Below, we discuss the data series used in the econometric analysis. In particular, we provide details on variables construction and we present the prodedure used for determining country groupings.
Output Aggregate output is real gross domestic product (real GDP) measured at constant prices (2005 US$), with purchasing power parity (PPP) adjustment. It is computed using the real GDP per capita chain series (RGDPCH) and the population series (POP) from PWT6.3, i.e., RGDPCH × POP.
Labor Labor input is retrieved from real GDP chain per worker (RGDPWOK) series in PWT6.3. It is derived as the ratio of real GDP to RGDPWOK.
Physical capital The capital input is constructed from aggregate investment data in PWT6.3 via the perpetual inventory method. Specifically, the stock of capital in time t is constructed as the accumulation of the past investments, k t = k t−1(1 − δ) + I t , where I is the capital flow or investment, and δ is the depreciation rate. The initial stock of capital is computed following Harberger’s (1978) approach as k t−1 = I t /(g + δ), where g is the growth rate of output. Specifically, we used a 5 year average growth rate of output to control for short-run fluctuations in output. Concerning capital depreciation, we follow Acemoglou and Zilboti (2001) assuming a constant annual depreciation rate of physical capital at 8 %. In order to test the robustness of this result, we also used depreciation rates of 4 % (the same as Nehru et al. 1995) and 6 % but the econometric estimations did not present any significant differentiations compared with those reported here.
Human capital Human capital is proxied using the Barro and Lee (2010) educational data. Nevertheless, the Barro and Lee (2010) data are available in 5-year intervals while the rest of our data are on annual basis. Hence, we assume a constant annual growth rate for human capital within each interval. In order to test the validity of this assumption, we proceeded by comparing our results with those of Nehru et al. (1995) who developed estimates of education stock on annual basis. The comparative analysis verified our assumption for the strong majority of the observations. Nevertheless, it should be noted that Nehru et al. (1995) provide estimates of the stock of education for a lower number of countries and for a shorter time period than those specified here. Hence, our comparison analysis was limited to countries in common in the two studies observed for the same time period.
The Barro and Lee (2010) educational data are utilized in our analysis following Henderson and Russell (2005) approach. In particular, we adopt Hall and Jones (1999) construction where education appears as an augmentation factor for labor using an exponential specification, \(h(\varepsilon)=exp\left(\phi(\varepsilon)\right)\) with \(\phi(\varepsilon)\) being a Mincerian piecewise linear function with zero intercept and slope varying along the time span. Following Psacharopoulos (1994) survey on the evaluation of the returns to education, those parameters are defined as being 0.134 for the first 4 years, 0.101 for the next 4 years and 0.068 for education beyond the eighth year.
This specification implicitly imposes perfect substitutability between human capital and physical labor (Acemoglou and Zilboti, 2001). Alternatively, we could have followed the Welch (1970) approach treating human capital as a separate factor of production. Following Griliches (1970) we used formal statistical testing to examine both hypotheses. In doing so, the production frontier model was estimated using human capital as a separate factor of production and then utilizing a simple t test we examined the hypothesis that the coefficients of human capital and labor are equal. The result rejects the alternative hypothesis validating our choice of using Hall and Jones (1999) construction.
Capital and labor prices The calculation of capital and labor prices follows the approach suggested by Mamuneas et al. (2006) by using the share of employee compensation in national income published by the Total Economy Growth Accounting Database of the Groningen Growth and Development Centre and National Account Statistics of the United Nations. Nevertheless, the use of aggregate price data in the labor decomposition equation may introduce measurement bias in the evaluation of substitution effects. If factor prices considerably deviate from their respective social marginal products, the estimated substitution effect may be over or under-estimated depending on the direction of these deviations. To deal with this possible bias, we follow Gollin (2002) approach in empirically quantifying substitution effect, minimizing the potential biases in our decomposition results.
Country groupings Initially, the countries in our sample were classified into five groups following the Barro and Lee (2010) categorization (i.e., Advanced Economies, South and Central America and the Caribbean, Asia and the Pacific, North Africa and Middle East, and Sub-Sahara Africa). However, the results arising from the econometric estimation of our multilateral aggregate production frontier model failed to converge. Our suspicion was that our country grouping did not reflect the actual technological differences across countries in the sample. Hence, we followed Simar (2003) approach to detect the potential outliers inside the groups and more accurate define country-grouping. Using a non-parametric DEA/FDH approach which does not envelop all data points and is more robust to extreme observations, we arrived at results suggesting that North African and Middle East countries exhibit different technological structures. The same conclusion was also produced for Sub-Saharan Africa, indicating the existence of two different sub-groups with different technological features. Furthermore, the non-parametric model suggested that Malta and Cyprus (that were initially included in Advanced Economies group) were suited to North Africa and Middle East groups, respectively, and the Philippines, Thailand and Malaysia were better represented to the Asia and Pacific group.
Hence, the 121 countries in the sample are classified into seven groups as follows. Advanced Economies: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hong Kong, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea Rep, Luxembourg, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, Taiwan, Turkey, United Kingdom, United States. South and Central America and the Caribbean: Argentina, Barbados, Belize, Bolivia, Brazil, Chile, Colombia, Costa Rica, Cuba, Dominican Republic, Ecuador, El Salvador, Guatemala, Guyana, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, Trinidad and Tobago, Uruguay, Venezuela. Asia and the Pacific: Bangladesh, Brunei, Cambodia, China, Fiji, Indonesia, Laos, Macao, Malaysia, Mongolia, Nepal, Pakistan, Papua New Guinea, Philippines, Sri Lanka, Thailand, Tonga, Vietnam. Middle East: Bahrain, Cyprus, Iran, Iraq, Jordan, Kuwait, Qatar, Saudi Arabia, Syria, United Arab Emirates. North Africa: Algeria, Egypt, Libya, Malta, Mauritania, Morocco, Tunisia. Sub-Saharan Group A: Burundi, Cameroon, Congo, Republic of, Cote d‘Ivoire, Gabon, Gambia, Kenya, Mauritius, Mozambique, Namibia, Rwanda, Senegal, South Africa, Swaziland, Uganda. Sub-Saharan Group B: Benin, Botswana, Central African Republic, Congo, Dem. Rep., Ghana, Lesotho, Liberia, Malawi, Mali, Niger, Sierra Leone, Sudan, Tanzania, Togo, Zambia, Zimbabwe.