Insignificant constant in OLS regression

[Sean O'Connor]

Hi folks,

Over the last number of weeks I've been creating a custom dataset. In short, I have geocoded sports capital grants by the Irish government. I have also merged this data with small area statistics from the 2011 census in order to have an idea of the regional characteristics of where these clubs are based.

A lot has been examined in regards to the political bias of the distribution of these grants, with regions in which the finance and minister of sport are based doing particularly well. I'm adding to the literature by looking at other potential actors who can perhaps manipulate the system, namely heads of key sporting organisations within Ireland.

I utilise two dependent variables, namely the difference between the amount of money a club applied for, and the grant which they were awarded (as a per cent). The second dependent variable is the amount which a club received for a grant.

For my political bias measure I use the distance in km between the hometown of a minister/head of a sporting organisation to a club.

All my variables are in logarithmic form. I also utilised the augmented dickey fuller test finding no evidence of variables having a unit root. My ministerial variables are in line with what past studies have found also, leading me to believe that my data is sound. One of my issues is that in some cases, I reduce the sample to take into account extremely large grants awarded and also focus on particular sports, my constant is insignificant.

My P>F is significant though with it reading 0.000 in nearly all cases. I include dummies to take into account differences in sports, along with year dummies too.

I'm wondering is it acceptable to present results which have an insignificant constant and a large standard error?

Also would anyone recommend any other robustness tests to carry out, to ensure robust results.

Kind regards,

Sean

[Carlo Lazzaro]

Sean:
in general, the answer is. yes, it is.
However, more positive and helpful comments may come if you post what you typed and what Stata gave you back via CODE delimiters (the FAQ explain why and how do so). Thanks.

[Sean O'Connor]

Carlo,

Here is sample of the results,

. regress logdiff logincome logpop logpoorhealth logfin logsport logpop19 logurban logunemployed loghigerpro sport1 sport2 sport3 sport4 sport5 sport6 sport7 sport8 s
> port9 sport10 sport11 sport12 sport13 sport14 sport15 sport16 sport17 sport18 sport19 sport20 sport21 sport22 sport23 sport24 sport25 sport26 sport27 sport28 sport2
> 9 sport30 sport31 sport32 sport33 sport34 sport35 sport36 sport37 sport38 sport39 sport40 sport41 sport42 y2002 y2003 y2004 y2005 y2006 y2007 y2008 y2012 y2014 y201
> 5 cou1 cou2 cou3 cou4 cou5 cou6 cou7 cou8 cou9 cou10 cou11 cou12 cou13 cou14 cou15 cou16 cou17 cou18 cou19 cou20 cou21 cou22 cou23 cou24 cou25 cou26 cou27 cou28 cou
> 29 cou30 cou31 cou32 cou33 cou34
note: sport40 omitted because of collinearity
note: y2005 omitted because of collinearity
note: cou24 omitted because of collinearity

      Source |       SS           df       MS      Number of obs   =     7,094
-------------+----------------------------------   F(92, 7001)     =      9.73
       Model |  171.092775        92  1.85970408   Prob > F        =    0.0000
    Residual |  1338.53035     7,001  .191191309   R-squared       =    0.1133
-------------+----------------------------------   Adj R-squared   =    0.1017
       Total |  1509.62313     7,093  .212832811   Root MSE        =    .43725

