Splitting data in regression analysis

[Dan Richard]

Hi,

I am new to Satalist so I apologise for any errors in my post.
I am currently running a regression model on unemployment (independent) and crime (dependent), using a panel-data approach of 50 U.S states between 2000-2015 with a multitude of control variables. I have used the xtreg command and it is a Fixed effects (FE) model.

I have ran my model i.e. 2000-2015 but now want to split my data into pre-recession (2000-2007) and post-recsession (2008-2013) periods. I am unsure weather this is econometrically correct? I have read the use of time-specific dummy variables may be useful however I wanted to understand if 'splitting the data' is acceptable to draw conclusions on?

Any help on this would greatly appreciated.
Thanks

[Carlo Lazzaro]

Dan:
welcome to the list.
Plugging among predictors a categorical variable (before/after crisis) sounds to me as a wiser approach.
Please see -help fvvarlist- for categorical variables (and interactions) creation.

[Dan Richard]

Hi Carlo,

Is the best way to do this to use the i.Year command on Stata? My concern is that this will only give me a coefficient on the unemployment variable for the overall time period (2000-2015) and not a coefficient for unemployment each individual time period (i.e. pre and post recession time periods?).

Thanks,
Dan

[Carlo Lazzaro]

Dan:
not quite.
With -i.year- you would estimate time fixed effects.
I meant something along the following lines:

g recession=0 if year<=2007
replace recession=1 if year>2007
label define recession 0 "Before recession" 1 "After recession"
label val recession recession

[Dan Richard]

Hi Carlo,

The image above is the output generated by Stata.

Could you advise me on how to interpret these results? (Concerning Unemployment and recession only)
As I explained before however, I wanted to obtain a coefficient on unemployment for each time period so I could see how the coefficient changes in magnitude or direction between periods, however these results only give me one coefficient? I am probably interpreting the results incorrectly so any guidance on this would be helpful?

[Carlo Lazzaro]

Dan:
for the future please post what you typed (that is missing in your present post) and what Stata gave you back (as you did) via CODE delimiters, not screnshot (see the FAQ on these topics). Thanks.
As far as you query is concerned:
- moving from before recession to after recession, reduces the -depvar- by 189.9299;
- each 1-unit increase in unemployment increases the -depvar- by 0.196296;
- I'm not clear with your research goal of obtaining a coefficient for unemployment for each time period.
Do you mea interacting -year- with -unemployment-?
I cannot say whether your model (and the fixed effect machinery) will allow you to do so, anyway, you can try plugging in, among your predictors, the following interaction:

c.unemployment##i.year

I'm editing this post tomake myself clearer with a toy-example:

. use "http://www.stata-press.com/data/r14/nlswork.dta", clear
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage c.tenure##i.year, fe

Fixed-effects (within) regression               Number of obs     =     28,101
Group variable: idcode                          Number of groups  =      4,699

R-sq:                                           Obs per group:
     within  = 0.1392                                         min =          1
     between = 0.1943                                         avg =        6.0
     overall = 0.1538                                         max =         15

                                                F(29,23373)       =     130.34
corr(u_i, Xb)  = 0.1394                         Prob > F          =     0.0000

