6.94 16.5  7.99 2.47  8.2  .4560811
55.1 0 1 2011  13.7 3.84 2.16  7.1 18.8  8.27 4.91 8.56  .3594698
58.9 0 1 2011 14.05 3.84 2.37 6.16 19.7  5.91 2.79 8.35 .41774705
57.5 0 1 2011  13.5 3.89 2.16 5.16 17.8  5.87 2.91 8.55  .6529851
60.7 0 1 2011 11.75 3.79 2.04 5.77 20.2  7.08 3.47 8.16  .6542733
52.1 0 1 2011    13 3.85 1.54 6.24   21  7.52 1.28 7.99  .2037037
56.7 0 1 2011  13.4 3.87 1.74 6.56 18.4  5.86 2.34 7.89 .08050848
56.2 0 1 2011  12.7 3.78 2.31 6.91   19  8.44 5.83 7.74 1.2456747
52.2 0 1 2011 12.25 3.76  2.2 5.77 19.2 10.87 1.99 8.22 .27027026
66.8 0 1 2011 15.75 3.76 2.32 6.61   20  9.77 4.85 8.62 1.0808271
  50 0 1 2011  13.2 3.58  1.9 4.53 36.7 12.77 3.17 8.38   .240616
80.2 0 0 2011 21.95 3.71 2.75 7.62 13.4 17.95 3.99  9.2 1.2492886
48.9 0 1 2011  10.6 3.57 1.84  4.6 19.8  7.29 1.56 6.61  1.042296
68.6 0 0 2011  16.9 3.75 2.48 7.47   17  9.84 5.59 8.25 1.8964144
57.2 0 1 2011  13.4 3.74 2.16 5.75   20  8.22 2.65 7.89   .362358
79.6 0 1 2011  20.4 4.09 2.62 6.68 18.3 10.25 4.31 9.58 1.6411786
56.2 0 1 2011 14.95 3.83 2.15 7.05 21.4  7.79 2.64 8.58  .8107549
64.6 0 1 2011  17.7  3.9 2.73  7.6 13.2  9.24 4.07 8.96 1.4227825
63.4 0 0 2011 14.95 3.87 1.37 6.63 20.3  8.92 1.24 7.95  .6138107
48.6 0 1 2011  11.6 3.92 1.86 5.86 16.7  5.69 3.38 7.61   1.05563
60.5 0 1 2011    14 3.57 2.49 5.62   20  8.06 1.46 8.57 2.5256975
58.3 0 1 2011 15.55 3.89 2.77 6.02 13.9 11.27 4.42 8.65 1.2542956
56.9 0 0 2011  15.7 3.89 2.06 8.34 19.2  9.19 2.95 8.35 .25809994
71.1 0 1 2011 20.15 3.81 2.54 7.06 12.7 14.96 3.29 8.96 1.0912875
55.4 0 1 2011  12.7 3.64 2.07 5.85 19.8  7.84 2.05 7.57  .5274489
56.2 0 1 2011 13.65 3.94  1.9 6.06 20.3  7.71 2.55 8.35 .10081613
42.3 0 1 2011 12.05 3.73 1.49 4.92 22.2  6.87 3.25 7.51  .7536606
70.1 0 1 2011  18.2 3.89 2.43 7.52 18.1   8.7 6.82 9.15 1.7281673
68.3 0 1 2011 19.65 3.98 2.71 7.76 13.5 11.34 5.34 9.41 1.0199556
75.6 0 1 2011 21.05 3.82 2.69 8.05 11.3 15.88 3.29 9.41 1.0696203
68.1 0 1 2011  18.6 3.87 2.58 7.96   18  9.71 3.78 8.35 1.0762751
49.2 0 1 2011 10.05 3.73 1.67 5.96 14.7 10.27 3.96 6.72 1.0111023
74.2 0 1 2011 19.85 3.86 2.72 7.05 14.7  9.07 4.85 9.27  .6369821
71.2 0 1 2011  18.3 4.08 2.58 6.91 15.5 10.76 4.59 9.04 1.0798122
53.4 0 1 2011 13.15 3.61 2.05 6.72   23  7.38 2.57 8.13  .2770506
  66 0 1 2011  15.9 3.84 2.58 5.67 16.8  6.74 1.84 8.24  .8953817
44.5 0 1 2011    10 3.84 2.09 6.02 19.3  4.13 4.71 8.26  1.339492
46.4 0 1 2011  9.35 3.66 2.24 5.29 23.3  7.43  3.2 7.94 1.0197086
67.6 0 0 2011 17.85 3.97 2.57 7.68 14.9 10.23 2.54    8 .58630586
91.8 0 1 2011  26.6 4.11 2.96 8.28 10.8 29.09 4.69 9.84  .6650397
60.9 0 1 2011 12.75 3.86 1.72 6.03 19.7  9.46 3.39 8.19  .4036187
71.7 0 0 2011  19.4 3.87 2.45 7.55 17.8 12.24 2.86 8.47 .45708305
45.8 0 1 2011   9.6 3.76 2.24 5.85 24.4  7.93 1.65 6.64  .4640605
78.6 0 1 2011  22.4 3.85 2.72 7.83 13.8 15.55 3.32 9.52  .9346126
