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st: RE: ivreg2 vs. Manual IV


From   "Schaffer, Mark E" <[email protected]>
To   <[email protected]>
Subject   st: RE: ivreg2 vs. Manual IV
Date   Mon, 7 Mar 2011 10:32:57 -0000

Erkal,

You've got a lot of dummy regressors and instruments, most of which are
not statistically significant, so my first guess would be something to
do with numerical accuracy.  You should tell us, though, which versions
of Stata and -ivreg2- you are using.

Here are a few things you can experiment with:

1.  Do your results slightly change again if you partial out the year
dummies with the -partial- option?

ivreg2 loghrearn age agesq YR* (educ=QTR*), robust partial(YR*)

2.  There are two official IV routines in Stata, -ivregress- and
-ivreg-.  The former is documented in Stata 11, the latter is not, but
its syntax is the same as that of -ivreg2-:

ivregress 2sls loghrearn age agesq YR* (educ=QTR*), robust

ivreg loghrearn age agesq YR* (educ=QTR*), robust

The reason to try out -ivreg- is that it is implemented using -regress-.
For that reason, it's likely to be very accurate in the face of
numerical challenges.

3.  What happens if, instead of using your QTR* instruments, you use
your predicted value (yhat) as your sole excluded instrument in your IV
estimation with -ivreg2-, -ivregress- and -ivreg-?  E.g.,

