Measuring the Sources of Economic Growth with Non-Parametric Methods: the Case of Baltic States Olegs Krasnopjorovs, PhD Student of the University of Latvia (Economics/Econometrics) Senior Economist, Monetary Policy Department, Bank of Latvia This work has been supported by the European Social Fund within the project «Support for Doctoral Studies at University of Latvia».

The aim of the research is to measure the sources of cross- country differences in income level and its growth rate within the EU during the first decade of 21-st century. (why some countries are rich and growing faster than others?) Results are obtained using both standard growth-accounting framework (parametric methods) and non-parametric (DEA: Data Envelopment Analysis) method; and a combination of these methods. Finally, a particular attention is brought to the economic growth engines in the Baltic States (Latvia, Estonia, Lithuania).

Production function: (relation between GDP and production factors)

Data Sample consists of 30 countries: EU advanced countries (Norway, USA and Japan) Time period: every year from 2000 to Y (output): Gross Value Added per hour worked (source: Eurostat, author’s calculations) K (input): capital stock per hour worked (source: Groningen Growth Accounting Database; Eurostat; author’s calculations). To check whether structural effects have substantial impact on results, alternative data series were used as well: Y adjustment: to account for the differences in economic structure and natural resource endowment (it was calculated how big output would be if economic structure and natural resource endowment would be the same in all countries); K adjustment: alternative assumptions used to calculate capital stock time series for countries for which data were not available (East European countries, including Latvia). All data were filtered with the Hodrick-Prescott filter (therefore fast economic growth during and recent economic slowdown have no effect on results).

DEA: F t is world technology frontier which in this particular case consists of 4 countries: Romania, Ireland, USA and Luxembourg. Other countries that are below the frontier are not efficient. Inefficiency is a vertical distance between a country and a frontier. LV: y = 12.6 but y = 17.8 can be reached with this level of k. Efficiency LV = 12.6 / 17.8 = 70%. y (income; labour productivity) in Latvia is lower than in USA both because of low capital stock and low efficiency.

Measuring the contribution of the sources of cross-country differences in income level

Measuring the contribution of the sources of cross-country differences in income growth

Measuring the contribution of the sources of cross-country differences in income level: results Cobb-Douglas: capital differences explain ~30-50% of cross-country income difference (depending on assumptions used). => 50-70% cross-country income level differences remain unexplained (i.e., explained by the residual “A”). DEA: capital differences explain ~100% of cross-country income differences.

Measuring the contribution of the sources of cross-country differences in income growth: results Cobb-Douglas: capital contribution is again ~30-55% (depends on time period and assumption used) DEA: capital contribution is much higher than under Cobb- Douglas decomposition.

Using parametric methods (Cobb-Douglas), capital accounts for about 40% of cross-country differences in income level and about 45% of cross country differences in income growth. The usage of non-parametric research methods (DEA) allows to increase the contribution of capital to the cross-country differences in income level and its growth rate to about 95%-98%. The result is similar to earlier research with a different country samples and time periods. Klenow and Rodriguez-Clare (1997) found that under Cobb-Douglas 60% of cross-country income difference remain unexplained (i.e., explained by a residual term “A”); Easterly and Levine (2001) report that A “explains” (under Cobb-Douglas) 50% of cross- country income level differences and 90% of income growth differences; Hsieh and Klenow (2010) summarize research results using Cobb-Douglas: cross-country income difference remain by 50-70% “explained” by A (meaning that it is not explained); Jerzmanowski (2007) finds that contribution of “A” is 50-70% under Cobb-Douglas assumption but only 20-45% using DEA.

Why the results differ so much between parametric method (Cobb-Douglas) and non-parametric method (DEA)? 1) Either Cobb-Douglas assumptions are not realistic (α=1/3; unit elasticity between capital and labour etc.) 2) Or technology available to the country depends on its capital endowment (K/L). DEA method can be used in a combination with Cobb-Douglas assumption in order to decompose the residual term “A” to the impact of the world technology frontier and the impact of efficiency. This can clear up whether statement (2) is true. If it is not true, the difference of results between Cobb-Douglas and DEA should be explained by statement (1).

