I’m conducting an analysis where I want to know how my outcome of interest, reemployment probability, represented with a binary variable (REEMP3), changes between two 6-month time periods (months 1-6; months 7-12); so, does reemployment probability increase or decrease in months 7-12 (PREPOSTPERIOD==1) relative to months 1-6 (PREPOSTPERIOD==0). As an added dimension, I want to know how the outcome changes between these two periods, within states coded according to strictness on four policies of interest. My policy variables are also binary; states are coded as stricter or less strict (1 or 0) on the four policy measures. So, I want to know, in stricter states (policy1==1), how did the probability of reemployment change in the second 6-month period, relative to the first; and how does this compare to how reemployment changed in less strict states (policy1==0). I have a bunch of individual-level and state-level covariates. I cluster SE’s at the state level.

I would also like to control for state and month FE. This is where it gets tricky. So, were I to exclude state and month FE, I would set up my logit model as follows. The first four independent variables are interactions of the binary policy variables and the time-period variable. The output is normal; no dropped variables (w/ exception of one very small occupational category)

Code:
logit reemp3 i.rq##i.prepostperiod_ma i.hidh##i.prepostperiod_ma i.lorh##i.prepostperiod_ma i.lorech##i.prepostperiod_ma b3.age_group b1.race_wbho b4.edu4 i.woman##i.marstdum1##i.ownkidd_18 b1.ind_nilf b1.uh_occmaj_b2 i.sampjl b1.durg ur_sa ur2_sa ur3_sa iur iur2 iur3 initrate initrate2 initrate3 empgrowth emp2 emp3 incrate_jhu stringd i.cutoff3n if sampall==1 & age>=18 & age<65 [pw=wtfinl], vce(cluster statefip) or
Here’s how I would set up the model with state and month FE. To prevent multicollinearity, I’m told I should drop the POSTPERIOD dummy, since it captures the same months for which I’d insert dummies. But, when I run the following, Stata ends up dropping the interacted policy and postperiod variables, along with the last five state dummies. What am I doing wrong? I had a lengthy, very helpful discussion in December with Clyde about another multicollinearity issue (here: https://www.statalist.org/forums/for...es-model/page4). This is different (I think!). Output pasted below...

Code:
logit reemp3 i.rq i.hidh i.lorh i.lorech i.rq#i.prepostperiod_ma i.hidh#i.prepostperiod_ma i.lorh#i.prepostperiod_ma i.lorech#i.prepostperiod_ma b3.age_group b1.race_wbho b4.edu4 i.woman##i.marstdum1##i.ownkidd_18 b1.ind_nilf b1.uh_occmaj_b2 i.sampjl b1.durg ur_sa ur2_sa ur3_sa iur iur2 iur3 initrate initrate2 initrate3 empgrowth emp2 emp3 incrate_jhu stringd i.cutoff3n i.statefip i.ymd9 i.ymd10 i.ymd11 i.ymd12 i.ymd13 i.ymd14 i.ymd15 i.ymd16 i.ymd17 i.ymd18 i.ymd19 i.ymd20 if sampall==1 & age>=18 & age<65 [pw=wtfinl], vce(cluster statefip) or
Code:
. logit reemp3 i.rq i.hidh i.lorh i.lorech i.rq#i.prepostperiod_ma i.hidh#i.prepostperiod_ma i.lorh#i.prepostperiod_ma i.lorech#i.prepostperiod_
> ma b3.age_group b1.race_wbho b4.edu4 i.woman##i.marstdum1##i.ownkidd_18 b1.ind_nilf b1.uh_occmaj_b2 i.sampjl b1.durg ur_sa ur2_sa ur3_sa iur i
> ur2 iur3 initrate initrate2 initrate3 empgrowth emp2 emp3 incrate_jhu stringd i.cutoff3n i.statefip i.ymd9 i.ymd10 i.ymd11 i.ymd12 i.ymd13 i.y
> md14 i.ymd15 i.ymd16 i.ymd17 i.ymd18 i.ymd19 i.ymd20 if sampall==1 & age>=18 & age<65 [pw=wtfinl], vce(cluster statefip) or

note: 1.rq#1.prepostperiod_ma omitted because of collinearity.
note: 1.hidh#1.prepostperiod_ma omitted because of collinearity.
note: 1.lorh#1.prepostperiod_ma omitted because of collinearity.
note: 1.lorech#1.prepostperiod_ma omitted because of collinearity.
note: 11.uh_occmaj_b2 omitted because of collinearity.
note: 51.statefip omitted because of collinearity.
note: 53.statefip omitted because of collinearity.
note: 54.statefip omitted because of collinearity.
note: 55.statefip omitted because of collinearity.
note: 56.statefip omitted because of collinearity.
note: 1.ymd20 omitted because of collinearity.
