Dealing w/ multicollinearity in logit model w/ FE (state, month)

[Claire McKenna]

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)

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...

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

. 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.

[Claire McKenna]

Clyde Schechter, since you were so helpful with this issue the last time (in December), any thoughts on why dropping the post-period dummy doesn't resolve the issue?

[Clyde Schechter]

I wanted to answer this post when I saw it earlier, but without knowing how the other variables are defined, and without example data, I really can't.

[Carlo Lazzaro]

Claire:
your model has tons of predictors.
Most of them do not seem to have any bearing on variations in the regressand.
As a general advice, I would consider a more parsimonious specification.

[Claire McKenna]

Thanks both. Clyde Schechter, let me see if I can provide some background. Hope it helps. I.RQ, I.HIDH, I.LORH, and I.LORECH are the policy variables. They are fixed, time invariant. A state's coded with a 1 or a 0 over the sample period (as they capture policy status prior to the sample period). POSTPERIOD captures 12 months; equals 1 for months March 2020 to August 2020, and 0 for months September 2019 to February 2020. All the other variables are individual-level and state-level controls. The state-level controls vary by month.

I've attached ~25 observations from my dataset; I'm not sure how else to include data here. I hope that's okay. sample_data.dta [FWIW, here's a second snippet, featuring a couple eligible sample members: sample_data2.dta]

Thank you.

[Carlo Lazzaro]

Claire:
I still think that you've to tidy your model up as it cannot be managed in its current specification.
I'd start off by testing the joint statistical significance of your categorical predictors via -testparm-.

[Claire McKenna]

Mmm. Okay. I can try that to start. The predictors are all pretty sensible, though something weird is happening with the state labor market slack measures, which I need to investigate further. But I'll try your suggestion. Thank you Carlo.

[Clyde Schechter]

I've attached ~25 observations from my dataset; I'm not sure how else to include data here.

The best way to show example data is with the -dataex- command. If you are running version 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.

Many of us, including me, will not open attachments from people we do not know. So I haven't looked at your example data.
Added: In any case, a sample of 25 observations is not sufficient for this situation. You have 43 variables in your model, so any data set with fewer than 44 observations will automatically have colinearities among the variables. And even if you are close to 44 observations, you are likely to have some near colinearities that may obscure what is going on. To troubleshoot this data I think an example of 100 observations would be the minimum to be barely adequate.

Based on your explanation of some of the variables, two thoughts occur to me. One is that perhaps they are mutually exclusive and exhaustive? Another is that some combinations of the policies uniquely identify some states.

Beyond that, I am also concerned about ur_sa through initrate_3. Their coefficients and standard errors are not really sensible. The simplest explanation is that they are simply in need of rescaling so that the coefficients and standard errors will be more "normal" numbers. Or there may be something seriously wrong with the data in those variables. In any case, variables with coefficients or standard errors like this are often indicative of trouble.

[Claire McKenna]

Thanks, Clyde Schechter. Here's an example dataset (~150 observations), featuring the variables of interest. Please let me know if there's anything else I should provide here. I'm looking into what might be the issue with ur_sa through initrate_3 (which are state-by-month variables representing different labor market conditions). Rescaling might be the solution. Thanks for your help.