Detailed decomposition of the sources of cross-country differences in income level Cobb-Douglas DEA

The direct effect of capital accumulation accounts ~40% of cross-country income differences (the result is very close to Cobb-Douglas case). k ↑ => y ↑. However, the indirect effect of capital accumulation is even stronger, and accounts ~60% of cross-country income differences. Indirect effect: higher capital endowment (i.e., higher K / L ratio) allows a country to use a more productive technology. k ↑ => A ↑ => y ↑. The indirect effect is ignored by Cobb-Douglas decomposition. Cobb-Douglas assumes that A is not related to k. In reality, however, there is strong relation between k and A. R 2 = 0.71 means that 71% of A cross-country differences can be explained with k differences.

The results prove that technology available to the country depends crucially on its capital endowment (k = K/L), so that (2) statement is true. The presence of indirect effect (k ↑ => A ↑ => y ↑) explains the difference in results between Cobb-Douglas and DEA decompositions. The result is similar to earlier studies, (ex. Jerzmanowski, 2007). Given direct and indirect effect of capital accumulation, investments have a greater role in economic growth than derived from a standard (Cobb- Douglas) growth-accounting practices. The contribution of efficiency to cross-country income level differences is not statistically significant (results are not stable and depend on assumptions used). Therefore rich countries are not more efficient than poor countries (the correlation between efficiency and income is not statistically significant).

Only countries with big capital endowment (high k=K/L) benefit from technical progress. Countries with high k are R&D (Research and Development) spending leaders: R&D spending is devoted to shift world technology frontier in high k segment. The effect of R&D spending by advanced countries is not enough for an upward shift of the frontier in a low k segment (technology invented in advanced countries are not sp productive in poor countries because of low k). In a low k segment world technology frontier Ft actually shifts downwards over time: (similar conclusion has reached in a previous research: Jerzmanowski (2007); Merkina, (2009); Kumar and Russell (2005)).

There are 2 ways how countries with low (k = K / L) can bear fruits from technical progress: 1) raise k to the level of advanced countries in order to benefit more from US, German etc. R&D spending; Strategy is performed by open economies: ex., new EU Member States, particularly, Latvia. 2) raise R&D spending. The only strategy available for closed economies (little or no transfer of world technical advances) ex. North Korea, Cuba. In either case, investments (to raise capital stock, or R&D spending, or both) are crucial for a country in order to bear fruits from technical progress.

Latvia, Estonia and Lithuania performed similarly during : physical capital accumulation was fast; R&D spending was low, and the improve of efficiency was moderate.

Conclusions Using parametric methods (Cobb-Douglas), the biggest part of cross-country differences in income level and its growth rate remain unexplained (i.e., explained by a residual “A”). However, using non-parametric DEA method, capital accumulation explain almost all cross- country differences (the role of unexplained part - “efficiency” is not significant). Technology available to the country depends crucially on its capital endowment (K/L), i.e. indirect effect of capital accumulation on income level k ↑ => A ↑ => y ↑ is important. Given direct and indirect effect of capital accumulation, investments have a greater role in economic growth than derived from a standard (Cobb-Douglas) growth-accounting practices. Only countries with big capital endowment (high k=K/L) benefit from world technical progress (they are R&D leaders: technologies invented in these countries are not so productive in countries with low capital endowment). Investments (to raise capital stock, or R&D spending, or both) are crucial for a country in order to bear fruits from technical progress. Latvia, Estonia and Lithuania performed similarly during : physical capital accumulation was fast; R&D spending was low, and the improve of efficiency was moderate.

References Easterly and Levine (2001) It's Not a Factor Accumulation: Stylized Facts and Growth Models. World Bank Economic Review, 2001, Volume 15, Isuue 2, p Hsieh and Klenow (2010) Development Accounting. American Economic Journal: Macroeconomics, Volume 2. p Jerzmanowski (2007) Total Factor Productivity Defferences: Appropriate Technology vs. Efficiency. European Economic Review, Volume 51, Issue 8, p – Klenow, Rodriguez-Clare (1997) The Neoclassical Revival in Growth Economics: Has it Gone Too Far? NBER Macroeconomics Annual MIT Press 1997, p Kumar and Russell (2005) Technological Change, Technological catch-up, and Capital Deepening: Relative Contribtuions to Growth and Convergence. The American Economic Review, June 2002, p. 527 – 548. Merkina (2009) Technological catch-up or resource rents: a production function approach to growth accounting. Journal of International Economics and Economic Policy, Volume 6, p. 59 – 82.

Thank you very much for attention!

Detailed decomposition of cross-country differences in income growth Cobb-Douglas DEA