-------------------------------------------------------------------------------
      logdiff |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
    logincome |   .2335903   .1773109     1.32   0.188    -.1139928    .5811734
       logpop |   .0017059   .0340232     0.05   0.960    -.0649899    .0684016
logpoorhealth |   .0005436   .0098318     0.06   0.956    -.0187296    .0198169
       logfin |    .043203   .0092826     4.65   0.000     .0250063    .0613998
     logsport |  -.0148294   .0074163    -2.00   0.046    -.0293675   -.0002912
     logpop19 |  -.0202466    .029678    -0.68   0.495    -.0784244    .0379313
     logurban |  -.0007655   .0060658    -0.13   0.900    -.0126563    .0111252
logunemployed |   .0403585   .0272819     1.48   0.139    -.0131223    .0938393
  loghigerpro |   .0100792    .023012     0.44   0.661    -.0350312    .0551896
       sport1 |  -.3751083   .2535193    -1.48   0.139     -.872083    .1218664
       sport2 |  -.3036962   .2537511    -1.20   0.231    -.8011252    .1937328
       sport3 |  -.3271582   .2536711    -1.29   0.197    -.8244303    .1701139
       sport4 |  -.3428759   .2547548    -1.35   0.178    -.8422724    .1565206
       sport5 |  -.3048707    .255053    -1.20   0.232    -.8048517    .1951104
       sport6 |  -.2757654    .255376    -1.08   0.280    -.7763798     .224849
       sport7 |  -.1546973   .2555217    -0.61   0.545    -.6555972    .3462026
       sport8 |  -.2324005   .2593193    -0.90   0.370    -.7407449     .275944
       sport9 |  -.1799072   .2549327    -0.71   0.480    -.6796524     .319838
      sport10 |  -.2395806   .2605841    -0.92   0.358    -.7504043    .2712431
      sport11 |  -.2612106   .2605542    -1.00   0.316    -.7719757    .2495544
      sport12 |  -.1764761   .2613258    -0.68   0.500    -.6887538    .3358017
      sport13 |  -.1942926   .2612304    -0.74   0.457    -.7063833    .3177981
      sport14 |  -.1995733   .2586752    -0.77   0.440     -.706655    .3075084
      sport15 |  -.1863863   .2619979    -0.71   0.477    -.6999815    .3272089
      sport16 |   -.369424   .2708058    -1.36   0.173    -.9002854    .1614375
      sport17 |  -.2379923   .2630494    -0.90   0.366    -.7536487    .2776641
      sport18 |  -.3609022   .2793352    -1.29   0.196    -.9084839    .1866794
      sport19 |  -.7622248   .2620559    -2.91   0.004    -1.275934   -.2485158
      sport20 |  -.2185605   .2583158    -0.85   0.398    -.7249378    .2878168
      sport21 |  -.2170487   .2571192    -0.84   0.399    -.7210802    .2869827
      sport22 |  -.1533494   .2736979    -0.56   0.575    -.6898802    .3831814
      sport23 |  -.4865816   .2719001    -1.79   0.074    -1.019588    .0464249
      sport24 |  -.1880634   .2726216    -0.69   0.490    -.7224843    .3463574
      sport25 |   -.248781   .2599058    -0.96   0.339     -.758275    .2607131
      sport26 |  -.2904589   .2970304    -0.98   0.328    -.8727285    .2918107
      sport27 |  -.2256332   .2554483    -0.88   0.377    -.7263893    .2751229
      sport28 |   -.362275   .2892462    -1.25   0.210    -.9292851    .2047352
      sport29 |  -.1178993    .320612    -0.37   0.713    -.7463959    .5105973
      sport30 |  -.2433861   .3029986    -0.80   0.422    -.8373552     .350583
      sport31 |  -.2897319   .2613311    -1.11   0.268      -.80202    .2225562
      sport32 |  -.1987088   .2792903    -0.71   0.477    -.7462023    .3487848
      sport33 |  -.3758679   .3211223    -1.17   0.242    -1.005365    .2536291
      sport34 |  -.2782871   .2812229    -0.99   0.322    -.8295691    .2729949
      sport35 |  -.0861838   .3353091    -0.26   0.797    -.7434913    .5711236
      sport36 |  -.1993903   .3357845    -0.59   0.553    -.8576296    .4588489
      sport37 |  -.6740176   .4006551    -1.68   0.093    -1.459423    .1113877
      sport38 |  -.5800191   .3205699    -1.81   0.070    -1.208433    .0483951
