How to Understand Output Variations in Interaction Terms: Comparing Two Coding Approaches

[Sabo Dong]

Hi all,

I would like some insights for understanding the output differences between the two settings around interaction terms. Here below are the codes:

xtset isin_num weekid
xtreg wncf institutional_dummy#post_1 if weekid >= 56 & weekid <= 64, fe

Here, isin_num is a unique code for open-ended funds. wncf is the abbreviation of weekly net cash flow. institutional_dummy equals 1 if a fund is for institutional investors and 0 otherwise. post_1 equals 1 when the first type of treatment occurs. These codes just represent the very basic version of my model, so I have not included more variables. I use # instead of ## as I have enrolled two-way fixed effects. Here below are the outputs:

There are some red flags. For example, it is said, "note: 1.institutional_dummy#1.post_1 omitted because of collinearity". It is also hard to understand why the software is giving coefficients for 0 1, 1 0, and 1 1 separately. So, I tried adding the interaction term manually. Theoretically, these two ways should generate the same results and meet the same issue. However, after running the code below, the results are not the same:

gen interact_1 = institutional_dummy*post_1, after(post_2)
xtreg wncf interact_1 if weekid >= 56 & weekid <= 64, fe

As you can see, there are no warnings after running this code. What is the reason for the difference between these two settings?

[Clyde Schechter]

I use # instead of ## as I have enrolled two-way fixed effects.

Use of # vs ## has nothing to do with two-way fixed effects. Either may be used with two-way fixed effects or without two-way fixed effects. The difference between # and ## is simply a question of which produces results in a more convenient way for answering your research questions. If you are primarily interested in the outcomes associated with each combination of the variables being interacted, then # is more convenient. If you are primarily interested in measuring or testing the extent of interaction between the variables, the ## approach is more convenient.

It is also hard to understand why the software is giving coefficients for 0 1, 1 0, and 1 1 separately.

So, you don't understand how the # operator works. It does exactly that. a#b expands to all pairs of values of a and values of b, except that one pair is omitted as a reference category. Since the # term corresponds to 3 variables, it is clearly not going to be equivalent to including a single homebrew product variable. And, in fact, -gen interact_1 = institutional_dummy*post_1, after(post_2)- is definitely not meaningful in your context, because this is how you calculate an interaction for continuous variables. But institutional_dummy and post_1 are both discrete variables.

As for the error message you got, about 1.institutional_dummy#1.post_1 omitted due to colinearity, this means that there is some important gap in your data. In order for these interactions to work in the normal way, it is important that all four combinations of institutional_dummy and post_1 be instantiated in the estimation sample. (Bear in mind that the estimation sample excludes any observations where any of the regression variables is missing.) So run

tab institutional_dummy post_1 if inrange(weekid, 56, 64) & !missing(isin_num, wncf)

I think you will find that one of the categories has 0 observations.

Alternatively, the colinearity may be with the isin_num fixed effect: it may be that there the combination institutional_dummy == 1 and post_1 == 1 characterizes all and only the observations associated with some particular subset of the isin_num's.

[Sabo Dong]

Hi Clyde,

Thank you for your patient explanations. Since your answer has too much information, I am somewhat overwhelmed. I need to understand your reply one by one.
My understanding is that # only enrolls the interaction term of institutional_dummy and post_1, while ## will enroll institutional_dummy, post_1, and their interaction term. Since I want to use the generalized DID model, I thought the information captured by the two-way fixed effects already fully covers the information that institutional_dummy and post_1 encompass. Enrolling these two dummies and two-way fixed effects simultaneously may cause serious collinearity. What do you think?


Regards,
Qianli

[Clyde Schechter]

You are already misunderstanding how # works when you refer to it as enrolling "the" interaction term of institutional_dummy and post_1. Institutional_dummy and post_1 are both dichotomous variables. Therefore there are four combinations of their values, which means that their full interaction requires three terms to represent. So there is no single interaction term that could be rightly called "the" interaction.

When you use ##, Stata does it differently. You still get three variables: one of which is called institutional_dummy (but actually is 1.institutional_dummy#0.post_1), another of which is called post_1 (but actually is 0.institutional_dummy#1.post_1) and 1.institutional_dummy#1.post_1. It is this last one that is the DID estimate of the treatment effect. As for your concern that institutional_dummy is colinear with the isin_num fixed effect and post_1 is colinear with the weekid effect, that is not a problem. Stata will recognize this fact and will omit the institutional_dummy and post_1 variables from the model. That leaves behind just the 1.institutional_dummy#1.post_1 term, which is the one you actually want.

Now, you may find that, in your specific data, the 1.institutional_dummy#1.post_1 term ends up omitted, as was the case for the similarly named term shown in #1. This means that your data is not appropriate to the analysis, and I outlined possible causes for this in #2. If you encounter this problem and are unable to ascertain the cause, please show example data when you post back, using the -dataex- command to do so. I will try to troubleshoot it for you.

If you are running version 18, 17, 16 or a fully updated version 15.1 or 14.2, -dataex- is already part of your official Stata installation. If not, run -ssc install dataex- to get it. Either way, run -help dataex- to read the simple instructions for using it. -dataex- will save you time; it is easier and quicker than typing out tables. It includes complete information about aspects of the data that are often critical to answering your question but cannot be seen from tabular displays or screenshots. It also makes it possible for those who want to help you to create a faithful representation of your example to try out their code, which in turn makes it more likely that their answer will actually work in your data.

