-------------------------------------------------------------------------------------------------------------------------------------------- name: log: /Users/home/Dropbox/Teaching 2018/IV Seminar/Exercise/iv_seminar_log.log log type: text opened on: 15 Oct 2018, 17:11:25 . . * Import data . use "angrist_evans_data.dta", clear // Note 'clear' options so you can rerun the do file. . . . ********** Regression Analysis . . . ***** Instrumental variables regression . eststo clear . . *** OLS Regression . eststo my_ols: reg workedind_moth morekids boy1st boy2nd black_mother /// > hisp_moth othrace_moth if Main == 1 Source | SS df MS Number of obs = 98,850 -------------+---------------------------------- F(6, 98843) = 349.77 Model | 505.232021 6 84.2053369 Prob > F = 0.0000 Residual | 23796.0047 98,843 .240745472 R-squared = 0.0208 -------------+---------------------------------- Adj R-squared = 0.0207 Total | 24301.2367 98,849 .245842009 Root MSE = .49066 ------------------------------------------------------------------------------ workedin~oth | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -.1246486 .0031969 -38.99 0.000 -.1309146 -.1183826 boy1st | -.001991 .0031222 -0.64 0.524 -.0081105 .0041285 boy2nd | -.0024875 .0031225 -0.80 0.426 -.0086075 .0036326 black_mother | .1234067 .0048662 25.36 0.000 .113869 .1329444 hisp_moth | -.0489864 .009398 -5.21 0.000 -.0674064 -.0305664 othrace_moth | .0270472 .0093368 2.90 0.004 .0087473 .0453472 _cons | .6029406 .0030939 194.88 0.000 .5968766 .6090047 ------------------------------------------------------------------------------ . . *** IV Regression (including both first stage and reduced form) . eststo my_iv: ivreg2 workedind_moth boy1st boy2nd black_mother /// > hisp_moth othrace_moth (morekids = samesex) if Main == 1, /// > first savefirst savefprefix(first) saverf saverfprefix(reduced) Stored estimation results ------------------------- -------------------------------------------------------------------------------------- name | command depvar npar title -------------+------------------------------------------------------------------------ reducedwor~h | ivreg2 workedin~oth 7 Reduced-form regression: workedind_moth firstmorek~s | ivreg2 morekids 7 First-stage regression: morekids -------------------------------------------------------------------------------------- First-stage regressions ----------------------- First-stage regression of morekids: Statistics consistent for homoskedasticity only Number of obs = 98850 ------------------------------------------------------------------------------ morekids | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- samesex | .0577765 .0031018 18.63 0.000 .051697 .063856 boy1st | -.004904 .0031018 -1.58 0.114 -.0109835 .0011755 boy2nd | -.0082533 .003102 -2.66 0.008 -.0143331 -.0021735 black_mother | .1216742 .0048176 25.26 0.000 .1122318 .1311167 hisp_moth | .1618037 .0093199 17.36 0.000 .1435367 .1800706 othrace_moth | .0347699 .0092725 3.75 0.000 .0165958 .0529439 _cons | .359756 .0031871 112.88 0.000 .3535092 .3660027 ------------------------------------------------------------------------------ F test of excluded instruments: F( 1, 98843) = 346.96 Prob > F = 0.0000 Sanderson-Windmeijer multivariate F test of excluded instruments: F( 1, 98843) = 346.96 Prob > F = 0.0000 Summary results for first-stage regressions ------------------------------------------- (Underid) (Weak id) Variable | F( 1, 98843) P-val | SW Chi-sq( 1) P-val | SW F( 1, 98843) morekids | 346.96 0.0000 | 346.98 0.0000 | 346.96 Stock-Yogo weak ID F test critical values for single endogenous regressor: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Sanderson-Windmeijer F statistic. Underidentification test Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified) Ha: matrix has rank=K1 (identified) Anderson canon. corr. LM statistic Chi-sq(1)=345.77 P-val=0.0000 Weak identification test Ho: equation is weakly identified Cragg-Donald Wald F statistic 346.96 Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. Weak-instrument-robust inference Tests of joint significance of endogenous regressors B1 in main equation Ho: B1=0 and orthogonality conditions are valid Anderson-Rubin Wald test F(1,98843)= 2.09 P-val=0.1486 Anderson-Rubin Wald test Chi-sq(1)= 2.09 P-val=0.1485 Stock-Wright LM S statistic Chi-sq(1)= 2.09 P-val=0.1486 Number of observations N = 98850 Number of regressors K = 7 Number of endogenous regressors K1 = 1 Number of instruments L = 7 Number