ivreg2 loghrearn age agesq YR* (educ=yhat), robust

Cheers,
Mark

> -----Original Message-----
> From: [email protected] 
> [mailto:[email protected]] On Behalf Of Erkal Ersoy
> Sent: 07 March 2011 03:16
> To: [email protected]
> Subject: st: ivreg2 vs. Manual IV
> 
> Hello Statalisters,
> 
> Apologies in advance if my question has already been answered 
> somewhere. It feels like the answer should be out there 
> somewhere, but I spent a lot of time looking for it and 
> couldn't get to it.
> 
> The essence of my question is possibly about the 
> inner-workings of the command "ivreg2." As illustrated below, 
> I keep getting different estimates on some coefficients when 
> I do a 2SLS estimation manually rather than using ivreg2 directly.
> 
> I am trying to evaluate the effect of education on earnings, 
> so please pay attention only to the coefficients on educ 
> (education), age and agesq (age squared). YR* are the years 
> of birth of individuals, and
> QTR* are the interaction terms of their years of birth with 
> quarters of birth--as done in Angrist and Krueger (1991).
> 
> In the ivreg2 regression, the coefficients on educ, age, and 
> agesq are 0.0775**, 0.0961, and -0.0011 respectively.
> When I go ahead and do the first and second stage regressions 
> by hand, I get 0.0775** on educ, 0.0694** on age, and -0.0007 
> on agesq.
> Note that I used ** to denote that the coefficient is 
> statistically significant at the 5% level.
> The fact that the coefficient on education stays the same is 
> comforting, but the 3 percentage-point change in the 
> coefficient of age is not... It also seems to become 
> statistically significant when the manual approach is used. I 
> have not been able to figure out why this is happening. Am I 
> overlooking something simple? or Is ivreg2 doing something 
> inherently that I am not aware of?
> 
> Thank you in advance and I look forward to hearing from you!
> 
> Best,
> Erkal
> 
> 
> Here is the output:
> 
> . ivreg2 loghrearn age agesq YR* (educ=QTR*), robust Warning 
> - collinearities detected
> Vars dropped:       YR57 YR58
> 
> IV (2SLS) estimation
> --------------------
> 
> Estimates efficient for homoskedasticity only Statistics 
> robust to heteroskedasticity
> 
>                                                       Number 
> of obs =     1930
>                                                       F( 30,  
> 1899) =    10.25
>                                                       Prob > 
> F      =   0.0000
> Total (centered) SS     =  442.0938306                
> Centered R2   =   0.2791
> Total (uncentered) SS   =  10400.84512                
> Uncentered R2 =   0.9694
> Residual SS             =  318.6885935                Root 
> MSE      =    .4064
> 
> --------------------------------------------------------------
> ----------------
>              |               Robust
>    loghrearn |      Coef.   Std. Err.      z    P>|z|     
> [95% Conf. Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
>         educ |   .0775441   .0160336     4.84   0.000     
> .0461187    .1089695
>          age |   .0960978   .1423516     0.68   0.500    
> -.1829063    .3751018
>        agesq |  -.0010697   .0017913    -0.60   0.550    
> -.0045807    .0024412
>         YR30 |   .0729663   .1068284     0.68   0.495    
> -.1364134    .2823461
>         YR31 |     .07704   .1309457     0.59   0.556    
> -.1796089    .3336889
>         YR32 |   .0973292    .163443     0.60   0.552    
> -.2230131    .4176716
>         YR33 |   .1417888   .1929499     0.73   0.462    
> -.2363861    .5199638
>         YR34 |  -.1038325   .2259978    -0.46   0.646      
> -.54678     .339115
>         YR35 |  -.0904907   .2650057    -0.34   0.733    
> -.6098924     .428911
>         YR36 |   .0211021   .2889079     0.07   0.942    
> -.5451469    .5873512
>         YR37 |  -.0095714   .3094713    -0.03   0.975    
> -.6161241    .5969812
>         YR38 |  -.1243342   .3284837    -0.38   0.705    
> -.7681505     .519482
>         YR39 |   .0318703     .33975     0.09   0.925    
> -.6340275    .6977681
>         YR40 |   -.012432   .3502283    -0.04   0.972    
> -.6988668    .6740027
>         YR41 |  -.0104493    .362811    -0.03   0.977    
> -.7215458    .7006471
>         YR42 |  -.0702727   .3685554    -0.19   0.849     
> -.792628    .6520826
>         YR43 |   .0575015   .3747713     0.15   0.878    
> -.6770368    .7920399
>         YR44 |   .0096079    .370298     0.03   0.979    
> -.7161628    .7353786
>         YR45 |    .002713   .3662465     0.01   0.994     
> -.715117     .720543
>         YR46 |  -.0635162   .3581167    -0.18   0.859     