Iteration 0:   log pseudolikelihood =  -22437923  
Iteration 1:   log pseudolikelihood =  -21171234  
Iteration 2:   log pseudolikelihood =  -21126355  
Iteration 3:   log pseudolikelihood =  -21126157  
Iteration 4:   log pseudolikelihood =  -21126157  

Logistic regression                                     Number of obs = 10,804
                                                        Wald chi2(43) =      .
                                                        Prob > chi2   =      .
Log pseudolikelihood = -21126157                        Pseudo R2     = 0.0585

                                                                    (Std. err. adjusted for 45 clusters in statefip)
--------------------------------------------------------------------------------------------------------------------
                                                   |               Robust
                                            reemp3 | Odds ratio   std. err.      z    P>|z|     [95% conf. interval]
---------------------------------------------------+----------------------------------------------------------------
                                              1.rq |   .8759639   .2052028    -0.57   0.572     .5534574    1.386399
                                            1.hidh |   .6605953   .1239371    -2.21   0.027     .4573386     .954186
                                            1.lorh |   1.063168    .082126     0.79   0.428     .9137966    1.236956
                                          1.lorech |   .8994186   .1450101    -0.66   0.511     .6557309    1.233667
                                                   |
                               rq#prepostperiod_ma |
                                              0 1  |   1.394841   .1676659     2.77   0.006     1.102063    1.765399
                                              1 1  |          1  (omitted)
                                                   |
                             hidh#prepostperiod_ma |
                                              0 1  |   .9149866   .1208369    -0.67   0.501       .70632    1.185299
                                              1 1  |          1  (omitted)
                                                   |
                             lorh#prepostperiod_ma |
                                              0 1  |   .9691477   .0887178    -0.34   0.732     .8099705    1.159607
                                              1 1  |          1  (omitted)
                                                   |
                           lorech#prepostperiod_ma |
                                              0 1  |    .800244   .1520383    -1.17   0.241     .5514457    1.161294
                                              1 1  |          1  (omitted)
                                                   |
                                         age_group |
                                            18-24  |   .9053318   .0962845    -0.94   0.350     .7349879    1.115155
                                            25-34  |   .9163359   .0900103    -0.89   0.374     .7558619     1.11088
                                            45-54  |   .9557471   .0701927    -0.62   0.538     .8276151    1.103717
                                            55-64  |   .8012826   .0686457    -2.59   0.010     .6774286    .9477808
                                                   |
                                         race_wbho |
                                       2 black nh  |   .6752778   .0780661    -3.40   0.001     .5383672    .8470058
                                3 hispanic/latino  |   .9729026   .1120415    -0.24   0.811     .7763244    1.219258
                                         other nh  |   .6696745   .0697663    -3.85   0.000     .5459919    .8213749
                                                   |
                                              edu4 |
                                   1 Less than HS  |   .9195733   .1157851    -0.67   0.505     .7184723    1.176963
                                      2 HS or GED  |   .9592269   .0896774    -0.45   0.656     .7986255    1.152125
                   3 Some college or Associate's'  |   1.025496   .0825591     0.31   0.754     .8758033    1.200774
                                                   |
                                           1.woman |   1.057105   .0891657     0.66   0.510     .8960246    1.247142
                                       1.marstdum1 |    1.42355   .1632607     3.08   0.002     1.136978    1.782351
                                                   |
                                   woman#marstdum1 |
                                              1 1  |   .7660572   .1336128    -1.53   0.127     .5442492    1.078263
                                                   |
                                        ownkidd_18 |
                      1: Own children, <18, in HH  |   .7174053   .1256241    -1.90   0.058     .5089927    1.011155
                                                   |
                                  woman#ownkidd_18 |
                    1#1: Own children, <18, in HH  |   1.387122   .2865239     1.58   0.113     .9253168    2.079404
                                                   |
                              marstdum1#ownkidd_18 |
                    1#1: Own children, <18, in HH  |   1.284939   .3104339     1.04   0.299     .8002715    2.063137
                                                   |
                        woman#marstdum1#ownkidd_18 |