50.3 0 1 2011   9.2 3.64 2.18 5.65 23.6 15.97 4.49 7.58 1.0134755
51.3 0 1 2011 13.65 3.94 2.24 5.46 20.6  9.35 2.26 8.29  .8460326
72.2 0 1 2011  20.2 3.93 2.64 6.99 15.6 13.69 4.45 9.34  .7417149
57.6 0 1 2011    12 3.86 1.69 5.49 21.3  8.21 2.14 8.06  .7221096
66.8 0 1 2011 15.45  3.9  2.2  6.7 17.9  7.32  4.4 8.56  .8914043
85.6 0 0 2011 22.75 4.15 2.72 7.44 13.1 12.69 3.88  9.5  2.652646
  75 0 1 2011  20.6 3.89 2.67 7.57 13.9 10.51 4.17 9.44 1.2144136
62.9 0 1 2011 13.65 3.85  2.2    6 19.6  7.46 3.83 8.11  .4311945
48.5 0 1 2011 10.45 3.76 1.75 5.65 18.5  4.59 3.04 6.26  .5842848
  58 0 1 2011  14.5 4.01 2.37    7 19.8  8.44  3.1 8.25  .6673511
72.7 0 1 2011  25.2 3.81 2.94 8.89 10.5 31.82 6.48 9.51  2.577552
65.5 0 0 2011  15.7 3.98 2.41 6.76   17  9.33 1.82 8.29 .52507377
69.8 0 1 2011  17.5 3.91 2.53  6.6 16.6   7.5 3.31 9.18  .8543578
76.5 0 1 2011  24.7 3.76 2.96 8.19   14 15.63 3.04 9.53 3.6226416
43.8 0 1 2011 10.35 3.72 1.67 4.57 20.6   5.9 6.62 7.79  .4065999
74.4 0 1 2011 20.35 3.89 2.72 7.63 13.5  13.1 4.72 9.26  .8925319
63.9 0 0 2011  13.2  3.8 1.83  7.2 19.2  8.38  1.8 7.57  .7063527
  81 0 1 2011  22.9 3.91 2.84 8.08  8.9 17.24 2.25 9.48 2.5624766
47.6 0 1 2011 12.95 3.94  1.5 6.39   18 11.06 1.67  7.9 .11355571
57.3 0 1 2011  13.6 3.89  2.1 6.11 15.9  8.91 2.71 7.76  .4054843
52.3 0 1 2011  13.3 3.76 2.36 5.98 18.7  7.62 2.99 7.46 .58191586
56.2 0 1 2011    14 3.87  1.4 5.71 20.2  9.27 3.23 8.55 .29615006
75.3 0 1 2011 21.15 4.05 2.78 7.15   14 12.86 4.69 9.49  .7491082
74.2 0 1 2011 22.55 3.94 2.71 8.09 15.9 10.28 4.41 9.48  1.280397
69.9 0 1 2011  18.5 4.14 2.62 7.13 18.3  7.39 5.02 9.39  .7268063
47.4 0 1 2011 12.05 3.93  1.9 5.97 25.5  6.44 2.55 7.58  .9306569
61.5 0 1 2011 14.85  3.8 2.18 7.08 24.2  9.45 2.27 8.53  .3454774
63.9 0 1 2011 15.95 3.98  2.6 6.86 14.8  8.15  3.7 8.69  .8595718
46.2 0 1 2011 11.85 3.84 1.96 5.68 19.8 10.75 2.45 7.42  .5396175
62.2 0 1 2011 13.75 3.84 2.34 7.11   16  8.66 2.78 7.97  .9928741
53.6 0 1 2011  12.3 3.81 2.15 5.42   20  8.52 2.35 7.73  .7520823
48.1 0 1 2011 14.35 4.32    . 8.52  9.1  5.75 5.45 8.78  4.871795
59.5 0 1 2011 12.05 3.82  2.4 6.29 16.2  7.89 9.68 8.14 1.2462147
  54 0 0 2011  12.8 3.87 1.83 5.66 21.4 10.99 3.07 7.01 .14380531
end

This is my first real post so please let me know how I can improve my posts in the future!

Many thanks,
Tim

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a helpful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex (which you did provide). Many of us will not open files due to virus concerns, we can't see what happened.

The panel data documentation (the pdf version) that comes with Stata has a good explanation of relevant issues in the section on xtreg. fe is essentially putting in a dummy for each panel - this lets each panel have a different intercept while maintaining the assumption that the parameters on the other variables are constant across panels.