> -.765412    .6383797
>         YR47 |  -.0433715    .343595    -0.13   0.900    
> -.7168054    .6300624
>         YR48 |   .0054387   .3286098     0.02   0.987    
> -.6386247    .6495021
>         YR49 |   -.099746   .3100412    -0.32   0.748    
> -.7074155    .5079235
>         YR50 |  -.0773254   .2898625    -0.27   0.790    
> -.6454454    .4907946
>         YR51 |   .0145518   .2642092     0.06   0.956    
> -.5032888    .5323923
>         YR52 |  -.0292709   .2321661    -0.13   0.900    
> -.4843081    .4257663
>         YR53 |   .0184112   .1987312     0.09   0.926    
> -.3710947    .4079172
>         YR54 |  -.0401541   .1639762    -0.24   0.807    
> -.3615416    .2812333
>         YR55 |  -.0174335   .1241698    -0.14   0.888    
> -.2608018    .2259348
>         YR56 |  -.0569723   .0847047    -0.67   0.501    
> -.2229904    .1090458
>        _cons |  -.7115404   2.495252    -0.29   0.776    
> -5.602144    4.179063
> --------------------------------------------------------------
> ----------------
> Underidentification test (Kleibergen-Paap rk LM statistic):   
>           87.887
>                                                    Chi-sq(87) 
> P-val =   0.4532
> --------------------------------------------------------------
> ----------------
> Weak identification test (Cragg-Donald Wald F statistic):     
>            1.147
>                          (Kleibergen-Paap rk Wald F 
> statistic):          1.139
> Stock-Yogo weak ID test critical values:  5% maximal IV 
> relative bias    21.12
>                                          10% maximal IV 
> relative bias    10.91
>                                          20% maximal IV 
> relative bias     5.69
>                                          30% maximal IV 
> relative bias     3.92
>                                          10% maximal IV size  
>           222.24
>                                          15% maximal IV size  
>           113.33
>                                          20% maximal IV size  
>            76.67
>                                          25% maximal IV size  
>            58.36
> Source: Stock-Yogo (2005).  Reproduced by permission.
> NB: Critical values are for Cragg-Donald F statistic and 
> i.i.d. errors.
> --------------------------------------------------------------
> ----------------
> Hansen J statistic (overidentification test of all 
> instruments):        82.395
>                                                    Chi-sq(86) 
> P-val =   0.5901
> --------------------------------------------------------------
> ----------------
> Instrumented:         educ
> Included instruments: age agesq YR30 YR31 YR32 YR33 YR34 YR35 
> YR36 YR37 YR38
>                       YR39 YR40 YR41 YR42 YR43 YR44 YR45 YR46 
> YR47 YR48 YR49
>                       YR50 YR51 YR52 YR53 YR54 YR55 YR56 
> Excluded instruments: QTR230 QTR231 QTR232 QTR233 QTR234 
> QTR235 QTR236 QTR237
>                       QTR238 QTR239 QTR240 QTR241 QTR242 
> QTR243 QTR244 QTR245
>                       QTR246 QTR247 QTR248 QTR249 QTR250 
> QTR251 QTR252 QTR253
>                       QTR254 QTR255 QTR256 QTR257 QTR258 
> QTR330 QTR331 QTR332
>                       QTR333 QTR334 QTR335 QTR336 QTR337 
> QTR338 QTR339 QTR340
>                       QTR341 QTR342 QTR343 QTR344 QTR345 
> QTR346 QTR347 QTR348
>                       QTR349 QTR350 QTR351 QTR352 QTR353 
> QTR354 QTR355 QTR356
>                       QTR357 QTR358 QTR430 QTR431 QTR432 
> QTR433 QTR434 QTR435
>                       QTR436 QTR437 QTR438 QTR439 QTR440 
> QTR441 QTR442 QTR443
>                       QTR444 QTR445 QTR446 QTR447 QTR448 
> QTR449 QTR450 QTR451
>                       QTR452 QTR453 QTR454 QTR455 QTR456 QTR457 QTR458
> Dropped collinear:    YR57 YR58
> --------------------------------------------------------------
> ----------------
> 
> . reg educ age agesq YR* QTR*
> note: YR42 omitted because of collinearity
> note: YR58 omitted because of collinearity
> 
>       Source |       SS       df       MS              Number 
> of obs =    1930
> -------------+------------------------------           F(116, 
>  1813) =    1.72
>        Model |  1172.63491   116  10.1089217           Prob > 
> F      =  0.0000
>     Residual |  10684.3231  1813  5.89317326           
> R-squared     =  0.0989
> -------------+------------------------------           Adj 
> R-squared =  0.0412
>        Total |   11856.958  1929  6.14668638           Root 
> MSE      =  2.4276
> 
> --------------------------------------------------------------
> ----------------
