Geography, institutions, and the making of comparative development

Abstract

While the direct impact of geographic endowments on prosperity is present in all countries, in former colonies, geography has also affected colonization policies and, therefore, institutional outcomes. Using non-colonized countries as a control group, I re-examine the theories put forward by La Porta et al. (J Law Econ Org 15(1):222–279, 1999 and Acemoglu et al. (Am Econ Rev 91(5), 1369–1401, 2001. I find strong support for both theories, but also evidence that the authors’ estimates of the impact of colonization on institutions and growth are biased, since they confound the effect of the historical determinants of institutions with the direct impact of geographic endowments on development. In a baseline estimation, I find that the approach of Acemoglu et al. (2001) overestimates the importance of institutions for economic growth by 28 %, as a country’s natural disease environment affected settler mortality during colonization and also has a direct impact on prosperity. The approach of La Porta et al. (1999) underestimates the importance of colonization-imposed legal origin for institutional development by 63 %, as Britain tended to colonize countries that are remote from Europe and thus suffer from low access to international markets.

Appendix 1: Remark on the endogeneity of colonisation

This remark and its proof show that the identification does not assume that colonization is orthogonal to either income or institutions. If colonization is correlated with $\widetilde{\nu }_{Y,i}$ $or$ $\widetilde{\nu }_{R,i}$, the colony dummies $\lambda _{Y}^{\prime }$ and $\lambda _{R}^{\prime }$ are biased, but the other coefficients are not affected.

Remark 1

Assume that

$$\begin{aligned} \widetilde{\nu }_{R,i}=\gamma _{R}C_{i}+\widetilde{\epsilon }_{R,i} \text{ and} \widetilde{\nu }_{Y,i}=\gamma _{Y}C_{i}+\widetilde{\epsilon }_{Y,i}, \end{aligned}$$

where, by construction, $\widetilde{\epsilon }_{R,i},\widetilde{\epsilon } _{Y,i}$ $\perp C_{i}$. Denote the expectation of the two-stage least square point estimates of $\theta _{R}$ and $\alpha$ in the estimation of () and (5) by $E\left[ \widehat{\theta }_{R} \right]$ and $E\left[ \widehat{a}\right]$. It is true that

$$\begin{aligned} E\left[ \widehat{\theta }_{R}\right] \left|_{\gamma _{R\ne 0} \text{ or} \gamma _{Y\ne 0}}\right.&= E\left[ \widehat{\theta }_{R}\right] \left|_{\gamma _{R=0} \text{ and} \gamma _{Y=0}}\right. =\theta _{R} \\ E\left[ \widehat{a}\right] \left|_{\gamma _{R\ne 0} \text{ or} \gamma _{Y\ne 0}}\right.&= E\left[ \widehat{a}\right] \left|_{\gamma _{R=0} \text{ and} \gamma _{Y=0}}\right. \end{aligned}$$

Proof

Consider first the structural model (1) and (2), with the impact of colonization policies (3) netted into the determinants of the rule of law.

$$\begin{aligned} Y_{i}&= \widetilde{\lambda }_{Y}+\widetilde{\delta }_{Y}C_{i}+\widetilde{ \alpha }R_{i}+\widetilde{\eta }_{Y}E_{i}+\widetilde{\nu }_{Y,i} \end{aligned}$$

(6)

$$\begin{aligned} R_{i}&= \widetilde{\lambda }_{R}+\widetilde{\delta }_{R}C_{i}+\widetilde{\eta }_{R}E_{i}+\widetilde{\beta }Y_{i}+C_{i}\widetilde{\theta }_{R}E_{i}+ \widetilde{\nu }_{R,i} \end{aligned}$$

(7)