[Sabo Dong]

Hi Clyde,

Here below are the screenshots:

[Clyde Schechter]

Without the example data, there is nothing I can do to help. Please retry -dataex- restricting it to only the necessary variables:

dataex institutional_dummy post_1 weekid isin_num wncf

[Sabo Dong]

Hi Clyde,

Here below are the results:
. dataex institutional_dummy post_1 weekid isin_num wncf

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. For more info, type help dataex
clear
input float(institutional_dummy post_1) int weekid long isin_num float wncf
0 0   1 1  35745.957
0 0   2 1   78811.87
0 0   3 1   223.5326
0 0   4 1  13873.967
0 0   5 1  -51522.19
0 0   6 1    4283.96
0 0   7 1  -58360.74
0 0   8 1 -1038.1361
0 0   9 1  -26602.93
0 0  10 1  109165.37
0 0  11 1  -14462.91
0 0  12 1  34145.555
0 0  13 1 -1751.5044
0 0  14 1 -1035908.9
0 0  15 1  -3294.835
0 0  16 1   5173.433
0 0  17 1 -1651.2992
0 0  18 1  158876.14
0 0  19 1    8996.35
0 0  20 1   3914.632
0 0  21 1  20352.076
0 0  22 1   32725.76
0 0  23 1   52145.39
0 0  24 1    9275.85
0 0  25 1  20669.066
0 0  26 1   7260.292
0 0  27 1    63034.5
0 0  28 1   564633.8
0 0  29 1  -47266.06
0 0  30 1  12811.512
0 0  31 1   62170.99
0 0  32 1   64135.42
0 0  33 1 -152204.23
0 0  34 1  288.41458
0 0  35 1  -56754.06
0 0  36 1   81206.45
0 0  37 1  -30479.61
0 0  38 1  -84513.43
0 0  39 1  -40587.65
0 0  40 1   68576.44
0 0  41 1   14804.65
0 0  42 1 -1777.9294
0 0  43 1 -11720.438
0 0  44 1  15474.997
0 0  45 1   93700.13
0 0  46 1  13813.927
0 0  47 1  -342812.5
0 0  48 1 -22504.836
0 0  49 1   5214.074
0 0  50 1 -125806.64
0 0  51 1   6065.018
0 0  52 1  1211.4541
0 0  53 1   8409.354
0 0  54 1  -97313.91
0 0  55 1  -37229.52
0 0  56 1   8066.885
0 0  57 1   49375.03
0 0  58 1 -1534.1667
0 0  59 1  33226.867
0 1  60 1  -3142.929
0 1  61 1  -1741.401
0 1  62 1  34251.895
0 1  63 1  -332785.3
0 1  64 1  33110.863
0 1  65 1  -78552.31
0 1  66 1    6296.06
0 1  67 1   169635.4
0 1  68 1   23789.04
0 1  69 1  -7954.732
0 1  70 1   53434.07
0 1  71 1 -17019.297
0 1  72 1  -392740.2
0 1  73 1   5149.748
0 1  74 1  23095.076
0 1  75 1   102468.9
0 1  76 1 -11853.813
0 1  77 1  26443.475
0 1  78 1  25024.127
0 1  79 1  1021871.6
0 1  80 1  -2746.002
0 1  81 1  22533.514
0 1  82 1   3865.076
0 1  83 1  2753.8235
0 1  84 1  -7353.799
0 1  85 1   1733.491
0 1  86 1  -16033.38
0 1  87 1 -147535.83
0 1  88 1 -19624.316
0 1  89 1  -20245.38
0 1  90 1  19172.129
0 1  91 1 -3063.5676
0 1  92 1  15635.622
0 1  93 1   5618.132
0 1  94 1   22472.89
0 1  95 1  -116060.7
0 1  96 1  -36021.04
0 1  97 1  14406.307
0 1  98 1   3311.627
0 1  99 1   25020.43
0 1 100 1   5594.805
end
label values isin_num isin_num
label def isin_num 1 "AT0000495288", modify

------------------ copy up to and including the previous line ------------------

Listed 100 out of 1564033 observations
Use the count() option to list more

.
end of do-file

[Clyde Schechter]

Sorry, I should have been more explicit about how to select the example for -dataex-: I made some assumptions about your data that it turns out are not at all true.

The sample has to contain several different isin_num's. And some of them must be for institutional investors and others not. In fact, I need a minimum of 2 isin_num's of each of those kind. These requirements are necessary for it to even be possible to run -xtreg, fe-.

To make the size of the sample manageable, I suggest you first -drop if !inrange(weekid, 56, 64)- so that the number of observations for each isin_num will be (at most) 9, and all of the observations will be at least potentially part of the estimation sample.

[Sabo Dong]

Hi Clyde, it's hard to find 1 1 pair. So I adjust the count to 950.

