# **3.7 Fully Endogenizing Institutions**

Our final robustness check seeks to endogenize as many of the instruments that we have used as possible; of particular concern is the possibility that governance may be endogenous to the income equation. To do so, we exploit the temporal nature of the panel to retrieve internal instruments based on the lags of the endogenous variables. Table 6 reports these results using the panel with enrollment rates as a proxy for human capital, and contemporaneous government effectiveness as the measure of governance.

The specifications are as follows: ( _S1_ ) System GMM estimates of (5), with governance, with one-period lagged GMM-style internal instruments and family and school resources treated as fully exogenous IV-style instruments;<sup>33</sup> ( _S2_ ) Specification ( _S1_ ), but without family and school inputs as exogenous instruments; ( _S3_ ) Specification ( _S1_ ), but with year dummies as additional exogenous instruments; ( _S4_ ) Specification ( _S1_ ), but with two-period lagged GMM-style internal instruments; ( _S5_ ) Specification ( _S1_ ), but with a broad governance measure; and ( _S6_ ) All variables in (3) included as explanatory variables in (5), with one-period lagged GMM-style internal instruments.

Table 6: Regressions of GDP per capita with internal instruments<sup>_†_</sup>

||(_S1_)|(_S2_)|(_S3_)|(_S4_)|(_S5_)|(_S6_)|
|---|---|---|---|---|---|---|
|Investment|-0.317|-0.352|0.189|0.147|0.553|-0.791|
|share|(0.37)|(0.42)|(0.20)|(0.20)|(0.26)<sup>_∗∗_</sup>|(0.35)<sup>_∗∗_</sup>|
|Net rate of|0.190|0.554|0.412|-0.332|-0.043|-0.013|
|depreciation|(1.15)|(0.78)|(1.22)|(0.73)|(0.75)|(0.78)|
|Human|1.651|1.674|1.471|1.277|1.323|0.816|
|capital|(0.34)<sup>_∗∗∗_</sup>|(0.32)<sup>_∗∗∗_</sup>|(0.30)<sup>_∗∗∗_</sup>|(0.22)<sup>_∗∗∗_</sup>|(0.18)<sup>_∗∗∗_</sup>|(0.48)<sup>_∗_</sup>|
|Governance|0.774|0.519|0.698|0.700||0.352|
||(0.26)<sup>_∗∗∗_</sup>|(0.15)<sup>_∗∗∗_</sup>|(0.21)<sup>_∗∗∗_</sup>|(0.13)<sup>_∗∗∗_</sup>||(0.18)<sup>_∗_</sup>|
|Broad|||||0.740||
|governance|||||(0.11)<sup>_∗∗∗_</sup>||
|Family||||||-0.550|
|resources||||||(0.29)<sup>_∗_</sup>|
|School||||||-1.086|
|resources||||||(0.56)<sup>_∗_</sup>|
|Constant|2.255|3.134|4.246|2.984|4.130|8.718|
||(3.42)|(2.38)|(2.83)|(1.66)<sup>_∗_</sup>|(1.73)<sup>_∗∗_</sup>|(5.12)<sup>_∗_</sup>|
|_F_|22.405<sup>_∗∗∗_</sup>|30.411<sup>_∗∗∗_</sup>|61.002<sup>_∗∗∗_</sup>|77.530<sup>_∗∗∗_</sup>|48.714<sup>_∗∗∗_</sup>|60.737<sup>_∗∗∗_</sup>|
|Arellano AR(1)|1.022|0.198|-1.170|-1.381|-0.106|-0.857|
|Arellano AR(2)|1.016|1.072|0.560|1.377|1.959<sup>_∗∗∗_</sup>|-0.052|
|Hansen _J_|39.123|53.451<sup>_∗∗∗_</sup>|45.149|88.030|82.110|63.305|
|_N_|445|808|445|445|511|445|

> _†_ Notes: All variables were transformed to logarithmic form. Heteroskedasticity- and autocorrelation-robust (asymptotic) standard errors reported in parentheses. A constant term and time dummies were included in the regressions, but not reported.<sup>_∗_</sup> indicates significance at 10 percent level,<sup>_∗∗_</sup> indicates significance at 5 percent level, and<sup>_∗∗∗_</sup> indicates significance at 1 percent level.

> 33Strictly speaking, system GMM also uses first differences of endogenous regressors as additional instruments, but this difference structure does not vary since additional lagged differences would lead to redundant moment conditions.

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