-------------------------------------------------------------------------------
      ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
       tenure |   .0460022   .0099618     4.62   0.000     .0264764     .065528
              |
         year |
          69  |   .0767027   .0164924     4.65   0.000     .0443764    .1090289
          70  |   .0171287   .0157895     1.08   0.278    -.0138198    .0480772
          71  |    .066154   .0153825     4.30   0.000     .0360034    .0963047
          72  |   .0666567   .0159018     4.19   0.000     .0354882    .0978253
          73  |   .0735309   .0151855     4.84   0.000     .0437662    .1032956
          75  |   .1023057   .0149763     6.83   0.000     .0729512    .1316602
          77  |   .1508128    .014786    10.20   0.000     .1218312    .1797944
          78  |   .1902381   .0155584    12.23   0.000     .1597427    .2207335
          80  |   .2171641   .0152967    14.20   0.000     .1871815    .2471466
          82  |   .2059075   .0150451    13.69   0.000     .1764181    .2353969
          83  |   .2302122    .015574    14.78   0.000     .1996861    .2607383
          85  |   .2760856   .0152147    18.15   0.000     .2462638    .3059074
          87  |   .2740928   .0150693    18.19   0.000     .2445561    .3036296
          88  |   .3541284    .015308    23.13   0.000     .3241237    .3841331
              |
year#c.tenure |
          69  |   -.001617   .0131544    -0.12   0.902    -.0274004    .0241664
          70  |   .0164736    .011756     1.40   0.161    -.0065688    .0395161
          71  |   .0059405   .0110512     0.54   0.591    -.0157206    .0276016
          72  |   .0061243   .0109935     0.56   0.577    -.0154238    .0276723
          73  |    .002744   .0106346     0.26   0.796    -.0181005    .0235884
          75  |  -.0117935   .0104658    -1.13   0.260    -.0323071    .0087201
          77  |  -.0146246     .01026    -1.43   0.154    -.0347348    .0054856
          78  |   -.020725   .0102293    -2.03   0.043    -.0407752   -.0006749
          80  |  -.0269004   .0101589    -2.65   0.008    -.0468125   -.0069883
          82  |  -.0230145   .0101088    -2.28   0.023    -.0428284   -.0032007
          83  |  -.0259333    .010093    -2.57   0.010    -.0457163   -.0061503
          85  |   -.026761   .0100576    -2.66   0.008    -.0464745   -.0070475
          87  |  -.0251743   .0100392    -2.51   0.012    -.0448518   -.0054969
          88  |   -.031173   .0100295    -3.11   0.002    -.0508316   -.0115144
              |
        _cons |   1.431128   .0108593   131.79   0.000     1.409843    1.452412
--------------+----------------------------------------------------------------
      sigma_u |  .38945547
      sigma_e |  .29661148
          rho |  .63289411   (fraction of variance due to u_i)
-------------------------------------------------------------------------------
F test that all u_i=0: F(4698, 23373) = 8.03                 Prob > F = 0.0000

[Dan Richard]

Hi Carlo,

Sorry I was unaware of how to do that, I hope this is ok.

. xtreg  TotalCrime Unemployment Income HighSchool Migrants Poverty Police Youth TOTCG recession c.Unemployment##i.Year, fe
note: Unemployment omitted because of collinearity
note: 2015.Year omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =       743
Group variable: State1                          Number of groups   =        50

R-sq:  within  = 0.7470                         Obs per group: min =        13
       between = 0.0056                                        avg =      14.9
       overall = 0.0494                                        max =        15

                                                F(36,657)          =     53.89
corr(u_i, Xb)  = -0.4639                        Prob > F           =    0.0000