* Example generated by -dataex-. For more info, type help dataex
clear
input float(institutional_dummy post_1) int weekid long isin_num float wncf
0 0 56   1      8066.885
0 0 57   1      49375.03
0 0 58   1    -1534.1667
0 0 59   1     33226.867
0 1 60   1     -3142.929
0 1 61   1     -1741.401
0 1 62   1     34251.895
0 1 63   1     -332785.3
0 1 64   1     33110.863
0 0 56   2     -234112.6
0 0 57   2      20998.31
0 0 58   2     -656401.5
0 0 59   2     -263600.3
0 1 60   2    -241152.84
0 1 61   2      -1496817
0 1 62   2     -526859.1
0 1 63   2     -341952.4
0 1 64   2     -681491.4
0 0 56   3     -19754.79
0 0 57   3     39047.066
0 0 58   3      99445.88
0 0 59   3     -985308.3
0 1 60   3     -15255.47
0 1 61   3     -968465.9
0 1 62   3     1901.6183
0 1 63   3     -10422.53
0 1 64   3      7810.473
0 0 56   4      445.5778
0 0 57   4     308.30035
0 0 58   4     -3412.659
0 0 59   4    -4584.8555
0 1 60   4    -27893.564
0 1 61   4     -2950.316
0 1 62   4    -1961.4437
0 1 63   4     -975.5118
0 1 64   4     1236.2948
0 0 56   5      20098.02
0 0 57   5    -472573.25
0 0 58   5     2326.8125
0 0 59   5      37742528
0 1 60   5       4432334
0 1 61   5     -238101.3
0 1 62   5     4671671.5
0 1 63   5       2539.57
0 1 64   5       7301013
0 0 56   6    -35059.543
0 0 57   6     -74267.35
0 0 58   6     -1487.422
0 0 59   6    -1037.1348
0 1 60   6      205934.2
0 1 61   6    -122.33308
0 1 62   6     -5731.178
0 1 63   6      6982.532
0 1 64   6    -2057.4844
0 0 56   7      3497.694
0 0 57   7      8958.083
0 0 58   7     1166.3859
0 0 59   7    -16501.238
0 1 60   7     -312.8821
0 1 61   7    -1604.6165
0 1 62   7    -14964.285
0 1 63   7      755.1668
0 1 64   7     1142.3815
0 0 56   8     -178635.2
0 0 57   8      8382.373
0 0 58   8     18107.678
0 0 59   8      6910.107
0 1 60   8      82770.11
0 1 61   8      63233.01
0 1 62   8     2531.8206
0 1 63   8      7092.278
0 1 64   8    -2026.6305
0 0 56   9     14078.024
0 0 57   9    -1266.1335
0 0 58   9     -15437.32
0 0 59   9      30154.19
0 1 60   9      -3320.39
0 1 61   9     -5400.283
0 1 62   9     -9239.877
0 1 63   9      1309.932
0 1 64   9      326.5454
0 0 56  10      45862.42
0 0 57  10      9285.265
0 0 58  10     31669.865
0 0 59  10     -893.4222
0 1 60  10     -2289.568
0 1 61  10     1028.2117
0 1 62  10    -13357.648
0 1 63  10     17803.766
0 1 64  10      6855.804
0 0 56  11      -38608.9
0 0 57  11     -2748.216
0 0 58  11     68.121796
0 0 59  11      3229.438
0 1 60  11     -6546.136
0 1 61  11      2214.268
0 1 62  11      -10989.4
0 1 63  11     -1461.424
0 1 64  11      2606.357
0 0 56  12    -105799.48
0 0 57  12    -102445.77
0 0 58  12      -1801.52
0 0 59  12      56314.29
0 1 60  12     -222150.2
0 1 61  12      84279.31
0 1 62  12    -103768.13
0 1 63  12    -29999.166
0 1 64  12      348551.9
0 0 56  13             0
0 0 57  13             0
0 0 58  13             0
0 0 59  13             0
0 1 60  13             0
0 1 61  13             0
0 1 62  13             0
0 1 63  13     17184.123
0 1 64  13             0
0 0 56  14             0
0 0 57  14             0
0 0 58  14             0
0 0 59  14             0
0 1 60  14             0
0 1 61  14             0
0 1 62  14             0
0 1 63  14     -66669.96
0 1 64  14             0
0 0 56  15    -74.372025
0 0 57  15     32.020264
0 0 58  15      566.7209
0 0 59  15      26.42867
0 1 60  15     23.893185
0 1 61  15     -62.68985
0 1 62  15      3093.985
0 1 63  15     -9.162262
0 1 64  15      79.58382
0 0 56  16             0
0 0 57  16             0
0 0 58  16             0
0 0 59  16             0
0 1 60  16             0
0 1 61  16             0
0 1 62  16             0
0 1 63  16             0
0 1 64  16             0
0 0 56  17      9685.229
0 0 57  17      9866.381
0 0 58  17      7096.991
0 0 59  17     -21557.23
0 1 60  17     -37315.92
0 1 61  17             0
0 1 62  17             0
0 1 63  17             0
0 1 64  17             0
0 0 56  18     -811122.6
0 0 57  18     -321219.5
0 0 58  18     25356.406
0 0 59  18      89503.11
0 1 60  18     -23406186
0 1 61  18    -153216.89
0 1 62  18     -28491198
0 1 63  18    -22479.137
0 1 64  18     -60888.16
0 0 56  19      -8769.88
0 0 57  19      8084.419
0 0 58  19     17488.639
0 0 59  19     235.27696
0 1 60  19     -674.6802
0 1 61  19      1672.677
0 1 62  19      110654.9
0 1 63  19     17631.781
0 1 64  19     11699.685
0 0 56  20     -92812.96
0 0 57  20     34067.285
0 0 58  20     250016.14
0 0 59  20     149897.31
0 1 60  20     -205852.8
0 1 61  20     -444406.4
0 1 62  20      78623.54
0 1 63  20     149956.81
0 1 64  20     130784.68
0 0 56  21             0
0 0 57  21     1134.4408
0 0 58  21     192.88327
0 0 59  21      566.8357
0 1 60  21             0
0 1 61  21     -3844.239
0 1 62  21    -14790.647
0 1 63  21             0
0 1 64  21             0
0 0 56  22      -8105333
0 0 57  22    .003379787
0 0 58  22    -.00343533
0 0 59  22     107.47716
0 1 60  22      -3306532
0 1 61  22      4751.743
0 1 62  22   .0021780157
0 1 63  22 .000016298478
0 1 64  22      -3550530
0 0 56  23     -982719.8
0 0 57  23     -53971.75
0 0 58  23    -122014.67
0 0 59  23     -480564.2
0 1 60  23    -3649239.5
0 1 61  23    -1818693.5
0 1 62  23     557780.25
0 1 63  23      455623.6
0 1 64  23     1352262.5
0 0 56  24     -20363.04
0 0 57  24    -30052.814
0 0 58  24     -98843.95
0 0 59  24     -75188.43
0 1 60  24      22403.42
0 1 61  24             0
0 1 62  24             0
0 1 63  24             0
0 1 64  24             0
0 0 56  25             0
0 0 57  25             0
0 0 58  25             0
0 0 59  25             0
0 1 60  25             0
0 1 61  25             0
0 1 62  25             0
0 1 63  25             0