* Example generated by -dataex-. For more info, type help dataex
clear
input double personid float year_month byte statefip float(reemp3 rq hidh lorh lorech prepostperiod_ma ur_sa ur2_sa ur3_sa iur iur2 iur3 initrate initrate2 initrate3 empgrowth emp2 emp3) double wtfinl
23622451 718 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00955   .0000912025  8.709837e-07 .0018336505  3.362274e-06  6.165236e-09  -.16638567    .02768419   -.0046062525  774.6097
19274221 717 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00946  .00008949159  8.465904e-07 .0017599835  3.097542e-06  5.451623e-09 -.015129555 .00022890343  -3.463207e-06 1007.2339
19276781 718 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00955   .0000912025  8.709837e-07 .0018336505  3.362274e-06  6.165236e-09  -.16638567    .02768419   -.0046062525   867.561
19622921 718 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00955   .0000912025  8.709837e-07 .0018336505  3.362274e-06  6.165236e-09  -.16638567    .02768419   -.0046062525  795.5599
23295261 717 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00946  .00008949159  8.465904e-07 .0017599835  3.097542e-06  5.451623e-09 -.015129555 .00022890343  -3.463207e-06  959.0402
22959441 717 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00946  .00008949159  8.465904e-07 .0017599835  3.097542e-06  5.451623e-09 -.015129555 .00022890343  -3.463207e-06 1114.1563
18922491 717 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00946  .00008949159  8.465904e-07 .0017599835  3.097542e-06  5.451623e-09 -.015129555 .00022890343  -3.463207e-06 1071.2867
19275881 718 15 1 0 1 0 0 0 .019 .000361 6.858999e-06     .00955   .0000912025  8.709837e-07 .0018336505  3.362274e-06  6.165236e-09  -.16638567    .02768419   -.0046062525 1371.2386
19274351 718 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00955   .0000912025  8.709837e-07 .0018336505  3.362274e-06  6.165236e-09  -.16638567    .02768419   -.0046062525 1282.4831
23296231 717 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00946  .00008949159  8.465904e-07 .0017599835  3.097542e-06  5.451623e-09 -.015129555 .00022890343  -3.463207e-06 1368.8686
23297411 718 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00955   .0000912025  8.709837e-07 .0018336505  3.362274e-06  6.165236e-09  -.16638567    .02768419   -.0046062525   757.553
23623741 718 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00955   .0000912025  8.709837e-07 .0018336505  3.362274e-06  6.165236e-09  -.16638567    .02768419   -.0046062525   638.431
23297411 717 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00946  .00008949159  8.465904e-07 .0017599835  3.097542e-06  5.451623e-09 -.015129555 .00022890343  -3.463207e-06  883.4711
23294781 718 15 0 0 1 0 0 0 .019 .000361 6.858999e-06     .00955   .0000912025  8.709837e-07 .0018336505  3.362274e-06  6.165236e-09  -.16638567    .02768419   -.0046062525  965.8373
18576671 716 15 0 0 1 0 0 0  .02   .0004 7.999999e-06      .0097     .00009409  9.126731e-07  .001760585 3.0996596e-06  5.457214e-09  .030259034  .0009156091   .00002770545  704.7217
19753971 718 38 0 1 1 0 0 0  .02   .0004 7.999999e-06    .007575  .00005738062  4.346582e-07 .0021761353  4.735565e-06  1.030523e-08   .02268563  .0005146379  .000011674886   345.624
20096401 719 38 0 1 1 0 0 0  .02   .0004 7.999999e-06     .01364   .0001860496  2.537716e-06 .0024973396  6.236705e-06 1.5575171e-08   .04537482  .0020588744   .00009342106  617.2639
24078991 719 38 1 1 1 0 0 0  .02   .0004 7.999999e-06     .01364   .0001860496  2.537716e-06 .0024973396  6.236705e-06 1.5575171e-08   .04537482  .0020588744   .00009342106  367.6291
23751481 719 38 0 1 1 0 0 0  .02   .0004 7.999999e-06     .01364   .0001860496  2.537716e-06 .0024973396  6.236705e-06 1.5575171e-08   .04537482  .0020588744   .00009342106  259.7091
23425851 718 38 0 1 1 0 0 0  .02   .0004 7.999999e-06    .007575  .00005738062  4.346582e-07 .0021761353  4.735565e-06  1.030523e-08   .02268563  .0005146379  .000011674886  463.7176