-------------------------------------------------------------------------------------
         TotalCrime |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
       Unemployment |   .0966797   .0918944     1.05   0.293    -.0837624    .2771218
             Income |   .0112565   .0089662     1.26   0.210    -.0063494    .0288625
         HighSchool |   .0067321   .0079051     0.85   0.395    -.0087903    .0222544
           Migrants |   .0780313   .0277428     2.81   0.005     .0235561    .1325066
            Poverty |   48.71014   9.849692     4.95   0.000     29.36947    68.05081
             Police |  -.2984332   .2804785    -1.06   0.288    -.8491755    .2523091
              Youth |   .1074687   .0366193     2.93   0.003     .0355636    .1793737
              TOTCG |  -.0658798   .0112357    -5.86   0.000     -.087942   -.0438176
          recession |  -298.3668   343.0545    -0.87   0.385    -971.9821    375.2485
       Unemployment |          0  (omitted)
                    |
               Year |
              2002  |  -368.1669   292.7322    -1.26   0.209    -942.9705    206.6366
              2003  |  -379.4704   300.2437    -1.26   0.207    -969.0233    210.0825
              2004  |  -197.7837   299.8283    -0.66   0.510    -786.5209    390.9536
              2005  |  -91.08073   301.3621    -0.30   0.763    -682.8298    500.6683
              2006  |  -398.8091   288.7708    -1.38   0.168     -965.834    168.2158
              2007  |  -336.0185   289.8194    -1.16   0.247    -905.1023    233.0654
              2008  |  -199.2803   277.5728    -0.72   0.473    -744.3171    345.7564
              2009  |   35.19003   274.7342     0.13   0.898    -504.2729     574.653
              2010  |   31.16998   270.2913     0.12   0.908    -499.5689    561.9089
              2011  |   6.831486   265.5592     0.03   0.979    -514.6156    528.2786
              2012  |  -121.5598   263.7558    -0.46   0.645    -639.4657    396.3462
              2013  |  -71.93492    266.255    -0.27   0.787    -594.7483    450.8785
              2014  |   -191.881     274.26    -0.70   0.484    -730.4129    346.6509
              2015  |          0  (omitted)
                    |
Year#c.Unemployment |
              2002  |   .1028646   .1140267     0.90   0.367    -.1210361    .3267652
              2003  |   .1132165    .112505     1.01   0.315    -.1076962    .3341293
              2004  |    .057738   .1159682     0.50   0.619     -.169975    .2854509
              2005  |  -.0074513   .1185145    -0.06   0.950    -.2401641    .2252615
              2006  |   .0321847   .1163639     0.28   0.782    -.1963053    .2606747
              2007  |  -.0402392    .115915    -0.35   0.729    -.2678478    .1873694
              2008  |  -.0230607   .1059873    -0.22   0.828    -.2311755     .185054
              2009  |  -.1366447   .0959978    -1.42   0.155    -.3251441    .0518547
              2010  |  -.1425046   .0959586    -1.49   0.138    -.3309271    .0459179
              2011  |  -.1483504   .0973943    -1.52   0.128     -.339592    .0428912
              2012  |  -.1389991   .0992809    -1.40   0.162    -.3339452    .0559471
              2013  |  -.1901316   .1020541    -1.86   0.063    -.3905231      .01026
              2014  |  -.2235618   .1099225    -2.03   0.042    -.4394036     -.00772
              2015  |  -.3637617   .1231523    -2.95   0.003    -.6055813    -.121942
                    |
              _cons |   -2921.93   1120.728    -2.61   0.009    -5122.569   -721.2899
--------------------+----------------------------------------------------------------
            sigma_u |  954.30321
            sigma_e |   245.4577
                rho |  .93794753   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
F test that all u_i=0:     F(49, 657) =    87.82             Prob > F = 0.0000

The aim of my study was to see if the coefficient on Unemployment changes between pre and post recession as literature suggests the crime-unemployment relationship is positive in pre-recession/economically good periods and negative in post-recession/economically bad periods, hence, I desired a coefficient for each period.

When I split the data into pre and post recession periods I obtained a positive coefficient in the pre-recession period and a negative coefficient in the post-recession period. With the exception of years 2005 and 2007, these results are similar to splitting the data into two periods and running two separate regressions.

In your opinion, would this be a more appropriate way of analysing the data?


Thanks,
Dan

[Clyde Schechter]

I think that for your goal of determining of the coefficient of unemployment is different in the pre and post recession years you need to do this:

gen byte recession = (year > 2007) if !missing(year)
xtreg TotalCrime i.recession##c.Unemployment other variables Ilike i.year Income etc., fe
margins recession, dydx(Unemployment)

If you want to run a hypothesis test that the coefficient changed after the onset of the recession, the statistics in the 1.recession#c.Unemployment row of the -xtreg- output will give you that. To see the actual pre- and post-recession coefficients themselves, look at the -margins- output.

[Carlo Lazzaro]

Dan:
thanks for providing further calrifications about your research goal (and using CODE delimiters appropriately).
However, if you're interested in investigating whether unemployment (rate?) changes between pre and post recession period, there's probably a better interaction to test, that would change your original regression code a bit:

xtreg  TotalCrime c.Unemployment##i.recession  Income HighSchool Migrants Poverty Police Youth TOTCG i.Year, fe

PS: I realized only now that my post crossed in the cyberspace with Clydes'reply.

[Dan Richard]

Carlo - Thank you for your continued input, my aim is not to see how unemployment changed between periods it is how crime changes between periods dependant on unemployment levels (per 100,000). I think your previous code was more appropriate for this analysis and I may use the interaction term you suggested.

