CHAPTER 13 - Pooling Cross Sections across Time: Simple Panel Data Methods#

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import stata_setup
stata_setup.config("C:/Program Files/Stata18/", "se" ,splash=False)

Example 13.1 Women’s Fertility over Time#

%%stata
u fertil1, clear
reg kids educ age agesq black-y84
test y74 y76 y78 y80 y82 y84

predict u, res
g u2 = u^2
qui reg u2 educ age agesq black-y84
display e(N) * e(r2)
. u fertil1, clear

. reg kids educ age agesq black-y84
      Source |       SS           df       MS      Number of obs   =     1,129
-------------+----------------------------------   F(17, 1111)     =      9.72
       Model |  399.610888        17  23.5065228   Prob > F        =    0.0000
    Residual |  2685.89841     1,111  2.41755033   R-squared       =    0.1295
-------------+----------------------------------   Adj R-squared   =    0.1162
       Total |   3085.5093     1,128  2.73538059   Root MSE        =    1.5548
------------------------------------------------------------------------------
        kids | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        educ |
  -.1284268   .0183486    -7.00   0.000    -.1644286    -.092425
         age |   .5321346   .1383863     3.85   0.000     .2606065    .8036626
       agesq |   -.005804   .0015643    -3.71   0.000    -.0088733   -.0027347
       black |   1.075658   .1735356     6.20   0.000     .7351631    1.416152
        east |    .217324   .1327878     1.64   0.102    -.0432192    .4778672
    northcen |    .363114   .1208969     3.00   0.003      .125902    .6003261
        west |   .1976032   .1669134     1.18   0.237    -.1298978    .5251041
        farm |  -.0525575     .14719    -0.36   0.721    -.3413592    .2362443
    othrural |
  -.1628537    .175442    -0.93   0.353    -.5070887    .1813814
        town |   .0843532    .124531     0.68   0.498    -.1599893    .3286957
      smcity |   .2118791    .160296     1.32   0.187    -.1026379    .5263961
         y74 |   .2681825    .172716     1.55   0.121    -.0707039    .6070689
         y76 |  -.0973795   .1790456    -0.54   0.587     -.448685    .2539261
         y78 |  -.0686665   .1816837    -0.38   0.706    -.4251483    .2878154
         y80 |  -.0713053   .1827707    -0.39   0.697      -.42992    .2873093
         y82 |  -.5224842   .1724361    -3.03   0.003    -.8608214    -.184147
         y84 |  -.5451661   .1745162    -3.12   0.002    -.8875846   -.2027477
       _cons |  -7.742457   3.051767    -2.54   0.011    -13.73033   -1.754579
------------------------------------------------------------------------------
. test y74 y76 y78 y80 y82 y84
 ( 1)  y74 = 0
 ( 2)  y76 = 0
 ( 3)  y78 = 0
 ( 4)  y80 = 0
 ( 5)  y82 = 0
 ( 6)  y84 = 0

       F(  6,  1111) =    5.87
            Prob > F =    0.0000

. 
. predict u, res

. g u2 = u^2

. qui reg u2 educ age agesq black-y84
. display e(N) * e(r2)
55.315374

. 

Example 13.2 Changes in the Return to Education and the Gender Wage Gap#

%%stata
u cps78_85, clear
reg lwage y85 educ y85educ exper expersq union female y85fem
display "Return to Education in 1978 is " _b[educ]*100 "%"
display "Return to Education in 1985 is " (_b[educ] + _b[y85educ])*100 "%"
. u cps78_85, clear

