use "https://stats.idre.ucla.edu/stat/stata/examples/greene/TBL16-2.DTA", clear generate w = wg+wp generate k = k1+i generate yr=year-1931 generate p1 = p[_n-1] generate x1 = x[_n-1] save table16-2
Table 16.4, OLS, page 687.
regress c p p1 w
Source | SS df MS Number of obs = 21
-------------+------------------------------ F( 3, 17) = 292.71
Model | 923.549937 3 307.849979 Prob > F = 0.0000
Residual | 17.8794524 17 1.05173249 R-squared = 0.9810
-------------+------------------------------ Adj R-squared = 0.9777
Total | 941.429389 20 47.0714695 Root MSE = 1.0255
------------------------------------------------------------------------------
c | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
p | .1929343 .0912102 2.12 0.049 .0004977 .385371
p1 | .0898847 .0906479 0.99 0.335 -.1013658 .2811351
w | .7962188 .0399439 19.93 0.000 .7119444 .8804931
_cons | 16.2366 1.302698 12.46 0.000 13.48815 18.98506
------------------------------------------------------------------------------
Table 16.4, 2SLS using reg3, page 687.
reg3 (c p p1 w), 2sls nodfk inst(t wg g yr p1 x1 k1)
Two-stage least-squares regression
----------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" F-Stat P
----------------------------------------------------------------------
c 21 3 1.135659 0.9767 279.0941 0.0000
----------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
c |
p | .0173022 .1180494 0.15 0.885 -.2317603 .2663647
p1 | .2162338 .107268 2.02 0.060 -.0100818 .4425495
w | .8101827 .0402497 20.13 0.000 .7252632 .8951022
_cons | 16.55476 1.320793 12.53 0.000 13.76813 19.34139
------------------------------------------------------------------------------
Endogenous variables: c p w
Exogenous variables: t wg g yr p1 x1 k1
------------------------------------------------------------------------------
Table 16.4, 2SLS using ivreg, page 687. The initial ivreg produces the correct coefficients but the standard errors are wrong. Additional code is necessary to obtain the correct standard errors.
ivreg c p1 (p w = t wg g yr p1 x1 k1)
Instrumental variables (2SLS) regression
Source | SS df MS Number of obs = 21
-------------+------------------------------ F( 3, 17) = 225.93
Model | 919.504138 3 306.501379 Prob > F = 0.0000
Residual | 21.9252518 17 1.28972069 R-squared = 0.9767
-------------+------------------------------ Adj R-squared = 0.9726
Total | 941.429389 20 47.0714695 Root MSE = 1.1357
------------------------------------------------------------------------------
c | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
p | .0173022 .1312046 0.13 0.897 -.2595153 .2941197
w | .8101827 .0447351 18.11 0.000 .7158 .9045654
p1 | .2162338 .1192217 1.81 0.087 -.0353019 .4677696
_cons | 16.55476 1.467979 11.28 0.000 13.45759 19.65192
------------------------------------------------------------------------------
Instrumented: p w
Instruments: p1 t wg g yr x1 k1
------------------------------------------------------------------------------
/* additional code to get correct standard errors, thanks to Kit Baum */
mat vpr=e(V)*e(df_r)/e(N)
mat se=e(b)
local nc=colsof(se)
forv i=1/`nc' { mat se[1,`i']=sqrt(vpr[`i',`i']) }
mat list se
se[1,4]
p w p1 _cons
y1 .11804942 .04024972 .10726797 1.3207925
Table 16.4, GMM, page 687. Uses ivgmm0 by Christopher F. Baum and David M. Drukker, available from SSC-Ideas. The program ivgmm0 can be downloaded typing search ivgmm0 in the command line (see How can I use the search command to search for programs and get additional help? for more information about using search). The standard errors are the same as Greene but the coefficients are slightly different. Results identical to Stata are produced by the program TSP. Some researchers suggest that Greene’s coefficients are due to the fact that he uses the results from prior analyses as his starting values.