The reduced from of the first stage (7) is

$$\begin{aligned} R_{i}=\lambda _{R}+\lambda _{R}^{\prime }C_{i}+\eta _{R}E_{i}+\theta _{R}C_{i}E_{i}+v_{R,i}, \end{aligned}$$

where $\lambda _{R}=\frac{\widetilde{\lambda }_{R}+\widetilde{\beta } \widetilde{\lambda }_{Y}}{1-\widetilde{\alpha }\widetilde{\beta }}$, $\lambda _{R}^{\prime }=\frac{\widetilde{\delta }_{R}+\widetilde{\beta } \widetilde{\delta }_{Y}+\widetilde{\beta }\gamma _{Y}+\gamma _{R}}{1- \widetilde{\alpha }\widetilde{\beta }}$, $\eta _{R}=\frac{\widetilde{\eta } _{R}+\widetilde{\beta }\widetilde{\eta }_{Y}}{1-\widetilde{\alpha } \widetilde{\beta }}$, $\theta _{R}=\frac{\widetilde{\theta }_{R}}{1- \widetilde{\alpha }\widetilde{\beta }}$ and $v_{R,i}=\frac{\widetilde{\beta } \gamma _{Y}+\gamma _{R}}{1-\widetilde{\alpha }\widetilde{\beta }}C_{i}+\frac{ \widetilde{\epsilon }_{R,i}+\widetilde{\beta }\widetilde{\epsilon _{Y,i}}}{1- \widetilde{\alpha }\widetilde{\beta }}.$ If either $\gamma _{Y}\ne 0$ or $\gamma _{R}\ne 0$, $v_{R,i}$ is correlated with the colonization dummy. Denote all estimated coefficients by a $\widehat{}$ superscript. The four FOCs of the OLS minimization problem yield the following point estimates for the coefficients

$$\begin{aligned}&\widehat{\lambda }_{R}^{\prime }=\frac{\sum \limits _{i,D=1}\left( Y_{i}-\left( \eta +\theta \right) X_{i}\right) }{N_{1}}-\frac{\sum \limits _{i,D=0}\left( Y_{i}-\eta X_{i}\right) }{N-N_{1}} \text{ and} \widehat{\lambda }_{R}=\frac{\sum \limits _{i,D=0}\left( Y_{i}-\eta X_{i}\right) }{N-N_{1}},\\&\widehat{\eta }_{R}=\frac{Cov\left(Y,X\vert D=0\right) }{ Var\left(X\vert D=0\right) } \text{ and} \widehat{\theta } _{R}=\frac{Cov\left(R,E\vert D=1\right) }{Var\left(E\vert D=1\right) }-\frac{Cov\left(R,E\vert D=0\right) }{Var\left( E\vert D=0\right) }. \end{aligned}$$

Due to the endogeneity of colonization, $E\left[ \widehat{\lambda }^{\prime } \right] \ne \lambda _{R}^{\prime }$, but $\widehat{\theta }_{R}$ is an unbiased estimator of $\theta :$

$$\begin{aligned} E\left[ \widehat{\theta }_{R}\right] =E\left[ \frac{\sum \limits _{i,D=1}\left( Y_{i}-\overline{Y}_{D_{i}=1}\right) \left( E_{i}- \overline{E}_{D_{i}=1}\right) }{\sum \limits _{i,D=1}\left( E_{i}-\overline{E }_{D_{i}=1}\right) ^{2}}-\frac{\sum \limits _{i,D=0}\left( Y_{i}-\overline{Y} _{D_{i}=0}\right) \left( E_{i}-\overline{E}_{D_{i}=0}\right) }{\sum \limits _{i,D=0}\left( E_{i}-\overline{E}_{D_{i}=0}\right) ^{2}}\right] \end{aligned}$$