. reg lwage y85 educ y85educ exper expersq union female y85fem

      Source |       SS           df       MS      Number of obs   =     1,084
-------------+----------------------------------   F(8, 1075)      =     99.80
       Model |  135.992074         8  16.9990092   Prob > F        =    0.0000
    Residual |  183.099094     1,075  .170324738   R-squared       =    0.4262
-------------+----------------------------------   Adj R-squared   =    0.4219
       Total |  319.091167     1,083   .29463635   Root MSE        =     .4127
------------------------------------------------------------------------------
       lwage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         y85 |   .1178062   .1237817     0.95   0.341     -.125075    .3606874
        educ |   .0747209   .0066764    11.19   0.000     .0616206    .0878212
     y85educ |   .0184605   .0093542     1.97   0.049      .000106     .036815
       exper |   .0295843   .0035673     8.29   0.000     .0225846     .036584
     expersq |  -.0003994   .0000775    -5.15   0.000    -.0005516   -.0002473
       union |   .2021319   .0302945     6.67   0.000     .1426888    .2615749
      female |  -.3167086   .0366215    -8.65   0.000    -.3885663    -.244851
      y85fem |    .085052    .051309     1.66   0.098    -.0156251     .185729
       _cons |   .4589329   .0934485     4.91   0.000     .2755707     .642295
------------------------------------------------------------------------------

. display "Return to Education in 1978 is " _b[educ]*100 "%"
Return to Education in 1978 is 7.4720913%

. display "Return to Education in 1985 is " (_b[educ] + _b[y85educ])*100 "%"
Return to Education in 1985 is 9.3181445%

. 

Example 13.3 Effect of a Garbage Incinerator’s Location on Housing Prices#

%%stata
u KIELMC, clear
reg rprice nearinc if year==1981
reg rprice nearinc if year==1978
eststo One: reg rprice y81 nearinc y81nrinc 
eststo Two: qui reg rprice y81 nearinc y81nrinc age agesq
eststo Three: qui reg rprice y81 nearinc y81nrinc age agesq intst land area rooms baths 
estout, cells(b(nostar fmt(2)) se(par fmt(2))) stats(r2 r2_a N, fmt(%9.3f %9.3f %9.0g) labels(R-squared Adj-R-squared Observations)) varlabels(_cons constant) varwidth(20) ti("Table 13.2 Effects of Incinerator Location on Housing Prices (rprice)")
est clear
reg lprice y81 nearinc y81nrinc 
reg lprice y81 nearinc y81nrinc age agesq lintst lland larea rooms baths 
. u KIELMC, clear

. reg rprice nearinc if year==1981

      Source |       SS           df       MS      Number of obs   =       142
-------------+----------------------------------   F(1, 140)       =     27.73
       Model |  2.7059e+10         1  2.7059e+10   Prob > F        =    0.0000
    Residual |  1.3661e+11       140   975815048   R-squared       =    0.1653
-------------+----------------------------------   Adj R-squared   =    0.1594
       Total |  1.6367e+11       141  1.1608e+09   Root MSE        =     31238
------------------------------------------------------------------------------
      rprice | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     nearinc |  -30688.27   5827.709    -5.27   0.000    -42209.97   -19166.58
       _cons |   101307.5   3093.027    32.75   0.000     95192.43    107422.6
------------------------------------------------------------------------------

. reg rprice nearinc if year==1978

      Source |       SS           df       MS      Number of obs   =       179
-------------+----------------------------------   F(1, 177)       =     15.74
       Model |  1.3636e+10         1  1.3636e+10   Prob > F        =    0.0001
    Residual |  1.5332e+11       177   866239953   R-squared       =    0.0817
-------------+----------------------------------   Adj R-squared   =    0.0765
       Total |  1.6696e+11       178   937979126   Root MSE        =     29432

------------------------------------------------------------------------------
      rprice | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     nearinc |  -18824.37   4744.594    -3.97   0.000    -28187.62   -9461.117
       _cons |   82517.23    2653.79    31.09   0.000     77280.09    87754.37
------------------------------------------------------------------------------

. eststo One: reg rprice y81 nearinc y81nrinc 

      Source |       SS           df       MS      Number of obs   =       321
-------------+----------------------------------   F(3, 317)       =     22.25
       Model |  6.1055e+10         3  2.0352e+10   Prob > F        =    0.0000
    Residual |  2.8994e+11       317   914632739   R-squared       =    0.1739
-------------+----------------------------------   Adj R-squared   =    0.1661
       Total |  3.5099e+11       320  1.0969e+09   Root MSE        =     30243

