Manual 2SLS Regression Produces Different Results to IVReg

[ryanwalter.xyz]

I am currently following along with Wooldridge's Introductory Econometrics, in which he performs a 2SLS regression of the wage equation

\text{log(Wage)} = \beta_0+\beta_1\text{Educ}+\beta_2\text{Exper}+\beta_3\text{Exper}^2+u_1

where \text{Educ} is endogenous, whilst \text{Exper} and \text{Exper}^2 are exogenous. The mother's and father's education are also assumed to be uncorrelated with u_1, so we use both of these as instrumental variables for \text{Educ}. Hence, the reduced form equation for \text{Educ} is

\text{Educ}=\pi_0+\pi_1\text{Exper}+\pi_2\text{Exper}^2+\pi_3\text{FatherEduc}+\pi_4\text{MotherEduc}+v_2

If I use ivreg to perform the 2SLS estimation, then I get the same results as Wooldridge:

Reg2SLS <- ivreg(formula=log(wage)~educ+exper+expersq | 
                                   exper+expersq+fatheduc+motheduc, 
                                   data=mroz)
summary(Reg2SLS)

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept)  0.0481003  0.4003281   0.120  0.90442   
educ         0.0613966  0.0314367   1.953  0.05147 . 
exper        0.0441704  0.0134325   3.288  0.00109 **
expersq     -0.0008990  0.0004017  -2.238  0.02574 *

However, if I perform the same process manually, like so:

S1OLS <- lm(formula = educ~exper+expersq+fatheduc+motheduc, data = mroz)

frame <- data.frame(Wage = mroz$wage, Educ = mroz$educ, 
                    FittedEduc = S1OLS$fitted.values,
                    Exper = mroz$exper, ExperSq = mroz$expersq)

S2OLS <- lm(formula = log(Wage)~FittedEduc+Exper+ExperSq, data=frame)
summary(S2OLS)

The results are different to that above:

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept)  0.1332094  0.3817364   0.349  0.72730   
FittedEduc   0.0568605  0.0310692   1.830  0.06793 . 
Exper        0.0421082  0.0142860   2.948  0.00338 **
ExperSq     -0.0008565  0.0004255  -2.013  0.04477 *

What is the reason for this? I am aware that performing this regression manually invalidates the standard errors and t statistics, but to the best of my understanding, the coefficients should not be effected. So why exactly does my manual regression fail?

PS: The following packages were used:

library(ivreg)
library(wooldridge)

[startz]

I believe, but am not sure, that the difference is that ivreg is only using 428 observations while S1OLS uses 753. No idea why this would be true.

[ryanwalter.xyz]

You are quite right. The cause of the problem is the NAs. After removing the NA rows, the manual regression gives the same results as the IVReg regression.