>         educ |      Coef.   Std. Err.      t    P>|t|     
> [95% Conf. Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
>          age |   .4445861   .4307161     1.03   0.302    
> -.4001659    1.289338
>        agesq |  -.0060692   .0054336    -1.12   0.264    
> -.0167259    .0045876
>         YR30 |  -.8890242   .9932762    -0.90   0.371     
> -2.83711    1.059062
>         YR31 |   .6960782   .9116261     0.76   0.445     
> -1.09187    2.484026
>         YR32 |   .6377634   .9109859     0.70   0.484    
> -1.148929    2.424456
>         YR33 |   1.800134   .8846079     2.03   0.042     
> .0651759    3.535092
>         YR34 |   .5381042   1.082161     0.50   0.619    
> -1.584309    2.660517
>         YR35 |  -2.185563   1.041604    -2.10   0.036    
> -4.228433   -.1426933
>         YR36 |  -.4344303   1.228448    -0.35   0.724    
> -2.843753    1.974892
>         YR37 |   .6838194   1.199013     0.57   0.569    
> -1.667774    3.035413
>         YR38 |  -1.465554   1.275869    -1.15   0.251    
> -3.967881    1.036773
>         YR39 |  -.1861233   1.234434    -0.15   0.880    
> -2.607185    2.234938
>         YR40 |  -1.394554   1.344123    -1.04   0.300    
> -4.030746    1.241638
>         YR41 |    1.02279   1.292272     0.79   0.429    
> -1.511709     3.55729
>         YR42 |  (omitted)
>         YR43 |  -.1970156   1.392313    -0.14   0.887    
> -2.927722     2.53369
>         YR44 |   1.018107   1.274471     0.80   0.424     
> -1.48148    3.517694
>         YR45 |  -1.504632   1.385526    -1.09   0.278    
> -4.222028    1.212764
>         YR46 |    .556196   1.250079     0.44   0.656     
> -1.89555    3.007942
>         YR47 |  -.7041711   1.166875    -0.60   0.546    
> -2.992731    1.584389
>         YR48 |   .2142667   1.132912     0.19   0.850    
> -2.007683    2.436216
>         YR49 |  -.6242047   1.097718    -0.57   0.570    
> -2.777129    1.528719
>         YR50 |  -.1981569   1.042875    -0.19   0.849     
> -2.24352    1.847206
>         YR51 |   .9638388   .9958603     0.97   0.333    
> -.9893155    2.916993
>         YR52 |   -.823932   .9013091    -0.91   0.361    
> -2.591645    .9437814
>         YR53 |  -.2495645   .8451451    -0.30   0.768    
> -1.907125    1.407996
>         YR54 |   .4278504   .8061783     0.53   0.596    
> -1.153286    2.008986
>         YR55 |   .2133633   .7942078     0.27   0.788    
> -1.344295    1.771022
>         YR56 |   .4657228   .6636603     0.70   0.483    
> -.8358964    1.767342
>         YR57 |   -.360123   .6362917    -0.57   0.571    
> -1.608065    .8878189
>         YR58 |  (omitted)
>       QTR230 |          1    1.13807     0.88   0.380    
> -1.232066    3.232066
>       QTR231 |  -1.492063   1.223388    -1.22   0.223    
> -3.891462    .9073353
>       QTR232 |         .6     1.2536     0.48   0.632    
> -1.858652    3.058652
>       QTR233 |  -2.897436    1.19813    -2.42   0.016    
> -5.247297   -.5475746
>       QTR234 |  -.6805556   1.179595    -0.58   0.564    
> -2.994063    1.632952
>       QTR235 |   2.121212   1.581181     1.34   0.180    
> -.9799165    5.222341
>       QTR236 |   .8214286   1.256395     0.65   0.513    
> -1.642706    3.285563
>       QTR237 |   .1666667    1.27945     0.13   0.896    
> -2.342685    2.676018
>       QTR238 |      2.375   1.128003     2.11   0.035     
> .1626788    4.587321
>       QTR239 |  -.1666667   1.232046    -0.14   0.892    
> -2.583047    2.249713
>       QTR240 |  -.2083333   1.108036    -0.19   0.851    
> -2.381495    1.964829
>       QTR241 |  -2.763636   1.060689    -2.61   0.009    
> -4.843937   -.6833361
>       QTR242 |  -.6941176   1.235027    -0.56   0.574    
> -3.116343    1.728108
>       QTR243 |       -.05   1.062791    -0.05   0.962    
> -2.134424    2.034424
>       QTR244 |       -1.3   1.005116    -1.29   0.196    
> -3.271307    .6713073
>       QTR245 |   .4444444   1.179595     0.38   0.706    
> -1.869063    2.757952
>       QTR246 |  -1.365546   .8761268    -1.56   0.119     
> -3.08387    .3527779
>       QTR247 |   .8033794   .6860974     1.17   0.242    
> -.5422451    2.149004
>       QTR248 |  -.2731092   .6737625    -0.41   0.685    
> -1.594542    1.048323
>       QTR249 |   1.271212   .6879242     1.85   0.065    
> -.0779952    2.620419
>       QTR250 |   1.114846    .792013     1.41   0.159     
> -.438508      2.6682
>       QTR251 |  -1.213636   .7500201    -1.62   0.106    
> -2.684631    .2573581
>       QTR252 |   .7857143   .6611588     1.19   0.235    
> -.5109989    2.082427
>       QTR253 |  -2.58e-14   .6799908    -0.00   1.000    
> -1.333648    1.333648
>       QTR254 |  -.8030303    .668171    -1.20   0.230    