------------------------------------------------------------------------------
      rprice | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         y81 |   18790.29   4050.065     4.64   0.000     10821.88    26758.69
     nearinc |  -18824.37   4875.322    -3.86   0.000    -28416.45   -9232.293
    y81nrinc |   -11863.9   7456.646    -1.59   0.113    -26534.67    2806.867
       _cons |   82517.23    2726.91    30.26   0.000      77152.1    87882.36
------------------------------------------------------------------------------

. eststo Two: qui reg rprice y81 nearinc y81nrinc age agesq
. eststo Three: qui reg rprice y81 nearinc y81nrinc age agesq intst land area r
> ooms baths 

. estout, cells(b(nostar fmt(2)) se(par fmt(2))) stats(r2 r2_a N, fmt(%9.3f %9.
> 3f %9.0g) labels(R-squared Adj-R-squared Observations)) varlabels(_cons const
> ant) varwidth(20) ti("Table 13.2 Effects of Incinerator Location on Housing P
> rices (rprice)")

Table 13.2 Effects of Incinerator Location on Housing Prices (rprice)
-----------------------------------------------------------
                              One          Two        Three
                             b/se         b/se         b/se
-----------------------------------------------------------
y81                      18790.29     21321.04     13928.48
                        (4050.06)    (3443.63)    (2798.75)
nearinc                 -18824.37      9397.94      3780.34
                        (4875.32)    (4812.22)    (4453.42)
y81nrinc                -11863.90    -21920.27    -14177.93
                        (7456.65)    (6359.75)    (4987.27)
age                                   -1494.42      -739.45
                                      (131.86)     (131.13)
agesq                                     8.69         3.45
                                        (0.85)       (0.81)
intst                                                 -0.54
                                                     (0.20)
land                                                   0.14
                                                     (0.03)
area                                                  18.09
                                                     (2.31)
rooms                                               3304.23
                                                  (1661.25)
baths                                               6977.32
                                                  (2581.32)
constant                 82517.23     89116.54     13807.67
                        (2726.91)    (2406.05)   (11166.59)
-----------------------------------------------------------
R-squared                   0.174        0.414        0.660
Adj-R-squared               0.166        0.405        0.649
Observations                  321          321          321
-----------------------------------------------------------

. est clear
. reg lprice y81 nearinc y81nrinc 

      Source |       SS           df       MS      Number of obs   =       321
-------------+----------------------------------   F(3, 317)       =     73.15
       Model |  25.1332147         3  8.37773824   Prob > F        =    0.0000
    Residual |  36.3057706       317  .114529245   R-squared       =    0.4091
-------------+----------------------------------   Adj R-squared   =    0.4035
       Total |  61.4389853       320  .191996829   Root MSE        =    .33842

------------------------------------------------------------------------------
      lprice | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         y81 |   .4569953   .0453207    10.08   0.000     .3678279    .5461627
     nearinc |   -.339923   .0545555    -6.23   0.000    -.4472595   -.2325865
    y81nrinc |   -.062649   .0834408    -0.75   0.453    -.2268167    .1015187
       _cons |   11.28542   .0305145   369.84   0.000     11.22539    11.34546
------------------------------------------------------------------------------

. reg lprice y81 nearinc y81nrinc age agesq lintst lland larea rooms baths 
      Source |       SS           df       MS      Number of obs   =       321
-------------+----------------------------------   F(10, 310)      =    116.91
       Model |  48.5621258        10  4.85621258   Prob > F        =    0.0000
    Residual |  12.8768595       310  .041538256   R-squared       =    0.7904
-------------+----------------------------------   Adj R-squared   =    0.7837
       Total |  61.4389853       320  .191996829   Root MSE        =    .20381