      sport39 |  -.2705459   .3206734    -0.84   0.399     -.899163    .3580712
      sport40 |          0  (omitted)
      sport41 |  -.1245987    .257741    -0.48   0.629    -.6298492    .3806517
      sport42 |  -.2036286   .2736376    -0.74   0.457    -.7400413     .332784
        y2002 |   .0770034   .0320381     2.40   0.016     .0141991    .1398077
        y2003 |   .0829499   .0321112     2.58   0.010     .0200023    .1458976
        y2004 |   .0947318   .0259948     3.64   0.000     .0437742    .1456895
        y2005 |          0  (omitted)
        y2006 |   .0625482    .024396     2.56   0.010     .0147247    .1103717
        y2007 |  -.0586731   .0235644    -2.49   0.013    -.1048664   -.0124798
        y2008 |  -.1997982   .0259991    -7.68   0.000    -.2507643   -.1488321
        y2012 |   .1445908   .0356467     4.06   0.000     .0747125    .2144691
        y2014 |    .118906   .0307544     3.87   0.000     .0586181    .1791939
        y2015 |    .110505   .0306586     3.60   0.000     .0504049    .1706051
         cou1 |   .1075559   .0684263     1.57   0.116    -.0265803    .2416921
         cou2 |   .1605351   .0676327     2.37   0.018     .0279545    .2931157
         cou3 |   .2042512   .0718852     2.84   0.005     .0633346    .3451679
         cou4 |   .1974642   .0723047     2.73   0.006      .055725    .3392034
         cou5 |   .2049819   .0745635     2.75   0.006     .0588148     .351149
         cou6 |   .0896104   .0664659     1.35   0.178     -.040683    .2199038
         cou7 |   .1281585   .0651094     1.97   0.049     .0005243    .2557927
         cou8 |   .2542966   .0633949     4.01   0.000     .1300235    .3785698
         cou9 |  -.0675319   .0694468    -0.97   0.331    -.2036686    .0686048
        cou10 |   .0617494   .0612524     1.01   0.313    -.0583238    .1818225
        cou11 |   .1175448   .0656129     1.79   0.073    -.0110764    .2461659
        cou12 |   .1771076   .0673272     2.63   0.009     .0451258    .3090894
        cou13 |   .0690826   .0644251     1.07   0.284    -.0572102    .1953754
        cou14 |   .0570711   .0598989     0.95   0.341    -.0603488     .174491
        cou15 |   .1119796   .0643817     1.74   0.082    -.0142281    .2381873
        cou16 |   .0654615   .0621251     1.05   0.292    -.0563226    .1872456
        cou17 |  -.0133968   .0643106    -0.21   0.835     -.139465    .1126713
        cou18 |   .0900145   .0581556     1.55   0.122    -.0239881    .2040171
        cou19 |  -.0400859   .0629936    -0.64   0.525    -.1635725    .0834007
        cou20 |  -.0313334   .0687061    -0.46   0.648    -.1660182    .1033515
        cou21 |   .0653036   .0632106     1.03   0.302    -.0586083    .1892154
        cou22 |  -.0302411   .0674153    -0.45   0.654    -.1623955    .1019134
        cou23 |  -.0030682   .0625044    -0.05   0.961    -.1255957    .1194593
        cou24 |          0  (omitted)
        cou25 |   .0541775   .0664285     0.82   0.415    -.0760424    .1843975
        cou26 |   .0131074   .0687803     0.19   0.849    -.1217228    .1479375
        cou27 |   .0265172   .0604567     0.44   0.661    -.0919963    .1450307
        cou28 |  -.0057899   .0712568    -0.08   0.935    -.1454748    .1338949
        cou29 |  -.0415261   .0639048    -0.65   0.516    -.1667988    .0837465
        cou30 |   .0423652   .0679218     0.62   0.533    -.0907821    .1755125
        cou31 |  -.0744962    .067117    -1.11   0.267    -.2060659    .0570735
        cou32 |   .0328482   .0679167     0.48   0.629    -.1002891    .1659856
        cou33 |   .0710231   .0726733     0.98   0.328    -.0714386    .2134847
        cou34 |   -.006543   .0691871    -0.09   0.925    -.1421706    .1290846
        _cons |    2.02601   1.842979     1.10   0.272    -1.586787    5.638807
-------------------------------------------------------------------------------