where $\nu _{R,i}=\frac{\widetilde{\beta }\gamma _{Y}+\gamma _{R}}{1- \widetilde{\alpha }\widetilde{\beta }}C_{i}+\frac{\widetilde{\epsilon } _{R,i}+\widetilde{\beta }\widetilde{\epsilon _{Y,i}}}{1-\widetilde{\alpha } \widetilde{\beta }}$, $\sum \limits _{i,D=1}\frac{\nu _{R,i}}{N_{1}}=\frac{ \widetilde{\beta }\gamma _{Y}+\gamma _{R}}{1-\widetilde{\alpha }\widetilde{ \beta }}+\sum \limits _{i,D=1}\frac{\widetilde{\epsilon }_{R,i}+\widetilde{ \beta }\widetilde{\epsilon _{Y,i}}}{1-\widetilde{\alpha }\widetilde{\beta }} \frac{1}{N_{1}}$, and $\sum \limits _{i,D=0}\frac{\nu _{R,i}}{N_{1}}=\sum \limits _{i,D=0}\frac{\widetilde{\epsilon }_{R,i}+\widetilde{\beta } \widetilde{\epsilon _{Y,i}}}{1-\widetilde{\alpha }\widetilde{\beta }}\frac{1 }{N-N_{1}}$. By construction,

$$\begin{aligned} E\left[ \left( \frac{\widetilde{\epsilon }_{R,i}+\widetilde{\beta } \widetilde{\epsilon _{Y,i}}}{1-\widetilde{\alpha }\widetilde{\beta }}-\sum \limits _{i,D=1}\frac{\frac{\widetilde{\epsilon }_{R,i}+\widetilde{\beta } \widetilde{\epsilon _{Y,i}}}{1-\widetilde{\alpha }\widetilde{\beta }}}{N_{1}} \right) \left( E_{i}-\sum \limits _{i,D=1}\frac{E_{i}}{N_{1}}\right) \right]&= 0 \\ E\left[ \left( \frac{\widetilde{\epsilon }_{R,i}+\widetilde{\beta } \widetilde{\epsilon _{Y,i}}}{1-\widetilde{\alpha }\widetilde{\beta }}-\sum \limits _{i,D=0}\frac{\frac{\widetilde{\epsilon }_{R,i}+\widetilde{\beta } \widetilde{\epsilon _{Y,i}}}{1-\widetilde{\alpha }\widetilde{\beta }}}{ N-N_{1}}\right) \left( E_{i}-\sum \limits _{i,D=0}\frac{E_{i}}{N-N_{1}} \right) \right]&= 0 \end{aligned}$$

Therefore, $E\left[ \widehat{\theta }_{R}\right] =\theta _{R}$ holds for any combination of $\gamma _{R}$ and $\gamma _{Y}$. Consequently, it is also true that $\frac{\partial E\left[ \widehat{\theta }_{R}\right] }{\partial \gamma _{R}}=\frac{\partial E\left[ \widehat{\theta }_{R}\right] }{\partial \gamma _{Y}}=0$. Next, consider the second-stage estimate of $\alpha$, $\widehat{\alpha }$. This coefficient for the rule of law is part of the solution to the second-stage least square minimization problem

$$\begin{aligned} \underset{\widehat{\lambda _{Y}},\widehat{\lambda _{Y}^{\prime }},\widehat{ \alpha },\widehat{\eta }_{Y}}{\min }\sum \limits _{i}\left( Y_{i}-\left( \widehat{\lambda _{Y}}+\widehat{\lambda _{Y}^{\prime }}C_{i}+\widehat{\alpha }\overrightarrow{R_{i}}+\widehat{\eta }_{Y}E_{i}\right) \right) ^{2} \end{aligned}$$

(8)

where $\overrightarrow{R_{i}}$ is the projection of $R_{i}$ obtained from the first stage. It is important to note that since the colony dummy $\widehat{\lambda }_{R}^{\prime }$ in the first-stage estimation is biased, it is not true that $E\left[ \overrightarrow{R_{i}}\right] =E\left[ R_{i} \right]$. This has, however, no consequence for $\widehat{\alpha }$, which depends only on with-group variations and covariances. The FOCs of the minimization problem (8) yield

$$\begin{aligned} \widehat{\lambda }_{R}^{\prime }&= \frac{\sum \limits _{i,D=1}\left( Y_{i}- \widehat{\alpha }\overrightarrow{R_{i}}-\widehat{\eta }_{Y}X_{i}\right) }{N_{1}}-\frac{\sum \limits _{i,D=0}\left( Y_{i}-\widehat{\alpha }\widetilde{R_{i}}-\widehat{\eta }_{Y}X_{i}\right) }{N-N_{1}},\end{aligned}$$

