9

# **B.  Regression results**

The nested CES production functions are estimated using a non-linear estimation method.<sup>10</sup> The sample size in each CES approach differs because countries with missing observations in any of the variables had to be dropped. Table 2 shows the estimated substitution elasticities corresponding to the case where human capital is part of the measured intangible capital residual (HR). All the statistically significant substitution elasticity estimates have a positive sign, which is encouraging. The lowest is that between K and E at 0.37 in the threelevel production function. It is also interesting to note that most of the significant elasticities of substitution are close to one.

A second round of regressions was carried out using the other measure of human capital that is related to schooling and labor productivity, HE. Table 3 shows the statistically significant elasticities of substitution, which also have a positive sign. A substitution elasticity approximately equal to 1 is likewise found for most of the nested functions.

The results provide some interesting findings. First and foremost, there is no sign that the elasticity of substitution between the natural resource (land) and other inputs is particularly low. Wherever land emerges as a significant input, it has an elasticity of substitution approximately equal to or greater than one. Second, by and large, the HE variable performs better in the estimation equations than the HR variable. Third, the best determined forms, with all parameters significant are those using HE, involving four factors and containing the following combinations: (a) K, HE and L are nested together and then combine with E; or (b) K, HE and E are nested together and then combine with L.<sup>11</sup> It is hard to distinguish between these two versions and so they are both used in the further analysis reported below.

From the nested CES production function estimations, the elasticity estimates of the institutional and economic indicators can be derived. Table 4 and Table 5 show the results for the four-factor production functions: [(K,HE,L)/E] and [(K,E,HE)/L] of Table 3, respectively. In both Tables, the variables on trade openness and private sector investment are found to be statistically significant. The elasticity estimates of these two variables are not very different from each other. The results imply that for every percent increase in trade openness, gross national income per capita increases by approximately 0.5 percent. None of the institutional indicators, on the other hand, has a statistically significant elasticity estimate.<sup>12</sup>

> 10 See Annex for more details.

> 11 “Inputs nested together” refers to the joint contribution of these inputs to the production of output, as indicated in Section III of this paper.

> 12 In the regression where the ‘residuals’ are expressed as a function of the institutional variables, we did find significant values for a few institutional variables, especially the rule of law, which was encouraging as that variable also emerges as important in other evaluations of inter-country differences in the World Bank (2005a) study. Unfortunately, the result did not hold when the more appropriate method was used.