[Marcos Almeida]

I believe the constant just "tells" us the Yhat when the covariates are set to zero (or the mean, if centered). That said, the p-value for the constant "tells" us it is not significantly diferent from zero when all the covariates are set to zero. Theoretically, IMHO, the coefficient of the constant is not bound to harm a model.

[Carlo Lazzaro]

Sean:
I would take one step aside from the main issue:
- your model is so full of predictors that I would find really difficult to investigate the meaning of each one of them and even harder to disseminate the results; I would strongly welcome a more parsimoniuos model (btw, despite the tons of predictors the R-sq is quite low; provided that it may be frequent in your reearch field, it strikes a bit, though);
- you have many dummies that you have presumably created by hand. Set aside the implilicit risk of errors, you can use your precious time more efficiently simply relying upon the wonderful capabilities of -fvvarlist-, which has also a virtuous link with commands such as -margins- and -marginsplot-, both deserving taking a thorough look at.

[Sean O'Connor]

Carlo and other researchers perhaps I could get your opinions on something. I've been playing around with my data recently and I've come to a bit of an issue.

The first regression takes into account differences amongst sports and years, while the second also includes counties. I notice the inclusion of the county dummies lowers the f-value quiet a bit. However, if I was to go in line with theory I probably should include the three dummies. As there is substantial differences in years, amongst different sports and different regions.

Not only this, but when I decompose my dataset to take into account individual sports I notice stat significance evidence of lobby group bias.

However, this only occurs when I include the county dummies. Also the f-value is lower with them without them.

I'm wondering should I include them? I can reason them out with theory but they don't appear to improve the overall fit of the model greatly.

regress loggrant loghigerpro logunemployed logurban logfai logirfu loggaa logsport logfin logpop logincome logpoorhealth logpop19p  i.sportcode i.year

      Source |       SS           df       MS      Number of obs   =     7,583
-------------+----------------------------------   F(62, 7520)     =     51.99
       Model |  3633.04627        62  58.5975205   Prob > F        =    0.0000
    Residual |  8475.34904     7,520   1.1270411   R-squared       =    0.3000
-------------+----------------------------------   Adj R-squared   =    0.2943
       Total |  12108.3953     7,582  1.59699226   Root MSE        =    1.0616