(9)

$$\begin{aligned} \widehat{\lambda }_{R}&= \frac{\sum \limits _{i,D=0}\left( Y_{i}-\widehat{ \alpha }\widetilde{R_{i}}-\widehat{\eta }_{Y}X_{i}\right) }{N-N_{1}}, \end{aligned}$$

(10)

$$\begin{aligned} 0&= \sum \limits _{i}\overrightarrow{R_{i}}\left( Y_{i}-\left( \widehat{ \lambda _{Y}}+\widehat{\lambda _{Y}^{\prime }}C_{i}+\widehat{\alpha } \widetilde{R_{i}}+\widehat{\eta }_{Y}E_{i}\right) \right) , \end{aligned}$$

(11)

$$\begin{aligned} 0&= \sum \limits _{i}E_{i}\left( Y_{i}-\left( \widehat{\lambda _{Y}}+ \widehat{\lambda _{Y}^{\prime }}C_{i}+\widehat{\alpha }\widetilde{R_{i}}+ \widehat{\eta }_{Y}E_{i}\right) \right). \end{aligned}$$

(12)

Define the following average within-group covariances and average within-group variances.

$$\begin{aligned} \widetilde{Cov}\left( Y,E\right)&\equiv \left( N-N_{1}\right) \left( Cov\left( \left. Y,E\right|D=0\right) \right) +N_{1}\left( Cov\left( \left. Y,E\right|D=1\right) \right) \\ \widetilde{Cov}\left( Y,\overrightarrow{R_{i}}\right)&\equiv \left( N-N_{1}\right) \left( Cov\left( \left. Y,\overrightarrow{R_{i}}\right|D=0\right) \right) +N_{1}\left( Cov\left( \left. Y,\overrightarrow{R_{i}} \right|D=1\right) \right) \\ \widetilde{Cov}\left( \overrightarrow{R_{i}},E\right)&\equiv \left( N-N_{1}\right) Cov\left( \left. \overrightarrow{R_{i}},E\right|D=0\right) +N_{1}\left( Cov\left( \left. \overrightarrow{R_{i}},E\right|D=1\right) \right) \\ \widetilde{Var}\left( E\right)&\equiv \left( N-N_{1}\right) Var\left( \left. E\right|D=0\right) +N_{1}Var\left( \left. E\right|D=1\right) \\ \widetilde{Var}\left( \overrightarrow{R_{i}}\right)&\equiv \left( N-N_{1}\right) Var\left( \left. \overrightarrow{R_{i}},E\right|D=0\right) +N_{1}Var\left( \left. \overrightarrow{R_{i}},E\right|D=1\right) \end{aligned}$$

These variances and covariances equal the standard definitions, except that the across-group differences in the mean between noncolonies and colonies are netted out. For example, the average within-group variance of $R_{i}$ is equal to the variance of $R_{i}$ in the entire sample if the mean of $R$ is equal in former colonies and in the noncolonies. With this notation, the point estimate of $\alpha$ equals

$$\begin{aligned} \widehat{\alpha }=\frac{\widetilde{Var}\left( E\right) \widetilde{Cov}\left( Y,R\right) -\widetilde{Cov}\left( Y,E\right) \widetilde{Cov}\left( R,E\right) }{\widetilde{Var}\left( E\right) \widetilde{Var}\left( R\right) -\left( \widetilde{Cov}\left( R,E\right) \right) ^{2}} \end{aligned}$$

(13)

Due to the presence of the standard small-sample instrumental variable bias, it is not generally true that $E\left[ \widehat{\alpha }\right] =\alpha$. However, since all of the elements in (13) depend exclusively on the within-group variation, the small sample bias of $\widehat{\alpha }$ is not affected by the endogeneity of colonization; i.e., $\frac{\partial E \left[ \widehat{\alpha }\right] }{\partial \gamma _{R}}=\frac{\partial E \left[ \widehat{\alpha }\right] }{\partial \gamma _{Y}}=0.$ $\square$