> -2.113496    .5074357
>       QTR255 |  -.5035842   .7193753    -0.70   0.484    
> -1.914476    .9073074
>       QTR256 |  -.3017078   .6028524    -0.50   0.617    
> -1.484066    .8806505
>       QTR257 |   .3812636    .625775     0.61   0.542    
> -.8460521    1.608579
>       QTR258 |  -.2581522   .7902837    -0.33   0.744    
> -1.808114     1.29181
>       QTR330 |        .75   1.154547     0.65   0.516    
> -1.514383    3.014383
>       QTR331 |  -1.414141   1.091119    -1.30   0.195    
> -3.554123    .7258406
>       QTR332 |        -.8   1.085649    -0.74   0.461    
> -2.929255    1.329255
>       QTR333 |  -.8307692   1.021097    -0.81   0.416    
> -2.833419     1.17188
>       QTR334 |      -.325   1.383937    -0.23   0.814    
> -3.039278    2.389278
>       QTR335 |   .4545455   1.173723     0.39   0.699    
> -1.847446    2.756536
>       QTR336 |   .0714286   1.350584     0.05   0.958    
> -2.577436    2.720293
>       QTR337 |  -1.444444   1.144375    -1.26   0.207    
> -3.688877    .7999876
>       QTR338 |   7.06e-15   1.213793     0.00   1.000     
> -2.38058     2.38058
>       QTR339 |  -.5714286   1.173723    -0.49   0.626     
> -2.87342    1.730562
>       QTR340 |   1.432692   1.090856     1.31   0.189    
> -.7067752     3.57216
>       QTR341 |   -1.69697   1.232046    -1.38   0.169     
> -4.11335    .7194102
>       QTR342 |      -.025   1.383937    -0.02   0.986    
> -2.739278    2.689278
>       QTR343 |       -.35   1.151505    -0.30   0.761    
> -2.608416    1.908416
>       QTR344 |       -1.5   .9175412    -1.63   0.102    
> -3.299549    .2995491
>       QTR345 |       1.25   1.051176     1.19   0.235    
> -.8116425    3.311643
>       QTR346 |   .6558442   .9781022     0.67   0.503    
> -1.262482     2.57417
>       QTR347 |   1.238095   .7491693     1.65   0.099    
> -.2312305    2.707421
>       QTR348 |  -.3928571   .7007837    -0.56   0.575    
> -1.767285    .9815712
>       QTR349 |   .9431034   .7056001     1.34   0.182    
> -.4407712    2.326978
>       QTR350 |   .1829574   .7686315     0.24   0.812    
> -1.324539    1.690454
>       QTR351 |  -.5772727   .7500201    -0.77   0.442    
> -2.048267    .8937217
>       QTR352 |   .5833333   .6871749     0.85   0.396    
> -.7644045    1.931071
>       QTR353 |  -.1785714   .6679801    -0.27   0.789    
> -1.488663     1.13152
>       QTR354 |  -.3909091   .6443608    -0.61   0.544    
> -1.654677    .8728586
>       QTR355 |  -.8377778   .7504168    -1.12   0.264     
> -2.30955    .6339948
>       QTR356 |  -.6129032   .6166074    -0.99   0.320    
> -1.822239    .5964325
>       QTR357 |   .0946292   .6554033     0.14   0.885    
> -1.190796    1.380054
>       QTR358 |   .5624123   .6680773     0.84   0.400    
> -.7478699    1.872695
>       QTR430 |        1.6   1.421449     1.13   0.260     
> -1.18785     4.38785
>       QTR431 |   .0555556    1.27945     0.04   0.965    
> -2.453796    2.564907
>       QTR432 |   .5444444   1.115399     0.49   0.626    
> -1.643157    2.732046
>       QTR433 |  -3.321678    .994517    -3.34   0.001    
> -5.272198   -1.371159
>       QTR434 |  -3.267857   1.256395    -2.60   0.009    
> -5.731991    -.803723
>       QTR435 |   1.025974   1.173723     0.87   0.382    
> -1.276017    3.327965
>       QTR436 |  -1.678571    1.52157    -1.10   0.270    
> -4.662786    1.305643
>       QTR437 |  -.8888889   1.144375    -0.78   0.437    
> -3.133321    1.355543
>       QTR438 |   1.041667   1.311046     0.79   0.427    
> -1.529653    3.612987
>       QTR439 |         -1   1.232046    -0.81   0.417     
> -3.41638     1.41638
>       QTR440 |      1.375   1.486587     0.92   0.355    
> -1.540603    4.290603
>       QTR441 |  -1.205742   .9197337    -1.31   0.190    
> -3.009591    .5981075
>       QTR442 |   .3777778   1.354043     0.28   0.780     
> -2.27787    3.033426
>       QTR443 |  -1.138889   1.179595    -0.97   0.334    
> -3.452397    1.174619
>       QTR444 |    -1.3125   .8884055    -1.48   0.140    
> -3.054906    .4299059
>       QTR445 |   1.833333   1.031526     1.78   0.076    
> -.1897704    3.856437
>       QTR446 |   .3035714   .8163883     0.37   0.710    
> -1.297589    1.904732
>       QTR447 |   .8154762   .8055747     1.01   0.312     
> -.764476    2.395428
>       QTR448 |   .4596273    .732702     0.63   0.531    
> -.9774016    1.896656
>       QTR449 |        .51   .7282758     0.70   0.484    
> -.9183478    1.938348
>       QTR450 |   .0662526    .732702     0.09   0.928    
> -1.370776    1.503281
>       QTR451 |     -1.475   .8142371    -1.81   0.070    