-------------------------------------------------------------------------------
     loggrant |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
  loghigerpro |  -.0987982   .0493194    -2.00   0.045     -.195478   -.0021184
logunemployed |  -.2126096   .0571403    -3.72   0.000    -.3246205   -.1005987
     logurban |   .0390068   .0123137     3.17   0.002     .0148685     .063145
       logfai |   .0512335   .0212281     2.41   0.016     .0096206    .0928465
      logirfu |  -.0450759   .0178806    -2.52   0.012    -.0801269    -.010025
       loggaa |   .0307933   .0212126     1.45   0.147    -.0107893    .0723759
     logsport |   -.098738   .0174163    -5.67   0.000    -.1328788   -.0645972
       logfin |  -.0618871     .01898    -3.26   0.001    -.0990932    -.024681
       logpop |   .0685787    .018686     3.67   0.000     .0319489    .1052086
    logincome |    .756162   .1748462     4.32   0.000     .4134145    1.098909
logpoorhealth |  -.0158159   .0329365    -0.48   0.631    -.0803806    .0487488
    logpop19p |   .0806889   .0645585     1.25   0.211    -.0458637    .2072415
              |
    sportcode |
           2  |  -.1298185     .03766    -3.45   0.001    -.2036426   -.0559944
           3  |  -.1751473   .0367436    -4.77   0.000     -.247175   -.1031197
           4  |   .0718141   .0654227     1.10   0.272    -.0564327     .200061
           5  |  -.6381395    .072909    -8.75   0.000    -.7810614   -.4952175
           6  |   -1.03961   .0753876   -13.79   0.000    -1.187391   -.8918295
           7  |  -.8888204   .0820435   -10.83   0.000    -1.049649   -.7279923
           8  |  -1.177836   .1342817    -8.77   0.000    -1.441066   -.9146066
           9  |  -1.974569   .0708176   -27.88   0.000    -2.113392   -1.835747
          10  |   -1.42275   .1456314    -9.77   0.000    -1.708229   -1.137272
          11  |  -1.351686   .1414087    -9.56   0.000    -1.628887   -1.074486
          12  |  -1.600075   .1537277   -10.41   0.000    -1.901425   -1.298726
          13  |  -1.041823   .1538115    -6.77   0.000    -1.343337     -.74031
          14  |  -2.498457   .1235386   -20.22   0.000    -2.740627   -2.256286
          15  |  -1.875008   .1587789   -11.81   0.000    -2.186259   -1.563757
          16  |  -.5415392   .2331021    -2.32   0.020    -.9984844    -.084594
          17  |  -1.897852   .1703317   -11.14   0.000     -2.23175   -1.563955
          18  |  -1.392869    .285732    -4.87   0.000    -1.952984   -.8327544
          19  |   -.035337   .1555039    -0.23   0.820    -.3401681    .2694941
          20  |  -1.514224   .1226583   -12.35   0.000    -1.754669    -1.27378
          21  |   -1.28315   .1057248   -12.14   0.000      -1.4904     -1.0759
          22  |  -1.274398   .2516227    -5.06   0.000    -1.767649   -.7811476
          23  |  -2.069863   .2336495    -8.86   0.000    -2.527882   -1.611845
          24  |  -1.358663   .2329792    -5.83   0.000    -1.815368    -.901959
          25  |  -.4257372    .135568    -3.14   0.002    -.6914884   -.1599861
          26  |  -1.523942   .3762479    -4.05   0.000    -2.261493   -.7863907
          27  |  -1.093699   .0798383   -13.70   0.000    -1.250204   -.9371933
          28  |  -2.295149   .3379156    -6.79   0.000    -2.957558    -1.63274
          29  |  -2.053676   .4767216    -4.31   0.000    -2.988184   -1.119169
          30  |  -.8778456   .3768132    -2.33   0.020    -1.616505   -.1391865
          31  |  -1.143671   .1566912    -7.30   0.000    -1.450829   -.8365125
          33  |  -1.344077    .284875    -4.72   0.000    -1.902512   -.7856427
          34  |  -1.692757   .4775486    -3.54   0.000    -2.628886   -.7566286
          35  |  -1.576368   .2516712    -6.26   0.000    -2.069714   -1.083022
          36  |  -1.921748   .5331485    -3.60   0.000    -2.966868   -.8766279
          37  |  -2.066121   .5332202    -3.87   0.000    -3.111382    -1.02086
          38  |  -1.905228    .753015    -2.53   0.011    -3.381348   -.4291085
          39  |   .0964159   .4766241     0.20   0.840    -.8379006    1.030732
          40  |  -1.032804   .4760711    -2.17   0.030    -1.966036   -.0995716
          42  |  -.7095284   .6138363    -1.16   0.248    -1.912819    .4937623
          43  |  -1.563416   .1140864   -13.70   0.000    -1.787058   -1.339775
          44  |  -2.786147   .2389724   -11.66   0.000      -3.2546   -2.317694
              |
         year |
        2003  |  -.0602795   .0570716    -1.06   0.291    -.1721557    .0515967
        2004  |  -.1141819   .0559517    -2.04   0.041     -.223863   -.0045009
        2005  |   -.016431   .0607036    -0.27   0.787     -.135427     .102565
        2006  |   .0153062   .0575133     0.27   0.790     -.097436    .1280483
        2007  |  -.0510352   .0559599    -0.91   0.362    -.1607323    .0586619
        2008  |  -.3981978   .0609832    -6.53   0.000    -.5177419   -.2786538
        2012  |  -.3831891   .0577516    -6.64   0.000    -.4963983   -.2699798
        2014  |   -.482317   .0538192    -8.96   0.000    -.5878177   -.3768163
        2015  |  -.4767951   .0526757    -9.05   0.000    -.5800543    -.373536
              |
        _cons |   2.754542   1.824743     1.51   0.131    -.8224647    6.331548
-------------------------------------------------------------------------------