0 1 64  25             0
0 0 56  26     -7092.341
0 0 57  26    -33150.063
0 0 58  26      563238.4
0 0 59  26    -133708.66
0 1 60  26    -14704.125
0 1 61  26     -10780.76
0 1 62  26    -1066118.4
0 1 63  26    -1093.0714
0 1 64  26      1850.108
0 0 56  27             0
0 0 57  27             0
0 0 58  27             0
0 0 59  27             0
0 1 60  27             0
0 1 61  27     -2956.959
0 1 62  27             0
0 1 63  27             0
0 1 64  27             0
0 0 56  28     -159306.9
0 0 57  28    -10245.005
0 0 58  28             0
0 0 59  28     -34907.09
0 1 60  28     -48744.66
0 1 61  28             0
0 1 62  28             0
0 1 63  28             0
0 1 64  28             0
0 0 56  29      188.4829
0 0 57  29      183.8247
0 0 58  29     306.20425
0 0 59  29    -117.66637
0 1 60  29      95.42142
0 1 61  29     -11723.02
0 1 62  29     189.61064
0 1 63  29      14.42878
0 1 64  29      107.6107
0 0 56  30    -190950.55
0 0 57  30      415493.9
0 0 58  30     4658796.5
0 0 59  30    -119281.73
0 1 60  30     131688.03
0 1 61  30    -3871876.5
0 1 62  30     -15552491
0 1 63  30    -175486.17
0 1 64  30    -24276.504
0 0 56  31    -30160.254
0 0 57  31       78533.8
0 0 58  31      30810.89
0 0 59  31         54731
0 1 60  31      11140.43
0 1 61  31     -77252.58
0 1 62  31     -95976.95
0 1 63  31     -7181.887
0 1 64  31    -13929.233
0 0 56  32     -25213.87
0 0 57  32    -21992.113
0 0 58  32     1815.9915
0 0 59  32    -16503.654
0 1 60  32     -12400.59
0 1 61  32     -89638.89
0 1 62  32     33111.652
0 1 63  32     -51497.66
0 1 64  32     21579.943
0 0 56  33     -2242.013
0 0 57  33      5814.381
0 0 58  33     2225.6184
0 0 59  33      827.7618
0 1 60  33      -5847.24
0 1 61  33      1860.582
0 1 62  33      -7779.12
0 1 63  33     -8329.382
0 1 64  33     1084.7443
0 0 56  34    -11451.486
0 0 57  34      5454.812
0 0 58  34    -33446.375
0 0 59  34      14605.74
0 1 60  34     -919459.7
0 1 61  34     -1836.949
0 1 62  34    -1618.1884
0 1 63  34     -3492.513
0 1 64  34       3079.23
0 0 56  35             0
0 0 57  35             0
0 0 58  35             0
0 0 59  35             0
0 1 60  35             0
0 1 61  35             0
0 1 62  35             0
0 1 63  35             0
0 1 64  35             0
0 0 56  36    -143599.13
0 0 57  36      35788.01
0 0 58  36      253146.9
0 0 59  36       52424.2
0 1 60  36     176881.56
0 1 61  36      181020.2
0 1 62  36     280646.75
0 1 63  36      492175.8
0 1 64  36      430482.7
0 0 56  37     -45612.11
0 0 57  37     -3902.401
0 0 58  37      116581.5
0 0 59  37      46511.63
0 1 60  37    -11876.222
0 1 61  37     -66360.34
0 1 62  37    -19305.414
0 1 63  37      58275.56
0 1 64  37      56043.05
0 0 56  38      16632.36
0 0 57  38      53719.78
0 0 58  38      99142.63
0 0 59  38     -9140.434
0 1 60  38     -5925.984
0 1 61  38      37250.22
0 1 62  38     -7344.907
0 1 63  38     -71606.08
0 1 64  38     -980350.5
0 0 56  39     23057.416
0 0 57  39     -85278.65
0 0 58  39     -12641.94
0 0 59  39      22902.83
0 1 60  39      176.1582
0 1 61  39             0
0 1 62  39             0
0 1 63  39             0
0 1 64  39             0
0 0 56  40      -58661.3
0 0 57  40     -5321.378
0 0 58  40     -34241.73
0 0 59  40      50.31568
0 1 60  40    -1974.8496
0 1 61  40     -12282.78
0 1 62  40    -21635.484
0 1 63  40     33314.137
0 1 64  40      3680.942
0 0 56  41    -159943.94
0 0 57  41    -36766.395
0 0 58  41     238.03743
0 0 59  41     1385.0343
0 1 60  41     -33933.53
0 1 61  41     -21981.78
0 1 62  41     -55687.11
0 1 63  41    -119996.44
0 1 64  41    -37247.195
0 0 56  42    -10848.788
0 0 57  42     2141851.3
0 0 58  42     -62512.76
0 0 59  42      366.4031
0 1 60  42     147.05914
0 1 61  42     -328887.8
0 1 62  42      36370.85
0 1 63  42     226170.88
0 1 64  42     186353.63
0 0 56  43     -26614.07
0 0 57  43      -1027241
0 0 58  43    -17481.566
0 0 59  43     -95146.29
0 1 60  43      90442.15
0 1 61  43      3671.041
0 1 62  43     -4555.403
0 1 63  43     -6406.346
0 1 64  43     1931.2682
0 0 56  44     -857714.6
0 0 57  44      48024.76
0 0 58  44     -240177.8
0 0 59  44     -513096.6
0 1 60  44     -361818.5
0 1 61  44    -1947299.8
0 1 62  44    -138177.98
0 1 63  44      205869.8
0 1 64  44      307614.8
0 0 56  45      90284.63
0 0 57  45     265715.84
0 0 58  45       85046.9
0 0 59  45      16229.53
0 1 60  45     -47574.62
0 1 61  45      451139.3
0 1 62  45     273735.44
0 1 63  45     -2972.127
0 1 64  45    -155100.13
0 0 56  46     2939.9846
0 0 57  46      191.5826
0 0 58  46     -158451.6
0 0 59  46     -50.02365
0 1 60  46      29185.31
0 1 61  46     -30.92883
0 1 62  46     -62491.11
0 1 63  46     -273550.4
0 1 64  46      373.2255
0 0 56  47     -494542.3
0 0 57  47    -1181963.8
0 0 58  47     138343.78
0 0 59  47    -214230.95
0 1 60  47     -44289.15
0 1 61  47     -887427.7
0 1 62  47       3610.55
0 1 63  47    -255326.56
0 1 64  47      4655.748
0 0 56  48     -143150.4
0 0 57  48    -4074353.5
0 0 58  48     143724.17
0 0 59  48    -36193.746
0 1 60  48     -45059.04
0 1 61  48     -77383.12
0 1 62  48      62756.27
0 1 63  48    -17460.713
0 1 64  48      147778.3
0 0 56  49    -215582.16
0 0 57  49      -30473.4
0 0 58  49     -172017.4
0 0 59  49    -115621.97
0 1 60  49    -145042.81
0 1 61  49             0
0 1 62  49             0
0 1 63  49             0
0 1 64  49             0
0 0 56  50     11832.873
0 0 57  50    -1932.3633
0 0 58  50      107227.1
0 0 59  50     -6329.241
0 1 60  50    -4692.2686
0 1 61  50     -6620.685
0 1 62  50     -610502.7
0 1 63  50      7033.992
0 1 64  50    -12857.884
0 0 56  51      6256.466
0 0 57  51     1625.8414
0 0 58  51     100876.78