ivgmm0 c p1 (p w = t wg g yr p1 x1 k1)
Instrumental Variables Estimation via GMM Number of obs = 21
Root MSE = 1.0255
Hansen J = 4.1098
Chi-sq( 4) P-val = 0.39135
------------------------------------------------------------------------------
| GMM
c | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
p | .0757916 .0615982 1.23 0.219 -.0449386 .1965218
w | .8493653 .0292499 29.04 0.000 .7920365 .9066941
p1 | .1662683 .0654933 2.54 0.011 .0379039 .2946327
_cons | 14.74433 .8966058 16.44 0.000 12.98702 16.50165
------------------------------------------------------------------------------
Instrumented: p w
Instruments: p1 t wg g yr x1 k1
------------------------------------------------------------------------------
Table 16.4, LIML, page 687. Currently there is no Stata solution for the LIML model.
Table 16.5, 2SLS, page 699.
reg3 (c p p1 w) (i p p1 k1) (wp x x1 yr), 2sls nodfk inst(t wg g yr p1 x1 k1)
Two-stage least-squares regression
----------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" F-Stat P
----------------------------------------------------------------------
c 21 3 1.135659 0.9767 279.0941 0.0000
i 21 3 1.307149 0.8849 50.89437 0.0000
wp 21 3 .7671548 0.9874 524.005 0.0000
----------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
c |
p | .0173022 .1180494 0.15 0.884 -.2196919 .2542963
p1 | .2162338 .107268 2.02 0.049 .0008844 .4315833
w | .8101827 .0402497 20.13 0.000 .729378 .8909874
_cons | 16.55476 1.320793 12.53 0.000 13.90316 19.20636
-------------+----------------------------------------------------------------
i |
p | .1502219 .1732292 0.87 0.390 -.1975503 .4979941
p1 | .6159434 .1627853 3.78 0.000 .2891382 .9427486
k1 | -.1577876 .0361262 -4.37 0.000 -.2303141 -.0852612
_cons | 20.27821 7.542704 2.69 0.010 5.135599 35.42082
-------------+----------------------------------------------------------------
wp |
x | .4388591 .0356319 12.32 0.000 .3673251 .5103931
x1 | .1466739 .0388361 3.78 0.000 .0687071 .2246406
yr | .1303956 .029141 4.47 0.000 .0718927 .1888985
_cons | 1.500296 1.147779 1.31 0.197 -.8039674 3.804559
------------------------------------------------------------------------------
Endogenous variables: c p w i wp x
Exogenous variables: t wg g yr p1 x1 k1
------------------------------------------------------------------------------
Table 16.5, OLS, page 699.
reg3 (c p p1 w) (i p p1 k1) (wp x x1 yr), ols
Multivariate regression
----------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" F-Stat P
----------------------------------------------------------------------
c 21 3 1.02554 0.9810 292.7075 0.0000
i 21 3 1.009447 0.9313 76.87538 0.0000
wp 21 3 .7671466 0.9874 444.5687 0.0000
----------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
c |
p | .1929343 .0912102 2.12 0.039 .0098223 .3760464
p1 | .0898847 .0906479 0.99 0.326 -.0920987 .271868
w | .7962188 .0399439 19.93 0.000 .716028 .8764095
_cons | 16.2366 1.302698 12.46 0.000 13.62133 18.85188
-------------+----------------------------------------------------------------
i |
p | .4796356 .0971146 4.94 0.000 .28467 .6746012
p1 | .3330387 .1008592 3.30 0.002 .1305554 .535522
k1 | -.1117947 .0267276 -4.18 0.000 -.1654525 -.0581369
_cons | 10.12579 5.465546 1.85 0.070 -.8467492 21.09833
-------------+----------------------------------------------------------------
wp |
x | .4394769 .0324076 13.56 0.000 .374416 .5045378
x1 | .14609 .0374231 3.90 0.000 .07096 .22122
yr | .1302452 .0319103 4.08 0.000 .0661826 .1943077
_cons | 1.497043 1.270031 1.18 0.244 -1.052651 4.046737
------------------------------------------------------------------------------
Table 16.5, 3SLS, page 699.