regress loggrant loghigerpro logunemployed logurban logfai logirfu loggaa logsport logfin logpop logincome logpoorhealth logpop19p i.year i.sportcode i.county

      Source |       SS           df       MS      Number of obs   =     7,583
-------------+----------------------------------   F(95, 7487)     =     35.93
       Model |  3791.68682        95  39.9124928   Prob > F        =    0.0000
    Residual |  8316.70849     7,487  1.11081989   R-squared       =    0.3131
-------------+----------------------------------   Adj R-squared   =    0.3044
       Total |  12108.3953     7,582  1.59699226   Root MSE        =     1.054

-------------------------------------------------------------------------------
     loggrant |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
  loghigerpro |  -.0489985   .0523996    -0.94   0.350    -.1517164    .0537193
logunemployed |  -.1090394   .0622674    -1.75   0.080     -.231101    .0130222
     logurban |  -.0132887   .0145811    -0.91   0.362    -.0418717    .0152943
       logfai |   .0604491   .0373234     1.62   0.105    -.0127152    .1336134
      logirfu |  -.0540334   .0480774    -1.12   0.261    -.1482786    .0402118
       loggaa |  -.0332126   .0231291    -1.44   0.151    -.0785522     .012127
     logsport |  -.0818258   .0184433    -4.44   0.000    -.1179798   -.0456718
       logfin |  -.1337954   .0224056    -5.97   0.000    -.1777166   -.0898742
       logpop |   .1072683   .0209504     5.12   0.000     .0661995     .148337
    logincome |  -.2298102   .4080065    -0.56   0.573    -1.029617    .5699971
logpoorhealth |  -.0036305   .0342179    -0.11   0.916    -.0707072    .0634462
    logpop19p |   .0983099    .070649     1.39   0.164     -.040182    .2368018
              |
         year |
        2003  |  -.0418567   .0569132    -0.74   0.462    -.1534225    .0697091
        2004  |  -.0324271   .0620569    -0.52   0.601     -.154076    .0892218
        2005  |   .1151039   .0743678     1.55   0.122    -.0306778    .2608857
        2006  |   .1140223   .0714007     1.60   0.110    -.0259432    .2539877
        2007  |   .0546304   .0711782     0.77   0.443    -.0848989    .1941597
        2008  |  -.2881585   .0741694    -3.89   0.000    -.4335513   -.1427657
        2012  |   -.389526   .0582052    -6.69   0.000    -.5036245   -.2754274
        2014  |  -.4494087   .0539482    -8.33   0.000    -.5551624    -.343655
        2015  |  -.4336512   .0528971    -8.20   0.000    -.5373443   -.3299581
              |
    sportcode |
           2  |   -.169239   .0379053    -4.46   0.000    -.2435439    -.094934
           3  |  -.1906378   .0369197    -5.16   0.000    -.2630108   -.1182649
           4  |      .0467   .0652932     0.72   0.474     -.081293     .174693
           5  |  -.6444995   .0727039    -8.86   0.000    -.7870195   -.5019795
           6  |  -1.049163   .0758606   -13.83   0.000    -1.197871   -.9004549
           7  |  -.9013549    .082002   -10.99   0.000    -1.062102   -.7406079
           8  |  -1.177664   .1335729    -8.82   0.000    -1.439504   -.9158231
           9  |  -1.988395   .0705994   -28.16   0.000     -2.12679   -1.850001
          10  |  -1.474179   .1453434   -10.14   0.000    -1.759093   -1.189265
          11  |   -1.38631   .1409164    -9.84   0.000    -1.662546   -1.110075
          12  |  -1.596462   .1530341   -10.43   0.000    -1.896451   -1.296472
          13  |  -1.054114   .1532257    -6.88   0.000    -1.354479   -.7537481
          14  |  -2.531282   .1234557   -20.50   0.000     -2.77329   -2.289274
          15  |  -1.894226    .158019   -11.99   0.000    -2.203988   -1.584465
          16  |  -.4717261   .2319465    -2.03   0.042    -.9264065   -.0170457
          17  |  -1.926445   .1695962   -11.36   0.000    -2.258901   -1.593989
          18  |  -1.386934   .2840673    -4.88   0.000    -1.943786   -.8300825
          19  |  -.0786224   .1551054    -0.51   0.612    -.3826726    .2254277
          20  |  -1.542844   .1224877   -12.60   0.000    -1.782955   -1.302734
          21  |  -1.267133   .1059974   -11.95   0.000    -1.474918   -1.059348
          22  |  -1.245714   .2503206    -4.98   0.000    -1.736412   -.7550153
          23  |  -2.094335   .2323287    -9.01   0.000    -2.549764   -1.638906
          24  |  -1.367633   .2317864    -5.90   0.000    -1.821999    -.913266