0 0 59  51     -77250.05
0 1 60  51      20024.56
0 1 61  51    -15113.636
0 1 62  51    -37912.094
0 1 63  51      22637.42
0 1 64  51      78538.17
0 0 56  52      8765.241
0 0 57  52      908.8856
0 0 58  52    -1904.1006
0 0 59  52     131780.22
0 1 60  52      319.1936
0 1 61  52      11729.16
0 1 62  52     1914.2885
0 1 63  52      833.1783
0 1 64  52     3125.9756
0 0 56  53      57.98108
0 0 57  53     -42.67604
0 0 58  53     165.36552
0 0 59  53    -23.635466
0 1 60  53     117.75964
0 1 61  53             0
0 1 62  53             0
0 1 63  53             0
0 1 64  53             0
0 0 56  54    -164434.06
0 0 57  54    -1114074.6
0 0 58  54     355343.75
0 0 59  54      41603.41
0 1 60  54    -263832.03
0 1 61  54     -754648.6
0 1 62  54      64912.51
0 1 63  54     190186.16
0 1 64  54     15261.262
0 0 56  55     -116024.9
0 0 57  55      -5893660
0 0 58  55     128510.98
0 0 59  55     -394336.5
0 1 60  55     -331277.3
0 1 61  55     -20297608
0 1 62  55      363489.9
0 1 63  55     2112921.8
0 1 64  55      78793.84
0 0 56  56    -1171951.4
0 0 57  56     -325238.7
0 0 58  56     -69166.87
0 0 59  56     -632297.1
0 1 60  56    -1222036.9
0 1 61  56             0
0 1 62  56             0
0 1 63  56             0
0 1 64  56             0
0 0 56  57      11654194
0 0 57  57     30597.475
0 0 58  57    -202978.38
0 0 59  57      36793.34
0 1 60  57     -46940.45
0 1 61  57      28511.57
0 1 62  57    -4690213.5
0 1 63  57    -1711081.5
0 1 64  57     -30802.84
0 0 56  58     36461.215
0 0 57  58    -22845.477
0 0 58  58       87751.8
0 0 59  58      -8031.26
0 1 60  58      5949.712
0 1 61  58    -2223455.5
0 1 62  58     -379397.1
0 1 63  58      51411.05
0 1 64  58     -34369.06
0 0 56  59     -80527.66
0 0 57  59     -58754.86
0 0 58  59     -79139.25
0 0 59  59    -69966.305
0 1 60  59       -114237
0 1 61  59             0
0 1 62  59             0
0 1 63  59             0
0 1 64  59             0
0 0 56  60     -206940.5
0 0 57  60     -52769.83
0 0 58  60    -16945.154
0 0 59  60    -13391.943
0 1 60  60    -171100.73
0 1 61  60     -171870.1
0 1 62  60     14167.502
0 1 63  60     187784.75
0 1 64  60     11780.248
0 0 56  61    -15097.154
0 0 57  61     -36390.44
0 0 58  61     -710.2857
0 0 59  61     -8055.861
0 1 60  61      464.6413
0 1 61  61     -414.6882
0 1 62  61      48.33933
0 1 63  61      837.8099
0 1 64  61     -944972.4
0 0 56  62      169.8873
0 0 57  62     -305.4855
0 0 58  62     4460.8564
0 0 59  62     -3273.859
0 1 60  62     -9975.335
0 1 61  62    -3437.8506
0 1 62  62     146182.63
0 1 63  62      2750.268
0 1 64  62     -1549.308
0 0 56  63    -144749.97
0 0 57  63     -142955.8
0 0 58  63     -71108.16
0 0 59  63    -101729.41
0 1 60  63     -352877.1
0 1 61  63     -93467.43
0 1 62  63             0
0 1 63  63             0
0 1 64  63             0
0 0 56  64     -338463.4
0 0 57  64     -80010.17
0 0 58  64     1221746.3
0 0 59  64        248665
0 1 60  64    -209844.64
0 1 61  64    -281555.72
0 1 62  64    -576972.75
0 1 63  64     -217920.7
0 1 64  64       89524.8
0 0 56  65     -20.87333
0 0 57  65     -99.76624
0 0 58  65    -10306.494
0 0 59  65    -134.42146
0 1 60  65      82.55276
0 1 61  65    -2906.3936
0 1 62  65     -8485.148
0 1 63  65     -45.74052
0 1 64  65      475.8479
0 0 56  66     2227.7834
0 0 57  66      11360.99
0 0 58  66     -2893.105
0 0 59  66      47327.45
0 1 60  66      51.26576
0 1 61  66      4211.849
0 1 62  66      5540.372
0 1 63  66      592.9185
0 1 64  66    -110.40018
0 0 56  67     -638905.8
0 0 57  67      489367.8
0 0 58  67      48764.48
0 0 59  67    -413307.25
0 1 60  67     -419016.1
0 1 61  67     -568017.5
0 1 62  67      -1299072
0 1 63  67     -156351.2
0 1 64  67    -177864.97
0 0 56  68     -11590.89
0 0 57  68    -12693.353
0 0 58  68      27200.54
0 0 59  68      56973.27
0 1 60  68     -6737.492
0 1 61  68    -15944.954
0 1 62  68    -11013.952
0 1 63  68      19467.47
0 1 64  68     -20568.42
0 0 56  69    -33.701775
0 0 57  69     -41677.65
0 0 58  69    -11.640644
0 0 59  69     -70.15089
0 1 60  69     -43268.33
0 1 61  69      82.42886
0 1 62  69     -43931.85
0 1 63  69    -102856.88
0 1 64  69     -562091.1
0 0 56  70      -86730.8
0 0 57  70    -192917.86
0 0 58  70      -8375.74
0 0 59  70    -116204.03
0 1 60  70       -206993
0 1 61  70     -221167.3
0 1 62  70    -209245.77
0 1 63  70     178841.84
0 1 64  70    -492491.25
0 0 56  71     -49743.77
0 0 57  71     -9288.664
0 0 58  71     -66828.92
0 0 59  71    -18730.521
0 1 60  71     -111935.7
0 1 61  71    -157535.03
0 1 62  71    -102732.52
0 1 63  71     -446133.1
0 1 64  71     -2702.263
0 0 56  72     -72096.65
0 0 57  72     -21263.46
0 0 58  72      8223.576
0 0 59  72    -310266.78
0 1 60  72     -217054.6
0 1 61  72    -3674.9646
0 1 62  72     -80563.01
0 1 63  72      35603.75
0 1 64  72     19654.453
0 0 56  73     514.59265
0 0 57  73     -2813.651
0 0 58  73     -24368.08
0 0 59  73     1354.1028
0 1 60  73     -8913.157
0 1 61  73             0
0 1 62  73             0
0 1 63  73             0
0 1 64  73             0
0 0 56  74     21215.795
0 0 57  74      -14136.6
0 0 58  74     -65401.91
0 0 59  74      439.2121
0 1 60  74      69354.13
0 1 61  74     -5136.806
0 1 62  74      109202.1
0 1 63  74     -51452.08
0 1 64  74      54805.55
0 0 56  75     -235987.6
0 0 57  75    -22.553844
0 0 58  75     -17.31742
0 0 59  75     134.49057
0 1 60  75     -2045.843
0 1 61  75     14.978568
0 1 62  75     134334.17
0 1 63  75     211.37874
0 1 64  75     -28.23104
0 0 56  76     121.13685
0 0 57  76     -7345.442
0 0 58  76      340.6558
0 0 59  76      -188.576
0 1 60  76      631.9694
0 1 61  76    -26094.555
0 1 62  76     -2854.735
0 1 63  76     -8053.558