------------------------------------------------------------------------------
      lprice | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         y81 |    .425974   .0284999    14.95   0.000     .3698963    .4820518
     nearinc |    .032232   .0474876     0.68   0.498    -.0612067    .1256708
    y81nrinc |  -.1315133   .0519712    -2.53   0.012    -.2337743   -.0292524
         age |  -.0083591   .0014111    -5.92   0.000    -.0111358   -.0055825
       agesq |   .0000376   8.67e-06     4.34   0.000     .0000206    .0000547
      lintst |  -.0614482   .0315075    -1.95   0.052    -.1234438    .0005474
       lland |    .099845    .024491     4.08   0.000     .0516554    .1480346
       larea |   .3507722   .0514865     6.81   0.000     .2494649    .4520794
       rooms |   .0473344   .0173274     2.73   0.007     .0132402    .0814285
       baths |   .0942767   .0277256     3.40   0.001     .0397225    .1488309
       _cons |   7.651756   .4158832    18.40   0.000     6.833445    8.470067
------------------------------------------------------------------------------

. 

Example 13.4 Effect of Worker Compensation Laws on Weeks out of Work#

%%stata
u injury, clear
reg ldurat afchnge highearn afhigh if ky==1
. u injury, clear

. reg ldurat afchnge highearn afhigh if ky==1
      Source |       SS           df       MS      Number of obs   =     5,626
-------------+----------------------------------   F(3, 5622)      =     39.54
       Model |  191.071442         3  63.6904807   Prob > F        =    0.0000
    Residual |   9055.9345     5,622  1.61080301   R-squared       =    0.0207
-------------+----------------------------------   Adj R-squared   =    0.0201
       Total |  9247.00594     5,625  1.64391217   Root MSE        =    1.2692

------------------------------------------------------------------------------
      ldurat | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     afchnge |   .0076573   .0447173     0.17   0.864    -.0800058    .0953204
    highearn |   .2564785   .0474464     5.41   0.000     .1634652    .3494918
      afhigh |   .1906012   .0685089     2.78   0.005     .0562973    .3249051
       _cons |   1.125615   .0307368    36.62   0.000     1.065359    1.185871
------------------------------------------------------------------------------

. 

Example 13.5 Sleeping versus Working#

%%stata
u slp75_81, clear
reg cslpnap ctotwrk ceduc cmarr cyngkid cgdhlth
. u slp75_81, clear

. reg cslpnap ctotwrk ceduc cmarr cyngkid cgdhlth

      Source |       SS           df       MS      Number of obs   =       239
-------------+----------------------------------   F(5, 233)       =      8.19
       Model |  14674698.2         5  2934939.64   Prob > F        =    0.0000
    Residual |  83482611.7       233  358294.471   R-squared       =    0.1495
-------------+----------------------------------   Adj R-squared   =    0.1313
       Total |  98157309.9       238  412425.672   Root MSE        =    598.58

------------------------------------------------------------------------------
     cslpnap | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     ctotwrk |  -.2266694    .036054    -6.29   0.000    -.2977029   -.1556359
       ceduc |  -.0244717   48.75938    -0.00   1.000    -96.09008    96.04113
       cmarr |   104.2139   92.85536     1.12   0.263    -78.72946    287.1574
     cyngkid |    94.6654   87.65252     1.08   0.281    -78.02739    267.3582
     cgdhlth |   87.57785   76.59913     1.14   0.254    -63.33758    238.4933
       _cons |
  -92.63404    45.8659    -2.02   0.045    -182.9989   -2.269152
------------------------------------------------------------------------------

. 

Example 13.6 Distributed Lag of Crime Rate on Clear-Up Rate#

%%stata
u crime3, clear
reg clcrime cclrprc1 cclrprc2 
. u crime3, clear

. reg clcrime cclrprc1 cclrprc2 

      Source |       SS           df       MS      Number of obs   =        53
-------------+----------------------------------   F(2, 50)        =      5.99
       Model |  1.42294697         2  .711473484   Prob > F        =    0.0046
    Residual |  5.93723904        50  .118744781   R-squared       =    0.1933
-------------+----------------------------------   Adj R-squared   =    0.1611
       Total |  7.36018601        52  .141542039   Root MSE        =    .34459
------------------------------------------------------------------------------
     clcrime | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
    cclrprc1 |  -.0040475   .0047199    -0.86   0.395    -.0135276    .0054326
    cclrprc2 |  -.0131966   .0051946    -2.54   0.014    -.0236302   -.0027629
       _cons |   .0856556   .0637825     1.34   0.185    -.0424553    .2137665
------------------------------------------------------------------------------

. 

