other variables that have been identified as important enter significantly.<sup>20</sup> Also, the instruments pass both the under- and over-identification tests, and in most cases satisfy the tests for weak instruments as well.

We now proceed to consider alternative variables for and permutations of our exogenous instruments.

Table 4: Regressions of GDP per capita with alternative controls<sup>_†_</sup>

||(_Z1_)|(_Z2_)|(_Z3_)|(_Z4_)|(_Z5_)|
|---|---|---|---|---|---|
|Investment|1.636|0.550|0.013|-1.067|0.970|
|share|(0.49)<sup>_∗∗∗_</sup>|(0.23)<sup>_∗∗_</sup>|(0.51)|(0.10)<sup>_∗∗∗_</sup>|(0.42)<sup>_∗∗_</sup>|
|Net rate of|1.672|0.821|4.464|-1.313|0.306|
|depreciation|(1.17)<sup>_∗∗∗_</sup>|(0.65)|(1.07)<sup>_∗∗∗_</sup>|(0.61)<sup>_∗∗_</sup>|(0.82)|
|Human|3.556|3.242||1.788|3.073|
|capital|(0.48)<sup>_∗∗∗_</sup>|(0.36)<sup>_∗∗∗_</sup>||(0.20)<sup>_∗∗∗_</sup>|(0.40)<sup>_∗∗∗_</sup>|
|Alternative|||7.981|||
|human capital|||(0.85)<sup>_∗∗∗_</sup>|||
|Constant|10.827<br>(1.75)<sup>_∗∗∗_</sup>|6.490<br>(1.72)<sup>_∗∗∗_</sup>|-17.418<br>(3.07)<sup>_∗∗∗_</sup>|0.491<br>(1.46)|6.067<br>(1.92)<sup>_∗∗∗_</sup>|
|Adj _R_<sup>2</sup>|0.528|0.649|0.173|0.832|0.541|
|Anderson _LR_|26.546<sup>_∗∗∗_</sup>|53.722<sup>_∗∗∗_</sup>|31.075<sup>_∗∗∗_</sup>|36.005<sup>_∗∗∗_</sup>|47.987<sup>_∗∗∗_</sup>|
|Cragg-Donald _F_|7.460|39.036|18.248|15.237|15.911|
|Hansen _J_|4.955<sup>_∗∗∗_</sup>|2.776|0.276|4.775|12.681<sup>_∗∗∗_</sup>|
|_N_|54|63|68|11|64|
||(_Z6_)|(_Z7_)|(_Z8_)|(_Z9_)|(_Z10_|
|Investment|0.761|0.972|0.895|-0.311|0.805|
|share|(0.43)<sup>_∗_</sup>|(0.37)<sup>_∗∗∗_</sup>|(0.41)<sup>_∗∗_</sup>|(0.47)|(0.49)<sup>_∗_</sup>|
|Net rate of|0.853|0.997|0.779|-1.392|1.303|
|depreciation|(1.00)|(0.88)|(1.13)|(0.66)<sup>_∗∗_</sup>|(1.56)|
|Human|3.070|3.139|2.538|0.707|1.897|
|capital|(0.46)<sup>_∗∗∗_</sup>|(0.48)<sup>_∗∗∗_</sup>|(0.75)<sup>_∗∗∗_</sup>|(0.36)<sup>_∗_</sup>|(1.14)<sup>_∗_</sup>|
|Governance|||0.203|1.654|0.320|
||||(0.22)|(0.30)<sup>_∗∗∗_</sup>|(0.55)|
|Constant|6.886<br>(2.20)<sup>_∗∗∗_</sup>|7.493<br>(2.29)<sup>_∗∗∗_</sup>|7.096<br>(1.98)<sup>_∗∗∗_</sup>|3.179<br>(1.91)<sup>_∗_</sup>|5.700<br>(1.79)<sup>_∗∗∗_</sup>|
|Adj _R_<sup>2</sup>|0.550|0.529|0.696|0.726|0.812|
|Anderson _LR_|31.628<sup>_∗∗∗_</sup>|31.680<sup>_∗∗∗_</sup>|9.507<sup>_∗∗∗_</sup>|13.461<sup>_∗∗∗_</sup>|1.091|
|Cragg-Donald _F_|9.108|9.127|3.096|4.508|0.245|
|Hansen _J_|1.907|1.933|1.521|0.034|4.395|
|_N_|64|64|64|23|64|

> _†_ Notes: All variables were transformed to logarithmic form. Huber-White (robust) standard errors reported in parentheses. _∗_ indicates significance at 10 percent level,<sup>_∗∗_</sup> indicates significance at 5 percent level, and<sup>_∗∗∗_</sup> indicates significance at 1 percent level.

An alternative way to qualify family inputs in the education production function is to recognize that families with a greater share of parental authority invested in the mother—usually due to

> 20The coefficient that is of tangential interest is the one on the infrastructure variable. One could make an argument that government effectiveness—in terms of the quality of public financial management—may affect growth through the infrastructure channel. However, we see here that infrastructure is an insignificant predictor of income levels in the second stage.

16