0 1 64  76     11490.944
0 0 56  77    -39051.035
0 0 57  77     18178.703
0 0 58  77     19509.648
0 0 59  77     -52164.97
0 1 60  77    -102228.37
0 1 61  77     12622.208
0 1 62  77             0
0 1 63  77             0
0 1 64  77             0
0 0 56  78    -134537.08
0 0 57  78      11098.65
0 0 58  78    -14604.633
0 0 59  78    -184113.17
0 1 60  78    -249983.47
0 1 61  78             0
0 1 62  78             0
0 1 63  78             0
0 1 64  78             0
0 0 56  79    -11946.936
0 0 57  79      66638.34
0 0 58  79      124065.2
0 0 59  79     200928.17
0 1 60  79     -38655.03
0 1 61  79    -127952.09
0 1 62  79      101709.6
0 1 63  79      45341.54
0 1 64  79      78514.84
0 0 56  80    -21451.127
0 0 57  80      14717.93
0 0 58  80     1983.0414
0 0 59  80      6359.082
0 1 60  80     -52373.21
0 1 61  80    -3588.1106
0 1 62  80      1558.514
0 1 63  80      7551.865
0 1 64  80      2449.886
0 0 56  81     -84695.63
0 0 57  81     -3882.955
0 0 58  81     539403.94
0 0 59  81    -119369.07
0 1 60  81      4299.898
0 1 61  81    -4563.8984
0 1 62  81     147290.02
0 1 63  81    -33286.035
0 1 64  81     10560.434
0 0 56  82     -530.4233
0 0 57  82      3350.204
0 0 58  82     11285.486
0 0 59  82      531.0495
0 1 60  82      794.2637
0 1 61  82     -1623.352
0 1 62  82      4974.241
0 1 63  82      357.0131
0 1 64  82    -177694.34
0 0 56  83     1971.3497
0 0 57  83       1611.36
0 0 58  83      6697.466
0 0 59  83    -10714.238
0 1 60  83      1308.368
0 1 61  83             0
0 1 62  83             0
0 1 63  83             0
0 1 64  83             0
0 0 56  84      -42574.7
0 0 57  84    -2949.0625
0 0 58  84    -21986.336
0 0 59  84     25549.756
0 1 60  84      45377.33
0 1 61  84             0
0 1 62  84             0
0 1 63  84             0
0 1 64  84             0
0 0 56  85     -161114.8
0 0 57  85    -101200.34
0 0 58  85     -3112.218
0 0 59  85    -154473.78
0 1 60  85     -54038.76
0 1 61  85             0
0 1 62  85             0
0 1 63  85             0
0 1 64  85             0
0 0 56  86     -26.88738
0 0 57  86      7700.189
0 0 58  86      11890.41
0 0 59  86    -28742.164
0 1 60  86     -60792.76
0 1 61  86             0
0 1 62  86             0
0 1 63  86             0
0 1 64  86             0
0 0 56  87    -1057737.4
0 0 57  87     -68036.59
0 0 58  87      163931.5
0 0 59  87       -275426
0 1 60  87     -860062.7
0 1 61  87             0
0 1 62  87             0
0 1 63  87             0
0 1 64  87             0
0 0 56  88    -157022.13
0 0 57  88       -248995
0 0 58  88      105754.5
0 0 59  88     -7163.166
0 1 60  88    -163624.73
0 1 61  88             0
0 1 62  88             0
0 1 63  88             0
0 1 64  88             0
0 0 56  89      7262.494
0 0 57  89     2808.8506
0 0 58  89     11079.354
0 0 59  89      49205.91
0 1 60  89      68579.41
0 1 61  89             0
0 1 62  89             0
0 1 63  89             0
0 1 64  89             0
0 0 56  90      24548.86
0 0 57  90      5267.916
0 0 58  90     17085.057
0 0 59  90     38120.777
0 1 60  90    -3521.9165
0 1 61  90             0
0 1 62  90             0
0 1 63  90             0
0 1 64  90             0
0 0 56  91    -1145.8489
0 0 57  91    -4248.5537
0 0 58  91     124.42747
0 0 59  91    -11384.238
0 1 60  91        83.248
0 1 61  91    -16908.215
0 1 62  91     -4979.584
0 1 63  91      319.7767
0 1 64  91     -8721.759
0 0 56  92     -57772.25
0 0 57  92       10206.2
0 0 58  92       4925.88
0 0 59  92     34231.504
0 1 60  92     -12512.07
0 1 61  92             0
0 1 62  92             0
0 1 63  92             0
0 1 64  92             0
0 0 56  93     222.10277
0 0 57  93     10097.338
0 0 58  93      379.2536
0 0 59  93     245.44644
0 1 60  93      47827.84
0 1 61  93     -64.18322
0 1 62  93      650.4734
0 1 63  93    -37556.383
0 1 64  93    -141476.73
0 0 56  94    -1657.9207
0 0 57  94      1926.171
0 0 58  94      2639.325
0 0 59  94     -6958.373
0 1 60  94     12541.947
0 1 61  94    -200807.44
0 1 62  94    -103801.19
0 1 63  94      1876.946
0 1 64  94    -1187.7537
0 0 56  95     -778283.7
0 0 57  95      342844.1
0 0 58  95      258960.1
0 0 59  95     -29165.05
0 1 60  95    -136240.58
0 1 61  95     1678840.4
0 1 62  95      -699.649
0 1 63  95     -486.8895
0 1 64  95       1214534
1 0 56  96     25114.164
1 0 57  96      -5195137
1 0 58  96    -299710.22
1 0 59  96     -434629.1
1 1 60  96    -12358.756
1 1 61  96      3715.533
1 1 62  96     268269.84
1 1 63  96       -491367
1 1 64  96     -205.5933
1 0 56  97     12.638595
1 0 57  97      970.1215
1 0 58  97      808.6724
1 0 59  97     2902.5444
1 1 60  97     -950.1722
1 1 61  97             0
1 1 62  97             0
1 1 63  97             0
1 1 64  97             0
0 0 56  98      3.008029
0 0 57  98      .5593362
0 0 58  98    -1.5731574
0 0 59  98     1.4998513
0 1 60  98     -5.577176
0 1 61  98      2.165316
0 1 62  98     -1.821187
0 1 63  98     -.9568659
0 1 64  98      5.174376
0 0 56  99      -51169.5
0 0 57  99     126087.14
0 0 58  99      29687.97
0 0 59  99     203087.27
0 1 60  99     16716.975
0 1 61  99    -232275.83
0 1 62  99        130105
0 1 63  99      77423.98
0 1 64  99     15761.196
0 0 56 100    -249670.16
0 0 57 100      18166.35
0 0 58 100      5679.181
0 0 59 100    -18310.818
0 1 60 100      -5979.62
0 1 61 100     -58761.26
0 1 62 100     -88052.12
0 1 63 100    -10087.388
0 1 64 100     2311.9302
0 0 56 101    -11883.918
0 0 57 101    -32572.775
0 0 58 101      80.31168
0 0 59 101    -1185.8425
0 1 60 101     4789.1987
0 1 61 101    -256.34186
0 1 62 101     1114.3809
0 1 63 101      1579.698
0 1 64 101    -129.04489
1 0 56 102    -1781.1162
1 0 57 102      761810.1
1 0 58 102     1072411.8
1 0 59 102     1039070.6