Thanks for the input Clyde, I also did as you suggested and obtained the following results

. xtreg TotalCrime i.recession##c.Unemployment i.Year Income HighSchool Migrants Poverty Police Youth TOTCG DeathPen, fe
note: 1.recession omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =       743
Group variable: State1                          Number of groups   =        50

R-sq:  within  = 0.7418                         Obs per group: min =        13
       between = 0.0023                                        avg =      14.9
       overall = 0.0537                                        max =        15

                                                F(24,669)          =     80.08
corr(u_i, Xb)  = -0.4709                        Prob > F           =    0.0000

------------------------------------------------------------------------------------------
              TotalCrime |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------------------+----------------------------------------------------------------
             1.recession |          0  (omitted)
            Unemployment |   .1406037   .0417833     3.37   0.001     .0585614    .2226459
                         |
recession#c.Unemployment |
                      1  |  -.1751107   .0388409    -4.51   0.000    -.2513755   -.0988459
                         |
                    Year |
                   2002  |  -104.8444    55.6655    -1.88   0.060    -214.1445    4.455723
                   2003  |  -110.6037   94.27026    -1.17   0.241    -295.7049    74.49753
                   2004  |  -96.53367   95.05399    -1.02   0.310    -283.1737    90.10639
                   2005  |   -166.519   102.6882    -1.62   0.105    -368.1491    35.11104
                   2006  |  -369.4891   101.5318    -3.64   0.000    -568.8484   -170.1298
                   2007  |  -474.5525   109.5162    -4.33   0.000    -689.5893   -259.5157
                   2008  |  -151.2357   153.4505    -0.99   0.325    -452.5382    150.0669
                   2009  |  -241.7451   172.9573    -1.40   0.163    -581.3496    97.85951
                   2010  |  -268.0589   176.6529    -1.52   0.130    -614.9198    78.80192
                   2011  |  -315.7569   178.4954    -1.77   0.077    -666.2354    34.72171
                   2012  |  -408.3058    180.022    -2.27   0.024    -761.7819    -54.8297
                   2013  |  -521.3037    179.461    -2.90   0.004    -873.6782   -168.9292
                   2014  |  -710.9725   184.2288    -3.86   0.000    -1072.709   -349.2363
                   2015  |  -828.9256    188.795    -4.39   0.000    -1199.628   -458.2236
                         |
                  Income |   .0161796   .0090791     1.78   0.075    -.0016474    .0340065
              HighSchool |   .0040221    .007797     0.52   0.606    -.0112875    .0193317
                Migrants |   .0777707   .0277966     2.80   0.005     .0231916    .1323498
                 Poverty |   49.03345   9.599759     5.11   0.000     30.18417    67.88274
                  Police |  -.2108817   .2782808    -0.76   0.449    -.7572905    .3355272
                   Youth |     .09153   .0358617     2.55   0.011      .021115    .1619451
                   TOTCG |  -.0712152   .0110616    -6.44   0.000    -.0929348   -.0494956
                DeathPen |   76.65132   54.11071     1.42   0.157    -29.59594    182.8986
                   _cons |  -2966.944   1110.604    -2.67   0.008    -5147.633   -786.2544
-------------------------+----------------------------------------------------------------
                 sigma_u |  955.20221
                 sigma_e |  245.74479
                     rho |  .93792106   (fraction of variance due to u_i)
------------------------------------------------------------------------------------------
F test that all u_i=0:     F(49, 669) =    84.24             Prob > F = 0.0000

I am unsure how to interpret these results? Could offer me any advice?
As I say I am looking to analyse how unemployment has caused changes in crime levels between pre and post crisis periods incase it needed clarifying.

Thanks

[Clyde Schechter]

Dan, I described how to interpret these results in #10:

If you want to run a hypothesis test that the coefficient changed after the onset of the recession, the statistics in the 1.recession#c.Unemployment row of the -xtreg- output will give you that. To see the actual pre- and post-recession coefficients themselves, look at the -margins- output.

You need to run the -margins- command shown there as well.

[Carlo Lazzaro]

Dan:
I do share Clyde's remark about -margins (and, I would add, -marginsplot-).
That said, in a hypothethical pre-margins- era, referring to the same panel (as you’re estimating within panel variance as years go by) and when adjusted for the remaining predictors, I would comment on -unemployment- as follows:

• in the pre-recession era, a 1-unit increase in unemployment rate increases the criminality rate by .1406037;
• in the post-recession, era a 1-unit increase in unemployment rate reduces the criminality rate by (.1406037-.1751107)=-0.034507.