of excluded instruments L1 = 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics consistent for homoskedasticity only Number of obs = 98850 F( 6, 98843) = 96.55 Prob > F = 0.0000 Total (centered) SS = 24301.23671 Centered R2 = 0.0187 Total (uncentered) SS = 55801 Uncentered R2 = 0.5727 Residual SS = 23845.76757 Root MSE = .4912 ------------------------------------------------------------------------------ workedin~oth | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -.0786855 .054109 -1.45 0.146 -.1847371 .0273661 boy1st | -.0018289 .0031312 -0.58 0.559 -.0079659 .004308 boy2nd | -.0021689 .003148 -0.69 0.491 -.0083389 .0040011 black_mother | .1178189 .008176 14.41 0.000 .1017942 .1338437 hisp_moth | -.0564035 .0128248 -4.40 0.000 -.0815397 -.0312673 othrace_moth | .0254631 .0095298 2.67 0.008 .0067851 .0441412 _cons | .5851267 .0211622 27.65 0.000 .5436496 .6266038 ------------------------------------------------------------------------------ Underidentification test (Anderson canon. corr. LM statistic): 345.769 Chi-sq(1) P-val = 0.0000 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 346.958 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. ------------------------------------------------------------------------------ Sargan statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: morekids Included instruments: boy1st boy2nd black_mother hisp_moth othrace_moth Excluded instruments: samesex ------------------------------------------------------------------------------ . . esttab my_ols my_iv first* reduced* using "motherworked", /// > title("IV Regression of Family Size and Probability of Mother Working") /// > mtitles("Mother worked (=1) OLS" "Mother worked (=1) IV" /// > "More than 2 children (=1) 1st Stage" /// > "Mother worked (=1) Reduced Form") /// > se label wrap noabbrev rtf /// > star(* 0.10 ** 0.05 *** 0.01) b(%8.2g) /// > compress one replace (output written to motherworked.rtf) . . /* Note: > Using eststo on ivreg2 is a little more complicated if you use it > to show you first stage or reduced form results. When you do this, > the command shows more than 1 regression at a time (ie the IV > estimates of the structural equation, as well as the first stage or > reduced form. > > To get estout to save and display the right regressions, you need to > name each regression when stroing them, then list the name of each > regression you want reported in the estta. > > To name OLS or structural IV regressions, just add a name immediately after > eststo. I have given the name "my_ols" to the OLS regression, and "my_iv" > to the structural equation estimates from ivreg2, above. > > To save and name first stage and reduced form regressions, the easiest > thing to do is copy what I have written. For the reduced form, use as > options: > saverf saverfprefix(reduced) > And for saving the first stage, use as options: > savefirst savefprefix(first) > Then, when you are ready to create the table, list the names of > any regressions you wanted reported, where the names of the > first stage and reduced form are (respectivelY): > first* reduced* > > Of course, a much easier option when it comes to saving the first > stage and reduced forms is to run these as OLS regressions > manually. This is what I suggest - and what I have done for the > next examples, where hours worked and income are the dependent variables. > */ . . eststo clear . . **** Dependent variable: The numbers of hours worked by the mother . . *** OLS Regression . eststo: reg hourswked_moth morekids boy1st boy2nd black_mother /// > hisp_moth othrace_moth if Main == 1 Source | SS df MS Number of obs = 98,850 -------------+---------------------------------- F(6, 98843) = 431.52 Model | 897557.228 6 149592.871 Prob > F = 0.0000 Residual | 34265066 98,843 346.661534 R-squared = 0.0255 -------------+---------------------------------- Adj R-squared = 0.0255 Total | 35162623.2 98,849 355.720576 Root MSE = 18.619 ------------------------------------------------------------------------------ hourswke~oth | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -4.492251 .1213135 -37.03 0.000 -4.730024 -4.254478 boy1st | .022371 .1184776 0.19 0.850 -.2098436 .2545856 boy2nd | -.0697142 .1184887 -0.59 0.556 -.3019506 .1625222 black_mother | 6.834207 .1846563 37.01 0.000 6.472283 7.196131 hisp_moth | .2486576 .3566234 0.70 0.486 -.45032 .9476352 othrace_moth | 3.077041 .3542993 8.68 0.000 2.382619 3.771463 _cons | 19.63899 .1174038 167.28 0.000 19.40888 