1 1 60 102     1998290.3
1 1 61 102             0
1 1 62 102             0
1 1 63 102             0
1 1 64 102             0
1 0 56 103    -2.1133602
1 0 57 103     2.1427753
1 0 58 103      -1.51848
1 0 59 103     .27435404
1 1 60 103     -.3640815
1 1 61 103     -.3450555
1 1 62 103     1.3548205
1 1 63 103      1.873113
1 1 64 103     -25.21345
1 0 56 104    -.06587801
1 0 57 104    -.03561351
1 0 58 104       .078668
1 0 59 104    -.04398422
1 1 60 104    .033677503
1 1 61 104    -.02220646
1 1 62 104   -.020523366
1 1 63 104     .04020548
1 1 64 104    -.05607264
0 0 56 105      5759.858
0 0 57 105     -46588.86
0 0 58 105       3199.73
0 0 59 105      45566.52
0 1 60 105     19687.844
0 1 61 105    -123530.47
0 1 62 105    -12857.132
0 1 63 105     1868.9143
0 1 64 105      60459.12
1 0 56 106     -391707.2
1 0 57 106    -178145.23
1 0 58 106    -1121511.3
1 0 59 106       -334900
1 1 60 106      43903.58
end
label values isin_num isin_num
label def isin_num 1 "AT0000495288", modify
label def isin_num 2 "AT0000495296", modify
label def isin_num 3 "AT0000495304", modify
label def isin_num 4 "AT0000497284", modify
label def isin_num 5 "AT0000497292", modify
label def isin_num 6 "AT0000500277", modify
label def isin_num 7 "AT0000500285", modify
label def isin_num 8 "AT0000611405", modify
label def isin_num 9 "AT0000613617", modify
label def isin_num 10 "AT0000613625", modify
label def isin_num 11 "AT0000615067", modify
label def isin_num 12 "AT0000615075", modify
label def isin_num 13 "AT0000619317", modify
label def isin_num 14 "AT0000619374", modify
label def isin_num 15 "AT0000619713", modify
label def isin_num 16 "AT0000620372", modify
label def isin_num 17 "AT0000639471", modify
label def isin_num 18 "AT0000645973", modify
label def isin_num 19 "AT0000647680", modify
label def isin_num 20 "AT0000647698", modify
label def isin_num 21 "AT0000659636", modify
label def isin_num 22 "AT0000659644", modify
label def isin_num 23 "AT0000662275", modify
label def isin_num 24 "AT0000673181", modify
label def isin_num 25 "AT0000673397", modify
label def isin_num 26 "AT0000674908", modify
label def isin_num 27 "AT0000675178", modify
label def isin_num 28 "AT0000675186", modify
label def isin_num 29 "AT0000685425", modify
label def isin_num 30 "AT0000697065", modify
label def isin_num 31 "AT0000703335", modify
label def isin_num 32 "AT0000703343", modify
label def isin_num 33 "AT0000708334", modify
label def isin_num 34 "AT0000708342", modify
label def isin_num 35 "AT0000711577", modify
label def isin_num 36 "AT0000721444", modify
label def isin_num 37 "AT0000722681", modify
label def isin_num 38 "AT0000739230", modify
label def isin_num 39 "AT0000739248", modify
label def isin_num 40 "AT0000746250", modify
label def isin_num 41 "AT0000746268", modify
label def isin_num 42 "AT0000746904", modify
label def isin_num 43 "AT0000765573", modify
label def isin_num 44 "AT0000767736", modify
label def isin_num 45 "AT0000778568", modify
label def isin_num 46 "AT0000779749", modify
label def isin_num 47 "AT0000779756", modify
label def isin_num 48 "AT0000785225", modify
label def isin_num 49 "AT0000785241", modify
label def isin_num 50 "AT0000801014", modify
label def isin_num 51 "AT0000802400", modify
label def isin_num 52 "AT0000802418", modify
label def isin_num 53 "AT0000805072", modify
label def isin_num 54 "AT0000805189", modify
label def isin_num 55 "AT0000805387", modify
label def isin_num 56 "AT0000805460", modify
label def isin_num 57 "AT0000810528", modify
label def isin_num 58 "AT0000810536", modify
label def isin_num 59 "AT0000812938", modify
label def isin_num 60 "AT0000813001", modify
label def isin_num 61 "AT0000815030", modify
label def isin_num 62 "AT0000817788", modify
label def isin_num 63 "AT0000822747", modify
label def isin_num 64 "AT0000822762", modify
label def isin_num 65 "AT0000823299", modify
label def isin_num 66 "AT0000826086", modify
label def isin_num 67 "AT0000856042", modify
label def isin_num 68 "AT0000856695", modify
label def isin_num 69 "AT0000856950", modify
label def isin_num 70 "AT0000857412", modify
label def isin_num 71 "AT0000857750", modify
label def isin_num 72 "AT0000858147", modify
label def isin_num 73 "AT0000858428", modify
label def isin_num 74 "AT0000859293", modify
label def isin_num 75 "AT0000859491", modify
label def isin_num 76 "AT0000918297", modify
label def isin_num 77 "AT0000932942", modify
label def isin_num 78 "AT0000936513", modify
label def isin_num 79 "AT0000952460", modify
label def isin_num 80 "AT0000952478", modify
label def isin_num 81 "AT0000986377", modify
label def isin_num 82 "AT0000A00G70", modify
label def isin_num 83 "AT0000A00G88", modify
label def isin_num 84 "AT0000A05S97", modify
label def isin_num 85 "AT0000A05SA6", modify
label def isin_num 86 "AT0000A07FQ5", modify
label def isin_num 87 "AT0000A07FR3", modify
label def isin_num 88 "AT0000A07FS1", modify
label def isin_num 89 "AT0000A08EF9", modify
label def isin_num 90 "AT0000A08EG7", modify
label def isin_num 91 "AT0000A090C9", modify
label def isin_num 92 "AT0000A09GQ9", modify
label def isin_num 93 "AT0000A09HQ7", modify
label def isin_num 94 "AT0000A09HR5", modify
label def isin_num 95 "AT0000A09YJ7", modify
label def isin_num 96 "AT0000A0ETV8", modify
label def isin_num 97 "AT0000A0EY50", modify
label def isin_num 98 "AT0000A0J755", modify
label def isin_num 99 "AT0000A0JDU3", modify
label def isin_num 100 "AT0000A0KLE8", modify
label def isin_num 101 "AT0000A0KML1", modify
label def isin_num 102 "AT0000A0LSR3", modify
label def isin_num 103 "AT0000A0LST9", modify
label def isin_num 104 "AT0000A0MRH4", modify
label def isin_num 105 "AT0000A0QQK1", modify
label def isin_num 106 "AT0000A0R2Q7", modify