23430651 718 38 0 1 1 0 0 0  .02   .0004 7.999999e-06    .007575  .00005738062  4.346582e-07 .0021761353  4.735565e-06  1.030523e-08   .02268563  .0005146379  .000011674886   520.642
24078191 719 38 0 1 1 0 0 0  .02   .0004 7.999999e-06     .01364   .0001860496  2.537716e-06 .0024973396  6.236705e-06 1.5575171e-08   .04537482  .0020588744   .00009342106  414.0225
20094691 719 38 0 1 1 0 0 0  .02   .0004 7.999999e-06     .01364   .0001860496  2.537716e-06 .0024973396  6.236705e-06 1.5575171e-08   .04537482  .0020588744   .00009342106  376.6195
22959441 716 15 0 0 1 0 0 0  .02   .0004 7.999999e-06      .0097     .00009409  9.126731e-07  .001760585 3.0996596e-06  5.457214e-09  .030259034  .0009156091   .00002770545 1067.3433
19753971 719 38 0 1 1 0 0 0  .02   .0004 7.999999e-06     .01364   .0001860496  2.537716e-06 .0024973396  6.236705e-06 1.5575171e-08   .04537482  .0020588744   .00009342106  336.8039
23752731 718 38 0 1 1 0 0 0  .02   .0004 7.999999e-06    .007575  .00005738062  4.346582e-07 .0021761353  4.735565e-06  1.030523e-08   .02268563  .0005146379  .000011674886  532.5828
23428541 718 38 0 1 1 0 0 0  .02   .0004 7.999999e-06    .007575  .00005738062  4.346582e-07 .0021761353  4.735565e-06  1.030523e-08   .02268563  .0005146379  .000011674886  348.8127
23949431 719 15 0 0 1 0 0 0  .02   .0004 7.999999e-06      .0105     .00011025  1.157625e-06  .002325738  5.409058e-06 1.2580052e-08     .696966     .4857616       .3385593  786.6038
23752641 719 38 0 1 1 0 0 0  .02   .0004 7.999999e-06     .01364   .0001860496  2.537716e-06 .0024973396  6.236705e-06 1.5575171e-08   .04537482  .0020588744   .00009342106  433.1915
22625071 716 15 0 0 1 0 0 0  .02   .0004 7.999999e-06      .0097     .00009409  9.126731e-07  .001760585 3.0996596e-06  5.457214e-09  .030259034  .0009156091   .00002770545 1011.4361
23752721 718 38 0 1 1 0 0 0  .02   .0004 7.999999e-06    .007575  .00005738062  4.346582e-07 .0021761353  4.735565e-06  1.030523e-08   .02268563  .0005146379  .000011674886  573.5391
23430611 718 38 0 1 1 0 0 0  .02   .0004 7.999999e-06    .007575  .00005738062  4.346582e-07 .0021761353  4.735565e-06  1.030523e-08   .02268563  .0005146379  .000011674886  322.3373
23622481 719 15 1 0 1 0 0 0  .02   .0004 7.999999e-06      .0105     .00011025  1.157625e-06  .002325738  5.409058e-06 1.2580052e-08     .696966     .4857616       .3385593  736.2949
19622921 719 15 1 0 1 0 0 0  .02   .0004 7.999999e-06      .0105     .00011025  1.157625e-06  .002325738  5.409058e-06 1.2580052e-08     .696966     .4857616       .3385593   815.636
20097241 719 38 0 1 1 0 0 0  .02   .0004 7.999999e-06     .01364   .0001860496  2.537716e-06 .0024973396  6.236705e-06 1.5575171e-08   .04537482  .0020588744   .00009342106  381.8292
18922491 716 15 0 0 1 0 0 0  .02   .0004 7.999999e-06      .0097     .00009409  9.126731e-07  .001760585 3.0996596e-06  5.457214e-09  .030259034  .0009156091   .00002770545 1068.9582
18579031 716 15 0 0 1 0 0 0  .02   .0004 7.999999e-06      .0097     .00009409  9.126731e-07  .001760585 3.0996596e-06  5.457214e-09  .030259034  .0009156091   .00002770545  753.3666
23624901 719 15 1 0 1 0 0 0  .02   .0004 7.999999e-06      .0105     .00011025  1.157625e-06  .002325738  5.409058e-06 1.2580052e-08     .696966     .4857616       .3385593  779.5862
23751401 718 38 0 1 1 0 0 0  .02   .0004 7.999999e-06    .007575  .00005738062  4.346582e-07 .0021761353  4.735565e-06  1.030523e-08   .02268563  .0005146379  .000011674886  704.6757
20438731 720 38 0 1 1 0 0 0 .021 .000441    9.261e-06    .016825  .00028308062  4.762831e-06 .0011983024 1.4359285e-06 1.7206766e-09  -.04535424  .0020570073  -.00009329402  357.9468
20303971 720 15 0 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584  756.8741
20301291 720 15 1 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584 1515.4074
22760651 716 38 0 1 1 0 0 0 .021 .000441    9.261e-06      .0033 .000010889999  3.593699e-08 .0006007483  3.608986e-07 2.1680922e-10   .20421916    .04170547     .008517056  357.0898