Example 13.7 Effect of Drunk Driving Laws on Traffic Fatalities#

%%stata
u traffic1, clear
reg cdthrte copen cadmn
. u traffic1, clear

. reg cdthrte copen cadmn

      Source |       SS           df       MS      Number of obs   =        51
-------------+----------------------------------   F(2, 48)        =      3.23
       Model |  .762579785         2  .381289893   Prob > F        =    0.0482
    Residual |  5.66369475        48  .117993641   R-squared       =    0.1187
-------------+----------------------------------   Adj R-squared   =    0.0819
       Total |  6.42627453        50  .128525491   Root MSE        =     .3435
------------------------------------------------------------------------------
     cdthrte | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       copen |  -.4196787   .2055948    -2.04   0.047    -.8330547   -.0063028
       cadmn |  -.1506024   .1168223    -1.29   0.204    -.3854894    .0842846
       _cons |  -.4967872   .0524256    -9.48   0.000    -.6021959   -.3913784
------------------------------------------------------------------------------

. 

Example 13.8 Effect of Enterprise Zones on Unemployment Claims#

%%stata
u ezunem, clear
reg guclms d82-d88 cez 
display exp(_b[cez])-1
predict u, res
g u2=u^2
g u_1=u[_n-1]
reg u2 d82-d88 cez
reg u d83-d88 cez u_1
. u ezunem, clear

. reg guclms d82-d88 cez 

      Source |       SS           df       MS      Number of obs   =       176
-------------+----------------------------------   F(8, 167)       =     34.50
       Model |  12.8826331         8  1.61032914   Prob > F        =    0.0000
    Residual |  7.79583815       167  .046681666   R-squared       =    0.6230
-------------+----------------------------------   Adj R-squared   =    0.6049
       Total |  20.6784713       175  .118162693   Root MSE        =    .21606
------------------------------------------------------------------------------
      guclms | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         d82 |   .7787595   .0651444    11.95   0.000     .6501469    .9073721
         d83 |  -.0331192   .0651444    -0.51   0.612    -.1617318    .0954934
         d84 |  -.0171382   .0685455    -0.25   0.803    -.1524655    .1181891
         d85 |    .323081   .0666774     4.85   0.000     .1914417    .4547202
         d86 |    .292154   .0651444     4.48   0.000     .1635413    .4207666
         d87 |   .0539481   .0651444     0.83   0.409    -.0746645    .1825607
         d88 |  -.0170526   .0651444    -0.26   0.794    -.1456652    .1115601
         cez |  -.1818775   .0781862    -2.33   0.021    -.3362382   -.0275169
       _cons |  -.3216319    .046064    -6.98   0.000    -.4125748   -.2306891
------------------------------------------------------------------------------

. display exp(_b[cez])-1
-.16629657

. predict u, res
(22 missing values generated)

. g u2=u^2
(22 missing values generated)

. g u_1=u[_n-1]
(23 missing values generated)

. reg u2 d82-d88 cez

      Source |       SS           df       MS      Number of obs   =       176
-------------+----------------------------------   F(8, 167)       =      0.85
       Model |  .025836793         8  .003229599   Prob > F        =    0.5570
    Residual |  .631857421       167  .003783577   R-squared       =    0.0393
-------------+----------------------------------   Adj R-squared   =   -0.0067
       Total |  .657694213       175  .003758253   Root MSE        =    .06151
------------------------------------------------------------------------------
          u2 | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         d82 |   -.015372   .0185462    -0.83   0.408    -.0519872    .0212432
         d83 |  -.0106696   .0185462    -0.58   0.566    -.0472848    .0259456
         d84 |   .0149802   .0195145     0.77   0.444    -.0235467     .053507
         d85 |   .0085615   .0189826     0.45   0.653    -.0289154    .0460384
         d86 |   .0103385   .0185462     0.56   0.578    -.0262767    .0469538
         d87 |   .0112266   .0185462     0.61   0.546    -.0253886    .0478418
         d88 |  -.0187891   .0185462    -1.01   0.312    -.0554043    .0178261
         cez |  -.0073174   .0222591    -0.33   0.743     -.051263    .0366281
       _cons |   .0446758   .0131141     3.41   0.001     .0187849    .0705667
------------------------------------------------------------------------------