                  1#1#1: Own children, <18, in HH  |   .7495964   .2058639    -1.05   0.294      .437582     1.28409
                                                   |
                                          ind_nilf |
                                                2  |    .294526   .1242367    -2.90   0.004     .1288459    .6732507
                                                3  |   .8449218   .3897243    -0.37   0.715     .3421336    2.086591
                                                4  |   .7630144   .3462639    -0.60   0.551      .313508    1.857021
                                                5  |   .7426147    .284665    -0.78   0.438     .3503275    1.574174
                                                6  |   .6189058   .2726112    -1.09   0.276     .2610318    1.467424
                                                7  |    .641471   .2559315    -1.11   0.266     .2934729    1.402122
                                                8  |   .9330527   .3859499    -0.17   0.867     .4147758    2.098935
                                                9  |    .625827   .2571176    -1.14   0.254     .2797324    1.400122
                                               10  |   .8877231   .3144192    -0.34   0.737      .443398    1.777302
                                               11  |   .5518519   .2135944    -1.54   0.125      .258443    1.178366
                                               12  |   .7979687   .3611106    -0.50   0.618     .3286891    1.937253
                                               13  |   .8836339   .3802865    -0.29   0.774     .3801401    2.054003
                                               14  |   .4842508   .4989079    -0.70   0.482     .0642843     3.64784
                                                   |
                                      uh_occmaj_b2 |
             professional and related occupations  |   1.149595   .0924962     1.73   0.083     .9818773     1.34596
                              service occupations  |   1.245314   .1368721     2.00   0.046     1.003976    1.544664
                    sales and related occupations  |   1.144675   .1539027     1.00   0.315     .8795027    1.489797
    office and administrative support occupations  |   1.026844   .0943187     0.29   0.773     .8576676    1.229391
       farming, fishing, and forestry occupations  |   .8031993   .3342352    -0.53   0.598     .3553145    1.815657
          construction and extraction occupations  |   1.057206   .1507861     0.39   0.697     .7993837    1.398183
installation, maintenance, and repair occupations  |   1.174744   .2552418     0.74   0.459     .7673593    1.798405
                           production occupations  |   1.212174   .1442737     1.62   0.106     .9599628    1.530649
   transportation and material moving occupations  |   1.143632   .1307977     1.17   0.241     .9139742    1.430996
                                     armed forces  |          1  (omitted)
                                                   |
                                          1.sampjl |   1.459405   .1067366     5.17   0.000     1.264507    1.684341
                                                   |
                                              durg |
                                        5-8 weeks  |   .7148107   .0386471    -6.21   0.000     .6429391    .7947166
                                       9-12 weeks  |   .6361483   .0478035    -6.02   0.000     .5490282    .7370927
                                      13-16 weeks  |   .5037342   .0474485    -7.28   0.000     .4188164    .6058696
                                      17-20 weeks  |   .4016522   .0605108    -6.05   0.000     .2989597    .5396197
                                      21-26 weeks  |   .4995176   .0538834    -6.43   0.000     .4043253    .6171215
                                      27-32 weeks  |   .3555218   .0883652    -4.16   0.000     .2184237    .5786726
                                      33-38 weeks  |   .4384225   .0661046    -5.47   0.000     .3262497     .589163
                                      39-44 weeks  |   .4156303   .1025017    -3.56   0.000     .2563221     .673951
                                      45-50 weeks  |   .3319299   .1188662    -3.08   0.002     .1645226    .6696797
                                      51-52 weeks  |   .3449078   .0759586    -4.83   0.000     .2239979    .5310826
                                        >52 weeks  |   .2238139   .0389275    -8.61   0.000      .159162    .3147275
                                                   |
                                             ur_sa |   3.30e-09   4.02e-08    -1.60   0.109     1.43e-19    76.45255
                                            ur2_sa |   8.03e+56   6.18e+58     1.70   0.088     2.94e-09    2.2e+122
                                            ur3_sa |   4.5e-135   6.8e-133    -2.02   0.043     3.6e-265    .0000561
                                               iur |   .0001876   .0021134    -0.76   0.446     4.85e-14      725261
                                              iur2 |   6.00e+23   5.48e+25     0.60   0.549     1.12e-54    3.2e+101
                                              iur3 |   1.91e-65   4.23e-63    -0.67   0.500     2.1e-253    1.8e+123
                                          initrate |   2.58e-21   8.56e-20    -1.43   0.152     1.63e-49    4.10e+07
                                         initrate2 |          .          .     1.59   0.112     5.2e-191           .
                                         initrate3 |          0          0    -1.26   0.209            0           .
