Problem with DID interpretation

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?

Code:

* 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

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