19.8691 ------------------------------------------------------------------------------ (est1 stored) . . *** IV Regression . eststo: ivreg2 hourswked_moth boy1st boy2nd black_mother /// > hisp_moth othrace_moth (morekids = samesex) if Main == 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics consistent for homoskedasticity only Number of obs = 98850 F( 6, 98843) = 203.66 Prob > F = 0.0000 Total (centered) SS = 35162623.24 Centered R2 = 0.0255 Total (uncentered) SS = 69777780 Uncentered R2 = 0.5089 Residual SS = 34267653.22 Root MSE = 18.62 ------------------------------------------------------------------------------ hourswke~oth | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -4.160836 2.051189 -2.03 0.043 -8.181093 -.1405791 boy1st | .0235392 .1186975 0.20 0.843 -.2091036 .256182 boy2nd | -.0674171 .1193359 -0.56 0.572 -.3013111 .166477 black_mother | 6.793916 .3099412 21.92 0.000 6.186443 7.40139 hisp_moth | .1951767 .4861694 0.40 0.688 -.7576979 1.148051 othrace_moth | 3.065619 .3612599 8.49 0.000 2.357562 3.773675 _cons | 19.51054 .8022268 24.32 0.000 17.93821 21.08288 ------------------------------------------------------------------------------ Underidentification test (Anderson canon. corr. LM statistic): 345.769 Chi-sq(1) P-val = 0.0000 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 346.958 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. ------------------------------------------------------------------------------ Sargan statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: morekids Included instruments: boy1st boy2nd black_mother hisp_moth othrace_moth Excluded instruments: samesex ------------------------------------------------------------------------------ (est2 stored) . . *** First Stage (using regress) . eststo: reg morekids samesex boy1st boy2nd black_mother /// > hisp_moth othrace_moth if Main == 1 Source | SS df MS Number of obs = 98,850 -------------+---------------------------------- F(6, 98843) = 206.81 Model | 294.679038 6 49.113173 Prob > F = 0.0000 Residual | 23472.8313 98,843 .23747591 R-squared = 0.0124 -------------+---------------------------------- Adj R-squared = 0.0123 Total | 23767.5104 98,849 .240442598 Root MSE = .48732 ------------------------------------------------------------------------------ morekids | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- samesex | .0577765 .0031018 18.63 0.000 .051697 .063856 boy1st | -.004904 .0031018 -1.58 0.114 -.0109835 .0011755 boy2nd | -.0082533 .003102 -2.66 0.008 -.0143331 -.0021735 black_mother | .1216742 .0048176 25.26 0.000 .1122318 .1311167 hisp_moth | .1618037 .0093199 17.36 0.000 .1435367 .1800706 othrace_moth | .0347699 .0092725 3.75 0.000 .0165958 .0529439 _cons | .359756 .0031871 112.88 0.000 .3535092 .3660027 ------------------------------------------------------------------------------ (est3 stored) . . *** Reduced Form (using regress) . eststo: reg hourswked_moth samesex boy1st boy2nd black_mother /// > hisp_moth othrace_moth if Main == 1 Source | SS df MS Number of obs = 98,850 -------------+---------------------------------- F(6, 98843) = 200.89 Model | 423631.721 6 70605.2868 Prob > F = 0.0000 Residual | 34738991.5 98,843 351.456264 R-squared = 0.0120 -------------+---------------------------------- Adj R-squared = 0.0120 Total | 35162623.2 98,849 355.720576 Root MSE = 18.747 ------------------------------------------------------------------------------ hourswke~oth | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- samesex | -.2403986 .119327 -2.01 0.044 -.4742782 -.006519 boy1st | .0439438 .1193273 0.37 0.713 -.1899363 .2778239 boy2nd | -.0330765 .1193335 -0.28 0.782 -.2669688 .2008157 black_mother | 6.28765 .1853351 33.93 0.000 5.924395 6.650904 hisp_moth | -.4780618 .3585409 -1.33 0.182 -1.180798 .224674 othrace_moth | 2.920947 .3567167 8.19 0.000 2.221787 3.620108 _cons | 18.01366 .1226099 146.92 0.000 17.77334 18.25397 ------------------------------------------------------------------------------ (est4 stored) . . esttab using "hourswkd", /// > title("IV Regression of Family Size and Mother's Hours Worked") /// > mtitles("Mother worked (=1) OLS" "Mother worked (=1) IV" /// > "More than 2 children (=1) 1st Stage" /// > "Mother worked (=1) Reduced Form") /// > se label wrap noabbrev rtf /// > star(* 0.10 ** 0.05 *** 0.01) b(%8.2g) /// > compress one replace (output written to hourswkd.rtf) . eststo clear . . **** Dependent variable: The total income of the mother . . *** OLS