[Sabo Dong]

Hi Clyde,
I think that things are clearer if I take one step back. If I did not include two-way fixed effects first, regressions would work.
Below are the results of
1) "xtreg wncf interact_1 if weekid >= 56 & weekid <= 64", the one using the home-brew interaction term,
2) "xtreg wncf institutional_dummy#post_1 if weekid >= 56 & weekid <= 64",
3) "xtreg wncf institutional_dummy##post_1 if weekid >= 56 & weekid <= 64",
4) and "xtreg wncf institutional_dummy##post_1 if weekid >= 56 & weekid <= 64, fe" respectively.

As you can see, the first two coefficients of the 2) and 3) models are the same. The only difference is the third one, where -704438.7 = -195735.2 - 256809.9 - 251893.5. So, I started to understand why you said # and ## have nothing to do with two-way fixed effects in #2 and #4. The results show no matter # and ##, both will consider the main effects of institutional_dummy and post_1, which will collinear with the future two-way fixed effects. And they present the 1.institutional_dummy#1.post_1 term in different ways, but the information behind it is essential the same.

As for your concern that institutional_dummy is colinear with the isin_num fixed effect and post_1 is colinear with the weekid effect, that is not a problem. Stata will recognize this fact and will omit the institutional_dummy and post_1 variables from the model. That leaves behind just the 1.institutional_dummy#1.post_1 term, which is the one you actually want.

My case may imply that sometime what is left are their main effects instead of 1.institutional_dummy#1.post_1 term (or 1 1), the one I actually want. At least, it may imply that how Stata decides which term to omit is somewhat unclear or unstable (for example 4) model).

So, I have to reconsider my home-brew interaction term, as it makes sure that institutional_dummy, post_1, and two-way fixed effects will not be simultaneously enrolled. What do you think?

[Clyde Schechter]

Yes, you are understanding it well now.