23091991 716 38 0 1 1 0 0 0 .021 .000441    9.261e-06      .0033 .000010889999  3.593699e-08 .0006007483  3.608986e-07 2.1680922e-10   .20421916    .04170547     .008517056  363.8397
20303731 720 15 0 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584 1094.7234
24283101 720 15 0 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584  951.3791
24417791 720 38 0 1 1 0 0 0 .021 .000441    9.261e-06    .016825  .00028308062  4.762831e-06 .0011983024 1.4359285e-06 1.7206766e-09  -.04535424  .0020570073  -.00009329402  449.9743
20097391 720 38 0 1 1 0 0 0 .021 .000441    9.261e-06    .016825  .00028308062  4.762831e-06 .0011983024 1.4359285e-06 1.7206766e-09  -.04535424  .0020570073  -.00009329402  367.2127
24078191 720 38 0 1 1 0 0 0 .021 .000441    9.261e-06    .016825  .00028308062  4.762831e-06 .0011983024 1.4359285e-06 1.7206766e-09  -.04535424  .0020570073  -.00009329402  383.9173
23949431 720 15 0 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584   887.395
24283951 720 15 0 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584 1591.7646
20300871 720 15 0 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584  737.0807
23094631 716 38 0 1 1 0 0 0 .021 .000441    9.261e-06      .0033 .000010889999  3.593699e-08 .0006007483  3.608986e-07 2.1680922e-10   .20421916    .04170547     .008517056  418.8556
24283661 720 15 0 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584  761.6678
24418931 720 38 0 1 1 0 0 0 .021 .000441    9.261e-06    .016825  .00028308062  4.762831e-06 .0011983024 1.4359285e-06 1.7206766e-09  -.04535424  .0020570073  -.00009329402  408.7913
20301771 720 15 0 0 1 0 0 0 .021 .000441    9.261e-06    .009975  .00009950063  9.925188e-07 .0018028006   3.25009e-06  5.859264e-09  -.15046646   .022640154    -.003406584  805.3245
23094191 716 38 0 1 1 0 0 0 .021 .000441    9.261e-06      .0033 .000010889999  3.593699e-08 .0006007483  3.608986e-07 2.1680922e-10   .20421916    .04170547     .008517056  630.1064
18718891 716 38 1 1 1 0 0 0 .021 .000441    9.261e-06      .0033 .000010889999  3.593699e-08 .0006007483  3.608986e-07 2.1680922e-10   .20421916    .04170547     .008517056   330.153
20439421 720 38 0 1 1 0 0 0 .021 .000441    9.261e-06    .016825  .00028308062  4.762831e-06 .0011983024 1.4359285e-06 1.7206766e-09  -.04535424  .0020570073  -.00009329402  371.1817
23093331 717 38 0 1 1 0 0 0 .021 .000441    9.261e-06      .0041     .00001681 6.8921004e-08 .0013652077  1.863792e-06  2.544463e-09  -.20380296    .04153565    -.008465087  518.4528
24081611 720 38 0 1 1 0 0 0 .021 .000441    9.261e-06    .016825  .00028308062  4.762831e-06 .0011983024 1.4359285e-06 1.7206766e-09  -.04535424  .0020570073  -.00009329402  455.5744
23428541 717 38 0 1 1 0 0 0 .021 .000441    9.261e-06      .0041     .00001681 6.8921004e-08 .0013652077  1.863792e-06  2.544463e-09  -.20380296    .04153565    -.008465087  357.1277
24619291 722 15 0 0 1 0 0 1 .022 .000484   .000010648     .05478    .003000849   .0001643865   .05526815    .003054568  .00016882035  -22.279873     496.3927     -11059.567  661.1515
20636201 722 15 0 0 1 0 0 1 .022 .000484   .000010648     .05478    .003000849   .0001643865   .05526815    .003054568  .00016882035  -22.279873     496.3927     -11059.567  751.9965
24418931 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144   412.927
24619251 721 15 1 0 1 0 0 0 .022 .000484   .000010648    .009825  .00009653064  9.484136e-07 .0019828796 3.9318115e-06 7.7963085e-09  -1.2507516    1.5643796     -1.9566503  684.3941
24417791 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  429.4841
24617751 721 15 1 0 1 0 0 0 .022 .000484   .000010648    .009825  .00009653064  9.484136e-07 .0019828796 3.9318115e-06 7.7963085e-09  -1.2507516    1.5643796     -1.9566503  912.1545
20438731 721 38 1 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  353.2391
24750461 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  498.8355
20774521 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  357.3046
24749041 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  516.2645