> -3.071941    .1219414
>       QTR452 |   1.595238   .7122414     2.24   0.025      
> .198338    2.992138
>       QTR453 |  -.2916667   .6937405    -0.42   0.674    
> -1.652281    1.068948
>       QTR454 |  -.6909091   .6814034    -1.01   0.311    
> -2.027327    .6455093
>       QTR455 |  -1.305556   .7007837    -1.86   0.063    
> -2.679984    .0688728
>       QTR456 |  -.7050691   .6329082    -1.11   0.265    
> -1.946375    .5362369
>       QTR457 |   .0455408   .6028524     0.08   0.940    
> -1.136817    1.227899
>       QTR458 |   .5735786   .6948996     0.83   0.409    
> -.7893094    1.936467
>        _cons |   5.374223     7.5253     0.71   0.475    
> -9.384946    20.13339
> --------------------------------------------------------------
> ----------------
> 
> . predict double yhat, xb
> 
> . reg loghrearn yhat age agesq YR*, robust
> note: YR42 omitted because of collinearity
> note: YR58 omitted because of collinearity
> 
> Linear regression                                      Number 
> of obs =    1930
>                                                        F( 30, 
>  1899) =    8.18
>                                                        Prob > 
> F      =  0.0000
>                                                        
> R-squared     =  0.1052
>                                                        Root 
> MSE      =  .45641
> 
> --------------------------------------------------------------
> ----------------
>              |               Robust
>    loghrearn |      Coef.   Std. Err.      t    P>|t|     
> [95% Conf. Interval]
> -------------+------------------------------------------------
> ----------
> -------------+------
>         yhat |   .0775439   .0191366     4.05   0.000      
> .040013    .1150748
>          age |   .0694072   .0339128     2.05   0.041     
> .0028969    .1359176
>        agesq |  -.0007319   .0004448    -1.65   0.100    
> -.0016041    .0001404
>         YR30 |   .0824261   .1079102     0.76   0.445    
> -.1292089    .2940611
>         YR31 |   .0952839   .1039415     0.92   0.359    
> -.1085676    .2991354
>         YR32 |   .1236817   .1023798     1.21   0.227     
> -.077107    .3244704
>         YR33 |    .175574   .0965876     1.82   0.069     
> -.013855    .3650029
>         YR34 |  -.0632905   .0979068    -0.65   0.518    
> -.2553067    .1287257
>         YR35 |  -.0438676   .1320984    -0.33   0.740    
> -.3029407    .2152056
>         YR36 |   .0731311    .119703     0.61   0.541    
> -.1616321    .3078943
>         YR37 |   .0471875   .1099594     0.43   0.668    
> -.1684665    .2628415
>         YR38 |  -.0635212    .119788    -0.53   0.596     
> -.298451    .1714086
>         YR39 |   .0960618   .1044298     0.92   0.358    
> -.1087474     .300871
>         YR40 |   .0544622   .1014802     0.54   0.592    
> -.1445622    .2534866
>         YR41 |    .058472   .1090039     0.54   0.592     
> -.155308    .2722521
>         YR42 |  (omitted)
>         YR43 |   .1284498   .1235006     1.04   0.298    
> -.1137613     .370661
>         YR44 |   .0805562   .1001809     0.80   0.421    
> -.1159199    .2770324
>         YR45 |   .0729855   .1031693     0.71   0.479    
> -.1293516    .2753226
>         YR46 |    .005405   .0995799     0.05   0.957    
> -.1898925    .2007024
>         YR47 |   .0235223   .0874715     0.27   0.788    
> -.1480281    .1950727
>         YR48 |   .0696297   .0827435     0.84   0.400    
> -.0926481    .2319075
>         YR49 |  -.0389337   .0825409    -0.47   0.637    
> -.2008141    .1229468
>         YR50 |  -.0205674   .0861564    -0.24   0.811    
> -.1895386    .1484038
>         YR51 |   .0665797     .08236     0.81   0.419    
> -.0949458    .2281053
>         YR52 |   .0173513   .0697737     0.25   0.804    
> -.1194899    .1541924
>         YR53 |   .0589519   .0642448     0.92   0.359    
> -.0670459    .1849496
>         YR54 |  -.0063706   .0611902    -0.10   0.917    
> -.1263777    .1136365
>         YR55 |    .008917    .057011     0.16   0.876    
> -.1028937    .1207278
>         YR56 |  -.0387302   .0522458    -0.74   0.459    
> -.1411954    .0637349
>         YR57 |   .0094559   .0524493     0.18   0.857    
> -.0934085    .1123202
>         YR58 |  (omitted)
>        _cons |   -.255431   .5957228    -0.43   0.668    
> -1.423771    .9129089
> --------------------------------------------------------------
> ----------------
> *
> *   For searches and help try:
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> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
> 


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