          25  |  -.4222761   .1350833    -3.13   0.002    -.6870773   -.1574749
          26  |  -1.391187   .3745434    -3.71   0.000    -2.125397   -.6569763
          27  |  -1.075647   .0798408   -13.47   0.000    -1.232157   -.9191366
          28  |  -2.363229   .3368247    -7.02   0.000      -3.0235   -1.702958
          29  |   -2.07293   .4743385    -4.37   0.000    -3.002767   -1.143094
          30  |  -.9424945   .3747032    -2.52   0.012    -1.677018    -.207971
          31  |  -1.207879   .1563894    -7.72   0.000    -1.514447   -.9013122
          33  |  -1.409991   .2836258    -4.97   0.000    -1.965977   -.8540047
          34  |   -1.79131   .4753001    -3.77   0.000    -2.723032   -.8595887
          35  |  -1.521952   .2512427    -6.06   0.000    -2.014458   -1.029446
          36  |  -1.961444   .5302006    -3.70   0.000    -3.000786   -.9221022
          37  |  -1.990399   .5320878    -3.74   0.000    -3.033441   -.9473577
          38  |  -1.832694    .748265    -2.45   0.014    -3.299504   -.3658844
          39  |   .2147184   .4765325     0.45   0.652    -.7194193    1.148856
          40  |  -1.077735   .4735988    -2.28   0.023    -2.006122   -.1493482
          42  |  -.6149759   .6110236    -1.01   0.314    -1.812754     .582802
          43  |  -1.563249   .1140136   -13.71   0.000    -1.786748    -1.33975
          44  |  -2.793633   .2378974   -11.74   0.000    -3.259978   -2.327287
              |
       county |
           2  |   .6360787   .2052065     3.10   0.002     .2338163    1.038341
           3  |   .5975108   .1974272     3.03   0.002      .210498    .9845236
           4  |   .4917607   .1809716     2.72   0.007     .1370056    .8465158
           5  |   .5112731   .2018006     2.53   0.011     .1156872     .906859
           6  |   .2892545   .1449712     2.00   0.046     .0050703    .5734388
           7  |   .0712982   .1204469     0.59   0.554    -.1648115    .3074079
           8  |  -.2873423   .1188832    -2.42   0.016    -.5203868   -.0542978
           9  |  -.1108365    .134687    -0.82   0.411    -.3748609    .1531878
          10  |   .1365111   .1242575     1.10   0.272    -.1070686    .3800908
          11  |   .2855251   .1399108     2.04   0.041     .0112607    .5597895
          12  |  -.1887262   .1209871    -1.56   0.119    -.4258948    .0484425
          13  |   .2112139   .1225024     1.72   0.085    -.0289252     .451353
          14  |   .2367532   .1121629     2.11   0.035     .0168824    .4566239
          15  |   .2149528   .1368756     1.57   0.116    -.0533618    .4832674
          16  |   .2182693   .1253407     1.74   0.082    -.0274337    .4639723
          17  |   .8316241   .1520652     5.47   0.000     .5335335    1.129715
          18  |   .2956575   .1287722     2.30   0.022     .0432279    .5480871
          19  |   .1097823   .1267504     0.87   0.386    -.1386841    .3582487
          20  |    .616297   .1609086     3.83   0.000     .3008708    .9317231
          21  |   .2211162   .1369177     1.61   0.106     -.047281    .4895134
          22  |   .2849739   .1380418     2.06   0.039     .0143732    .5555747
          23  |   .3085458   .1480367     2.08   0.037     .0183522    .5987394
          24  |    .659901   .1534404     4.30   0.000     .3591147    .9606873
          25  |   .3441669   .1392843     2.47   0.013     .0711305    .6172032
          26  |   .5742841   .1560863     3.68   0.000     .2683112     .880257
          27  |   .2556778   .1197229     2.14   0.033     .0209874    .4903683
          28  |   .0584679   .1421929     0.41   0.681    -.2202702     .337206
          29  |   .1977397   .1265268     1.56   0.118    -.0502884    .4457678
          30  |   .0862083   .1300676     0.66   0.507    -.1687608    .3411774
          31  |   .2540976   .1394228     1.82   0.068    -.0192101    .5274054
          32  |   .2681752   .1282007     2.09   0.036     .0168657    .5194846
          33  |   .2440777   .1420397     1.72   0.086    -.0343599    .5225153
          34  |   .0893366   .1329609     0.67   0.502    -.1713041    .3499773
              |
        _cons |   13.35235   4.121811     3.24   0.001      5.27244    21.43225
-------------------------------------------------------------------------------