24938541 722 15 0 0 1 0 0 1 .022 .000484   .000010648     .05478    .003000849   .0001643865   .05526815    .003054568  .00016882035  -22.279873     496.3927     -11059.567  1219.836
24750281 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  371.1504
24417541 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  484.7811
20438351 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  373.9177
20303731 721 15 0 0 1 0 0 0 .022 .000484   .000010648    .009825  .00009653064  9.484136e-07 .0019828796 3.9318115e-06 7.7963085e-09  -1.2507516    1.5643796     -1.9566503 1120.9953
20303971 721 15 0 0 1 0 0 0 .022 .000484   .000010648    .009825  .00009653064  9.484136e-07 .0019828796 3.9318115e-06 7.7963085e-09  -1.2507516    1.5643796     -1.9566503  839.1937
24750441 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  498.8355
20636201 721 15 0 0 1 0 0 0 .022 .000484   .000010648    .009825  .00009653064  9.484136e-07 .0019828796 3.9318115e-06 7.7963085e-09  -1.2507516    1.5643796     -1.9566503  778.9029
24416381 721 38 1 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  452.1086
20973401 722 15 0 0 1 0 0 1 .022 .000484   .000010648     .05478    .003000849   .0001643865   .05526815    .003054568  .00016882035  -22.279873     496.3927     -11059.567  901.8695
24415141 721 38 0 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  393.1503
24283661 721 15 0 0 1 0 0 0 .022 .000484   .000010648    .009825  .00009653064  9.484136e-07 .0019828796 3.9318115e-06 7.7963085e-09  -1.2507516    1.5643796     -1.9566503  735.7643
24747581 721 38 1 1 1 0 0 0 .022 .000484   .000010648    .016125   .0002600156 4.1927515e-06 .0009936253  9.872912e-07  9.809974e-10   -.4310331    .18578954     -.08008144  394.8541
24618301 721 15 1 0 1 0 0 0 .022 .000484   .000010648    .009825  .00009653064  9.484136e-07 .0019828796 3.9318115e-06 7.7963085e-09  -1.2507516    1.5643796     -1.9566503  694.6114
18752381 716 45 0 0 1 1 1 0 .024 .000576   .000013824      .0064     .00004096 2.6214397e-07  .001019045 1.0384528e-06 1.0582301e-09   .04548142  .0020685596   .00009408104 2608.3381
23130781 716 45 1 0 1 1 1 0 .024 .000576   .000013824      .0064     .00004096 2.6214397e-07  .001019045 1.0384528e-06 1.0582301e-09   .04548142  .0020685596   .00009408104 3725.9525
23130321 716 45 0 0 1 1 1 0 .024 .000576   .000013824      .0064     .00004096 2.6214397e-07  .001019045 1.0384528e-06 1.0582301e-09   .04548142  .0020685596   .00009408104 2169.5585
18755141 716 45 1 0 1 1 1 0 .024 .000576   .000013824      .0064     .00004096 2.6214397e-07  .001019045 1.0384528e-06 1.0582301e-09   .04548142  .0020685596   .00009408104 2784.2911
21184471 722 49 0 0 1 0 1 1 .025 .000625   .000015625 .032899998   .0010824099 .000035611283  .017125264   .0002932747  5.022406e-06   -8.825028     77.88113      -687.3032 1946.8851
23170061 716 50 0 1 0 0 0 0 .025 .000625   .000015625       .006       .000036      2.16e-07 .0008849686  7.831695e-07  6.930804e-10           0            0              0  517.0318
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22840811 716 50 1 1 0 0 0 0 .025 .000625   .000015625       .006       .000036      2.16e-07 .0008849686  7.831695e-07  6.930804e-10           0            0              0  468.8364
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20514341 720 50 0 1 0 0 0 0 .025 .000625   .000015625     .01625   .0002640625  4.291015e-06  .001661406 2.7602696e-06  4.585928e-09 -.031657882  .0010022215  -.00003172821  322.7622
23167041 717 49 0 0 1 0 1 0 .025 .000625   .000015625      .0043     .00001849  7.950701e-08  .000807548  6.521337e-07  5.266292e-10    .2359663    .05568008     .013138623  3048.389
18884291 717  8 0 0 0 0 1 0 .025 .000625   .000015625     .00628   .0000394384  2.476732e-07  .000857534  7.353645e-07     6.306e-10   .14971824    .02241555     .003356017 2799.7421
23465301 717 45 0 0 1 1 1 0 .025 .000625   .000015625     .00656   .0000430336 2.8230042e-07 .0011292454  1.275195e-06 1.4400082e-09 -.013640444  .0001860617  -2.537964e-06 3059.9985
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end
format %tm year_month