. reg u d83-d88 cez u_1

      Source |       SS           df       MS      Number of obs   =       154
-------------+----------------------------------   F(8, 145)       =      0.74
       Model |  .267609183         8  .033451148   Prob > F        =    0.6551
    Residual |  6.54536157       145  .045140425   R-squared       =    0.0393
-------------+----------------------------------   Adj R-squared   =   -0.0137
       Total |  6.81297075       153  .044529221   Root MSE        =    .21246

------------------------------------------------------------------------------
           u | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         d83 |  -1.33e-09   .0640599    -0.00   1.000    -.1266119    .1266119
         d84 |  -.0105917   .0675446    -0.16   0.876     -.144091    .1229075
         d85 |  -.0070611   .0656315    -0.11   0.914    -.1367792    .1226569
         d86 |  -3.38e-10   .0640599    -0.00   1.000    -.1266119    .1266119
         d87 |  -4.28e-09   .0640599    -0.00   1.000    -.1266119    .1266119
         d88 |  -4.11e-09   .0640599    -0.00   1.000    -.1266119    .1266119
         cez |   .0388363   .0785217     0.49   0.622    -.1163587    .1940313
         u_1 |  -.1965359   .0807187    -2.43   0.016    -.3560731   -.0369986
       _cons |   1.65e-09   .0452972     0.00   1.000    -.0895281    .0895281
------------------------------------------------------------------------------

. 

Example 13.9 County Crime Rates in North Carolina#

%%stata
u crime4, clear
eststo hetrosk: qui reg clcrmrte i.year clprbarr clprbcon clprbpri clavgsen clpolpc
predict u, res
eststo robust: qui reg clcrmrte i.year clprbarr clprbcon clprbpri clavgsen clpolpc, r
estout, cells(b(nostar fmt(4)) se(par fmt(4))) stats(r2 r2_a N, fmt(%9.3f %9.3f %9.0g) labels(R-squared Adj-R-squared Observations)) varlabels(_cons constant) varwidth(20) ti("Dependent Variable is clcrmrte")
est clear
. u crime4, clear

. eststo hetrosk: qui reg clcrmrte i.year clprbarr clprbcon clprbpri clavgsen c
> lpolpc
. predict u, res
(90 missing values generated)

. eststo robust: qui reg clcrmrte i.year clprbarr clprbcon clprbpri clavgsen cl
> polpc, r

. estout, cells(b(nostar fmt(4)) se(par fmt(4))) stats(r2 r2_a N, fmt(%9.3f %9.
> 3f %9.0g) labels(R-squared Adj-R-squared Observations)) varlabels(_cons const
> ant) varwidth(20) ti("Dependent Variable is clcrmrte")

Dependent Variable is clcrmrte
----------------------------------------------
                          hetrosk       robust
                             b/se         b/se
----------------------------------------------
82.year                    0.0000       0.0000
                              (.)          (.)
83.year                   -0.0999      -0.0999
                         (0.0239)     (0.0216)
84.year                   -0.0479      -0.0479
                         (0.0235)     (0.0203)
85.year                   -0.0046      -0.0046
                         (0.0235)     (0.0241)
86.year                    0.0275       0.0275
                         (0.0241)     (0.0215)
87.year                    0.0408       0.0408
                         (0.0244)     (0.0235)
clprbarr                  -0.3275      -0.3275
                         (0.0300)     (0.0515)
clprbcon                  -0.2381      -0.2381
                         (0.0182)     (0.0312)
clprbpri                  -0.1650      -0.1650
                         (0.0260)     (0.0351)
clavgsen                  -0.0218      -0.0218
                         (0.0221)     (0.0250)
clpolpc                    0.3984       0.3984
                         (0.0269)     (0.0759)
constant                   0.0077       0.0077
                         (0.0171)     (0.0146)
----------------------------------------------
R-squared                   0.433        0.433
Adj-R-squared               0.422        0.422
Observations                  540          540
----------------------------------------------