[Nick Cox]

I support everything Carlo says on the intercept. In fact I would go further.

Sometimes with variations on y = b_0 + b_1 x there are grounds for thinking that the limiting behaviour justifies forcing the model through the origin. In the simplest case there might be physical or other laws implying proportionality y = b x.

When log y = b_0 + b_1 log x_1 + other stuff and so forth the equivalent grounds for forcing would be that log y = 0 when all predictors are 0 and so that y = 1 when all the other antilogged predictors are 1 and all the indicators are 0.. I suspect that to be a condition which is no sense privileged; in fact I would be amazed if it had any substantive or special interpretation for you, particularly as in many cases the units of measurement are arbitrary (e.g whether you measure urban as percent or per thousand; if that example is guessed wrongly there will be others).

In short, leave the intercept alone. It does no harm and indeed omitting it will complicate interpretation.

On the model as whole I have to express a prejudice that it is over-complicated, but then I have not grappled with the data and am not familiar with the context. I would use Poisson regression here, not regression with a logged response. See Bill Gould's instant classic blog post on this.

[Sean O'Connor]

Thank you for the reply Nick!

[Carlo Lazzaro]

Sean:
as usual, Nick gave precious advice.
From my side, I would not question the way you tackle the data analysis substantively, but I still express a strong concern about the number of predictors included in both of your regression models.
Isn't a feasible way to keep things simple even though not simpler?