[Clyde Schechter]

OK. First the easy part: the varibles ur*_sa and iur* and initrate* that have these bizarre coefficients. It seems that ur2_sa is the square of ur_sa, and ur3_sa is the cube of ur_sa. And similarly for the other families of variables. So you are doing cubic polynomial fits here. There's nothing inherently wrong with doing that, although, frankly, unless you have a good reason to expect a cubic polynomial relationship, you probably shouldn't be doing it. Be that as it may, the problem is that when you start taking squares and cubes of numbers that are far from 1, or whose reciprocals are far from1, the numbers become very extreme. In your case the mean values of the ur_sa , iur, and initrate variables are or magnitude 0.02, 0.01, and 0.004, respectively. So when you take squares and cubes you get these extremely small values, and that requires that the corresponding coefficients (or odds ratios) also take on extreme values due to this scaling. Now, in principle, this isn't a problem. But in computer arithmetic, it is. And the estimations of regression coefficients become numerically unstable in this context. But, it turns out, you have an even bigger problem than scaling with these variables

Summary for variables: ur_sa
Group variable: reemp3

  reemp3 |       Min      Mean       Max
---------+------------------------------
       0 |      .019  .0223306      .025
       1 |      .019  .0235405      .025
---------+------------------------------
   Total |      .019  .0226139      .025
----------------------------------------

Summary for variables: iur
Group variable: reemp3

  reemp3 |       Min      Mean       Max
---------+------------------------------
       0 |     .0033   .013654    .05478
       1 |     .0033   .009807     .0329
---------+------------------------------
   Total |     .0033  .0127531    .05478
----------------------------------------

Summary for variables: initrate
Group variable: reemp3

  reemp3 |       Min      Mean       Max
---------+------------------------------
       0 |  .0006007  .0050934  .0552681
       1 |  .0006007  .0023546  .0171253
---------+------------------------------
   Total |  .0006007   .004452  .0552681
----------------------------------------

These variables are not discernibly different in the different categories of reemp3, but the distributions are not quite identical. So Stata is trying to quantify these minuscule differences in the tails of those distributions, and further more to parse that into linear, quadratic, and cubic components. These variables probably don't belong in your model at all. If they do, at most use them linearly. But I think they probably should just be omitted. If there is a strong theoretical reason why they should be used, then I would look very carefully into why their distributions, in your data, are so close to completely independent of reemp3: something apparently is wrong with the data if this is the case.

As for the collinearities leading to omitted terms, I am unable to do a complete analysis of this because, as it happens, in your sample the combination of lorech == 0 and prepostperiod_ma == 1 is always associated with reemp3 = 0. This leads to the following warning message when I try to reproduce (a simplified version of) your regression:

note: 0.lorech#1.prepostperiod_ma != 0 predicts failure perfectly;
      0.lorech#1.prepostperiod_ma omitted and 9 obs not used.

The omission of that variable might help break some other colinearities, but the omission of those 9 observations might introduce new ones.

Nevertheless I have noted that there are strong dependencies among the variables rq, hidh, lorh, and lorech. In particular, of the 2^4 = 16 possible combinations of 0/1 values for these, only 6 actually occur in the pre-period, and only 4 in the post-period. Perhaps in your full data set some more occur. But it seems that there are some strong relationships among these variables, and that is where these colinearities are coming from. You need to reconsider what these variables are and why so many of the theoretically possible combinations never actually happen, and then revise your model so that you are looking at variables that are not so redundant as these. I'm sorry I can't be more specific than that.

[Claire McKenna]

Clyde, thanks so much for taking the time, and for all this. I'll remove the squared and cubed versions of the state labor market variables; I can't justify removing them altogether, since my outcome is individual reemployment. I'll definitely look into whether something happened with merging, or something somewhere in the data prep process (though spot-checking, the figures seems reasonable...)

As to the dependencies between the policy variables, it makes sense, as states that are strict on one measure are likely to be strict on others. An advisor suggested possibly doing a PCA analysis... I have some things to think about!