reg3 (c p p1 w) (i p p1 k1) (wp x x1 yr), 3sls inst(t wg g yr p1 x1 k1)
Three-stage least squares regression
----------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" chi2 P
----------------------------------------------------------------------
c 21 3 .9443305 0.9801 864.5909 0.0000
i 21 3 1.446736 0.8258 162.9808 0.0000
wp 21 3 .7211282 0.9863 1594.751 0.0000
----------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
c |
p | .1248904 .1081291 1.16 0.248 -.0870387 .3368194
p1 | .1631439 .1004382 1.62 0.104 -.0337113 .3599992
w | .790081 .0379379 20.83 0.000 .715724 .8644379
_cons | 16.44079 1.304549 12.60 0.000 13.88392 18.99766
-------------+----------------------------------------------------------------
i |
p | -.0130791 .1618962 -0.08 0.936 -.3303898 .3042316
p1 | .7557238 .1529331 4.94 0.000 .4559805 1.055467
k1 | -.1948482 .0325307 -5.99 0.000 -.2586072 -.1310893
_cons | 28.17785 6.793768 4.15 0.000 14.86231 41.49339
-------------+----------------------------------------------------------------
wp |
x | .4004919 .0318134 12.59 0.000 .3381388 .462845
x1 | .181291 .0341588 5.31 0.000 .1143411 .2482409
yr | .149674 .0279352 5.36 0.000 .094922 .2044261
_cons | 1.797216 1.115854 1.61 0.107 -.3898181 3.984251
------------------------------------------------------------------------------
Endogenous variables: c p w i wp x
Exogenous variables: t wg g yr p1 x1 k1
------------------------------------------------------------------------------
Table 16.5, I3SLS, page 699.
reg3 (c p p1 w) (i p p1 k1) (wp x x1 yr), 3sls ireg3 inst(t wg g yr p1 x1 k1)
Iteration 1: tolerance = .37125491
..
Iteration 24: tolerance = 7.049e-07
Three-stage least squares regression, iterated
----------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" chi2 P
----------------------------------------------------------------------
c 21 3 .9565088 0.9796 970.3072 0.0000
i 21 3 2.134327 0.6209 56.77951 0.0000
wp 21 3 .7782334 0.9840 1312.188 0.0000
----------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
c |
p | .1645096 .0961979 1.71 0.087 -.0240348 .3530539
p1 | .1765639 .0901001 1.96 0.050 -.0000291 .3531569
w | .7658011 .0347599 22.03 0.000 .6976729 .8339294
_cons | 16.55899 1.224401 13.52 0.000 14.15921 18.95877
-------------+----------------------------------------------------------------
i |
p | -.3565316 .2601568 -1.37 0.171 -.8664296 .1533664
p1 | 1.011299 .2487745 4.07 0.000 .5237098 1.498888
k1 | -.2602 .0508694 -5.12 0.000 -.3599022 -.1604978
_cons | 42.89629 10.59386 4.05 0.000 22.13271 63.65987
-------------+----------------------------------------------------------------
wp |
x | .3747792 .0311027 12.05 0.000 .3138191 .4357394
x1 | .1936506 .0324018 5.98 0.000 .1301443 .257157
yr | .1679262 .0289291 5.80 0.000 .1112263 .2246261
_cons | 2.624766 1.195559 2.20 0.028 .2815124 4.968019
------------------------------------------------------------------------------
Endogenous variables: c p w i wp x
Exogenous variables: t wg g yr p1 x1 k1
------------------------------------------------------------------------------
Table 16.5, page 699. Currently there are not Stata solutions for the LIML, FIML, GMM (H2SLS) and GMM (H3SLS) models.