4.1 Group Frontiers
We estimate the group-specific production frontier of (1) using the likelihood function of (4) and compute technical efficiency according to (7) for each countries.
Table 2 presents parameter estimates of the two groups in the first two columns and the last column shows parameter estimates of the common frontier that is yielded by estimating the pooled data of the two groups under (4). It is noteworthy that the appropriateness of the common frontier relies on the assumption that the two groups of countries adopt the same production technology, which appears to be incorrect.
8 The World Bank classifies countries into four groups according to the per capita GNI in 2013, calculated using the World Bank Atlas method, i.e., low-income economies ($1,045 or less), lower-middle-income (more than $1,045 but less than $4,125), upper-middle-income (more than
$4,125 but less than $12,746), and high-income economies ($12,746 or more). The first two groups of countries are defined as our low income group and the latter two groups of countries are defined as our high income group.
14
Table 1. Descriptive Statistics
All Countries Low Income High Income Variable Names Mean (Standard
Deviation)
Mean (Standard Deviation)
Mean (Standard Deviation)
real GDP* 363583.3456
(1112646.4144) capital stock* 1100348.0640
(3544011.4854)
Note: *: measured by millions of 2005 U.S$.
**: measured by million persons.
***: measured by kilotons.
Most of the coefficient estimates in Table 2 attain at least the 5% level of significance. Among them, the estimates of u is positive and significant in those three models, implying that the production efficiency be considered. The omission of it may results in inconsistent parameter estimates. A country with higher quality of labor, i.e., a higher hc value, tends to have higher technical efficiency, since its coefficient estimates are significantly negative. A higher degree of openness
stimulates a country’s production efficiency, due possibly to the fact that the country may have more opportunities to import and mimic foreign countries’ production technology and managerial ability. A high income country emits more Co2 tends to be more efficient. This may be arisen from the fact that the more emission of Co2 by a country, the less likely it employ resources to dispose Co2. The reverse is true for low income countries, which may be ascribable to the fact that the production
technologies adopted by those countries are not so advanced as to produce more Co2 emission.
To confirm that these two groups of countries undertake different technology we estimate a common frontier using the pooled data of them and the parameter estimates are show in the last column of Table 2. The likelihood ratio test statistic for the null
15
hypothesis that the two groups of countries assume the same technology is equal to 53.12, which is decisively rejected at the 1% level of significance with the degrees of freedom 14. These parameter estimates can be used to compute measures of technical changes, returns to scale, and technical efficiency score, and the results are shown in Table 3.
Both groups of countries are producing with increasing returns to scale
technology, but a representative high income country is closer to the stage of constant returns to scale due to its measure of returns to scale is greater than that of low
income countries. Moreover, the average speed of technical advance of high income countries is much quicker than that of low income countries. This is anticipated, since the labor quality of high income countries is higher, which support the use of more complicated capital invested by firms. In addition, high income countries usually involve in more R&D expenditure, which is the main source of enhancing technology.
Conversely, the average technical efficiency score of low income countries is slightly greater than that of high income countries.
4.2 The Meta-production Frontier
In the second stage, we pool both groups of countries and replace their observed output (real GDP) by the fitted counterparts, obtained from the first stage. Table 4 presents parameter estimates of the meta-production frontier. Vast majority of the parameter estimates are significant at the 1% level. Following Kumbhakar (1990), we specify the inefficiency term of Mjit in (12) as:
2
1 exp
M M M M M
jit Vjit Ujit Vjit t t ujit
where u is a half-normal random variable. We next apply these estimates with (14) Mjit to calculate the measure of TGR. Table 5 summarizes various efficiency estimates of different groups. Both groups tend to undertake similar technology since their average TGRs are quite close to each other. The overall efficiency measures, MTE, of low and high income countries are 0.9302 and 0.9059, respectively. Low income countries are producing a little more technically efficient.
16
Table 2. Parameter Estimates of Group and Common Frontiers
Low Income High Income Common Frontier Variable Names Parameter
Estimates Environmental Variable
hc -0.03028***
Log-likelihood 1612.67 3024.07 4610.08
sample size 1189 2419 3608
Note: *: Significant at the 10% level. **: Significant at the 5% level.
***: Significant at the 1% level.
17
Table 3. Measures of returns to scale and technical changes Low Income
Table 4. Parameter Estimates of the Meta-Frontier Variable Names Parameter
Estimates
Environmental Variable
t 0.0845*** 0.0258
Note: *: Significant at the 10% level.
**: Significant at the 5% level.
***: Significant at the 1% level.
18
Table 5. Various Efficiency Measures
Low Income High Income All Countries TE (Standard Dev.) 0.9411
This paper employs the newly developed meta-production frontier by Huang et al. (2014) to compare technical efficiency scores for the low and high income countries, in addition to the consideration of the common effects. The stochastic frontier model with the common effects, proposed by Hsu et al. (2013), is exploited by this paper to estimate the macro-production frontier, using country-level data. The low and high income countries are found to utilize different production technologies and to take the increasing returns to scale technology, but the latter countries are closer to the constant returns to scale. The speed of technical advance for high income countries is faster than that of low income countries. However, the overall technical efficiency score of low income countries is greater than that of high income countries, due mainly to technical efficiency rather than TGR, while the difference between the two groups is not large.