Regression . eststo: reg totalinc_moth morekids boy1st boy2nd black_mother /// > hisp_moth othrace_moth if Main == 1 Source | SS df MS Number of obs = 98,850 -------------+---------------------------------- F(6, 98843) = 484.40 Model | 6.6433e+11 6 1.1072e+11 Prob > F = 0.0000 Residual | 2.2593e+13 98,843 228573418 R-squared = 0.0286 -------------+---------------------------------- Adj R-squared = 0.0285 Total | 2.3257e+13 98,849 235280156 Root MSE = 15119 ------------------------------------------------------------------------------ totalinc_m~h | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -3998.074 98.50748 -40.59 0.000 -4191.147 -3805 boy1st | 48.20639 96.20467 0.50 0.616 -140.3536 236.7664 boy2nd | 38.80512 96.21369 0.40 0.687 -149.7726 227.3828 black_mother | 5577.801 149.9423 37.20 0.000 5283.915 5871.686 hisp_moth | -244.419 289.5809 -0.84 0.399 -811.9941 323.156 othrace_moth | 3131.471 287.6936 10.88 0.000 2567.595 3695.347 _cons | 10936.12 95.33278 114.72 0.000 10749.27 11122.97 ------------------------------------------------------------------------------ (est1 stored) . . *** IV Regression . eststo: ivreg2 totalinc_moth boy1st boy2nd black_mother /// > hisp_moth othrace_moth (morekids = samesex) if Main == 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics consistent for homoskedasticity only Number of obs = 98850 F( 6, 98843) = 209.64 Prob > F = 0.0000 Total (centered) SS = 2.32572e+13 Centered R2 = 0.0260 Total (uncentered) SS = 3.33738e+13 Uncentered R2 = 0.3212 Residual SS = 2.26535e+13 Root MSE = 15138 ------------------------------------------------------------------------------ totalinc_m~h | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -2393.903 1667.751 -1.44 0.151 -5662.635 874.8283 boy1st | 53.86079 96.5088 0.56 0.577 -135.293 243.0146 boy2nd | 49.9241 97.0279 0.51 0.607 -140.2471 240.0953 black_mother | 5382.78 252.0024 21.36 0.000 4888.864 5876.696 hisp_moth | -503.2862 395.2875 -1.27 0.203 -1278.036 271.4631 othrace_moth | 3076.184 293.7279 10.47 0.000 2500.487 3651.88 _cons | 10314.39 652.2629 15.81 0.000 9035.981 11592.8 ------------------------------------------------------------------------------ Underidentification test (Anderson canon. corr. LM statistic): 345.769 Chi-sq(1) P-val = 0.0000 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 346.958 Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53 Source: Stock-Yogo (2005). Reproduced by permission. ------------------------------------------------------------------------------ Sargan statistic (overidentification test of all instruments): 0.000 (equation exactly identified) ------------------------------------------------------------------------------ Instrumented: morekids Included instruments: boy1st boy2nd black_mother hisp_moth othrace_moth Excluded instruments: samesex ------------------------------------------------------------------------------ (est2 stored) . . *** First Stage (using regress) . eststo: reg morekids samesex boy1st boy2nd black_mother /// > hisp_moth othrace_moth if Main == 1 Source | SS df MS Number of obs = 98,850 -------------+---------------------------------- F(6, 98843) = 206.81 Model | 294.679038 6 49.113173 Prob > F = 0.0000 Residual | 23472.8313 98,843 .23747591 R-squared = 0.0124 -------------+---------------------------------- Adj R-squared = 0.0123 Total | 23767.5104 98,849 .240442598 Root MSE = .48732 ------------------------------------------------------------------------------ morekids | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- samesex | .0577765 .0031018 18.63 0.000 .051697 .063856 boy1st | -.004904 .0031018 -1.58 0.114 -.0109835 .0011755 boy2nd | -.0082533 .003102 -2.66 0.008 -.0143331 -.0021735 black_mother | .1216742 .0048176 25.26 0.000 .1122318 .1311167 hisp_moth | .1618037 .0093199 17.36 0.000 .1435367 .1800706 othrace_moth | .0347699 .0092725 3.75 0.000 .0165958 .0529439 _cons | .359756 .0031871 112.88 0.000 .3535092 .3660027 ------------------------------------------------------------------------------ (est3 stored) . . *** Reduced Form (using regress) . eststo: reg totalinc_moth samesex boy1st boy2nd black_mother /// > hisp_moth othrace_moth if Main == 1 Source | SS df MS Number of obs = 98,850 -------------+---------------------------------- F(6, 98843) = 206.76 Model | 2.8828e+11 6 4.8046e+10 Prob > F = 0.0000 Residual | 2.2969e+13 98,843 232377922 R-squared = 0.0124 -------------+---------------------------------- Adj R-squared = 0.0123 Total | 2.3257e+13 