Difference between IV and 2SLS

[Kelsi Cheng]

SEM as follows:
1. hours=a1*lwage+b1*educ+b2*age+b3*kidslt6+b4*nwifei nc+u1
2. lwage=a2*hours+b1*educ+b2*exper+b3*expersq
I regress these equtions with 2 methods(which I thought should be respectively IV and 2SLS)
(1)The first command is:
reg lwage educ age kidslt6 nwifeinc exper expersq
predict lwage_hat,xb
reg hours lwage_hat educ age kidslt6 nwifeinc
(2)The second command:
ivregress 2sls hours educ age kidslt6 nwifeinc (lwage=exper expersq)
My question is :
1. Why the coefficients with these two methods are different? The former one is greater than the latter one
2. AND what exactly is the differences between IV and 2SLS?
3. And if my commands are incorrect, what should be the correct ones with IV and 2SLS?
Many thanks!

[Scott Merryman]

The first stage must include all the instruments not just the excluded instruments. Also,doing 2SLS by hand will give you the wrong variance-covariance matrix, residuals, ect. Note, the -first- option will display the first stage regression. See also this: https://www.stata.com/statalist/arch.../msg00307.html

. webuse hsng2,clear
(1980 Census housing data)

. qui reg hsngval pcturb famin

. predict double xb
(option xb assumed; fitted values)

. qui reg rent pctur  xb

. est store r1

. qui ivregress 2sls rent pcturban (hsngval = faminc ), first

. est store r2

. est table r1 r2

----------------------------------------
    Variable |     r1           r2      
-------------+--------------------------
    pcturban | -.50641181   -.50641181  
          xb |  .00319383               
     hsngval |               .00319383  
       _cons |  113.81433    113.81433  
----------------------------------------