                                         empgrowth |   1.026503   .0358656     0.75   0.454     .9585611    1.099262
                                              emp2 |   1.002132   .0018383     1.16   0.246     .9985354    1.005741
                                              emp3 |   1.000203   .0001074     1.89   0.059     .9999926    1.000414
                                       incrate_jhu |   .9996615   .0001283    -2.64   0.008     .9994101    .9999129
                                           stringd |   1.009898   .0055966     1.78   0.076     .9989877    1.020927
                                        1.cutoff3n |   1.204709   .1094021     2.05   0.040     1.008283      1.4394
                                                   |
                                          statefip |
                                                5  |   .5474853   .1628406    -2.03   0.043     .3056303    .9807277
                                                6  |   .7088491   .0787637    -3.10   0.002     .5701283    .8813227
                                                8  |   .6208228   .1714694    -1.73   0.084     .3613003    1.066761
                                                9  |   .7189693   .1354696    -1.75   0.080     .4969644    1.040149
                                               10  |   .9189624   .1377839    -0.56   0.573     .6849731    1.232883
                                               11  |    .649819   .1030442    -2.72   0.007     .4762273    .8866874
                                               13  |   .9209017   .0895944    -0.85   0.397     .7610269    1.114363
                                               15  |   .9149104    .104705    -0.78   0.437     .7310794    1.144966
                                               16  |   1.447961   .1215811     4.41   0.000     1.228241    1.706985
                                               17  |   .6666431   .1042136    -2.59   0.009     .4907141    .9056456
                                               19  |   1.151438   .1322751     1.23   0.220      .919297    1.442198
                                               20  |   1.228915   .1738412     1.46   0.145     .9313474    1.621556
                                               21  |   1.139818   .1656932     0.90   0.368     .8572311     1.51556
                                               23  |   .6316927   .1850776    -1.57   0.117     .3557255    1.121752
                                               24  |   .6147948   .0446059    -6.70   0.000     .5333005    .7087422
                                               25  |   .6545012   .1038723    -2.67   0.008     .4795357    .8933056
                                               26  |   2.299786    .637242     3.01   0.003     1.336073    3.958629
                                               27  |   .8193352   .0659604    -2.48   0.013     .6997386    .9593727
                                               28  |   1.669741   .3574309     2.39   0.017     1.097584    2.540156
                                               29  |   1.148785   .1399677     1.14   0.255     .9047499    1.458643
                                               30  |   1.664098   .2325977     3.64   0.000     1.265328    2.188542
                                               31  |   1.656605   .1573445     5.31   0.000     1.375219    1.995566
                                               32  |   1.340935   .1634444     2.41   0.016     1.055981    1.702783
                                               33  |   .6338442   .1345354    -2.15   0.032      .418131    .9608436
                                               34  |   .8104846   .1040483    -1.64   0.102     .6301868    1.042366
                                               35  |   1.050071   .1562071     0.33   0.743     .7845039    1.405537
                                               36  |   .7467416   .1153147    -1.89   0.059     .5517273    1.010686
                                               37  |   1.003764   .1816936     0.02   0.983     .7039694    1.431231
                                               38  |    .735203   .0910294    -2.48   0.013      .576787    .9371285
                                               40  |   1.012734   .1135587     0.11   0.910     .8129227    1.261657
                                               41  |   1.082134   .2020508     0.42   0.672     .7504963    1.560318
                                               42  |   .8352292   .1290433    -1.17   0.244     .6170135     1.13062
                                               44  |   .8123845   .1488013    -1.13   0.257     .5673491     1.16325
                                               45  |   .7801361   .1288627    -1.50   0.133     .5643768    1.078379
                                               46  |   1.158982    .111123     1.54   0.124     .9604249    1.398587
                                               47  |   1.244327   .1920411     1.42   0.157     .9195294    1.683849
                                               48  |   1.174027   .1647468     1.14   0.253     .8917274    1.545695
                                               49  |   .7521419   .1802977    -1.19   0.235     .4701715    1.203215
                                               50  |     1.2256   .1100059     2.27   0.023     1.027893    1.461335
                                               51  |          1  (omitted)
                                               53  |          1  (omitted)
                                               54  |          1  (omitted)
                                               55  |          1  (omitted)
                                               56  |          1  (omitted)
                                                   |
                                            1.ymd9 |   .5254365   .2632841    -1.28   0.199     .1967899    1.402936
                                           1.ymd10 |   .4938725   .2484605    -1.40   0.161     .1842413    1.323862
                                           1.ymd11 |   .4226503   .2169267    -1.68   0.093     .1545607    1.155748
                                           1.ymd12 |   .5955043   .2787812    -1.11   0.268     .2379035    1.490627
                                           1.ymd13 |   .5502248   .2544128    -1.29   0.196     .2223115    1.361816
                                           1.ymd14 |   .3811032   .1696496    -2.17   0.030     .1592674    .9119235
                                           1.ymd15 |   .6239076   .3885574    -0.76   0.449     .1840809    2.114618
                                           1.ymd16 |   .8106054   .1555722    -1.09   0.274     .5564756    1.180791
                                           1.ymd17 |   1.066924   .1583095     0.44   0.662     .7976873    1.427034
                                           1.ymd18 |   1.035925   .1403874     0.26   0.795     .7942812    1.351083
                                           1.ymd19 |   1.034614   .1145833     0.31   0.759     .8327376    1.285431
                                           1.ymd20 |          1  (omitted)
                                             _cons |   2.566342   2.396611     1.01   0.313     .4115374    16.00368
--------------------------------------------------------------------------------------------------------------------
Note: _cons estimates baseline odds.