98,849 235280156 Root MSE = 15244 ------------------------------------------------------------------------------ totalinc_m~h | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- samesex | -138.3114 97.0288 -1.43 0.154 -328.4867 51.86389 boy1st | 65.60038 97.02902 0.68 0.499 -124.5753 255.7761 boy2nd | 69.68163 97.03406 0.72 0.473 -120.504 259.8672 black_mother | 5091.504 150.7021 33.79 0.000 4796.129 5386.878 hisp_moth | -890.6286 291.5416 -3.05 0.002 -1462.046 -319.2106 othrace_moth | 2992.948 290.0583 10.32 0.000 2424.437 3561.459 _cons | 9453.171 99.69819 94.82 0.000 9257.764 9648.579 ------------------------------------------------------------------------------ (est4 stored) . . esttab using "totalinc", /// > title("IV Regression of Family Size and Mother's Income") /// > mtitles("Mother worked (=1) OLS" "Mother worked (=1) IV" /// > "More than 2 children (=1) 1st Stage" /// > "Mother worked (=1) Reduced Form") /// > se label wrap noabbrev rtf /// > star(* 0.10 ** 0.05 *** 0.01) b(%8.2g) /// > compress one replace (output written to totalinc.rtf) . eststo clear . . **************************************************************************** . **** Interpratation Questions **** . **************************************************************************** . /* > > *Question:* > Why do you think that Angrist and Evans need an IV strategy? Why > can’t they get causal estimates by just running OLS regression of number of > children on parental labor supply? Could they control for any ommitted variable > bias by adding controls? > > *Answer:* > Angrist and Evans are interested in the effect of family size on labor supply, > such as whether or not a parent works, how many hours they worked, and how > much they earned. But there are any number of reasons why family sizes differ > between individuals, in ways that are likely to also affect labor supply. > > Some examples of possible confounders include age, educational level (more > educated people tend to have less children), personality (if someone does > not get along well with other peoples, it can be harder to both have good > jobs and find a partner), and attitude towards work (people that are more > career driven may purposefully put off having children). But there are > many more possible confounders. > > Rather than trying to identify and control for each possible confounder, > a more desirable strategy would be to find a way to isolate variation in the > number of children a parent has that is as good as random. > > *Question:* > Why might the first two children being of the same sex serve as a valid > instrument for having more than than 2 children? Consider both relevance and > exogeneity. > > *Answer:* > To try to identify exogenous (as good as random) variation in family size, > Angrist and Evans use whether or not parents' first two children were of the > same sex to predict whether or not they had a third child. > > The hypothesis is that both children being of the same sex is a relevant > predictor of having one or more additional children because parents are often > thought to have preferences for child gender or gender mix. If parents want a > girl and they have only had boys, they may be more likely to have an additional > child. Or they might think that it is beneficial for boys to have sisters and > girls to have brothers. To the extent that these preferences do exist, then > having the first two children from the same sex should be a relevant predictor > of having 3 or more children. > > The argument for validity of the instrument is that birth gender itself is > already as good as random, hence having two children of the same sex should > also be as good as random. Since birth gender is random, only a couple of > possibilities would seem to pose a potential problem to instrument exogeniety. > > One concern is that having two children of the same sex might tend to have > a direct effect on labor supply other than through it's effect on number of > children. Using the controls for having a sex of the first child and the sex > child (boy1st and boy2nd) controls for the direct effects of gender of the first > two children, so it is only a unique direct effect of having two children of the > same gender that the researcher needs to worry about. This would be true for > instance if having two children of the same sex allowed parents to leverage > economies of scale (eg less time spent clothes shopping, taking both children to > the same afterschool