. est clear

. 
%%stata
g usq=u^2
g u_1=u[_n-1]
reg usq i.year clprbarr clprbcon clprbpri clavgsen clpolpc
reg u i.year clprbarr clprbcon clprbpri clavgsen clpolpc u_1
. g usq=u^2
(90 missing values generated)

. g u_1=u[_n-1]
(91 missing values generated)

. reg usq i.year clprbarr clprbcon clprbpri clavgsen clpolpc

      Source |       SS           df       MS      Number of obs   =       540
-------------+----------------------------------   F(10, 529)      =      1.09
       Model |  .037538086        10  .003753809   Prob > F        =    0.3655
    Residual |   1.8170922       529  .003434957   R-squared       =    0.0202
-------------+----------------------------------   Adj R-squared   =    0.0017
       Total |  1.85463029       539  .003440873   Root MSE        =    .05861
------------------------------------------------------------------------------
         usq | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        year |
         83  |   .0047299   .0090756     0.52   0.602    -.0130988    .0225586
         84  |  -.0015107   .0089263    -0.17   0.866    -.0190461    .0160247
         85  |   .0172255   .0089255     1.93   0.054    -.0003082    .0347591
         86  |   .0025074   .0091722     0.27   0.785    -.0155109    .0205258
         87  |   .0086536   .0092732     0.93   0.351    -.0095631    .0268703
             |
    clprbarr |  -.0145322   .0113867    -1.28   0.202     -.036901    .0078365
    clprbcon |   .0018215   .0069255     0.26   0.793    -.0117833    .0154264
    clprbpri |   .0052474   .0098633     0.53   0.595    -.0141286    .0246234
    clavgsen |   .0034765   .0083903     0.41   0.679     -.013006     .019959
     clpolpc |   .0016434   .0102101     0.16   0.872    -.0184138    .0217006
       _cons |   .0181115   .0064787     2.80   0.005     .0053843    .0308388
------------------------------------------------------------------------------

. reg u i.year clprbarr clprbcon clprbpri clavgsen clpolpc u_1

      Source |       SS           df       MS      Number of obs   =       450
-------------+----------------------------------   F(10, 439)      =      2.35
       Model |  .564663977        10  .056466398   Prob > F        =    0.0102
    Residual |  10.5288381       439  .023983686   R-squared       =    0.0509
-------------+----------------------------------   Adj R-squared   =    0.0293
       Total |  11.0935021       449  .024707132   Root MSE        =    .15487
------------------------------------------------------------------------------
           u | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        year |
         84  |  -.0004163   .0234297    -0.02   0.986    -.0464646    .0456319
         85  |   .0006335   .0232143     0.03   0.978    -.0449915    .0462585
         86  |    .002122   .0234036     0.09   0.928    -.0438751    .0481191
         87  |   .0012379   .0234019     0.05   0.958    -.0447558    .0472317
             |
    clprbarr |   .0082875   .0330698     0.25   0.802    -.0567074    .0732823
    clprbcon |  -.0036161   .0200155    -0.18   0.857    -.0429542    .0357221
    clprbpri |   .0017131    .027855     0.06   0.951    -.0530326    .0564588
    clavgsen |  -.0125831   .0245006    -0.51   0.608    -.0607362      .03557
     clpolpc |   .0214883   .0282688     0.76   0.448    -.0340706    .0770473
         u_1 |  -.2332117   .0488802    -4.77   0.000      -.32928   -.1371435
       _cons |  -.0007033   .0165046    -0.04   0.966    -.0331411    .0317346
------------------------------------------------------------------------------

.