activities, etc). > > A second concern is that although gender of children conceived is as good as > random, parents may choose to selectively terminate pregnancies. If selection > is related to gender, then having two children of the same gender will no longer > be random. > > *Question:* > How do the estimates change between OLS and IV? And the standard errors? > > *Answer:* > Both OLS and IV estimates of family size on labor supply find negative effects. > However, the IV estimates of the effect of family size (measured by having 3 or > more children) on mother's income is about 40% smaller than the OLS estimates. > Similarly, the estimated effect on probability of employment is about 33% (or 4 > percentage points) smaller. The effect on hours worked per week is smaller, with > estimated effect of -4.2 hours vs -4.5 in OLS. For every variable, the standard > error of the esimates is smaller in the OLS regression than in IV, as expected. > > > *Question:* > Evaluate the instrument relevance and weakness using the ivreg2 output. Can the > test of overidentifying restrictions tell us anything about the instrument > exogeneity in this case? > > *Answer:* > The F-test of excluded instruments is equal to 346.96, indicating that the > weak instrument is relevant and far above the F-statistic of 10 used as a rule > of thumb to ensure the instrument is not weak. The underidentification test > indicates that the regression has very good size properties. The test of > overidentifying restrictions can not be used for falsification of instrument > validity here, since the test requires more than 1 instrument and only 1 is used. > > */ . . ***** IV Regression with more than 1 instrument . . ivreg2 hourswked_moth boy1st black_mother /// > hisp_moth othrace_moth (morekids = boys2 girls2) if Main == 1 IV (2SLS) estimation -------------------- Estimates efficient for homoskedasticity only Statistics consistent for homoskedasticity only Number of obs = 98850 F( 5, 98844) = 244.31 Prob > F = 0.0000 Total (centered) SS = 35162623.24 Centered R2 = 0.0254 Total (uncentered) SS = 69777780 Uncentered R2 = 0.5089 Residual SS = 34270366.71 Root MSE = 18.62 ------------------------------------------------------------------------------ hourswke~oth | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- morekids | -4.022781 2.036661 -1.98 0.048 -8.014562 -.030999 boy1st | .0234299 .118702 0.20 0.844 -.2092218 .2560816 black_mother | 6.778118 .3086893 21.96 0.000 6.173098 7.383138 hisp_moth | .1737987 .4847137 0.36 0.720 -.7762227 1.12382 othrace_moth | 3.0603 .3611515 8.47 0.000 2.352456 3.768144 _cons | 19.42318 .7872115 24.67 0.000 17.88027 20.96609 ------------------------------------------------------------------------------ Underidentification test (Anderson canon. corr. LM statistic): 350.729 Chi-sq(2) P-val = 0.0000 ------------------------------------------------------------------------------ Weak identification test (Cragg-Donald Wald F statistic): 175.977 Stock-Yogo weak ID test critical values: 10% maximal IV size 19.93 15% maximal IV size 11.59 20% maximal IV size 8.75 25% maximal IV size 7.25 Source: Stock-Yogo (2005). Reproduced by permission. ------------------------------------------------------------------------------ Sargan statistic (overidentification test of all instruments): 0.319 Chi-sq(1) P-val = 0.5721 ------------------------------------------------------------------------------ Instrumented: morekids Included instruments: boy1st black_mother hisp_moth othrace_moth Excluded instruments: boys2 girls2 ------------------------------------------------------------------------------ . . /* > > *Question:* > When using two instruments (whether the first two children were both > boys (boys2) or both girls (girl2) for having 3 or more children, > what can you conclude from the test of overidentifying restrictions? > > *Answer:* > For the test of overidentifying restrictions, we fail to reject the null > hypothesis that the instruments are both exogenous (p=0.5721). This does not > mean that we conclude the instruments are valid, just that we do not find > evidence against that assumption from this test. > > Note that when running the IV regression with boys2 and girls2 as instruments, > I had to drop either boys1st or boys2nd becuase of collinearity with boys2. > If I had not, then boys2 would have been omitted and I would have again a > regression with only one instrument, whether both children were girls. > */ . end of do-file